Answer:
A. Between 14 and 15.
Step-by-step explanation:
Let x be the one leg of the right triangle.
We have been given that the legs of a right triangle are in the ratio of 3 to 1. So, the other leg of the right triangle would be 3x.
We are also told that the length of the hypotenuse of the triangle is √40.
Using Pythagoras theorem, we can set am equation as:
[tex]x^2+(3x)^2=(\sqrt{40})^2[/tex]
Let us solve for x.
[tex]x^2+9x^2=40[/tex]
[tex]10x^2=40[/tex]
[tex]\frac{10x^2}{10}=\frac{40}{10}[/tex]
[tex]x^2=4[/tex]
Take square root of both sides:
[tex]x=\sqrt{4}[/tex]
[tex]x=2[/tex]
The other leg would be [tex]3x\Rightarrow 3\cdot 2=6[/tex].
The perimeter of the triangle would be:
[tex]\text{Perimeter of triangle}=2+6+\sqrt{40}[/tex]
[tex]\text{Perimeter of triangle}=2+6+6.324555[/tex]
[tex]\text{Perimeter of triangle}=14.324555[/tex]
Therefore, the perimeter of the triangle is between 14 and 15 and option A is the correct choice.
An ice cream shop sold 48 vanilla milkshake in a day which is 40% of the total number of milkshake sold that day.What was the total number of milkshake that the ice cream shop sold that day?
Answer:the total number of milkshake that the ice cream shop sold that day is 120
Step-by-step explanation:
Let x represent the total number of
vanilla milkshakes that the ice cream shop sold that day.
The ice cream shop sold 48 vanilla milkshakes in a day which is 40% of the total number of milkshake sold that day. It means that
40/100 × x = 48
0.4 × x = 48
0.4x = 48
x = 48/0.4 = 120
A certain food has a gluten ratio of 13\,\text{mg}13mg13, start text, m, g, end text of gluten per \text{L}Lstart text, L, end text of the food. What is the gluten ratio in micrograms per milliliter \left(\dfrac{\mu\text{g}}{\text{mL}}\right)( mL μg )left parenthesis, start fraction, mu, start text, g, end text, divided by, start text, m, L, end text, end fraction, right parenthesis?
Answer:
The gluten ratio in micrograms per milliliter is 13 µg/mL.
Step-by-step explanation:
Consider the provided information.
It is given that the food has a gluten ratio of [tex]13 \frac{mg}{L}[/tex].
Now we need to convert gluten ratio in micrograms per milliliter
To convert mg to micro grams use the information shown below:
1 mg = 1000 micro-grams.
1 L = 1000 milliliter
Now, substitute 1 mg = 1000 micro-grams and 1 L = 1000 milliliter in the above ratio.
[tex]13( \frac{1000 \ micro-grams}{1000 \ milliliter} )= 13( \frac{micro-grams}{milliliter})[/tex]
Hence, the gluten ratio in micrograms per milliliter is 13 µg/mL.
Answer:
the answer is 4μm to the power of⁻1
Step-by-step explanation:
khan academy said
Find a polynomial equation that has zeros at x = 0, x = -5 and x = 6
Answer:
The answer to your question is x³ + 11² + 30x
Step-by-step explanation:
Data
x = 0; x = - 5; x = 6
Process
1.- Equal the zeros to zero
x₁ = 0; x₂ + 5 = 0; x₃ + 6 = 0
2.- Multiply the results
x(x + 5)(x + 6) = x [ x² + 6x + 5x + 30]
3.- Simplify
= x [ x² + 11x + 30]
4.- Result
= x³ + 11² + 30x
The polynomial equation with zeros at x = 0, x = -5, and x = 6 is x^3 - x^2 - 30x.
To find a polynomial equation with zeros at x = 0, x = -5, and x = 6, you would use the relationship between zeros and factors of a polynomial. Each zero corresponds to a factor of the polynomial; for x = 0, the factor is x, for x = -5, the factor is (x + 5), and for x = 6, the factor is (x - 6). Therefore, the polynomial equation that has these zeros can be constructed by multiplying these factors together.
The result is the polynomial equation:
f(x) = x(x + 5)(x - 6)
Expanding this product gives:
f(x) = x³ - x² - 30x
An urn contains 12 balls, of which 4 are white.
Three players successively draw from the urn, A first, then B, then C, then A, and so on. The winner is the fist one to draw a white ball.
Find the probability of winning for each player if:
a) each ball is replaced after being drawn.
b) the balls that are withdrawn are not replaced.
The probability of a player winning depends on whether balls are replaced after each draw. With replacement, the probabilities remain constant and A has a higher chance of winning (9/20) compared to B and C (11/40 each). Without replacement, the probabilities change after each turn and require complex computation.
Explanation:This is a probability problem involving sequence of events. The outcome is dependent on whether the balls are replaced or not after each draw.
For case a), if each ball is replaced after being drawn, the probabilities for A, B, and C stay constant each round. There are 4 white balls out of 12 total, so the probability of drawing a white ball is 4/12 = 1/3. Because the players draw successively and stop once a white ball is drawn, we need to consider the rounds of draws. For A to win, a white ball needs to be drawn on the 1st, 4th, 7th turns, and so on. For B to win, a white ball needs to be drawn on the 2nd, 5th, 8th rounds, and so forth. Similar logic applies to player C. Using geometric distribution to compute these, we have [tex]P(A) = 1/3 * (2/3)^0 + 1/3 * (2/3)^3 + 1/3 * (2/3)^6 +... = 9/20.[/tex] Applying similar logic to players B and C, we get P(B) = P(C) = 11/40. (Note that the sum of P(A), P(B), and P(C) = 1, which verifies our calculation is correct.)
For case b), if the balls are not replaced after each draw, the probability changes after each turn. Initially the probability of drawing a white ball is 4/12 = 1/3, then it becomes 4/11, 4/10, and so forth if a white ball is not drawn, and 3/11, 3/10, and so forth if a white ball is drawn. Therefore a recursive method computing the probability is needed in this case and the calculation could be quite complicated depending on when we stop the game.
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Can the positive integer p be expressed as the product of two integers, each of which is greater than 1?1) 31 < p < 372) p is odd
Answer:
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Step-by-step explanation:
Consider the provided information.
Can the positive integer p be expressed as the product of two integers, each of which is greater than 1.
Statement 1: 31 < p < 37
The value of p is greater than 31 and less than 37.
Thus the possible values of p are: 32, 33, 34, 35, 36
All these numbers can be expressed as the product of two integers. Each of which is greater than 1,
Hence, statement 1 Alone is Sufficient.
Statement 2: p is odd
The statement is not sufficient because All prime numbers are odd numbers and if p is a prime number then p can't be expressed as the product of two integers, each of which is greater than 1.
Although if p is odd it is not necessarily to be prime for example 9 is an odd number but not a prime number. 9 can be expressed as the product of two integers, each of which is greater than 1.
Therefore, statement 2 Alone is not sufficient.
Final answer:
1. Statement 1 alone is sufficient to determine if the integer p can be expressed as the product of two integers greater than 1 or not.
2. Statement 2 alone is not sufficient.
Explanation:
Consider the provided information. Can the positive integer p be expressed as the product of two integers, each of which is greater than 1.
Statement 1: 31 < p < 37
The value of p is greater than 31 and less than 37. The possible values of p are 32, 33, 34, 35, 36. All these numbers can be expressed as the product of two integers each greater than 1. Therefore, statement 1 alone is sufficient.
Statement 2: p is odd
The statement is not sufficient as odd numbers like 9 can be expressed as the product of two integers each greater than 1. Not all odd numbers are prime. Thus, statement 2 alone is not sufficient.
The unemployment rate has risen more than a percentage point to 8.8% in February from 6.7% last November. What is the relative change in the unemployment rate expressed as a percentage? The unemployment rate has risen what percent?
Answer:
7.6
Step-by-step explanation:
Final answer:
The relative change in the unemployment rate expressed as a percentage is approximately 31.34%.
Explanation:
The relative change in the unemployment rate expressed as a percentage can be computed by taking the difference between the two unemployment rates and dividing it by the initial unemployment rate. In this case, the initial unemployment rate was 6.7% and the new unemployment rate is 8.8%, so the change is 8.8% - 6.7% = 2.1%. To express this change as a percentage, we divide the change by the initial unemployment rate and multiply by 100: (2.1% / 6.7%) * 100 = 31.34%. Therefore, the unemployment rate has risen by approximately 31.34%.
A transformation named T maps triangle XYZ to triangle X'Y'Z'. The transformation is a(n) _____.
The transformation T could be translation, rotation, reflection, or dilation, altering the position, orientation, or size of the triangle.
The transformation T mapping triangle XYZ to triangle X'Y'Z' could be any of the basic rigid transformations in geometry: translation, rotation, reflection, or dilation.
- A translation involves shifting the entire triangle by a certain distance in a certain direction without changing its orientation or shape.
- A rotation rotates the triangle around a fixed point (e.g., the origin or a specific vertex), altering its orientation but maintaining its shape and size.
- A reflection flips the triangle across a line (e.g., the x-axis, y-axis, or an arbitrary line), producing a mirror image with reversed orientation.
- A dilation scales the triangle uniformly, either enlarging or shrinking it while maintaining its shape and proportions.
To determine which transformation T specifically represents, additional information is needed, such as the coordinates of the vertices X, Y, Z and X', Y', Z', or any constraints or properties of the transformation provided. Each type of transformation has distinct characteristics that can be identified through geometric properties and transformations of coordinates.
The function s(w) = 4w + 40 gives the total number of skateboards a company built w weeks after its office was relocated.
What is the meaning of the y-intercept?
A.No skateboards were built 10 weeks before the office was relocated.
B.The company built a total of 10 skateboards the week its office was relocated.
C.The company built a total of 40 skateboards the week its office was relocated.
D.No skateboards were built 40 weeks before the office was relocated.
Answer:
Option C. The company built a total of 40 skateboards the week its office was relocated
Step-by-step explanation:
Let
s ----> the total number of skateboards
w ---> the number of weeks
we have
[tex]s(w)=4w+40[/tex]
This is the equation of the line in slope intercept form
where
The slope is [tex]m=4\ \frac{skateboard}{week}[/tex]
The y-intercept is [tex]b=40\ skateboard[/tex]
Remember that
The y-intercept is the value of the function s when the value of variable w is equal to zero
In the context of the problem
The company built a total of 40 skateboards the week its office was relocated
If it is snowing, there is an 80% chance that class will be canceled. If it is not snowing, there is a 95% chance that class will go on. Generally, there is a 5% chance that it snows in NJ in the winter. If we are having class today, what is the chance that it is snowing?
Answer:
[tex]P(S|\bar{C} ) = 0.1739[/tex]
Step-by-step explanation:
We define the probabilistic events how:
S: Today is snowing
C: The class is canceled
If it is snowing, there is an 80% chance that class will be canceled, it means
P( C | S ) = 0.8 conditional probability
If it is not snowing, there is a 95% chance that class will go on
[tex]P( \bar{C} | \bar{S}) = 0.95[/tex]
and P(S) = 0.05
We need calculate
[tex]P( S |\bar{C} ) = \frac{P(\bar{C} | S) P(S)}{P(\bar{C})}[/tex]
[tex]P(\bar{C}) = P( \bar{C}|S)P(S) + P( \bar{C}|\bar{S})P(\bar{S})[/tex]
How
[tex]P(C | S) = 0.8[/tex] then [tex]P( \bar{C} | S) = 0.2[/tex]
[tex]P (\bar{C})[/tex] = (0.2)(0.5) + (0.95)(0.5)
=0.575
[tex]P(S |\bar{C} ) = \frac{(0.2)(0.5)}{(0.575)}[/tex]
[tex]P(S|\bar{C} ) = 0.1739[/tex]
DeAndre is 15 miles into a 51-mile backpacking trip in the wilderness. DeAndre can hike 9 miles per day. How many more days does DeAndre need to finish?
Answer:
Step-by-step explanation:
miles left to travel=51-15=36
more days required=36/9=4 days.
Answer: it will take 4 more days before DeAndre finishes
Step-by-step explanation:
DeAndre is 15 miles into a 51-mile backpacking trip in the wilderness. This means that he has already covered 15 miles and the total number of miles is 51. Number of miles left is 51 - 15 = 36 miles.
DeAndre can hike 9 miles per day. The number of days that it will take him to cover 36 miles would be 36/9 = 4 days
A construction company needs to remove tons of dirt from a construction site. They can remove tons of dirt each hour. How long will take to remove the dirt.
Question:
A construction company needs to remove 24 tons of dirt from a construction site. They can remove 3/4 tons of dirt each hour. How long will it take to remove dirt
Answer:
It takes 32 hours to remove the dirt
Step-by-step explanation:
Given:
Total amount dirt to be removed = 24 tons
Dirt that can removed in one hour = 3/4 tons
To Find:
Time taken to remove all the dirt =?
Solution:
Let the time taken to remove the dirt from the company be x.
Then
x = [tex]\frac{ \text { total amount of dirt in the company}}{\text{ amount of dirt removed in one hour}}[/tex]
Substituting the given values , we get
x = [tex]\frac{24}{\frac{3}{4}}[/tex]
x = [tex]24\times \frac{4}{3}[/tex]
x = [tex] \frac{96}{3}[/tex]
x= 32
The derivative of the function B is given by B′(t)=8e0.2cost, and B(2.2)=4.5. If the linear approximation to B(t) at t=2.2 is used to estimate B(t), at what value of t does the linear approximation estimate that B(t)=9 ?
Answer:
t=2.83
Step-by-step explanation:
Linear Approximation Of Functions
The equation of a line is given by
[tex]y=y_o+m(x-x_o)[/tex]
Where m is the slope of the line and [tex](x_o,y_o)[/tex] are the coordinates of a point through which the line goes.
Given a function B(t), we can build an approximate line to model the function near one point. The value of m is the derivative of B in a specific point [tex](t_o, B_o)[/tex]. The equation becomes
[tex]B(t)=B_o+B'(t_o)(t-t_o)[/tex]
Let's collect our data.
[tex]B'(t)=8e^{0.2cost},\ B_o=B(2.2)=4.5[/tex]
Let's find the required values to build the approximate function near [tex]t_0=2.2[/tex]. We evaluate the derivative in 2.2
[tex]B'(2.2)=8e^{0.2cos2.2}=7.11[/tex]
The function can be approximated by
[tex]B(t)=4.5+7.11(t-2.2)[/tex]
Once we have B(t), we are required to find the value of t, such that
[tex]B(t)=9[/tex]
Or equivalently:
[tex]4.5+7.11(t-2.2)=9[/tex]
Rearranging
[tex]\displaystyle t-2.2=\frac{9-4.5}{7.11}[/tex]
Solving for t
[tex]\displaystyle t=\frac{9-4.5}{7.11}+2.2[/tex]
[tex]\boxed{t=2.83}[/tex]
We find the equation of the linear approximation at t=2.2 using B(2.2) and B'(2.2). We then solve this equation for t when the linear approximation equals 9. This gives us the time at which the linear approximation estimates B(t) = 9.
Explanation:To solve for the time when the linear approximation gives an output of 9, we need to find the equation of the tangent line (i.e., the linear approximation) at t = 2.2. The linear approximation to a function at a particular point is given by the formula L(t) = f(a) + f'(a)*(t-a), where f is the function, a is the point, and f' denotes the derivative of the function.
Given that B(2.2) = 4.5 and B'(t) = 8e0.2cos(t), we can substitute these into the linear approximation formula to get L(t) = 4.5 + 8e0.2cos(2.2)*(t-2.2).
Next, we solve this equation for t when L(t) = 9: 9 = 4.5 + 8e0.2cos(2.2)*(t-2.2). Solving the equation for t gives the time at which the linear approximation estimates B(t) = 9.
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Grant is trying to make money to help pay for college by taking a job with Brian's bike taxis if Baltimore. He has an agreement with Brian to rent the bike for $35.00 a night. He charges customers $3.75 for every mile he transports them. If grant needs to make at least $15.00 a day, how many miles would he need to ride?
Answer: he would need to ride at least 13.3 miles
Step-by-step explanation:
The total amount that Grant needs to make in a day is greater than or equal to $15.
He has an agreement with Brian to rent the bike for $35.00 a night.
He charges customers $3.75 for every mile he transports them. If he transports the customers over x miles, his total revenue would be
3.75 × x = 3.75x
Profit = revenue - cost. Therefore,
his profit would be
3.75x - 35
Therefore,
3.75x - 35 ≥ 15
3.75x ≥ 15 + 35 = 50
x ≥ 50/3.75
x ≥ 13.3
One pound of tomatoes costs $1.59.One pound of bananas costs $1.87. How much more do 5 pounds of tomatoes costs than 2 pounds of bananas? Show your work
when you multiply $1.59 by 5 you get $7.95
when you multiply $1.87 by 2 you get $4.74
so when you subtract them you get $3.21
List each term of the domain
{(-4, 3), (-4, 4), (-3, 1), (1, 1)}
Kind of struggling on this, would really appreciate the help!
Answer:
Domain: {-4, -3, 1 }
Step-by-step explanation:
As we know that domain of a relation basically consists of all the first elements or x-coordinates of order pairs.
As the relation is : {(-4, 3), (-4, 4), (-3, 1), (1, 1)}
So,
Domain: {-4, -3, 1 }
Note: We can not duplicate an element when we determine the domain of any relation. As -4 was present in first and second order pairs i.e. (-4, 3), (-4, 4). But, we have to write it only once when we write the domain of any relation.
So, the domain will be listed as:
Domain: {-4, -3, 1 }
Keywords: domain, relation
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A truck hauled 136 cubic feet of sand to a construction site. The sand is dumped into a cone-shaped pile 6 feet in height. What is the approximate diameter of the pile of sand, in feet
18.614 because a=πh(r^2)/3 pretty sure thats the formula but the answer is correct
The approximate diameter of the pile of sand in the cone that sand was dumped in is 9.30 feet.
What is the approximate diameter?A cone is a 3-dimensional object that consists of a ciruclar base and a vertex. The diameter is twice the length of the radius.
Radius = √[volume / (1/3 x π x height)]
√[136 / (1/3 x 22/7 x 6)]
√[136 / 6.29 = 4.65
Diameter = 4.65 x 2 = 9.30 feet
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Quadrilateral ABCD is a parallelogram if both pairs of opposite sides are congruent. Show that quadrilateral ABCD is a parallelogram by finding the lengths of the opposite side pairs. What is the length of BC?
In parallelogram ABCD, opposite sides AB and DC are both 8 units long, and AD and BC are both 5 units long.
To show that quadrilateral ABCD is a parallelogram, we need to demonstrate that both pairs of opposite sides are congruent. We can do this by finding the lengths of the opposite side pairs and showing that they are equal.
Let's denote the points as follows:
- A, B, C, D are the vertices of the quadrilateral ABCD.
- AB and DC are opposite sides, and AD and BC are opposite sides.
Given that AB = 8 units and AD = 5 units, we need to find the lengths of DC and BC.
Since ABCD is a parallelogram, opposite sides are congruent. Therefore, DC = AB = 8 units.
To find BC, we know that BC = AD = 5 units.
Thus, we have:
- AB = DC = 8 units
- AD = BC = 5 units
Since both pairs of opposite sides are congruent, quadrilateral ABCD is a parallelogram.
The length of BC is 5 units.
In the given case, The length of BC is 8 units.
To show that quadrilateral ABCD is a parallelogram, we need to demonstrate that both pairs of opposite sides are congruent.
Let's denote the lengths of the sides as follows: AB, BC, CD, and DA.
Given that ABCD is a parallelogram, we know that opposite sides are equal in length.
Therefore, we can equate the lengths of AB to CD and BC to DA.
Let's assume that the length of side AB (and thus CD, since they are opposite and equal) is given as 8 units.
We are asked to find the length of side BC (which will be equal to the length of side DA).
Since we do not have any additional information such as angles or diagonals, we cannot calculate the length of BC directly.
However, if we are given that ABCD is a parallelogram, then by definition, the lengths of opposite sides are equal.
Therefore, without loss of generality, we can state that the length of BC is also 8 units, which is equal to the length of AB.
Thus, we have shown that both pairs of opposite sides are congruent:
AB = CD = 8 units
BC = DA
Since AB = 8 units and AB = CD, it follows that CD = 8 units.
Similarly, since AB = CD and AB = 8 units, by the properties of a parallelogram, BC must also be equal to 8 units.
Therefore, the length of BC is 8 units, confirming that quadrilateral ABCD is indeed a parallelogram.
Mister Rogers is fencing another new rectangular garden in his neighborhood. One side of the garden faces the road and needs to be pretty. The other three sides just need to be functional. The pretty fencing costs $35 per linear foot and the functional fencing costs $18 per linear foot. Mr. Rogers has $ 3000 to build his fence. What dimensions of the garden give him the maximum area?
Answer:
length of the pretty side and length of the side oppositte to the pretty side = 37.91 ft
length of the other two sides = 27.52 ft
Step-by-step explanation:
The mathematical problem is:
Max A = b1*h
subject to: 35*b1 + 18*(2*h + b2) <= 3000
Where
A: area of the garden
b1: length of the pretty side
b2: length of the side oppositte to the pretty side
h: length of the other two sides
Replacing with b1 = b2 and taking only the equality sign in the restriction (in the maximum all the money will be spent), we get:
35*b1 + 18*(2*h + b1) = 3000
35*b1 + 36*h + 18*b1 = 3000
53*b1 + 36*h = 3000
b1 = 3000/53 - (36/53)*h
Substituing in Area's formula
A = (3000/53 - (36/53)*h)*h
A = (3000/53)*h - (36/53)*h^2
In the maximum, the derivative of A is equal to zero
dA/dh = 3000/53 - 2*(36/53)*h =
3000/53 - 72/35*h = 0
h = (3000/53)*(35/72)
h = 27.52 ft
then,
b1 = 3000/53 - (36/53)*27.52
b1 = 37.91 ft =b2
The dimensions of the garden that give Mr. Rogers the maximum area are approximately: Length (L) = 28.3 feet and Width (W) = 41.7 feet.
To find the dimensions of Mr. Rogers's garden that will give him the maximum area while staying within his budget, we need to set up and solve a problem involving optimization with constraints.
First, let's define the variables:
Let the length of the garden (which faces the road and requires pretty fencing) be denoted as [tex]L[/tex].Let the width of the garden be denoted as [tex]W[/tex].The cost of fencing:
Pretty fencing costs $35 per linear foot, and it is only needed for one side of the garden (the length L).Functional fencing costs $18 per linear foot, and it is needed for the other three sides (two widths W and the remaining length L).The total cost of fencing can be expressed as follows:
[tex]35L + 18(2W + L) = 3000[/tex]
Simplifying this equation:
[tex]35L + 36W + 18L = 3000[/tex]
[tex]53L + 36W = 3000[/tex]
To find the dimensions that maximize the area, we need to express the area in terms of one variable and use calculus to find the maximum. Let's solve for one variable in terms of the other. We'll solve for [tex]W[/tex]:
[tex]53L + 36W = 3000[/tex]
[tex]36W = 3000 - 53L[/tex]
[tex]W = \frac{3000 - 53L}{36}[/tex]
Now, express the area [tex]A[/tex] as a function of [tex]L[/tex]:
[tex]A = L \cdot W[/tex]
[tex]A = L \left(\frac{3000 - 53L}{36}\right)[/tex]
[tex]A = \frac{3000L - 53L^2}{36}[/tex]
To find the maximum area, we take the derivative of [tex]A[/tex] with respect to [tex]L[/tex] and set it to zero:
[tex]\frac{dA}{dL} = \frac{3000 - 106L}{36}[/tex]
Set the derivative to zero and solve for [tex]L[/tex]:
[tex]\frac{3000 - 106L}{36} = 0[/tex]
[tex]3000 - 106L = 0[/tex]
[tex]106L = 3000[/tex]
[tex]L = \frac{3000}{106}[/tex]
[tex]L \approx 28.3[/tex]
Now we use this value of [tex]L[/tex] to find the corresponding value of [tex]W[/tex]:
[tex]W = \frac{3000 - 53 \times 28.3}{36}[/tex]
[tex]W \approx \frac{3000 - 1499.9}{36}[/tex]
[tex]W \approx \frac{1500.1}{36}[/tex]
[tex]W \approx 41.7[/tex]
The following is the graph of f(x) = sin (x-180 degrees) -1
True
False
Answer:
True
Step-by-step explanation:
Check the values of [tex]f(x)[/tex] at [tex]x=0,\pm0.5\pi,\pm\pi,\pm1.5\pi,\pm2\pi[/tex]
[tex]x \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ f(x)\\0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin(0-180)-1=-1\\0.5\pi \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin(0.5\pi-180)-1=-2\\\pi \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin(\pi-180)-1=-1\\1.5\pi \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin(1.5\pi-180)-1=0\\2\pi \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin(2\pi-180)-1=-1\\-0.5\pi \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin(-0.5\pi-180)-1=0\\-\pi \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin(-\pi-180)-1=-1\\\\[/tex]
[tex]-1.5\pi \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin(-1.5\pi-180)-1=-2\\-2\pi \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin(-2\pi-180)-1=-1[/tex]
Each [tex](x,y)[/tex] point is on the graph.
Hence graph represents the given function.
There are 34 students in anatomy class and 37 students in physics class. If there are 48 students in total, how many students are in both classes?
Answer: 23
Step-by-step explanation:
let x=no. of students in both classes
no. of students in anatomy = 34
no. of students in anatomy only= 34 -x
no. of students in physics= 37
no. of students in physics only=37-x
48 = 34-x + 37-x + x
48 = 34 - x + 37
48 = 71 - x
x = 71 - 48
x = 23
Therefore the number of students in both classes are 23
Final answer:
To find the number of students in both the anatomy and physics classes, we can use the concept of sets and intersection. The number of students in both classes is 23.
Explanation:
To find the number of students in both the anatomy and physics classes, we can use the concept of sets and intersection. Let's assume A represents the set of students in the anatomy class, B represents the set of students in the physics class, and U represents the universal set of all students.
According to the given information, |A| = 34, |B| = 37, and |U| = 48.
The number of students in both classes can be found by using the formula:
|A ∩ B| = |A| + |B| - |U|
Substituting the values, we get:
|A ∩ B| = 34 + 37 - 48
|A ∩ B| = 71 - 48
|A ∩ B| = 23
Therefore, there are 23 students in both the anatomy and physics classes.
A sandwich shop has three types of sandwiches: ham, turkey, and chicken. Each sandwich can be ordered with white bread or multi-grain bread. Customers can add any combination of the six available toppings
To calculate the number of different sandwich combinations at a sandwich shop, one multiplies the basic sandwich configurations (3 types of sandwiches on 2 types of bread, totaling 6) by the possible topping combinations (2^6 = 64, including the option of no toppings), resulting in 384 different sandwich combinations.
Explanation:The question revolves around combinatorial mathematics, focusing on calculating the number of different sandwich combinations available at a sandwich shop with a given set of ingredients. The shop offers three types of sandwiches (ham, turkey, and chicken), each of which can be ordered on either white bread or multi-grain bread. Additionally, customers can add any combination of the six available toppings to their sandwiches. To calculate the total number of possible sandwich combinations, one would need to consider the choices for the type of sandwich, the bread, and the combinations of toppings.
For the sandwich and bread choices, since there are three types of sandwiches and two types of bread, there are a total of 3 * 2 = 6 basic sandwich configurations. For the toppings, since customers can choose any combination of the six available toppings, including the option of having no toppings at all, the total number of topping combinations can be calculated using the formula for combinations of a set: 2n, where n is the number of items (toppings) to choose from. Therefore, there are 26 = 64 possible topping combinations.
The total number of different sandwich combinations available can be calculated by multiplying the basic sandwich configurations by the topping combinations, which gives 6 * 64 = 384 different sandwich combinations. This calculation showcases the versatility of the menu and the vast array of options available to customers at the sandwich shop.
Let's say:
Ham sandwich: H
Turkey sandwich: T
Chicken sandwich: C
White bread: W
Multigrain bread: M
The representation using set notations would be:
[ (H,W), (H,M), (T,W), (T,M), (C,W), (C,M) ]
Complete question is here:
Represent the sample space using set notation.A sandwich shop has three types of sandwiches: ham, turkey, and chicken. Each sandwich can be ordered with white bread or multi- grain bread.
Mr. Kim's age in years is 6 more than 3 times the age of his daughter. Mr. Kim is 48 years old. How old, in years is Mr. Kim's daughter?
Answer:
14
Step-by-step explanation:
48 - 6 = 42
42 divided by 3 = 14.
Mr. Kim's daughter is 14 years old.
Mr. Kim's daughter is 14 years old. This was determined by setting up the equation 48 = 3x + 6 and solving for x step-by-step, which resulted in x = 14.
To find Mr. Kim's daughter's age, we can set up an equation based on the problem statement.
Let's denote the daughter's age by x.
According to the problem, Mr. Kim's age is 6 more than 3 times his daughter's age. This can be written as:
48 = 3x + 6
We need to solve for x step-by-step:
Subtract 6 from both sides of the equation:
48 - 6 = 3x
Simplify the left side:
42 = 3x
Divide both sides by 3:
[tex]\frac{42}{3}[/tex] = x
Simplify the right side:
x = 14
Therefore, Mr. Kim's daughter is 14 years old.
Two planes are flying around the world. The first plane is flying at 300 miles per hour (mph) and is 350 miles ahead of the second plane. The second plane is flying at 400 mph. How long will it take for the second plane to catch the first plane?
Answer:
It takes 3.5 hours for the second plane to catch the first plane.
Step-by-step explanation:
From the information given:
Rate of the first plane = 300 miles per hourRate of the second plane = 400 miles per hourThe first plane is 350 miles ahead of the second plane.To find when the second plane catches the first plane, the distances of both planes must be equal.
We can use Distance = Rate x Time.
Let t be the time.
Distance of the first plane = Rate x Time = [tex]300\cdot t + 350[/tex]
Distance of the second plane = Rate x Time = [tex]400\cdot t [/tex]
Distance of the second plane = Distance of the first plane
[tex]400\cdot t=300\cdot t + 350[/tex]
Solving for t.
[tex]100\cdot t = 350[/tex]
t = 3.5 hours
It takes 3.5 hours for the second plane to catch the first plane.
The distance travelled by the two planes is an illustration of a linear function.
It will take the second plane 3.5 hours to catch up with the first plane
Let t represent time and d represent distance
The distance traveled by the first plane is represented as:
[tex]\mathbf{d_1 = 350 + 300t}[/tex]
The distance traveled by the second plane is represented as:
[tex]\mathbf{d_2 = 400t}[/tex]
Both planes will be at the same distance, when d1 = d2.
So, we have:
[tex]\mathbf{400t = 350 + 300t}[/tex]
Subtract 300t from both sides
[tex]\mathbf{400t - 300t = 350}[/tex]
Subtract
[tex]\mathbf{100t = 350}[/tex]
Divide both sides by 100
[tex]\mathbf{t = 3.50}[/tex]
Hence, it will take the second plane 3.5 hours to catch up with the first plane
Read more about distance at:
https://brainly.com/question/16228790
Yesterday Mike bought 2 gallons of regular gasoline and 3 gallons of premium gasoline at a gas station for $13.60 today he bought 3 gallons of regular gasoline and 4 gallons a premium gasoline for $18.95 if the prices do not change how much does one gallon of premium gasoline cost
Answer:
Cost of 1 gallon of Regular gasoline is $2.45 and Cost of 1 gallon of Premium gasoline is $2.90.
Step-by-step explanation:
Let the Cost of Regular gasoline be 'x'.
Let the Cost of Premium gasoline be 'y'.
Given:
Amount of regular gasoline bought yesterday = 2 gallons
Amount of premium gasoline bought yesterday = 3 gallons
Total Cost of yesterday = $13.60
Now we know that Total Cost of yesterday is equal to sum of Amount of regular gasoline bought yesterday multiplied by Cost of Regular gasoline and Amount of Premium gasoline bought yesterday multiplied by Cost of premium gasoline.
Framing in equation form we get;
[tex]2x+3y=13.60 \ \ \ \ equation\ 1[/tex]
Also Given:
Amount of regular gasoline bought today = 3 gallons
Amount of premium gasoline bought Today = 4 gallons
Total Cost of Today = $18.95
Now we know that Total Cost of Today is equal to sum of Amount of regular gasoline bought Today multiplied by Cost of Regular gasoline and Amount of Premium gasoline bought Today multiplied by Cost of premium gasoline.
Framing in equation form we get;
[tex]3x+4y=18.95 \ \ \ \ equation\ 2[/tex]
Now Multiplying equation 1 by 3 we get;
[tex]2x+3y=13.60\\\\3(2x+3y)=13.60\times3\\\\6x+9y= 40.80 \ \ \ \ \ equation\ 3[/tex]
Now Multiplying equation 2 by 2 we get;
[tex]3x+4y=18.95\\\\2(3x+4y)=18.95\times2\\\\6x+8y= 37.90 \ \ \ \ \ \ equation\ 4[/tex]
Subtracting equation 4 from equation 3 we get;
[tex](6x+9y)- (6x+8y)= 40.80-37.90\\\\6x+9y-6x-8y= 2.9\\\\y=\$2.90[/tex]
Substituting the value of y in equation 1 we get;
[tex]2x+3y=13.60\\\\2x+3\times2.90 =13.60\\\\2x+8.7=13.6\\\\2x=13.6-8.7\\\\2x=4.9\\\\x=\frac{4.9}{2} =\$2.45[/tex]
Hence Cost of 1 gallon of Regular gasoline is $2.45 and Cost of 1 gallon of Premium gasoline is $2.90.
What is the slope of the line containing the midpoint of the segment with endpoints at (0, 0) and (2, 3) and the midpoint of the segment with endpoints at (5, 0) and (6, 3)? Express your answer in simplest form.
Answer:
The slope = 0.
Step-by-step explanation:
The midpoint of the first line =
(0+2)/2, (0+3)/ 2
= (1, 1.5).
For the second line :
(5+6)/2 , (0+3)/2
= (5.5, 1.5).
The required slope = rise / run
= (1.5-1.5)/(5.5-1))
= 0/4.5
= 0.
Answer:
0
Step-by-step explanation:
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There are 30 students in Bobby's class. 40% of the students have blue eyes. How many students in Bobby's class have blue eyes?
A. 12
B. 18
C. 28
D. 42
E. 75
Answer:
12
Step-by-step explanation:
Number of students in Bobby's class = 30
40% of the students have blue eyes.
It means 40 out of 100 students will have blue eyes.
Then we have to find how many out of 30 students will have blue eyes.
Let us take the number of blue-eyed students out of 30 to be x.
Then:
[tex]\frac{40}{100}=\frac{x}{30}\\x=\frac{40}{100}\times30\\x=12[/tex].
Hence 12 out of 30 students will have blue eyes.
look at the figure below:
Which step should be used to prove that point P is equidistant from points R and Q?
If any one side and any one common angle are equal in triangles PQR and PRS, then their corresponding sides are also equal.
If two sides and one included angle are equal in triangles PQS and PRS, then their third sides are equal.
In triangles PQR and PQS, if one side and one angle are equal, then their corresponding sides and angles are also equal.
In triangles PRS and PQS, all three angles are equal.
Answer:
The correct option is
If two sides and one included angle are equal in triangles PQS and PRS, then their third sides are equal.
Step-by-step explanation:
Given:
RS ≅ SQ
∠PSR ≅ ∠PSQ = 90°
To Prove:
point P is equidistant from points R and Q
i.e PR ≅ PQ
Proof:
In ΔPSR and Δ PSQ
PS ≅ PS ……….{Reflexive Property}
∠PSR ≅ ∠PSQ = 90° …………..{Measure of each angle is 90° given}
RS ≅ QS ……….{Given}
ΔPSR ≅ ΔPSQ ….{By Side-Angle-Side Congruence test}
∴ PR ≅ PQ .....{Corresponding Parts of Congruent Triangles}
i.e point P is equidistant from points R and Q .......Proved
help me with 17.
(I know the image is upside down, but there's a flip button and u can click It to flip it)
Answer:
look at the photo below for the answer.
:)
In the figure, BP is an angle bisector of ∠CBD. Find x if m∠1 = 4x - 8 and m∠2 = 3x + 2.
A) 5
B) 7
C) 9
D) 10
I am spacing out the words of the link for the picture, so just put the symbols/letters into place. https://www. usatestprep.com /modules/questions /files /image/ 451840.j pg
Answer:
Option D) 10
Therefore the value of x is 10.
Step-by-step explanation:
Given:
BP is an angle bisector of ∠CBD.
m∠1 = 4x - 8 and
m∠2 = 3x + 2.
To Find:
x = ?
Solution:
Angle Bisector:
A line that splits an angle into two equal angles.
Bisect means to divide into two equal parts.
Here, BP is an angle bisector of ∠CBD.
∴ m∠ 1 = m∠ 2
Substituting the given values we get
[tex](4x-8)=(3x+2)\\\\4x-3x=8+2\\\\x=10\\\\\therefore x = 10[/tex]
Therefore the value of x is 10.
A T-shirt makes wants to open his first store. If he chooses the store on Main Street, he will pay $640 in rent and will charge $30 per T-shirt. If he chooses the store on Broad Street, he will pay $450 in rent and will charge $25 per T-shirt. How many T-shirts would he have to sell in 1 month to make the same profit at either location?
Answer:38 t-shirts
Step-by-step explanation:
P=30t-640 main street
p=25t-450 broad street
30t-640=25t-450
30t-25t-640=-450
5t-640+640=-450+640
5t/5=190/5
t=38
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