The student asked for the four smallest positive angles where cosine equals ½. By using the unit circle, the angles of 60° and 300° are identified as solutions, with their general solutions given by θ = π/3 + 2kπ and θ = 5π/3 + 2kπ. The four smallest positive answers are thus 60°, 300°, 420°, and 660°.
Explanation:The student is asking for the four smallest positive angles θ for which the cosine is equal to ½. To find these angles, it helps to recall the unit circle and the fact that the cosine of an angle corresponds to the x-coordinate of a point on the unit circle. The angles with a cosine of ½ in the first 360° (or 2π radians) are those where the corresponding points on the unit circle are at (½, √3/2) and (½, -√3/2). These points correspond to angles of 60° (or π/3 radians) and 300° (5π/3 radians) respectively. However, these are not the only solutions when considering multiple rotations around the circle.
The general solutions for cosine equaling ½ in terms of radians are given by:
θ = π/3 + 2kπ, where k is an integer.θ = 5π/3 + 2kπ, where k is an integer.The four smallest positive solutions correspond to setting k=0 and k=1 in the above equations, yielding the angles:
θ = π/3 (60°)θ = 5π/3 (300°)θ = π/3 + 2π (60° + 360° = 420°)θ = 5π/3 + 2π (300° + 360° = 660°)Note that these angles are measured in degrees for simplicity, but they can be converted to radians by using the equivalence 180° = π radians. To convert these angles to radians, simply divide by 180 and multiply by π.
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rabbits population can double every 30 days if there are 10 rabbits on a farm how many rabbits will be on the farm after 120 days
Answer:
Step-by-step explanation:
= 10(1+1)^4 the final answer is 160
How I got 4 is you divide 30\ 120 =4
After 120 days there will be 160 rabbits on the farm.
What is equation?"It is a mathematical statement which consists of equal symbol between two algebraic expressions."
For given question,
Rabbits population can double every 30 days.
Initially there are 10 rabbits in a farm.
So, after 30 days there would be 10 × 2 = 20 rabbits.
After next 30 days, there would be
20 × 2
= 10 × 4
= 10 × 2²
= 40 rabbits.
Let t be the number of days and x be the number of rabbits.
So, we have an equation:
[tex]x=10\times2^{\frac{t}{30} }[/tex]
No, we find the number of rabbits after 120 days.
t = 120
So, the equation becomes,
[tex]x=10\times2^{\frac{t}{30} }\\\\x=10\times2^{\frac{120}{30} }\\\\x=10\times2^{4}\\\\x=10\times 16\\\\x=160[/tex]
Therefore, after 120 days there will be 160 rabbits on the farm.
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PLS HELP!
Rohan is checking in poodles for a dog show. A miniature poodle must be between 10 in. and 15 in. at the shoulder. The body length must be no more than 16 in. In addition, the poodle’s shoulder height must be no more than 1 in. longer than its body length.
The graph shows the feasible region, where x represents the poodle’s body length and y represents the shoulder height.
Which ordered pairs meet all the constraints for a successful poodle measurement and make sense in context of the situation?
Select each correct answer.
(15, 11)
(11, 9)
(11, 14)
(10, 12)
(12, 10.5)
Answer:
(15, 11) and (12, 10.5).
Step-by-step explanation:
Let x represents the poodle’s body length and y represents the shoulder height.
A miniature poodle must be between 10 in. and 15 in. at the shoulder.
[tex]10\leq y\leq 15[/tex]
The body length must be no more than 16 in.
[tex]0\leq x\leq 16[/tex]
The poodle’s shoulder height must be no more than 1 in. longer than its body length.
[tex]y\le1+x[/tex]
From the below figure it is clear that only two points (15, 11) and (12, 10.5) lie in the feasible region.
Therefore, ordered pairs (15, 11) and (12, 10.5) meet all the constraints for a successful poodle measurement and make sense in context of the situation.
The perimeter of an equilateral triangle is 156 feet find the length of each side
Answer:
52 feet
Step-by-step explanation:
In an equilateral triangle, all three sides are equal in length.
If we let s represent the length of one side, the perimeter P of the triangle can be expressed as:
[tex]P = 3s[/tex]
Given that the perimeter is 156 feet, we can set up the equation:
[tex]3s = 156[/tex]
To find s, divide both sides of the equation by 3:
[tex]\dfrac{3s}{3}=\dfrac{156}{3}[/tex]
[tex]s=52[/tex]
Therefore, the length of each side of the equilateral triangle is:
[tex]\large\boxed{52 \textsf{ feet}}[/tex]
A scale drawing of a kitchen is shown below. The scale is 1 : 20.
Show your work to determine the area of the room in square feet.
Answer:
Step-by-step explanation:
B
What is the area of trapezoid ABCD ?
Enter your answer as a decimal or whole number. Do not round at any steps.
__units²
A tow truck charges a service fee of $50 and an additional fee of $1.75 per mile. What distance was Marcos's car towed if he received a bill for $71?
To find the distance Marcos's car was towed, subtract the service fee from the total bill amount. Then divide the remaining bill amount by the additional fee charged per mile. The distance towed is 12 miles.
Explanation:To find the distance Marcos's car was towed, we need to subtract the service fee from the total bill amount. The additional fee charged per mile is $1.75, so we can calculate the number of miles towed by dividing the remaining bill amount by $1.75.
Let's assume the distance towed is 'x' miles.
The total bill amount is $71, and the service fee is $50. Therefore, the additional fee charged for the distance towed is $71 - $50 = $21.
So we can write the equation:
$21 = $1.75 * x
To solve for 'x', we divide both sides of the equation by $1.75:
x = $21 / $1.75
x = 12 miles
Therefore, Marcos's car was towed for a distance of 12 miles.
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How to find the equation of an exponential function given two points?
The measures of the three angles of a triangle are given. Find the value of x and state whether the triangle is acute, obtuse or right. x + 10, x − 20, x + 25
A. x = 25, acute
B. x = 55, acute
C. x = 65, right
Answer:
x=55 acute
Step-by-step explanation:
Because of the 3-6 theorum of triangles
Help please pre calculus
put 7.6*10^-4 into the equation:
10log(1/7.6*10^-4)
this equals 31.19 db
The cross section of a beehive reveals it is made of regular hexagons. what is the measure of each angle in a regular hexagon?
What is the answer because I don't get it
____ patterns have regular elements spaced at regular intervals.
What is the unit rate for 644.8 ft in 31 s?
divide feet by seconds
644.8 / 31 = 20.8 feet per second
Answer:
644.8 divided by 31 and you should get 20.8Step-by-step explanation:
644.8 divided 31=20.8 just put it in the calculator and you can get your answer :)the weight of a full steel bead tire is approximately 800 grams, while a lighter wheel weighs only 700 grans. What is the weight of each tire in pounds? There are 453.592 grams in one pound. Round answers to 2 decimal places.
Answer:
Weight of full steel bead tire=1.76 pounds
weight of lighter wheel=1.54 pounds.
Step-by-step explanation:
it is given that:
The weight of a full steel bead tire is approximately 800 grams.
lighter wheel weighs only 700 grams.
Now we are given conversion that:
There are 453.592 grams in one pound.
Hence, 1 gram=1/453.592 pounds.
Hence, weight of a full steel bead tire is:
[tex]\dfrac{800}{453.592}pounds=1.76pounds[/tex]
Also weight of lighter wheel in pounds is:
[tex]\dfrac{700}{453.592}pounds\\\\=1.54 pounds[/tex]
A box contains 14 scarves in unique colors. If 4 scarves are picked randomly from the box,__________ different combinations are possible if the order doesn't matter.
Answer: 363242880
Step-by-step explanation:
We know that the of to calculate the number of combinations, we use the formula :-
[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex], where n : the total number of items
r: the number of items being chosen at a time.
Given: The total number of scarves contained in a box= 14
The number of scarves picked = 4
The number of different combinations is given by :-
[tex]^{14}C_4=\dfrac{14!}{(14-4)4!}\\\\=\dfrac{14\times13\times12\times11\times10!}{10!4!}\\\\=\dfrac{14\times13\times12\times11}{4\times3\times2}=363242880[/tex]
Hence, If 4 scarves are picked randomly from the box, 363242880 different combinations are possible if the order doesn't matter.
Please help with a multiple choice question!!
Relationship B has a greater rate than Relationship A. This graph represents Relationship A.
Which equations could represent Relationship B?
Select each correct answer.
A) y=1/2x
B)y = 3x
C)y = 2.2x
D)y = 1.4x
Elizabeth bought 4 drinks and some nachos. The nachos cost $6, and she spent a total of $18. How much did each drink cost? Use d to represent the cost of each drink. A. ; each drink cost $4. B. ; each drink cost $6. C. ; each drink cost $2. D. ; each drink cost $3.
The drink costs $3 for each.
The correct option is (D)
What is Algebra?Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols.
Number of drinks= 4
Cost of Nachos = $6.
Total money spend =$18
After removing the prices from total money spend, we will get the price for 4 drinks
So, 18-6= $12
Cost for 4 drinks =12
Cost of 1 drink =12/4 = $3
Hence, each drink cost $3.
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A line slope is 1 and its y intercept is 2 what is its equation in slope intercept form
Write your answer using integers proper fractions and improper fractions in simplest form
[tex]\[ y = x + 2 \][/tex] is the equation in slope-intercept form.
To find the equation of a line given its slope and y-intercept, we use the slope-intercept form: ( y = mx + b ), where ( m ) is the slope and ( b ) is the y-intercept.
Given that the slope ( m = 1 ) and the y-intercept ( b = 2 ), we substitute these values into the equation:
[tex]\[ y = 1x + 2 \][/tex]
[tex]\[ y = x + 2 \][/tex]
This is our equation in slope-intercept form.
Now, let's show the detailed calculation:
1. Start with the slope-intercept form: ( y = mx + b ).
2. Substitute ( m = 1 ) and ( b = 2 ) into the equation: ( y = 1x + 2 ).
3. Simplify: ( y = x + 2 ).
So, the equation of the line is \( y = x + 2 \). This means the line has a slope of 1 and passes through the point (0,2) on the y-axis.
For the following figure, complete the statement for the specified points.
Points A, S, Q, and R are _____.
collinear
coplanar
both collinear and coplanar
neither collinear nor coplanar
Answer:
D. Neither collinear nor coplanar
Step-by-step explanation:
We know that,
Collinear points - are the points which lie in the same straight line.
Coplanar points - are the points which lie in the same plane.
From the figure, we see that,
The points A, S, and R lie in the same line but Q does not lie in the same line.
The points A and Q lie in the same plane but others do not lie in the same plane.
Hence, we get,
These points are neither collinear nor coplanar.
Thus, option D is correct.
Person is randomly selected. what is the probability that the person is:
a.color-blind given that the person is male? 69/133
b.male and color-blind?
The probability that a person is color-blind given they are male is 69/133. Calculating the probability of being both male and color-blind requires additional information about the total and male population. This showcases the importance of context in probability calculations.
Explanation:The question involves calculating the probability of specific conditions related to color-blindness and gender. To address both parts of the question:
For part a, the probability that a person is color-blind given that the person is male is directly provided as 69/133. This means out of all males considered, approximately 51.88% have color-blindness.For part b, determining the probability of being male and color-blind would require more specific data, such as the total number of people or the ratio of males to females, and how many among them are color-blind. If we consider the probability for a male to be color-blind is 69/133, this probability is only valid within the male population; it does not directly give us the probability of being both male and color-blind unless the total population is known and the proportion of males within that population is specified.Understanding probabilities in genetics, like color-blindness, often involves considering various factors including the overall population and specific subgroups within that population (such as males in this case).
There are 30 homes in Neighborhood A. Each year, the number of homes increases by 20%. Just down the road, Neighborhood B has 45 homes. Each year, 3 new homes are built in Neighborhood B.
Part A: Write functions to represent the number of homes in Neighborhood A and Neighborhood B throughout the years. (4 points)
Part B: How many homes does Neighborhood A have after 5 years? How many does Neighborhood B have after the same number of years? (2 points)
Part C: After approximately how many years is the number of homes in Neighborhood A and Neighborhood B the same? Justify your answer mathematically. (4 points)
Part A)
y = total houses, x = number of years
Neighborhood A y = 30*(1.20)^x
Neighborhood B : y = 45 +3x
Part B) neighborhood A has : 30 *1.2^5 = 74.65 = 75 houses
neighborhood B has: 45 +3(5) = 45 +15 = 60 houses
Part C)
30* 1.2^x = 45 +3x =
x = 3.3
check:
30 *1.2^3.3 = 54.75 = 55
45 + 3(3.3) = 45+9.9 = 54.9 =55
so 3.3 years round to 3 years
Answer:
Part A)
y = total houses, x = number of years
Neighborhood A y = 30*(1.20)^x
Neighborhood B : y = 45 +3x
Part B) neighborhood A has : 30 *1.2^5 = 74.65 = 75 houses
neighborhood B has: 45 +3(5) = 45 +15 = 60 houses
Part C)
30* 1.2^x = 45 +3x =
x = 3.3
check:
30 *1.2^3.3 = 54.75 = 55
45 + 3(3.3) = 45+9.9 = 54.9 =55
so 3.3 years round to 3 years
Step-by-step explanation:
Solve for x. 7(x + 1) = 21
x = 2
x = 20/7
x = 22/7
x = 4
Quadrilateral FGHI is dilated with respect to the origin by a scale factor of 1/3 . What are the coordinates of G’?
Answer:
D
Step-by-step explanation:
you divide the x and y axis by 3
Got it right on EDG
Clyde Cement wants to analyze a shipment of bags of cement. He knows the weight of the bags is normally distributed so he can use the standard normal distribution. He measures the weight of 600 randomly selected bags in the shipment. Next, he calculates the mean and standard deviation of their weights. The mean is 50 lbs and the standard deviation is 1.5 lbs. What percentage of the bags of cement will weigh less than 50 lbs.? 50 60 75 80
Answer:
50%
Step-by-step explanation:
First, draw a normal distribution plot to use for the analysis of the data. Starting at the mean in the centre. Add one standard deviation for each interval to the right, and subtract one standard deviation for each interval to the right. See attached image. According to the empirical rule, 68% of data lies within one standard deviation of the mean, 95 % of the data is within two st. dev. and 99.7% of the data is within 3 st. dev. of the mean.
From the graph it can be deducted that half of the data will lie below 50, which makes it 50%.
An easier way of determining the answer is to use the definition of a mean. A mean is the number that,when all the data is placed in ascending order, lies right in the middle of all the data.
In a normal distribution, 50% of the values lie below the mean. Therefore, 50% of the bags will weigh less than 50 lbs.
The question involves understanding the properties of a normal distribution where the mean weight of the bags is 50 lbs, and the standard deviation is 1.5 lbs. To determine the percentage of bags weighing less than 50 lbs, we look at the standard normal distribution. Since 50 lbs is the mean, exactly 50% of the bags will weigh less than this amount. This is because, in a normal distribution, the mean divides the distribution so that half the values are below the mean and half are above it.
2y+7x=4;x=5,10,15 PLEASE HELP ASAP!!!!
Final answer:
To solve the equation 2y+7x=4 for x=5, x=10, and x=15, substitute each value into the equation and solve for y to get y=-15.5, y=-33, and y=-50.5 respectively. It’s important to check the solutions by substituting them back into the original equation.
Explanation:
To solve the given linear equation 2y+7x=4 for different values of x (x=5, x=10, x=15), we need to substitute these values of x into the equation and solve for y. Here’s how it can be done:
For x=5: 2y + 7(5) = 4.Suzie purchased a dress on sale for $27.20. This is 85% of the original price. What was the original price?
The original price of the dress purchased by Suzie is given by the equation A = $ 32
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the original price of the dress be A
Now , the equation will be
The cost of the purchase = $ 27.20
The percentage of the cost of purchase = 85 %
So ,
The original price of the dress x percentage of the cost of purchase = cost of the purchase
Substituting the values in the equation , we get
A x ( 85/100 ) = 27.20
On simplifying the equation , we get
Multiply by 100 on both sides of the equation , we get
85A = 2720
Divide by 85 on both sides of the equation , we get
A = 2720/85
A = $ 32
Therefore , the value of A is $ 32
Hence , the original price of the dress is $ 32
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The measure of ∠ABC is 46°. What is the measure of its intercepted arc AC?
46°
92°
144.44°
23°
Thank you!
Help please pre calculus
put 7.6*10^-4 into the given formula as the denominator of the fraction:
10log(1/7.6*10^-4) = 31.19
Two separate single-factor anovas provide exactly the same information that is obtained from a two-factor analysis of variance.
a. True
b. False
Please help me?
3x - 4y = 7
3x + 2y = -5
When the second equation is subtracted from the first, the resulting equation is _____.
A. -6y = -12
B. -6y = 12
C. -2y = -12
D. 2y = 12
what type of figures are shown?Which scale factor changes the small to the large version
Answer: Kites, 1.5
Step-by-step explanation: Here to help from da interim checkpoint :)