Answer:
The center of the circle is (-2 , 3) ⇒ 3rd answer
Step-by-step explanation:
The equation of a circle is (x - h)² + (y - k)² = r², where
(h , k) are the coordinates of its centerr is the radius of it∵ The equation of the circle is x² + 4x + y² - 6y = 12
- Lets make a completing square for x² + 4x
∵ x² = (x)(x)
∵ 4x ÷ 2 = 2x
- That means the second term of the bracket (x + ...)² is 2
∴ The bracket is (x + 2)
∵ (x + 2)² = x² + 4x + 4
∴ We must add 4 and subtract 4 in the equation of the circle
∴ (x² + 4x + 4) - 4 + y² - 6y = 12
Lets make a completing square for y² - 6y
∵ y² = (y)(y)
∵ -6y ÷ 2 = -3y
- That means the second term of the bracket (y + ....) is -3
∴ The bracket is (y - 3)
∵ (y - 3)² = y² - 6y + 9
∴ We must add 9 and subtract 9 in the equation of the circle
∴ (x² + 4x + 4) - 4 + (y² - 6y + 9) - 9= 12
Now lets simplify the equation
∵ (x + 2)² + (y - 3)² - 13 = 12
- Add 13 to both sides
∴ (x + 2)² + (y - 3)² = 25
- Compare it with the form of the equation of the circle to
find h and k
∵ (x - h)² + (y - k)² = r²
∴ h = -2 and k = 3
The center of the circle is (-2 , 3)
Solve the system of equations.
-5y+6x=40
3y-8x=-46
x=
y=
Answer:
X=5
Y=-2
Step-by-step explanation:
Answer:
x = 5
y = -2
Step-by-step explanation:
Let's solve the system of equations, this way:
-5y + 6x = 40
3y - 8x = -46
******************
-5y + 6x = 40
6x = 40 + 5y
x = (40 + 5y)/6
******************
Substituting x and solving for y in the 2nd equation:
3y - 8x = - 46
3y - 8 * [(40 + 5y)/6] = - 46
3y - (320 + 40y)/6 = - 46
18y - 320 - 40y = - 276 (Multiplying by 6 at both sides)
-22y = - 276 + 320 (Adding 320 at both sides)
-22y = 44
y = -44/22
y = -2
**************************
Solving for x in the 1st equation:
-5y + 6x = 40
-5 * - 2 + 6x = 40
10 + 6x = 40
6x = 40 - 10 (Subtracting 10 at both sides)
6x = 30
x = 30/6
x = 5
Vera claimed the solution set on the number line represents the inequality Negative 78.9999 greater-than-or-equal-to x. A number line going from negative 82 to negative 78. A closed circle is at negative 79. Everything to the left of the circle is shaded. Which error did Vera make? Vera wrote the inequality with the variable on the left side of the relation symbol. Vera wrote a relation symbol that does not represent the direction of the ray. Vera selected an inequality that does not include –79 in its solution set. Vera used the wrong number in her inequality.
Answer:
Vera used the wrong number in her inequality.
Step-by-step explanation:
Inequalities are graphed to present a clearer picture of their behavior
To graph an inequality, the following are required steps
(1) Locate the indicated number on the other side of the inequality sign variable x in the inequality equation (in this case we have 78.9999 ≥ x)
(2) Draw a number line and place an open or shaded circle around around the number specified in the inequality equation depending on whether the variable is also equal to the number
(3) Shade the possible numbers of the variable
In this case Vera used 78.999 in the equation and 79 on the graph
Answer:
Vera used the wrong number in her inequality.
Step-by-step explanation:
Vera graphed the inequality -78.9999 ≥ x. However, she plotted the point at -79, not -78.9999. Thus, we can tell the answer is Vera used the wrong number in her inequality.
Hope this helps! I got it right on E d g e n u i t y. Plz give me brainliest, it will help me achieve my next rank.
A soccer ball is kicked from the ground with an initial upward velocity of 90 feet per second. The equation h=-16t^2+90t gives the height h of the ball after t seconds. Find the maximum height of the ball.
Answer:
[tex]h_{max} = 30.012\,ft[/tex]
Step-by-step explanation:
The maximum height of the soccer can be determined with the help of the First Derivative and Second Derivative Tests, whose expression are introduced below:
[tex]\frac{dh}{dt} = -32\cdot t + 90[/tex]
[tex]-32\cdot t + 90 = 0[/tex]
[tex]t = 0.356\,s[/tex]
[tex]\frac{d^{2}h}{dt^{2}} = -32[/tex]
According to both tests, the critical value leads to maximum height. Then:
[tex]h_{max} = -16\cdot (0.356)^{2}+90\cdot (0.356)[/tex]
[tex]h_{max} = 30.012\,ft[/tex]
To estimate the average annual expenses of students on books and class materials a sample of size 36 is taken. The sample mean is $850 and the sample standard deviation is $54. A 99% confidence interval for the population mean is:_______.A) $823.72 to $876.28.
B) $832.36 to $867.64.
C) $826.82 to $873.18.
D) $825.48 to $874.52.
Answer:
C) $826.82 to $873.18.
Step-by-step explanation:
Sample mean (M) = $850
Standard deviation (s) = $54
sample size (n) = 36
Z for 99% confidence interval (Z) = 2.576
The confidence interval is determined by the following relationship:
[tex]M \pm Z*\frac{s}{\sqrt{n}}[/tex]
Applying the given values, the lower (L) and upper (U) values are:
[tex]850 \pm 2.576*\frac{54}{\sqrt{36}}\\L=\$826.82\\U=\$873.18[/tex]
The answer is C) $826.82 to $873.18.
Francisco's game involves a bag of 3 green, 2 yellow, 4 red, and 3 black marbles. Andrew wants to increase the likelihood of selecting a yellow marble. How can the game be modified to make drawing a yellow marble more likely? Select all that apply.XAndrew should add more green marbles to the bag.-Andrew should add more yellow marbles to the bag.-Andrew should remove from the bag 1 green, 1 black, and 2 red marbles.XAndrew should add more black marbles to the bag-Andrew should triple the number of yellow marbles in the bag.
To increase the likelihood of selecting a yellow marble Andrew should:
-Add more yellow marbles to the bag
-Remove from the bag 1 green, 1 black, and 2 red marbles
-Triple the number of yellow marbles in the bag
Answer:
B,C,E
Step-by-step explanation:
just did it
According to the journal of irreproducible results, any obtuse angle is a right angle! c d b p here is their argument. given the obtuse angle x, we make a quadrilateral abcd with \dab = x, and \abc = 90 , and ad = bc. say the perpendicular bisector to dc meets the perpendicular bisector to ab at p. then pa = pb and pc = p
d. so the triangles p ad and p bc have equal sides and are congruent. thus \pad = \pbc. but pab is isosceles, hence \pab = \pba. subtracting, gives x = \pad \pab = \pbc \pba = 90 . this is a preposterous conclusion – just where is the mistake in the "proof" and why does the argument break down there?
Answer:
The mistake stems from the assumption that angle dab and abc are both 90 and ad = bc and that the perpendicular bisector of dc is different from the perpendicular bisector to ab because they are the same and abcd is a rectangle.
Step-by-step explanation:
If ∡dab = ∡abc and side ab is equal to side bc which are opposite sides, ten then ab is parallel to bc which means the quadrilateral is parallelogram. Also since two angles of the four angles of the parallelogram are 90 degrees then the parallelogram is a rectangle.
The bisector of one side of a rectangle will also bisect the opposite side of the rectangle. Therefore the bisector of dc is the same as the bisector of ab and it meets ab at the midpoint of ab. Therefore p is now at the midpoint of ab and there are no triangles pad and pbc.
A rectangle is constructed with its base on the diameter of a semicircle with radius 2 and with its two other vertices on the semicircle. What are the dimensions of the rectangle with maximum area?
Answer:
L = 2*√2
w = √2
Step-by-step explanation:
Given:
A rectangle is constructed with its base on the diameter of a semicircle with radius 2 and with its two other vertices on the semicircle.
Find:
What are the dimensions of the rectangle with maximum area?
Solution:
- Let the length and width of the rectangle be L and w respectively.
- We know that Length L lie on the diameter base. So , L < 4 and the width w is less than 2 . w < 2.
- Using the Pythagorean Theorem, we relate the L with w using the radius r = 2 of the semicircle.
r^2 = (L/2)^2 + (w)^2
sqrt (4 - w^2 ) = L / 2
L = 2*sqrt (4 - w^2 ) L < 4 , w < 2
- The relation derived above is the constraint equation and the function is Area A which is function of both L and w as follows:
A ( L , w ) = L*w
- We substitute the constraint into our function A:
A ( w ) = 2*w*sqrt (4 - w^2 )
- Now we will find the critical points for width w for which A'(w) = 0
A'(w) = 2*sqrt (4 - w^2 ) - 2*w^2 / sqrt (4 - w^2 )
0 = [2*sqrt (4 - w^2 )*sqrt (4 - w^2 ) - 2*w^2] / sqrt (4 - w^2 )
0 = 2*(4 - w^2 ) - 2*w^2
0 = -4*w^2 + 8
8/4 = w^2
w = + sqrt ( 2 ) ..... 0 < w < 2
- From constraint equation we have:
L = 2*sqrt (4 - 2 )
L = 2*sqrt(2)
what is the approximate volume of the cylinder? use 3.14 for TT 7 cm radius 26 cm height
The volume of the cylinder is [tex]4000.36 \ cm^3[/tex]
Explanation:
Given that the radius of the cylinder is 7 cm
The height of the cylinder is 26 cm
We need to find the volume of the cylinder.
The volume of the cylinder can be determined using the formula,
[tex]Volume = \pi r^2 h[/tex]
Let us substitute the values [tex]\pi= 3.14[/tex] , [tex]r=7[/tex] and [tex]h=26[/tex] in the above formula.
Thus, we have,
[tex]Volume = (3.14)(7)^2(26)[/tex]
Simplifying the terms, we get,
[tex]Volume = (3.14)(49)(26)[/tex]
Multiplying the terms, we have,
[tex]Volume = 4000.36 \ cm^3[/tex]
Thus, the approximate volume of the cylinder is [tex]4000.36 \ cm^3[/tex]
Find the range and the interquartile range.
57,96,72,63,88
The range is 39
The interquartile range is 32
Explanation:
The given data is [tex]57,96,72,63,88[/tex]
Let us arrange the data in ascending order.
Thus, we have,
[tex]57,63,72,88,96[/tex]
We need to determine the range and interquartile range of the data.
Range:
The range of the data is the difference between the highest and the lowest value in the given data.
Highest value = 96
Lowest value = 57
Range = Highest value - Lowest value
= 96 - 57
= 39
Thus, the range of the data is 39
Interquartile range:
The interquartile range is the difference between the upper quartile and the lower quartile in the given data.
From, the given data, we have, 3 quartiles. They are [tex]Q_1 , Q_2[/tex] and [tex]Q_3[/tex]
[tex]Q_2=72[/tex]
[tex]Q_1=\frac{57+63}{2} =60[/tex]
[tex]Q_3=\frac{88+96}{2} =92[/tex]
Interquartile range = [tex]Q_3-Q_1[/tex]
= [tex]92-60[/tex]
= [tex]32[/tex]
The interquartile range is 32
List the data set from least to greatest:
57, 63, 72, 88, 96
Range: Highest value - Lowest value = answer
Range: 96 - 57 = 39
(IQR) Interquartile Range: Upper quartile - Lower quartile = answer
(IQR) Interquartile range: 88.5 - 57.5 = 31
For how many values of k is it true that |k - 3| + 2 is equal to one?
A) One
B) Two
C) None
D) More than two
Answer:
C) None
Step-by-step explanation:
|k - 3| + 2 = 1
|k - 3| = -1
Which is not possible because a mod can never be negative
Final answer:
There are zero values of k that make the equation |k - 3| + 2 = 1 true because the absolute value of any number cannot be negative.
Explanation:
To determine for how many values of k the equation |k - 3| + 2 = 1 is true, we need to consider what the absolute value represents. The absolute value of a number is its distance from 0 on the number line, regardless of direction.
Thus, |k - 3| represents the distance of k from 3.
First, we simplify the equation by subtracting 2 from both sides:
|k - 3| = -1
Since the absolute value of a number is always non-negative, there can be no real number k that would make |k - 3| equal to -1.
Therefore, there are zero values of k that would satisfy the original equation.
Most evenings after dinner Duarte spends 30 3030 minutes playing chess with his dad. Write an equation for the number of minutes, m mm, that Duarte spent playing chess with his dad if they played chess together e ee evenings
Answer:
im sorry but that question makes o sense
Step-by-step explanation:
A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent. Do you agree with this statement
Answer:
No, Mutually exclusive events and Independent events are not the same.
Step-by-step explanation:
Mutually exclusive events and Independent events are not the same.
Mutually Exclusive Events:Mutually exclusive events are those events that cannot occur together, i.e. they cannot take place at the same time.
For example, the events of tossing a Head and Tails are mutually exclusive. This is because when a coin is flipped it cannot land on both sides at once.
Independent Events:Independent events are those events that can occur at the same time without affecting each other, i.r. they are not dependent on the occurrence of other events in the sample space.
For example, on rolling two fair die the events of first die rolling 4 and the second die rolling 1 are independent.
Final answer:
Mutually exclusive events cannot occur simultaneously, which means P(A AND B) = 0. Independent events occur independently of each other, and their combined probability is P(A AND B) = P(A)P(B). They are different concepts; being mutually exclusive does not imply events are independent.
Explanation:
No, the statement that mutually exclusive events and independent events are the same is incorrect. Mutually exclusive events are two or more events that cannot happen at the same time. For example, when tossing a coin, the events of landing on heads and tails are mutually exclusive because the coin cannot land on both sides at once. This means that P(A AND B) = 0 for mutually exclusive events A and B.
Independent events, however, are those where the occurrence of one event does not affect the probability of the other event occurring. In other words, events A and B are independent if the probability of A occurring is the same, regardless of whether B has occurred, and vice-versa. This means that P(A AND B) = P(A)P(B) for independent events A and B.
Therefore, while mutually exclusive events must have a combined probability of zero (they cannot both occur), independent events are characterized by one event's occurrence not influencing the probability of the other event occurring. Essentially, mutually exclusive deals with the impossibility of events happening simultaneously, whereas independence is about the absence of any causal connection between them.
Determine whether the statement is sometimes, always, or never true.
If ax + b - 4 = b and a doesn't = 0 then x = 4/a
sometimes
always
not enough information provided
never
Answer:
always true
Step-by-step explanation:
Adding 4-b to both sides of the equation gives ...
ax = 4
Then dividing by "a" gives ...
x = 4/a
This is always true when a≠0.
A prism with a base area of 8 cm² and a height of 6 cm is dilated by a factor of 54 . What is the volume of the dilated prism? Enter your answer, as a decimal, in the box
Question:
A prism with a base area of 8 cm² and a height of 6 cm is dilated by a factor of 5/4 .
What is the volume of the dilated prism?
Enter your answer, as a decimal, in the box.
Answer:
The volume of the dilated prism is [tex]93.75 \ {cm}^{3}[/tex]
Explanation:
A prism with a base area of 8 cm² and a height of 6 cm
The volume of the prism can be determined by the formula, [tex]V=Bh[/tex]
Volume of the prism is given by
[tex]V=Bh[/tex]
[tex]V=(8)(6)[/tex]
[tex]V=46\ cm^3[/tex]
Thus, the volume of the prism is [tex]46 \ {cm}^{3}[/tex]
It is also given that the volume of the dilated prism is dilated by a factor of [tex]\frac{5}{4}[/tex]
Hence, the new volume is given by
[tex]Volume = 48(\frac{5}{4} )^3[/tex]
[tex]=48(\frac{125}{64} )[/tex]
[tex]=48(1.953125)[/tex]
[tex]=93.75 \ {cm}^{3}[/tex]
Thus, the volume of the dilated prism is [tex]93.75 \ {cm}^{3}[/tex]
Final answer:
The volume of the dilated prism is 93.75 cm³ after applying the dilation factor of 5/4 to the original volume.
Explanation:
To find the volume of the dilated prism, we must apply the dilation factor to the original dimensions of the prism. Since a volume is a three-dimensional measure, the dilation affects all three dimensions (the base area and the height). The dilation factor is given as 5/4.
We must raise this factor to the third power when dealing with volumes, since we are dealing with three dimensions. Therefore, the original volume, V, of the prism is the base area multiplied by the height, which is:
V = 8 cm² × 6 cm = 48 cm³.
Applying the dilation factor, the volume V' of the dilated prism is:
V' = V × (5/4)³.
First, calculate:
(5/4)³3 = 125/64.
Then multiply the original volume by this factor:
V' = 48 cm³ × (125/64) = (48 × 125) / 64 = 6000 / 64 = 93.75 cm³.
A parabola can be drawn given a focus of ( 6 , − 5 ) (6,−5) and a directrix of y = 1 y=1. Write the equation of the parabola in any form. -12 -10 -8 -6 -4 -2 2 4 6 8 10 12 -12 -10 -8 -6 -4 -2 2 4 6 8 10 12
Answer:
y = -(1/12)(x -6)² -2
Step-by-step explanation:
The vertex of the parabola is halfway between the focus and the directrix, so has y-coordinate (-5+1)/2 = -2. The difference in the y-coordinates between the focus and the vertex is ...
p = -5 -(-2) = -3
An equation of the parabola with vertex (h, k) and focus-vertex distance p can be written:
y = 1/(4p)(x -h)² +k
For (h, k) = (6, -2) and p = -3, the equation is ...
y = (-1/12)(x -6)² -2
a. I have five coins in my pocket – four are fair, and the other is weighted to have a 70% chance of coming up heads. I pull one out at random and flip it three times. What is the conditional probability that I get four heads given I pulled out the weighted coin?
Answer:
The conditional probability that I get four heads given I pulled out the weighted coin = 0.2401
Step-by-step explanation:
Probability of getting 4 heads from 4 trials for a fair coin = 0.5⁴
But given that it is the weighted coin that is pulled out,
The probability of getting 4 heads from 4 trials = 0.7⁴ = 0 2401
HELP PLEASE!
Solve the system of equations
[tex]\left \{ {x+4y=-2} \atop {-5x+5y=10}} \right.[/tex]
Answer: x = - 2
y = 0
Step-by-step explanation:
The given system of linear equations is expressed as
x + 4y = - 2 - - - - - - - - - - - - - 1
- 5x + 5y = 10- - - - - - - - - - - - - 2
We would eliminate x by multiplying equation 1 by 5 and equation 2 by 1. It becomes
5x + 20y = - 10
- 5x + 5y = 10
Adding both equations, it becomes
25y = 0
Dividing both sides by 25, it becomes
y = 0/25 = 0
Substituting y = 0 into equation 1, it becomes
x + 4 × 0 = - 2
x = - 2
The system of equations have only one solution.
A bag contains 4 red, 5 blue, and 6 green marbles: One blue marble is selected and NOT replaced. If a 2nd marble is drawn, what is the probability that the 2nd marble drawn is a blue marble? Write your answer as a simplified fraction.
Answer:
2/7
Step-by-step explanation:
To find the this first you need the total number of marbles minus one since the blue marble was taken.
4+5+6-1=14
after one blue marble being picked there are 4 blue left, so the fraction is
4/14 and after being simplified it is 2/7
Answer:
the true is the answer is g
Step-by-step explanation:
Please someone help me on 2 problems 25 points ya boy be struggling
Answer:
6) x = 17 ft
7) 42 in
Step-by-step explanation:
6) length of the tangents are equal.
2x - 7 = 27
2x = 34
x = 17
7) if you draw a line from T passing through the centre of the circle, it will divide the triangle into two congruent triangles
Perimeter = 2(5+7+9) = 42 in
What are the eight-digit grid coordinates for benchmark 86 (circled in red)?
Without a map or structured dataset, it is not possible to provide the eight-digit grid coordinates for benchmark 86 as requested.
Explanation:The student asked for the eight-digit grid coordinates for benchmark 86, which is circled in red. To determine the eight-digit grid coordinates, we need a map with grid lines or specific information that provides the exact location of benchmark 86. Unfortunately, the data provided does not contain adequate information to pinpoint the exact eight-digit grid coordinates for this benchmark. Grid coordinates are typically derived from a more structured dataset or map rather than the types of numbers presented in the question. Those appear to be an arbitrary sequence of numbers and are not formatted as grid coordinates, which usually consist of an easting and a northing.
If the risk-free rate is 7 percent, the expected return on the market is 10 percent, and the expected return on Security J is 13 percent, what is the beta of Security J
Answer:
0.02 or 2% = Beta
Step-by-step explanation:
Given that,
Risk-free rate = 7 percent
Expected return on the market = 10 percent
Expected return on Security J = 13 percent
Therefore, the beta of Security J is calculated as follows;
Expected return on Security J = Risk-free rate + Beta (Expected return on the market - Risk-free rate)
13 percent = 7 percent + Beta (10 percent - 7 percent)
0.13 - 0.07 = 0.03 Beta
0.06 = 0.03 Beta
0.06 ÷ 0.03 = Beta
0.02 or 2% = Beta
Use the value of the linear correlation coefficient r to find the coefficient of determination and the percentage ofthe total variation that can be explained by the linear relationship between the two variables. r = 0.885 (x = weight of male, y = waist size of male)
Answer:
Step-by-step explanation:
The coefficient of determination = [tex]r^{2} = 0.885^{2}[/tex] = 0.7832
It means about 78% variation in waist size of males can be explained by their weight and about 23% can not be explained.
A CHAIR regular is 349.It is on clearance for 30% off and a customer uses a 15% off coupon after that. What is the final cost of the chair before sales tax
Answer:
$207.655
Step-by-step explanation:
Firstly, we calculate the value taken off the cost by the clearance sales tag.
That would be 30/100 * 349 =104.7
We subtract this from the original = 349-104.7 = 244.3
Now, he applied a 15% coupon. That would be 15/100 * 244.3 = 36.645
The cost of the chair before sales tax = 244.3-36.645 = 207.655
If a student places in the 99th percentile on an exam, she performed better than 99% of all students who completed the exam. Her performance is similar to a statement based on a __________.
Answer:
Cumulative frequency distribution
Step-by-step explanation:
Cumulative frequency distribution is a form of a frequency distribution that represents the sum of a class and all classes below it. Remember that frequency distribution is an overview of all distinct values (or classes of values) and their respective number of occurrences.
Final answer:
Placing in the 99th percentile means a student did better than 99% of test takers, akin to scoring beyond the second standard deviation, a high achievement.
Explanation:
If a student places in the 99th percentile on an exam, this indicates that her performance was better than 99% of all students who completed the exam. Her achievement is akin to being beyond the second standard deviation in the context of a normal distribution, showing an exceptional score. In the given context, this means she likely scored higher than what is considered the range for the majority of her peers.
Being in the 90th percentile would indicate that 90 percent of test scores were at or below that mark, a clear demonstration of high achievement compared to peers. In educational measurement, the choice between absolute rating and relative ranking can greatly affect the evaluation of student performance. With relative ranking, a student's performance is compared against that of their peers, such as being in the top 10% as opposed to achieving a specific score percentage, which would be an absolute rating.
Phillip Esten operates a mail store in which he offers various services such as packaging items for shipment, delivering items to overnight services, and a fax machine. Esten has been charging $2.00 per page for the fax service, but a new store has opened in a nearby shopping center that is charging $1.00 per page. Esten lowers his price to $.50 per page, knowing this charge will not always cover his cost. Esten's actions:
Answer:
constitute meeting the competition.
Step-by-step explanation:
Philip Esten action from the above scenario tries to meet up with the new competition he is encountering.
He operates a mail store where he renders services such as delivering of item overnight, and charging of fax service with each page for a fee of $2.00 for clients. He has a competition in the business environment where he now has direct competitors who offers the same service and product type to clients.
In this case, his competitors tend to attract more customers, both new and Esten old customers, because his competitors are rendering the same services at a cheaper fee to build a better brand of product / services for the store and buying the trust of customers now and for the future.
Esten with the knowledge of how business competition an works, reduces his price of charge to $.50 to attract more people or customers back to his store and tries to drive off the competitors, knowing quite well that this charges will not cover his cost .
Graph the function g(x)= -3/(x^2-4) . What is the domain of g(x)? Explain your reasoning. Do not completely trust calculator or computer graphs of this function.
can anyone help
Answer:
Find where the expression [tex]\frac{3}{(x+2)(x-2)}[/tex]
is undefined.
List all of the vertical asymptotes:
[tex]x=2, -2[/tex]
This is what your graph would look like:
Jane must select three different items for each dinner she will serve. The items are to be chosen from among five different vegetarian and four different meat selections. If at least one of the selections must be vegetarian, how many different dinners could Jane create?
A. 30
B. 40
C. 60
D. 70
E. 80
Answer:
E. 80
Step-by-step explanation:
First consider exactly what the problem is asking. You have to make a dinner and AT LEAST one of the dishes has to be vegetarian. So then we could have all three be vegetarian (V V V), 2 vegetarian with one meat (V V M), or one vegetarian with 2 meat (V M M). If I can find the number of arrangements possible for each of the possibilities and add them, we should have our answer.
Consider first the all vegetarian option. There are 5 vegetarian meals on the menu and we may choose 3 of them. This will be a combination since the order in which we choose doesn't matter. For example if my 5 vegetarian dishes are salad, hummus, rice, lentils and pasta, it doesn't matter what order I serve them in, since they will all be a part of the meal. Simply put, placing hummus, rice, and lentils on the table is the same as placing rice, lentils and hummus on the table if everybody shares the dishes. If I had specific guests assigned to the each dish then the order would matter, and it would be a permutation. For example if three of Jane's guests, (lets say Mike, Frank, and Bob) are going to have a specific dish, then the arrangement where Mike has rice, Bob has lentils, and Frank has pasta is different from the arrangement where Mike has lentils, Bob has rice, and Frank has pasta. Since there is no mention of a specific order this has to go in, it is safe to assume a combination. So how many ways can we choose 3 vegetarian dishes from 5 options? This will be 5 C 3.
So we found that (V V V) gives us 5 C 3, so lets examine the other remaining cases. (V V M) implies from 5 vegetarian options we can choose 2 and from 4 meat options we choose one. Then (V V M) gives us 5 C 2 * 4 C 1. Likewise for (V M M) we can say 5 C 1 * 4 C 2.
Putting it all together we have 5 C 3 + 5 C 2 * 4 C 1 + 5 C 1 * 4 C 2. 10 + 10*4 +5 *6 =80.
The population of a city is expected to increase by 7.5% next year. If p represents the current population, which expression represents the expected population next year.
Answer:
Population next year = 1.075p
Step-by-step explanation:
The current population can be represented by 1 p the increase in the population number by next year is 7.5% p or 7.5/100 p that equals to 0.075p. The expression that represents the expected population by next year is:
Population next year = This year population + expected growth
Population next year = 1p + 0.075p = 1.075p
Given Information:
Population rate = 7.5 %
Current population = p
Required Information:
Population next year = ?
Answer:
Population next year = 1.075p
Step-by-step explanation:
The rate of increase in the population is given as 7.5 %
We know that the current population is equal to p
The population in the next year would be the sum of current population and 7.5 % of current population.
Population next year = current population + 7.5% of current population
Population next year = p + 7.5% of p
Population next year = p + 0.075*p
Population next year = p(1 + 0.075)
Population next year = p(1.075)
Population next year = 1.075p
A local elementary school is having a bake sale fundraiser. The students are selling 30 cupcakes, 10 pies, and 60 cookies. What is the ratio of the number of cupcakes to the total number of baked goods?
10:3
7:3
3:7
3:10
Answer:
3:10
Step-by-step explanation:
Solution to the question is in the attached picture.
Answer:
3:10 trust
Step-by-step explanation:
Factor the expression. 6x^2 + 5x + 1
(3x – 1)(2x – 1)
(3x – 1)(2x + 1)
(3x + 1)(2x + 1)
(3x + 1)(2x – 1)
Answer:
Option C
Step-by-step explanation:
6x² +5x + 1
6x² + 3x + 2x + 1
3x(2x + 1) + 1(2x + 1)
(3x + 1)(2x + 1)
Answer: C
Step-by-step explanation: Answer is C