Graph the polygon with the given vertices and its image after a dilation with scale factor k.
A(0, 5), B( 10,-5), C(5,-5); k= 120%

Given expression q=p+7

Expression can be defined as contains one or more variables and constants with one or more arithmetic operators.

Simply put the p values in the expression. solve it and get the q values.

q=p+7 in the place of p submit p=0

q=0+7

q=7

q=p+7  in the place of p submit p=2

q=2+7

q=9

q=p+7  in the place of p submit p=3

q=3+7

q=10

Therefore, The values of q are 7,9,10

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The missing numbers are:

7,9 and 10 when 0, 2, and 3 respectively.

Two algebraic expressions having the same value and symbol '=' in between are called an equation.

Given:

An equation,

q = p + 7.

Substituting the values of p:

When p = 0,

q = 0 + 7

q = 7.

When p = 2,

then q = 9.

And when p = 3,

q = 10

Therefore, all the required values are given above.

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Answer:

D. 0.79

Step-by-step explanation:

To find the probability that a Hospitality Management student has visited 21 or more states, we need to sum up the probabilities of the categories that represent students who have visited 21 states or more.

The probabilities of the categories are as follows:

Visited 21–30 states: 45% = 0.45

Visited 31–40 states: 19% = 0.19

Visited 41–50 states: 15% = 0.15

So, the total probability of a student having visited 21 or more states is:

0.45 + 0.19 + 0.15 = 0.79.

Therefore, the probability that a Hospitality Management student has visited 21 or more states is 0.79 or 79%.

The given expression is proved.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

here, we have.

tan∅/(1+ sec∅)

=(sin∅/cos∅)/(1+ sec∅)                  [tan∅=(sin∅/cos∅)]

=(sin∅/cos∅)/(1+1/cos∅)

=sin∅/1+cos∅

multiplying both numerator & denominator by 1-cos∅, we get,

=sin∅(1-cos∅)/ sin^2∅

=(1-cos∅)/sin∅

=cosec∅ - cot∅

Hence, The given expression is proved.

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The mean and the standard deviation are  144 and 4.3200

from the question, we have the following parameters that can be used in our computation:

Proportion, p = 64%

Sample size, n = 225

The mean is calculated as

Mean = np

Substitute the known values in the above equation, so, we have the following representation

Mean = 64% * 225

Mean = 144

The standard deviation is calculated as

SD = √Mean * (1 - p)

substitute the known values in the above equation, so, we have the following representation

SD = √144 * (1 - 64%)

Evaluate

SD = 4.3200

Hence, the mean is 144

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Complete question

Coffee: The National Coffee Association reported that 64% of U.S. adults drink coffee daily. A random sample of 225 U.S. adults is selected. Round your answers to at least four decimal places as needed.

(a) Find the mean

(b) Find the standard deviation

Step-by-step explanation:

7.

the probability of picking a defective missile with the first pull is

5/22

the probability of picking a working missile with the first pull is

17/22 = ((22-5)/22)

I have to assume that the picked missiles are not put back into the main pile after the check.

and I have to assume that the sequence of the pulled missiles don't matter.

a.

all are defective.

since there are only 5 defective missiles, there is only one possibility out of all the possibilities to pull 5 out of 22 to get 5 defective missiles.

the possible combinations to pull 5 out of 22 :

C(22, 5) = 22! / ((22 - 5)! × 5!) =

= 22×21×20×19×18×17/(5×4×3×2) =

= 22×21×19×3×17 = 447,678

and we have one desired situation (all 5 are defective).

so, the probability is

1/447678 = 0.000002233748364... = 2.233748364e-006

b.

all 5 are functional.

the total possible cases to pull 5 out of 22 are still

447,678.

the desired cases are all cases to pull 5 out of the 17 (22 - 5) functional missiles.

that is

C(17, 5) = 17! / ((17 - 5)! × 5!) =

= 17×16×15×14×13 / (5×4×3×2) =

= 17×2×14×13 = 6,188

so, the probability to get one of these cases is

6188 / 447678 = 0.013822435...

The probability of picking a defective missile with the first pull is 5/22

The probability of picking a working missile with the first pull is 17/22

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

If we assume that the picked missiles are without replacements and the sequence of the pulled missiles don't matter,

Therefore, the probability that:

a. all are defective is 2.233748364e-006

Since there are only 5 defective missiles, there is only one way to get 5 defective missiles out of 22 possible outcomes.

The possible combinations to pull 5 out of 22 :

C(22, 5) = 22! / ((22 - 5)! × 5!) =

= 22×21×20×19×18×17/(5×4×3×2) =

= 22×21×19×3×17 = 447,678

and we have one desired situation (all 5 are defective).

so, the probability is 1/447678 = 0.000002233748364... = 2.233748364e-006

b. all 5 are functional is 0.013822435

the total possible cases to pull 5 out of 22 are still 447,678.

The ideal scenario is for all incidents to result in the removal of 5 of the 17 (22 - 5) operational missiles.

that is

C(17, 5) = 17! / ((17 - 5)! × 5!) =

= 17×16×15×14×13 / (5×4×3×2) =

= 17×2×14×13 = 6,188

so, the probability to get one of these cases is

6188 / 447678 = 0.013822435

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Answer:

Step-by-step explanation:

A = l x w

A = 105.1m x 67.1m

A = 7052.21m

Convert to yds.

7052.21 / 0.9144  =  7712.4

To the nearest whole, the area is 7712 yds2.

Note that the size of angle x = 115°. This is a problem relating to the sum of angles in a circle. See the computation below.

The sum of angles in a circle is always equal to 360 degrees or 2π radians.

This means that the sum of the measures of the angles formed by any number of rays or line segments that meet at a common point, or vertex, and whose endpoints lie on the circle, will always add up to 360 degrees or 2π radians. This property is often used in geometry and trigonometry to solve problems involving circles and angles.

With regard to the above problem,

We are given three angles in a circle named as follows:

a) 81°

b) 164°

c) x

The above rule state that

81 + 164 + x = 360°

thus, x = 360 - 81 - 164

x = 360 -245

x = 115°

Thus the value of ∠x is  115°

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Full Question:

See attached image.

As per the probability, the value of E(X) is option (a) 0.8

In statistics, the expected value or mean is a measure of central tendency that represents the average outcome of a random variable over an infinite number of trials.

To find the expected value of X, we need to calculate the probability of each possible outcome and multiply it by its corresponding value. In this case, the possible outcomes are 0 and 1, and their probabilities can be calculated as follows:

The probability of drawing a 0 is 4/5 because there are 4 zeros in the list and 5 total numbers.

The probability of drawing a 1 is 1/5 because there is only one 1 in the list and 5 total numbers.

Using these probabilities, we can calculate the expected value of X as follows:

E(X) = (0 x 1/5) + (1 x 4/5)

The first term in this equation represents the probability of drawing a 0, multiplied by its value (which is 0), and the second term represents the probability of drawing a 1, multiplied by its value (which is 1). Simplifying this equation gives:

E(X) = 4/5 =0.8

Therefore, the answer to this problem is (a) 0.8, since the expected value of X is 0.8 of the possible outcomes.

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The probability of Rosh winning the tournament is 50%, which means the probability of one of the other three players winning is 50% divided by 3, or approximately 16.67% each. Therefore, the probability that Craig wins the tournament is 16.67%.

The value of the length /MK/ is 10 units

Recall that in an isosceles reangle, two sides are equal and the base angles are equal

We can use the cosine rule to find the length MK

N² = K²+M² - 2KMCosN

This implies that /MK/² = 5²+5²-2*5*5*cos110

⇒25+25-50*-0.9990

= 50+49.95

=99.95  this can be approximated to 100

the /MK/ = √100= 10 units

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According to the given statement Nevada's property prices have grown more rapidly , median home value 148,880 and median house values will be 15.6.

The selling price of the middle property in a list of properties listed by highest sale price through lowest over a predetermined time period is the median house price. Thus, if 71 homes were sold, the median home price would correspond to the sale price of the 36th home.

Rate of change for Pennsylvania  [tex]= (97000 - 42400) / (2000 - 1950) = 1092[/tex]

Rate of change for Nevada [tex]= (142000 - 53700) / (2000 - 1950) = 1816[/tex]

As a result, Nevada's property prices have grown more rapidly.

b) Median home value of Pennsylvania in 2010[tex]= 42400 + 1092 * (2010 - 1950) = $148,880[/tex]

c) Pennsylvania[tex]= 42400 + 1092x[/tex]

Nevada[tex]= 53700 + 1816x[/tex]

[tex]42400 + 1092x = 53700 + 1816x\\724x = 11300\\x = 15.6[/tex]

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so we're assuming the compounding period is annual, so hmmm let's call our sum "P", how much is it at simple and compound interest anyway?

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\dotfill &2 \end{cases} \\\\\\ A = P[1+(0.05)(2)] \implies \boxed{A = 1.10P} \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annual, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases} \\\\\\ A = P\left(1+\frac{0.05}{1}\right)^{1\cdot 2} \implies \boxed{A = 1.1025P}[/tex]

now, the larger one will be the compound interest one, so, let's subtract the simple interest one from it to get 6.90

[tex]1.1025P~~ - ~~1.10P~~ = ~~6.90\implies 0.0025P=6.90 \\\\\\ P=\cfrac{6.90}{0.0025}\implies {\Large \begin{array}{llll} P=2760 \end{array}}[/tex]

Answer:

36.

Step-by-step explanation:

o find F'(4), we need to use the chain rule of differentiation. The chain rule states that if F(x) = f(g(x)), then F'(x) = f'(g(x)) * g'(x).

Given that f(-2) = 5, f'(-2) = 9, f'(4) = 3, g(4) = -2, and g'(4) = 4, we can calculate F'(4) as follows:

F'(4) = f'(g(4)) * g'(4) = f'(-2) * g'(4) = 9 * 4 = 36

Therefore, F'(4) = 36.

Answer:

120

Step-by-step explanation:

The total number of medals won is 150, and the circle graph shows that the proportion of medals won as gold is 20 percent, as silver is 30 percent, and as bronze is 50 percent.

To find the number of gold and bronze medals won, we need to calculate the total number of medals won in each category by multiplying the total number of medals by the proportion of medals won in each category.

Gold medals: 150 * 20% = 30

Bronze medals: 150 * 50% = 75

So, a total of 30 + 75 = 105 medals were won as gold and bronze.

Step-by-step explanation:

22x + 2y = -14

2y = -22x - 14

y = -11x - 7

Answer:

Step-by-step explanation:

К счастью, другое маленькое дерево поблизости заметило растущее дерево и дало несколько интересных советов о том, как удерживать его распускающиеся листья новыми и интересными способами. Было забавно испытать на других маленьких деревьях множество различных способов расположения листьев. Другие маленькие деревья вскоре заметили это и начали поворачивать свои немногочисленные листья под углом. Другие маленькие деревья могли лишь слегка приподнять свои листья.

Растущее дерево решило, что будет немного приподнимать листья на радость другим деревьям. Но, в конце концов, все маленькие деревья начали отращивать больше листьев на ветвях, которые тянулись еще дальше. С каждым сезоном многие листья невозможно было приподнять. Некоторые из растущих деревьев продолжали шептаться, в то время как некоторые научились громко смеяться, некоторым, казалось, нравилось плакать и падать духом, а некоторые росли вдали от группы из-за того, как многие времена года влияли на них и на другие деревья и животных вокруг них.

За прошедшие годы родительские деревья время от времени мельком смотрели вниз, чтобы увидеть, как растут их семена, и они поднимали свои ветви к небу, чтобы пропустить солнечный свет через полог. Все растущие деревья заметят это и поднимут головы, чтобы насладиться солнечным светом. Те, кто не обращал внимания на поведение своего родительского дерева, обычно подражали другим растущим деревьям и умудрялись собирать немного солнечного света. Иногда растущее дерево переставало расти, потому что не могло достичь солнечного света. Его листья не будут такими обильными, а его ветви будут тянуться дальше, чтобы быть ближе к солнечному свету других растущих деревьев. По прошествии многих сезонов растущие деревья становились все выше и теперь можно было видеть, что их место среди кроны деревьев было довольно тесным.

The solution to the question on the equilibrium of the cheese and bagels have been given below

a) If the equilibrium price of cream cheese and the equilibrium quantity of bagels have both risen, this could be caused by a fall in the price of flour, one of the inputs used to produce bagels.

This decrease in the cost of production would cause the supply of bagels to increase, leading to a rightward shift in the supply curve. At the same time, the demand for bagels would increase as consumers substitute away from other breakfast foods and toward bagels, leading to a rightward shift in the demand curve.

These two shifts would result in a higher equilibrium price for cream cheese, since bagels and cream cheese are complements. The increased demand for bagels would lead to an increase in the demand for cream cheese, causing the demand curve for cream cheese to shift rightward.

The diagram below illustrates this relationship. The initial equilibrium is at point A, with a price of P1 and a quantity of Q1. After the decrease in the price of flour, the supply curve for bagels shifts rightward to S', and the demand curve for bagels shifts rightward to D'. The new equilibrium is at point B, with a higher price of P2 and a higher quantity of Q2. The increase in the demand for bagels leads to an increase in the demand for cream cheese, causing the demand curve for cream cheese to shift rightward to D'''. The new equilibrium for cream cheese is at point C, with a higher price of P3 and a higher quantity of Q3.

b) If the equilibrium price of cream cheese has risen but the equilibrium quantity of bagels has fallen, this could be caused by a rise in the price of milk, one of the inputs used to produce cream cheese.

This increase in the cost of production would cause the supply of cream cheese to decrease, leading to a leftward shift in the supply curve. At the same time, the demand for cream cheese would decrease as consumers substitute away from cream cheese and toward other breakfast foods, leading to a leftward shift in the demand curve.

These two shifts would result in a higher price for cream cheese, but a lower quantity of bagels consumed. The decreased demand for cream cheese would lead to a decrease in the demand for bagels, causing the demand curve for bagels to shift leftward.

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The graphing points of the equation is given in the table.

An equation is a statement that asserts the equality of two expressions, the expressions are written one on each side of an '=' equal to sign.

Given equation is [tex]y=2^{x+5} +1[/tex].

To find the graphing points of the functions:

By assuming the value for x and substitute in the given function to find the values of y.

[tex]if x=-2,y=2^{-2+5} +1=9\\ifx=-1, y=2^{-1+5} +1=17\\if x=0,y=2^{0+5} +1=33\\if x=1,y=2^{1+5} +1=65\\ifx=2,y=2^{2+5} +1=129[/tex]

It is given the table format as,

                 x                [tex]y=2^{x+5} +1[/tex]

                -2                     9

                -1                      17

                 0                     33

                  1                     65

                  2                   129  

Hence, these are all the graphing points of the equation.

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The zeros of the given polynomial function are 3

Zero of a polynomial are numerical values at which the polynomial will equal zero. In other words, zeros of a polynomial are numerical values of the variable which give zero when we plug into the polynomial.

For example, for a polynomial p(x) the zeros are the value of 'x' which satisfies p(x) = 0. This means by identifying the x-intercepts, we may determine the polynomial's zeros.

In the case of a graph, we can determine the zeros of a polynomial by observing the points at which the graph line will cut the x-axis. In simple words, we can say that the x-coordinates of the points where the graph meets the x-axis are the zeros of the polynomial.  

Here we have a graph

In the given graph the polynomial function meets the x-axis three times at three different points.

Therefore,

The zeros of the given polynomial function are 3

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Answer:

[tex]x = 9[/tex]

Step-by-step explanation:

Solving For #7

We will use the Angle Bisector Theorem

The angle bisector theorem states that in a triangle, the angle bisector of any angle will divide the opposite side in the ratio of the sides containing the angle.

In the figure provided in #7 we see that QS bisects ∠Q forming two smaller triangles ΔPQS and ΔQRS

According to the angle bisector theorem:

[tex]\dfrac{PQ}{QR} = \dfrac{PS}{RS}\\\\\textrm{Or, alternatively}\\\\\dfrac{QR}{PQ} = \dfrac{RS}{PS}\\[/tex]

Given
[tex]QR = 12.6\\PQ = 7\\RS = x\\PS = 5\\\\[/tex]

[tex]\dfrac{PQ}{QR} = \dfrac{PS}{RS}\\\\\textrm{Or, alternatively}\\\\\dfrac{QR}{PQ} = \dfrac{RS}{PS}\\\\\\\rightarrow \dfrac{12.6}{7} = \dfrac{x}{5}[/tex]

If we multiply by [tex]5[/tex] both sides of the equation we can get rid of the denominator 5 on the right side:
[tex]\rightarrow \dfrac{12.6}{7} \times 5 = x\\\\9 = x\\\\\boxed{x = 9}[/tex]

Answer:

1/5

Step-by-step explanation:

Answer:

The solution is 1/5 or 0,2

Step-by-step explanation:

[tex] \displaystyle \sf\lim_{x \to 3} \frac{ {x}^{2} - 5x + 6 }{2 {x}^{2} - 7x + 3} \: \: \: \: \: \: \: \: \: \\\\ = \displaystyle \sf\lim_{x \to 3} \frac{(x - 2)(x - 3)}{(2x - 1)(x - 3)} \\\\ = \displaystyle \sf\lim_{x \to 3} \frac{(x - 2)\cancel{(x - 3)}}{(2x - 1)\cancel{(x - 3)}} \\\\ = \displaystyle \sf \lim_{x \to 3} \frac{(x - 2)}{(2x - 1)} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\\\ \sf x = 3 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\\\ \sf = \frac{(3 - 2)}{(2(3) - 1)} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\\\ = \boxed{\sf \frac{1}{5} \: or \: 0.2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

Using sine law and cosine law, s is 13.6 units and T is 37.7 degrees while U is 59.3 degrees

The Law of Cosines, also known as the Cosine Formula, is a fundamental mathematical relationship between the sides and angles of a triangle. It states that the dot product of two sides of a triangle is equal to the product of the third side and the cosine of the angle between the two sides.

The general form of the Law of Cosines is:

C^2 = A^2 + B^2 - 2ABcos(C)

where C is the angle between sides A and B, and A, B, and C are the lengths of the sides of the triangle. The formula can be rearranged to solve for any one of the sides or angles given the other two.

In this problem, we can easily solve for s.

s² = 8² + 12² - 2(8)(12)cos83

s² = 184.601

s = √184.601

s = 13.6 units

The value of angle T is calculated using sine law;

13.6 / sin 83 = 8 / sin T

sin T = 8(sin 83) / 13.6

sin T = 0.58385

T = sin⁻¹(0.58385)

T = 37.7°

Using sum of angle in a triangle;

T + S + U = 180°

83 + 37.7 + U = 180

U = 180 - 120.7

U = 59.3°

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Answer:

3% increase

Step-by-step explanation:

a) The distribution of the mean weight of 10 apples picked at random is normally distributed.

b) The mean, μ, is 45 oz.

What is normal distribution and mean?

normal distribution: The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean.

Mean: In mathematics, a mean is the average of a data set, which is calculated by adding all of the numbers together and then dividing the total of the numbers by the number of numbers.

a) The distribution of the mean weight of 10 apples picked at random is approximately normally distributed. This is because, according to the Central Limit Theorem, when the sample size is sufficiently large, the distribution of the sample mean becomes normal regardless of the underlying population distribution.

Here, we have a sample size of 10, which is considered large enough to apply the Central Limit Theorem. Also, we know that the underlying population distribution of the weight of a single apple is normal.

b) The mean weight of 10 apples picked at random is simply the mean of the individual weights of those 10 apples. Since the individual weights of the apples are normally distributed with a mean of 45 oz and a standard deviation of 3 oz, the mean weight of 10 apples will also be normally distributed with a mean equal to the mean of the individual weights, which is 45 oz.

Therefore, the mean, μ, is 45 oz.

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The Expression with coefficient 4 and -9 is 4j and -9j.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

We have to write the coefficient as 4 and -9.

As, coefficient is the number which is just before the variable like in 2x 'x' is the variable and '2' is the coefficient.

So, with coefficient 4 the expression is 4j

and, with coefficient  -9 the expression is -9j.

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The equation of the polynomial is P(x) = 1/27(x + 3)(x + 2)(x - 1)(x - 3)^2

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have the following readings:

A polynomial is represented as

P(x) = a * (x - zero)^multiplicity

Using the above as a guide, we have the following:

P(x) = a * (x + 3)(x + 2)(x - 1)(x - 3)^2

The y-intercept is 2

So, we have

a * (0 + 3)(0 + 2)(0 - 1)(0 - 3)^2 = 2

This gives

a = -1/27

Hence, the expression is P(x) = 1/27(x + 3)(x + 2)(x - 1)(x - 3)^2

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The probability that the sum of the numbers rolled is either a multiple of 3 or an even number is 24/36 = 2/3

The two events are mutually exclusive

"Information available from the question"

Stacy rolls a pair of six-sided fair dice.

Now, According to the question:

Let the probability of getting a multiple of 3 is "A"

Let the probability of getting an even number is "B"

Total number of outcomes=36

Total number of favorable outcomes  of either a multiple of 3 or an even number are:-

(1,1) ,(1,2) ,(2,1) ,(1,3) ,(3,1) ,(2,2) ,(1,5) (5,1) ,(3,3) ,(2,4) ,(4,2) ,(2,6) ,(6,2) ,(3,5) ,(5,3) ,(4,4) ,(6,4) ,(4,6) ,(5,5) ,(6,6)

Probability = Number of fav. outcomes/ Total no. of outcomes

The probability that the sum of the numbers rolled is either a multiple of 3 or an even number will be given by counting the numbers that are either even or multiples of 3 and then dividing by the number of possible outcomes, 36.

In our case this will be;

24/36 = 2/3

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Answer:

Below

Step-by-step explanation:

Here is what the graph should look like ...you can see that he will have 0 fence left to paint  ( 0 = y ) when time = 3 hrs

The next two terms of the number sequence 2,3,5,9,17,33,65 are given as follows:

129, 257.

This is a recursive number sequence, as each term is obtained multiplying the previous term by 2 and then subtracting one.

Then the term after 65 is given as follows:

65 x 2 - 1 = 130 - 1 = 129.

The term after 129 is given as follows:

2 x 129 - 1 = 257.

Then the next two terms are 129 and 257.

More can be learned about number sequences at https://brainly.com/question/29633561

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