The city of Oakdale wishes to see if there is a linear relationship between the temperature and the amount of electricity used (in kilowatts). Using the estimated regression equation found by using Temperature as the predictor variable, find a point estimate Kilowatt usage when the Temperature is 90 degrees outside?

Answer:

Dear Laura Ramirez

Answer to your query is provided below

Option B is correct

Step-by-step explanation:

In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. 

Also,

By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.

Here, if you see( 16+24)>38

So, the set of numbers can be measures of a

triangle.

Answer:

The claim that needs to be tested is that the proportion of people who prefer mechanical methods of water sanitizing truly exceeds the proportion of people who have no sanitizing methods preferences. This can be expressed as the population proportion of people who prefer mechanical methods of water sanitizing is significantly higher than 0.5.

This is a hypothesis test for a  population proportion.

The test will have null and alternative hypothesis:

[tex]H_0: \pi=0.5\\\\H_a:\pi>0.5[/tex]

Test statistic z = 0.972

P-value = 0.166

At a significance level of 0.05, there is not enough evidence to support the claim that the proportion of people who prefer mechanical methods of water sanitizing truly exceeds the proportion of people who have no sanitizing methods preferences.

Step-by-step explanation:

We have to construct a hypothesis test for the population proportion. We need to test the claim that the proportion of people who prefer mechanical methods of water sanitizing truly exceeds the proportion of people who have no sanitizing methods preferences.

As the survey is done as a yes/no question, the null hypothesis would state that the amount of people who prefer mechanical methods of water sanitizing is not significantly different from the proportion of people who have no sanitizing methods preferences. That can be expressed as the population proportion equals 0.5, so both proportions are equal.

The alternative hypothesis would state that the proportion of people who prefer mechanical methods of water sanitizing truly exceeds the proportion of people who have no sanitizing methods preferences. This could be expressed as the population proportion significantly bigger than 0.5.

Then, the null and alternative hypothesis are written:

[tex]H_0: \pi=0.5\\\\H_a:\pi>0.5[/tex]

The significance level is assumed to be 0.05.

The sample has a size n=209.

The sample proportion is p=0.536.

[tex]p=X/n=112/209=0.536[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.5*0.5}{209}}\\\\\\ \sigma_p=\sqrt{0.001196}=0.035[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.536-0.5-0.5/209}{0.035}=\dfrac{0.034}{0.035}=0.972[/tex]

This test is a right-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=P(z>0.972)=0.166[/tex]

As the P-value (0.166) is greater than the significance level (0.05), the effect is  not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the proportion of people who prefer mechanical methods of water sanitizing truly exceeds the proportion of people who have no sanitizing methods preferences.

Answer:

A)  m∠3 + m∠4 = 180

Step-by-step explanation:

Both angles make a straight line which has an angle of 180.

Answer:

A

Step-by-step explanation:

You see how the line t is horizontal. That's 180 degree angle. So when broken out with angles 3 and 4, it should still add to 180

Answer: 12

Step-by-step explanation:

Answer:

The longer diagonal has a length of 7.3 meters.

The angles are 31.65° and 18.35°

Step-by-step explanation:

If one angle of the parallelogram is 50°, another angle is also 50° and the other two angles are the supplement of this angle. so the other three angles are:

50°, 130° and 130°.

The longer diagonal will be the one opposite to the bigger angle (130°), and this diagonal divides the parallelogram in two triangles.

Using the law of cosines in one of these two triangles, we have:

[tex]diagonal^2 = a^2 + b^2 - 2ab*cos(130\°)[/tex]

[tex]diagonal^2 = 3^2 + 5^2 - 2*3*5*(-0.6428)[/tex]

[tex]diagonal^2 = 53.284[/tex]

[tex]diagonal = 7.3\ meters[/tex]

So the longer diagonal has a length of 7.3 meters.

To find the angles that this diagonal forms with the sides, we can use the law of sines:

[tex]a / sin(A) = b/sin(B)[/tex]

[tex]5 / sin(A) = diagonal / sin(130)[/tex]

[tex]sin(A) = 5 * sin(130) / 7.3[/tex]

[tex]sin(A) = 0.5247[/tex]

[tex]A = 31.65\°[/tex]

The other angle is B = 50 - 31.65 = 18.35°

Please check the image attached for better comprehension.

The process used to collect data will affect the validity and the bias of the study.

The way data is gathered is very important for making sure a study is accurate and doesn't have any unfair influences. Validity means how well the information collected correctly shows the things the study is trying to find out. If the way data is collected is not done correctly, it can cause incorrect or untrustworthy results, making the study less reliable

Bias means when we make mistakes or go away from the correct value or truth. If the way we collect data is biased, it can lead to unfair outcomes or favor certain groups.

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Answer:

(C)90 – 10y = 5x

Step-by-step explanation:

Given:

x = number of times she hiked the 5-mile trail

y = number of times she hiked the 10-mile trail

Maria hikes a total of 90 miles

Therefore, total distance hiked can be represented by the equation:

5x+10y=90

Subtract 10y from both sides, we have:

5x=90-10y

This is option C.

Answer:

C

Step-by-step explanation:

Answer:

Minimum 08 adults / drivers

Maximum 10 adults / drivers

Step-by-step explanation:

Total students are 30

Each car can take total 5 incl. drive

There needs to be 7 cars taking the 30 students, which also means there have to be minimum 7 drivers / adults.

Min. passengers = 30 + 7

Of course, there will be space for 3 more in the 8th car since 5 x 8 = 40

Answer:

XE[-4/5,4/5]

Step-by-step explanation:

I can't explain it sorry

Answer:

-4/5 ≤ x ≤ 4/5

Step-by-step explanation:

| 5/2 x | + 2 ≤ 4

| 5/2 x | ≤ 2

| x |  ≤ 4/5

x ≤ 4/5

x ≥ - 4/5

-4/5 ≤ x ≤ 4/5

Answer:

-4(8-3x)>or =6x-8

Step-by-step explanation:

open d bracket

-32+12x >or = 6x-8

collect like terms

12x-6x >or =-8+32

6x = 24

divide both sides by 6

x= 4

Answer:

The probability that at exactly one of them does exactly two language classes is 0.32.

Step-by-step explanation:

We can model this variable as a binomial random variable with sample size n=2.

The probability of success, meaning the probability that a student is in exactly two language classes can be calculated as the division between the number of students that are taking exactly two classes and the total number of students.

The number of students that are taking exactly two classes is equal to the sum of the number of students that are taking two classes, minus the number of students that are taking the three classes:

[tex]N_2=F\&S+S\&G+F\&G-F\&S\&G=12+4+6-2=20[/tex]

Then, the probabilty of success p is:

[tex]p=20/100=0.2[/tex]

The probability that k students are in exactly two classes can be calcualted as:

[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{2}{k} 0.2^{k} 0.8^{2-k}\\\\\\[/tex]

Then, the probability that at exactly one of them does exactly two language classes is:

[tex]P(x=1) = \dbinom{2}{1} p^{1}(1-p)^{1}=2*0.2*0.8=0.32\\\\\\[/tex]

Answer:

A = 1.02 P

Step-by-step explanation:

A = P + 0.02P

Formula in Factorized form

(Taking P common)

A = P(1+0.02) [The required factorized from]

Then,

A = 1.02 P

Answer:

[tex]\cos (\theta)[/tex]

Step-by-step explanation:

[tex]\dfrac{\tan (\theta) \cot (\theta)}{\sec (\theta)}= \\\\\\\dfrac{\dfrac{\sin (\theta)}{\cos (\theta)}\cdot \dfrac{\cos (\theta)}{\sin (\theta)}}{\dfrac{1}{\cos (\theta)}}= \\\\\\1\cdot \cos (\theta)=\\\\\\\boxed{\cos (\theta)}[/tex]

Hope this helps!

Answer:

He sold it at 5100

Step-by-step explanation:

Find the 15% of 6000

6000 *15%

6000*.15

900

At a loss means subtract

6000-900

5100

He sold it at 5100

Answer:

4) 69

Step-by-step explanation:

Nos dicen que en una fiesta hubo 25 ordenes mas de coca cola que de pepsi y que en total fueron 113 pedidos, por lo tanto:

Sea C pedidos de coca cola

Sea P pedidos de pepsi

C + P = 113

C = P + 25

Reemplazamos:

P + 25 + P = 113

2*P = 113 - 25

P = 88/2

P = 44

Ahora para saber el numero de pedidos de coca cola:

C = 44 + 25

C = 69

Lo que quiere decir que fueron 4) 69 pedidos la respuesta correcta.

Answer:

(a)First Row, First Column =1

(b)First Row, second Column =0

(c)Second Row, First Column =0

(d)Second Row, second Column =1

Step-by-step explanation:

Given matrix [tex]M=\left(\begin{array}{ccc}-5&3\\-8&5\end{array}\right)[/tex]

The Inverse of a 2X2 matrix

[tex]A=\left(\begin{array}{ccc}a&b\\c&d\end{array}\right)[/tex]

can be found using the following:

[tex]A^{-1}=\dfrac{1}{ad-bc} \left(\begin{array}{ccc}d&-b\\-c&a\end{array}\right)[/tex]

Therefore:

[tex]M^{-1}=\dfrac{1}{(5*-5)-(3*-8)} \left(\begin{array}{ccc}5&-3\\8&-5\end{array}\right)\\=-1\left(\begin{array}{ccc}5&-3\\8&-5\end{array}\right)\\=\left(\begin{array}{ccc}-5&3\\-8&5\end{array}\right)[/tex]

Next, we find the product [tex]M^{-1}M[/tex]

[tex]M^{-1}M=\left(\begin{array}{ccc}-5&3\\-8&5\end{array}\right)\left(\begin{array}{ccc}-5&3\\-8&5\end{array}\right)\\=\left(\begin{array}{ccc}-5*-5+3*-8&-5*3+3*5\\-8*-5+5*-8&-8*3+5*5\end{array}\right)\\=\left(\begin{array}{ccc}1&0\\0&1\end{array}\right)[/tex]

Therefore:

(a)First Row, First Column =1

(b)First Row, second Column =0

(c)Second Row, First Column =0

(d)Second Row, second Column =1

NOTE: The multiplication of a matrix and its inverse always gives the identity matrix as seen above,

Answer:

  y = (2/3)x -4

Step-by-step explanation:

Simplify the given equation.

  y - 0 = (2/3)(x - 6)

  y = (2/3)x -4

Answer:

Its C

Step-by-step explanation:

just took the test.

Hope this helps! :)

Answer:

  see below for a graph

Step-by-step explanation:

A graphing calculator makes this short work.

__

You can find the x- and y-intercepts by setting the opposite variable to zero.

First equation x-intercept is the solution to 2x +0 = 1: x = 1/2. The y-intercept of that equation is the solution to 2·0 +y = 1: y = 1. The graph is the line through these points.

Second equation x-intercept is the solution to 2x +4·0 = 12: x = 6. The y-intercept is the solution to 2·0 +4y = 12: y = 3. The graph is the line through these points.

Answer:

The two distributions are each nearly symmetric.

Step-by-step explanation:

Symmetric distributions are those in which the data occurs in regular frequencies.

If we calculate the difference between the two standard deviations we find that it is only  0.022 which may be due to the physical or chemical properties of water or salt. So it lies within the same range and is almost symmetrical.

We cannot say that the distributions do not overlap on the same range of temperatures because they lie within the same range.

These two options are also incorrect as they are totally opposite of each other. Suppose the  distribution of salt water boiling temperatures is left-skewed then the distribution of tap water boiling temperatures cannot be  right-skewed as they have the same range and vice versa.

Answer:

A). The two distributions are each nearly symmetric.

Step-by-step explanation:I took the test

Answer:

Due to the higher coefficient of variation, 2009's GMAT scores show a more dispersed distribution

Step-by-step explanation:

To verify how dispersed a distribution is, we find it's coefficient of variation.

Coefficient of variation:

Mean of [tex]\mu[/tex], standard deviation of [tex]\sigma[/tex]. The coefficient is:

[tex]CV = \frac{\sigma}{\mu}[/tex]

Which year's GMAT scores show a more dispersed distribution

Whichever year has the highest coefficient.

2009:

Mean of 500, standard deviation of 90. So

[tex]CV = \frac{90}{500} = 0.18[/tex]

2010:

Mean of 570, standard deviation of 85.5. So

[tex]CV = \frac{85.5}{570} = 0.15[/tex]

Due to the higher coefficient of variation, 2009's GMAT scores show a more dispersed distribution

2009's GMAT scores show a more dispersed distribution.

Given that in 2009: Mean = 500 and standard deviation = 90.

In 2010: Mean = 570 and standard deviation = 85.5.

If the standard deviation is higher then the scores will be more dispersed.

Note that: 90 > 85.5. And 90 corresponds to 2009.

So, 2009's GMAT scores show a more dispersed distribution.

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Answer:  c) B' = (6, -3)

Step-by-step explanation:

The simplest way is to rotate the graph.

Rotating the graph 1 time to the left (counterclockwise) = 90°

Rotating the graph 2 times to the left (counterclockwise) = 180°

Rotating the graph 3 times to the left (counterclockwise) = 270°

The longer way is to reflect over the x-axis and over the y-axis, which is the same as a rotation of 180°

Z = (x, y)    →     Z' = (-x, -y)

the image below shows the graph rotated 2 times = 180°

Answer:

c

Step-by-step explanation:

Answer:

The 95% confidence interval for the difference between the proportion of women who drink alcohol and the proportion of men who drink alcohol is (-0.102, -0.014) or (-10.2%, -1.4%).

Step-by-step explanation:

We want to calculate the bounds of a 95% confidence interval of the difference between proportions.

For a 95% CI, the critical value for z is z=1.96.

The sample 1 (women), of size n1=1000 has a proportion of p1=0.494.

[tex]p_1=X_1/n_1=494/1000=0.494[/tex]

The sample 2 (men), of size n2=1000 has a proportion of p2=0.552.

[tex]p_2=X_2/n_2=552/1000=0.552[/tex]

The difference between proportions is (p1-p2)=-0.058.

[tex]p_d=p_1-p_2=0.494-0.552=-0.058[/tex]

The pooled proportion, needed to calculate the standard error, is:

[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{494+552}{1000+1000}=\dfrac{1046}{2000}=0.523[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.523*0.477}{1000}+\dfrac{0.523*0.477}{1000}}\\\\\\s_{p1-p2}=\sqrt{0.000249+0.000249}=\sqrt{0.000499}=0.022[/tex]

Then, the margin of error is:

[tex]MOE=z \cdot s_{p1-p2}=1.96\cdot 0.022=0.0438[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=(p_1-p_2)-z\cdot s_{p1-p2} = -0.058-0.0438=-0.102\\\\UL=(p_1-p_2)+z\cdot s_{p1-p2}= -0.058+0.0438=-0.014[/tex]

The 95% confidence interval for the difference between proportions is (-0.102, -0.014).

Answer:

a2+b2=c2

Step-by-step explanation:

find the saqure roof of two

Answer:

(∞,∞), (a /a∉R)

Step-by-step explanation:

Answer:

(a) When p = 5, the demand is inelastic and when p = 10, then the demand is elastic.

(b) The demand will be unitary when the price will be approximately equal to 9.24.

(c) If the unit price is lowered slightly from $10, then the revenue will increase.

(d) If the unit price is increased slightly from $5, then the revenue will decrease.

Step-by-step explanation:

We are given the demand equation for the Roland portable hairdryer where x (measured in units of a hundred) is the quantity demanded per week and p is the unit price in dollars.

[tex]x=15(256-p^{2} )[/tex]  where; (0 ≤ p ≤ 15)

Firstly, we will find the elasticity of demand as only then we can identify that demand is elastic or not.

So, the formula for the elasticity of demand is given by;

          E(p)  =  [tex]-\frac{p \times f'(p)}{f(p)}[/tex]

                   =  [tex]-\frac{p\times \frac{dx}{dp}[15(256-p^{2})] }{15(256-p^{2})}[/tex]  

                   =  [tex]-\frac{p\times 15[0-2p] }{15(256-p^{2})}[/tex]

                   =  [tex]\frac{30p^{2} }{15(256-p^{2})}[/tex]

           E(p)  =  [tex]\frac{2p^{2} }{256-p^{2}}[/tex]    

(a) When p = 5, then E(p) is given by;

            E(5)  =  [tex]\frac{2\times 5^{2} }{256-5^{2}}[/tex]

                    =  [tex]\frac{50 }{231}[/tex]  =  0.22 < 1

Since the elasticity at p = 5 is less than 1, so we can say that the demand is inelastic.

When p = 10, then E(p) is given by;

            E(10)  =  [tex]\frac{2\times 10^{2} }{256-10^{2}}[/tex]

                    =  [tex]\frac{200 }{156}[/tex]  =  1.28 > 1

Since the elasticity at p = 10 is more than 1, so we can say that the demand is elastic.

(b) The demand is said to be unitary when the value of price elasticity would be equal to 1, i.e.;

when E(p) = 1

          [tex]\frac{2p^{2} }{256-p^{2}}=1[/tex]

          [tex]2p^{2} =256-p^{2}[/tex]

          [tex]3p^{2} =256[/tex]

           [tex]p^{2} =\frac{256}{3}[/tex]

            [tex]p=\sqrt{\frac{256}{3} }[/tex]  = 9.24

So, the demand will be unitary when the price will be approximately equal to 9.24.

(c) As we know that the price elasticity at $10 is elastic, i.e. E(10) > 1, this means that when unit price is lowered slightly from $10, then the revenue will increase because due to fall in price the demand will increase.

(d) As we know that the price elasticity at $5 is inelastic, i.e. E(5) < 1, this means that when unit price is increased slightly from $5, then the revenue will decrease because due to increase in price the demand will fall.

Answer:

[tex]n=\frac{0.5(1-0.5)}{(\frac{0.025}{1.64})^2}=1075.84[/tex]  

And rounded up we have that n=1076

Step-by-step explanation:

Information given

[tex]ME= 0.025[/tex] represent the desired margin of error

Solution

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by  and . And the critical value would be given by:

[tex]t_{\alpha/2}=-1.64, t_{1-\alpha/2}=1.64[/tex]

The margin of error for the proportion interval is given by this formula:  

[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]    (a)  

We can assume that the best estimate for the true proportion is [tex]\hat p=0.5[/tex]. And on this case we have that [tex]ME =\pm 0.025[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex]   (b)  

And replacing into equation (b) the values from part a we got:

[tex]n=\frac{0.5(1-0.5)}{(\frac{0.025}{1.64})^2}=1075.84[/tex]  

And rounded up we have that n=1076

Answer: Significantly low.

Step-by-step explanation:

Ok, we know that out of 1700 randomly selected, only 4 of them are girls.

Then the frequency is:

p = 4/1700

Now, using the subjective judgement (meaning that it is based on the opinion only, there is no real math involved)

I can conclude that the number of girls is significantly low, meaning that out of 1700 births we have 4 girls, then the other 1694 must be boys.

Answer:

(-7)(-1.2) = 8.4

(-2.5)(-2) = 5

(2.5)(-2) = -5

(7)(-1.2) = -8.4

Step-by-step explanation:

Multiplication.

Answer:

  9/2

Step-by-step explanation:

It is the ratio between y-values for consecutive x-values. Perhaps the easiest two points to work with are ...

  (x, y) = (0, 1), (1, 9/2)

The rate of change you're looking for is (9/2)/1 = 9/2.

Answer:

D. 9/2

Step-by-step explanation:

Edge 2021

Answer:

The degree of the polynomial is 3.

By the fundamental theorem of algebra, the function has three roots.

Two roots are given, so there must be one root remaining.

By the complex conjugate theorem, imaginary roots come in pairs.

The final root must be real.

Step-by-step explanation:

The number of roots remaining of the polynomial function f(x) = x³ − 7x − 6, with two roots -2, and 3 already given is 1. The nature of the root will be real.

A polynomial function is a function (say f(x)), which is defined over a polynomial expression in x. It is of the form,

f(x) = a₀ + a₁x + a₂x² + a₃x³ + ... + aₙxⁿ, where a₀, a₁, a₂, ..., aₙ are constants, x is a variable, and n ≥ 0.

Degree of the polynomial function = n, the highest power of x.

The fundamental theorem of algebra is that the number of roots or solutions of a polynomial function = The degree of the polynomial function.

According to the complex conjugate theorem, if a polynomial function has complex roots, they will always exist in conjugate pairs, that is, if one root is of the form a + bi, the other root will be a - bi.

We are given a polynomial function f(x) = x³ - 7x - 6. Two roots of the equation are given as -2, and 3.

The degree of the equation = 3, so by the fundamental theorem of algebra number of roots = 3.

2 roots are given, so the number of roots remaining = 1.

Since none of the given roots are complex, the third root can not be complex, as complex roots always exist in conjugate pairs, coming from the complex conjugate theorem. So, the remaining root will be real in nature.

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Answer:

C. 2.75P

Step-by-step explanation:

The original value was P.

It increased by 275%. That means it increased by 275% of P.

275% of P = 2.75P

The increase in value is 2.75P.

Now we add the increase to the original value of P to find today's value.

2.75P + P = 3.75P

Answer: C. 2.75P