write an equation (a) in slope intercept form and (b) in standard form for the line passing through (-3,6) and parallel x+2y=5

Answer:

50%

Step-by-step explanation:

27 to 30 is exactly the "box" of the box plot and that, by definition, contains 50% of the results.

Answer:

50%

Step-by-step explanation:

Hope this will help

Answer:

The population density is 618.93 per square mile.

Step-by-step explanation:

It is given that,

No. of people, N = 70,000

The radius of a city's town hall, r = 6 miles

We need to find the population density. It can be calculated by the formula i.e. number of people divided by area of land such that,

[tex]P=\dfrac{N}{A}\\\\P=\dfrac{N}{\pi r^2}\\\\P=\dfrac{70000}{\pi (6)^2}\\\\P=618.93\ \text{per square mile}[/tex]

So, the population density is 618.93 per square mile.

Answer:

alternative hypothesis : H₁ :

Recent  Gasoline surveys felt that gasoline price in Texas was significantly lower than the national average

Alternative Hypothesis : H₁: μ < $1.298 a gallon

Step-by-step explanation:

Explanation:-

Given A recent gasoline survey said that the national average price of gasoline was $1.298 a gallon

Population average μ= $1.298 a gallon

sample size 'n' = 37

Sample mean (x⁻) = $1.192 a gallon

Sample standard deviation 'S' = $0.0436

Null hypothesis :H₀ : μ =  $1.298 a gallon

Alternative Hypothesis : μ < $1.298 a gallon

Degrees of freedom : ν = n-1= 37-1=36

t₀.₀₂₅ = 1.688

Test statistic

                       [tex]t = \frac{x^{-}-mean }{\frac{S}{\sqrt{n} } }[/tex]

                       [tex]t = \frac{1.192-1.298 }{\frac{0.0436}{\sqrt{37} } }[/tex]

                     t =  -14.8044

|t| = |-14.8044| > 1.688

Null hypothesis is rejected

Alternative hypothesis is accepted

Recent  Gasoline surveys felt that gasoline price in Texas was significantly lower than the national average

Answer:

Yes- these answers are equivalent.

Step-by-step explanation:

In the expression 7(2d+3), the 7 is outside the parentheses, meaning everything inside the parentheses is multiplied by 7.

2d X 7 = 14 d

3 X 7 = 21

7(2d+3) = 14d + 21

Yes, the expressions are equivalent.

By combining numbers, variables, functions in mathematics we get an expression.

Example : 4p+2, 3x-4y etc

Given expressions are 14d+21 and 7(2d+3)

Here, simplifying the expression 7(2d+3) we get,

7(2d+3) = (7×2d)+(7×3) = 14d+21

Therefore, the given two expressions are equal to each other, i.e same.

Learn more about expression here :

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Answer:

16

Step-by-step explanation:

there are 2 tbs of whipped cream per sundae so you have to divide 32 by 2 and get 16

Answer:  8

Step-by-step explanation:

For every 1 sundae, the shop uses 4 spoonfuls of sprinkles. The ratio of sundaes to spoonfuls of sprinkles is 1:4.

The shop used 32 spoonfuls of sprinkles.

Since the number of spoonfuls of sprinkles was multiplied by 8, we also need to multiply the number of sundaes by 8.

The shop made 8 sundaes.

Answer:

Step-by-step explanation:

Hello!

Distribution in attachment.

The variable of interest is:

X: Number of successes after flipping a coin 5 times.

If you check the binomial criteria:

The number of trials is fixed: n=5

There are only two possible outcomes "success" or "failure"

Each flip of the coin is independent of the others.

The probability of success in the same from one trial to another, in this case, if we consider the coin to be balanced, the probability of success is p=0.5

The histogram shows the probability of obtaining X number of success in 5ve flips of a coin (y-axis) vs the number of successes counted each (x-axis)

Statements:

1) The bar for any number k represents the probability of getting k successes in 5 flips. Correct. The histogram shows the probability of obtaining X number of success in 5ve flips of a coin (y-axis) vs the number of successes counted each (x-axis). Each bar represents the probability of success for each possible value.

2) The number of successes, k, can range from 0 (no success) to 5 (all successes). Correct. The variable count the number of successes after flipping a coin 5 times. It can happen that you flip it and all the flips turn to be failures (X=0), that you flip it 5 times and only one turns out to be a success and the other 4 are failures (X=1), and so on until you flip it 5 times and all flips are successes (X=5)

3) Each coin flip is independent; it is not affected by any other coin flip. Correct, if not, this variable wouldn't have a binomial distribution as specified in the text.

4) For 5 coin flips, P(2 heads) = P(3 heads). Correct

Looking at the histogram, the bars for "2 successes" and "3 successes" have the same height, a little above 0.3, this means that both values have the same probability of occurrence.

5) The sum of the probabilities shown in the binomial distribution is p.

Incorrect.

For the binomial distribution "p" represents the probability of success for each trial, in this case, flipping the coin once.

For this distribution, as well as for other probability distribution, the sum of all probabilities is always 1, if not, then it is not a probability distribution.

I hope this helps!

Answer:

Lets make this easier for you guys. The correct answers are 1 through 4.

The bar for any number k represents the probability of getting k successes in 5 flips.

The number of successes, k, can range from 0 (no success) to 5 (all successes).

Each coin flip is independent; it is not affected by any other coin flip.

For 5 coin flips, P(2 heads) = P(3 heads

Step-by-step explanation:

Correct on edge :))

Answer:

[tex]P(A|B) = \frac{32}{49}[/tex]

Step-by-step explanation:

We use the conditional probability formula to solve this question. It is

[tex]P(A|B) = \frac{P(A \cap B)}{P(B)}[/tex]

In which

P(A|B) is the probability of event A happening, given that B happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(B) is the probability of B happening.

We have that:

[tex]P(A \cap B) = \frac{4}{7}, P(B) = \frac{7}{8}[/tex]

So

[tex]P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{\frac{4}{7}}{\frac{7}{8}} = \frac{4}{7}*\frac{8}{7} = \frac{32}{49}[/tex]

Then

[tex]P(A|B) = \frac{32}{49}[/tex]

Answer: (x+8)²

Step-by-step explanation:

When you complete the square, the factor is squared. You want to first factor the equation.

x²+16x+64=0

(x+8)(x+8)=0

Now that we have factored the equation, we can put in into squares.

(x+8)²

Answer

8 and 0 (Khan)

Answer:

279 and 950

Step-by-step explanation:

Outliers are numbers that are significantly greater or lesser than the other numbers in the data set.

The other numbers are very close together on a numerical scale, with the exception of 279 and 950.

Therefore, these two numbers are the outliers.

The outliers are 279 and 950

Learn more about the outlier here: https://brainly.com/question/9933184?referrer=searchResults

Answer:

Use the Rational Zero Theorem to list all possible rational zeros of the function. Use synthetic division to evaluate a given possible zero by synthetically dividing the candidate into the polynomial. Repeat step two using the quotient found with synthetic division.

Step-by-step explanation:

One of the methods to finding zeros and factors of higher degree polynomial functions is using the Remainder theorem.

The zeros of polynomial refer to the values of the variables present in the polynomial equation for which the polynomial equals 0.

The methods to finding zeros and factors of higher degree polynomial functions

Hence, one of the methods to finding zeros and factors of higher degree polynomial functions is using the Remainder theorem.

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Answer:

a) The 99% confidence interval is from 14.8% to 23.2%.

b) The confidence interval tells us that the true proportion of mislabeled is within 14.8% and 23.2%, with a 99% confidence. In other words, if we take samples of the same size, 99% of the samples will have a proportion within 0.148 and 0.232.

c) The confidence interval calculation take into account the sample size, so the width (or precision) of the interval depends on the sample size.

The only criticism that could be analyzed is to see if the sample is representative of the population.

Step-by-step explanation:

a) We have to calculate a 99% confidence interval for the proportion.

The sample proportion is p=0.19.

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.19*0.81}{585}}\\\\\\ \sigma_p=\sqrt{0.000263}=0.016[/tex]

The critical z-value for a 99% confidence interval is z=2.576.

The margin of error (MOE) can be calculated as:

[tex]MOE=z\cdot \sigma_p=2.576 \cdot 0.02=0.042[/tex]

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

[tex]LL=p-z \cdot \sigma_p = 0.19-0.042=0.148\\\\UL=p+z \cdot \sigma_p = 0.19+0.042=0.232[/tex]

The 99% confidence interval for the population proportion is (0.148, 0.232).

The answer is 1/3

please see the attached picture for full solution

Hope it helps

Good luck on your assignment

Answer: 1/3

Step-by-step explanation: To subtract mixed numbers, first subtract the fractions.

Notice here however that we have 1/6 - 5/6

which will give us a negative fraction.

Since this will cause us a lot of trouble, instead,

let's rewrite the first mixed number.

We can do this by thinking of 3 and 1/6 as 2 + 1 and 1/6 or 2 + 7/6

by changing 1 and 1/6 into an improper fraction.

So 3 and 1/6 can be written as 2 and 7/6.

So we have 2 and 7/6 -  2 and 5/6.

Now, subtract the fractions.

So we have 7/6 - 5/6 which is 2/6.

Then subtract the whole numbers.

2 - 2 is 0.

However, we don't need to include 0 in our answer.

We can write our answer as 2/6.

However, 2/6 is not in lowest terms.

So divide the numerator and denominator by 2 to get 1/3.

So 3 and 1/6 - 2 and 5/6 is 1/3.

Answer:

4-5 12 -13

Step-by-step explanation:

Answer:

26 feet

Step-by-step explanation:

Let the length of the required wire =l

The height of the tree =24 cm

We want the tree to fall to the ground 10 feet away from the base.

Ths problem forms a right triangle which I have drawn and attached below.

To determine the length of the wire l required, we use Pythagoras theorem to solve for the hypotenuse of the right triangle.

[tex]B$y Pythagoras theorem: Hypotenuse^2=Opposite^2+Adjacent^2\\$Therefore:\\l^2=24^2+10^2\\l^2=676\\$Take the square root of both sides\\l=\sqrt{676}\\ l=26$ feet[/tex]

Thw wire must be 26 feet long to reach the ground.

Answer:

Area of rectangle = [tex]196\,m^2[/tex]

Length of rectangle = 14 m

Width of rectangle = 14 m

Step-by-step explanation:

Given:

Perimeter of rectangle is 56 m

To find: the maximized area of a rectangle and the length and width

Solution:

A function [tex]y=f(x)[/tex] has a point of maxima at [tex]x=x_0[/tex] if [tex]f''(x_0)<0[/tex]

Let x, y denotes length and width of the rectangle.

Perimeter of rectangle = 2( length + width )

[tex]=2(x+y)[/tex]

Also, perimeter of rectangle is equal to 56 m.

So,

[tex]56=2(x+y)\\x+y=28\\y=28-x[/tex]

Let A denotes area of rectangle.

A = length × width

[tex]A=xy\\=x(28-x)\\=28x-x^2[/tex]

Differentiate with respect to x

[tex]\frac{dA}{dx}=28-2x[/tex]

Put [tex]\frac{dA}{dx}=0[/tex]

[tex]28-2x=0\\2x=28\\x=14[/tex]

Also,

[tex]\frac{d^2A}{dx^2}=-2<0[/tex]

At x = 14, [tex]\frac{d^2A}{dx^2}=-2<0[/tex]

So, x = 14 is a point of maxima

So,

[tex]y=28-x=28-14=14[/tex]

Area of rectangle:

[tex]A=xy=14(14)=196\,m^2[/tex]

Length of rectangle = 14 m

Width of rectangle = 14 m

Answer:

The number of pencils in the box A is 70

The number of pencils in the box B is 42

Step-by-step explanation:

The number of pencils in the box A is a

The number of pencils in the box B is b

We have:

a + b = 112

a - (1/5)a = b + (1/5)a

or

a + b = 112

a - (2/5)a = b

or

a + b = 112

(3/5)a = b

or

a + (3/5)a = 112

or

(8/5)a = 112

or

a = 112*(5/8)

or

a = 70

=> b = 112 - 70 = 42

Hope this helps!

Answer:

B) Mia Hamm helped her soccer team at the University of North Carolina at Chapel Hill win four NCAA titels.

Step-by-step explanation:

The first option is an opinion, not a fact.

Answer:

37.67%

Step-by-step explanation:

Suppose initially a price of $ 100

Increasing per month at a rate of 2.7%. Which is equal to 0.027

Now applying the formula:

Vf = Vi * (1 + m) ^ n

where Vf is the final quantity, Vi is the initial value, m is the rate and n is the number of months.

We know that 1 year, is 12 months, since the rate is monthly means, n = 12, we replace:

Vf = 100 * (1 + 0.027) ^ 12

Vf = 137.67

It means price increase in 1 year = 137.67 - 100 = 37.67

Which means that n a year increases to 37.67%

saying it is cloudy is the defining that it's so gloomy outside or is probably paraphrasing to how someone feels

hope this helps

Answer: 35

Step-by-step explanation:

The number of combinations of r things selected out of n things is given by

[tex]^nC_r= \dfrac{n!}{r!(n-r)!}[/tex]

Given , the total number of types of toppings available = 7

The number of toppings needed to be selected = 4

Then, the number of ways to do this would be

[tex]^7C_4=\dfrac{7!}{4!(7-4)!}\\\\=\dfrac{7\times6\times5\times4!}{4!3!}\\\\=\dfrac{7\times5}{1}=35[/tex]

Hence, the number of combinations of 5 scoops of ice cream and 4 toppings are possible = 35.

Answer:

  (a, b, c) = (8, 3, 2)

Step-by-step explanation:

Remove cubes from under the radical. Combine terms.

  [tex]\sqrt[3]{16} +2\sqrt[3]{54} =\sqrt[3]{2^3\cdot 2}+2\sqrt[3]{3^3\cdot 2}\\\\=2\sqrt[3]{2}+2\cdot 3\sqrt[3]{2}=(2+6)\sqrt[3]{2}\\\\=8\sqrt[3]{2}\equiv a\sqrt[b]{c}\ \longrightarrow\ \boxed{(a,b,c)=(8,3,2)}[/tex]

Answer:

2.8 hours or 2hrs 8 min

Step-by-step explanation:

money paid per hour=16+9=$25

money paid by luis=70

time=70/25= 2.8 hrs

=2 hours and 8 minutes

hope this helps u :)

Answer:

Step-by-step explanation:

Midline is the horizontal line that passes exactly in the middle between the graph's maximum and minimum points.

Amplitude is the vertical distance between the midline and one of the extremum points.

Period is the distance between two consecutive maximum points, or two consecutive minimum points (these distances must be equal).

To find the formula for [tex]g(x)[/tex]. First, let's use the given information to determine the function's amplitude, midline, and period.

The midline of a sinusoidal function passes exactly in the middle of its extreme values. So we can find the midline by finding the average of the maximum and minimum values.

The midline passes exactly between the minimum value 1, and the maximum value 11, so the midline equation is

[tex]midline=y=\frac{11+1}{2} =6[/tex]

The extremum points are 5 units above or below the midline, so the amplitude is 5.

The maximum point is 0.5 units to the right of the minimum point, so the period is [tex]2\cdot 0.5 =1[/tex]. We multiply by 2 because the distance between consecutive minimum and maximum points is always [tex]\frac{1}{2}[/tex] of the period.

The general sinusoidal equation [tex]y=a\cos(bx)+d[/tex] is the result of horizontal and vertical shifts, reflections, and stretches of the parent equation [tex]y=\cos(x)[/tex] where

The amplitude is 5, so [tex]|a|=a=5[/tex].

The midline is y = 6, so d = 6.

The period is 1, so b = [tex]\frac{2\pi }{1}=2\pi[/tex].

The formula for [tex]g(x)=5\cos(2\pi x)+6[/tex].

Answer:

a) A sample size of 195 is needed.

b) Smaller

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.999}{2} = 0.0005[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.0005 = 0.9995[/tex], so [tex]z = 3.27[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

a. How large a sample must be drawn so that a 99.9% confidence interval for will have a margin of error equal to 4.1.

We need a sample size of n.

n is found when [tex]M = 4.1[/tex]

We have that [tex]\sigma = 17.5[/tex]

So

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

[tex]4.1 = 3.27*\frac{17.5}{\sqrt{n}}[/tex]

[tex]4.1\sqrt{n} = 3.27*17.5[/tex]

[tex]\sqrt{n} = \frac{3.27*17.5}{4.1}[/tex]

[tex](\sqrt{n})^{2} = (\frac{3.27*17.5}{4.1})^{2}[/tex]

[tex]n = 194.8[/tex]

Rounding up

A sample size of 195 is needed.

b. If the required confidence level were 95%, would the necessary sample size be larger or smaller?

Same as above for n, the difference is that z would be 1.96 instead of 3.27. So a smaller sample size.

Answer:

a) The null hypothesis is given as

H₀: μ₀ ≥ 38.2 minutes

The alternative hypothesis is given as

Hₐ: μ₀ < 38.2 minutes

b) The null hypothesis is given as

H₀: μ₀ = $58,291

The alternative hypothesis is given as

Hₐ: μ₀ ≠ $58,291

c) The null hypothesis is given as

H₀: μ₀ ≤ 133.0 mg

The alternative hypothesis is given as

Hₐ: μ₀ > 133 mg

d) The null hypothesis is given as

H₀: μ₀ = 161.9 bushels

The alternative hypothesis is given as

Hₐ: μ₀ ≠ 161.9 bushels

e) The null hypothesis is given as

H₀: μ₀ ≤ 42.8 years

The alternative hypothesis is given as

Hₐ: μ₀ > 42.8 years

Step-by-step explanation:

In hypothesis testing, the null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test. It usually maintains that, with random chance responsible for the outcome or results of any experimental study/hypothesis testing, its statement is true.

The alternative hypothesis usually confirms the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test. It usually maintains that significant factors other than random chance, affect the outcome or results of the experimental study/hypothesis testing and result in its own statement.

Taking the statements one at a time

a) The assertion is that the new average time workers spent commuting to work in Verona is now less than the old average.

The null hypothesis would be there isn't enough evidence to conclude that the new average time workers spent commuting to work in Verona is now less than the old average. That is, the new average time workers spent commuting to work in Verona is now equal to or more than the old average.

The alternative hypothesis is that the new average time workers spent commuting to work in Verona is now less than the old average.

Mathematically, if μ₀ = new average time workers spent commuting to work in Verona.

The null hypothesis is given as

H₀: μ₀ ≥ 38.2 minutes

The alternative hypothesis is given as

Hₐ: μ₀ < 38.2 minutes

b) Although the question isn't complete,

The null hypothesis is that there isn't a significant difference between whatever is being compared in the complete question and the mean salary for all men in that profession.

The alternative hypothesis is that there is significant difference between whatever is being compared in the complete question and the mean salary for all men in that profession.

Mathematically, if μ₀ = Mean of whatever is being compared in the complete question

The null hypothesis is given as

H₀: μ₀ = $58,291

The alternative hypothesis is given as

Hₐ: μ₀ ≠ $58,291

c) The claim to be proved is that the average caffeine content for coffee served in a local restaurants is higher.

The null hypothesis is that the average caffeine content for coffee served in a local restaurants is not higher than the standard figure of 133 mg for an 8 ounce cup. That is, the average caffeine content for coffee served in a local restaurants is not higher than the standard figure of 133 mg for an 8 ounce cup.

The alternative hypothesis is that average caffeine content for coffee served in a local restaurants is higher than the standard figure of 133 mg for an 8 ounce cup.

Mathematically, if μ₀ = average caffeine content for coffee served in a local restaurants.

The null hypothesis is given as

H₀: μ₀ ≤ 133.0 mg

The alternative hypothesis is given as

Hₐ: μ₀ > 133 mg

d) The economist claims that the average yield per acre this year is different from the average yield per acre in recent years.

Hence, the null hypothesis is that there is no significant difference between the average yield per acre this year and the average yield per acre in recent years.

The alternative hypothesis is that there is significant difference between the average yield per acre this year and the average yield per acre in recent years.

Mathematically, if μ₀ = the average yield per acre this year

The null hypothesis is given as

H₀: μ₀ = 161.9 bushels

The alternative hypothesis is given as

Hₐ: μ₀ ≠ 161.9 bushels

e) The sociologist suspects that the average age of all self-described fly fishermen is higher than 42.8 years.

Hence, the null hypothesis is that the average age of all self-described fly fishermen is not higher than 42.8 years. That is, the average age of all self-described fly fishermen is equal to less than 42.8 years.

The alternative hypothesis is that the average age of all self-described fly fishermen is higher than 42.8 years.

Mathematically, if μ₀ = average age of all self-described fly fishermen.

The null hypothesis is given as

H₀: μ₀ ≤ 42.8 years

The alternative hypothesis is given as

Hₐ: μ₀ > 42.8 years

Hope this Helps!!!

Answer:

They should not be exactly the same but they should be close.

Step-by-step explanation:

The first thing that we must take into account is the following:

Experimental probability is the result of an experiment, and theoretical probability is based on the mathematical model developed in probability theory. With the above, we can affirm that the precision of the results of the experiments depends directly on the sample size of the experiment and the precision is greater when the sample size is greater.

This means that the odds are most likely not the same, they must be very close since it has been repeated a considerable number of times and the more times it is done the closer they will be to being the same.

Answer:−2x=−8

4sin2(x)−1=0

2x+3=3

Step-by-step explanation:

Answer:

A)  [tex]B = \{\left[\begin{array}{ccc}1&0\\0&1 \end{array}\right], \left[\begin{array}{ccc}0&1\\1&0 \end{array}\right] \}[/tex]

B) [tex]M_{B} = \left[\begin{array}{ccc}-2\\-7\end{array}\right][/tex]

Step-by-step explanation:

Let [tex]A = \left[\begin{array}{ccc}a&b\\c&d \end{array}\right][/tex] where a, b, c and d are real numbers

Since A is said to be a half magic square matrix, a = d, b = c.

The matrix A therefore becomes  [tex]A = \left[\begin{array}{ccc}a&b\\b&a \end{array}\right][/tex] where [tex]a,b \epsilon R[/tex]

A can therefore be manipulated as:

[tex]A = a \left[\begin{array}{ccc}1&0\\0&1 \end{array}\right] + b \left[\begin{array}{ccc}0&1\\1&0 \end{array}\right][/tex]

The matrices [tex]\left[\begin{array}{ccc}1&0\\0&1 \end{array}\right][/tex] and [tex]\left[\begin{array}{ccc}0&1\\1&0 \end{array}\right][/tex] are apparently linearly independent and therefore form a basis B for V

[tex]B = \{\left[\begin{array}{ccc}1&0\\0&1 \end{array}\right], \left[\begin{array}{ccc}0&1\\1&0 \end{array}\right] \}[/tex]

B) Find the coordinate vector [M]_B of M [-2 -7, -7 -2]

 [tex]M = \left[\begin{array}{ccc}-2&-7\\-7&-2 \end{array}\right][/tex]

[tex]M[/tex] can be written in the form [tex]M = a\left[\begin{array}{ccc}1&0\\0&1 \end{array}\right] + b\left[\begin{array}{ccc}0&1\\1&0 \end{array}\right][/tex]

[tex]M = \left[\begin{array}{ccc}-2&-7\\-7&-2 \end{array}\right] = -2\left[\begin{array}{ccc}1&0\\0&1 \end{array}\right] -7\left[\begin{array}{ccc}0&1\\1&0 \end{array}\right][/tex]

The coordinate vector is therefore, [tex]M_{B} = \left[\begin{array}{ccc}-2\\-7\end{array}\right][/tex]

Answer:

Hello There Again. The correct answer is D.

Explanation: Why is D. Because 5x2=10 which everyone know that 5x2=10x3x1=30 So the best choice will be D.

Hope It Helps!