Find the distance between the two points.

(−1, −3), (1, 3)

Answer:

the leading coefficient of a polynomial is the coefficient of the term with the highest degree of the polynomial

so the answer should be the second one -7+6x+5x^2

17.7 gallons of gas would she require to travel 413 miles at this rate when Jenny used 9 gallons of gas to travel 210 miles.

Given that,

Jenny used 9 gallons of gas to travel 210 miles.

We have to find how many gallons of gas would she require to travel 413 miles at this rate.

We know that,

Jenny used 9 gallons of gas to travel 210 miles.

Then

Rate = 210 miles/9 gallons

= 23.3 miles/gallon.

So,

Nicole can achieve a fuel efficiency of 23.3 miles per gallon.

He has a 413-mile drive ahead of him.

So,

413/23.3 = 17.7 gallons needed.

Therefore, 17.7 gallons of gas would she require to travel 413 miles at this rate when Jenny used 9 gallons of gas to travel 210 miles.

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Answer:

Im pretty sure it is E=8

Step-by-step explanation:

Answer:

E=8

Step-by-step explanation:

took the test :)

The difference in the proportion of males and the proportion of females that smoke is 0.08

In a sample of 61 males, 15 smoke, while in a sample of 48 females, 8 smoke.

The given parameters are:

                             Male           Female

Sample                  61                  48

Smokers               15                   8

The proportion is calculated using:

p = Smoker/Sample

So, we have:

Male = 15/61 = 0.25

Female = 8/48 = 0.17

The difference is then calculated as:

Difference = 0.25 - 0.17

Evaluate

Difference = 0.08

Hence, the difference in the proportion of males and the proportion of females that smoke is 0.08

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Answer:

15x+28

Step-by-step explanation:

15x+10+18

15x+28

49 inches in feet is 4.08333.

You can easily convert 49 inches into feet using each unit definition:

Inches

inch = 2.54 cm = 0.0254 m

Feet

foot = 12 inch = 0.3048 m

Performing the inverse calculation of the relationship between units, we obtain that 1 foot is 0.24489796 times 49 inches.

A foot is zero times forty-nine inches.

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The probability that the second card is higher in rank than the first card can be calculated using the fact that the probability of drawing a higher card is equal to the probability of drawing a lower card.

Let's denote P(higher) as the probability of the second card being higher than the first, P(lower) as the probability of the second card being lower than the first, and P(same) as the probability of the second card being the same rank as the first.

Using this notation, we can express the probability of the second card being higher in rank than the first as follows:

P(higher) = 1 - P(lower) - P(same)

Therefore, the probability that the second card is higher in rank than the first card is 1 minus the probability of the second card being lower than the first card minus the probability of the second card being the same rank as the first card.

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A graphical device used for enumerating sample points in a multiple-step experiment is a tree diagram.

A tree diagram is a visual representation that helps organize and enumerate all possible outcomes or sample points in a multi-step or sequential experiment. It consists of branches or lines that represent different choices or events at each step of the experiment, and the branches split and multiply as the experiment progresses. The final outcomes or sample points are represented as endpoints of the branches.

Tree diagrams are commonly used in probability theory and statistics to calculate probabilities and analyze complex experiments involving multiple stages or events. They provide a clear and systematic way to visualize and enumerate all possible outcomes, making them a helpful tool in analyzing and solving probability problems.

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Answer:

72 breakfasts

Step-by-step explanation:

number of entrees: 4

number of drinks: 6

number of vitamins: 3

four times six times three =

72

An algebraic expression like (3+5) x (4-1) is a combination of numbers and at least one operation.

The 87% confidence interval for the size of the candles is (3.503 ounces, 3.937 ounces).

To calculate the 87% confidence interval, follow these steps:

1. Identify the sample size (n=15), sample mean (3.72 ounces), and standard deviation (0.963 ounces).

2. Determine the critical value (z) for an 87% confidence interval using a standard normal distribution table or calculator. For an 87% CI, the critical value is approximately 1.534.

3. Calculate the standard error (SE) using the formula SE = standard deviation / sqrt(n). In this case, SE = 0.963 / sqrt(15) ≈ 0.248.

4. Multiply the critical value (z) by the standard error (SE) to find the margin of error (MOE): MOE = 1.534 * 0.248 ≈ 0.380.

5. Find the lower limit of the confidence interval by subtracting the MOE from the sample mean: 3.72 - 0.380 = 3.503 ounces.

6. Find the upper limit of the confidence interval by adding the MOE to the sample mean: 3.72 + 0.380 = 3.937 ounces.

So, the 87% confidence interval for the size of the candles is (3.503 ounces, 3.937 ounces).

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Answer:

B is correct.

Step-by-step explanation:

On number line and sequencing also, -3 is less than -2.

Answer:

b is correct -2 is less than-3

Answer:Number of miles Erin jogged altogether= 7 miles

Step-by-step explanation:

Number of miles jogged on Monday =2 miles

Number of miles jogged on Wednesday =3 miles

Number of miles jogged on Friday =2 miles

Number of miles jogged altogether= 2 miles+3 miles+2 miles=7 miles

a. The composite scores for each location are as follows: Location A: 84.34, Location B: 81.05, Location C: 82.63 (b)  Based on the composite scores, Location A should be chosen for the clothing store.

To determine the composite score for each location, we need to calculate the weighted sum of the factor ratings.

a. The composite score for each location is calculated as follows:

Location A:

Composite score = (Convenience of access * Weight) + (Parking facility * Weight) + (Frontage * Weight) + (Shopper traffic * Weight) + (Operating cost * Weight) + (Neighbourhood * Weight)

Composite score = (0.10 * 92) + (0.15 * 91) + (0.19 * 96) + (0.31 * 79) + (0.10 * 70) + (0.15 * 69)

Composite score = 84.34

Location B:

Composite score = (0.10 * 70) + (0.15 * 73) + (0.19 * 89) + (0.31 * 95) + (0.10 * 95) + (0.15 * 81)

Composite score = 81.05

Location C:

Composite score = (0.10 * 72) + (0.15 * 75) + (0.19 * 74) + (0.31 * 80) + (0.10 * 92) + (0.15 * 96)

Composite score = 82.63

b. Based on the composite scores, we can see that Location A has the highest score of 84.34, followed by Location C with a score of 82.63, and Location B with a score of 81.05. Therefore, Location A should be chosen for the clothing store.

After calculating the composite scores for each location based on the factor ratings and weights, it is determined that Location A has the highest composite score and should be chosen for the clothing store.

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To determine the degree of a polynomial function given in factored form, a good first step is to count the highest power of the variable in the factored expression.

In factored form, a polynomial function is expressed as the product of linear factors or irreducible quadratic factors.

Each factor represents a root or zero of the function.

The degree of a polynomial is determined by the highest power of the variable in the expression.

To find the degree of the function, examine each factor in the factored form.

For linear factors, the degree is 1 since the highest power of the variable is 1.

For irreducible quadratic factors, the degree is 2 since the highest power of the variable is 2.

By observing the highest power in the factored expression, you can determine the degree of the polynomial function.

If the highest power is 1, the polynomial has a degree of 1 (linear function). If the highest power is 2, the polynomial has a degree of 2 (quadratic function). And so on.

It's important to note that the degree of a polynomial corresponds to the highest power of the variable in the expression and not the number of factors.

The number of factors indicates the number of roots or zeros of the polynomial, but it doesn't determine the degree.

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Answer:

10

Step-by-step explanation:

Answer:

10 shoes

Step-by-step explanation:

Step 1: State what is known

Giles has 10 socks for every 5 pairs of shoes

He has 20 socks

Step 2: Set up the ratio

Let 'x' represent how much shoes Giles has

10 socks : 5 shoes

20 socks : x shoes

Step 3: Convert ratio into fraction

\(\frac{Socks}{Shoes}\)

10 socks : 5 shoes = \(\frac{10}{5}\)

20 socks : x shoes = \(\frac{20}{x}\)

Step 4: Set ratio equal to each other and solve

\(\frac{10}{5}=\frac{20}{x}\\ 10x = 100\\\frac{10x}{10}=\frac{100}{10}\\x = 10\)

Therefore Giles has 10 shoes when he has 20 socks

The number of possible ways are there to distribute 10 identical cookies to 4 children such that all cookies are distributed and at most one child gets no cookies are 330.

There are 10 cookies to be distributed among 4 children. The condition is that at most 1 child get no cookies.

So, we will use the formula of combination that is ⁿCₐ where, n is the total things and a is the things to be selected.

ⁿCₐ = n!/(n-a)!a!

Now, the possible combination set are two, one in which only three child get cookies and one in which all gets cookies.

So, we should write,

Combinations = ¹⁰C₄ + ¹⁰C₃

Combination = 210 + 120

Combination = 330

So, the total ways are 330.

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The sum of two positive numbers is 120. The product of those numbers will be maximum if both numbers are equal to 60 and the maximum value is 3600.

Suppose we have a function f(x). At the extreme point (maximum/minimum), it holds:

      f ' (x) = 0

In the given problem, let the two numbers be a and b. Then,

a + b = 120 or

a = 120 - b   (equation 1)

f(b) = a x b = (120 - b) x b

f(b) = -b² + 120b

At the maximum point, the derivative with respect to b is zero,

f ' (b) = 0

-2b + 120 = 0

b = 120 / 2 = 60

Substitute b = 60 to equation 1,

a = 120 - 60 = 60

Hence, the two numbers that give maximal value of the product is 60 and 60. The product is 60 x 60 = 3600.

We can conclude that the maximum value of the product of those two numbers is 3600.

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The mean is calculated by adding up all the numbers in the data set and dividing by the total number of values. In this case, the sum of the numbers is 105 and there are 16 values, so the mean is 6.56 cups of coffee per week on average.

To find the median, we need to arrange the numbers in order from smallest to largest. The ordered list is: 1, 1, 2, 2, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 36. The median is the middle value, which is 6.

In this case, the median is a better measure of central tendency because the data set includes an outlier value of 36 cups per week. This single value skews the mean and makes it less representative of the majority of employees' coffee consumption. The median, on the other hand, is not affected by outliers and represents the middle value in the data set, which is more reflective of the typical coffee consumption for this office.

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The shortest distance from the origin to the curve x2 + xy + y2 = 3 is √(6-2√7) and the longest distance is √(6+2√7).

We have to find the shortest and longest distances from the origin to the curve x^2 + xy + y^2 = 3. This can be done using the Lagrange multiplier technique.

Given, x^2 + xy + y^2 = 3.

We have to minimize and maximize the distance of the origin from the given curve. The distance of the origin from the point (x, y) is given by √(x²+y²).

Therefore, we have to minimize and maximize the function f(x, y) = √(x²+y²) subject to the constraint x^2 + xy + y^2 = 3.

Now, we have to form the Lagrange function.

L(x, y, λ) = f(x, y) + λ(g(x, y))

where, g(x, y) = x2 + xy + y2 - 3L(x, y, λ) = √(x²+y²) + λ(x2 + xy + y2 - 3)

Now, we have to find the partial derivatives of L with respect to x, y, and λ.

∂L/∂x = x/√(x²+y²) + 2λx+y = 0 ............. (1)

∂L/∂y = y/√(x²+y²) + λx+2λy = 0 ............. (2)

∂L/∂λ = x² + xy + y² - 3 = 0 ............. (3)

Solving equations (1) and (2), we get x/√(x²+y²) = 2y/x.

Since x and y cannot be equal to 0 simultaneously, we can say that x/y = ±2.

Substituting x = ±2y in equation (3), we get y²(5±2√7) = 9.

Now, we can solve for x and y to get the values of (x, y) at which the minimum and maximum value of the distance of the origin occurs.

Using x = 2y, we get y²(5+2√7) = 9 ⇒ y = ±3/√(5+2√7)

Using x = -2y, we get y²(5-2√7) = 9 ⇒ y = ±3/√(5-2√7)

Therefore, the four points at which the distance is minimum and maximum are {(2/√(5+2√7), 1/√(5+2√7)), (-2/√(5+2√7), -1/√(5+2√7)), (2/√(5-2√7), -1/√(5-2√7)), (-2/√(5-2√7), 1/√(5-2√7))}.

To find the minimum and maximum distances, we can substitute these points in f(x, y) = √(x²+y²).

After substituting, we get the minimum distance as √(6-2√7) and the maximum distance as √(6+2√7).

Therefore, the shortest distance from the origin to the curve x^2 + xy + y^2 = 3 is √(6-2√7) and the longest distance is √(6+2√7).

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Answer:

Unitary cost= $1.75

Step-by-step explanation:

Giving the following information:

He spent $21 on 12 single-scoop ice cream cones.

To calculate the unitary cost, we need to use the following formula:

Total cost= number of units*unitary cost

Unitary cost= total cost / number of units

Unitary cost= 21 / 12

Unitary cost= $1.75

The exponential function for the table is given as follows:

\(y = 0.02(4)^x\)

The simple radical form of the expression is given as follows:

\(\sqrt{8} = 2\sqrt{2}\)

An exponential function has the definition presented as follows:

\(y = ab^x\)

In which the parameters are given as follows:

The parameter values for the exponential function in this problem are given as follows:

Hence the exponential function for the table is given as follows:

\(y = 0.02(4)^x\)

For the simple radical form, we have that 8 = 2 x 4, hence:

\(\sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}\)

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The percentage of the flock that has spots is 35%.

To find the percentage of the flock that has spots, we need to divide the number of sheep with spots by the total number of sheep and then multiply by 100 to get the percentage.

In this case, we have 182 white sheep and 98 spotted sheep, so the total number of sheep in the flock is 182 + 98 = 280.

To find the percentage of sheep with spots, we divide the number of spotted sheep (98) by the total number of sheep (280) and then multiply by 100:

(98/280) x 100 = 35%

This means that 65% of the flock is white.

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We have evaluated (f ° g)(3) = 68. The correct answer is a) 68.

The given functions are:f(x) = 4x + 8g(x) = x² + 2x

Now, we need to find (f ° g)(3). This can be done by substituting the value of g(3) into f(x).Therefore, firstly, we have to calculate g(3):g(x) = x² + 2x

Putting x = 3, we get:g(3) = (3)² + 2(3) = 9 + 6 = 15

Now, we need to calculate f(g(3)):f(g(3)) = f(15)f(x) = 4x + 8

Putting x = 15, we get:f(g(3)) = 4(15) + 8 = 60 + 8 = 68

Therefore, (f°g)(3) = 68. Hence, the correct option is a) 68.

Explanation:A composition of two functions is a way of combining two functions such that the output of one function is the input of the other function. The notation f ° g represents the composition of functions f and g, where f ° g (x) = f(g(x)).To calculate f(g(x)), we first need to calculate g(x). Given:g(x) = x² + 2xTo find (f ° g)(3), we need to evaluate f(g(3)).Substituting the value of g(3), we get:f(g(3)) = f(15) where,g(3) = 15f(x) = 4x + 8Therefore,f(g(3)) = f(15) = 4(15) + 8 = 68Hence, (f ° g)(3) = 68

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Answer:

1) 9/10 + 4/5 + 5/6 = 2 8/15

2) 14/15 + 2/9 + 1/5 = 1 16/45

==============================================

Solution:

\( \bold{1)} \: \tt \frac{9}{10} + \frac{4}{5} + \frac{5}{6} \\ \\⟹ \tt \frac{9}{10} + \frac{4}{5} \\ = \tt \frac{9 \times 1}{10 \times 1} + \frac{4 \times 2}{5 \times 2} = \frac{9 + 8}{10} = \frac{17}{10} \\ \\ ⟹\tt \frac{17}{10} + \frac{5}{6} \\ = \tt \frac{17 \times 3}{10 \times 3} + \frac{5 \times 5}{6 \times 5} = \frac{51 + 25}{30} = \frac{76}{30} \: or \: 2 \frac{16}{30} = 2 \frac{8}{15} \\ \\ \\ \\ \bold{2)} \tt \: \: \frac{14}{15} + \frac{2}{9} + \frac{1}{5} \\ \\⟹ \tt \frac{14 \times 3}{15 \times 3} + \frac{2 \times 5}{9 \times 5} = \frac{42 + 10}{45} = \frac{52}{45} \\ \\⟹ \tt \frac{52}{45} + \frac{1}{5} \\ = \frac{52 \times 1}{45 \times 1} + \frac{1 \times 9}{5 \times 9} = \frac{52 + 9}{45} = \frac{61}{45} = 1 \frac{16}{45} \)

The correct answer is a. Any time an experiment involves more than one hypothesis test.

The experimentwise alpha level is a concern when conducting multiple hypothesis tests within the same experiment. In such cases, the likelihood of making at least one Type I error (rejecting a true null hypothesis) increases with the number of tests performed. The experimentwise alpha level represents the overall probability of making at least one Type I error across all the hypothesis tests.

When conducting multiple tests, if each individual test is conducted at a significance level of α (e.g., α = 0.05), the experimentwise alpha level increases, potentially leading to an inflated overall Type I error rate. This means there is a higher chance of erroneously rejecting at least one null hypothesis when multiple tests are performed.

To control the experimentwise error rate, various methods can be used, such as the Bonferroni correction, Šidák correction, or the False Discovery Rate (FDR) control procedures. These methods adjust the significance level for individual tests to maintain a desired level of experimentwise error rate.

In summary, the experimentwise alpha level is a concern whenever an experiment involves multiple hypothesis tests to avoid an increased risk of making Type I errors across the entire set of tests.

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Answer:

Part-A: refer to the attachment

Part-B: (10,11)

Part-C: yes

step-by-step explanation:

Part-A:

refer to the attachment

(I used a online graphing calculator to graph the equations which made the work easy)

Part-B:

When two lines share exactly one common point, they are called the intersecting lines and the point is called the point of interception

Looking at the graph,we can understand that the two lines share a common point at (10,11),

hence,

The lines intercept at the point (10,11)

Part C :

well, to find the answer of this part, we can consider doing equality check by substituting the value of the point we got.

The point (10,11) means that the left and right hand side of both of the equations i.e \(\text{y=x+1 and y=-x+21}\) are equal when x and y equal to 10 and 11 respectively.

So let's justify the points:

equation-1:

substitute the value of x and y respectively:

simplify addition:

equation-2:

substitute the value of x and y respectively:

simplify addition:

so,

Yes,the coordinates of the point of intersection satisfy both equations simultaneously

Answer:

h

Step-by-step explanation:

The z-score of 2 for a sample has a mean of 100 and a standard deviation of 6 is 112.

The value that would correspond to the z-score of 2 for a sample with a mean of 100 and standard deviation of 6 can be calculated using the formula for z-score:
z = (x - mean) / standard deviation

In this case, we want to find the value of x that corresponds to a z-score of 2. We can rearrange the formula to solve for x:
x = (z * standard deviation) + mean

Substituting the values given in the question:
x = (2 * 6) + 100
x = 12 + 100
x = 112

Therefore, the value that corresponds to the z-score of 2 for this sample is 112.

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Answer:x=-7+1/2

Step-by-step explanation:You move all terms to the left: x-15/2-(2x)=0

then add all the numbers together, and all the variables:-1x-15/2=0

You multiply all the terms by the denominator:-1x*2-15=0

Multiply elements:-2x-15=0

You move all terms containing x to the left, all other terms to the right-2x=15

x=15/-2

x=-7+1/2