This is a multiple choice question


The area under the standard normal curve corresponding to -0.3 < Z < 1.6 is…?

A. 0.3273
B. 0.4713
C. 0.5631
D. 0.9542

The conclusion that is correct in a two-tailed test at α = .05 is There appears to be no difference in the mean occupancy rates.

From the given values:

Thus, the P-value = 0.1791

Interpret results. Since the P-value (0.1791) is greater than the significance level (0.05), we failed to reject the null hypothesis.

From the above test, we do not have sufficient evidence in favor of the claim that there is a difference in the mean occupancy rates.

Thus, option A is correct.

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so we can say that statement b is also False.The mean of the first distribution is -2, while the mean of the second distribution is 6. As a result, the two normal distributions are not centered at the same place.

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The statement "The two normal distributions have the same spread" is false, and the statement "The two normal distributions are centered at the same place" is false as well.Explanation:Normal Distribution: A normal distribution is a statistical distribution that is symmetric about its mean, showing that data near the mean is more frequent in occurrence than data far from the mean. To describe the distribution of data, it is frequently utilized, and it is frequently utilized in inferential statistics.A normal distribution is defined by two parameters: its mean (μ) and its standard deviation (σ). The mean (μ) is the center of the distribution, while the standard deviation (σ) indicates how spread out the data is from the mean of the distribution.The spread of a distribution is determined by its standard deviation (σ). The standard deviation is the measure of dispersion, which shows how much the data deviates from the mean. As a result, the standard deviation (σ) determines the spread of the normal distribution.Here are the given parameters of the two normal distributions:Distribution 1:Mean = -2Standard deviation = 3.7Distribution 2:Mean = 6Standard deviation = 3.7According to the parameters of the two normal distributions mentioned above, we may deduce that the two normal distributions have the same standard deviation. The spread of the distributions is measured by the standard deviation (σ), therefore we can say that statement a is False.However, the mean of the two normal distributions is not the same, so we can say that statement b is also False.The mean of the first distribution is -2, while the mean of the second distribution is 6. As a result, the two normal distributions are not centered at the same place.

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the point (3/8, -15/8, 0) on the plane z = 4x + 2y + 3 is closest to the origin. To find the point (x, y, z) on the plane z = 4x + 2y + 3 that is closest to the origin, we can use the concept of orthogonal projection.

The closest point will be the point on the plane that is closest to the origin, which is the orthogonal projection of the origin onto the plane.

First, we need to find the normal vector of the plane. The coefficients of x, y, and z in the equation of the plane give us the normal vector. So, the normal vector of the plane is (4, 2, -1).

Next, we need to find the projection of the origin onto the plane. The projection of a vector v onto a plane with normal vector n is given by the formula:

\(proj_n(v) = v - ((v . n) / ||n||^2) * n\)

where "." denotes the dot product, "||n||" denotes the magnitude of the normal vector, and "proj_n(v)" denotes the projection of v onto the plane with normal vector n.

In this case, the vector v is the origin, which is (0, 0, 0), and the normal vector is (4, 2, -1). So, we can calculate the projection of the origin onto the plane as follows:

\(proj_n(v) = (0, 0, 0) - (((0, 0, 0) . (4, 2, -1)) / ||(4, 2, -1)||^2) * (4, 2, -1)\)

= (0, 0, 0) - (0 / 21) * (4, 2, -1)

= (0, 0, 0)

Therefore, the projection of the origin onto the plane is the origin itself.

Finally, we can find the coordinates of the point on the plane that is closest to the origin by setting z = 0 in the equation of the plane:

0 = 4x + 2y + 3

Solving for y, we get:

y = (-2x - 3/2)

So, the coordinates of the point on the plane that is closest to the origin are:

x = 3/8

y = -15/8

z = 0

Therefore, the point (3/8, -15/8, 0) on the plane z = 4x + 2y + 3 is closest to the origin.

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Our assumption that two consecutive elements of the Fibonacci sequence can be divisible by 13 is false, and the proposition is proved.

We begin with the fact that the Fibonacci sequence is an increasing sequence; that is, each element is greater than the one before it.

The sequence is defined as follows:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817, 39088169, 63245986, 102334155, 165580141, 267914296, 433494437, 701408733, 1134903170, 1836311903, and so on.

Now, let us prove the proposition by contradiction. Assume that there are two consecutive elements of the Fibonacci sequence that are divisible by 13. Then there must be some integer n such that:

F(n) = 13m, andF(n + 1) = 13p,

where m and p are integers.

Since the Fibonacci sequence is defined recursively by F(n) = F(n-1) + F(n-2), we can obtain an expression for F(n-2) in terms of F(n) and F(n-1):

F(n-2) = F(n) - F(n-1)Since F(n) and F(n-1) are both divisible by 13, their difference must also be divisible by 13.

Therefore, F(n-2) is divisible by 13 as well. However, this contradicts the well-ordering principle, which states that every non-empty set of positive integers has a least element.

Since the Fibonacci sequence is an increasing sequence, there must be some least element k such that F(k) is divisible by 13 but F(k-1) is not. But this means that F(k-2) cannot be divisible by 13, which contradicts our assumption that both F(n) and F(n-1) are divisible by 13.

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a. To determine the altitude of the rock climber 2 hours after she begins her climb, we substitute t = 2 into the equation for a(t):

a(2) = -10(2)^2 + 60(2) = 80

Therefore, the altitude of the rock climber 2 hours after she begins her climb is 80 meters.

b. To determine the altitude of the rock climber 3 hours after she begins her climb, we substitute t = 3 into the equation for a(t):

a(3) = -10(3)^2 + 60(3) = 90

Therefore, the altitude of the rock climber 3 hours after she begins her climb is 90 meters.

c. To determine the average rate of change of the altitude of the rock climber between 2 and 3 hours after she begins her climb, we need to calculate the difference in altitude over the difference in time:

average rate of change = (a(3) - a(2)) / (3 - 2) = (90 - 80) / 1 = 10

Therefore, the average rate of change of the altitude of the rock climber between 2 and 3 hours after she begins her climb is 10 meters per hour.

d. To determine the instantaneous rate of change of the altitude of the rock climber 3 hours after she begins her climb, we need to take the derivative of the altitude function with respect to time:

a'(t) = -20t + 60

Substituting t = 3, we get:

a'(3) = -20(3) + 60 = 0

Therefore, the instantaneous rate of change of the altitude of the rock climber 3 hours after she begins her climb is 0 meters per hour.

e. The instantaneous rate of change value found in part d) represents the slope of the tangent line to the altitude function at t = 3, which corresponds to the rock climber's velocity at that instant. Since the instantaneous rate of change is 0, this tells us that the rock climber's velocity at that instant is 0, i.e., the rock climber has stopped moving.

Answer:

The answer is B {y | y ≥ –8}

Step-by-step explanation:

I just did it

Answer:

(B) {y | y ≥ –8}

Step-by-step explanation:

On a coordinate plane, an absolute value graph has a vertex at (6, negative 8).

The function g(x) = |x – 6| – 8 is graphed. What is the range?

{y | y > –8}

{y | y ≥ –8}

{y | y < –8}

{y | y is all real numbers}

Answer:

Each small truck can hold a total of 110 boxes.

Step-by-step explanation:

It says three small delivery trucks can hold 330. That meant all three together. So you just have to do 330 divided by 3 and you get 110. So that's the number of boxes ONE small truck can hold. Also, If u do it backward, 3 x 110 =330.

Rafael is fertilizing his garden. The garden is in the shape of a rectangle. Its length is 16 feet and its width is 13 feet. Suppose each bag of fertilizer covers 26 square feet. How many bags will he need to cover the garden?​

step 1

Find the area of the garden

Remember that the area of a rectangle is equal to

A=L*W

we have

L=16 ft

W=13 ft

substitute

A=16*13

A=208 ft^2

step 2

we know that

each bag of fertilizer covers 26 square feet

so

Applying proportion

1/26=x/208

solve for x

x ----> number of bags

x=(1/26)*208

x=8 bags

therefore

Every polynomial function of odd degree with real coefficients will have at least one real root or zero.

This statement is known as the Fundamental Theorem of Algebra. It states that a polynomial of degree n, where n is a positive odd integer, will have at least one real root or zero.

The reason behind this is that when a polynomial of odd degree is graphed, it exhibits behavior where the graph crosses the x-axis at least once. This implies the existence of at least one real root.

For example, a polynomial function of degree 3 (cubic polynomial) with real coefficients will always have at least one real root. Similarly, a polynomial function of degree 5 (quintic polynomial) with real coefficients will also have at least one real root.

It's important to note that while a polynomial of odd degree is guaranteed to have at least one real root, it may also have additional complex roots.

The Fundamental Theorem of Algebra ensures the existence of at least one real root but does not specify the total number of roots.

In summary, every polynomial function of odd degree with real coefficients will have at least one real root or zero, as guaranteed by the Fundamental Theorem of Algebra.

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The lateral area of this regular pentagonal pyramid is 210 in².

In Mathematics and Geometry, the lateral surface area of a rectangular prism can be calculated and determined by using this mathematical equation or formula:

LSA = 2(LH + LW + WH)

Where:

Similarly, the lateral area of a regular pentagonal pyramid can be calculated by using this mathematical equation or formula:

Lateral area = 5/2 × base edge × slant height

Lateral area = 5/2 × 6 × 14

Lateral area = 5 × 3 × 14

Lateral area = 210 in².

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Answer:

Step-by-step explanation:

34.79

Triangles

Looking at the image, It is safe to say there are two similar triangles having similar base and sides there.

Triangle BAC has the same base as Triangle DAC

Therefore, the vertices of the angle B is equivalent to the vertice of angle D

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Answer:

If 3 brownies require 3/4 cups of flour, then 12 brownies will require 12/3*(3/4) = 3 cups of flour.

Step-by-step explanation:

Answer:

3 cups of flour

Step-by-step explanation:

We know

3/4 cups of flour = 3 brownies

? = 12 brownies

12 brownies are 4 times 3 brownies, so we take 3/4 cups of flour times 4

3/4 times 4 = 3 cups of flour

So, you need 3 cups of flour for 12 brownies

Answer:

6 early-admission tickets.

Step-by-step explanation:

20% / 100 = 0.2 ; Dividing a percentage by 100 will give you its actual value, instead of the percentage.

0.20 x 30 tickets = 6 early-admission tickets. ; What we're saying here is that since 0.20 and 20% are the same, we can figure out what 20% of 30 is, which is 6.

Answer:

1/2 ; 1/4

Step-by-step explanation:

Number of cards in a deck = 52

Number of red cards = 26

Number of spades = 13

Probability of event A :

P(A) = required outcome / Total possible outcomes

P( red card) = number of red cards / total cards in deck

P(red card) = 26 / 52 = 1/2

P(spade) = number of spades / total cards in deck

P(red card) = 13 / 52 = 1 / 4

A sample size of 329 would be required to be 99% confident that the estimated proportion of women-owned businesses not providing employee benefits is within 6 percentage points of the true population proportion.

To calculate the required sample size, we can use the formula:

n = (\(z^2\) * p * q) /\(e^2\)

where n is the sample size, z is the z-score corresponding to the desired level of confidence (in this case, 2.576 for 99% confidence), p is the estimated population proportion (0.165, based on the NWBC's finding), q is 1-p, and e is the maximum error we want to tolerate (in this case, 0.06 or 6 percentage points).

Substituting the values, we get:

n = (2.576^2 * 0.165 * 0.835) / \(0.06^2\)

Solving for n, we get:

n ≈ 329

Therefore, a sample size of 329 would be required to be 99% confident that the estimated proportion of women-owned businesses not providing employee benefits is within 6 percentage points of the true population proportion. Note that this assumes a simple random sample and that the population size is much larger than the sample size, so the finite population correction is not needed.

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Answer:

None of them.

Step-by-step explanation:

Each and every straight line is of one kind in terms of its pattern: it can be presented in the view of \(y = kx + b\): \(k\) is the slope or gradient of the line, \(b\) is the y-intercept of the line. I will not let the cat out of the bag if I say that any parallel lines do not intersect one another, hence they should have the same value of coefficient \(k\).

\(2x + 4y = 16 \Leftrightarrow x + 2y = 8 \Leftrightarrow 2y = -x + 8 \Leftrightarrow y = - \frac{1}{2}x + 4\)

Therefore, our line has \(k = - \frac{1}{2}\) and \(b = 4\) coefficients.

(A) \(k = 2, b = 5;\)

(B) \(k = -1, b = 4;\)

(С) \(k = -1, b = 8;\)

(D) \(k = 2, b = 5;\)

Recapitulating this: none of them have the same coefficient \(k\), thus none of them suit us.

Answer:you put the equations together then add the x’s and 20+10 together then subtract 30 from 10 so it should be -20

Step-by-step explanation:

The inequality to represent the possible number of hours Kat can afford to book the DJ is 80x + 225 ≤ 970 and one possible length Kat can afford to book the DJ is 9 hours.

(a) Let x be the number of hours that Kat can book the DJ. Then, the total cost of the DJ is 80x, and the total cost of the party is 80x + 225.

Since Kat has $410 saved and will earn another $560, the total amount she can spend on the party is $410 + $560 = $970.

Therefore, we can write the following inequality to represent the possible number of hours Kat can afford to book the DJ:

80x + 225 ≤ 970

b) To solve for x, we can start by subtracting 225 from both sides of the inequality:

80x ≤ 745

Then, we can divide both sides by 80:

x ≤ 9.3125

Since Kat can only book the DJ in whole hours, the largest integer less than or equal to 9.3125 is 9. Therefore, one possible length Kat can afford to book the DJ is 9 hours.

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Step-by-step explanation:

\( \frac{r - p}{7} = s \\ cross \: multiply \\ 7s = r - p \\ \: \: move \: the \: variable \: to \: the \: \\ right \\ - p = 7s - r \\ change \: the \: signs \\ p = - 7s + r \\ p = r - 7s\)

Answer:

p= -7S+r

Step-by-step explanation:

p=-7S+r ( gotta write at least 20 characters)

Answer:

6120

Step-by-step explanation:

i)

15/100 × 7200

=1080 ( the amount of discount based on the marked prize )

ii) 7200-1080=6120

In summary, the composition of two functions, f ∘ g, combines the outputs of the function g as inputs to the function f.

The composition of two functions, f ∘ g, is a new function that is formed by applying the output of the function g as the input of the function f.

To find the composition of f ∘ g, follow these steps:

1. Start with the function g(x) and evaluate it for a given input value, let's call it 'a'. This will give you g(a).
2. Take the output g(a) and use it as the input for the function f(x). Evaluate f(x) with this input value to get f(g(a)).
3. The final result f(g(a)) is the value of the composition of the two functions f ∘ g at the input 'a'.

In terms of composition notation, f ∘ g is read as "f composed with g" or "f of g". It represents the order in which the functions are applied: g is applied first, and then f is applied to the result of g.

In summary, the composition of two functions, f ∘ g, combines the outputs of the function g as inputs to the function f.

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Step-by-step explanation:

Since the number of days for classes is 20 and the total days in November is 30

% = Number of days for classes

_____________________ *100

Total days in November

% = 20/30 *100

% = 66.7%(approximately)

Answer:

Step-by-step explanation:

The degrees around a point = 360, so

1. x + 95 + 3y + 80 = 360 so

2. x + 3y = 185

3. 65 + 3y = 185 and

3y = 120 so

y = 40

Answer:

y=40

Step-by-step explanation:

sum of all 3 angles : 240

3y+240=360

3y=360-240=120

y=3÷120

y=40

The level of scale of measurements is the ratio scale for the data of the average weight of newborn babies in ounces.

There are four scales of measurement: Nominal, Ordinal, Interval, and Ratio.

Nominal scale: In this scale, categories are nominated names (hence “nominal”). There is no inherent order between categories. Put simply, one cannot say that a particular category is superior/ better than another.

Ordinal scale:  The various categories can be logically arranged in a meaningful order. However, the difference between the categories is not “meaningful”.

Interval scale:  The values (not categories) can be ordered and have a meaningful difference, but doubling is not meaningful. This is because of the absence of an “absolute zero”.

Ratio scale:  The values can be ordered to have a meaningful difference, and doubling is also meaningful. There is an “absolute zero”.

Therefore, the level of scale of measurements is the ratio scale for the data of average weight of newborn babies in ounces.

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To find the unit vector that points in the same direction as the vector A + 2B, we first calculate the vector A + 2B and then divide it by its magnitude to obtain the unit vector. The unit vector that points in the same direction as A + 2B is (14/15)i^ - (4/9)j^.

The vector A = 12i^ + 14j^ and the vector B = 15i^ - 17j^ are given.

To find the vector A + 2B, we perform the vector addition by adding the corresponding components: A + 2B = (12i^ + 14j^) + 2(15i^ - 17j^).

Simplifying, we get A + 2B = 12i^ + 14j^ + 30i^ - 34j^ = (12 + 30)i^ + (14 - 34)j^ = 42i^ - 20j^.

Next, we calculate the magnitude of the vector A + 2B using the formula: |A + 2B| = √((42)^2 + (-20)^2) = √(1764 + 400) = √2164 ≈ 46.5.

To find the unit vector in the same direction as A + 2B, we divide the vector A + 2B by its magnitude: (42i^ - 20j^) / 46.5.

Dividing each component by 46.5, we get the unit vector: (42/46.5)i^ - (20/46.5)j^.

Simplifying the fractions, we have: (14/15)i^ - (4/9)j^.

Therefore, the unit vector that points in the same direction as A + 2B is (14/15)i^ - (4/9)j^.

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Answer:

8.125 Litres

Step-by-step explanation:

Given:

Initial volume of hand sanitizer in the storage = 12 litres

Volume of dispensers:

350 ml

600 ml

475 ml

580 ml

650 ml

720 ml and

500 ml

To find:

Volume of sanitizer left after filling all the dispensers = ?

Solution:

The volume of sanitizer left can be calculated by subtracting sum of volumes of all the dispensers from the Initial total volume of the storage cabinet.

First of all, let us convert them into the same units i.e. litres.

We know that 1 Litre = 1000 ml

So,

350 ml = 0.350 Litres

600 ml = 0.600 Litres

475 ml = 0.475 Litres

580 ml = 0.580 Litres

650 ml = 0.650 Litres

720 ml = 0.720 Litres

500 ml = 0.500 Litres

Total volume of dispensers = 0.350 + 0.600 + 0.475 + 0.580 + 0.650 + 0.720 + 0.500 = 3.875 Litres

Let us subtract the total volume of dispensers from the initial volume of storage cabinet to find the volume remaining the storage cabinet.

Volume that remain in the storage cabinet = 12 - 3.875 = 8.125 Litres