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There is not enough evidence to conclude that the mean is less than 14 hours, as the p-value of the test is greater than 0.05, using the t-distribution.

At the null hypothesis, it is tested if the mean is not less than 14 hours, hence:

[tex]H_0: \mu \geq 14[/tex]

At the alternative hypothesis, it is tested if there is enough evidence that the mean is less than 14 hours, hence:

[tex]H_1: \mu < 14[/tex]

The test statistic is given by the equation presented as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which the parameters are defined as follows:

In the context of this problem, the values of these parameters are:

[tex]\overline{x} = 13.5, \mu = 14, s = 3, n = 64[/tex]

Hence the test statistic is:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{13.5 - 14}{\frac{3}{\sqrt{64}}}[/tex]

t = -1.33.

Using a z-distribution calculator, with a left-tailed test, as we are testing if the mean is less than a value, with t = -1.33 and 64 - 1 = 63 df, the p-value of the test is of 0.094.

Since the p-value of the test is greater than the significance level of 0.05, there is not enough evidence to conclude that the mean is less than 14 hours.

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Answer:

Figure A was translated right 4 units and up 2 units

Probability that S assumes a value between 280 and 320 inclusive is 0.853.

S = Σ[tex]X_{i}[/tex] where  [tex]X_{i}[/tex] has a uniform distribution on 1, 2, 3, 4, 5, with mean 3 and variance (25 – 1)/12 = 2 (result known, or calculated via E[[tex]X^{2}[/tex]] = 11, or from book of formulae, p10, with a = 1, b = 5, h = 1).

So S ~ N(300, 200) approximately.

P(280 ≤ S ≤ 320) = [tex]P(\frac{279.5-300}{\sqrt{200} } < Z < \frac{320.5-300}{\sqrt{200} })[/tex]

                           = [tex]P(-1.450 < Z < 1.450)[/tex]

                           = 0.853.

Hence, probability is 0.853.

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Answer:

------------------------

Correct choice is B.

Answer:

b)  -6

Step-by-step explanation:

The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:

[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]

Given the interval is [-2, 0]:

Substitute the endpoints of the interval into the function and solve:

[tex]\begin{aligned}x=-2 \implies f(-2)&=4\left(\dfrac{1}{2}\right)^{-2}\\& = 4(4)\\&=16\end{aligned}[/tex]

[tex]\begin{aligned}x=0 \implies f(0)&=4\left(\dfrac{1}{2}\right)^{0}\\& = 4(1)\\&=4\end{aligned}[/tex]

Therefore:

[tex]\begin{aligned}\implies\dfrac{f(b)-f(a)}{b-a}&=\dfrac{f(0)-f(-2)}{0-(-2)}\\\\&=\dfrac{4-16}{0+2}\\\\&=\dfrac{-12}{2}\\\\&=-6\end{aligned}[/tex]

The proportional equation between y and x^2 is:

y = 3*x^2

We know that y is directly proportional to x^2, then we can write:

y = k*x^2

Where k is the constant of proportionality.

We also know that when x = 10, the value of y is 300, replacing that in the above equation we get:

300 = k*(10)^2

Now we can solve this for k:

300 = k*100

300/100 = k

3 = k

Then the equation is:

y = 3*x^2

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A sequence of transformations maps ∆ABC to ∆A′B′C′. The sequence of transformations that maps ∆ABC onto ∆A′B′C′ is a reflection across the line x = -3 followed by a reflection across the line y = x.

Given that both triangles are congruent, we can infer or deduce that there were no dilations or contractions. Hence, since we are moving in a clockwise direction, we can submit that this was not a rotation but a reflection.

Hence the first sequence of reflection was such that:

∆ABC reflects onto ∆A′B′C′ across the line x = -3; followed by
a reflection across the line y = x.

Note that in geometry, reflection refers to the mirror image of an image. The line through which an image reflects is called the line of reflection.

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Answer:

19 and 21|

Step-by-step explanation:

a + (a+2) = 40

2a + 2 = 40

2a = 40 - 2

2a = 38

a = 38/2

a = 19

a+2 = 21

Check:

19 + 21 = 40

a ) The required measure of x = 90°

b ) The height of the right angled triangle = = [tex]\sqrt{244}[/tex]

Given is a triangle with measure 15, 20 and 25

a ) Since a perpendicular is dropped from above

the two angles of x are equal because the angle is bisected by an angle bisector

So to check whether the angle x is a right angled or not

we can use the pythagoras theorem and check if the LHS = RHS or not

LHS = 15² + 20² = 225 + 400 = 625

and RHS = 25² = 625

Since LHS = RHS thus the angle is 90 degrees

b ) The height of the right triangle ;

by using the Pythagoras theorem again

12.5² + h² = 20²  { side 25 is bisected = 12.5 }

h² = 400 - 156.25

h = [tex]\sqrt{244}[/tex]

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Answer:

Step-by-step explanation

Answer:

6 students

Step-by-step explanation:

[tex]\frac{1}{5} = \frac{x}{30}[/tex]
[tex]30 = 5x[/tex]
[tex]6=x[/tex]

The given infinite series is divergent.

Given,

[tex]\sum \limits^\infty_{n=1 }{(-1)^{n+1}\frac{3n^2+n+1}{2n^2-1}}[/tex]

it is in the form,

[tex]\sum \limits^\infty_{n=1 }{(-1)^{n+1}\ a_n[/tex]

If the series is convergent then it satisfies,

i)[tex]b_{n+1}\ \leq\ b_n\ for\ all\ n[/tex]

ii)[tex]\lim_{n \to \infty} a_n =0[/tex]

if any of the above condition dissatisfies then the series is divergent

First check the 2nd condition,

[tex]\lim_{n \to \infty}\frac{3n^2+n+1}{2n^2-1}}\\\\= \lim_{n \to \infty}\frac{n^2(3+\frac{1}{n}+\frac{1}{n^2})}{n^2(2-\frac{1}{n^2})}}\\\\=\frac{3+0+0}{2-0}\\\\=\frac{3}{2}[/tex]

Here, [tex]\lim_{n \to \infty} a_n \neq 0[/tex]

Thus, the given series is divergent.

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The value of the function  (f - g)(x) is x² + 3x + 5

A function is defined as a relation between a set of inputs having one output each.

In a simpler terms, a function relates input and output.

Therefore, let's solve the function (f - g)(x)

f(x) =  √16x⁴

g(x) = 3x² - 3x - 5

Therefore,

(f - g)(x) = f(x) - g(x)

(f - g)(x) = √16x⁴ - (3x² - 3x - 5)

(f - g)(x) = √16x⁴ - 3x² + 3x + 5

(f - g)(x) = 4x² - 3x² + 3x + 5

Therefore,

(f - g)(x) = x² + 3x + 5

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⇒[tex]3x^{2} -13x-10\\=3x^{2} -15x+2x-10\\=(3x^{2} -15x)+(2x-10)\\=3x(x-5)+2(x-5)\\=(x-5)(3x+2)[/tex]

⇒The answer is  (x-5)(3x+2)

By solving a linear equation, it can be calculated that

There are 4 guppies in  each family

What is a linear equation?

At first it is important to know about equation.

An equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sigh

A one degree equation is known as linear equation.

Here a linear equation needs to be solved

Let the number of guppies in each family be x

Allison has 2 aquariums.

In each aquarium she has 2 families of guppies and 3 tetras.

Total number of fishes Allison have = 2(2x + 3) = 4x + 6

Leigh has 1 aquarium with 10 tetras and 3 families of guppies.

Total number of fishes Leigh have  = 3x + 10

By the problem,

4x + 6 = 3x + 10

4x - 3x = 10 - 6

x = 4

There are 4 guppies in each family

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The correlation coefficient that is most likely to match a line of best fit of the form y = mx + b for this situation is of:

0.9.

The correlation coefficient is an index that measures correlation between two variables, assuming numeric values between -1 and 1.

If the correlation coefficient is positive, the relation is positive, that is, they are direct proportional. If the correlation coefficient is negative, they are inverse proportional.

If the absolute value of the correlation coefficient is greater than 0.6, the relationship between the two variables is classified as strong.

In the context of this problem, the variables are listed as follows:

The total price increases with the number of bananas bought, and there is a strong positive relationship between these two variables, hence the coefficient should be greater than 0.6 and the correct option is:

0.9.

The problem is given by the image shown at the end of the answer.

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The value of d in the expression, 4d/5+3 = -2-d/5, is -5.

According to the question,

We have the following expression:

4d/5+3 = -2-d/5

Now, moving the terms with the same variables on the left hand side will result in the change of the sign from minus to plus:

4d/5+d/5 -3 = -2

5d/5+3 = -2

d+3 = -2

Now, moving 3 from the left hand side to the right hand side will result in the change of the sign from plus to minus:

d = -2-3

We know that two negative integers are added but the sign before the result remains negative.

d = -5

Hence, the value of d is -5.

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Step-by-step explanation:

so, let's do the multiplications and squaring. and then compare the result with the target.

(x + a)² + b = x² + 2ax + a² + b

and the original expression is

x² - 4x + 19

x² = x² done

2ax = -4x

2a = -4

a = -2

a² + b = 19

(-2)² + b = 19

4 + b = 19

b = 15

so, the result is

(x - 2)² + 15

Answer: (x-2)^2+15

Step-by-step explanation:

Given x^2-4x+19

=here b=-4 and c=19

B=b/2=-4/2=-2

C=c-B^2=19-(-2)^2=19-4-15

so

(x-B)^2+C

(x-2)^2+15

According to the SSS Postulate, two triangles are congruent if three of one triangle's sides are congruent with three of another triangle's sides.

A postulate is an assertion that is not backed by any evidence. Axiom is another name for a postulate. For instance, you would believe Pam if she said that all of her siblings were at least five feet one tall since you are aware of her height and that of all of her siblings, who are all taller than her.

When two figures or objects in geometry have the same shapes, sizes, or are mirror images of one another, they are said to be congruent.

Shapes that are identical to one another are said to be congruent. Both the matching sides and the corresponding angles match. We must examine all of the shapes' angles and sides in order to accomplish this. Two shapes that are similar to one another can be stacked perfectly.

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When quadratic function is subtracted from cubic function, the resultant equation is cubic.

So, It is true.

Function is defined as, In any equation of two variable, we make change in one  accompanied by second.

For example, [tex]F(x)=2x+1[/tex] when we make changes in x , different values of y will obtain.

Quadratic function in which maximum power of variable is two. Similarly, the function which has maximum power on variable is three is called cubic function.

To solve the given problem, let suppose we have,

Quadratic function:[tex]f(x)=x^{2} +x+1[/tex]

Cubic function: [tex]g(x)= x^{3}+x^{2} +x+1[/tex]

According to question,

Subtract quadratic function from cubic function,we get

[tex]g(x)-f(x)=( x^{3}+x^{2}+x+1)-(x^{2} +x+1 )[/tex]

⇒ [tex]h(x)=x^{3} +1[/tex]

It is a cubic function.

Thus, given statement is True.

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Step-by-step explanation:

I assume our task is to find that point of time, when it reaches the highest point.

and the function is

h(t) = -16t² + 96t + 112

well, a maximum or minimum of a curve (function) is found as a zero solution of the first derivative of the function.

given the nature of the function, the extreme point has to be a maximum (the firecracker goes up and then down again).

h'(t) = -32t + 96

we are looking for the zero :

0 = -32t + 96

32t = 96

t = 3 seconds

so, after 3 seconds, the firecracker reaches its highest point, which is at

-16×3² + 96×3 + 112 = -16×9 + 96×3 + 112 =

= -144 + 288 + 112 = 256 ft

FYI - we know for x = 0 (the starting point) the height of the starting window was 112 ft.

Step-by-step explanation:

Andy and Emily each go to a hardware store to buy wire. The table shows the cost y in dollars for x inches of the wire they need. Andy needs 24 feet of the wire. Emily needs 15 yards of the wire. How much will each of them spend for wire?​

Looking at your chart:

cost/length in inches

6/100 = $0.06 per inch

8.1/135 = $0.06 per inch

9.6/160 = $0.06 per inch

10.8/180 = $0.06 per inch

So the rate stays at a constant rate of $0.06 per inch.

Andy needs 24 feet or 288 inches at a constant rate of $0.06 per inch.

= 288 * $0.06  

= $17.28

________________________________

Emily needs 15 yards or 540 inches at a constant rate of $0.06 per inch.

= 540 * $0.06  

= $32.40

Answer: (f+g)(x) = 6x²- 4x + 6

Step-by-step explanation:

We add f(x) and g(x) together, (4x²-5x+8) + (2x²+x-2)

Add like terms together, (4x²+2x²) + (-5x+x) +(8-2)

We are left with (f+g)(x) = 6x²- 4x + 6

The null and alternative hypothesis regarding the test on whether the mean error is of zero is given by the following option:

D. H0: μ = 0 minutes, H1: μ ≠ 0 minutes.

The first step in identifying the hypothesis is to identify the claim tested, given as follows:

The mean prediction error is equals to zero.

At the null hypothesis, it is tested if there is not enough evidence to go against the claim, hence we suppose that the mean is of zero minutes, as follows:

H0: μ = 0 minutes.

At the alternative hypothesis, it is tested if there is enough evidence to reject the null hypothesis, that is, if there is enough evidence to conclude that the mean prediction error is different of zero minutes, hence it is given as follows:

H1: μ ≠ 0 minutes.

Thus option D gives the correct null and alternative hypothesis in the context of this problem.

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