A sample of 68 electric motors had a mean efficiency of 0.595 (assume that the standard deviation is known to be 0.05). Let μ represent the mean efficiency of electric motors of this type.


Find the P-value for testing H0 : μ ≥ 0.6 versus H1 : μ < 0.6.



P-value =

Answer:

The distance should be [tex]3\sqrt{13[/tex]

Step-by-step explanation:

Distance formula

Answer:

o37%

Step-by-step explanation:

3/8 is 37%, 4/8 is 50% because it's half full, for eights just go up 13, or subtract 13, it's a little hard for me to explain, sorry

Linearization is the idea in calculus where if you zoom in really close onto a section of the graph, the curve and the tangent line will be extremely similar to each other.

We can use this idea and approximate nearby values to the tangent line.

The parent graph of a square root function is [tex]f(x)=\sqrt{x}[/tex].

There are two methods in which we can calculate the approximate value of [tex]\sqrt{101}[/tex] by using linearization techniques.

Let's use the nearest perfect square to [tex]\sqrt{101}[/tex], which is [tex]\sqrt{100}[/tex]. When drawing the graph of the square root function, we use the point (100, 10) because where x = 100, y = 10 on a square root function.

Now, we have a point that the tangent line passes through, and we want to find the slope.

We can do so by taking the derivative of [tex]f(x) =\sqrt{x}[/tex].

Plug in x = 100 to find the slope of the tangent line here.

The slope of the tangent line at x = 100 is 1/20. Now, we can use the point and the slope of the tangent line to determine the equation for the tangent line.

(100, 10), m = 1/20

Point-slope equation:

To find the value of y at x = 101, plug this into the tangent line equation.

201/20 is equal to 10.05. Let's estimate the error of this calculation to the actual value of [tex]\sqrt{101}[/tex], inputted into a calculator.

We get [tex]\sqrt{101}=10.04987562[/tex], which is extremely close to 10.05. Our estimate using linearization only has an error of 0.00012.

You may have noticed that the first method uses little calculus, apart from taking the derivative of f(x).

The more "calculus-y" method involves finding the change in y in terms of the change of x.

We know that dy/dx is the the change in y due to a change in x, so we can use this to find the change in y when x = 101.

Solve for dy by mutliplying dx to both sides of the equation.

The change in x is 1, because 101 - 100 = 1.

We want to find the change in y when x = 100, and has a change of 1. Therefore, we have:

Plug these values into the equation [tex]dy=\frac{1}{2\sqrt{x} } \cdot dx[/tex] and solve for dy.

The change in y when x = 100 with a change of 1 is 1/20. We know when x = 100 the y-value is 10. Therefore, when x = 101, the change in y is 1/20, so y = [tex]10\frac{1}{20} = \frac{201}{20} = 10.05[/tex].

You can see that we get the same answer with either method.

Answer:4

Step-by-step explanation:

Answer:

-5/3

Step-by-step explanation:

10-15=-5

6-3=3

Answer:

-5/3

Step-by-step explanation:

m=y2-y1/x2-x1

10-15-(-5)

6-3=3

-5/3

hope this helped :3

sorry if it is wrong

Answer:

Step-by-step explanation:

If y= -5 when x= -20  that means x is 4 times y

y=  8.75  when x= 35

Answer:

Our equation is:

[tex]\displaystyle y=-\frac{1}{4}x[/tex]

When x=35, y=-35/4 or -8.75.

Step-by-step explanation:

We know that y varies directly with x.

The standard equation is:

[tex]y=kx[/tex]

We know that y is 5 when x is -20.

So, let’s substitute 5 for y and -20 for x and solve for k, our constant of variation. So:

[tex]5=k(-20)[/tex]

Divide both sides by -20:

[tex]\displaystyle k=-\frac{1}{4}[/tex]

Therefore, our constant of variation is -1/4.

Hence, our equation is:

[tex]\displaystyle y=-\frac{1}{4}x[/tex]

To find y when x=35, let’s substitute 35 for x. So:

[tex]\displaystyle y=-\frac{1}{4}(35)=-\frac{35}{4}=-8.75[/tex]

So, when x=35, y=-8.75.

Answer:

Colour ---- Probability

Blue ----- 0.2

Red ------- 0.4

Yellow ------ 0.4

Step-by-step explanation:

Given

Colour ---- Probability

Blue ----- 0.2

Red -------

Yellow ------

Required

Complete the table

In probability, all probabilities add up to 1.

i.e.

[tex]P(Blue) + P(Red) + P(Yellow) = 1[/tex]

Substitute 0.2 for P(Blue)

[tex]0.2 + P(Red) + P(Yellow) = 1[/tex]

[tex]P(Red) + P(Yellow) = 1 - 0.2[/tex]

[tex]P(Red) + P(Yellow) = 0.8[/tex]

From the question, we understand that the frequency of yellow and red balls are the same.

Hence:

[tex]P(Red) = P(Yellow)[/tex]

[tex]P(Red) + P(Yellow) = 0.8[/tex] becomes

[tex]P(Red) + P(Red) = 0.8[/tex]

[tex]2P(Red) = 0.8[/tex]

Make P(Red) the subject

[tex]P(Red) = 0.4[/tex]

Recall that:

[tex]P(Red) = P(Yellow)[/tex]

Hence,

[tex]P(Yellow) = 0.4[/tex]

So, the complete table is:

Colour ---- Probability

Blue ----- 0.2

Red ------- 0.4

Yellow ------ 0.4

Answer:

16

Step-by-step explanation:

i would try but not 100% sure

Answer:

You would have to rent 10 movies for the cost to be the same.

Step-by-step explanation:

20+1.5x=3.5x

-1.5x on both sides

20=2x

x=10

Answer:

You would have to rent 8 movies at the first store and 10 movies at the second

Step-by-step explanation:

Answer:

It travels 530 more miles on the first trip than the second trip and travels 469 more miles on the first trip than the third trip.

Step-by-step explanation:

Take 872-342=530 so then that's your answer to the first part of the question, now do the same thing just plug in the different numbers: 872-403=469

Answer:

$1226.78<x<$1301.22

Step-by-step explanation:

The formula for calculating confidence interval is expressed as;

CI = xbar ± z×(s/√n)

Given

Mean (xbar) = $1264

z is the z score at 90% CI = 1.645

s is the standard deviation = $150

n is the sample size = 44

Substitute

CI = 1264±1.645(150/√44)

CI = 1264±1.645(150/6.63)

CI = 1264±1.645(22.624)

CI = 1264±37.22

CI = (1264-37.22, 1264+37.22)

CI = (1226.78, 1301.22)

Hence the confidence interval of the mean is $1226.78<x<$1301.22

Answer:

The answer is B, or the second one

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Sam should have bought 3.09 yards of fabric instead of 2.4 yards

So, Option D is correct.

Step-by-step explanation:

Total fabric needed by Sam = 2.75

According to directions on a sewing pattern they say to buy an extra 12.5%

So, extra fabric would be: 12.5% of 2.75

Solving

Now adding 0.343 into 2.75 to get extra fabric quantity:

2.75+0.343

=3.09

Therefore Sam should have bought 3.09 yards of fabric instead of 2.4 yards

So, Option D is correct.

Answer:

3rd option.) 1/8a^12

Step-by-step explanation:

(2a⁴)^-3

=1/(2a⁴)³

=1/8a^12

Answer: The next one is 3. 7/2v^2

Step-by-step explanation: In case you needed help with that

Answer:

P(t) = 1000e^(0.01155)t

Step-by-step explanation:

Let the population of barangay be expressed according to the exponential formula;

P(t) = P0e^kt

P(t) is the population of the country after t years

P0 is the initial population

t is the time

If barangay has 1000 initially, this means that P0 = 1000

If the population doubles after 60years then;

at t = 60, P(t) = 2P0

Substitute into the formula

2P0 = P0e^k(60)

2 = e^60k

Apply ln to both sides

ln2 = lne^60k

ln2 = 60k

k = ln2/60

k = 0.01155

Substitute k = 0.01155 and P0 into the expression

P(t) = 1000e^(0.01155)t

Hence an exponential model for barangay's population is

P(t) = 1000e^(0.01155)t

Answer:m∠11 = 11x

m∠13 = 10x + 12

Step-by-step explanation:

m∠11 = 11x

m∠13 = 10x + 12

Given:

Fixed cost = $3,450

Variable cost = $12 per basketball

Selling price = $25 per basketball

Number of basketball sold = 300

To find:

Whether Rebotar did break even.

Solution:

According to the question,

Cost of 1 basketball = $12

Cost of 300 basketball = $12×300

We know that,

Total cost = Fixed cost + Variable cost

[tex]TC=3450+12(300)[/tex]

[tex]TC=3450+3600[/tex]

[tex]TC=7050[/tex]

So, the total cost is $7050.

Now,

Selling price of a basketball = $25

Selling price of 300 basketball = $25×300

Total revenue is

[tex]TR=25\times 300[/tex]

[tex]TR=7500[/tex]

So, total revenue is $7500.

At break even situation the profit is zero. In other words, the total revenue is equal to total cost.

Since, [tex]TC\neq TR[/tex], therefore, Rebotar did not break even.

Answer:

Since the profit is positive, Rebotar not only broke even, they had earnings.

Step-by-step explanation:

Function Modeling

The costs, incomes, and profits of Rebotar Inc. can be modeled by means of the appropriate function according to known conditions of the market.

It's known their fixed costs are $3,450 and their variable costs are $12 per basketball produced and sold. Thus, the total cost of Rebotar is:

C(x) = 12x + 3,450

Where x is the number of basketballs sold.

It's also known each basketball is sold at $25, thus the revenue (income) function is:

R(x) = 25x

The profit function is the difference between the costs and revenue:

P(x) = 25x - (12x + 3,450)

Operating:

P(x) = 25x - 12x - 3,450

P(x) = 13x - 3,450

If x=300 basketballs are sold, the profits are:

P(300) = 13(300) - 3,450

P(300) = 3,900 - 3,450

P(300) = 450

Since the profit is positive, Rebotar not only broke even, they had earnings.

Answer:

Slope, [tex]m=\dfrac{1}{5}[/tex]

Step-by-step explanation:

It is given that,

A road rises 20 feet for every 100 feet in horizontal distance.

Rise (vertical distance) = 20 feet

Run (horizontal distance) = 100 feet

Slope of the road is given by the ratio of rise to the run. It can be calculated as :

[tex]m=\dfrac{20}{100}\\\\=\dfrac{1}{5}[/tex]

So, the slope is [tex]\dfrac{1}{5}[/tex].

Answer:

0.9 or 90%

Step-by-step explanation:

The probability of shot is 47%

The probability of no shot is 100 -47 = 53%

The dot plot is made from the 10 repeated shots which recorded 25 scores.

The number of dots on the fifth tick is 9 of 10 shots

therefore; 9/10 = 0.9, which 90 in percentage.    

The approximate probability that a 47% shooter makes 5 or more shots in 10 attempts [tex]\dfrac{12}{25}[/tex] or 0.48.

Given information:

A basketball player claims to make 47% of her shots from the field.

It s required to simulate the player taking sets of 10 shots, assuming that her claim is true. Twenty-five repetitions of the simulation were performed.

The dot plot shows the simulated number of makes in each set of 10 shots.

The dots in the 5 shot mark is 9, that in 6 shot mark is 2 and that in 7 shot mark is 1.

So, the approximate probability that a 47% shooter makes 5 or more shots in 10 attempts can be calculated as,

[tex]P(x\geq5)=\dfrac{9+2+1}{30}\\=\dfrac{12}{25}[/tex]

Therefore, the approximate probability that a 47% shooter makes 5 or more shots in 10 attempts [tex]\dfrac{12}{25}[/tex] or 0.48.

For more details, refer to the link:

https://brainly.com/question/11740746

Answer:

Step-by-step explanation:

- 2 ≤ x ≤ 1

x ∈ [ - 2 , 1 ]

Answer:

How we will solve:

- 2 ≤ x ≤ 1

x ∈ [ - 2 , 1 ]

Answer:

Sometimes you have to think a little out of order to do this type of problem.... but here goes an explanation.

Step-by-step explanation:

8 is less than looks like this:        8 <

6 more than looks like this:          +6

3 times a number x is:                 3x

So

8 < 3x+6 meets the criteria

The inequality will be 8 < 3x+6 if the 8 is less than 6 more than 3 times a number x; the answer is 8 < 3x+6.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

It is given that:

The sentence as an inequality 8 is less than 6 more than 3 times a number x:

From the question:

Here x is any real number:

The inequality will be:

8 < 3x+6 which represents 8 is less than 6 more than 3 times a number x

Thus, the inequality will be 8 < 3x+6 if the 8 is less than 6 more than 3 times a number x; the answer is 8 < 3x+6.

Learn more about inequality here:

brainly.com/question/19491153

#SPJ2

Answer:

Step-by-step explanation:

Using the sample size formula

n= (zs/e)²

z is the z score at 99% = 2.58

s is the standard deviation = 250

e is the sample mean = 50

Substitute

n = (2.58×250/50)²

n = (2.58×5)²

n = (12.9)²

n=166.41

hence the sample size is 166.41

Answer: [tex]y=-x-5[/tex]

Step-by-step explanation:

Slope intercept form is [tex]y=mx+b[/tex], so we have to find a way to substitute the given information into the equation. We have [tex]m[/tex] because it gives us the slope.  The slope is -1, as the directions state. Now, we substitute it in and solve for b:

After getting the y-intercept, you have the full equation!

Answer:

$2025

Step-by-step explanation:

Hope that helps!

Answer:

The expected number of boys a family might have is 2.5.

Step-by-step explanation:

Let X denote the number of boys in a family with 5 children.

The probability of a boy is, p = 0.50.

The child can either be a by or a girl independently.

The random variable X follows a binomial distribution with parameters n = 5 and p = 0.50.

The probability mass function is:

[tex]p_{X}(x)={5\choose x}(0.50)^{x}(1-0.50)^{5-x};\ x=0,1,2...5[/tex]

Compute the expected number of boys a family might have as follows:

[tex]E(X)=\sum x\cdot p_{X}(x)[/tex]

x                                      p (x)                                           x · p (x)

0       [tex]p(0)={5\choose 0}(0.50)^{0}(1-0.50)^{5-0}=0.03125[/tex]          [tex]0\times 0.03125=0[/tex]

1        [tex]p(1)={5\choose 1}(0.50)^{1}(1-0.50)^{5-1}=0.15625[/tex]          [tex]1\times 0.15625=0.15625[/tex]

2       [tex]p(2)={5\choose 2}(0.50)^{2}(1-0.50)^{5-2}=0.3125[/tex]           [tex]2\times 0.3125=0.625[/tex]

3       [tex]p(3)={5\choose 3}(0.50)^{3}(1-0.50)^{5-3}=0.3125[/tex]           [tex]3\times 0.3125=0.9375[/tex]

4       [tex]p(4)={5\choose 4}(0.50)^{4}(1-0.50)^{5-4}=0.15625[/tex]         [tex]4\times 0.15625=0.625[/tex]

5       [tex]p(5)={5\choose 5}(0.50)^{5}(1-0.50)^{5-5}=0.03125[/tex]         [tex]5\times 0.03125=0.15625[/tex]

Then,

[tex]E(X)=\sum x\cdot p_{X}(x)[/tex]

         [tex]=0+0.15625+0.625+0.9375+0.625+0.15625\\\\=2.5[/tex]

Thus, the expected number of boys a family might have is 2.5.

Answer:

A C E F

Step-by-step explanation:

Answer:

A, C, E, and F.

Answer:

The value of x is 4

Step-by-step explanation:

In a right triangle, if a segment is drawn from the right angle ⊥ to the hypotenuse like the given figure, then

∵ The length of one side of the right triangle = (x + 2)

∵ The length of the hypotenuse = x + 5

∴ (x + 2)² = x (x + 5)

∵ (x + 2)² = (x + 2)(x + 2)

∴ (x + 2)(x + 2) = x(x + 5)

→ Simplify the two sides

∵ (x)(x) + (x)(2) + (2)(x) + (2)(2) = (x)(x) + (x)(5)

∴ x² + 2x + 2x + 4 = x² + 5x

→ Add the like terms in the left side

∴ x² + 4x + 4 = x² + 5x

→ Subtract x² from both sides

∵ x² - x² + 4x + 4 = x² - x² + 5x

∴ 4x + 4 = 5x

→ Subtract 4x from both sides

∴ 4x - 4x + 4 = 5x - 4x

∴ 4 = x

∴ The value of x is 4

Answer:

y=2

Step-by-step explanation:

the image and preimage are 6 units apart so thhe line of reflection is in the middle at 3 units and is a line that is paralel to the x-axis

y=2