Trucks in a delivery fleet travel a mean of 100 miles per day with a standard deviation of 23 miles per day. The mileage per day is distributed normally. Find the probability that a truck drives between 86 and 125 miles in a day. Round your answer to four decimal places.

Answer:

[tex]x = 9\ or\ x = 1[/tex]

Step-by-step explanation:

Given

[tex]x = 5 + \sqrt{16}[/tex]

Required

Find the value of x

[tex]x = 5 + \sqrt{16}[/tex]

We start by taking the square root of 16; Square root of 16 is +4 or -4; So, we have:-

[tex]x = 5 \±4[/tex]

The expression above can be split into two; This is as follows

[tex]x = 5 + 4\ or\ x = 5 - 4[/tex]

[tex]x = 9\ or\ x = 1[/tex]

Hence, the solution to [tex]x = 5 + \sqrt{16}[/tex] is B. 1 and C. 9

Answer:

its b and c

Step-by-step explanation:

the guy who answered first said so

also i just did it

u/4 - 4 = -20

Add 4 to both sides:

u/4 = -16

Multiply both sides by 4:

u = -64

Answer:

u=-64

Step-by-step explanation:

u/4 -4 = -20

First add 4 to both sides.

u/4=-16

Now multiply both sides by 4

u=-64

Answer:

15

Step-by-step explanation:

PEMDAS

3x3 = 9

3+3 = 6

9+6 = 15

By the BODMAS rule we get, 3 + 3 × 3 + 3 =​ 15

The acronym BODMAS rule is used to keep track of the right sequence of operations to do when solving mathematical issues. Brackets (B), order of powers or roots (O), division (D), multiplication (M), addition (A), and subtraction (S) are all represented by this acronym (S).

3 + 3 × 3 + 3 =​

3 × 3 = 9

3 + 9 + 3 = 15.

Therefore, the correct answer is 15.

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Answer:

a) 26.33 kg/d and 29.67 kg/d

b) 94.5%

Step-by-step explanation:

a. Find a 99% confidence interval for the true mean milk production.

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{1-0.99}{2} = 0.005[/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]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/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.

[tex]M = 2.575*\frac{2.25}{\sqrt{12}} = 1.67[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 28 - 1.67 = 26.33 kg/d

The upper end of the interval is the sample mean added to M. So it is 28 + 1.67 = 29.67 kg/d

The 99% confidence interval for the true mean milk production is between 26.33 kg/d and 29.67 kg/d

b. If the farms want the confidence interval to be no wider than ± 1.25 kg/d, what level of confidence would they need to use?

We need to find z initially, when M = 1.25.

[tex]M = z*\frac{2.25}{\sqrt{12}} = 1.67[/tex]

[tex]1.25 = z*\frac{2.25}{\sqrt{12}} = 1.67[/tex]

[tex]2.25z = 1.25\sqrt{12}[/tex]

[tex]z = \frac{1.25\sqrt{12}}{2.25}[/tex]

[tex]z = 1.92[/tex]

When [tex]z = 1.92[/tex], it has a pvalue of 0.9725.

1 - 2*(1 - 0.9725) = 0.945

So we should use a confidence level of 94.5%.

Answer:

No

Step-by-step explanation:

If they were opposite, they would be equal.

But they are not, (on one of the spaces in between them is smaller and one is larger.)

Hope I have helped you, since it seems I haven't helped "other people" the last time :/

Answer:

No

Step-by-step explanation:

Answer:

A 95% confidence interval for the mean number of chips in a bag of Chips Ahoy Cookies is [1187.96, 1288.44].

Step-by-step explanation:

We are given that statistics students at the Air Force Academy (no kidding) purchased some randomly selected bags of cookies and counted the chocolate chips.

Some of their data are given below; 1219, 1214, 1087, 1200, 1419, 1121, 1325, 1345, 1244, 1258, 1356, 1132, 1191, 1270, 1295, 1135.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                          P.Q.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean number of chocolate chips = [tex]\frac{\sum X}{n}[/tex] = 1238.2

            s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex]  = 94.3

            n = sample of car drivers = 16

            [tex]\mu[/tex] = population mean number of chips in a bag

Here for constructing a 95% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.

So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-2.131 < [tex]t_1_5[/tex] < 2.131) = 0.95  {As the critical value of t at 15 degrees of

                                             freedom are -2.131 & 2.131 with P = 2.5%}  

P(-2.131 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.131) = 0.95

P( [tex]-2.131 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]2.131 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

P( [tex]\bar X-2.131 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.131 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.131 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.131 \times {\frac{s}{\sqrt{n} } }[/tex] ]

                                   = [ [tex]1238.2-2.131 \times {\frac{94.3}{\sqrt{16} } }[/tex] , [tex]1238.2+2.131 \times {\frac{94.3}{\sqrt{16} } }[/tex] ]

                                   = [1187.96, 1288.44]

Therefore, a 95% confidence interval for the mean number of chips in a bag of Chips Ahoy Cookies is [1187.96, 1288.44].

The greatest number is 6.23 times 10 superscript 12.

The number is written in the form [tex]a \times 10^b[/tex] where we have [tex]1 \leq a < 10[/tex]

The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10. We can for a time, ignore the value of 'a' for two comparable quantities and only compare their orders(this type of comparison is useful when difference is too big, like size of human to size of a star etc sort of comparisons).

We are given that the number so;

A.6.23 x 10^12 is equivalent to rolling the decimal 12 times to the right.

B.6.23 x 10^8 is equivalent to rolling the decimal 8 times to the right.

C.6.23 x 10^-6 is equivalent to rolling the decimal 6 times to the left.

D.6.23 x 10^3 is equivalent to rolling the decimal 3 times to the right.

This shows the 10 has been multiplied by itself thrice.

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Answer:

First, you can graph the y-intercept. The y-intercept would be (0,3) or in your equation, the number 3. Next, you could create a table by substituting values for x such as 1, 2, 3, or 4. This will give you easy numbers to graph. Instead of creating a table, perhaps you want to graph this by plotting the slope. Since the slope is 3/2, is means that it is going up, because the number is positive. An easy way to start would be starting at your y-intercept, (0,3), you could go two to the right and three up. That is a point. Then you could go the way down; two to the left and three down. Finally, you can draw a line connecting the points together.

I hope this helped you! Have a great rest of your day!

Answer:  x = -10

Step-by-step explanation:

see image

A) congruent sides implies congruent angles A = 64°

B) Use the Triangle Sum Theorem: 64° + 64° + B = 180° --> B = 52°

C) B and C are complimentary angles: 52° + C = 90°  --> C = 38°

D) Use the Triangle Sum Theorem knowing that congruent sides implies congruent angles: 38° + 2D = 180°  --> D = 71°

∠2) D and ∠2 are supplementary angles: 71° + ∠2 = 180°  --> ∠2 = 109°

Solve for x:

109° = x + 119

 -10  = x

Answer:

x = -10

Step-by-step explanation:

Find the measure of angle m∠2

The triangles are isosceles triangles, the base angles are equal.

The other base angle is also 64°.

Using Triangle Sum Theorem.

64 + 64 + y = 180

y = 52

The top angle is 52°.

The whole angle is 90°.

90 - 52 = 38

The second triangle has base angles equal.

Using Triangle Sum Theorem.

38 + z + z = 180

z = 71

The two base angles are 71°.

Angles on a straight line add up to 180°.

71 + m∠2 = 180

m∠2 = 109

The measure of m∠2 is 109°

Find the value of x

m∠2 = x + 119

109 = x + 119

x = 109 - 119

x = -10

Answer:

3.025

Step-by-step explanation:

3.4-1/2(0.75)

3.4-0.375

3.025

Answer:

63.00

Step-by-step explanation:

25.1 × 2.51

Multiply.

= 63.001

Round to two decimal places.

63.00

Answer:

63.00

Step-by-step explanation:

when u multiply 25.1 by 25.1 you get 630.01. Then u have to move the decimal over to the left once and then u get 63.00

Answer:

Fraction of the figure shaded = [tex]\frac{13}{16}[/tex]

Step-by-step explanation:

Ratio of the areas of the given circles are 1 : 4 : 16

Then the radii of the circles will be in the ratio = [tex]\sqrt{1}:\sqrt{4}:\sqrt{16}[/tex]

                                                                             = 1 : 2 : 4

If the radius of the smallest circle = x units

Then the radius of the middle circle = 2x units

and the radius of the largest circle = 4x units

Area of the smallest circle = πx²

Area of the middle circle = π(2x)² = 4πx²

Area of the largest circle = π(4x)²= 16πx²

Area of the region which is not shaded in the middle circle = πx²(4 - 1)

                                                                                                  = 3πx²

Therefore, area of the shaded region = Area of the largest circle - Area of the region which is not shaded

= 16πx² - 3πx²

= 13πx²

Fraction of the figure which is not shaded = [tex]\frac{\text{Area of the shaded region}}{\text{Area of the largest circle}}[/tex]

= [tex]\frac{13\pi x^{2} }{16\pi x^{2} }[/tex]

= [tex]\frac{13}{16}[/tex]

Answer:

d) 01-13 = Penguin, 14-34 = Iguana, 35-56 = Parrot, 57-99 & 00 = Turtle

Step-by-step explanation:

13 − 01 + 1 = 13

34 − 14 + 1 = 21

56 − 35 + 1 = 22

99 − 57 + 1 + 1 = 44

Answer:

d = 3 in

Step-by-step explanation:

Since we are trying to find the diameter, and the diameter is given to us as 3 in, our diameter is 3 in.

Answer:

The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is (-11.937, -6.863).

Step-by-step explanation:

We have to calculate a 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams.

The sample 1 (Fiberglass), of size n1=26 has a mean of 33.4 and a standard deviation of 2.2.

The sample 2 (Carbon), of size n2=26 has a mean of 42.8 and a standard deviation of 4.3.

The difference between sample means is Md=-9.4.

[tex]M_d=M_1-M_2=33.4-42.8=-9.4[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{2.2^2}{26}+\dfrac{4.3^2}{26}}\\\\\\s_{M_d}=\sqrt{0.186+0.711}=\sqrt{0.897}=0.9473[/tex]

The critical t-value for a 99% confidence interval is t=2.678.

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

[tex]MOE=t\cdot s_{M_d}=2.678 \cdot 0.9473=2.537[/tex]

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

[tex]LL=M_d-t \cdot s_{M_d} = -9.4-2.537=-11.937\\\\UL=M_d+t \cdot s_{M_d} = -9.4+2.537=-6.863[/tex]

The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is (-11.937, -6.863).

In this way, we can calculate the individual duration of each one and the duration time, knowing that the sample means:

The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is -11.937 and -6.863.

We have to calculate a 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams. The sample 1 (Fiberglass), of size n1=26 has a mean of 33.4 and a standard deviation of 2.2. The sample 2 (Carbon), of size n2=26 has a mean of 42.8 and a standard deviation of 4.3. The difference between sample means is Md=-9.4.

[tex]Sm_d= \sqrt{\frac{\sigma^2_1}{n_1} +\frac{\sigma^2_2}{n_2}} = \sqrt{(0.186)+(0.711) }= 0.9473[/tex]

The critical t-value for a 99% confidednce interval is t=2.678. The margin of error (MOE) can be calculated as:

[tex]MOE=t*8M_d = (2.678)(0.9473)= 2.537[/tex]

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

[tex]LL= M_d-t*SM_d = -9.4-2.537= -11.937\\UL= M_d+t*SM_d= -9.4+2.537= -6.863[/tex]

The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is (-11.937, -6.863).

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Answer:

x=-52

Step-by-step explanation:

1/3x=-17 1/3

x=-52

Answer:

Null hypothesis = H₀ = There food preferences among vole species are independent of one another.

Alternate hypothesis = H₁ = There is a relationship between voles and food preference.

Expected meadow vole/apple slices = 29.983051

Expected common vole/apple slices = 28.016949

Expected meadow vole/peanut butter-oatmeal = 31.016949

Expected common vole/peanut butter-oatmeal = 28.983051

Chi-square value = χ² = 2.154239

Degree of freedom = 1

Critical value = 3.841

χ² < Critical value

We failed to reject H₀

We do not have significant evidence at the given significance level to show that there is a relationship between voles and food preference.

Step-by-step explanation:

He frequently traps the moles and has noticed what appears to be a preference for a peanut butter-oatmeal mixture by the meadow voles vs apple slices are usually used in traps, where the common voles seem to prefer the apple slices.

So he conducted a study where he used a peanut butter-oatmeal mixture in half the traps and the normal apple slices in his remaining traps to see if there was a food preference between the two different voles.

Null hypothesis = H₀ = There food preferences among vole species are independent of one another.

Alternate hypothesis = H₁ = There is a relationship between voles and food preference.

Data collected by Dr. Pagels:

                                              meadow voles     common voles      Row Total

apple slices                                     26                          32                      58

peanut butter-oatmeal                   35                          25                     60

Column Total                                   61                          57                     118

Where 118 is the grand total.

The expected number is given by

Expected = (row total)×(column total)/grand total

Expected meadow vole/apple slices = 58×61/118

Expected meadow vole/apple slices = 29.983051

Expected common vole/apple slices = 58×57/118

Expected common vole/apple slices = 28.016949

Expected meadow vole/peanut butter-oatmeal = 60×61/118

Expected meadow vole/peanut butter-oatmeal = 31.016949

Expected common vole/peanut butter-oatmeal = 60×57/118

Expected common vole/peanut butter-oatmeal = 28.983051

The chi-square statistic value is given by

χ² = Σ(Observed - Expected)²/Expected

χ² = (26 - 29.983051)²/29.983051 + (32 - 28.016949)²/28.016949 + (35 - 31.016949)²/31.016949 + (25 - 28.983051)²/28.983051

χ² = 2.154239

The degrees of freedom is given by

DoF = (row - 1)×(col - 1)

For the given case, we have 2 rows and 2 columns

DoF = (2 - 1)×(2 - 1)

DoF = 1

The given level of significance = 0.05

The critical value from the chi-square table at α = 0.05 and DoF = 1 is found to be

Critical value = 3.841

Conclusion:

Reject H₀ If χ² > Critical value

We reject the Null hypothesis If the calculated chi-square value is more than the critical value.

For the given case,

χ² < Critical value

We failed to reject H₀

We do not have significant evidence at the given significance level to show that there is a relationship between voles and food preference.

Answer:

-3+(-5)

Checking our answer:

Adding this does indeed give -8

Answer:

Answer C

Step-by-step explanation:

You are balancing this equation out by subtracting 7x from both sides. This means you are using the subtraction property of equality.

Answer:

Step-by-step explanation:

5x(x + 3) + 6(x + 3)

The final answer is

( 5x + 6 ) ( x + 3 )

Hope this helps you

Answer:

3(7) + 2* |7 - 8| - 12 = 11

Step-by-step explanation:

3(7) + 2* |7 - 8| - 12

21 + 2* |-1| - 12

21 + 2* 1 - 12

21 + 2 - 12

23 - 12 = 11

Hope this helps! :)

Answer:

33.777 yd = 0.030886 km

Step-by-step explanation:

==>Given:

33.777 yd

==>Required:

Convert 33.777 yd to km to 6 decimal places, using the metric and U.S systems.

==>Solution:

To convert, note that 1 km = 1093.6133 yd.

Thus,

1 km = 1093.6133 yd

x km = 33.777 yd

Cross multiply

1 × 33.777 = 1093.6133 × x

33.777 = 1093.6133x

Divide both sides by 1093.6133, to solve for x

33.777/1093.6133 = x

0.03088569 = x

x ≈ 0.030886 (to 6 decimal places)

Therefore, 33.777 yd = 0.030886 km

Answer:

Yearly budget= $3840

Monthly budget= $320

Step-by-step explanation:

His budget will be calculated first by rounding off to the nearest$10 all his monthly spending.

For groceries= $176.47

Round off=$ 180.00

For phone =$ 78.66

Round off = $80.00

For gas = $62.37

Round off= $60.00

His total round off = $180+$80+$60

His total round off = $320

Before the round off, his total spending was $176.47+$78.66+$62.37

= $317.5

So his monthly budget should be $320

And yearly budget =$ 320*12

Yearly budget= $3840

Answer:

  5

Step-by-step explanation:

Substitute the given values and do the arithmetic.

  [tex]0.3y+\dfrac{y}{z}=0.3\cdot 10+\dfrac{10}{5}=3+2=\boxed{5}[/tex]

The 4 angles need to add to 360.

2 of them are 70

The other two need to equal 360-140 = 220

They are both the same so one angle needs to equal 220/2 = 110

Now find x:

X + 60 = 110

Subtract 60 from both sides:

X = 50. The answer is D

Answer:

48.3 cm²

Step-by-step explanation:

Let A be the area of the yellow region

A= the area of the square - the area of the quarter square

A= 15²-(15²*π)/4= 48.28≈ 48.3 cm²

Answer:

[tex]y = -3/2x + 4[/tex]

Step-by-step explanation:

[tex](2,1) and (6,-5).\\x_1 = 2\\x_2 = 6\\y_1 =1\\y_2 =-5\\\frac{y-y_1}{x-x_1} = \frac{y_2-y_1}{x_2-x_1}\\ \\\frac{y-1}{x-2} = \frac{-5-1}{6-2}\\\\\frac{y-1}{x-2} = \frac{-6}{4} \\Cross-Multiply\\4(y-1) = -6(x-2)\\4y-4=-6x+12\\4y =-6x+12+4\\4y = -6x+16\\Divide through-by ; 4\\\frac{4y = -6x+16}{4} \\\\y = -\frac{3}{2} x +4[/tex]

Answer:

20% jumped the turnstile

80% paid

Step-by-step explanation:

We can calculate the percent of people that jumped it by dividing the number that did by the total:

12/60 = 0.2, which is 20%

If 20% jumped it, then this means 80% paid.

Answer:

jumped= 20%

paid= 80%

Step-by-step explanation:

[tex]\frac{12}{60}[/tex]×100 = 20%

[tex]\frac{48}{60}[/tex]×100 = 80%

━━━━━━━☆☆━━━━━━━

▹ Answer

(3x + 4) * (4x - 5)

▹ Step-by-Step Explanation

12x² + x - 20

Rewrite

12x² + 16x - 15x - 20

Factor out

4x(3x + 4) - 15x - 20

4x(3x + 4) - 5(3x + 4)

Factor

(3x + 4) * (4x - 5)

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

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The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

How large of a sample of state employees should be taken if we want to estimate with 98% confidence the mean salary to be within $2,000? The population standard deviation is assumed to be $10,500. z-value for 98% confidence level is 2.326.

Answer:

Sample size = n = 150

Step-by-step explanation:

Recall that the margin of error is given by

[tex]$ MoE = z \cdot (\frac{\sigma}{\sqrt{n} } ) $\\\\[/tex]

Re-arranging for the sample size (n)

[tex]$ n = (\frac{z \cdot \sigma }{MoE})^{2} $[/tex]

Where z is the value of z-score corresponding to the 98% confidence level.

Since we want mean salary to be within $2,000, therefore, the margin of error is 2,000.

The z-score for a 98% confidence level is 2.326

So the required sample size is

[tex]n = (\frac{2.326 \cdot 10,500 }{2,000})^{2}\\\\n = (12.212)^{2}\\\\n = 149.13\\\\n = 150[/tex]

Therefore, we need to take a sample size of at least 150 state employees to estimate with 98% confidence the mean salary to be within $2,000.