Solve for x.
Question 4 options:

A)

8

B)

–8

C)

9

D)

–9

Answer:

We expect 95% of head breadths to be between 4.3 inches and 7.5 inches.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 5.9 inches, standard deviation = 0.8 inches.

We expect 95% of head breadths to be between

Within 2 standard deviations of the mean, so:

5.9 - 2*0.8 = 5.9 - 1.6 = 4.3 inches

5.9 + 2*0.8 = 5.9 + 1.6 = 7.5 inches

We expect 95% of head breadths to be between 4.3 inches and 7.5 inches.

Answer:

hope it helps...

Step-by-step explanation:

Answer:

Hello!

Distributive property: a(b+c)=ab+ac

Minus and plus sign.

Then multiply by the numbers.

Hope this helps!

Thanks!

Have a great day!

Step-by-step explanation:

Answer:

Explain what?? May I ask

Answer:

False

True

True

False

Yw hope this helped yall

Step-by-step explanation:

The equation represents this situation is

3x + 1/2 x (3x + - 17) = x + (3x - 17 ) + 20 — False

x = 40 — True

Brinley and Seth exercised for a combined 95 minutes —-True

Mackenzie exercised for 26 minutes. — False

Answer:

two points in the xy plane has cartesian coordinate (2,-4) and (-3,3) where the units are in m determine.

a) the distance between these points and

b) their polar coordinates.

9514 1404 393

Answer:

  405 mph; 325 mph

Step-by-step explanation:

The total of their speeds is ...

  2920 mi/(4 h) = 730 mi/h

If s represents the speed of the slower plane, then we have ...

  s + (s+80) = 730

  2s = 650 . . . . . . .  subtract 80

  s = 325 . . . . . . . divide by 2

  s+80 = 405 . . .  find the faster speed

The speeds of the planes are 405 mi/h and 325 mi/h.

Answer:

f(x+2) = 3(x+2)^2 + 2(x+2) + 1

Step-by-step explanation:

Replace x with x+2 and you get the solution above. Hope this helps!

Answer:

y-2=0(x-3)

Step-by-step explanation:

Answer:

Ok tell me which mathematic game

Answer:

The intermediate step is determining what a is, knowing also that (x+a)²=x²+(2a)x+a².

Also, x²-16x= -68 (in the form (x+a)²=b) is (x-8)²=-4

Step-by-step explanation:

x²-16x=-68

x²-16x+68=0

I suppose the intermediate step is finding (x+a)².

Remember that (x+a)²=x²+(2a)x+a², so 'a' will be half the coefficient of x (number beside x, not x²). The coefficient of x here is -16, so a is -8.

(x-8)²=x²-16x+64

So, if we can create 'x²-16x+64' out of 'x²-16x+68', we'll be on our way:

x²-16x+68=0

(x²-16x+64)+4=0

(x-8)²+4=0

(x-8)²=-4

Answer:

no and no

Step-by-step explanation:

1. 9+6 = 15 not 17

2. 9 - 3 = 6 not 5

please leave a like if this answers your question

Answer:

d. D: (-∞ , ∞) , R: (-10 , ∞)

Step-by-step explanation:

Answer: 0.1974

Step-by-step explanation:

Let X be a random variable that denotes the gas mileage (in miles per gallon) of the individual sedan.

Given: Population mean: [tex]\mu=20[/tex]

Standard deviation: [tex]\sigma=2[/tex]

The probability that the gas mileage (in miles per gallon) of your single, individual sedan is between 19.5 and 20.5:

[tex]P(19.5<x<20.5)=P(\dfrac{19.5-20}{2}<\dfrac{x-\mu}{\sigma}<\dfrac{20.5-20}{2})\\\\=P(-0.25<z<0.25)=2P(0.25)-1 [P(-z<Z<z)=2P(Z<z)-1]\\\\=2(0.5987)-1=0.1974[/tex]

The required probability=0.1974

Answer:

[tex] {a}^{3} - {b}^{3} [/tex]

[tex] = (a - b)( {a}^{2} + ab + {b}^{2} )[/tex]

Hence, simplified.

Answer:

2nd option

Step-by-step explanation:

Answer:

630 ml

Step-by-step explanation:

1 glass contains 180 ml juice

7/2 glasses contains = 180 × 7/2 = 630 ml

Answer:

t = 4 seconds

Step-by-step explanation:

Given that,

The height of the tennis ball above the ground can be found using the function y = -12.5x + 50

where x is the time in seconds the tennis ball has been in the air.

We need to find how many seconds did it take the tennis ball to reach the ground.

When it reaches the ground, y = 0

So,

-12.5x + 50 = 0

12.5x = 50

x = 4 seconds

So, it will take 4 seconds for the ball to reach the ground.

Answer:

a) By the Central Limit Theorem, it is approximately normal.

b) The standard error of the distribution of the sample mean is 1.8333.

c) 0.1379 = 13.79% of the samples will have a mean useful life of more than 38 hours.

d) 0.7939 = 79.39% of the samples will have a mean useful life greater than 34.5 hours

e) 0.656 = 65.6% of the samples will have a mean useful life between 34.5 and 38 hours

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 36 hours and a standard deviation of 5.5 hours.

This means that [tex]\mu = 36, \sigma = 5.5[/tex]

a. What can you say about the shape of the distribution of the sample mean?

By the Central Limit Theorem, it is approximately normal.

b. What is the standard error of the distribution of the sample mean? (Round your answer to 4 decimal places.)

Sample of 9 means that [tex]n = 9[/tex]. So

[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{5.5}{\sqrt{9}} = 1.8333[/tex]

The standard error of the distribution of the sample mean is 1.8333.

c. What proportion of the samples will have a mean useful life of more than 38 hours?

This is 1 subtracted by the pvalue of Z when X = 38. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{38 - 36}{1.8333}[/tex]

[tex]Z = 1.09[/tex]

[tex]Z = 1.09[/tex] has a pvalue of 0.8621

1 - 0.8621 = 0.1379

0.1379 = 13.79% of the samples will have a mean useful life of more than 38 hours.

d. What proportion of the sample will have a mean useful life greater than 34.5 hours?

This is 1 subtracted by the pvalue of Z when X = 34.5. So

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{34.5 - 36}{1.8333}[/tex]

[tex]Z = -0.82[/tex]

[tex]Z = -0.82[/tex] has a pvalue of 0.2061.

1 - 0.2061 = 0.7939

0.7939 = 79.39% of the samples will have a mean useful life greater than 34.5 hours.

e. What proportion of the sample will have a mean useful life between 34.5 and 38 hours?

pvalue of Z when X = 38 subtracted by the pvalue of Z when X = 34.5. So

0.8621 - 0.2061 = 0.656

0.656 = 65.6% of the samples will have a mean useful life between 34.5 and 38 hours

Answer:

Step-by-step explanation:

use the distance formula

dist = sqrt[ (x2-x1)^2 + (y2-y1)^2 ]

where point one ,P1,  is A and point 2, P2,  is C, so

P1 = (x1,y1) = (-7,3)

P2 =(x2,y2) = (0,6)

then

dist = sqrt[ (0 - (-7))^2 + (6-3)^2 ]

dist = sqrt [ 7^2 + 3^2 ]

dist = sqrt [49 +9 ]

dist = sqrt [58]

dist = 7.6157....

AC = 7.6 ( rounded to nearest tenth)

Answer:

C

Step-by-step explanation:

A is just the opposite value of the second integral.

B is just 3 times the first.

D-you can write a sum of integrals over the same intervals as one integral of the sum of the integrands of those integrals over that same interval. The answer would be 3(8)+-2.

For choice C, we would need more information.

Answer:

x=34.5

Step-by-step explanation:

(3x+18)° and 93° lie along a straight line. The angles in a straight line add up to 180. So:

3x+18+93=`80

2x=180-111

x=69/2

x=34.5

Answer:

f(x)=x-5/3x

Step-by-step explanation:

Answer:

[tex]\begin{array}{ccccccccccccccc}{1} & {3} & {4} & {12} & {15} & {18}& {18 } & {26} & {29} & {30} & {32} & {57} & {58} & {61} \\ \end{array}[/tex]

Step-by-step explanation:

Given

[tex]\begin{array}{ccccccccccccccc}{1} & {[ \ ]} & {4} & {[ \ ] } & {15} & {18}& {[ \ ] } & {[ \ ]} & {29} & {30} & {32} & {[ \ ]} & {58} & {[ \ ]} \\ \end{array}[/tex]

Required

Fill in the box

From the question, the range is:

[tex]Range = 60[/tex]

Range is calculated as:

[tex]Range = Highest - Least[/tex]

From the box, we have:

[tex]Least = 1[/tex]

So:

[tex]60 = Highest - 1[/tex]

[tex]Highest = 60 +1[/tex]

[tex]Highest = 61[/tex]

The box, becomes:

[tex]\begin{array}{ccccccccccccccc}{1} & {[ \ ]} & {4} & {[ \ ] } & {15} & {18}& {[ \ ] } & {[ \ ]} & {29} & {30} & {32} & {[ \ ]} & {58} & {61} \\ \end{array}[/tex]

From the question:

[tex]IQR = 20[/tex] --- interquartile range

This is calculated as:

[tex]IQR = Q_3 - Q_1[/tex]

[tex]Q_3[/tex] is the median of the upper half while [tex]Q_1[/tex] is the median of the lower half.

So, we need to split the given boxes into two equal halves (7 each)

Lower half:

[tex]\begin{array}{ccccccc}{1} & {[ \ ]} & {4} & {[ \ ] } & {15} & {18}& {[ \ ] } \\ \end{array}[/tex]

Upper half

[tex]\begin{array}{ccccccc}{[ \ ]} & {29} & {30} & {32} & {[ \ ]} & {58} & {61} \\ \end{array}[/tex]

The quartile is calculated by calculating the median for each of the above halves is calculated as:

[tex]Median = \frac{N + 1}{2}th[/tex]

Where N = 7

So, we have:

[tex]Median = \frac{7 + 1}{2}th = \frac{8}{2}th = 4th[/tex]

So,

[tex]Q_3[/tex] = 4th item of the upper halves

[tex]Q_1[/tex]= 4th item of the lower halves

From the upper halves

[tex]\begin{array}{ccccccc}{[ \ ]} & {29} & {30} & {32} & {[ \ ]} & {58} & {61} \\ \end{array}[/tex]

We have:

[tex]Q_3 = 32[/tex]

[tex]Q_1[/tex] can not be determined from the lower halves because the 4th item is missing.

So, we make use of:

[tex]IQR = Q_3 - Q_1[/tex]

Where [tex]Q_3 = 32[/tex] and [tex]IQR = 20[/tex]

So:

[tex]20 = 32 - Q_1[/tex]

[tex]Q_1 = 32 - 20[/tex]

[tex]Q_1 = 12[/tex]

So, the lower half becomes:

Lower half:

[tex]\begin{array}{ccccccc}{1} & {[ \ ]} & {4} & {12 } & {15} & {18}& {[ \ ] } \\ \end{array}[/tex]

From this, the updated values of the box is:

[tex]\begin{array}{ccccccccccccccc}{1} & {[ \ ]} & {4} & {12} & {15} & {18}& {[ \ ] } & {[ \ ]} & {29} & {30} & {32} & {[ \ ]} & {58} & {61} \\ \end{array}[/tex]

From the question, the median is:

[tex]Median = 22[/tex] and [tex]N = 14[/tex]

To calculate the median, we make use of:

[tex]Median = \frac{N + 1}{2}th[/tex]

[tex]Median = \frac{14 + 1}{2}th[/tex]

[tex]Median = \frac{15}{2}th[/tex]

[tex]Median = 7.5th[/tex]

This means that, the median is the average of the 7th and 8th items.

The 7th and 8th items are blanks.

However, from the question; the mode is:

[tex]Mode = 18[/tex]

Since the values of the box are in increasing order and the average of 18 and 18 do not equal 22 (i.e. the median), then the 7th item is:

[tex]7th = 18[/tex]

The 8th item is calculated as thus:

[tex]Median = \frac{1}{2}(7th + 8th)[/tex]

[tex]22= \frac{1}{2}(18 + 8th)[/tex]

Multiply through by 2

[tex]44 = 18 + 8th[/tex]

[tex]8th = 44 - 18[/tex]

[tex]8th = 26[/tex]

The updated values of the box is:

[tex]\begin{array}{ccccccccccccccc}{1} & {[ \ ]} & {4} & {12} & {15} & {18}& {18 } & {26} & {29} & {30} & {32} & {[ \ ]} & {58} & {61} \\ \end{array}[/tex]

From the question.

[tex]Mean = 26[/tex]

Mean is calculated as:

[tex]Mean = \frac{\sum x}{n}[/tex]

So, we have:

[tex]26= \frac{1 + 2nd + 4 + 12 + 15 + 18 + 18 + 26 + 29 + 30 + 32 + 12th + 58 + 61}{14}[/tex]

Collect like terms

[tex]26= \frac{ 2nd + 12th+1 + 4 + 12 + 15 + 18 + 18 + 26 + 29 + 30 + 32 + 58 + 61}{14}[/tex]

[tex]26= \frac{ 2nd + 12th+304}{14}[/tex]

Multiply through by 14

[tex]14 * 26= 2nd + 12th+304[/tex]

[tex]364= 2nd + 12th+304[/tex]

This gives:

[tex]2nd + 12th = 364 - 304[/tex]

[tex]2nd + 12th = 60[/tex]

From the updated box,

[tex]\begin{array}{ccccccccccccccc}{1} & {[ \ ]} & {4} & {12} & {15} & {18}& {18 } & {26} & {29} & {30} & {32} & {[ \ ]} & {58} & {61} \\ \end{array}[/tex]

We know that:

The 2nd value can only be either 2 or 3

The 12th value can take any of the range 33 to 57

Of these values, the only possible values of 2nd and 12th that give a sum of 60 are:

[tex]2nd = 3[/tex]

[tex]12th = 57[/tex]

i.e.

[tex]2nd + 12th = 60[/tex]

[tex]3 + 57 = 60[/tex]

So, the complete box is:

[tex]\begin{array}{ccccccccccccccc}{1} & {3} & {4} & {12} & {15} & {18}& {18 } & {26} & {29} & {30} & {32} & {57} & {58} & {61} \\ \end{array}[/tex]

Answer:

3x+x^2-6

Step-by-step explanation:

Have a great rest of your day.

Bye

Answer:

5/20 x 4/15 =1/15

6/7 x 7/6 =1

2 x 7/10 =7/5

Hope this helps!

Answer:

5 mph

Step-by-step explanation:

Answer:

15 mph = rate of boat in still water

Step-by-step explanation:

D = RT

Let R = rate of boat in still water

Rate down stream = R + 5

Time down stream = 20/(R + 5)

Rate upstream = R - 5

Time upstream = 20/(R - 5)

Total time = 20/(R + 5) + 20/(R - 5) = 3

                    20(R - 5) + 20(R + 5) = 3(R + 5)(R - 5)

                     20R - 100 + 20R + 100 = 3R^2 - 75

                                  3R^2 + 40R - 75 = 0

                                  (3R + 5)(R - 15) = 0

                                      R = -5/3  or  15

Rate cannot be negative, so R = 15 mph = rate of boat in still water  

Answer:

One time

Step-by-step explanation:

The probability of picking a purple marble once is 1/6, so if I pick a marble 6  times, then (1/6)*6=1