A car wash detailed 264 cars in 8 hours. At what rate did the car wash detail cars in cars per hour? ​

The standard deviation of the data will be;

⇒ 4.13

What is Standard deviation?

Standard deviation is the measure of dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

Given that;

The data set is,

⇒ 23, 19, 28, 30, 22

Now,

Since, The data set is,

⇒ 23, 19, 28, 30, 22

Hence, The mean = 23 + 19 + 28 + 30 + 22 / 5

                            = 122/5

                            = 24.4

So, The standard deviation is;

√ (23 - 24.4)² + (19 - 24.4)²+(28 - 24.4)² + (30 - 24.4)² + (22 - 24.4)²/ (5-1)

⇒ √ 1.96 + 29.16 + 12.96 + 31.36 + 5.76 / 4

⇒ √ 81.2/4

⇒ √20.3

⇒ 4.13

Thus, The standard deviation of the data will be;

⇒ 4.13

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To calculate the standard deviation of the data set, we can use the formula:

$$ \sigma = \sqrt{\frac{1}{n}\sum_{i=1}^{n} (x_i - \mu)^2} $$

Where:

$x_i$ is each data point

$\mu$ is the mean of the data set

$n$ is the number of data points

For the data set given, the mean is $\mu = 24.4$

Plugging in the values into the formula, we get:

$$ \sigma = \sqrt{\frac{1}{5}\sum_{i=1}^{5} (x_i - 24.4)^2} = \sqrt{\frac{1}{5}( (23-24.4)^2 + (19-24.4)^2 + (28-24.4)^2 + (30-24.4)^2 + (22-24.4)^2 )} $$

After evaluating the expression, we get:

$$ \sigma = \sqrt{\frac{1}{5}(1.96 + 5.76 + 3.36 + 5.76 + 0.36)} = \sqrt{\frac{1}{5}(18.2)} = \sqrt{3.64} = 1.91 $$

So the standard deviation of the data set is 1.91.

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Answer:

DEF = 110

Step-by-step explanation:

Supplementary angles add to 180

3x+5  +2x = 180

Combine like terms

5x +5 = 180

Subtract 5 from each side

5x = 175

Divide each side by 5

5x/5 = 175/5

x =35

DEF = 3x+5

     = 3*35 +5

    = 105+5

   = 110

Answer:

option b is correct option

Step-by-step explanation:

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Answer:

[tex]x^4 - 1 = (x- 1)(x + 1)(x^2 + 1)[/tex]

[tex]2x^2 - 4x - 240 = 2(x + 10) (x - 12)[/tex]

Step-by-step explanation:

Given

[tex]1.\ x^4 - 1[/tex]

[tex]2.\ 2x^2 - 4x - 240[/tex]

Required

Factor

[tex]1.\ x^4 - 1[/tex]

Express as difference of two squares

[tex]x^4 - 1 = (x^2 - 1)(x^2 + 1)[/tex]

Express [tex]x^2 - 1[/tex] as difference of two squares

[tex]x^4 - 1 = (x- 1)(x + 1)(x^2 + 1)[/tex]

[tex]2.\ 2x^2 - 4x - 240[/tex]

Expand

[tex]2x^2 - 4x - 240 = 2x^2 -24x + 20x - 240[/tex]

Factorize

[tex]2x^2 - 4x - 240 = 2x(x -12) + 20(x - 12)[/tex]

Factor out x - 12

[tex]2x^2 - 4x - 240 = (2x + 20) (x - 12)[/tex]

Factor out 2

[tex]2x^2 - 4x - 240 = 2(x + 10) (x - 12)[/tex]

Answer:

C

Step-by-step explanation:

We know that function h represents an object's height in feet after x seconds.

In that case, option A) h(15) = 100 means that after 15 seconds, the object's height is 100 feet.

Option B) h(100) = 15 means that after 100 seconds, the object's height is 15 meters.

Therefore, neither A nor B are correct.

Option C) h(15) - h(0) = 100 means that between the zeroth and 15th second, their difference is 100 feet.

In other words, the object's height increased by 100 feet over the first 15-second period.

Option C is correct.

For Option D), it gives us the average rate of change. (h(15) - h(0)) / (15) = 100 means that for the first fifteen seconds, the height of the object increased at an average rate of 100 feet per second.

Answer:

Hello! answer: 10

Step-by-step explanation:

you do a^2+b^2=c^2 meaning

8 × 8 + 6 × 6 will equal a number which then we have to find out the square root of that number meaning what number you can multiply by itself to get that number so...

8 × 8 = 64

6 × 6 = 36

64 + 36 = 100

√100 = 10

10 × 10 = 100 therefore the missing length is 10 hope that helps!

The value of x will be 2.067.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ eˣ = 7.9

Now,

Since, The expression is,

⇒ eˣ = 7.9

Take natural log both side, we get;

⇒ ln eˣ = ln 7.9

⇒ x = ln 79 - ln 10

⇒ x = 4.369 - 2.302

⇒ x = 2.067

Thus, The value of x = 2.067

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Answer: 178 minutes

21.02 x 100 = 2102

2102 - 500 = 1602

1602 / 9 = 178

Answer:The value of log base 3 log base 2 log base √3 81 is -a)1 b) 2 c)3 d) 0

Answer:

4

Step-by-step explanation:

Define [tex]\log_a b=c\implies a^c=b[/tex].

Let

[tex]\log_3 81=x[/tex].

Using our definition [tex]\log_a b=c\implies a^c=b[/tex], we have:

[tex]3^x=81[/tex]

Solving for [tex]x[/tex]:

[tex]x=\boxed{4}\text{ from simply knowing that }3^4=81[/tex]

Or

Algebraically solve step-by-step by taking the log of both sides:

[tex]\log 3^x=\log 81[/tex]

Using log property [tex]\log a^b=b\log a[/tex], rewrite:

[tex]x\log 3=\log81[/tex]

Divide both sides by log(3):

[tex]x=\frac{\log 81}{\log 3}=\boxed{4}[/tex]

Answer: 40 coins. Doesn't your profile say college?

Given:

The function is:

[tex]f(x)=x^2[/tex]

This function is stretched by a factor of 9 to g(x).

To find:

The equation of function function g(x).

Solution:

The vertical stretch is defined as:

[tex]g(x)=kf(x)[/tex]           ...(i)

If [tex]0<k<1[/tex], then the function f(x) compressed vertically by factor k.

If [tex]k>1[/tex], then the function f(x) stretched vertically by factor k.

The given function f(x) is stretched by a factor of 9 to g(x).  So the value of k is 9.

Substituting [tex]k=9[/tex] in (i), we get

[tex]g(x)=9f(x)[/tex]

[tex]g(x)=9x^2[/tex]            [tex][\because f(x)=x^2][/tex]

Therefore, the required function is [tex]g(x)=9x^2[/tex].

Answer:

d.18

Step-by-step explanation:

as x goes up by 1, y goes up 18

Answer:

90

Step-by-step explanation:

Answer:

think it's the last one

Step-by-step explanation:

sorry if i'm wrong

9514 1404 393

Answer:

  D) y-intercept: (0, -10); vertex: (2, -2); zeros: none

Step-by-step explanation:

The graph does not cross the x-axis, so there are no real zeros. It crosses the y-axis at (0, -10), so that is the y-intercept.

These observations match choice D.

Answer:

3

Step-by-step explanation:

slope of line = gradient of line

= [tex]\frac{10-4}{3-1}[/tex]

= 3

Answer:

xy(3x+10)(3x-10)

Answer:

v=3.14 r 2 h

3.14 (2)(2)(7)= 87.9

Answer:

The answer for the Volume is 87.9 to 1d.p or 88in³ to the nearest tenth

Step-by-step explanation:

Volume of a cylinder =pir²h

r=d/2=4/2=2in

V=3.14×2²×7

V=3.14×4×7

V=87.92in³

V=87.9in³ to 1d.p

V=88in³ to the nearest tenth

Answer:

192 inches^3 or 192 cubic inches

Step-by-step explanation:

48 one inch cubes means the base area is 48inches^2. 48inches^2 multiplied by 4 inches = 192inches^3

Answer: 192 square inches

Step-by-step explanation: it says that he can fill the bottom of the box with 48 once inch cubes, and since the cubes are an inch tall, the cubes would cover an inch of the box's height. The box's total height is 4, so you would need to multiply 4 by 48 to get the total number of cubes that can fit in the box, aka the volume of the box.

Given :

An airplane flying at an altitude of 37,000 feet is still A horizontal distance of 100 miles (100 miles = 5280 ft) from the airport.

To Find :

What angle of depression does the airplane need to use to reach the runway?

Solution :

Let, angle of depression is [tex]\theta[/tex] .

So,

[tex]tan\ \theta = \dfrac{ Altitude \ in \ which \ plane \ is \ flying}{Horizontal \ Distance}\\\\tan \ \theta = \dfrac{37000}{5280}\\\\tan \ \theta = 7.00\\\\\theta = tan^{-1} 7\\\\\theta = 81.87^o[/tex]

Hence, this is the required solution.

Answer:

256

Step-by-step explanation:

The digits can only be one of four numbers.

4*4*4*4 = 4^4 = 256

gradient or slope=y2 -y1

x2 - x1

so for A, p is x1 and 3 is y1..

For B, 6 is x2 and p is y2

2= p - 3

6 - p

2 ( 6 - p) = p - 3

12 - 2p = p - 3

-2p + p = -3 - 12

-p = - 15

p = 15

Answer:

Time taken = 0.85 and 0.59 (Approx.)

Step-by-step explanation:

Given:

Initial height = 4 feet

Initial upward velocity = 23 f/s

Equation;

h = 4 + 23t - 16t² for h = 12 feet

Find:

Time taken

Computation:

h = 4 + 23t - 16t² for h = 12 feet

12 = 4 + 23t - 16t²

16t² -23t + 8 = 0

t = [-b±√b²-4ac] / 2a

t = [23±√23²-(4)(16)(8)] / 2(16)

t = [23±√529-512] / 32

t = [23±4.12]/32

Time taken = 0.85 and 0.59 (Approx.)

Answer:

-3/2

Step-by-step explanation: Divide 12 by 8 and you get 3/2. Since the sign alters, the ratio is negative.

Answer:

a) 68%.

b) 84%.

c) Approximately 2.5% of cars are traveling at a speed greater than or equal to 80 mph.

d) Approximately 2.5% of cars are traveling at a speed greater than or equal to 80 mph.

e) Between 60 mph and 80 mph.

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 of 70 mph, standard deviation of 5 mph.

(a) Approximately what percent of cars are travelling between 65 and 75 mph?

70 - 5 = 65

70 + 5 = 75

Within 1 standard deviation, so approximately 68%.

(b) If the speed limit on this stretch of highway is 65 mph, approximately what percent of cars are traveling faster than the speed limit?

The normal distribution is symmetric, which means that 50% of the measures are below the mean, and 50% are above.

65 is one standard deviation below the mean, so of the cars below the mean, 68% are above 65 mph.

0.68*50% + 50% = 34% + 50% = 84%.

84%.

(c) What percent of cars are traveling at a speed greater than or equal to 80 mph?

80 = 70 + 2*10

2 standard deviations above the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean. Due to the symmetry of the normal distribution, of the other 5%, 2.5% is at least 2 standard deviations below the mean and 2.5% is at least 2 standard deviations above the mean. Then:

Approximately 2.5% of cars are traveling at a speed greater than or equal to 80 mph.

(d) What percent of cars are traveling at a speed greater than 80 mph?

Same as item c, as in the normal distribution, the probability of an exact value is considered to be 0.

(e) 95% of cars are traveling between what two speeds?

Within two standard deviations of the mean.

70 - 2*5 = 60 mph

70 + 2*5 = 80 mph.

Between 60 mph and 80 mph.

Answer:

w<32

Step-by-step explanation: