A(n) ___
is a numerical summary of a population.

Data

6,9,5,0,5,3,7,5,2,7,10,2,9,8,0,6,2,6,6,3,6,9,7,7,4,1,6,8

Answer:

(a) shown in the attachment

(b) 0.54

(c) 5.32

(a) The frequency distribution table has been added to this response.

The table contains four columns:

First column (x): The discrete values of the marks

Second column (f): The corresponding frequency of the marks

Third column (d) : The difference between each mark(x) and the assumed mean(A). i.e d = x - A (Where A = 6 from the question)

Fourth column (fd): The product of the first column and the third column. i.e f * d

(b) From the table, it can be deduced that the modal score is 6

This is because the score 6 has the highest number of frequency which is 6

(c) If a student is selected at random, the probability P(>5), that the student scored more than 5 is given as follows;

P( >5 ) = [The sum of frequencies of marks greater than 5] / [Total frequency]

P( >5 ) = [6 + 4 + 2 + 3 + 1] / [28]

P( >5 ) = 15 / 28 = 0.54

Therefore, the probability that the student scored more than 5 is 0.54

(d) To get the arithmetic mean, M, from the assumed mean A = 6, we use the following relation;

M = A + [∑fd / N]           -----------(*)

Where

N = total frequency = 28

A = 6

∑fd = sum of the items on the fourth column = -19

Substitute these values into equation (*)

M = 6 + [-19 / 28]

M = 149 / 28

M = 5.32

Therefore, the arithmetic mean is 5.32

Answer:

(a) At 21.46 psi, the TPMS trigger a warning for this car.

(b) The probability that the TPMS will trigger a warning is 0.0001.

(c) The probability that the tire’s inflation is within the recommended range is 0.6826.

Step-by-step explanation:

We are given that tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 26% below the target pressure. Suppose the target tire pressure of a certain car is 29 psi (pounds per square inch).

(a) It is stated that TPMS warns the driver when the tire pressure of the vehicle is 26% below the target pressure.

So, the TPMS trigger a warning for this car when;

Pressure = 29 psi - 26% of 29 psi

               = [tex]29-(0.26 \times 29)[/tex]  = 21.46 psi

At 21.46 psi, the TPMS trigger a warning for this car.

(b) Suppose tire pressure is a normally distributed random variable with a standard deviation equal to 2 psi.

Let X = The pressure at which TPMS will trigger a warning

So, X ~ Normal([tex]\mu=29, \sigma^{2} =2^{2}[/tex])

Now, the probability that the TPMS will trigger a warning is given by = P(X [tex]\leq[/tex] 21.46)

        P(X [tex]\leq[/tex] 21.46) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{21.46-29}{2}[/tex] ) = P(Z [tex]\leq[/tex] -3.77) = 1 - P(Z < 3.77)

                                                              = 1 - 0.9999 = 0.0001

The above probability is calculated by looking at the value of x = 3.77 in the z table which has an area of 0.9999.

(c) The manufacturer’s recommended correct inflation range is 27 psi to 31 psi.

So, the probability that the tire’s inflation is within the recommended range is given by = P(27 psi < X < 31 psi)

     P(27 psi < X < 31 psi) = P(X < 31 psi) - P(X [tex]\leq[/tex]27 psi)

     P(X < 31 psi) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{31-29}{2}[/tex] ) = P(Z < 1) = 0.8413

     P(X [tex]\leq[/tex] 27 psi) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{27-29}{2}[/tex] ) = P(Z [tex]\leq[/tex] -1) = 1 - P(Z < 1)

                                                        = 1 - 0.8413 = 0.1587

Therefore, P(27 psi < X < 31 psi) = 0.8413 - 0.1587 = 0.6826.

At 21.46 psi, the TPMS trigger a warning for this car.

The probability that the TPMS will trigger a warning is 0.0001.

The probability that the tire’s inflation is within the recommended range is 0.6826.

Given that,

Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 26% below the target pressure.

Suppose the target tire pressure of a certain car is 29 psi (pounds per square inch).

We have to determine,

At what psi will the TPMS trigger a warning for this car.

What is the probability that the TPMS will trigger a warning.

What is the probability that the tire’s inflation is within the recommended range.

According to the question,

So, the TPMS trigger a warning for this car when;

Pressure = 29 psi - 26% of 29 psi

[tex]Pressure = 29- (0.26 \times 29) = 21.46psi[/tex]

At 21.46 psi, the TPMS trigger a warning for this car.

Let X = The pressure at which TPMS will trigger a warning

So, X ~ Normal [tex]\mu = 29, \sigma^2 = 2^2\\[/tex]

Now, the probability that the TPMS will trigger a warning is given by = P(X≤  21.46).

[tex]P(X\leq 21.46) = P (\dfrac{X-\mu}{\sigma}\leq \dfrac{21.46-29}{2}) = P(Z\leq -3.77) = 1-P(Z<3.77) \\\\= 1-0.9999 = 0.0001[/tex]

The above probability is calculated by looking at the value of x = 3.77 in the z table which has an area of 0.9999.

So, the probability that the tire’s inflation is within the recommended range is given by = P(27 psi < X < 31 psi)

[tex]P(27psi<X<31psi) = P(X<31psi)-P(X\leq psi)\\\\P(X<31psi) = P(\dfrac{x-\mu}{\sigma}\leq \dfrac{31-29}{2}) = P(Z<1) = 0.8413\\\\P(X<27psi) = P(\dfrac{x-\mu}{\sigma}\leq \dfrac{27-29}{2}) = P(Z\leq -1) = 1-P(Z<1) = 0.8413\\[/tex]

Therefore, , P(27 psi < X < 31 psi) = 0.8413 - 0.1587 = 0.6826.

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Answer:

The surface area is 7600

I would really appreciate brainliest!

Step-by-step explanation:

L=Ph

L=(40x2 50x2) 20

L=3600

S= L+2B

S=3600 +2(40x50)

S= 3600+4000

S= 7600

Answer: Hi!

There are three different rectangles that make up this closed box. We need to calculate the area of them to find the surface area of this shape. Here are the measurements:

Rectangle 1: 40 * 20

Rectangle 2: 50 * 20

Rectangle 3: 50 * 40

Note that there are two of each type of rectangle, so when we are done calculating the area of each rectangle we will multiply each by 2.

Rectangle 1: 40 * 20 = 800(2) = 1600

Rectangle 2: 50 * 20 = 1000(2) = 2000

Rectangle 3: 50 * 40 = 2000(2) - 4000

Now, we add the areas together: 1600 + 2000 + 4000 = 7600

The surface area of this closed box is 7600cm squared.

Hope this helps!

Answer:

1.02×10¹ = 10.2

Step-by-step explanation:

We have given a number in scientific notation as follows 1.02×10¹

We need to convert it into standard notation.

1 is in ones place, 0 is in tenths place and 2 is in hundredths place.

[tex]1.02\times 10^1=\dfrac{102}{100}\times 10\\\\=\dfrac{102}{10}\\\\=10.2[/tex]

So, the standard notation of 1.02×10¹ is 10.2

Answer:

√2

1.414

Step-by-step explanation:

ⁿ√x₁*x₂*x₃*...*xₙ

√8*1/4

√2

1.414

The geometric mean between 8 and 1/4 is; 1.414.

According to the question:

In essence, the geometric mean can be evaluated as follows;

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Answer:

Forecasted earning = $160,200

Tax rate = 27.84%

Step-by-step explanation:

The calculation of forecasted earning and tax rate is shown below:-

Earnings before income and taxes = Sales - Cost of goods sold - Depreciation Expense

= $1,362,000 - $830,000 - $310,000

= $222,000

So,

Forecasted Free cash flow = Net Income + Depreciation  

$470,200 = Net Income + $310,000

Net Income = $470,200 - $310,000

= $160,200

Now, the Tax rate is

Net Income = EBIT × (1 - Tax Rate)

$160,200 = $222,000 × (1 - Tax rate)

(1 - Tax rate) = $160,200 ÷ $222,000

(1 - Tax rate) = 0.721622

Tax rate = 27.84%

Answer:

There are multiple ways this can be said :

Answer:

third answer

point Y, ray YZ, angle XYZ

Step-by-step explanation:

These can all be found on the figure are; point Y, ray YZ, angle XYZ. Hence, option C is correct.

An angle requires two straight line/ line segments/rays, such that they're connected on one of their endpoints.

The point of their joint is called vertex of that angle.

Those two line segments forming it are called arms of that angle.

The angle is the degree of rotation that it will take for the moving side to go from initial side to the position it is currently on...

These can all be found on the figure are; point Y, ray YZ, angle XYZ.

Hence, option C is correct.

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Answer:

x = (-5 ± 2√10) / 3

Step-by-step explanation:

5 − 10x − 3x² = 0

Write in standard form:

-3x² − 10x + 5 = 0

Solve with quadratic formula:

x = [ -b ± √(b² − 4ac) ] / 2a

x = [ -(-10) ± √((-10)² − 4(-3)(5)) ] / 2(-3)

x = [ 10 ± √(100 + 60) ] / -6

x = (10 ± 4√10) / -6

x = (-5 ± 2√10) / 3

Step-by-step explanation:

[tex]5 - 10x - 3 \times 2 = 0[/tex]

[tex]multiply \: the \: numbers \\ \\ 5 - 10 x- 6 = 0[/tex]

[tex]collect \: like \: terms \\ \\ 5 - 6 - 10x[/tex]

[tex] - 1 - 10x = 0[/tex]

[tex] - 10x = 1[/tex]

[tex]divide \: both \: sides \: of \: the \: equation \: by \: - 10[/tex]

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

[tex]alt \: form \: = \\ \\ = 0.1 \\ x = - 10 {}^{ - 1} [/tex]

Hope this helps. :)

Answer:

Se requiere 12 cajas con 4 manzanas y 3 duraznos cada una.

Step-by-step explanation:

Se requiere el menor número posible de manzanas y duraznos para obtener el mayor número de cajas. Puesto que no se considera cortar fruta alguna en porciones y sabiendo que hay más manzanas que duraznos, se determina la razón mínima de manzanas por duraznos:

[tex]x = \frac{48\,manzanas}{36\,duraznos}[/tex]

[tex]x = \frac{4 manzanas}{3\,duraznos}[/tex]

Se requiere 4 manzanas por cada 3 duraznos. Entonces, cada caja debe contener 3 duraznos y 4 manzanas. El número máximo de cajas es:

[tex]n = \frac{48\,manzanas}{4\,\frac{manzanas}{caja} } = \frac{36\,duraznos}{3\,\frac{duraznos}{caja} }[/tex]

[tex]n = 12\,cajas[/tex]

Se requiere 12 cajas con 4 manzanas y 3 duraznos cada una.

Answer:

[tex]\approx \bold{602\ m}[/tex]

Step-by-step explanation:

Given the following dimensions:

XY=966 ​m

[tex]\angle XYZ[/tex]​ = 38°24', and

[tex]\angle YZX[/tex] = 94°6'

To find:

Distance between points X and Z.

Solution:

Let us plot the given values.

We can clearly see that it forms a triangle when we join the points X to Y, Y to Z and Z to X.

The [tex]\triangle XYZ[/tex] has following dimensions:

XY=966 ​m

[tex]\angle XYZ[/tex]​ = 38°24', and

[tex]\angle YZX[/tex] = 94°6'

in which we have to find the side XZ.

Kindly refer to the image attached.

Let us use the Sine rule here:

As per Sine Rule:

[tex]\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}[/tex]

Where  

a is the side opposite to [tex]\angle A[/tex]

b is the side opposite to [tex]\angle B[/tex]

c is the side opposite to [tex]\angle C[/tex]

[tex]\dfrac{XZ}{sin\angle Y} = \dfrac{XY}{sin\angle Z}\\\Rightarrow \dfrac{966}{sin94^\circ6'} = \dfrac{XZ}{sin38^\circ24'}\\\Rightarrow XZ=\dfrac{966}{sin94^\circ6'} \times sin38^\circ24'\\\Rightarrow XZ=\dfrac{966}{0.997} \times 0.621\\\Rightarrow XZ=601.69 \m \approx \bold{602\ m}[/tex]

Answer:

Total Price = 1.07(0.65x)= 0.6955x.

Step-by-step explanation:

The discount percentage is, d% = 35%.

The sales tax percentage is, s% = 7%.

The variable x represent the original cost of the item(s).

The discount is subtracted from the original amount.

So, the discounted amount will be, 0.65x.

And the sales tax is added to the original amount.

So, the value of tax plus price will be, 1.07x.

Then the final price of the item(s) will be:

Total Price = 1.07(0.65x)= 0.6955x.

Answer:

It's C for those on edgenuity

Step-by-step explanation:

Answer:

It might be 168 centimetres

Step-by-step explanation:

Answer:

The entire floor can contain approximately 4178 fans

Step-by-step explanation:

The first step is to calculate the area of the basketball floor.

we can do this by multiplying the length by the breadth as such 94 X 50 = 4700 square feet.

The second step is to calculate the area occupied by 8 of the fans. We can do this by multiplying 3 ft by 3ft = 9 square feet.

From this, it will be easier to estimate the area occupied by only one fan. This can be got by dividing 9 square feet by 8.  

This is = 1.125 square feet.

To get the number of students it can occupy, we divide the total area of the court by the area occupied by one student.

4700/ 1.125 =4177.8 [tex]\approx[/tex] 4178 fans

Answer:

  x ≠ -2 or 3

Step-by-step explanation:

No denominator can be zero, so ...

  x +2 ≠ 0

  x ≠ -2

__

  x -3 ≠ 0

  x ≠ 3

__

  g(x) ≠ 0 . . . . . true for all x; no restriction needed for this

__

The appropriate restrictions are x ∉ { -2, 3 }.

Answer:

According to the graph, there are 6 pumpkins with the mass of 9kg to 12kg and 4 pumpkins with the mass of 0kg to 3kg.

In order to find how many pumpkins more, you have to subtract it so it will be 6 pumpkins - 4 pumpkins = 2 pumpkins.

Therefore, there are 2 more pumpkins with the mass of 9 to 12kg compared to the pumpkins with the mass of 0 to 3kg.

Answer:

2

Step-by-step explanation:

Answer:

y+6 = 3/5(x-4)

Step-by-step explanation:

Point slope form is

y-y1 = m(x-x1)

where m is the slope and (x1,y1) is a point on the line

y --6 = 3/5( x-4)

y+6 = 3/5(x-4)

Answer:

The inverse represents the temperature F corresponding to a temperature C.

The domain of the inverse function is all real numbers.

194°F

Step-by-step explanation:

Let C= y

y= 5/9 (F - 32),

F= 9/5y + 32

But y= C, hence;

F= 9/5 C +32

The inverse represents the temperature F corresponding to a temperature C.

Given;

F= 9/5 C +32

The domain of the inverse function is all real numbers.

Given C= 90°

F= 9/5 C +32

F= 9/5 (90°) +32

F= 194°F

Answer:

13.75

Step-by-step explanation:

The expected value of the hourly wage is the sum of the probabilities (percentage of time spent on each job) multiplied by the payoff (money earned) from each possible occurrence (job): 0.6 × 11 + 0.25 × 19 + 0.15 × 16 = $13.75.

The average hourly wage will be equal to 13.75 hours.

An average is a single number chosen to represent a group of numbers; it is often the sum of the numbers divided by the number of numbers in the group.

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Given that work at a convenience store 60% of your time, and earn $11.00 an hour. Referee games at your city park 25% of your time, and earn $19.00 an hour. Do your elderly neighbor’s housework 15% of your time, and earn $16.00 an hour.

The expected value of the hourly wage will be calculated as below:-

The expected value of the hourly wage is the sum of the probabilities (percentage of time spent on each job) multiplied by the payoff (money earned) from each possible occurrence (job):

0.6 × 11 + 0.25 × 19 + 0.15 × 16 = $13.75.

Therefore, the average hourly wage will be equal to 13.75 hours.

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Answer: a.) About 54% of the variation in distance that the driver can see is explained by a linear relationship with the driver's age.

b.) The correlation coefficient, r, is -0.736.

Step-by-step explanation:

The coefficient of determination is denoted [tex]R^2 \ or \ r^2[/tex]  which gives the percent of the variance in the dependent variable that is predictable from the independent variable.

Given, [tex]r^2= 0.542[/tex]

That means 54% of the variation in distance that the driver can see is explained by a linear relationship with the driver's age.

Also, [tex]r=\sqrt{0.542}\approx\pm0.736[/tex] , where r determines the correlation coefficient.

As driver;s age increases the distance he can see decreases, so there is a negative correlation between them.

So r= -736.

Hence, The correlation coefficient, r, is -0.736.

So, the correct options are a.) and b.)

Answer:

The correct option is c.

Step-by-step explanation:

The margin of error is the range of values lower than and more than the sample statistic in a confidence interval. It is the number of percentage point by which the sample result will differ from the population result.

The general formula to margin of error is:

[tex]MOE=CV\times\frac{SD}{\sqrt{n}}[/tex]

Here,

CV = critical value

SD = standard deviation

n = sample size

Now, if the computed minimum sample size needed for a particular margin of error is not a whole number, then round the value of n up to the next larger whole number.

Thus, the correct option is c.

Answer & Step-by-step explanation:

Slope-intercept form:

[tex]y=mx+b[/tex]

m is the slope and b is the y-intercept. Insert the given slope:

[tex]y=-5x+b[/tex]

To find the y-intercept, take the given coordinate point and insert:

[tex](-9_{x},-5_{y})\\\\-5=-5(-9)+b[/tex]

Solve for b:

Simplify multiplication:

[tex]-5=45+b[/tex]

Subtract 45 from both sides:

[tex]-50=b\\\\b=-50[/tex]

The y-intercept is -50. Insert:

[tex]y=-5x-50[/tex]

[tex]m=-5\\b=-50[/tex]

Use the slope formula for when you have two points:

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{rise}{run}[/tex]

The slope is the change in the y-axis over the change in the x-axis, or rise over run. Insert the points:

[tex](2_{x1},4_{y1})\\(10_{x2},2_{y2})[/tex]

[tex]\frac{2-4}{10-2}=\frac{-2}{8}=-\frac{2}{8}=-\frac{1}{4}[/tex]

The slope is [tex]-\frac{1}{4}[/tex] . Insert:

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

Now follow the steps from the last problem to find the y-intercept. Choose a point and insert into the equation:

[tex](2_{x},4_{y})\\\\4=-\frac{1}{4}(2)+b[/tex]

Solve for b:

Simplify multiplication:

[tex]-\frac{1}{4}*\frac{2}{1}=-\frac{2}{4}=-\frac{1}{2}[/tex]

Re-insert:

[tex]4=-\frac{1}{2} +b[/tex]

Subtract b from both sides:

[tex]4-b=-\frac{1}{2} +b-b\\\\4-b=-\frac{1}{2}[/tex]

Subtract 4 from both sides:

[tex]4-4-b=-\frac{1}{2}-4\\\\-b=-\frac{1}{2}-4[/tex]

Simplify subtraction:

[tex]-\frac{1}{2}-4=-\frac{1}{2} -\frac{4}{1} =-\frac{1}{2} -\frac{8}{2} \\\\-\frac{1}{2} -\frac{8}{2}=-\frac{9}{2}[/tex]

Re-insert:

[tex]-b=-\frac{9}{2}[/tex]

Divide both sides by -1 to make the variable positive (can be seen as -1b):

[tex]b=\frac{9}{2}[/tex]

The y-intercept is [tex]\frac{9}{2}[/tex] .

Write the equation:

[tex]y=-\frac{1}{4}x+\frac{9}{2}[/tex]

:Done

Answer:

Total number of people in the concert

= 186

Step-by-step explanation:

There are 80 people in level 2

Then in level one

The dimensions of the room are 62 feet by 31 feet.

15 people fit in a 3 feet by 6 feet space.

Area of the room= 62*31= 1922 feet²

area of 15 people space= 3*6= 18 feet²

To know how many 15 people we get in the 2nd level

=Area of room/area of 15 people space

= 1922/18

= 106.77

= 106 (we round down because this is human being.)

Total number of people in the concert

= 106+80

= 186

First thing to do is distribute the [tex]-3[/tex]:

[tex]-3(x+n)=x\\-3x+-3n=x[/tex]

Now we're gonna solve for [tex]x[/tex]:

[tex]-3x-3n=x\\-4x=3n\\x=-\frac{3n}{4}[/tex]

To solve for [tex]n[/tex]:

[tex]-3x-3n=x\\-3n=4x\\n=-\frac{4x}{3}[/tex]

Answer:

1.6101529

Step-by-step explanation:

Given the following :

Number of samples (n) = 210

Sample mean (x) = 5

Population standard deviation = 0.9

Population mean (m) = 4.9

Since the standard deviation of the population is known, we can use the z statistic

Z = (x - m) / standard error

Standard error = sd / √n

Standard error = 0.9 / √210

Standard error = 0.9 / 14.491376

Standard error= 0.0621059

Z statistic = (5 - 4.9) / 0.0621059

Z statistic = 0.1 / 0.0621059

Z statistic = 1.6101529

Answer:

= 0.1 miles per minute

Step-by-step explanation:

= 1.5 miles / 15 min.

= 0.1 miles per minute

Answer:

1280 sq inches

Step-by-step explanation:

A = LW

A = 40 in. * 32 in.

A = 1280 sq inches

Answer:

Step-by-step explanation:

Since the TV screen is a rectangle

Area of a rectangle = l × w

where

l is the length / height

w is the width

From the question

height = 32 inches

width = 40 inches

Substitute the values into the above formula

That's

Area of TV screen = 32 × 40

We have the answer as

Hope this helps you