the childrens museum sells caps and t-shirts for a total of 278 items at its annual fundraiser. They take in a total of $2110. Caps cost 8$ and t shirts cost $7. How many caps did they sell?

The 12th term of the sequence with a first term of -9 and common difference of 2 is 13

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

An nth term of arithmetic term is given as:

[tex]a_n=a+(n-1)d[/tex]

where a is the first term and d is the common difference and n is the term.

Given that a = -9, d = 2

The 12th term of the sequence is:

a₁₂ = -9 + (12 - 1)2

a₁₂ = -9 + 22

a₁₁ = 13

The 12th term of the sequence is 13

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Answer: Let's call the area of Brad's rectangular backyard "A". The area of the white circle is "C". The area of the gray region, the portion of the yard that the water from the sprinkler does not reach, is "G".

We know that the sum of the areas of the white circle and the gray region is equal to the area of Brad's backyard:

C + G = A

Therefore, the expression to represent the gray region is:

G = A - C

Step-by-step explanation:

Force is required to make an object move, and force acts differently on objects depending on the type of motion it exhibits. In the case of curvilinear motion, a special force comes into the picture, i.e., centripetal force – literally meaning “centre seeking.” Centripetal force is the force acting towards the centre of the circular path. In this article, let us discuss what centripetal force is and how it is different from centrifugal force.

Assuming that an unfair coin is tossed with outcomes of HH, HT, TH, and TT, and the probability is 0.40, 0.92, 0.29, and 0.55, then the given probabilities do not form a valid probability model for the sample space of two coin tosses.

The given probabilities do not form a valid probability model for the sample space of two coin tosses since a valid probability model must satisfy the following conditions:

To calculate the sum of the probabilities, we simply add up all of the given probabilities:

0.40 + 0.92 + 0.29 + 0.55 = 2.16

In this case, the sum of the probabilities is 2.16, which is greater than 1. Hence, the given probabilities do not form a valid probability model for the sample space of two coin tosses.

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The statement that involves descriptive statistics is -

Option A) The Alcohol, Tobacco, and Firearms Department reported that Houston had 1,791 registered gun dealers in 1997.

What are two categories of field statistics?

There are two categories of field statistics. Descriptive and inferential statistics. Both of them help analysts to make sense of row after row data.

Descriptive statistics presents quantifiable descriptions in a simple way. Inferential statistics is used to draw conclusions that go beyond the raw data only. It is used in making judgments, inferences to deeper general conditions.

The Alcohol, Tobacco, and Firearms Department reported that Houston had 1,791 registered gun dealers in 1997.

Descriptive statistics are useful in describing the basic features of the data being analyzed. They simply provide what the raw data shows. They simplify huge amounts of data sensibly and make it presentable in a manageable form.

With regard to the question, raw data is available stating that the registered gun dealers were 1791 in 1997. It, therefore, involves descriptive statistics.

Therefore, the correct answer is option A.

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Which of the following statements involve descriptive statistics as opposed to inferential statistics?

A) The Alcohol, Tobacco, and Firearms Department reported that Houston had 1,791 registered gun dealers in 1997.

B) Based on a survey of 400 magazine readers, the magazine reports that 45% of its readers prefer double-column articles.

C) The FAA samples 500 traffic controllers in order to estimate the percent retiring due to job-stress-related illness.

D) Based on a sample of 300 professional tennis players, a tennis magazine reported that 25% of the parents of all professional tennis players did not play tennis.

Answer:

Step-by-step explanation:

To calculate the value of Andrea's savings account after 8 years, we need to find the balance after compounding the interest for 96 months (8 years x 12 months per year). We can use the formula for compound interest:

A = P * (1 + r/n)^(nt)

where:

A is the balance after t years,

P is the initial balance ($1700),

r is the annual interest rate (2.5%),

n is the number of times interest is compounded in a year (12),

t is the number of years (8).

Converting the interest rate to a decimal and dividing by the number of times compounded per year:

r/n = 2.5% / 12 = 0.021

Plugging in the values into the formula:

A = 1700 * (1 + 0.021)^(12 * 8) = 1700 * (1.021)^96

Calculating the value:

A = 1700 * 2.8412 = 4860.80

So, the value of Andrea's account after 8 years would be $4860.80.

The 95% confidence interval for mean of the population is CI = (3.81,6.19).

What is confidence interval?

The confidence interval for the population mean can be found when we know the sample mean and the margin of error of the interval. This last value depends on the standard deviation, the sample size and the confidence level of the interval.

The sample size is n = 100.

The sample mean is x' = 5

The sample standard deviation is s = 6

The confidence level is 1 - α = 0.95

Find the Probability Distribution.

Let [tex]x_1,x_2,....,x_n[/tex] be a random sample of size n taken from a normal distribution with unknown mean μ and unknown variance σ².

The random variable t with formula t = (x' - μ) / (s/√n) has a t distribution with (n - 1) degrees of freedom.

[tex]t_\frac{\alpha}{2}[/tex]

1 - α = 0.95

α = 1 - 0.95

α = 0.05

α / 2 = 0.05 / 2

α / 2 = 0.025

The degree of freedom is -

d.f = n - 1

d.f = 100 - 1

d.f = 99

So, [tex]t_\frac{\alpha}{2}[/tex] using the t-distribution table is -

[tex]t_\frac{\alpha}{2} = 1.984[/tex]

To illustrate the use of the table, note that the t-value with 99 degrees of freedom having an area of 0.025 to the right is [tex]t_\frac{\alpha}{2} = 1.984[/tex].

Then the Confidence interval is -

CI = x' ± [tex]t_{\frac{\alpha}{2},n-1}[/tex] × s/√n

CI = 5 ± 1.984 × 6/√100

CI = 5 ± 1.984 × 6/10

CI = 5 ± 1.984 × 0.6

CI = (5 - 1.19) (5 + 1.19)

CI = (3.81,6.19)

Therefore, the confidence interval is CI = (3.81,6.19).

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A random sample of 100 observations from a population yields a mean equal to 5 and a standard deviation equal to 6. What is the 95% confidence interval for the mean of the population?

Step-by-step explanation:

a probability is always the ratio of

desired cases / totally possible cases

the "group" is the totally possible cases = 119.

we pick 1 student.

female AND off-campus.

there are only 20 students that satisfy that criteria.

the probabilty for this event is then

20/119 = 0.168067227... ≈ 0.168

male AND on-campus.

there are 34 students that satisfy that criteria.

the probability for this event is then

34/119 = 0.285714286... ≈ 0.286

off-campus OR male.

there are 20+11 = 31 students off-campus.

and there are 34+11 = 45 male students.

the overlapping number of 11 students we need to count only once.

so, there are 20+11+34 = 65 students off-campus or male (incl. the on-campus males, as this is an or-criteria).

the probabilty for this event is then

65/119 = 0.546218487... ≈ 0.546

on-campus OR female.

there are 54+34 = 88 students on-campus.

and there are 54+20 = 74 female students.

the overlapping number of 54 students we need to count only once.

so, there are 54+34+20 = 108 students on-campus or female.

the probabilty for this event is then

108/119 = 0.907563025... ≈ 0.908

For the given normal distribution, The 97th percentile of the cholesterol measurements is 218.8 mg/dL.

The normal distribution, also known as the Gaussian distribution or bell curve, is a continuous probability distribution that is symmetrical around its mean value. It is a widely used distribution in many fields, including finance, engineering, and the natural sciences, due to its important properties, such as the central limit theorem.

To find the 97th percentile of a normal distribution with mean 200 and standard deviation 10, we need to find the value x such that P(X < x) = 0.97, where X is a random variable representing the cholesterol measurement.

This value can be found using a standard normal distribution table (or Z-table), which gives the cumulative probabilities for a standard normal distribution with mean 0 and standard deviation 1.

We first standardize our random variable X by subtracting the mean and dividing by the standard deviation:

Z = (X - 200) / 10

So,

P(X < x) = P((X - 200) / 10 < (x - 200) / 10)

                   = P(Z < (x - 200) / 10) = 0.97.

Using the Z-table, we can find the Z-score corresponding to a cumulative probability of 0.97: Z = 1.88.

Finally, we can convert back to the original units for X by multiplying the Z-score by the standard deviation and adding the mean:

x = 10 * 1.88 + 200 = 218.8

So, the 97th percentile of the cholesterol measurements is 218.8 mg/dL.

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Answer:

350

Step-by-step explanation:

calculator

Answer: [tex]5.301[/tex] x [tex]10^{7}[/tex]

Answer: x10^7

Step-by-step explanation: 5.301 = x10^7

The correct graph is the last one (where the shaded region is on the right side)

Here we have the system of inequalities below:

y ≤ 1/2x+1

y > -2x+4

The first inequality is:

y ≤ 1/2x+1

Here we have a solid line with positive slope, and the shaded region is below that line.

The second inequality is:

y > -2x+4

This time we will have a dashed line with negative slope, and the shaded region must be above the line, then the correct option will be the last option.

(where the shaded region is on the right quadrant)

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Answer:

The current population in Algeria can be calculated by solving the equation P = 38(1+r)^t, where P is the population in millions after t years. Setting t = 0 gives us the current population: P = 38(1+r)^0 = 38, so the current population in Algeria is 38 million.

The reasons for the steps are given below.

The value of x is -4.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 7 is an equation.

We have,

-2(4x + 3) = 26

[ The distributive property of multiplication over addition ]

-2(4x) + -2(3) = 26

-8x - 6 = 26

[ Adding 6 on both sides ]

-8x - 6 + 6 = 26 + 6

-8x = 32

[ Divide -8 into both sides ]

-8x/-8 = 32/-8

x = -4

Thus,

The reasons for the steps are given above.

x = -4

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Step-by-step explanation:

Since we have 9 people and 13 burgers, the problem set up is dividing 13 burgers between 9 people

[tex] \frac{13 \: burgers}{9 \: people} [/tex]

= 1.44 burgers per person

Answer:

Step-by-step explanation:

To find out the part of the report that the coach has left to write, we first need to find out how much of the report he has already written. On Saturday, he wrote 1/8 of the report, and on Sunday, he wrote 1/2 of the report.

So, the total part of the report that the coach has written is:

1/8 + 1/2 = 5/8

Now, we subtract this fraction from 1 to find the part of the report that the coach still has to write.

1 - 5/8 = 3/8

So, the coach has 3/8 of the report left to write.

The Residual is 0.944 kg.

The discrepancy between a response variable's observed value and its expected value as predicted by the regression line.

Given:

Residual is typically defined as actuals minus predicted.

The prediction is calculated from

W = −6.07 + 0.1693L

W = −6.07 + 0.1693(48)

W = 2.0564 kg

And, The actual was 3 kg

So, the residual

= 3 - 2.0564

= 0.9436

= 0.944 kg

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All possible values of 'x' such that the distance between the points is 17 is, x = 19 or x = 3.

The distance formula between two points (x₁, y₁) and (x₂, y₂) is,

[tex]D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2[/tex].

Given, (x₁, y₁) = (11, 6) and (x₂, y₂) = (x,- 9) and the distance between them

is 17 units.

Therefore, The equation can be constructed as,

[tex]17 = \sqrt{(x - 11)^2 + (- 9 - 6)^2[/tex].

[tex]17 = \sqrt{(x - 11)^2 + 225[/tex].

Taking squares on both sides to remove the square root we have,

289 = (x - 11)² + 225.

289 = x² - 22x + 121 + 225.

x² - 22x + 57 = 0.

x² - 19x - 3x + 57 = 0.

x(x - 19) - 3(x + 19) =0.

x = 19 or x = 3 are the two possible points.

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The absolute value of this difference is 18 miles, so the walk diagonally across the rectangle park is approximately 18 miles shorter than walking along the two sides of it.

A rectangle is just a square with four perpendicularly in the Euclidean plane. An equiangular quadrant or a quadrant that appears to have identical angles are other names for it. A straight angle is another choice for the parallelogram. A square has four edges that are the same length. Quadrilaterals with four equal edges and four 90° edges are called rectangles. As a consequence, it is occasionally referred to as a "equirectangular square".

Here,

The length of the diagonal of the rectangle can be found using the Pythagorean theorem:

d = √(8^2 + 6^2) ≈ 10

So the length of the diagonal is approximately 10 miles.

To find the distance of walking along the two sides of the rectangle, we can use the formula for the perimeter of a rectangle:

P = 2l + 2w

where P is the perimeter, l is the length, and w is the width.

In this case, we have:

P = 2(8) + 2(6) = 28

So the distance of walking along the two sides of the rectangle is 28 miles.

The difference between walking along the two sides and walking diagonally can be found by subtracting the distance of walking along the two sides from the length of the diagonal:

10 - 28 ≈ -18

The absolute value of this difference is 18 miles, so the walk diagonally across the park is approximately 18 miles shorter than walking along the two sides of it.

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The equations which give exponential graphs are y = 5ˣ and y = (1/5)ˣ.

What is an exponential graph?

A curve that depicts an exponential function is known as an exponential graph. A curve with a horizontal asymptote and either an increasing slope or a decreasing slope is called an exponential graph. The graph begins as a horizontal line and then grows or decays slowly at first before accelerating.

The general formula for an exponential function is,

           f(x) = aˣ

Where the input values of the function, which is x, appear as the exponent of the function.

The values x can be all real numbers.

The base of the function (a)  should be a constant. It should be greater than 0 and should not be equal to 1.

Following the above prerequisites, the equations which give exponential graphs are y = 5ˣ and y = (1/5)ˣ.

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Answer:

(3^2*2h^4)

Step-by-step explanation:

Step-by-step explanation:

Amounts he payed first = $480

Monthly amount he pays = $73

No of months he payed it for = 12

Additional amount he payed = 73 × 12 = 876

Total amount = 480 + 876 = $1356

The Volume of the given pyramid is 66.7[tex]cm^{3}[/tex].

Volume is defined as the amount of space occupied by any three-dimensional objects. The unit of volume for any solid objects is measured using cubic units.

In this pyramid, length = 5cm, width = 5cm and height = 8cm.

Volume of pyramid is given by , V= [tex]\frac{1}{3}*l*w*h.[/tex]

                                                     V=[tex]\frac{1}{3} *5*5*8[/tex]

                                                        = [tex]\frac{200}{3}[/tex]

                                                     V=66.7[tex]cm^{3}[/tex]

Hence, the volume of the given pyramid is 66.7[tex]cm^{3}[/tex].

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Answer:

the possible values of x such that the distance between (11, 6) and (x, -9) is 17 are 19 and 3.

Step-by-step explanation:

We can use the distance formula to find the possible values of x:

d = √[(x2 - x1)^2 + (y2 - y1)^2]

17 = √[(x - 11)^2 + (-9 - 6)^2]

289 = (x - 11)^2 + 225

64 = (x - 11)^2

±8 = x - 11

Solving for x in both equations, we get:

x - 11 = 8 or x - 11 = -8

x = 19 or x = 3

Therefore, the possible values of x such that the distance between (11, 6) and (x, -9) is 17 are 19 and 3.

Step-by-step explanation:

x÷12

2/3/12

2×12/3

24/3

8

Answer:

1 4

2 c³,c²,c,-11

3 1/3

4 -1

5 3/4

Answer:

solution

we assume the negative part because their is no squares of negative number.

10²-2(-10)-100

we get answer which is 20

The fractional value for [tex]$0.23\overline{72}$[/tex] is 261 / 1100.

What is fraction?

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.

The decimal value is given as -

[tex]$0.23\overline{72}$[/tex]

To convert [tex]$0.23\overline{72}$[/tex] repeating into a fraction, begin writing this simple equation -

[tex]n=$0.23\overline{72}$[/tex] ..... (1)

Notice that there are 2 digits in the repeating block (72), so multiply both sides by 1 followed by 2 zeros, i.e., by 100.

[tex]100n=$0.2372\overline{72}$[/tex] .... (2)

Now subtract equation 1 from equation 2 to cancel the repeating block (or repetend) out.

[tex]100n-n=$0.2372\overline{72}$ - $0.23\overline{72}$[/tex]

[tex]99n = 23.49[/tex]

n = 23.49 / 99

n = 2349 / 9900

n = 261 / 1100

Therefore, the fraction is 261 / 1100.

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The value of x is 2 so that the volume is 48 m³

The area of a rectangle is the region occupied within the boundary of the rectangle.

The formula of the area of a rectangle is used to find the area occupied by the rectangle within its boundary. The area of a rectangle is obtained by multiplying its length and width (breadth).

Area of a Rectangle = Length × Width

Volume of a rectangular solid is the product of the length, width, and height.

Volume of a rectangular solid in terms of the area of the base. The area of the base B is equal to Length × Width

Base = Length × Width

Volume of rectangular solid = Base × Height

Given:

Length of rectangular piece of metal = 10 - 2x

Breadth of rectangular piece of metal = 8 - 2x

Area of rectangle = Length × Width

(10 - 2x) (8 - 2x) = 24

80 - 20x - 16x + 4x² = 24

4x² - 36x + 56 = 0

x² - 9x + 14 = 0

x² - 7x - 2x + 14 = 0

x(x - 7) -2(x - 7) = 0

(x - 2)(x - 7) = 0

x = 2 and x = 7(Not possible)

when x = 2 cm (height)

Volume = Area of Base × height

Volume = 24 × 2

Volume = 48 cm³

So, the value of x is 2.

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