help with this please

Volume of cylinder = πr^2h

400π = πr^2 *25

r^2 = 400/25

r ^2= 16

r =4 feet

radius = 4 feet

To solve this problem, we need to standardize the IQ scores using the z-score formula:

z = (x - μ) / σ

where x is the IQ score, μ is the mean IQ, and σ is the standard deviation.

For x = 95, we have:

z = (95 - 105) / 15 = -0.67

For x = 115, we have:

z = (115 - 105) / 15 = 0.67

Now, we can use a standard normal table or a calculator to find the probability that a z-score is between -0.67 and 0.67. Using a standard normal table, we find:

P(-0.67 < z < 0.67) = 0.4978

Therefore, the probability that a randomly selected adult has an IQ between 95 and 115 is 0.4978 or about 49.78%.

Answer:

Median: 1, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 5, 5, 6 : 4

Mean: 3.42 (3.42857142857)

Mean would change

FIRST OPTION

Answer:

Step-by-step explanation:

[tex]\mathrm{-4x^3-12x^3+9x^2}[/tex]

Combine like terms:-

[tex]\mathrm{-4x^3-12x^3=\bf-16x^3}[/tex]

[tex]\mathrm{-16x^3+9x^2}[/tex]

Therefore, -16x³ + 8x² is equivalent to -4x³-12x³+9x².

______________________

Hope this helps! :)

By combining like terms in the given expression, we get -16x^3 + 9x^2, which matches with one of the options provided, confirming it as the correct answer.

To find the equivalent expression, we just need to add or subtract the like terms. In the given expression -4x^3 - 12x^3 + 9x^2, the like terms are -4x^3 and -12x^3. These can be combined by performing the arithmetic operation stated, which is subtraction in this case.

So, -4x^3 - 12x^3 = -16x^3. Hence, the simplified form of the original expression would be -16x^3 + 9x^2.

To simplify the expression −4x3−12x3+9x2, you can combine like terms. The terms with the same variable and exponent can be added or subtracted. In this case, the terms -4x3 and -12x3 can be combined to give -16x3. So, the expression becomes -16x3+9x2 .

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Maurice will get 4,547.3 pesos for his trip to Mexico.

To determine how many pesos Maurice will get for his trip when exchanging $370 at a rate of 12.29 pesos per dollar, follow these steps:

1. Identify the amount of dollars Maurice wants to exchange: $370

2. Identify the exchange rate: 1 dollar = 12.29 pesos

3. Multiply the amount of dollars by the exchange rate to find the total amount of pesos: $370 x 12.29 pesos/dollar

By following these steps, Maurice will get $370 x 12.29 = 4,547.3 pesos for his trip to Mexico.

Therefore, 4,547.3 pesos will he get for his trip

This is a problem of multiplication.

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Answer: Let's say that there are a total of x counters in the bag. Then, the ratio of blue counters to red counters is 2:1, so there are 2y blue counters and y red counters for some value of y.

The ratio of small counters to large counters is 1:2, so let's say there are z small counters and 2z large counters.

We know that the rest of the blue counters that are not large are small, and that the ratio of large blue counters to small blue counters is 3:1. So, we can set up the equation:

2z - k = 3k

where k is the number of small blue counters. Solving for k, we get:

k = z/5

So, the number of large blue counters is:

2z - k = 9z/5

The fraction of counters that are red and small is given by:

y/z

Substituting the values we have found, we get:

y/z = (1/3)(2y/x)/(1/5)((2/5)x/(2/3)) = 10/27

Therefore, the fraction of counters that are red and small is 10/27.

Step-by-step explanation:

If we start with one penny and double the amount each day for 30 days, we will have a total of $10,737,418.23 at the end of the month.

To find the total amount of money after 30 days using a geometric series, we can start by noting that the amount of money earned each day is double the amount earned the previous day. If we let P be the initial penny on the first day, then the amount earned on the second day is 2P, the amount earned on the third day is 2(2P) = 2²P, the amount earned on the fourth day is 2(2²P) = 2³P, and so on. We can write the total amount of money earned over 30 days as:

P + 2P + 2²P + 2³P + ... + 2²⁹P

This is a geometric series with first term P and common ratio 2. We can use the formula for the sum of a geometric series to find the total amount of money earned:

total = P(1 - 2³⁰)/(1 - 2) = P(1 - 2³⁰)/(-1)

Simplifying this expression, we get:

total = P(2³⁰ - 1)

Substituting P = $0.01 (one penny), we get:

total = $0.01(2³⁰ - 1) = $10,737,418.23

Therefore, if we start with one penny and double the amount each day for 30 days, we will have a total of $10,737,418.23 at the end of the month.

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complete question;

If we have one penny the first day, we double that penny the next day, we then double the previous day's pennies, and so on for a 30-day month what geometric series should you use to find the total amount of money after 30 days, and what is that total?

If the loan is paid off in full after 8 remaining payments, the borrower is entitled to a refund of $218.87 of the finance charge.

The Rule of 78 is a method used by lenders to calculate how much of the finance charge on a loan should be refunded to the borrower if the loan is paid off early.

Formula to calculate the portion of the finance charge that has been earned by the lender so far. The formula is:

                     [ n / (n(n+1)/2) ] × I

Where n is the total number of payments in the loan and I is the finance charge.

Here we have

The finance charge = 747

Total payments = 24

First, Add up the number of payments made so far and the remaining number of payments to get the total number of payments in the loan:

=>  24 + 8 = 32.

Using the formula (n / (n(n+1)/2)) x I

[ 32 / (32(32+1)/2) ] x 747 = 0.707 x 747 = 528.13

This implies the lender has earned $528.13 of the finance charge so far.

Subtract the amount earned by the lender so far from the total finance charge to find the amount of unearned interest:

=> 747 - 528.13 = 218.87

Therefore,

If the loan is paid off in full after 8 remaining payments, the borrower is entitled to a refund of $218.87 of the finance charge.

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Note that the rocket with the greatest acceleration is Rocket 3.

To find the rocket with the greatest acceleration, the formula to be used is;

Acceleration = net force/mass

Calculating the acceleration of each rocket sing the given data, we get:

Accel eration of rocket 1 = 12.0N/ 0.528 kg = 22.7m/s²

Acceleration of rocket 2 = 8.0N/ 0.426 kg = 18.8m/s²

Acceler ation of rocket 3 = 12.0N/ 0.515 kg = 23.3m/s²

Acceleration of rocket 4 = 8.0N/ 0.477 kg = 16.8m/s²

Given the above, we can confidently state that Rocket 3 is the rocket with the highest acceleration.

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Answer:

1 and 4

Step-by-step explanation:

Delivery is a service, most services are not tangible and are from one person to another (person transporting from a to b) and a 'good' is a product/item where most of them are tangible (phone, CD's, etc).

The degree of each vertex in the graph below is 2

To find the degree of each vertex in a graph, you need to count the number of edges that are incident on that vertex. The degree of a vertex is the number of edges connected to it.

Observe the given graph and count the number of edges to find the degree of the vertices

Here we have a graph

The number of vertices in the graph is 5

As we can see that each vertex is connected by 2 edges  

As we know the degree of a vertice is equal to the number of edges associated with vertices

Hence, the degree of each vertex is 2

Therefore,

The degree of each vertex in the graph below is 2

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The bearing of point A from B is 45° with the distance between them as 8km. The bearing of point C from point A is 135° with distance between them as 6km.

Bearing is usually measured in degrees, with 0° indicating the reference direction (usually North), and increasing clockwise to 360°. It refers to the direction or angle between a reference direction and a point or object.

The distance from point B to point A is 8km and the bearing of point A from point B is 45° while the bearing of point B from point A is 225°.

The distance from point C to point A is 6km and the bearing of point C from point A is 135° while the bearing of point A from point C is 225°.

The distance from point B to point C can be derived using cosine rules when the angle A in the triangle ABC is known

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Answer:

Step-by-step explanation:

FOIL

9x² -27x +27x -81  middle terms cancel

9x² - 81

We can see here that the Pythagorean theorem can help one determine whether the roped off area is in the shape of a right triangle because the converse of Pythagorean Theorem is actually used to prove that a triangle is a right triangle.

Let's understand the definition and meaning of  Pythagorean Theorem.  Pythagorean Theorem is actually seen as the fundamental concept that is used to describe the relationship that exists  between all the sides of a right-angled triangle.

The theorem actually states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Mathematically, it can be expressed as a² + b² = c², where "a" and "b" are the lengths of the two shorter sides, and "c" is the length of the hypotenuse.

When we don't know that a triangle is a right-angle triangle, we use the converse to prove it.

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Answer:

The down payment of $42,600 at 15% would be $6,390.

Let's use a system of equations to represent the problem.

Let m be the number of multi-colored yarn rolls Laura bought and let s be the number of solid colored yarn rolls she bought.

From the problem, we know that:

m + s = 25 (Laura bought a total of 25 rolls of yarn)

4m + 3s = 88 (the total cost of the yarn rolls was $88)

We can use the first equation to solve for one variable in terms of the other. For example, if we solve for s, we get:

s = 25 - m

Now we can substitute this expression for s into the second equation:

4m + 3(25 - m) = 88

Simplifying this equation, we get:

m = 13

So Laura bought 13 multi-colored yarn rolls and 12 solid colored yarn rolls (since 13 + 12 = 25).

Emilia needs 5/2 pints or 2 1/2 pints of baking soda to mix with 5 gallons of water. We used proportionality to solve answer.

What is proportionality ?

Proportionality refers to the relationship between two variables or quantities where they maintain a constant ratio or relative size to each other, even as one of the variables changes.

The cleaning solution requires 3/8 pint of baking soda mixed with 3/4 gallon of water. To find out how much baking soda Emilia needs to mix with 5 gallons of water, we need to use proportionality.

We can set up the following proportion to find the amount of baking soda needed:

(3/4 gallon) / (3/8 pint) = (5 gallons) / x

where x is the amount of baking soda needed in pints.

To solve for x, we can cross-multiply and simplify:

3/4 * x = 3/8 * 5

3x/4 = 15/8

Multiplying both sides by 4/3, we get:

x = (15/8) * (4/3) = 5/2

Therefore, Emilia needs 5/2 pints or 2 1/2 pints of baking soda to mix with 5 gallons of water.

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Answer:

1) 3 lbs for 4.50

Step-by-step explanation:

The first option sells hamburger at 1.50 a pound whereas option two sells hamburger at 1.60

To write an equation for the total amount they spent at the restaurant, we need to add the bill and the tip. The tip is 18% of the bill, which means we need to multiply the bill by 0.18. The equation is:

total=bill+tiptotal=85.60+0.18×85.60

To find the total amount they spent, we need to simplify the equation by using the distributive property and then evaluate it:

totaltotaltotaltotal​=85.60+0.18×85.60=85.60(1+0.18)=85.60×1.18=100.91​

Therefore, they spent $100.91 at the restaurant.

The mean of the data-set shown on the dot plot is given as follows:

6.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

The dot plot shows the number of times that each observation appears, hence the observations are given as follows:

2, 3, 6, 6, 7, 8, 8, 8.

The sum of the observations is given as follows:

2 + 3 + 2 x 6 + 7 + 3 x 8 = 48.

There are 8 observations, hence the mean is given as follows:

48/8 = 6.

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The balance of an account with the principal of $6500 at a rate of 5% invested for 12 years is; $11673.07.

It follows from the task content that the balance in an account with the principal of $6500 at a rate of 5% invested for 12 years is to be determined.

By the compound interest formula; the amount in the account, A is;

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

where P = 6500, r = 5% = 0.05 and t = 12, n = 1.

Therefore;

A = 6500 (1 + 0.05)^(12)

A = 6500 (1.05)^12

A = $11673.07.

Ultimately, the amount in the account after 12 years is; $11673.07.

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(d) If the population was not normally distributed, we couldn't compute these CIs without additional assumptions or using non-parametric methods.

(a) For n=26, the degrees of freedom (df) = 25.

From the t-table, t-value for 96% CI is approximately 2.060.

CI = x ± t*(s/√n) = 115 ± 2.060*(10/√26) = (110.3, 119.7).

(b) For n=15, df=14, t-value ≈ 2.145. CI = 115 ± 2.145*(10/√15) = (108.9, 121.1).

(c) For n=26, the t-value for 90% CI ≈ 1.706. CI = 115 ± 1.706*(10/√26) = (111.4, 118.6).

(d) If the population was not normally distributed, we couldn't compute these CIs without additional assumptions or using non-parametric methods.

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This prompt has to do with the construction of lines and geometrical shapes. See the steps to constructing another line equal to AB below.

To Construct: segment RS with length equal to AB

Step 1:  Draw a work line t. Pick a point on t; call it R. Put point of compass on A and pencil on B. This distance will be the radius of an arc.

Place point of compass at R and, using radius from previous step, make an art that intersects t at S. RS is the required line segment.

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The model predicts that there will be 89.3 million vinyl album sales in the country in the year 2030 by using quadratic equation.

Define quadratic equation?

A quadratic equation is a polynomial equation of the second degree, meaning it contains at least one squared term (x²). The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and x is the variable. The values of a, b, and c determine the shape of the parabola, which is the graph of a quadratic equation.

To predict the number of vinyl album sales in the year 2030, we need to substitute x = 20 into the polynomial:

[tex]0.2x^2 + 0.3x + 3.3[/tex]

[tex]= 0.2(20)^2 + 0.3(20) + 3.3[/tex]

[tex]= 80 + 6 + 3.3[/tex]

[tex]= 89.3[/tex]

Therefore, the model predicts that there will be 89.3 million vinyl album sales in the country in the year 2030.

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The surface area of the cylinder in terms of π is 32.48π in2.

Surface area is a measurement of the total area of a given surface of a three-dimensional object. It is a two-dimensional measurement and is expressed in units such as square feet or square meters. Surface area is an important concept in mathematics, physics, engineering, and other sciences. It is used to measure the size of objects, calculate the volume of a space, and to calculate the area of an object’s surface. Surface area can also be used to calculate pressure, force, and energy, as well as other properties of an object.

This is calculated by using the formula for the surface area of a cylinder, which is 2πr2 + 2πrh. In this case, the radius of the cylinder (r) is equal to the diameter (2.8 inches) divided by two; therefore, the radius is 1.4 inches. The height (h) of the cylinder is 3 inches. Substituting these values into the formula, the surface area of the cylinder is 2π (1.4)2 + 2π (1.4) (3) = 32.48π in2.

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The surface area of the rectangular prism is 100 square miles.

We have,

To find the surface area of a rectangular prism, we need to add the areas of all its faces.

A rectangular prism has six faces, each of which is a rectangle.

The formula for the surface area of a rectangular prism is:

Surface area = 2lw + 2lh + 2wh

where l, w, and h are the length, width, and height of the rectangular prism, respectively.

Given the values of length, breadth, and height, we can substitute them into the formula:

Surface area = 2(2 mi × 4 mi) + 2(2 mi × 7 mi) + 2(4 mi × 7 mi)

Surface area = 16 mi² + 28 mi² + 56 mi²

Surface area = 100 mi²

Therefore,

The surface area of the rectangular prism is 100 square miles.

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Probability that a randomly selected subject tested negative AND did not use marijuana is 0.052 (or 5.2%).

Probability is the likelihood that an event will occur. It is a measure of the chance that something will happen, expressed as a number between 0 and 1, where 0 means that the event is impossible, and 1 means that the event is certain. Probability can be used to predict the outcomes of certain events, to determine the likelihood of certain outcomes, or to make decisions about risk. Probability can also be used in statistics to make predictions about a population or a sample.

The total number of subjects included in the study was 298.

Contingency Table
   
Used Marijuana  Did Not Use Marijuana
Positive Test  144   25
Negative Test  4   154

The probability that a randomly selected subject did not use marijuana is 0.517 (or 51.7%).

The probability that a randomly selected subject tested negative AND did not use marijuana is 0.052 (or 5.2%).

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