A thrill ride swings passengers back and forth, a little higher each time up to 137 feet. Suppose the height of the swing after 30 seconds is 45 feet. How much higher will the ride swing

Answer:

Step-by-step explanation:

Since △PQR ~ △STU, their corresponding angles are congruent, and their corresponding sides are proportional.

First, we can find the measure of angle Q as follows:

m∠Q = 180 - m∠P - m∠R = 180 - 70 - 46 = 64 degrees

Next, we can use the fact that the sides of the similar triangles are proportional to set up the following proportions:

frac{ST}{21} = frac{SU}{14} and frac{ST}{28} = frac{TU}{21}

Solving for ST gives us:

ST = frac{21}{14} SU = frac{3}{2} SU

and

ST = frac{28}{21} TU = frac{4}{3} TU

Substituting these values into the second proportion, we get:

frac{3}{2} SU = frac{4}{3} TU

Multiplying both sides by 2/3, we get:

SU = frac{8}{9} TU

Now we can use the fact that the angles in a triangle add up to 180 degrees to find the measure of angle T.

m∠T = 180 - m∠S - m∠U = 180 - m∠S - (180 - m∠P - m∠R)

m∠T = m∠P + m∠R - m∠S = 70 + 46 - m∠S = 116 - m∠S

Finally, we can use the fact that the angles in △STU add up to 180 degrees to find the measure of angle S.

m∠S + m∠T + m∠U = 180

Substituting the previously found values for m∠T and SU into the equation, and solving for m∠S gives us:

m∠S = 52 degrees

Therefore, the missing measures are:

SU = 6 x 8/9 = 16/3

ST = 3/2 x 6 = 9

TU = 4/3 x 9 = 12

m∠S = 52 degrees

m∠T = 116 - 52 = 64 degrees

m∠U = 180 - 52 - 64 = 64 degrees

A student should score 598 in order to win the award.

To calculate how high should a student score be to win this award, we use the z-score formula.

z=(x-μ)/σ

Where,

μ= Mean of the scores on this exam

σ= Standard deviation of the scores on this exam

z= Z-score

x= Scores on this exam

By substituting the given values in the formula, we get

z=(x-μ)/σ

[tex]= (x-538)/30[/tex]

To find the highest 2.5%, we use the normal distribution table which gives us the Z-score corresponding to 0.975. The highest 2.5% is on each side of the normal distribution curve. Therefore, we have to subtract the area from the highest score, then divide by two.

Subtracting 0.975 from 1 gives us the area to the left of this point on the table which is equal to 0.025.Z = 1.96.

So the score should be one standard deviation above the mean. Thus, the score a student needs to get in the top 2.5% of statewide scores is

   [tex]Z = (x - 538) / 30[/tex]

[tex]1.96 = (x - 538) / 30x - 538 = 1.96 * 30x - 538 = 58.8 + 538x = 597.8[/tex]

The score a student needs to get in the top 2.5% of statewide scores is 598, rounded up to the next integer.

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Answer:

1/2

Step-by-step explanation:

options in a 6 sided die= 1,2,3,4,5,6

greater than 3 = 4,5,6

so three  sides  out of a 6 sided die is greater than three

P(not greater than 3) = [tex]\frac{6-3}{6} = \frac{1}{2}[/tex]

Answer:

1/2 or 0.5

Step-by-step explanation:

The probability of rolling a number greater than 3 on a six-sided die is 3/6 or 1/2, since there are three numbers (4, 5, 6) out of six that are greater than 3.

To find the probability of not rolling a number greater than 3, we can subtract the probability of rolling a number greater than 3 from 1:

P(not greater than 3) = 1 - P(greater than 3)

P(not greater than 3) = 1 - 1/2

P(not greater than 3) = 1/2

Therefore, the probability of not rolling a number greater than 3 is 1/2 or 0.5.

Player A's weight was 0.208 standard deviations below the mean weight of the football team.

To calculate the standard deviation, we first need to calculate the mean weight of the football team

Mean weight = (sum of all weights) / (number of team members)

(174+176+178+184+185+185+185+185+188+190+200+202+205+206+210+211+211+212+212+215+215+220+223+228+230+232+241+241+242+245+247+250+250+259+260+260+265+265+270+272+273+275+276+278+280+280+285+285+286+290+290+295+302) / 52

= 225.5 pounds

Now we can calculate the standard deviation using the following formula:

Standard deviation = sqrt((sum of (x - mean)^2) / N)

Where x is the weight of a team member, N is the total number of team members.

We can simplify this formula by calculating the variance first:

Variance = (sum of (x - mean)^2) / N

So we have

Variance = ((174-225.5)^2 + (176-225.5)^2 + ... + (302-225.5)^2) / 52

= 10764.35

Now we can calculate the standard deviation

Standard deviation = sqrt(Variance)

= sqrt(10764.35)

= 103.76

To find out how many standard deviations above or below the mean Player A's weight was, we can use the following formula

Z-score = (x - mean) / standard deviation

Where x is Player A's weight, mean is the mean weight of the team, and standard deviation is the standard deviation we just calculated.

So we have

Z-score = (204 - 225.5) / 103.76

= -0.208

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The given question is incomplete, the complete question is:

Following are the published weights (in pounds) of all of the team members of Football Team A from a previous year.

174, 176, 178, 184, 185, 185, 185, 185, 188, 190, 200, 202, 205, 206, 210, 211, 211, 212, 212, 215, 215, 220, 223, 228, 230, 232, 241, 241, 242, 245, 247, 250, 250, 259, 260, 260, 265, 265, 270, 272, 273, 275, 276, 278, 280, 280, 285, 285, 286, 290, 290, 295, 302

median = 241

the first quartile = 205.5

the third quartile = 272.5

Assume the population was Football Team A. When Player A played football, he weighed 204pounds. How many standard deviations above or below the mean was he?

Answer: slope=4

Step-by-step explanation:

[tex]Slope=\frac{y2-y1}{x2-x1}[/tex]

[tex]Slope=\frac{4- - 4}{3-2}[/tex]

[tex]Slope=\frac{4+4}{3-2}[/tex]

[tex]Slope=4[/tex]

The expressions 6 × 3+6 × 8 and 6(3 + 8), respectively, indicate the combined size of the two rooms.

A plane figure's overall area is the sum of all of the distinct area shapes that make up that plane figure.

We have two regions that take on the characteristics of a rectangle based on the information provided.

The office area = 18 square feet

There are 48 square feet in the sitting room.

The two chambers now have a combined size of 18 + 48 = 66 square feet.

Now, the expressions that better represent the total area of the two rooms can be written as 6 × 3+6 × 8 and 6(3 + 8).

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Answer:

3.1% of Ramon's earning are spent on electricity.

Step-by-step explanation:

Ramon's monthly salary

= $1,710

Electricity rent

=$53.60

*work show below*

[tex]\frac{53.60}{1,710} *100[/tex]

0.0313450292397661*100=3.134502923976608

3.134502923976608 rounded to the nearest tenth is 3.1%...

Thus my-our answer checks out! have a great day bestie!

The probability of randomly chosen, a 50-year-old or older voter from the winning party is 45.84%

Given the table of values

From the table of values, we have the winning party to be

New Democratic

From the column of New Democratic, we have

Total = 9422

50-year-old or older voter = 4319

So, the required probability is

Probbaility = 4319/9422

Evaluate

Probbaility = 0.45839524517

This gives

Probbaility = 45.839524517%

Approximate

Probbaility = 45.84%

Hence, the probability is 45.84%

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Answer:

D

Step-by-step explanation:

Volume: π*[tex]r^{2} *h[/tex]= π*[tex]4^{2}[/tex]*6.2=311.49

According to the solution we have come to find that, The missing sides are t=ST=9 and s=RT=12.

what is right angle triangle?

A right angle triangle, also known as a right triangle, is a triangle that has one angle measuring 90 degrees, which is also known as a right angle. The side opposite to the right angle is called the hypotenuse, and the other two sides are called legs or catheti. The Pythagorean theorem, which states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse, is a fundamental property of right triangles. Right triangles are important in mathematics and physics, and they have many applications in geometry, trigonometry, and calculus.

We can use the fact that the two triangles are similar to set up a proportion and solve for the missing sides.

AB/RS = BC/ST = AC/RT

Substituting the given values:

5/RS = 3/9 = 4/s

Solving for RS:

RS = (5/3) * 9 = 15

Solving for RT:

RT = (4/5) * 15 = 12

Therefore, the missing sides are t=ST=9 and s=RT=12.

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Based on the information, the area of the figure would be: 86.13 units ²

To find the area of the figure we must perform the following procedure:

1. Find the area of the triangle with the following formula:

height * base / 2 = area of the triangle

6 * 6 / 2 = area of the triangle

18 = area of the triangle

2. Find the area of the rectangle with the following formula:

height * base = area of rectangle

6 * 9 = area of the rectangle

54 = area of rectangle

3. Find the area of the semicircle with the following formula:

[tex]\pi[/tex]  * r² / 2 = area of the semicircle

[tex]\pi[/tex]  * 3² / 2 = area of the semicircle

[tex]\pi[/tex]  * 9 / 2 = area of the semicircle

28.27 / 2 = area of the semicircle

14.13 = area of the semicircle

4. We must add the area of all the figures to find the total area.

14.13 + 54 + 18 = 86.13 units ²

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When the Rhoads family fills their above-ground pool with approximately 3,205 gallons of water, they add a weight of approximately 503,432.61 pounds to the pool.

We can use the given weight of water per gallon to find the total weight of water added to the pool:

Weight of 1 gallon of water = 8.34 pounds

Number of gallons of water in the pool = 3,205 gallons

Radius of the pool = 6 feet (half of the diameter)

Volume of the pool = π × (Radius)^2 × Depth

The depth of the pool is not given, so let's assume it is 4 feet (a common depth for above-ground pools):

Volume of the pool = π × (6 feet)^2 × 4 feet

Volume of the pool ≈ 452.39 cubic feet

Number of gallons of water in the pool = Volume of the pool ÷ 7.48

Number of gallons of water in the pool ≈ 60,381.71 gallons

Total weight of water added to the pool = Weight of 1 gallon of water × Number of gallons of water in the pool

Total weight of water added to the pool ≈ 503,432.61 pounds

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_____The given question is incomplete, the complete question is given below:

A gallon of water weighs 8.34 pounds. The Rhoads family has a round, 12-foot diameter, above-ground pool. How much weight is added to the pool when it is filled with 3, 205 gallons of water?

The polynomial equation roots are the values of x that make the equation equal to zero.

Graphing calculator and the system of equations are used to find the roots of a polynomial equation. To find the roots of a polynomial equation, follow the below methods ,Use a Graphing Calculator to Graph the Equation. Graphing the equation is one of the easiest ways to find the roots of a polynomial equation. By looking at the graph, you can see where the equation crosses the x-axis. If it crosses the x-axis, then the value of x where it crosses is a root of the polynomial equation.

Another way to find the roots of a polynomial equation is to use a system of equations. In a system of equations, you have two equations that you solve simultaneously. To use a system of equations, you will need to know the degree of the polynomial equation, the coefficients of the terms, and the values of the constants.

We can also use synthetic division to find the roots of a polynomial equation. Synthetic division is a way to divide a polynomial by a linear factor. If the result is zero, then the value of x that you divided by is a root of the polynomial equation.

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As a general rule, a Z-score of - 3.0 to 2.0 recommends that a stock is exchanged inside three standard deviations of its mean.

A Z-Score is a statistical estimation of a score's relationship to the mean in a gathering of scores.

A Z-score can uncover to a merchant on the off chance that worth is normal for a predefined informational collection or on the other hand assuming it is abnormal.

As a general rule, a Z-score of - 3.0 to 2.0 recommends that a stock is exchanged inside three standard deviations of its mean.

Merchants have created numerous techniques that utilize z-score to distinguish connections between's exchanges, and exchanging positions, and assess exchanging systems.

The higher (or lower) a z-score is, the further away from the mean the fact is. This isn't really positive or negative; it just shows where the information lies in a regularly conveyed test. This implies it comes down to inclination while assessing speculation or opportunity. For instance, a few financial backers utilize a z-score scope of - 3.0 to 3.0 on the grounds that 99.7% of regularly conveyed information falls here, while others could utilize - 1.5 to 1.5 in light of the fact that they favor scores nearer to the mean.

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Option C, 12, is the correct answer. To spray the vegetables 5 times each hour, we need to determine how often the spray should occur.

Since there are 60 minutes in an hour, and we want the vegetables to be sprayed 5 times in that hour, we can divide 60 by 5 to get the interval between each spray:

60 ÷ 5 = 12

This means that the interval between each spray should be 12 minutes. Therefore, we should set the timer for 12 minutes in order to spray the vegetables 5 times each hour.

Option C, 12, is the correct answer.

It is important to note that this assumes the vegetable display is in operation for the entire hour without interruption. If the display is turned off or there are other factors that interrupt the timing, the frequency of sprays may be affected. Additionally, the optimal frequency of sprays may vary depending on the specific vegetables and the environment they are in.

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The value of the perimeter, p, of the smaller trapezium is 113.

The perimeter of the trapezium is the distance round the trapezium and for this given diagram it can be calculated using congruence theorem.

The Congruence Theorems are a set of geometric principles that state when two geometric figures are congruent, which means they have the same size and shape.

Applying congruence theorem, we will have the following equation;

Side length: x/42

Area: 200/288

Perimeter : p/162

x/42 = p/162 ------ (1)

200/288 = p/162 ---- (2)

from (1), p = (162x)/42 = 3.857x

Substitute the value of p into (2)

200/288 = (3.857x)/162

162(200/288) = 3.857x

112.5 = 3.857x

x = 29.17

p = 3.857 x 29.17

p = 112.5

p ≈113

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Answer:

The answer is 2.

Answer:

The equation 3^4 x 2^3 = 6^4+3 is incorrect.

To evaluate the left side of the equation, we first simplify each term using exponent rules:

3^4 = 3 x 3 x 3 x 3 = 81

2^3 = 2 x 2 x 2 = 8

So 3^4 x 2^3 = 81 x 8 = 648

To evaluate the right side of the equation, we simplify the exponent first:

6^4+3 = 6^4 x 6^3 = 1296 x 216 = 279936

Therefore, the corrected equation should be:

3^4 x 2^3 = 648 = 6^4 - 288

Notice that 6^4 - 288 is equal to the original value of 279936, but the equation has been written correctly by moving the 3 to the other side of the equation and changing the operation from addition to subtraction.

Answer: 21

Step-by-step explanation:because 21 savage is #1

Step-by-step explanation:

We can also solve the equation x² + 4x + 4 = 8 by rearranging the terms and using the quadratic formula:

x² + 4x + 4 - 8 = 0

x² + 4x - 4 = 0

Applying the quadratic formula, we have:

x = (-b ± √(b² - 4ac)) / 2a

where a = 1, b = 4, and c = -4. Substituting these values, we get:

x = (-4 ± √(4² - 4(1)(-4))) / 2(1)

x = (-4 ± √32) / 2

Simplifying the square root of 32, we get:

x = (-4 ± 4√2) / 2

x = -2 ± 2√2

Therefore, the solutions to the equation x² + 4x + 4 = 8 are x = -2 + 2√2 and x = -2 - 2√2.

Answer:

2x + 18y

Step-by-step explanation:

-5x - 3y + 7x + 21y  ----> (combine like terms)

2x - 3y + 21 y   ---> (combine like terms)

2x + 18y

Answer:

[tex]\huge\boxed{\sf 2(x + 9y)}[/tex]

Step-by-step explanation:

= -5x - 3y + 7x + 21y

= -5x + 7x - 3y + 21y

= 2x + 18y

So, take 2 as a common factor

[tex]\rule[225]{225}{2}[/tex]

To create an 80% alcohol solution, the pharmacist must therefore mix 2.17 cm3 of pure alcohol with 10 cm3 of the 8% alcohol solution.

A value or combination of values that satisfy an equation or system of equations are referred to as solutions in mathematics. For instance, if we substitute x = 2 into the equation, we get 2(2) + 3 = 7, which is a true statement, hence the answer to the equation 2x + 3 = 7 is x = 2. Similar to this, an equation system may have one or more solutions that simultaneously fulfil every equation in the system. Finding answers to equations or systems of equations is a key component of many branches of mathematics and has significant applications.

given

Find out how much pure alcohol is now contained in the 8% solution to start.

An 8% alcohol solution in 10 cm3 contains:

There are 0.8 cm3 of pure alcohol in 0.08 x 10 cm3.

Let's now calculate the amount of pure alcohol that has to be added to achieve an 80% solution using the alligation method.

We must add pure alcohol to the solution to raise the concentration from 8% to 100%. In order to connect 100% to 8% in the left column, we place 100% in the right column. There is a 92% discrepancy between these two percentages.

We put 80% in the middle column because we aim to arrive at an 80% solution. Between 80% and 100%, there is a 20% difference.

Now, we may construct the subsequent equation:

20/92 = x/10

After finding x, we obtain:

[tex]x = 2.17 cm^3[/tex]

To create an 80% alcohol solution, the pharmacist must therefore mix 2.17 cm3 of pure alcohol with 10 cm3 of the 8% alcohol solution.

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The exact value of side lengths of triangle are d= [tex]\frac{8}{\sqrt{3} }[/tex] and h=[tex]\frac{5\sqrt{2} }{2}[/tex]

A triangle is a closed, two-dimensional shape that consists of three straight sides and three angles. It is one of the basic shapes in geometry and is often used in various mathematical and scientific contexts.

The three sides of a triangle are usually named using lowercase letters a, b, and c, and the three angles are named using uppercase letters A, B, and C, with the opposite angles and sides having the same letter. The sum of the angles in a triangle is always 180 degrees, and this property is known as the Angle Sum Theorem.

Triangles can be classified based on their side lengths and angles. Based on the side lengths, triangles can be classified as:

Scalene triangle: A triangle in which all three sides have different lengths.

Isosceles triangle: A triangle in which two sides have the same length, and the third side has a different length.

Equilateral triangle: A triangle in which all three sides have the same length.

Let's start with the first triangle. We can use the trigonometric ratios for a 30-60-90 triangle:

sin(60) = opposite / hypotenuse = d / (2d) = [tex]\frac{1}{2}[/tex]

cos(60) = adjacent / hypotenuse = 4 / (2d) = [tex]\frac{1}{2\sqrt{3} }[/tex]

Solving for d:

d = 2 * sin(60) = 2 *[tex]\frac{1}{2}[/tex]  = 1

2d = 4 / cos(60) = [tex]\frac{4}{\frac{1}{2\sqrt{3} }}[/tex] = [tex]\frac{8}{\sqrt{3} }[/tex]

So d = 1 and 2d = [tex]\frac{8}{\sqrt{3} }[/tex] in the first triangle.

For the second triangle, we can use the trigonometric ratios for a 45-45-90 triangle:

sin(45) = opposite / hypotenuse = [tex]\frac{h}{5}[/tex]

cos(45) = adjacent / hypotenuse = [tex]\frac{h}{5}[/tex]

Since sin(45) = cos(45) = [tex]\frac{1}{\sqrt{2} }[/tex], we can solve for h:

h = 5 * sin(45) = 5 * [tex]\frac{1}{\sqrt{2} }[/tex] = [tex]\frac{5\sqrt{2} }{2}[/tex]

So h =  [tex]\frac{5\sqrt{2} }{2}[/tex] in the second triangle.

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Wi represents the weight of the course, and xi represents the grade received for that course.

Care must be taken when assigning variables to weights and observations, because the average grade point average (GPA) is the average grade received for each hour of coursework taken.

Therefore, each grade must be weighed against the number of credits for that course.

For example, if two courses are worth 3 credits and one course is worth 6 credits, then the GPA would be calculated by adding the three grades together and then dividing by the sum of the credits (3+3+6=12).

In this case, a grade of A in the 6 credit course would have a greater impact on the GPA than the same grade in the 3 credit course.

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Answer:

Y-intercept → -6

Slope → -1/4

Step-by-step explanation:

#1 Put your information into slope-intercept form or  "y=mx+b" form where

and so:

y= m x + b

y=-6 x  - [tex]\frac{1}{4}[/tex]

GOOD LUCK!!!!

The probability that the number of lost-time accidents occurring over a period of 8 days will be no more than 5 is 0.6695

This scenario can be modeled using the Poisson distribution, which is a probability distribution that describes the number of events that occur in a fixed time period when the events occur independently and at a constant rate.

The mean rate of lost-time accidents per day is given as 0.6. Therefore, the mean rate of lost-time accidents over 8 days is

Mean rate = (0.6 accidents/day) x (8 days) = 4.8 accidents

Let X be the number of lost-time accidents occurring over 8 days. Then, X follows a Poisson distribution with parameter λ = 4.8.

To find the probability that the number of lost-time accidents occurring over a period of 8 days will be no more than 5, we need to calculate

P(X ≤ 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

Using the Poisson probability mass function, we get

P(X = k) = (e^(-λ) × λ^k) / k!

where k is the number of lost-time accidents.

Substituting λ = 4.8 and k = 0, 1, 2, 3, 4, 5 in the above formula, we get

P(X = 0) = (e^(-4.8) × 4.8^0) / 0! = 0.0082

P(X = 1) = (e^(-4.8) × 4.8^1) / 1! = 0.0393

P(X = 2) = (e^(-4.8) × 4.8^2) / 2! = 0.0944

P(X = 3) = (e^(-4.8) × 4.8^3) / 3! = 0.1573

P(X = 4) = (e^(-4.8) × 4.8^4) / 4! = 0.1888

P(X = 5) = (e^(-4.8) × 4.8^5) / 5! = 0.1815

Therefore,

P(X ≤ 5) = 0.0082 + 0.0393 + 0.0944 + 0.1573 + 0.1888 + 0.1815 = 0.6695

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The result is a very large negative number, specifically -2,176,782,192. Therefore: 4a²−b⁶ = -2,176,782,192, when a=6 and b=36.

An equation is a mathematical statement that shows the equality between two expressions. It usually consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=).

The expressions on both sides can contain variables, constants, and mathematical operations such as addition (+), subtraction (-), multiplication (*), division (/), exponentiation (^), and others. The goal of an equation is to find the values of the variables that make both sides equal.

For example, the equation "2x + 3 = 7" means that the sum of 2 times the variable x and 3 is equal to 7. The solution to this equation is x = 2, because when we substitute x = 2 into the equation, we get 2(2) + 3 = 7, which is a true statement.

by the question.

To evaluate the expression 4a²−b⁶ when a=6 and b=36, we substitute the values of a and b into the expression:

[tex]4(6)^{2} - (36)^{6}[/tex]

Simplifying the expression:

[tex]4(36) - 2,176,782,336\\144 - 2,176,782,336[/tex]e

[tex]= -2,176,782,192,[/tex]

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To calculate the probability that at least 1 of 5 randomly selected American children (ages 3 to 5) is read to every day by someone at home.

To find the probability that none of the 5 children are read to, we can use the fact that the probability that a single child is not read to every day is 1 - 0.58 = 0.42. We can then use the multiplication rule to find the probability that none of the 5 children are read to, which is (0.42)⁵ = 0.0075. Finally, we can use the complement rule to find the probability that at least 1 child is read to every day, which is 1 - 0.0075 = 0.9925. Therefore, the probability that at least 1 of 5 randomly selected American children (ages 3 to 5) is read to every day by someone at home is 0.9925.

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