What is the area of this compound figure?

5 minus a number is less than -9: 5 - x < -9.

The product of 2 and a number is a minimum of 34: 2x ≥ 34.

Answer:

2.    [tex]2n\geq 34[/tex]

3.    [tex]5-n < -9[/tex]

Step-by-step explanation:

The product of 2 numbers is multiplication.

"a minimum of" is greater than or equal to.

A number minus a number is subtraction.

2.

"The product of 2 and a number" can be written as [tex]2n[/tex].

"a minimum of 34" can be written as [tex]\geq 34[/tex]

So all together

[tex]2n\geq 34[/tex]

3.

"5 minus a number" can be written as [tex]5-n[/tex]

"less than -9" can be written as [tex]< -9[/tex]

So all together

[tex]5-n < -9[/tex]

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Answer:

Value of account after t years is
[tex]A = \boxed{190( 1.0178)^{4t}}[/tex]

Percentage of growth per year

CAGR = [tex]\boxed{7.31\%}[/tex]

Step-by-step explanation:

The generalized equation for the accrued value of an amount P(the principal) deposited at i% annual interest compounded n times a year for t years is

[tex]A = P\left(1 + \dfrac{r}{n}\right)^{nt}[/tex]

where r = i/100, the interest rate expressed as a decimal

Given P = $190
i = 7.1% ==> r = 7.1/100 = 0.071

Since the interest is compounded quarterly and there are 4 quarters in a year, the interest is compounded 4 times a year so n = 4

[tex]A = 190 \left(1 + \dfrac{0.071}{4}\right)^{4t}[/tex]

[tex]A = 190\left(1 + 0.01775\right)^{4t}}\\\\A = 190( 1.01775)^{4t}[/tex]\

Rounding the annual growth rate to 4 decimal places gives

[tex]A = P(1.0178)^{4t}[/tex]

In one year, the investment of $190 will grow to
[tex]A = 190(1.0178)^{4}[/tex]

[tex]A = $203.89[/tex]

Compound Annual Growth = = 203.89 - 190 = $13.89

Compound Annual Growth Rage(CAGR) = $13.89/$190 = 0.073105

As a percentage, CAGR Percent = 0.073105 x 100 = 7.3105% or rounded to nearest hundredth it would be 7.31%

The standard form of 3x² - 9x + 2 is 3x² - 9x + 2.

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.

Given:

A quadratic function,

3x² - 9x + 2.

The standard form of the quadratic function is

ax² + bx + c.

The standard form of 3x² - 9x + 2 is 3x² - 9x + 2.

Therefore, 3x² - 9x + 2.

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Answer:

B. x=3

Step-by-step explanation:

3x+4y=12

9x-4y=24

Add 9x and 3x

Subtract -4y from 4y which will cancel out

Add 12 and 24

12x=36

divide both sides by 12

x=3

The volume of the cone in terms of π is 96π inches³.  

The cone has a base radius of 6 inches and the height of the cone is 8 inches. Therefore, the volume of cone can be found as follows:

volume of cone = 1 / 3 πr²h

where

Therefore,

r = 6 inches

h = 8 inches

Hence,

volume of cone = 1 / 3 × π × 6² × 8

volume of cone = 1  / 3 × π × 36 × 8

volume of cone = 12 × 8 × π

volume of cone = 96π inches³

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The equation of the second road is y = -3x + 10

The location of the mail box = (0, 0)

The first road passes through the points (3, 1) and (9,3)

The slope of the line is the change in y coordinate with respect to the change in x coordinate

The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the values in the equation

m = 3-1 / 9-3

m = 2/6

m = 1/3

The next road is 90 degrees to the first road

Then the slope of the second line will be

m1 = -1/m

= -1/(1/3)

= -3

The second road passing through the point (3, 1)

The equation of line

y = mx + b

Substitute the given values in the equation

1 = -3 × 3 + b

1 = -9 + b

b = 1 +9

b = 10

Therefore, the equation will be y = -3x + 10

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The value of the given function f(4 + h) - f(4) is 5h(x)² + 40h(x)

A function is a mathematical concept that maps a set of inputs to a set of outputs with a definite rule. In mathematics, a function is a set of ordered pairs (input, output) where each input is associated with exactly one output. The input is usually referred to as the argument of the function and the output is the value of the function at that argument.

f(x) = 5x²

f(4 + h) - f(4)

f(4 + h(x)) = 5(4 + h(x))²

f(4) = 80

Substituting the values into each other;

5(4+h(x))² - 80

f(4 + h) - f(4) = 5h(x)² + 40h(x)

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The amount Maggie will need in savings when she retires is $1,204,519.62 and  her payment be if she had 1.2 million is $4522.40

In investment, an annuity is a series of payments made at equal intervals

a) To calculate the amount Maggie will need in savings when she retires

Pm= {1 + r/j)pm - 1

Pm = (1+6.2%/12)4500 - 1

Pm (1+0.0052)4500 -1

Pm= (1.0052)4499

Simplifying to have

Pm = $4522.40

b) To  calculate much could her payment be if she had 1.2 million dollars in her account but her interest dropped to 5.5

Pm= {1 + r/j)pm - 1 +d

Where d is the savings

Pm = (1+5.5%/12)4500 - 1 + 1.2m

Pm= (1+5.5%/12) 4499 + 1.2m

PM = (1.0046)4499 + 1,200,000

Pm = 1,204,519.62

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Answer:

Step-by-step explanation:

35tu

(5 and 7 are like terms, and you put the 't' and 'u' in alphabetical order)

Answer:

ut=35

Step-by-step explanation:

5×u×t×7=0

collect like terms

ut=5×7

ut=35

The  probability that a product will operate properly within an expected time frame is the dimension of quality known as reliability

The probability is the ratio of the number of favorable outcomes to the total number of outcomes. The value of the probability is varies from zero to one

Here, the product will operate properly within an expected time frame is the dimension of quality

Reliability is expressed as the probability that a given item will perform its intended function with no failures for a given period of time under a given set of conditions that means the reliability is the complementary to the failure of probability

Therefore, the given statement is know as the reliability

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Answer:

x = 6, y = -3

Step-by-step explanation:

[tex]\frac{x}{y + 1} = -3\\\frac{y}{x-3} = -1[/tex]

x = -3(y+1) - Isolate for x or y (I chose x)

x = -3y -3

Plug in x into y

[tex]\frac{y}{x-3} = -1\\\frac{y}{(-3y -3) - 3} = -1\\\frac{y}{-3y -6} = -1\\y = -1(-3y - 6)\\y = 3y + 6\\-2y = 6\\y = -3[/tex]

Plug y back into equation

[tex]\frac{x}{y+ 1} = -3\\\frac{x}{(-3)+ 1} = -3\\\frac{x}{-2} = -3\\x = -3(-2)\\x = 6[/tex]

There are many ways that baseball players and basketball players can be selected from a group of athletes who play both sports.

One way is to use a selection process that allows for both players to be chosen based on their individual merits. For example, a team could use a combination of criteria such as previous performance, physical fitness, athleticism, and skill level to select the most suitable players for each sport. This could be done by assigning each player a score based on these criteria and then selecting the highest scoring players for each position.Another way to select players from a group of athletes playing both sports is to use a draft system. This system would allow teams to choose players based on the team's needs, rather than individual merits. This could be done by assigning each player an overall ranking and then allowing teams to select players in order of their ranking. A third way to select players from a group of athletes playing both sports is to have a tryout or combine where players can showcase their skills and abilities. This allows teams to evaluate players in a more comprehensive way and make sure they are selecting the best players for their team. Finally, teams can also use a combination of the above methods to select players. For example, they could use a combination of a draft system, individual merit selection, and a tryout/combine to get a better idea of which players are the best fit for their team. Overall, there are many different ways that teams can select baseball players and basketball players from a group of athletes playing both sports. The method chosen will depend on the team's individual needs and preferences.

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How many different combinations of baseball players and basketball players can be selected from a group of baseball players and basketball players?

The number of seconds does the firework hit the ground is 3 seconds

From the information given, we have the quadratic function;

y = -16x² + 32x + 48

To determine the value of x , let's reduce the expression, we get;

-2x² + 4x + 6

Now, let's factorize the terms

Multiply the coefficient by the constant and find the pair factors

-2x² + 6x - 2x + 6

Factorize in pairs, we get;

-2x(x -3) - 2(x -3)

Then, we have the expressions

-2x - 2 = 0

solve for x

x = -1

x - 3 = 0

x = 3

Hence, the value is 3 seconds

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Answer:

3

Step-by-step explanation:

i took the test

The probability of rolling a sum less than or equal to 6 when rolling a pair of six-sided dice is 5/18 or approximately 0.2778.

To calculate the probability of rolling a sum less than or equal to 6 when rolling a pair of six-sided dice, we need to find the number of ways the dice can be rolled to get a sum less than or equal to 6 and divide it by the total number of possible outcomes.

There are 6 x 6 = 36 possible outcomes when rolling a pair of dice, since there are 6 possible outcomes for each die. To get a sum less than or equal to 6, the only possible outcomes are:

1+1 = 2

1+2 = 3

1+3 = 4

1+4 = 5

2+1 = 3

2+2 = 4

2+3 = 5

3+1 = 4

3+2 = 5

4+1 = 5

There are 10 possible outcomes that result in a sum less than or equal to 6. Therefore, the probability of rolling a sum less than or equal to 6 is:

P(sum less than or equal to 6) = number of favorable outcomes / total number of possible outcomes

P(sum less than or equal to 6) = 10 / 36

Simplifying this fraction, we get:

P(sum less than or equal to 6) = 5 / 18

Therefore, the probability of rolling a sum less than or equal to 6 when rolling a pair of six-sided dice is 5/18 or approximately 0.2778 when rounded to four decimal places.

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We can interpret from the results that the distribution of data might be negatively skewed.

In the given question it is mentioned that while Morgan was analyzing her data, she notices that the value of her mean is quite a bit smaller than the value of her median.

As we know that, in statistics, when the mean is smaller than the median and mode, it indicates a negatively skewed distribution.

A negatively skewed distribution or left skewed distribution is a type of distribution in which more values are concentrated on the right side of the distribution graph while the left side of the graph is longer.

Hence, we can interpret from these information that the distribution of data of Morgan are negatively skewed.

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Answer:

Step-by-step explanation:

Perimeter is equal to 2 times length and 2 times the width.

This problem says the length is twice the width.

Let's use 2w for the length:

Here's the equation:

2L + 2W = 156

Substitute 2W for the length,

2(2W) + 2W = 156

4W + 2W = 156

6W = 156

6W/6 = 156/6

w = 26

so length is 2 times 26 = 56 Length = 56 m

Answer:

100 dispenses

Step-by-step explanation:

To check the answer:

Gumballs: 200 - (1*100) = 100

Explanation: 200 gumballs - (1 gumball * 100 dispenses) = 100 gumballs left.

Chocolate Candies: 900 - (8*100) = 100

Explanation: 900 candies - (8 candies * 100 dispenses) = 100 candies left.

Answer:

  100

Step-by-step explanation:

Given a candy machine with 200 gumballs dispensed 1 at a time, and another with 900 chocolates dispensed 8 at a time, you want to know how many dispenses from each will result in equal counts left in the machines.

The number of remaining gumballs after d dispenses is ...

  g = 200 -d

The number of remaining chocolates after d dispenses is ...

  c = 900 -8d

The number remaining in each machine will be equal when ...

  g = c

  200 -d = 900 -8d . . . . . substitute the above expressions

  7d = 700 . . . . . . . . . . add 8d -200

  d = 100 . . . . . . . . . divide by 7

100 dispenses from each machine will make the number of candies in the machines equal.

The correlation between your daily calorie intake and your GPA is not likely to be immediately apparent, and it would require further investigation to determine whether there is a positive or negative correlation, or no linear relationship between the two variables.

It is difficult to predict the correlation between your daily calorie intake and your GPA as they are not obviously related variables. However, it is possible that there may be a weak or indirect relationship between the two variables.

          If a person is consuming a well-balanced diet with the right amount of nutrients, vitamins, and minerals, they may have the energy and focus necessary to perform well academically. In this case, there may be a positive correlation between calorie intake and GPA. Alternatively, if a person is consuming an excessive amount of calories from unhealthy foods, they may be more likely to experience health problems that could impact their academic performance. In this case, there may be a negative correlation between calorie intake and GPA.

      On the other hand, there may be no direct linear relationship between the two variables, and other factors such as sleep, stress, exercise, and overall health may have a greater impact on academic performance than daily calorie intake.

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Answer: 28xy(7x^2-1)

Step-by-step explanation:

28x^3yx7z^2-7x4xy

196x^3-28xy

Joan paid with $19.00, she should receive $19.00 - $12.00, which equals $11.30 in change.So Joan should receive 11.30 in change.

Joan should receive $11.30 in change. To calculate this, we must start with the total cost of her items, which comes to $10.20 ($1.20 for the milk, $4.70 for the sandwich, and $3.30 for the sherbet). To this we must add the tax, which was $1.80. This brings the total cost to $12.00. Joan should receive $11.30 in change. To get this answer, we can use the following formula: Change = Total Payment - (Cost of Items + Tax). In this case, the formula would look like this: Change = 19.00 - (1.20 + 4.70 + 3.30 + 1.80). After calculating, the answer is 11.30. So Joan should receive 11.30 in change.

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You need 4 digits to number all 178 buildings on a street.

In the decimal number system, digits are the symbols used to represent numbers. The 10 digits of the decimal numeral system are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. By utilizing them in various combinations and places, these digits are used to represent all possible decimal integers. A digit's value is also affected by its position in a number according to the place value system. For instance, the digits 1 and 2 in the number 123 each stand for one hundred, twenty, and three respectively. Digits are the fundamental components of numbers and are frequently used in daily life for calculations, measurement, and counting.

To find the number of digits in a number, you can take the logarithm of the number with base 10 and add 1. So, using the logarithm function, you can calculate:

log10(178) + 1 = 2.25 + 1 = 3.25

Therefore, you need 4 digits to number all 178 buildings on a street.

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Rounding to the nearest tenth, the volume of the basketball is: V ≈ 381.7 cubic inches ≈ 381.8 cubic inches (rounded to the nearest tenth)

Volume is a measure of the amount of space occupied by an object or a substance. It is typically measured in cubic units such as cubic meters, cubic centimeters, cubic feet, or cubic inches.

For solid objects, volume refers to the amount of space the object occupies in three-dimensional space.

The diameter of a basketball is 9.2 inches, which means the radius is half of that, or:

r = 9.2 / 2 = 4.6 inches

The formula for the volume of a sphere is:

V = (4/3)πr³

Substituting the radius into the formula, we get:

V = (4/3)π(4.6)³

V ≈ 381.7 cubic inches

Therefore, Rounding to the nearest tenth, the volume of the basketball is: V ≈ 381.7 cubic inches ≈ 381.8 cubic inches (rounded to the nearest tenth)

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The z value of 0.2 indicates the standardized difference between the sample mean and population mean

The z value is a standardized score that tells us how many standard deviations a sample mean is from the population mean. In other words, it helps us determine the likelihood that the difference between the two means is due to chance or some other factor.

Typically, we use a significance level (often denoted by alpha) to determine if the z value is significant or not. If the z value falls within the critical values for the chosen significance level, we reject the null hypothesis and conclude that there is a significant difference between the two means. If the z value falls outside the critical values, we fail to reject the null hypothesis and conclude that there is not a significant difference.

In your case, with a z value of 0.2, it is important to consider what significance level was used in the test. If the chosen significance level was 0.05. Since 0.2 falls within this range, we would fail to reject the null hypothesis and conclude that there is not a significant difference between the sample mean and population mean.

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Answer:

False

If we wanted to solve this equation, we can use this expression:

Maria must have spent $5.93, making her statement false.

To accurately represent the shoe sizes for men and women separately, it would be better to compute the mean or median shoe size for each group separately and compare them.

The problem with either the mean or the median as a measure of center in this case is that the data is not separated by gender, and the shoe size distributions for men and women are likely to be different. Therefore, computing the mean or median shoe size across all students may not accurately represent the typical shoe size for men or women separately.

For example, if the men in the sample have, on average, larger shoe sizes than the women, then the mean shoe size across all students may be biased towards the larger sizes, even though the majority of the students are women. On the other hand, if there are a few male students with very large shoe sizes, then the median shoe size across all students may be biased towards the larger sizes as well, even if most of the students are women with smaller shoe sizes.

To accurately represent the shoe sizes for men and women separately, it would be better to compute the mean or median shoe size for each group separately and compare them. Alternatively, a better measure of center might be to report the mode, which represents the most common shoe size in the data.

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Answer:

csc(t) = -3/2

Step-by-step explanation:

Given sin(-t) = 2/3, we can find the value of csc(t) as follows:

sin(-t) = 2/3

sin(t) = -2/3 (since the sine function is an odd function)

Since csc(t) = 1/sin(t), we have:

csc(t) = 1/sin(t) = 1/(-2/3) = -3/2

Answer:

[tex]\displaystyle \csc(t)=-\frac{3}{2}[/tex]

Step-by-step explanation:

[tex]\displaystyle \sin(-t)=\frac{2}{3}\\\\\sin(t)=-\frac{2}{3}\\ \\\frac{1}{\sin(t)}=\frac{1}{-\frac{2}{3}}\\\\\\\csc(t)=-\frac{3}{2}[/tex]

The second step can be done because sin(-t) is an odd function.

Answer:

Step-by-step explanation:

An expression to display a loss of 42 yards on the football field would be: -42 yards.

The negative sign in front of the number 42 indicates a loss or a decrease in the yards, which represents a loss of 42 yards on the football field.

The length of the shortest leg of T is approximately 18.33 units. We are given that the length of the altitude drawn to the hypotenuse (h) is 8, and the length of the hypotenuse (c) is 20.

We can start by using the area formula for a triangle:

Area = 1/2 * base * height

In this case, the base is the length of the hypotenuse (c), and the height is the length of the altitude (h). So we have:

Area = 1/2 * c * h

Substituting the given values, we get:

Area = 1/2 * 20 * 8 = 80

We also know that T is a right triangle, so we can use the Pythagorean theorem:

a^2 + b^2 = c^2

Substituting the given values, we get:

a^2 + b^2 = 20^2

a^2 + b^2 = 400

We can now solve for b by substituting a in terms of h (using the formula for the area of a triangle) and simplifying:

Area = 1/2 * base * height

80 = 1/2 * 20 * h

h = 8

a = (2 * Area) / c

a = (2 * 80) / 20

a = 8

Substituting a and h in the Pythagorean theorem equation, we get:

8^2 + b^2 = 20^2

64 + b^2 = 400

b^2 = 336

b = sqrt(336)

b ≈ 18.33

Therefore, the length of the shortest leg of T is approximately 18.33 units.

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