Work out the area of the shaded semicircle shown below.
If your answer is a decimal, give it to 2 d.p.
1.68

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.

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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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

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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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.

The rectangular prism's volume can be represented by a cube whose dimensions are 6 inches.

A right rectangular prism is what?

The right rectangular prism has two simultaneous end panels that are orthogonal to each of the bases, two adjacent lateral faces, and four rectangle-shaped lateral faces. The faces of an oblique prism, a non-right oblong prism, are parallelograms. Alternative name for a right rectangular prism is a cuboid.

To begin, determine the rectangular prism's volume. To calculate this, multiply the length by the breadth by the height, which equals 9 ×4 ×6. 216 cubic inches make up this.

The side length of a cube with a 216 cubic inch capacity must now be determined. The recipe for A cube's volume is equal to its side length raised to the third power (cubed). You are now attempting to determine where s³= 216 This can also be expressed as s = ∛216.

The only thing left to do is to discover the number that, when multiplied by itself three times, equals 216, or its cubic root. It is quite easy to determine that 6× 6× 6, sometimes known as 6 cubed, equals 216. This indicates that the cube's side length is 6 inches.

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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

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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From the graphs below, we can see that the solution of the given system of linear equations is (3,0.5).

What is meant by a system of linear equations?

A collection of one or more linear equations containing the same variables is known as a system of linear equations. An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation is invariably a straight line equation. A group of diverse straight line equations make up a system of linear equations.

We are given two linear equations:

y = -1/2 x + 2

y = 1/2x - 1

As mentioned earlier, these are equations of two straight lines with slopes -1/2 and 1/2.

Now the solution of the equation is the intersecting point of these straight lines. We graph these equations and found the intersecting point.

Therefore, from the graphs below, the solution of the given system of linear equations is (3,0.5).

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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:

First option: 37°, 11°,  132°

Step-by-step explanation:

The sum of the three interior angles of a triangle must add up to 180°

Only the first option 37°, 11° and 132° add up to 180°
37 + 11 + 132 = 48 + 132 = 180°

You don't need to add up all the other sets of angles completely. Just look at the units place

Option 2, units sum = 4 + 6 + 1 =11; does not end in a 0, ends in 1

Option 3: units sum = 1 + 0 + 2; does not end in a 0, ends in 3

Option 4: units sum = 0 + 1 + 5 ends in a 6

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

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

Step-by-step explanation:

28x^3yx7z^2-7x4xy

196x^3-28xy

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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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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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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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]

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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Answer:

X=63

Y=63

Z=72

Step-by-step explanation:

The value for angle X

X + 85 + 32 = 180°

X + 117 = 180°

X = 180° - 117°

X = 63°

Since <x and <y are vertically opposite

<X and <Y = 63°

Remember vertically opposite are the same.

The value for angle z

Z + 45 + Y = 180°

Z + 45 + 63 = 180°

Z° + 108° = 180° - 108°

Z = 72°

Therefore

Value for X = 63°

Value for Y = 63°

Value for Z = 72°

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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a) The distribution is roughly symmetric and bimodal. b) The histogram has two modes, which may be due to the different shoe size scales used for men and women in the U.S. but not in Europe.

The histogram of European shoe sizes of 269 male and female college students converted from their reported US shoe sizes is not visible based on the information provided, but the questions are clear.

a) The shape of the distribution is not visible, but it is mentioned that it is "roughly symmetric and bimodal".

b) There are two modes in the histogram. This could be because shoe sizes in the United States are defined differently for men and women, but not in Europe. As a result, the histogram of the distribution of European shoe sizes for both men and women may show two distinct peaks.

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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.

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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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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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.

Answer:

After substituting -4 for "a" and 16 for "b", the equation can be simplified and solved.

-The equation 2 (2x - 11) + 6 = -4x + 16

Expanding the equation on the left-hand side, we get:

4x - 22 + 6 = -4x + 16

Simplifying, we get:

10 = -10x + 32

Subtracting 32 from both sides, we get:

-22 = -10x

Dividing both sides by -10, we get:

x = 2.2

This means that there is exactly one solution, which is x = 2.2. So, statement 3 is true.

-The equation 4x - 8 (x - 2) = -4x + 16

Expanding the equation on the left-hand side, we get:

4x - 8x + 16 = -4x + 16

Combining like terms, we get:

-4x + 16 = -4x + 16

This equation is true for all values of x, so there are infinitely many solutions. So, statement 2 is true.

-The equation 10 + x + 2 - 6x = -4x + 16

Expanding the equation on the left-hand side, we get:

10 + x + 2 - 6x = -4x + 16

Combining like terms, we get:

-5x + 12 = -4x + 16

Adding 4x to both sides, we get:

-x + 12 = 16

Adding x to both sides, we get:

12 = 16

This equation is not true for any values of x, so there are no solutions. So, statement 1 is true.

-The equation 9x +3 - 13x + 6 = -4x + 16

Expanding the equation on the left-hand side, we get:

9x + 3 - 13x + 6 = -4x + 16

Combining like terms, we get:

-4x + 9 = -4x + 16

Adding 4x to both sides, we get:

9 = 12

This equation is not true for any values of x, so there are no solutions. So, statement 1 is true.

Therefore, the true statements are:

-The equation 2 (2x - 11) + 6 = ax + b has no solution.

-The equation 4x - 8 (x - 2) = ax + b has infinitely many solutions.

-The equation -5 (4x-6) 14 = ax + b has exactly one solution.