if you have to choose a complete meal from one of 3 meats, one of 4 vegetables, and one of 7 desserts, how many different choices are there? question 17 options:

Similarly, there are 10 choices for the first number, 9 choices for the second number, and 8 choices for the third number. Therefore, the total number of possibilities is[tex]26 × 25 × 24 × 23 × 22 × 10 × 9 × 8 = 14,776,320[/tex] possibilities.

Fundamental Counting Principle and how to count with and without replacement.The Fundamental Counting Principle (FCP) states that if there are m ways to perform an event and n ways to perform a second event, then there are m × n ways to perform both events. For example, suppose there are 2 shirts, 3 pants, and 4 pairs of shoes in your closet. Using the FCP, you can calculate the number of outfit combinations: 2 × 3 × 4 = 24.If you are allowed to use characters more than once (with replacement), the number of different possibilities for a password can be calculated by multiplying the number of choices for each character type. There are 26 lowercase letters, so there are 26 choices for the first letter, 26 choices for the second letter, and so on. Similarly, there are 10 digits, so there are 10 choices for each number.

Therefore, the total number of possibilities is [tex]26 × 26 × 26 × 26 × 26 × 10 × 10 × 10 = 26^5 × 10^3 = 11,881,376,000[/tex] possibilities.If you may only use each letter or number one time, then you cannot repeat any choices. Therefore, the number of possibilities is reduced. There are 26 choices for the first letter, 25 choices for the second letter (since one has already been used), and so on.

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The width of the rectangle is 5 meters.

To find the width of the rectangle, let's use the formula for the area of a rectangle, which is:

Area = length x width

We know that the area of the rectangle is 65 square meters. We also know that the length of the rectangle is 8 meters more than the width. Let's call the width "w". Then, the length can be expressed as:

length = w + 8

Substituting this expression for length into the formula for the area, we get:

65 = (w + 8) x w

Simplifying and solving for w, we get:

w² + 8w - 65 = 0

Using the quadratic formula, we get:

w = (-8 ± √(8² + 4(1)(65))) / (2(1))

w = (-8 ± √(324)) / 2

w = (-8 ± 18) / 2

We take the positive value for w since the width cannot be negative:

w = (-8 + 18) / 2

w = 5

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Since the two angles are complementary, their sum is 90 degrees. Let x be the measure of the other angle in degrees. Then:

x + 53 = 90

Subtracting 53 from both sides, we get:

x = 37

Therefore, the measure of the other angle is 37 degrees.

Answer: 7x - 7y + 21

Step-by-step explanation:

7( x - y + 3) = 7x - 7y + 21

Answer: 3

Step-by-step explanation: I just know

Answer: Simplifying this equation, we get the ANSWER 5

Step-by-step explanation: Since g(x) = 3, we can plug this into the given equation 4x-7.

now we rewrite the given equation, which is now 4(3)-7

Now we find 4(3), simplifying/multiplying that, we get 12.

We minus 12 by 7 which is 5

Carter has 13 dimes in his piggy bank

To solve this equation, we need to use the distributive property to simplify the equation:
(x dimes x 10 cents) + (37-x nickels x 5 cents) = $3.10
We can then solve for the number of dimes by isolating the dimes on one side of the equation:
x dimes x 10 cents = $3.10 - (37-x nickels x 5 cents),By dividing both sides of the equation by 10 cents, we can solve for the number of dimes, x:
x dimes = ($3.10 - (37-x nickels x 5 cents)) / 10 cents

Plugging in the value of 37 coins and solving the equation, we get:
x dimes = (3.10 - (37 -x nickels x 5 cents)) / 10 cents
x dimes = (3.10 - 185 + 5x) / 10 centsx dimes = (3.10 - 180) / 10 centsx dimes = 1.30 / 10 centsx dimes = 13 dimes
Therefore, Carter has 13 dimes in his piggy bank.

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Since the range of observed values is 1, which is less than two standard deviations away from 10, the observed value is not significantly different from the expected value and thus the number of girls in 10 births is not significantly low.

Standard deviation is a measure of how spread out numbers are in a data set. It is calculated by taking the square root of the variance. Variance is the average of the squared differences from the mean. Standard deviation provides an indication of how much variation there is in the data set, and is often used in statistical analysis.

The range rule of thumb is a statistical method used to determine whether a given phenomenon is significantly different from an expected value. It states that if the range of observed values is greater than two standard deviations of the expected value, then the observed values are significantly different from the expected value.

In this particular case, the expected value is 10 girls in 10 births, and the observed value is 1 girl in 10 births. Since the range of observed values is 1, which is less than two standard deviations away from 10, the observed value is not significantly different from the expected value and thus the number of girls in 10 births is not significantly low.

The range rule of thumb is one way to determine whether observed values are significantly different from expected values, but there are other methods available as well.

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Answer:

The value of t is 9.

Step-by-step explanation:

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:

slope = (y2 - y1) / (x2 - x1)

In this case, we are given two points: (t, 5) and (10, -4), and the slope is given as -9. So we can set up the equation:

-9 = (-4 - 5) / (10 - t)

Simplifying, we get:

-9 = -9 / (10 - t)

Multiplying both sides by (10 - t), we get:

-9(10 - t) = -9

Expanding the left side, we get:

-90 + 9t = -9

Adding 90 to both sides, we get:

9t = 81

Dividing both sides by 9, we get:

t = 9

Therefore, the value of t is 9.

Answer:

3

Step-by-step explanation:

Number of people in the choir = 80

Number of women = half of 80 = 40

Number of men in the choir is ¼ of the women = 40/4 = 10

Number of men plus women = 10 +40 = 50

Number of children = 80 - 50 = 30

Ratio of children to men = n:1 = 30:10

Divide both sides by 10

30:10 = 3:1

n = 3

250 is the total surface area of the solid.

How do you determine surface area?

The whole surface of a three-dimensional form is referred to as its surface area. The surface area of a cuboid with six rectangular faces may be calculated by adding the areas of each face.

                         Instead, you may write out the cuboid's length, width, and height and apply the formula surface area (SA)=2lw+2lh+2hw.

Each side of a cube with side length = 5  has an area of 25; the overall area is 6 x 25 = 150

A cube with sides of length 5 has an area of 25 on each side, making its overall area 6 x 25 or 150.

Both have a combined area of 150 + 150 = 300

300 - 25 - 25 = 250 is the result from each of the two cubes.

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There are 5²⁵ possible ways to select 25 cans of soda from 5 types, while there are [5¹⁸] (25 choose 7) possible ways to select 25 cans with at least 7 Dr. Peppers, and only [3²²] (25 choose 3) possible ways to select 25 cans with only 3 Dr. Peppers available.

(a) Since there are five types of soda and we are selecting 25 cans, we can choose any type of soda for each can. Therefore, the number of ways to select 25 cans of soda is 5²⁵.

(b) If we must include at least seven Dr. Peppers, then we can choose the remaining 18 cans from any of the five types of soda (including Dr. Pepper). We can choose 7 Dr. Peppers in (25 choose 7) ways. Therefore, the number of ways to select 25 cans of soda with at least seven Dr. Peppers is (25 choose 7) [5¹⁸].

(c) If there are only three Dr. Peppers available, then we must choose all three Dr. Peppers and select the remaining 22 cans from the four types of soda (excluding Dr. Pepper). We can choose the remaining 22 cans in 4²² ways. Therefore, the number of ways to select 25 cans of soda with only three Dr. Peppers available is 3 [4²²].

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Complete question:

From an unlimited selection of five types of soda, one of which is Dr. Pepper, you are putting 25 cans on a table.

(a) Determine the number of ways you can select 25 cans of soda.

(b) Determine the number of ways you can select 25 cans of soda if you must include at least seven Dr. Peppers.

(c) Determine the number of ways you can select 25 cans of soda if it turns out there are only three Dr. Peppers available.

Therefore, the inequality that can be used to determine p, the maximum number of people who can go to the amusement park, is p ≤ 30.

In mathematics, inequalities are statements that compare two values or expressions and indicate whether they are equal, greater than, or less than each other. An inequality is typically represented by a symbol, such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).

Given by the question.

Let's assume that the maximum number of people that can go to the amusement park is p. The cost of parking is $8.75, and the cost of admission for each person is $15.50.

Then, the total cost for p people can be calculated as:

Total cost = (Cost of parking) + (Cost of admission per person x number of people)

Total cost = $8.75 + $15.50p

The group has no more than $480 to spend, so we can set up an inequality:

Total cost ≤ $480

$8.75 + $15.50p ≤ $480

Subtracting $8.75 from both sides:

$15.50p ≤ $471.25

Dividing both sides by $15.50:

p ≤ 30.35

Since the number of people cannot be a decimal, we round down to the nearest whole number: p ≤ 30.

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Therefore, a monthly payment of $168.62 must be made to pay off the $3,500 balance on the credit card in two years.

Percent is a way of expressing a number as a fraction of 100. The symbol for percent is "%". Percentages are used in many different contexts, such as finance, economics, statistics, and everyday life.

Here,

To calculate the monthly payment required to pay off the $3,500 balance on a credit card that charges 16.5% interest, compounded monthly, in two years, we can use the formula for the present value of an annuity:

[tex]PMT = PV * r / (1 - (1 + r)^{-n})[/tex]

where PMT is the monthly payment, PV is the present value of the loan, r is the monthly interest rate, and n is the total number of payments.

First, we need to convert the annual interest rate of 16.5% to a monthly interest rate:

r = 0.165 / 12

= 0.01375

Next, we need to calculate the total number of payments over two years:

n = 2 * 12

= 24

Now we can plug in the values into the formula:

[tex]PMT = 3500 * 0.01375 / (1 - (1 + 0.01375)^{-24}) = $168.62[/tex]

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Answer:

Step-by-step explanation:

As per the combination concept, there are 735,471 ways to choose 16 shows from a set of 24.

To find the number of ways to choose 16 shows from a set of 24, we can use the formula for combinations, which is:

ⁿCₓ = n! / x!(n-x)!

Where n is the total number of objects in the set (in this case, 24), and x is the number of objects we want to choose (in this case, 16). The exclamation mark (!) denotes the factorial function, which means multiplying the number by all positive integers less than itself.

Plugging in the numbers, we get:

²⁴C₁₆ = 24! / 16!(24-16)! = 735471

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Answer: 3.9b−2.6

Step-by-step explanation: Hope this helps

Answer:

1.3b

Step-by-step explanation:

The equation is -2.6+3.9b. A negative number acts like subtraction, so we would subtract 2.6 from 3.9 to get 1.3. The b is still there, and we don't know what it is, so we simplify the equation to 1.3b.

Sorry, this explanation isn't the best. Hope it helped! :)

The value of x in the given triangle is 1.82 cm using the angle bisector theorem.

A triangle is a polygon with three edges and three vertices. It belongs to the basic geometric shapes. A triangle with the parts A, B, and C is referred to as triangle ABC. Any three points that are not collinear in Euclidean geometry result in a separate triangle and a distinct plane. A triangle is a type of polygon with three sides; the triangle's apex is the point where the two longest sides meet. Two sides are brought together at an angle.

What is angle bisector theorem?

The ratios of the two segments that a line that bisects the opposing angle splits a triangle's side into are the subject of the angle bisector theorem in mathematics. It contrasts their proportionate lengths with the other two triangle sides' proportional lengths.

In the given triangle,

5/6=x/4-x

20-5x=6x

20=11x

x=20/11= 1.82 cm

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Answer:

31/21

Step-by-step explanation:

First step is to add 17 and 14 = 31

The denominator of the fraction(bottom number stays the same)

so the answer is 31/21

Let me know if it helps

Answer:

EXACT FORM: 31/21

DECIMAL FORM: 1.476190

MIXED NUMBER FORM: 1 10/21

Step-by-step explanation:

Slope of each graph are [tex]\frac{6}{5}[/tex],[tex]\frac{-1}{3}[/tex] and 1 respectively.

Slope of a line in mathematics is defined as the ratio of the change in the y coordinate w.r.t the change in the x coordinate.

Both the change in the y-coordinate and the net change in the x-coordinate are denoted by y₂-y₁ and x₂-x₁, respectively.

Thus, the formula for the change in y-coordinate with regard to the change in x-coordinate is

m=y₂-y₁/ x₂-x₁

Taking two points as per observation

Point1: (x₁ y₁)=(0,-3)

Point2:(x₂, y₂)=(5/2,0)

Slope of line=y₂-y₁/ x₂-x₁

=[tex]\frac{0+3}{5/2-0}[/tex]

=[tex]\frac{6}{5}[/tex]

Taking two points as per observation

Point1: (x₁ y₁)=(0,3)

Point2:(x₂, y₂)=(2,2)

Slope of line=y2-y1/x2-x1

=[tex]\frac{2-3}{2-0}[/tex]

=-⅓

Taking two points as per observation

Point1: (x₁ y₁)=(-2,0)

Point2:(x₂, y₂)=(0,2)

Slope of line=y2-y1/x2-x1

=[tex]\frac{2-0}{0+2}[/tex]

=1

Hence, Slope of each graph are 6/5,-⅓ and 1 respectively.

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Step-by-step explanation:

hope this is correct

Ben's net earnings after 5 years are $171,563.23, and Arthur's net earnings after 5 years are $163,534.49.

To calculate their net earnings, we first need to calculate their total earnings from their investments, and then subtract their initial investments.

For Ben:

Using the compound interest formula: A = P(1 + r/n)^(nt)

A = future value of the investment

P = initial principal (investment)

r = annual interest rate (as a decimal)

n = number of times interest is compounded per year

t = number of years

A = 500,000(1 + 0.06/12)^(12 * 5)

A ≈ $671,563.23

Net earnings for Ben: $671,563.23 - $500,000 = $171,563.23

For Arthur:

A = 600,000(1 + 0.05/4)^(4 * 5)

A ≈ $763,534.49

Net earnings for Arthur: $763,534.49 - $600,000 = $163,534.49

Ben's net earnings after 5 years are $171,563.23, and Arthur's net earnings after 5 years are $163,534.49.

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Ben invested $500,000 at an annual interest rate of 6%, compounded monthly, for 5 years. Arthur invested $600,000 at an annual interest rate of 5%, compounded quarterly, for 5 years. What are their net earnings after 5 years?

The equivalent equation to f(x) = 7(x - 60) - 28 is f(x) = 7x - 448 and the y-intercept is -448

Given that

f(x) = 7(x - 60) - 28

To produce an equivalent equation that reveals the y-intercept of the function f(x) = 7(x-60) - 28, we need to simplify the expression by evaluating it when x = 0, since this will give us the y-intercept.

When the brackets are expanded, we have the following

f(x) = 7x - 420 - 28

Evaluate the like terms

So, we have

f(x) = 7x - 448

So, substituting x = 0 into f(x) gives:

f(0) = 7(0) - 448

Evaluate the expression

f(0) = -448

Therefore, the y-intercept is -448.

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The quadratic function to represent the total area of the park and its path is given by: f(x) = 2x² + 18x + 36.

In this problem, we are given that the length of a rectangular park is twice its width, and it is surrounded by a 3-foot wide path.

We are required to write a quadratic function to represent the total area of the park and its path.

The rectangular park can be represented as follows:

Length = 2x (twice the width)

Width = x

Therefore, the total length of the park including the 3-foot wide path can be represented as (2x + 2*3),

and the total width of the park including the 3-foot wide path can be represented as (x + 2*3).

The area of the park is given by the product of its length and width.

Thus, the area of the park can be represented as follows: Area of the park = (2x + 6)(x + 6)

To represent this as a quadratic function,

we can simplify the above expression using the distributive property.

Area of the park = 2x² + 6x + 12x + 36 = 2x² + 18x + 36.

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The equation of the line in slope-intercept form is y = 6x + 55.

Equations can involve variables, which are placeholders for unknown values that we wish to find. For example, the equation x + 3 = 7 asserts that the value of x plus 3 is equal to 7. We can solve for x by subtracting 3 from both sides of the equation, obtaining x = 4.

Equations can be linear or nonlinear, and they can involve one or more variables. They can be represented in various forms, such as standard form, slope-intercept form, or quadratic form.

To find the equation of the line in point-slope form, we need to first find the slope of the line. We can use any two points from the table to find the slope using the formula:

slope = (change in y)/(change in x)

Let's use the first and last points in the table:

slope = (295 - 175)/(40 - 20) = 120/20 = 6

Now we can use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is any point on the line. Let's use the first point (20, 175):

y - 175 = 6(x - 20)

To write this equation in slope-intercept form, we need to isolate y:

y - 175 = 6x - 120

y = 6x + 55

So the equation of the line in slope-intercept form is y = 6x + 55.

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a) r = 30 cm

b) The angle AOC is 0.523598775 radian

c) The area of the shaded region is 541.9 cm²

d) The perimeter of the shaded region is 106.8 cm.

The area of a circle is a measure of the size of the surface of the circle. It is calculated by multiplying the radius of the circle (the length from the center of the circle to its edge) by itself, and then multiplying the result by the constant pi (3.14). The formula for calculating the area of a circle is A = πr2, where “A” represents the area, “π” is pi, and “r” is the radius of the circle.

The radius of the circle, r, can be determined by the Pythagorean theorem. Since AC = 36 cm and AP = 6 cm, the hypotenuse of the right triangle formed by AC and AP is the radius of the circle, r. By applying the Pythagorean theorem, we get:

r² = 362 + 62

r² = 1296

r = √1296

r = 36 cm

b) The angle AOC is 0.523598775 radians

The angle AOC can be determined using the formula for arc length. The arc length of ABC is 36 cm and the radius of the circle is 30 cm. Therefore, the angle AOC is:

AOC = 36/30

AOC = 1.2 radians

c) The area of the shaded region is 541.9 cm²

The area of the shaded region can be determined using the formula for the area of a sector. The angle AOC is 1.2 radians and the radius of the circle is 30 cm. Therefore, the area of the shaded region is:

Area = (1.2)(30)(30)/2

Area = 541.9 cm²

d) The perimeter of the shaded region is 106.8 cm

The perimeter of the shaded region can be determined using the formula for the circumference of a circle. The radius of the circle is 30 cm. Therefore, the perimeter of the shaded region is:

Perimeter = 2π(30)

Perimeter = 106.8 cm

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Answer:

Step-by-step explanation:

To find out how much more fabric is required for the chair than the footstool, we need to subtract the amount of fabric required for the footstool from the amount of fabric required for the chair.

The amount of fabric required for the chair is 5/7 of a yard.

The amount of fabric required for the footstool is 2/3 of a yard.

So to find the difference, we need to subtract:

5/7 - 2/3

To do this, we need to find a common denominator, which is 21 in this case. We get:

(15/21) - (14/21) = 1/21

Therefore, Aron needs 1/21 more yard of fabric to cover the chair than the footstool.

The total number of biscuits the baker should place into each, according to the declaration, is 12.

The mathematical expressions consist of at least a couple of integers or issues, no fewer than one math procedure, and a sentence. It's achievable to multiply, divide, add, or remove with this algebraic method. An expression's form is as follows: Expression: (Math Operator, Number/Variable, Arithmetic Operator)

The total number of cookies in both batches is:

36 + 48 = 84

To divide the cookies into seven equal groups, we need to divide the total number of cookies by 7:

84 / 7 = (12 x 7) / 7 = 12

So the baker should put 12 cookies into each of the seven groups.

A numerical expression that shows how to determine the total number of cookies the baker should put into each group with parentheses is:

(36 + 48) / 7 = (84) / 7 = 12

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Answer:

33

Step-by-step explanation:

43-10=33 sarah has 33 bananas ledt