Use the graphing tool to graph the equation of the cosine function . Then determine the amplitude and the period of the function.1/2

Answer: 5 mm 6 mm

Step-by-step explanation:

The equation of the line that goes through the point (0, -4) and has a slope of 2 is y = 2x - 4.

The relationship between the coordinates of each point (x, y) on a line is represented by the equation of a line, which is linear in the variables x and y. All of the points on the line satisfy the equation, in other words.

We can use the point-slope form of the equation of a line to find the equation of the line that goes through the point (0, -4) and has a slope of 2.

The point-slope form of the equation of a line is:

y - y₁ = m(x - x₁)

where (x₁, y₁) is a point on the line and m is the slope of the line.

Plugging in the values, we get:

y - (-4) = 2(x - 0)

Simplifying, we get:

y + 4 = 2x

Subtracting 4 from both sides, we get:

y = 2x - 4

Therefore, the equation of the line that goes through the point (0, -4) and has a slope of 2 is y = 2x - 4.

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The probability of winning the Exacta bet if you pick the horses at random is given by P ( A ) = 0.26 %

Given data ,

The Kentucky Derby had 20 horses running in the race in 2016. The number of ways to pick the first horse is 20, as any of the 20 horses could finish in the first spot. Once the first horse is picked, there are 19 remaining horses that could finish in the second spot.

Therefore, the total number of outcomes for two horses finishing in the first two spots (i.e., the Exacta bet) is 20 multiplied by 19, which is 380.

Since there is only one winning Exacta combination out of the 380 possible outcomes, the probability of winning the Exacta bet by randomly picking two horses is 1/380, which is approximately 0.0026, or 0.26%.

Hence , the probability is 0.26 %

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Quadratic Expression: is an expression with the variable with the highest exponent being 2

General form: ax^2 + bx + c

Greatest common factor (GCF): the largest whole number that divides evenly into a set of numbers

When factoring out the GCF of this expression we must look at the "a" term and "c" term

[tex]8(x^2-3)[/tex] which is the expression factored.

Answer:

[tex]\bold{f(x) = 375(2.5)^{-x}+ 33}[/tex]

Step-by-step explanation:

An exponential function of form f(x) = ba^(-x) + c has a horizontal asymptote of y = c as x approaches infinity, and a y-intercept of (0, b + c). We can use the given information to set up a system of equations and solve for the unknowns.

The horizontal asymptote is given as y = 33, so we have:

c = 33

The y-intercept is given as (0, 408), so we have:

b + c = 408

Substituting c = 33, we get:

b + 33 = 408

b = 375

So the function we're looking for is of the form:

[tex]\bold{f(x) = 375a^{-x}+ 33}[/tex]

To find a, we use the fact that the function passes through P(2, 93):

93 = 375a^(-2) + 33

60 = 375a^(-2)

a^2 = 375/60

a^2 = 6.25

a = [tex]\sqrt{6.25 } =2.5[/tex]

Therefore, the exponential function that satisfies the given conditions is:

[tex]\bold{f(x) = 375(2.5)^{-x}+ 33}[/tex]

The ratio 5 1⁄2 : 2 3⁄4 can be expressed in simplest form as 11 : 7.

Ratio is a mathematical comparison between two numbers, usually expressed as a fraction. It is used to compare quantities or measurements, and is a useful tool for understanding relationships between different values. Ratios can be used to solve problems and make decisions, as well as to measure and compare proportions in different situations.

This can be derived by multiplying the numerators and denominators of the two ratios by the same number, in this case 2. The resulting fractions are 11⁄2 and 5⁄2, which can then be simplified to 11 : 7.

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The volume of the composite solid, rounded to the nearest hundredth, is: 213.33 cubic centimeters.

The solid given is composed of two square pyramids. Therefore, to find the volume of the composite solid, apply the formula below:

Volume of composite solid = 2(1/3 * length * width * height)

Given the following dimensions:

Length = 8 cm

Width = 8 cm

Height = 5 cm

Plug in the values:

Volume of composite solid = 2(1/3 * 8 * 8 * 5)

≈ 213.33 cubic centimeters (to the nearest hundredth).

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The area of a triangle ABC is 496.25 square feet. Therefore, option B is the correct answer.

Given that, in the triangle ABC, m∠B = 83°, a = 25 feet, and c = 40 feet.

The area of a triangle can be expressed using the lengths of two sides and the sine of the included angle. Area of a triangle = ½ ab sin C.

Here, area of a triangle = 1/2 ×25×40 sin83°

= 25×20×0.9925

= 496.25 square feet

Therefore, option B is the correct answer.

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Note that where the above conditions are given, the probability of A ∩ B is 1/20 and the probability of the union of A  and B P( A∪B) = 2/5. See the explanation below.

We are given that A and B are events that are independent, P(A∩B), we can rightly state that:

P(A∩B ) = P(A) x P (B)

(1/5) x  (1/4)
= 1/20

For P(A∪B)
⇒ P( A ∪B) = P (A ) + P(B) - P(A ∩B)

We can substitute the probabilities to derive:

P(A∪B)  = (1/5) + (1/4) - (120)

We can write the above as:

⇒ 4/20 + 5/20 - 1/20
= 8/20

Simplifying , we get:

P(A∪B)  = 2/5

Hence it is correct to state that the P(A ∩ B) = 1/20, while P(A∪B) = 2/5.

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They have different end behavior as x approaches -∞ but the same end behavior as x approaches ∞.

The correct option is D.

From the given points, we can write an exponential function in the form of f(x) = abˣ, where a and b are constants.

Using the point (-4, 9): 9 = ab⁻⁴

Using the point (0, 1): 1 = ab⁰ = a

Using the point (1, 0): 0 = ab¹

Using the point (5, -2): -2 = ab⁵

Solving these equations, we get a = 1 and b = 1/3. So, the function f(x) = 1(1/3)ˣ = (1/3)ˣ.

For function g(x), we can see that as x approaches -∞, g(x) approaches ∞ , and as x approaches ∞, g(x) approaches 0.

This is because as x gets more negative, 24 times 2⁻ˣ becomes a larger positive number, and as x gets larger, 2ˣ becomes a larger positive number causing the product to approach zero.

Therefore, the two functions have different end behavior as x approaches -∞ but the same end behavior as x approaches ∞, making option D the correct answer.

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Answer:

mark me brilliant

Step-by-step explanation:

The factory produces one box of potato chips every 4 minutes, which means in one minute, it produces 1/4 boxes.

So, in 20 minutes, the factory would produce:

(1/4) x 20 = 5 boxes

Therefore, the factory would make 5 boxes filled with potato chips in 20 minutes.

Answer:

Step-by-step explanation:

17

The equivalent expression using associative property is; 5×(3×12).

Given expression is; [(5 × 3) × 12]

The associative property is a property of addition and multiplication that allows the grouping of numbers or variables without changing the result.

For addition: (a + b)+c = a+(b + c)

For multiplication: (a × b) ×c = a × (b × c)

In simpler terms, it means that you can add or multiply a set of numbers in any order, and still get the same result.

Therefore, the equivalent expression to [(5 × 3) × 12] using only the associative property would have the same operands but a different grouping. One possibility would be;

[(5 × 3) × 12] = [5 × (3 × 12]

Both expressions simplify to 180.

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The two companies charge the same when the amount of sugar is 20 thirds per second and the cost when the two companies charge the same is $8,125.

What is amount?

Amount is a term used to describe the quantity or size of something. It can refer to a specific quantity of a substance, such as an amount of money or an amount of a particular material, or it can refer to a more abstract concept, such as an amount of time or effort.

To find the amount of sugar for which the two companies charge the same, we need to set the two costs equal to each other and solve for the amount of sugar.

Let x be the amount of sugar in third per second. Then, the cost C1 charged by the first company is:

C1 = 4500 + 175.25x

And the cost C2 charged by the second company is:

C2 = 3995 + 200.50x

To find the amount of sugar for which the two companies charge the same, we set C1 equal to C2:

4500 + 175.25x = 3995 + 200.50x

Solving for x, we get:

25.25x = 505

x = 20

Therefore, the two companies charge the same when the amount of sugar is 20 thirds per second.

To find the cost when the two companies charge the same, we can substitute x = 20 into either of the cost equations. Let's use C1:

C1 = 4500 + 175.25x

C1 = 4500 + 175.25(20)

C1 = 8125

Therefore, the cost when the two companies charge the same is $8,125.

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The formula for compound interest is given by:

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

Where:

A = final amount

P = principal (initial amount)

r = annual interest rate (as a decimal)

n = number of times the interest is compounded per year

t = time (in years)

Using this formula, we can calculate the final amount of the CD as follows:

A = 2250(1 + 0.03/4)^(4*2)

A = 2250(1 + 0.0075)^8

A = 2250(1.0075)^8

A = 2250(1.063853)

A = $2398.12 (rounded to the nearest cent)

Therefore, the CD will be worth approximately $2398.12 at maturity.

Casey will earn $595.42 more interest with annual compound interest compared to annual simple interest over 10 years.

Simple interest is paid just on the initial amount deposited or borrowed and is computed as a percentage of the principal amount. In other words, interest earned or charged is calculated purely on the principal amount, without taking into consideration interest from prior periods. On the other hand, compound interest adds the principal amount to the interest earned or charged in prior periods to determine the interest earned or charged in the current period. In comparison to simple interest, compound interest results in higher overall interest payments or earnings since the interest generated or charged climbs exponentially over time. Compound interest is more prevalent and beneficial for long-term investments in general.

The compound interest is given as:

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

Substituting the values of P = 500, n = 1, r = 0.06 and t = 10 we have:

[tex]A = P(1 + r/n)^{(nt)} = 500 * (1 + 0.06/1)^{(1*10)} = $895.42[/tex]

Now, simple interest is given as:

SI = Prt = 500 * 0.06 * 10 = $300

Now, the difference is:

895.42 - 300 = $595.42

Hence, Casey will earn $595.42 more interest with annual compound interest compared to annual simple interest over 10 years.

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The point-slope equation of a line that passes through the points (5, 2) and (-1,-6) include the following: B. y - 2 = 4/3(x - 5).

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-6 - 2)/(-1 - 5)

Slope (m) = -8/-6

Slope (m) = 4/3.

At data point (5, 2) and a slope of 4/3, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 2 = 4/3(x - 5)

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The box that replaces the question mark is Box D.

Option D is the correct answer.

We have,

In a figure pattern, the concept used involves identifying and recognizing the underlying rules or principles that govern the sequence of figures.

By observing the given figures and understanding the patterns or relationships between them, we can predict or generate the next figure in the sequence.

From the pattern,

We see that,

The figure is rotating clockwise.

Now,

The box that replaces the question mark would be:

Box D

Thus,

The box that replaces the question mark would be Box D

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The probability that all men will be interview first is 0.05.

Probability helps with finding out the likelihood of the occurrence of an event and measures chance of an event happening.

Given data:

Men = 3

Women = 3

Total people:

= 3 + 3

= 6

Probabilities of men:

P(first man) = 3/6 = 1/2

P(second man) = 2/5

P(third man) = 1/4

Required probability is:

P(first 3 men) = 1/2 * 2/5 * 1/4

P(first 3 men) = 0.05

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120 is the simple interest owed for the use of the money.

What does the phrase "simple interest" mean?

From the time when money was first lent until the time that it should be paid back with interest, this time frame is considered the borrowing period. The term or deadline for this is also an option. A percentage of the principle is how interest is most commonly computed.

P = $2000, r = 6%, t = 1 year

simple interest = P * r * t/100

                         = 2000 * 6 * 1/100

                        = 120

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The simple interest owed for the use of the money is $120.

Simple interest is the interest charge on a loan calculated using only the original principal amount and a fixed interest rate. It does not use compounding, which causes borrowers to pay interest on principal and interest that accumulates over numerous payment periods.

The simple interest formula is as follows:

SI = P * r * t

where I denotes simple interest, P denotes principal, r denotes interest rate (in decimal), and t denotes time period (in years).

When we substitute the provided values, we get:

SI = $2000 * 0.06 * 1

SI = $120

As a result, the simple interest for the usage of the money is $120.

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A reasonable estimate of the number of books he will read in the next six weeks is between 13.8 - 1.4 = 12.4 and 13.8 + 1.4 = 15.2 books.

Normal usually refers to the word "normal" in a normal distribution with mean μ and standard deviation σ, the z-score of a measure X is;

Z = (X - μ)/ σ

We are given that;

Books= 6.9

Number of weeks= 3

Error= + 0.7

Now,

The margin of error is the range of values that are likely to contain the true value of a measurement. In this case, the margin of error is + 0.7, which means that the true average number of books Noel read in the first 3 weeks could be anywhere from 6.9 - 0.7 = 6.2 to 6.9 + 0.7 = 7.6.

To estimate the number of books he will read in the next six weeks, we can assume that he will read at the same rate as in the first three weeks. This means that we can use a proportion to find the estimated number of books:

3/6 = (6.9 +/- 0.7)/x

where x is the estimated number of books in the next six weeks. Solving for x, we get:

x = (6.9 +/- 0.7) * (6/3) x = (6.9 +/- 0.7) * 2 x = 13.8 +/- 1.4

Therefore, by Statistics the answer will be 13.8 - 1.4 = 12.4 and 13.8 + 1.4 = 15.2 books.

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Step-by-step explanation:

a. #(x) = 0.23x^2 - 0.46x + 7.54 (numbers rounded to two decimal places)

b. To find the year at which the number of households living in poverty is at a minimum, we need to find the vertex of the quadratic function. The x-value of the vertex is given by -b/2a. Plugging in the values for a and b from the function in part (a), we get:

x = -(-0.46)/(2*0.23) = 1

So the minimum occurs in the year 1999 + 1 = 2000 (rounded to the nearest year).

c. To find the number of households living in poverty in 2000, we need to evaluate the function at x = 1 (since 2000 is 1 year after 1999). Plugging in x = 1 into the function from part (a), we get:

#(1) = 0.23(1)^2 - 0.46(1) + 7.54 = 7.40

So there were approximately 7400 households living in poverty in Asturias in 2000 (rounded to one decimal place).

Answer:

Part A: Experiment: Rolling a fair six-sided die.

Part B: Sample space: {1, 2, 3, 4, 5, 6}. This sample space was determined by listing all possible outcomes of rolling a fair six-sided die.

I hope that's what you are looking for.

Answer:

(xyz + 1)

Step-by-step explanation:

We can use the identity:

[tex]a^2 - b^2 = (a + b)(a - b)[/tex]

to solve for the blank in this equation.

On the left side, we can identify a difference of two squares (a² - b²).

We can see that there is already an (a - b) term on the right, so in the blank, we just have to construct an (a + b) term:

(xyz + 1)

This satisfies the equation:

(xyz)² - 1 = (xyz + 1) · (xyz - 1)

Answer:

--------------------

Area of the rectangle:

Area of the two triangles:

Area of trapezoid is the sum of the areas we found above:

The matching answer choice is B.

The exponential decay can be written as:

y = 550mg*(1 - 0.066)^t

A general exponential decay can be written as:

y = A*(1- r)^x

Where A is the initial amount, r is the rate of decay, and x is the variable.

Here we know that we start with a sample of 550 mg, and this sample decays at a rate of 6.6% per year.

Then the amount of sample that we have after t years is given by the exponential decay:

y = 550mg*(1 - 0.066)^t

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The area of the composite figure that is composed of triangles and a rectangle is: 154 mm².

The composite figure given comprises two different triangles and one rectangle. Therefore, to find the area of the composite figure, we need to calculate the area of each shape in the figure.

Area of rectangle = length * width = (7 + 7) * 4

= 14 * 4

Area of rectangle = 56 mm²

Area of the larger triangle = 1/2 * base * height

= 1/2 * 14 * 11

= 77 mm²

Area of the smaller triangle = 1/2 * 14 * 3

= 21 mm²

Therefore, area of the composite figure = 56 + 77 + 21

= 154 mm²

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