A function is given.
g(x) =
4
x + 5
; x = 0, x = h
(a) Determine the net change between the given values of the variable.


(b) Determine the average rate of change between the given values of the variable.

The sinusoidal expression of the function is D(t) = -cos(3t)

A sinusoidal alternating current can be represented by the equation i = I sin ωt, where i is the current at time t and I the maximum current. In a similar way we can write for a sinusoidal alternating voltage v = V sin ωt, where v is the voltage at time t and V the maximum voltage.

here, we have to,

to determine the sinusoidal expression:

When he pushes off, he is 1 m behind the center.

This means that:

Amplitude, a = 1.

But we use, a = -1 because he is behind

The graph has a minimum point at (0,-1) and then intersects its midline at (π/6, 0).

So, the period B is: 2π/B = 4 * π/6 and the vertical shift (d) is 0

Simplify 2π/B = 4 * π/6

2π/B = 2π/3

By comparison, we have:

B = 3

The function is given as:

a cos(Bt) + d

Substitute the calculated values

D(t) = -cos(3t)

Hence, the sinusoidal expression of the function is D(t) = -cos(3t)

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Answer:

period and he completes a swing in ten seconds

The grades that Angie need to receive in her next test so that her average is 92 is 91.

The average is defined as the mean value a given data set. The formula to calculate the mean of a given data set is:

Average = Sum of the observations / Total number of observations

Assume the marks that Angie needs in her next test is represented by x.

Given that Angie has reviewed grades of 88, 96, 92, and 93 on her last 4 tests. Therefore, the grades she need to receive in her next test so her average is 92 is:

Average = Sum of the grades of all test / Total Number of test

92 = (88+96+92+93+x)/5

460 = 369+x

460 - 369 = x

x = 91

Hence, she needs 91 grades in her next test.

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The complete question is:

Angie has reviewed grades of 88, 96, 92, and 93 on her last 4 tests. what grade will she need to receive in her next test so that her average of all test is 92?

The rate at which its unemployment changes  is, 54.6 %

Rate is a ratio of change in one quantity w.r.t. change in another quantity. The net change in one quantity is written as, Δy and the net change in another quantity is written as, Δx.

So formula for the rate is,

m = change in one quantity/change in another quantity = Δy/Δx

Given that,

The initial number of unemployed workers was 3.4 million and the final number was 5.5 million.

The change in the number of unemployed workers is:

5.5 million - 3.4 million = 2.1 million

To find the initial number of employed workers, we need to subtract the initial number of unemployed workers from the total population:

76 million - 3.4 million = 72.6 million

Now, we can calculate the initial unemployment rate as:

3.4 million / 72.6 million = 0.0469 or 4.69%

Similarly, the final unemployment rate is:

5.5 million / 76 million = 0.0724 or 7.24%

The change in the unemployment rate is:

(0.0724 - 0.0469) / 0.0469 ≈ 0.546 or 54.6%

Therefore, the unemployment rate increased by about 54.6%, which is closest to answer choice A. It increased by about 27%.

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Answer:

Step-by-step explanation:

Let's call the present value of the loan P. The payments of $1,550 in 1 year and $2,400 in 4 years can be expressed as an ordinary annuity with semi-annual payments. We can calculate the present value of this annuity using the formula:

PV = A * (1 - (1 + r)^-n) / r

where

A = $1,550 / 2 = $775 (semi-annual payment)

n = (4 x 2) + 2 = 10 (number of semi-annual periods)

r = 0.045 / 2 = 0.0225 (semi-annual interest rate)

So,

PV = $775 * (1 - (1 + 0.0225)^-10) / 0.0225 = $8,100.40

Thus, the present value of the loan is P = $8,100.40.

Next, we can calculate the present value of the payment of $1,050 in 24 months and the balance in 30 months.

The payment of $1,050 in 24 months can be expressed as a single amount due in 24 months. The present value of this payment can be calculated as:

PV = $1,050 / (1 + 0.0225)^(24/2) = $1,000.54

So, the balance of the loan after this payment would be P - $1,000.54 = $8,099.86.

The balance in 30 months can be expressed as an ordinary annuity due with semi-annual payments. We can calculate the present value of this annuity using the formula:

PV = A * (1 - (1 + r)^-n) / r

where

A = ($8,099.86) / 6 = $1,349.98 (semi-annual payment)

n = 6 (number of semi-annual periods)

r = 0.0225 (semi-annual interest rate)

So,

PV = $1,349.98 * (1 - (1 + 0.0225)^-6) / 0.0225 = $7,999.86

Therefore, the payment required in 30 months for the rescheduled option to settle the loan is $1,349.98 per semi-annual period.

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The functions f(x) = x³ + x² - 2x + 3 and g(x) = log(x) + 2 have same range as (-∞,∞) or {y : y∈R}.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The given functions are -

f(x) = x³ + x² - 2x + 3

g(x) = log(x) + 2

The graph for function f(x) is plotted.

The function f(x) is a cubic function.

The domain for the function is (-∞,∞) or {x : x∈R}.

The range for the function is (-∞,∞) or {y : y∈R}.

The x-intercept for the function is (-2.37442376,0).

The y-intercept for the function is (0,3).

The graph for function g(x) is plotted.

The function g(x) is a logarithmic function.

The domain for the function is (0,∞) or {x : x>0}.

The range for the function is (-∞,∞) or {y : y∈R}.

The x-intercept for the function is (0.01,0).

The y-intercept for the function is not available.

Therefore, both functions have same range,

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The given expression is proved.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

here, we have.

tan∅/(1+ sec∅)

=(sin∅/cos∅)/(1+ sec∅)                  [tan∅=(sin∅/cos∅)]

=(sin∅/cos∅)/(1+1/cos∅)

=sin∅/1+cos∅

multiplying both numerator & denominator by 1-cos∅, we get,

=sin∅(1-cos∅)/ sin^2∅

=(1-cos∅)/sin∅

=cosec∅ - cot∅

Hence, The given expression is proved.

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Answer:

6.7 weeks.

Step-by-step explanation:

65.00 x 6.7 = 435.50

Answer:

Step-by-step explanation:

He has $65 on the first week. He’s missing $370. If he can save $18 a week. 370/18 = 20.5. But they’re asking for the total weeks it’ll take. So add the first week. 20.5 + 1 = 21.5

not mine but he did he get it right

The value of the variable y is 3

From the information given, we have that;

ACDF∼VWYZ

Given that the lengths are;

Since the diagrams are equivalent, then,

A/VZ = CD/YW

substitute the values, we have;

12/3y - 1 = 9/6

cross multiply

3y - 1 = 12(6)/9

divide the values

3y - 1 = 8

collect like terms

3y = 9

Make 'y' the subject

y =3

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The amount of money the company makes per shirt  $18.90

Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The chances that event will occur is measured by probability.

Probability of Event = Favorable Outcomes/Total Outcomes

                                 = X/n

To calculate the expected profit per shirt, we need to consider the two possible outcomes:

the shirt is defective or not defective.

If the shirt is not defective, the company makes a profit of $20.

If the shirt is defective, the company incurs a cost of $35 and no profit.

The probability of a shirt being defective is 0.02, so the probability of a shirt not being defective is:

= 1 - 0.02

= 0.98.

Therefore, the expected profit per shirt can be calculated as:

Expected profit = (probability of not defective) x (profit per non-defective shirt)

+ (probability of defective) x (cost per defective shirt)

Expected profit = 0.98 x $20 + 0.02 x (-$35)

Expected profit = $19.60 - $0.70

Expected profit = $18.90

So the company really makes $18.90 per shirt, taking into account the cost of defective shirts.

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The intervals of each behavior of the function are given as follows:

a) Increasing: (-∞, -1).

b) Decreasing: (-1, 1).

c) Constant: (1, 3).

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable .

here, we have,

to classify the function as increasing, decreasing or constant:

The function is increasing when the graph moves right and up.

The function is decreasing when the graph moves right and down.

The function is constant when the graph of the function is an horizontal line.

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Answer:

The rate of change of the velocity of the wave with respect to the depth of the water is 3/2 meters per second per meter when the depth is 2 meters. This can be found by taking the derivative of v(h) with respect to h, which is 3/2√h. When h is 2, the rate of change is 3/2√2, which is equal to 3/2 meters per second per meter.

Answer:

48 kicks

Step-by-step explanation:

If she shoots 40 times and misses 8, we can create a ratio to represent the number of total shots to the number of misses:

40/8 = 60/x X represents the amount she will miss if she takes 60 shots.

We can find the value of x by using cross multiplication:

480 = 40x. We can now isolate x by dividing both sides by 40:

X = 12.

Melinda will miss 12 out of 60 shots.

She will make 48 kicks.

The fomulas of the sequence are a(n) = 3200(1.09)^n-1 and a(n) = a(n - 1) * 1.09

from the question, we have the following parameters that can be used in our computation:

First term, a = 3200

Increment, r = 9%

To find the explicit formula, we can use the formula for compound interest:

a(n) = a * (1 + r)^n-1

So, we have

a(n) = 3200(1.09)^n-1

For the recursive formula, we have

a(n) = a(n - 1) * 1.09

This is because the product of the current term and the incremnt rate gives the next term

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radius = 9 cm

height = 26,5 cm

as we know that

volume of cylinder = πr^2h

= 3,14x9x9x2x26,5

= 13.480 cm cubic

Answer:

Step-by-step explanation:

To simplify the expression X^(12/7) * Y^(35/7) into its simplest form, we need to find the greatest common divisor (GCD) of the exponents 12/7 and 35/7 and divide both exponents by the GCD. Here's the step-by-step process:

Find the GCD of 12/7 and 35/7. To do this, we'll use the Euclidean algorithm method:

a. Divide the larger number, 35, by the smaller number, 12, and get the remainder: 35 ÷ 12 = 2 with a remainder of 11.

b. Divide the smaller number, 12, by the remainder, 11, and get the quotient and remainder: 12 ÷ 11 = 1 with a remainder of 1.

c. The last non-zero remainder, 1, is the GCD of 12/7 and 35/7.

Divide both exponents by the GCD, 1:

a. X^(12/7) becomes X^(12/7 ÷ 1) = X^12.

b. Y^(35/7) becomes Y^(35/7 ÷ 1) = Y^35.

Replace the original exponents in the expression with the simplified exponents: X^12 * Y^35.

So, the expression X^(12/7) * Y^(35/7) is simplified as X^12 * Y^35, which is written as a single radical in its simplest form.

[tex]~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] ~\dotfill\\\\ x^{\frac{12}{7}}y^{\frac{35}{7}}\implies \left( x^{12} y^{35} \right)^{\frac{1}{7}}\implies \sqrt[7]{x^{12} y^{35}}\implies \sqrt[7]{x^{7+5} (y^5)^7} \\\\\\ \sqrt[7]{x^7 x^5 (y^5)^7}\implies {\Large \begin{array}{llll} x y^5\sqrt[7]{x^5} \end{array}}[/tex]

The system of linear equations representing the given situation is: 2x + y = 10 and 2x + 3y = 22. Solving this system, we find that it takes 6 minutes to jog around the park.

a. Let's use x to represent the number of minutes it takes to jog around the block and y to represent the number of minutes it takes to jog around the park.

From the problem statement, we know that:

2x + y = 10 (jog around the block twice and the park once in 10 minutes)

2x + 3y = 22 (jog around the block twice and the park three times in 22 minutes)

These are the two linear equations that represent the given situation.

b. We can solve this system of equations to find the value of y, which represents the number of minutes it takes to jog around the park.

We can start by eliminating x from the equations. Subtracting the first equation from the second, we get:

(2x + 3y) - (2x + y) = 22 - 10

2y = 12

y = 6

So, it takes 6 minutes to jog around the park.

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Complete question:

You can jog around your block twice and the park once in 10 minutes. you can jog around your block twice and the park 3 times in 22 minutes.

a. write a system of linear equations that represents this situation. let x represent the number of minutes it takes you to jog around your block and y represent the number of minutes it takes you to jog around the park. system of equations:

b. how long does it take you to jog around the park? it takes you minutes to jog around the park.

OD) Is simple non-randon sampling

Step-by-step explanation:

because Claudia randomly choose a sample from each group.

Four rational numbers between 1/5 and 1/6 are; 41/240, 42/240, 43/240, 44/240

A rational number is defined as a number that can be expressed as the quotient of fraction p/q of two integers, a numerator p, and a non-zero denominator q.

First, we have to make the denominators the same.

We multiply 1/5 by 48 and 1/6 by 40 to get:

48/240 and 40/240

Thus, the other rational numbers between them are;

41/240, 42/240, 43/240, 44/240

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Complete question is;

Find four rational numbers between 1/5 and 1/6 ​

Answer:

yes

Step-by-step explanation:

2*(4+7) = ( 2 * 4 ) + ( 2 * 7 )

The simplified form of the expression xy( x³y⁵ - x⁷ ) is x⁴y⁶ - x⁸y.

Given the expression in the question;

xy( x³y⁵ - x⁷ )

To simplify the expression, apply distributive property.

xy( x³y⁵ - x⁷ )

xy( x³y⁵ ) - xy( x⁷ )

xy( x³y⁵ ) - xy( x⁷ )

Multiply xy and ( x³y⁵ )

x⁴y⁶ - xy( x⁷ )

Multiply xy and ( x⁷ )

x⁴y⁶ - x⁸y

Therefore, the simplified form is x⁴y⁶ - x⁸y.

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The information regarding the addition is explained below.

Adding 29 + 46:

Student 1: May use the traditional column addition method, lining up the digits in the ones, tens, and hundreds place and carrying over if necessary.

Student 2: May use the breaking apart method, where they break apart the numbers into smaller parts (e.g. 20 + 40) and then add the pieces together.

Student 3: May use a number line, counting up from 29 by the increments of 46 until they reach the sum.

Subtracting 54 - 28:

Student 4: May use the traditional column subtraction method, lining up the digits in the ones, tens, and hundreds place and borrowing if necessary.

Using bundled things to explain regrouping in the addition problem 167 + 59:

First, separate the numbers into bundles of ten.

Next, show how you can regroup the ones as ten ones to make a bundle of ten.

Then add the tens and hundreds place to get the answer 226.

Using bundled things to explain regrouping in the subtraction problem 231 - 67:

First, separate the numbers into bundles of ten.

Next, show how you can regroup the tens as ten tens to make a bundle of a hundred.

Then subtract the hundreds place and the tens place to get the answer 164.

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Some way to solve binary operations are listed below

By definition, binary operations involve performing arithmetic operations on two operands in a specific way.

An example of a binary expression is a + b

Where a and b are the operands & + is the operator

Some common binary operations and how to solve them are highlited below

Other operations are

Multiplication (*), Division (/) and Modulus

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The value of the length /MK/ is 10 units

Recall that in an isosceles reangle, two sides are equal and the base angles are equal

We can use the cosine rule to find the length MK

N² = K²+M² - 2KMCosN

This implies that /MK/² = 5²+5²-2*5*5*cos110

⇒25+25-50*-0.9990

= 50+49.95

=99.95  this can be approximated to 100

the /MK/ = √100= 10 units

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By the given graph we can conclude that the solution of the equation (i.e point of intersection of lines) is (-2, -2).

To solve the system of equations, graph the given two lines' first equation. Now determine whether the lines are parallel, intersect, or are the same line.

In the next step, we need to Identify the solution to the system.

If the lines are intersected, the point of intersection is the solution.

If the lines are parallel, the system will have no solution.

If the lines are the same or coincident, then the system will have an infinite number of solutions.  

Here we have

y = x  ----- (1)

y = 2x+2 ---- (2)

From (1) and (2)

=> y = 2y + 2

=> 2y - y = -2

=> y = - 2

Hence, the solution of the given system of the equation is (-2, -2)

We can check it by graphing the lines as shown figure.  

Therefore,

By the given graph we can conclude that the solution of the equation (i.e point of intersection of lines) is (-2, -2).

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The output value of y when input value x is -7:   -6

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

Vertical line test:-

Whenever we want to check given expression is a function or not we can check it by a vertical line test, in this test we check for a single image of x , we are getting a single image or more.

If we get more images then it will not be a function.

For example, let us take, y² = 4ax

y = ±√4ax

For single value of x we get two values of y

Hence, it will not be a function.

Given that,

A graph of a function,

And input value x  = -7

output value y = ?

As it can be seen in the graph,

For input value x  = 0

output value of y = -2

Similarly,

for input value x  = -7

It can be seen in the graph that

the value of y = -6

Hence, the value of y is -6

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The lengths for which the area will be less than 175 cm² are less than 25 cm

From the question, we have the following parameters that can be used in our computation:

Width = 7 cm

Area = Less than  175 cm²

The formula of area is represented as

Area = Length * Width

Using the above as a guide, we have the following:

Length * Width < 175

substitute the known values in the above equation, so, we have the following representation

Length * 7 < 175

Divide by 7

Length < 25

Hence, the length is less than 25

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Answer:12

Step-by-step explanation:30-6=24

24 divided by 2 =12

Relationship among AC, A'C', and A"C'' is all the three sides are corresponding sides

a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".

To widen or enlarge an opening or hollow structure beyond its usual size in simple way changes the the size.

The scale factors is the factor in which each linear measure of the figure is multiplied.

AC is a smaller triangle which is dilated to get A'C' and this A'C' is dilated to get A''C''.

the relationship among AC, A'C', and A"C'' is all the three sides are corresponding sides with a scale factor.

Hence,  relationship among AC, A'C', and A"C'' is all the three sides are corresponding sides

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