(8-12) x (8 x 4) +7²

The inverse of the rational function h(x) = (2 · x + 3) / (4 · x - 5) is the rational function h⁻¹(x) = (5 · x + 3) / (4 · x - 2).

In this problem we have the definition of a rational function:

h(x) = (2 · x + 3) / (4 · x - 5)

Of which we must determine the inverse of the rational function by using algebraic properties:

h⁻¹(x) = f(x)

First, use the following substitution on h(x):

x = h(x)

h⁻¹(x) = x

Second, substitute in the rational equation:

x = [2 · h⁻¹(x) + 3] / [4 · h⁻¹(x) - 5]

Third, clear h⁻¹(x) in the expression by algebraic properties:

x · [4 · h⁻¹(x) - 5] = 2 · h⁻¹(x) + 3

(4 · x - 2) · h⁻¹(x) = 5 · x + 3

h⁻¹(x) = (5 · x + 3) / (4 · x - 2)

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The value of ∠ DEG = 20° in the given triangle. The value of b in the given triangle is 22.6.

a) ∠ DEG = ? if ∠DFE = 70°

Here, ∠F = ∠D = 70°

∠G = 90°

Sum of triangle = 180°

∠D + ∠E + ∠G = 180°

70° + 90° + x = 180°

160° + x = 180°

x = 180° - 160°

x = 20°

b) if a = 8 , c =24 then b = ?

∠DGE is right angle. It follows Pythagoras theorem:

What is pythagoras theorem?

DG² + GE² = DF²

8² + X² = 24²

X² = 576 - 64

X² = 512

X = 22.6

Hence, the value of b in the given triangle is 22.6.

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The length of UT if, The line UV || RS, UV is 12 less than UT, RT = 42, and RS = 21 is,24.

Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline.

Given:

The line UV || RS,

UV is 12 less than UT,

RT = 42, and RS = 21,

Write the equation for the UV and UT,

UV = UT - 12

Calculate the value of UT as shown below,

UT / RT = UV / RS     (For parallel lines, the ratio should be the same)

UT / 42 = (UT - 12) / 21

21 × UT / 42 = (UT - 12)

UT / 2 = (UT - 12)

UT = 2UT - 24

2UT - UT = 24

UT = 24

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Using a system of equations, Mike should invest $66,000 in investment A and $24,000 in investment B to earn $5,220 from both funds per year.

We can solve a system of equations to determine the amounts that should be invested in each fund to earn the stated amount yearly.

A system of equations is also called simultaneous equations because they can be solved together.

The total investible funds = $90,000

The expected annual earnings = $5,220

The earnings from investment A = 5% or 0.05

The earnings from investment B = 8% or 0.08

A + B = 90,000  ... Equation 1

0.05A + 0.08B = 5,220 ... Equation 2

Multiply equation 1 by 0.05:

0.05A + 0.05B = 4,500 ... Equation 3

Subtract Equation 3 from Equation 2:

0.05A + 0.08B = 5,220

-0.05A + 0.05B = 4,500

=0.03B = 720

= 24,000 (720/0.03)

B = $24,000

From Equation 1, substitute B = 24,000 to get A:

A + B = 90,000

A + 24,000 = 90,000

= 66,000

A = $66,000

Thus, we can conclude that Mike with $90,000 should invest $66,000 in Investment A earning 5% per year, and $24,000 in Investment B earning 8% annually to earn a total of $5,220 from both funds.

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Step-by-step explanation:

y = mx + b

m = 3

b = 2

y = 3x + 2

______________________

y = mx + b

m = 1/2

b = -1

y = 1/2x + (-1)

y = 1/2x -1

Answer:

377 is answer

Step-by-step explanation:

12.33-25 +6

396-25+6

377

Answer:

56.7C

Step-by-step explanation:

The highest temperature on the was 56.7C and it is recorded in United States on 10 July 1913

The difference between the low temperature and the high temperature on Tuesday is -1.1°C.

From the information given, the temperature Monday evening was 16.4 c the temperature dropped an average of 1 1/4 degrees each hour for the next 14 hours until it reached its lowest temperature for the day on Tuesday.

Therefore, the temperature on Tuesday will be:

= 1 1/4(14)

= 17.5

The difference in the temperature will then be:

= 16.4°C - 17.5°C

= -1.1°C.

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The speed from City A to City B is 873.33 mi/h.

What is the speed, distance and time?

That is speed = distance ÷ time. Or to put it another way, distance divided by speed will give you the time. Provided you know two of the inputs you can work out the third.

Let's call the speed from City A to City B x. The speed on the return trip was 1.2x. The total distance traveled was 2400 + 2400 = 4800 mi. The total time taken was 330 minutes, which is 330/60 = 5.5 hours. The average speed is the total distance traveled divided by the total time taken, so:

4800 mi / 5.5 h = 873.33 mi/h

The total speed for both legs of the trip is 873.33 + 873.33 = 1746.66 mi/h

The speed for just one leg of the trip is half of the total speed, so the speed from City A to City B is 1746.66/2 = 873.33 mi/h.

Hence, the speed from City A to City B is 873.33 mi/h.

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She should divide both sides by -5 while she multiplied by -5 on other side and she also did not change the > symbol to a < symbol

The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities1, is at the core of social justice theories. However, because it frequently has different meanings to different people, it is prone to misunderstanding in public discourse. However, some distinctions are shared.

We are given

-5x - 3.5>6.5

Since, we have to solve for x

so, we will isolate x on anyone side

step-1:

Add both sides by 3.5

-5x - 3.5+3.5>6.5+3.5

-5x>10

step-2:

Divide both sides by -5

we know that whenever we divide both sides by negative sign , it's inequality gets revered

so, we get

-5x/5<-50/-5

we get

x<10

so,

She should divide both sides by -5 while she multiplied by -5 on other side and she also did not change the > symbol to a < symbol

The complete question is : Parul attempted to solve an inequality but made one or more errors. Her work and the graph she drew are shown below. What errors did Parul make? Check all that apply. She added 3.5 to both sides when she should have subtracted. She should have divided both sides by as her first step. She divided one side by -5 while multiplying the other side by -5. She did not change the > symbol to a < symbol. She used a closed circle instead of an open circle on the number line.

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Step-by-step explanation:

the domain is the interval or set of all valid x- (or input-)values. in our case here t-values.

the graph shows us

0 <= t <= 35

For the given condition on the graph, the domain of the function is

0 ≤ t ≤ 36.

A function is an expression, rule, or law in mathematics that describes a connection between one variable (the independent variable) and another variable (the dependent variable). Functions are common in mathematics and are required for the formulation of physical connections in the sciences. A function is defined as a relationship between a group of inputs that each have one output. A function is a connection between inputs in which each input is associated to exactly one output.

Here,

The correct answer is option B. 0 ≤ t ≤ 36

To do this question, the main thing is to look at picture.

We know from the graph that this is a quadratic function, So t has to be less than some positive number.

{ if t → -∞, H(t) → -∞, not in the line with the actual situation}

and look at the graph, the point where H(t) equals zero, one is 0 and one is 36.

The domain for the function is 0 ≤ t ≤ 36 for given condition in the graph.

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Answer:

the equation 10 = x - y

Step-by-step explanation:

Let x represent the initial value of the investment, and let y represent the amount of money that each person receives after the investment is withdrawn.

We know that the cost of withdrawing the investment is $10, so we can write the equation 10 = x - y. We also know that each person receives $40, so we can write the equation y = 40.

We can now solve for x by substituting the value of y into the first equation. Since y = 40, we can substitute 40 for y in the equation 10 = x - y to get 10 = x - 40. Solving this equation for x, we find that x = 50.

Therefore, the initial value of the investment was $50.

Answer:

Below

Step-by-step explanation:

bench     +   ( bench + 57)     = 1007

2 bench = 950

bench = $ 475

Answer:

its the first option explanation is up top

[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex][tex]\begin{cases} h=1\\ k=3 \end{cases}\implies y=a(x-1)^2 + 3\hspace{5em}\textit{we also know that} \begin{cases} x=2\\ y=5 \end{cases} \\\\\\ 5=a(2-1)^2 + 3\implies 2=a(1)^2\implies \cfrac{2}{(1)^2}\implies 2=a \\\\\\ ~\hfill {\Large \begin{array}{llll} y=2(x-1)^2 +3 \end{array}} ~\hfill[/tex]

Interest in $2800 when deposited $7,000 in an account earning 10% interest compounded annually.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest. Simple Interest (S.I.) is a way for figuring out how much interest will accrue on a specific principal sum of money at a certain rate of interest. For instance, if someone borrows $5000 at a rate of 10 p.a. for two years, they will pay S.I. on the borrowed money for those two years.

Given

Principal = $7000

Rate = 10%

Time = 4 years

Using simple interest formula,

PRT

7000 × 0.1× 4

2800

Interest in $2800 when deposited $7,000 in an account earning 10% interest compounded annually.

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Answer: 3,248.70

Step-by-step explanation: You can use this formula when working with compound interest:

B=p(1+r)t

In this formula, B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.

The interest is the balance minus the principal.

solve

Write the rate as a decimal.

10%=0.10

Calculate the balance.

B

= p(1+r)t

= $7,000(1+0.10)4

= $7,000(1.10)4

= $7,000(1.4641)

= $10,248.70

Now use this to find the interest, which is the balance minus the principal.

$10,248.70–$7,000=$3,248.70

The interest will be $3,248.70.

Answer:

Step-by-step explanation:

To determine the ratio of the note B to middle C, we can divide the frequency of B by the frequency of C. Using the information provided, the frequency of B is 493.9 Hz and the frequency of C is 261.6 Hz. The ratio of B to C is therefore 493.9 / 261.6, which is approximately equal to 1.89. This means that the note B is approximately 1.89 times higher in pitch than the note C.

The distance between any coordinate (x,y) and the origin is given by the equation presented as follows:

D = square root of (x² + y²).

The angle between these coordinates and the positive x-axis is given as follows:

Angle = arctan(y/x).

The distance between two points on a coordinate line is equivalent to the hypotenuse of a right triangle.

The sides of the triangle are represented by the differences of the x-coordinates and the y-coordinates of each point.

For the origin, the coordinates are (0,0), hence the distance of any point from the origin is given by the equation presented as follows:

D = square root of (x² + y²).

For the angle, we have that:

Hence the tangent is applied, as follows:

tan(Angle) = y/x

Angle = arctan(y/x).

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The solution to the given integration problem is;

[tex]\frac{[(x^{2} + 1)x^{\frac{3}{2} } *(3x^2 - 2)]}{15} + C[/tex]

We want to integrate the function x³[√(x² + 1)dx]

This is expressed as;

∫x³[√(x² + 1)dx]

Preparing for substitution we have;

∫2x[x²√(x² + 1)/2dx]

Make u = x²

du/dx = 2x

dx = (1/2x) du

Thus, we now have;

¹/₂∫u√(u + 1)du

¹/₂∫(u^(3/2) - √u) du

Applying power rule and solving this gives us;

[tex]\frac{(x^2 + 1)x^{\frac{5}{2} } }{5} - \frac{(x^2 + 1)x^{\frac{3}{2} } }{3}[/tex]

= [(x² + 1)^(3/2) (3x² - 2)]/15 + C

Thus, that is the solution of solving the integration problem.

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a) The hypothesis are given as follows:

b) The test statistic is of: z = 0.94.

c) The p-value is of: 0.1736.

At the null hypothesis, it is tested if there is not enough evidence that p1 is greater than p2, that is, if the subtraction is of zero, hence:

[tex]H_0: p_d = 0[/tex].

At the alternative hypothesis, it is tested if there is enough evidence that p1 is greater than p2, that is, if the subtraction is greather than zero, hence:

[tex]H_1: p_d > 0[/tex].

For each sample, the mean and the standard error are given as follows:

Hence, for the distribution of differences, the mean and the standard error are given as follows:

The test statistic is given by the division of the estimate of the proportion of differences by the standard error, hence:

z = 0.0395/0.0421 = 0.94.

We have a right-tailed test, as we are testing if the mean is greater than a value, with z = 0.94. Hence, looking at the z-table, the p-value is of:

0.1736.

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Given is the equation of a line with slope of m = 3 and [y] intercept of c = -8.

The general equation of a straight line is -

Other possible equations of lines are -

We have the equation of line as -

y = 3x - 8

The given is the equation of a line with slope of m = 3 and [y] intercept of c = -8.

Therefore, given is the equation of a line with slope of m = 3 and [y] intercept of c = -8.

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Answer:

Step-by-step explanation:

It is likely that Sharon's calculated mean time is the better estimate of the actual mean time for the whole class. This is because she collected data from a larger sample of the class (10 students) than Gerald (4 students). A larger sample size generally results in a more accurate estimate of the population mean.

It is more likely for the mean time calculated by Sharon to be better estimate than that of Gerald.

Mean of a set of data is defined as the average of all the values. It gives the exact middle point of the data set.

Given,

Mean time to complete the assignment taken from 4 students by Gerald = 38 minutes.

Mean time to complete the assignment taken from 10 students by Sharon = 32 minutes

Population size = 30 students

When the sample size is more closer to the population size, the sample mean would be more closer to the actual mean.

So Sharon's estimate is a better option.

Hence the estimate value of mean calculated by Sharon is more likely to be closer to the actual mean.

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The numbers as they appear from left to right on a horizontal number line is Horizontal number line.

This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally or vertically. As we move towards the right side of a horizontal number line, the numbers increase; as we move towards the left, the numbers decrease.

What's the equation of a horizontal line?

Horizontal lines have a slope of 0. Thus, in the slope-intercept equation y = mx + b, m = 0. The equation becomes y = b, where b is the y-coordinate of the y-intercept.

-2.76

-2.57

-2.5

-1.85

-1.58

2.5

2.85

On a number line, we have this horizontal line, meaning it moves left and right, and zero is placed in the middle.

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The graph in the problem is interpreted as follows

What interpretation can be made from the y-intercept?

the y-intercept shows start the timing started when the cheetah is not running

How can the point (3.0, 12) on the graph above be interpreted? At 3.0 s the cheetah was running at 12 m/s

What is the output value of this graph when the input value is 5.0?

the output is 30

Does the graph above have a constant rate of change?

No, the rate of change varies

The term "rate of change" describes the rate at which something changes over time.

Thus, it is not the amount of individual changes themselves but rather the acceleration or deceleration of changes (i.e., the rate).

When the ratio of the output to the input remains constant at every given point along the function, the rate of change is said to be constant.

The slope is another name for the constant rate of change. The rate of change for linear functions will be constant.

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Part A:

This data appears to be modeling a geometric sequence because the time to complete each station is increasing by a constant factor. For example, the time to complete station 2 is 4 minutes, which is double the time it took to complete station 1. Similarly, the time to complete station 3 is 8 minutes, which is double the time it took to complete station 2, and so on.

Part B:

To find the time Aurora will take to complete station 5 using a recursive formula, we can use the formula:

a_n = a_1 * r^(n-1)

where a_n is the time it takes to complete station n, a_1 is the time it takes to complete station 1, and r is the common ratio (the factor by which the time increases from one station to the next).

We are given that a_1 = 2 and a_2 = 4, so we can solve for r:

r = a_2 / a_1

= 4 / 2

= 2

Then we can use this value of r to find the time it takes to complete station 5:

a_5 = a_1 * r^(5-1)

= 2 * 2^4

= 2 * 16

= 32

Therefore, Aurora will take 32 minutes to complete station 5.

Part C:

To find the time Aurora will take to complete station 9 using an explicit formula, we can use the formula:

a_n = a_1 * r^(n-1)

where a_n is the time it takes to complete station n, a_1 is the time it takes to complete station 1, and r is the common ratio (the factor by which the time increases from one station to the next).

We are given that a_1 = 2 and a_2 = 4, so we can solve for r:

r = a_2 / a_1

= 4 / 2

= 2

Then we can use this value of r to find the time it takes to complete station 9:

a_9 = a_1 * r^(9-1)

= 2 * 2^8

= 2 * 256

= 512

Therefore, Aurora will take 512 minutes to complete station 9.

say no more

The correct option  4 and 25; the degrees of freedom for the critical value of f.

The essential value F's degrees of freedom are (k-1,n-k).

Four sample groups are provided to us, so,

k = 5.

Additionally, we know that each of the five groups has six observations, therefore

n = 5*6

n = 30

The crucial factor F can vary in freedom.

(k-1,n-k)

(5-1, 30 - 5)

(4,25).

Its degrees of freedom again for critical F value are as a result (4,25).

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Answer:

  A.  $510.75

  B.  $6,129.00

  C.  8.63%

Step-by-step explanation:

You want the monthly payments, total amount paid, and fraction going to interest for the payoff of a $5600 credit card balance at an annual rate of 17% interest.

The monthly payments can be found using the amortization formula:

  A = P(r/12)/(1 -(1 +r/12)^(-12)) . . . . . P is the principal amount, r is the rate

This formula gives the monthly payment for payoff in 1 year.

  A = 5600(0.17/12)/(1 -(1 +0.17/12)^-12) ≈ 510.75

The monthly payment is $510.75.

You will have made 12 monthly payments of $510.75, for a total of ...

  12 ×  $510.75 = $6,129.00

You will have paid $6,129.00.

The fraction of your total payoff that goes to interest is ...

  (6129 -5600)/6129 = 1 -(5600/6129) ≈ 0.0863 = 8.63%

About 8.63% of your total payment is interest.

__

Additional comment

Spreadsheets and calculator apps can be used to find these values. You need to be careful to specify that payments are made at the end of the month.

The amount to interest is slightly more than half the interest that would be due if the interest rate were used to calculate simple interest. Our answer of 8.63% is slightly higher than 17%/2 = 8.5%, so passes the reasonableness check.

a. The probability of defective shells from the given samples are:

a. Probability of zero defective shells of samples is equal to 0.9510.

b. Probability of one defective shells of samples is equal to 0.04803

c. Probability of more than 1 defective shells of samples is equal to 0.00107.

As given in the question,

Total number of batches = 350

Sample size used to test for each batch 'n' = 5

Actual defective shells (success) 'p' = 1%

                                                           = 0.01

Actual non-defective shells ' 1 - p ' = 1 - 0.01

                                                         = 0.99

a. Probability of zero defective shells from the given samples is

=  ⁵C₀ × ( 0.01 )⁰ × (0.99)⁵⁻⁰

= [ (5!)/(5-0)!0! ] × 1 × ( 0.99)⁵

= 0.9510

b. Probability of 1 defective shells from the given samples is

= ⁵C₁ × ( 0.01 )¹ × (0.99)⁵⁻¹

= [ (5!)/(5-1)!1! ] × 0.01 × ( 0.99)⁴

= 5 × 0.01 × 0.9606

=0.04803

c. Probability of more than 1 defective shells from the given samples is

= P(2) + P(3) + P(4) + P(5)

= ⁵C₂ × ( 0.01 )²× (0.99)⁵⁻² + ⁵C₃ × ( 0.01 )³ × (0.99)⁵⁻³ + ⁵C₄× ( 0.01 )⁴ × (0.99)⁵⁻⁴+ ⁵C₅× ( 0.01 )⁵× (0.99)⁵⁻⁵

= 0.00097 + 0.000098 +0.000000044 +0.0000000001

=0.00107

Therefore, the probability of following conditions are as follow:

a. Probability of zero defective shells of samples is equal to 0.9510.

b. Probability of one defective shells of samples is equal to 0.04803

c. Probability of more than 1 defective shells of samples is equal to 0.00107.

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-3+9. -6

------= ---

-2+3. -1

the answer is 6

Andrea could use 28÷7 = 4 this division problem to check her work.

Check one-by-one:

A. 0÷4=7

The answer to 7 divided by 0 is 0. This is due to the fact that dividing a non-zero number by zero is mathematically impossible. See complete response below.

B. 7÷4 = 28

7 * 4 = 28 is the correct value where this value is 1.7

C. 14÷4 = 7

The value of the above is not equated because 3.5 ≠ 7

D. 21÷7 = 4

Where 21÷7  is 3. Hence this is also not a correct answer.

E. 28÷7=4

7 * 4 = 28, which is correct equation.

Hence, Andrea could use 28÷7 = 4 this division problem to check her work.

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