A manufacturer earned $55 per hour of labor when it opened. Each year the
manufacturer earns an additional 7% per hour. Write a function that gives the
amount A(t) that the plant earns per hour t years after it opens.
Write a exponential function

Answer:

\(3\)

Step-by-step explanation:

\(\mathrm{Let\ the\ age\ of\ Sophia\ be\ }x\mathrm{\ and\ age\ of\ Mohal\ be\ }x+2.\\\mathrm{Given,}\\\mathrm{Product\ of\ their\ ages = 15}\\\mathrm{or,\ }x(x+2)=15\\\mathrm{or,\ }x^2+2x=15\\\mathrm{or,\ }x^2+2x-15=0\\\mathrm{or,\ }x^2+5x-3x-15=0\\\mathrm{or,\ }x(x+5)-3(x+5)=0\\\mathrm{or,\ }(x+5)(x-3)=0\\\mathrm{i.e.}\ x=-5\ \mathrm{or}\ 3.\)

\(x=-5\ \mathrm{is\ disgarded\ because\ age\ cannot\ be\ negative.}\\\mathrm{So\ the\ age\ of\ Shopia,\ }x=3\)

Answer:

a. Length = 13 yards and Width = 21 yards.

b. Area of rectangle = 273 square yards.

Step-by-step explanation:

Let the length of the rectangular garden be L

Let the width of the rectangular garden be W

Given the following data;

Perimeter of garden = 68 yards

Translating the word problem into an algebraic equation, we have;

W = 2L - 5 ......equation 1

Note: The formula for calculating the perimeter of a rectangle is;

\(P = 2L + 2W\)

68 = 2L + 2W ........equation 2

Substituting eqn 1 into eqn 2;

68 = 2L + 2(2L - 5)

68 = 2L + 4L - 10

68 = 6L - 10

6L = 68 + 10

6L = 78

L = 78/6

L = 13 yards

To find the width;

W = 2L - 5

W = 2(13) - 5

W = 26 - 5

W = 21 yards.

b. To find the area of the garden;

Area of rectangle = length * width

Area of rectangle = 13 * 21

Area of rectangle = 273 square yards.

The positions will be filled in 56,280 ways

There are 11 qualified candidates applying for 7 positions. The order of the positions does not matter. after choosing a position the number of persons drop so we solve as follows

For the position of president

11 combination 1 = 11

For the position of secretary

10 combination 1 = 10

For the position of treasurer

10 combination 1 = 10

For the position of three directors

8 combination 3 = 56 ways

the total number of ways to fill these positions is

11 x 10 x 9 x 56 = 56,280.

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Answer:

4 1/2 minutes

Step-by-step explanation:

.

The probability that an employee posted to country A at age 30 will survive to age 40 if she remains in that country is 2 x 10⁻⁶³

Probability is a mathematical concept that describes the likelihood of a specific event occurring within a set of possible outcomes

Let's start by defining some terms. The force of mortality, also known as the death rate, is the number of deaths per unit time per unit of population.

The probability of survival is the chance that an individual will live past a certain age. In our case, we want to know the probability of surviving from age 30 to age 40 while living in country A.

To calculate the probability of survival, we will use the formula:

\(P(x) = e^{-qx}\)

Where P(x) is the probability of survival at age x and qx is the force of mortality at age x.

First, we will calculate the force of mortality for the first five years after arrival in country A using the equation given in the question:

90x+1 = (6 - 1)9x+1

For x = 30, we have:

90(30) + 1 = (6 - 1)9(30) + 1

2701 = 5 * 891 + 1

2701 = 4445 + 1

2700 = 4445

So, q30 = 4445/30 = 148.5

Next, we will use this value to calculate the probability of survival for the first five years in country A:

\(P30 = e^{-q3} = e^{-148.5} = 1.2 \times 10^{-64}\)

Since the force of mortality for those who have lived in country A for at least five years is 50% greater than the US Life Tables, 2002, Females, we can calculate the force of mortality for the next 10 years as follows:

qx = 1.5 x qx from US Life Tables

Using the values from Table 3.11, we have:

q31 = 1.5 x 98,424 = 147,636

q32 = 1.5 x 98,362 = 147,543

q33 = 1.5 x 98,296 = 147,444

q34 = 1.5 x 98,225 = 147,338

q35 = 1.5 x 98,148 = 147,222

q40 = 1.5 x 97,500 = 146,250

Finally, we can use these values to calculate the probability of survival from age 31 to age 40:

\(P31 = e^{-q31} = e^{-147,636} = 1.3 \times 10^{-65}\\ \\P32 = e^{-q32} = e^{-147,543} = 1.4 \times 10^{-66}\\\\P33 = e^{-q33} = e^{-147,444} = 1.5 \times 10^{-67}\\\\P34 = e^{-q34} = e^{-147,338} = 1.6 \times 10^{-68}\\\\P35 = e^{-q35} = e^{-147,222} = 1.7 \times 10^{-69}\\\\P40 = e^{-q40} = e^{-146,250} = 2.0 \times 10^{-63)}\\\\\)

Complete Question:

When posted overseas to country A at age x, the employees of a large company are subject to a force of mortality such that, at exact duration t years after arrival overseas (t = 0,1,2,3,4), 90x+1 = (6 - 1)9x+1 where qx+t is on the basis of US Life Tables, 2002, Females. For those who have lived in country A for at least five years the force of mortality at each age is 50% greater than that of US Life Tables, 2002, Females, at the same age. Some lx values for this table are shown in Table 3.11.

An extract from the United States Life Tables, 2002,

Females. Age,

x 30 31 32 33 34 35 40

1x 98,424 98,362 98,296 98,225 98,148 98,064  97,500

Calculate the probability that an employee posted to country A at age 30 will survive to age 40 if she remains in that country.

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Answer:

B

Step-by-step explanation:

They are all true. However there is no all of the above option and the only answer that is correct and not flat out given to you I think it's that one.

Answer:

Garden y median =6, garden z median =3

Answer: Look at the explanation please

Step-by-step explanation:

Garden Y has the median of 6 inches

Garden Z has the median of 4 inches

A comparative inference about thre two gardens would look like something like this

The flowers in Garnden Y generally grow taller than the flowers that are in Garden Z

Hopes this helps :)

Answer:

yes the is enough imformation because of the tick marks

Step-by-step explanation:

Triangle 1. Angle-Side-Angle (ASA) Congruence

Triangle 2. Side-Angle-Side (SAS) Congruence

Triangle 3. Angle-Side-Angle (ASA) Congruence / Side-Angle-Side (SAS) Congruence

As per the given confidence interval, the given statement "in forming a 95% confidence interval for a population mean from a sample size of 20, we can proceed with large sample inference" is false.

Confidence interval,

in probability , confidence interval refers the probability that a population parameter will fall between a set of values for a certain proportion of times.

Given,

in forming a 95% confidence interval for a population mean from a sample size of 20, we can proceed with large sample inference.

Here we need to find the given statement is true or false.

While we looking into the given question, we have identified that the value of

Confidence interval = 95%

Sample size = 20

Then the sample inference is calculated as, if we were to take 20 different samples and compute a 95% confidence interval for each sample, then approximately 95 of the 100 confidence intervals will contain the true mean value (μ).

Therefore, the statement is in correct.

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From the circle the value of angle x is 90 degrees

We have to find the value of x

The radius of the circle is 18.5

As we observe the figure the angle x is opposite to the 90 degrees

The angle x and angle 90 degrees are vertical angles

We know that the vertical angles are equal or same

∠x = 90 degrees

Hence, the value of angle x is 90 degrees from the circle

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Answer:

x = 3 + √(22/3) and x = 3 - √(22/3).

Step-by-step explanation:

Step 1: Divide both sides by the coefficient of x^2 to get the coefficient of x^2 equal to 1.

3x^2 - 18x + 5 = 0

x^2 - 6x + 5/3 = 0

Step 2: Move the constant term to the right-hand side of the equation.

x^2 - 6x = -5/3

Step 3: Take half of the coefficient of x, square it, and add it to both sides of the equation.

x^2 - 6x + 9 = -5/3 + 9

(x - 3)^2 = 22/3

Step 4: Solve for x by taking the square root of both sides of the equation.

x - 3 = ±√(22/3)

x = 3 ± √(22/3)

Answer:

Its A

Step-by-step explanation:

Soure: Trust me bro

Answer:

D

Step-by-step explanation:

line (7,-3)  yes

slope-2  yes

can be rewritten as y=-2x+ 11yes

line (-7, 3) NO

Answer: $3004166.02

Step-by-step explanation: Alrighty then so first we need a formula to solve which is A=Pe^rt which is the compounded continously formula you can find online or a textbook. The formula you should use a calculator to solve is $1,000,000e^0.055(20)= $3,004,166.024

Answer:

y=-5x+6

Step-by-step explanation:

Answer: 3cups

Step-by-step explanation:

List all of the solutions.

3cups = 48 = y = cups = x =

Answer:

3cups

Step-by-step explanation:

Answer:

So, 100 fish taken from Lake A would have a mean length of 50 cm and 100 fish taken from Lake B would have a mean length of 140 cm

Step-by-step explanation:

1 fish from Lake A would be 0.5 cm long you calculate that by dividing 70 from 35 and you calculate the fish from Lake B by dividing 30 from 42 which would be 1.4 cm, (english is not my first language so I hope you understood everything :D)

The values of

1. cosθ = √3/2

2. sinθ = √3/2

3. tanθ = 1

4. sec θ = 2/√3

5. cosec θ = 2/√3

6. cot θ = 1

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

cosθ = adj/hyp

sinθ = opp/hyp

tanθ = opp/adj

sec θ = 1/cosθ

cosec θ = 1/sinθ

cot θ = 1/tanθ

We need to find the hypotenuse of the triangle

x² = 3² +3²

x = √9+9

x = √18

x = 2√3

cosθ = 3/2√3 = 6√3/12

= √3/2

2. sinθ = 3/2√3 = √3/2

3. tanθ = 3/3 = 1

4. sec θ = 2/√3

5. cosec θ = 2/√3

6. cot θ = 1

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Answer:

The equation is

y=0.5x+2

Answer:

simelier means the same except diffrent size the only one that doesn't fit that is

b B only

Hope This Helps!!!

Answer:

x = -10

Step-by-step explanation:

(x - 3) - 2(x + 6) = -5

Distribute

x-3 -2x-12 = -5

Combine like terms

-x -15 = -5

Add 15 to each side

-x-15+15 = -5+15

-x=10

Multiply each side by -1

x= -10

Answer:

c

Step-by-step explanation:

HCF/GCF 32 and 48

listing factor

32: 1, 2, 4, 8, 16, 32

48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

HCF: 16

prime factorization

32: 2 x 2⁴

48: 3 x 2⁴

HCF: 2⁴ = 16

.65 * 120 = 6.5 * 12 = 65 * 1.2 = 65 + 13 = 78 students ate pizza

double check

78 / 120 = 0.65

please give brainliest

The equation of the exponential graph shown over the x-y coordinate is y=100.(1/2)x.

The equation of the exponential graph represent the exponential function with the initial value and common ratio.The equation of the exponential graph is given as,

\(y=ab^x\)

Here, (a) is the initial value and (b) is the common ratio.

In the graph given in the problem, the initial value is 100 where the value of x is zero, such as,

\(x=0; y=100\)

Put these values in the above equation.

\(100=ab^0\\100=a\times1\\100=a\)

Now, when the value of x is 2 in the graph, the value of y is 25. Put these values again in the equation.

\(25=(100)b^2\\b=\sqrt{\dfrac{25}{100}}\\b=\sqrt{\dfrac{1}{4}}\\b=\dfrac{1}{2}\)

The value of b is 2 and a is 100. Thus, the equation of the exponential graph shown over the x-y coordinate is y=100.(1/2)x.

\(y=100\times(\dfrac{1}{2})^x\)

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Using the inequality rule we know that 11 is greater than -11, (11 > -11).

Mathematical expressions with inequalities are those in which the two sides are not equal.

Contrary to equations, we compare two values in inequality.

Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Two expressions in inequality aren't always equal, which is denoted by the symbols >, <, ≤, or ≥.

So, let's say the inequality equation looks like this: A

Right now, A is valued at

Let p be used to representing the initial number.

P equals 11, so

Let q be used to representing the second number.

Q has a value of -11.

-11 and 11 are both numbers that are greater than zero.

Then, 11 > -11 ... (1)

A has a value of 11 > -11.

Therefore, using the inequality rule we know that 11 is greater than -11, (11 > -11).

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Correct question:
Is 11 greater than, equal to, or less than -11?

Answer:

85

Step-by-step explanation:

255 ÷ 3 = 85

85×2= 170 This is how much student tickets were sold.

255 - 170= 85

85 adult tickets were sold.

Answer:

Hi there!

Your answer is:

The smaller integer is -6

The larger integer is -5

Step-by-step explanation:

Two consecutive integers:

x, x+1

Product= multiply

(x) × (x+1) = x^2 - 6

x^2 + x= x^2 -6

-x^2

x= -6

Plug back in

First integer (smaller):

-6

Second integer (larger):

-6+1

-5

Check your work!

(-6) × (-6+1)

(-6)× (-5)

30 = (-6)^2 -6

30 = 36-6

30= 30 ✓✓✓✓

That's how we determine that this is the correct answer

Hopefully this helps

The two consecutive integers whose product is 6 less than the square of the smaller number integers are \(-6\) and \(-5\).

Let the two consecutive integers be \(x\) and \(x+1\\\) respectively.

Given, the product of both the integers is 6 less than the square of the smaller number.

So we can write it in equation form as, \(x\times (x+1)+6= x^{2}\)

On solving ,\(x^{2} +x+6=x^{2}\)

Further,\(x+6=x^{2} -x^{2}\)

Or,\(x+6=0\\x=-6\)

Now the other integer be  \(-6+1\) or \(-5\).

Hence the two consecutive integers are \(-6\) and \(-5\).

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Answer:

22

Step-by-step explanation:

Answer:

probs D

Step-by-step explanation:

i got A but im really thinking D hmm

Answer:

827.5 I guess is the answer

Answer:

6 827.472 8.27471 × 102

5 827.47 8.2747 × 102

4 827.5 8.275 × 102

3 827 8.27 × 102

2 830 8.3 × 102

1 800 8 × 102

827.4715

Sig Figs

7

Decimals

4

Scientific Notation

8.274715 × 102

Words

eight hundred twenty-seven point four seven one five

Answer:

27.5

Step-by-step explanation:

To find the mean you basically just add all of the numbers then divide by how many there are.

So, for this problem, 19+22+24+45=110

110/4=27.5

Hope this helped!!

Answer:

a- Vernon practiced soccer 5  3/4hours this week. He practiced 4  1/3hours on weekdays and the rest over the weekend.

Step-by-step explanation:

Hope this helps