If Kamina can do a job in 43 hours and Simon and Kamina working together can do the same job in 15 hours, find how
long it takes Simon to do the job alone.
hours
Answer:

(a) 1.25 dollars per apple

(b) Akia can buy 8 apples

(c) Christian can buy 4 apples

The corner store apples at a rate of $1.25 per apple.

Let c be the total cost of apples, n be the number of apples, and r be the ratio of the amount in dollars to the number of apples.

The formula rate is given as:

r = C/n

(a) So, the ratio of the amount in dollars to the number of apples will be:

r = c/n

r = $1.25 / 1 = 1.25 dollars/ apple

(b) Now, the number of apples that Akia can buy is:

r = c / n

n = c / r

n = [ $10 / ( 1.25 dollars/apple) ]

n = 8

(c) The number of apples that Christian can buy is:

n = c / r

n = 6 / 1.25

n = 4.8

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The complete question is mentioned below:

The corner store sells apples at a rate of 1.25 dollars per apple.

a. What is the ratio of the amount in dollars to the number of apples?

b. Akia is only able to spend $10 on apples. How many apples can she buy?

c. Christian has $6 in his wallet and wants to spend it on apples. How many apples can Christian buy?

we have that

the diameter is two times the radius

so

in this problem

D=2r

D=2(4)=8 cm

Answer:

3.999 millimeters.

Step-by-step explanation:

To find the height of the cylinder, we can use the formula for the volume of a cylinder:

V = πr²h

Given that the radius (r) of the cylinder is 4 millimeters and the volume (V) is 200.96 cubic millimeters, we can substitute these values into the formula and solve for the height (h).

200.96 = π(4²)h

200.96 = 16πh

To solve for h, we can divide both sides of the equation by 16π:

200.96 / (16π) = h

Using a calculator, we can calculate the approximate value of h:

h ≈ 200.96 / (16 × 3.14159)

h ≈ 3.999

Therefore, the height of the cylinder is approximately 3.999 millimeters.

Answer:

straight line = 180°

2x+3x+5x= 180 combine like terms

10x=180

x=18

Option A is correct. The value of function (f/g)(x) is found to be  \(\sqrt[3]{3x}\)/(3x+2) where the condition is that  x ≠  -2/3.

In mathematics, function composition is an operation in which two functions, f and g, form a new function, h, in such a way that h(x) = g(f(x)). This signifies that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.

The new function obtained by performing f first and then g is the combination of two functions g and f.

Given:

f(x) = \(\sqrt[3]{3x}\)

g(x) = 3x + 2

(f/g)(x) =  \(\sqrt[3]{3x}\)/(3x+2)

Also, the denominator should not be equal to 0.

So, 3x + 2 ≠ 0

     x ≠  -2/3

Therefore, the value of function  is found to be  \(\sqrt[3]{3x}\)/(3x+2) where the condition is that  x ≠  -2/3. So, Option A is correct

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Check the picture below.

\(\textit{Law of Sines} \\\\ \cfrac{a}{\sin(\measuredangle A)}=\cfrac{b}{\sin(\measuredangle B)}=\cfrac{c}{\sin(\measuredangle C)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{h}{\sin(157^o)}=\cfrac{240}{\sin(6^o)}\implies h\sin(6^o)=240\sin(157^o) \\\\\\ h=\cfrac{240\sin(157^o)}{\sin(6^o)}\implies h\approx 897.1~cm\)

Make sure your calculator is in Degree mode.

Answer:

Step-by-step explanation:

{15,16,17,18,19,20,21}

Step-by-step explanation:

Using rule of logs

log2  x^3     =   3 log2  x

Answer: The probability of rolling a 2 on a 6-sided die is 1/6.

Step-by-step explanation:

The probability of getting 2 on the die P(2) is 1/6.

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

Given, We roll a six-sided die,

So, Sample space N(S) = 1, 2, 3, 4, 5, 6 = 6.

N(2) = 1

∴ The probability of getting the number 2 when we throw a die is

P(2) = N(2)/N(S).

P(2) = 1/6.

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Answer:

n=5

Step-by-step explanation:

6 + 2n =16

2n÷2= 10÷2

n = 5

Answer: A

Explanation:

Answer:

A. (–4, –3)

Step-by-step explanation:

This is in case any one else had the answer on a different letter.

The model predicts the population to be 671,520 in 14 years

An exponential function is a mathematical function of the form \(R^{x}\) where x is a variable and R is a constant.

Exponential functions form exponential curves with decreasing or increasing slope depending on the magnitude of the variable x.

Population, P(t) = 480,000\(e^{-0.024t}\),

when t = 14

substitute t = 14 into the equation,

Population, P(t) = 480, 000\(e^{-0-024 x 14}\) = 480, 000 x 1.399 = 671,520

In conclusion, the Population of the model after 14 years is 671,520

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The percent of her monthly pay that goes to rent will be 20%.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

In this situation, Dimple gets paid $4,800 per month and then she pays $960 a month for rent.

The percent of her monthly pay that goes to rent will be:

= 960 / 4800 × 100

= 20%

The percentage is 20%.

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Answer:

1000 ft/min

Step-by-step explanation:

Rate of change in ft per min is 1000 ft per 1 minute from reading the graph

The value of x in this proposition would be the first option i.e. \(-13\frac{1}{4}\)

4/11= -33/x+5,

to get the value of x we need to get the x to the left hand side,

4(x+5)= -33,

4x+20 = -33.

subtracting 20 from both the sides,

4x= -33-20

4x = -53.

dividing both the sides by 4,

x= -53/4

x= \(-13\frac{1}{4}\) ,

which is option A in the given question

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Answer:

6.03, 4, 10.03

Step-by-step explanation:

The definition of an integer is an a whole number that's not a fraction. None of these numbers are fractions, therefore they are integers. The answer is all of them :)

A) The monthly payment (PMT) for the loan is $-244.13.

B) The total interest for the loan is $1,718.20 (rounded to the nearest cent).

To find the monthly payments (PMT) and the total interest for the loan, we use the formula for calculating the PMT for a loan with a fixed interest rate, known as the Amortizing Loan Payment Formula:

PMT = P × r × (1 + r)^n / ((1 + r)^n - 1)

Where:

PMT = Monthly payment

P = Principal amount (loan amount)

r = Monthly interest rate (annual interest rate divided by 12)

n = Number of months in the loan term

Given:

No of periods = 48

Principal amount (P) = $10,000

Annual interest rate = 8%

Loan term = 4 years

First, let's calculate the monthly interest rate (r):

r = Annual interest rate / 12 months

r = 8% / 12

r = 0.08 / 12

r = 0.00667 (rounded to 5 decimal places)

Next, we calculate the number of months in the loan term (n):

n = Loan term in years × 12 months/year

n = 4 years × 12

n = 48

Let's put the values into the formula to calculate the monthly payment (PMT):

PMT = $10,000 × 0.00667 × (1 + 0.00667)^48 / ((1 + 0.00667)^48 - 1)

PMT = $-244.13 (rounded to the nearest cent)

B) To calculate the total interest, we can multiply the monthly payment by the number of months in the loan term, and then subtract the principal amount:

Total interest = (PMT × n) - P

Total interest = ($157.08 × 48) - $10,000

Total interest = $1,718.20

Thus, the total interest for the loan is  $1,718.20 (rounded to the nearest cent).

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Answer:

none of this makes sense

Step-by-step explanation:

jim

Step-by-step explanation:

The actual base of the building is 1890 square feet.

A rectangle is a two-dimensional figure with length and width.

The area of a rectangle is Length x width.

We have,

1 inch = 15 feet

Rectangular base:

Length = 4.2 in

Width = 2 in

So,

4.2 in = 4.2 x 15 feet = 63 feet

2 in = 2 x 15 = 30 feet

Now,

The actual base of the building.

= 63 x 30

= 1890 square feet

Thus,

1890 square feet.

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Answer:

B

Step-by-step explanation:

The measure of arc ILR is 223 degrees

The sum of angle on a straight line is 180 degrees

Given the following parameter

∠ICR = (3x + 5)°, and

∠RCL = (x – 1)°.

Taking the sum:

3x + 5 + x - 1 = 180

4x + 4 = 180

4x = 176

x = 176/4

x = 44

arc ILR = 180 + arcRL
arc ILR = 180 + 44 - 1

arc ILR = 223 degrees

Hence the measure of arc ILR is 223 degrees

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The equation to calculate the yearly interest earned on your investment of $750 at a 16% interest rate is: Interest = $750 * 0.16.

To write the equation for calculating the yearly interest earned on an investment, we can use the formula:

Interest = Principal * Rate

Where:

- Principal is the initial investment amount.

- Rate is the interest rate expressed as a decimal.

In this case, you invested $750, and the annual interest rate is 16%. To use the decimal form of the interest rate, we divide it by 100:

Rate = 16% = 16/100 = 0.16

Substituting the values into the equation:

Interest = $750 * 0.16

To calculate the interest, we multiply the principal by the interest rate:

Interest = $750 * 0.16 = $120

Therefore, the equation to calculate the yearly interest earned on your investment of $750 at a 16% interest rate is:

Interest = $750 * 0.16

Now, let's complete a table to show the growth of your investment over multiple years. We'll assume the interest is compounded annually.

Year | Initial Investment | Interest Earned | Total Value

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

 1        $750                 $120              $870

 2        $870                 $139.20          $1009.20

 3        $1009.20            $161.47          $1170.67

 4        $1170.67            $187.31          $1357.98

 5        $1357.98            $217.28          $1575.26

In each year, we calculate the interest earned by multiplying the initial investment by the interest rate (16% or 0.16). The total value is obtained by adding the initial investment and the interest earned. This process is repeated for each subsequent year.

The table shows the growth of your investment over five years, demonstrating how the interest compounds and increases the total value each year.

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The difference between the actual quotient and the estimated quotient of 54,114 ÷ 29 is approximately 66.3448275862068965517241379.

To find the difference between the actual quotient and the estimated quotient of 54,114 ÷ 29, we need to first calculate the actual quotient and then the estimated quotient.

Actual quotient:

Dividing 54,114 by 29, we get:

54,114 ÷ 29 = 1,866.3448275862068965517241379 (approximated to 28 decimal places)

Estimated quotient:

Rounding the dividend, 54,114, to the nearest thousand gives us 54,000. Rounding the divisor, 29, to the nearest ten gives us 30. Now, we can perform the division with the rounded values:

54,000 ÷ 30 = 1,800

Difference between actual and estimated quotient:

Actual quotient - Estimated quotient = 1,866.3448275862068965517241379 - 1,800 = 66.3448275862068965517241379

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Answer:

C. The quotient is a rational number

Step-by-step explanation:

The qoutient of 4 and -36 would be ,  4/-36 = -1/9

-1/9 is not undefined

-1/9 is not an integer

-1/9 is not an irrational number

-1/9 is a rational number

The system of linear equations 3y = x + 6 and 6y - 2x = 12 has infinitely many solutions.

Given the system of euqation in the question;

We can solve this system of linear equations using the substitution method:

From the first equation, we can rewrite x in terms of y as:

x = 3y - 6

Substituting this expression for x in the second equation, we get:

6y - 2(3y - 6) = 12

Simplifying this equation, we get:

6y - 6y + 12 = 12

The equation simplifies to 12 = 12.

This means that the two equations are equivalent and represent the same line in the xy-plane.

The system has infinitely many solutions, and all points on the line satisfy both equations.

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The work done in pulling the stranded climber to safety is approximately 34,903.68 Joules.

The work done in raising the climber, harness, and cable to the top of the rock face can be calculated using the formula W = Fd, where W is the work done, F is the force applied, and d is the distance traveled.

Weight of climber, harness, and cable = (56 kg + 0.7 kg) x 9.8 m/s^2 = 554.36 N

So, the force applied to raise them is 554.36 N.

Therefore, the work done in raising the climber, harness, and cable to the top of the rock face is:

W = Fd = 554.36 N x 63 m = 34,903.68 J

So, the work done in pulling the stranded climber to safety is approximately 34,903.68 Joules.

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Finding the work done in pulling a stranded climber to safety. In an unfortunate accident, a rock climber finds herself stuck 17 m from the top of a 80 m rock face. Rescuers sent to help the climber lower a harness attached to a cable that will pull the climber to the top of the rock face. If the climber, secured in the harness, weighs 56 kg and the cable weighs 0.7kgm, how much work is done in raising the climber, harness, and cable to the top of the rock face? Note: the weight of the climber and cable is really a mass so you will need to multiply the mass in kg by the acceleration due to gravity (approximately 9.8ms2).