At the beginning of the year, Kaylee had $60 in savings and saved an additional $12 each week thereafter. Jack started the year with $95 and saved $5 every week. Let K represent the amount of money Kaylee has saved t weeks after the beginning of the year and let J represent the amount of money Jack has saved t weeks after the beginning of the year. Write an equation for each situation, in terms of t, and determine the number of weeks after the beginning of the year until Kaylee and Jack have the same amount of money saved.

Answer:

The answer can be 1 2/5.

Step-by-step explanation:

5/5 is a whole. That two extra 1/5ths, turn into 2/5ths.

The next three terms are -2.56, -1.024 and -0.4096

The definition of the function is given as

Sequence -100, -40, -16, -6.4

The above definitions imply that we simply multiply 0.4 to the previous term to get the current term

Using the above as a guide,

so, we have the following representation

Next term = -6.4 * 0.4 = -2.56

Next term = -2.56 * 0.4 = -1.024

Next term = -1.024 * 0.4 = -0.4096

This means tat the next three terms are -2.56, -1.024 and -0.4096

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Answer:

9/70

Step-by-step explanation:

Given that:

70 students choose to attend one of three after school activities: football, tennis or running.

There are 30 boys. 13 students choose football, of which 9 are girls. 31 students choose tennis. 9 girls choose running.

A student is selected at random.

What is the probability this student chose running?

Since it asking for the probability of this student (randomly select) chose running. And we can see that there are 9 girls choose running.

Therefore, we also know 70 students is the total

Hence, the answer is 9/70

9/70 is in simplest form already.

~lenvy~

Answer:

9/70

Step-by-step explanation:

Important info:

Solution:

Probability of this student (randomly select) chose running. And we can see that there are 9 girls choose running.

Thus, 70 students is the total

Therefore, the answer is 9/70

9/70 can't be simplify.

[RevyBreeze]

The radius of the base of the cone is 40cm

First, we need to determine the area of the sector

The formula for the area of a sector is expressed as;

Area = 144/360 ×3.14 × 10²

Find the values and substitute

Area = 0. 4 × 314

Multiply the values

Area= 125. 6 cm²

Divide the base area by pie to determine the radius, we have;

Base radius = 125.6/3.14

Divide the values, we get;

Base radius = 40cm

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Answer:

5/6, 0.83 or 83%

Step-by-step explanation:

Answer:

Probabilities

Decimal: \(0.91\)

Fraction: \(\frac{91}{100}\)

Percentage: \(91\)%

Step-by-step explanation:

Writing out information

2 comedy CDs

3 science-fiction CDs

7 adventure CDs

10 random CDs

22 total CDs

The chosen CD is not a comedy.

Solving probability for each

Decimals rounded to nearest 100th

Comedy:

\(2:22\\0.09\\\frac{2}{22}\)

Science-fiction:

\(3:22\\0.14\\\frac{3}{22}\)

Adventure:

\(7:22\\0.32\\\frac{7}{22}\)

Random:

\(10:22\\0.45\\\frac{10}{22}\)

Finding the total of the non-comedy

\(0.14+0.32+0.45=0.91\)

\(0.91=91\)%

Conclusion

Probabilities

Decimal: \(0.91\)

Fraction: \(\frac{91}{100}\)

Percentage: \(91\)%

To find the combined rate of all the individuals working together, you must add the individual rates.

When calculating the combined rate of individuals working together, you need to add up the individual rates. Each worker contributes their own rate of work or productivity, and by adding these rates together, you can determine the combined rate at which they are working collectively.

This allows you to assess the overall efficiency and output of the team or group. By summing up the individual rates, we have better understanding of the overall productivity and performance of the group.

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Answer:

6/8

Step-by-step explanation:

Multiply both the denominator and numerator by 2.

Answer:

To calculate how much you would have to deposit today to accumulate the same amount of money that $75 monthly payments at a rate of 3.5% compounding monthly for 10 years in an annuity would earn, we can use the formula for the present value of an annuity due:

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

where:

- PV is the present value of the annuity due (the amount you would have to deposit today)

- PMT is the monthly payment ($75)

- r is the annual interest rate (3.5%)

- n is the number of times interest is compounded per year (12 for monthly compounding)

- t is the number of years (10)

PV = 75 × ((1 - (1 + 0.035/12)^(-12×10)) / (0.035/12)) × (1 + 0.035/12) = **$7,360.47**

Therefore, you would have to deposit **$7,360.47** today to accumulate the same amount of money that $75 monthly payments at a rate of 3.5% compounding monthly for 10 years in an annuity would earn.

Answer:

Step-by-step explanation:

Answer: 5 yards

Step-by-step explanation:

1. Look at the vertical parts of the drawing from right to left

2. Notice that the longest vertical part is 11 yards

3. Notice that the other labels vertical part is 6 yards

4. Notice that the third vertical part, the one with the ? is 11 yds - 6 yds since the two shorter vertical parts would make a line as long as the longest vertical part of they were put together. Since this is the case the missing part is 11 yds-6 yds = 5 yds.

Answer:

\(g(x) = -x^2 + 3\)

Step-by-step explanation:

Given

\(f(x) = x^2\)

Required

Determine g(x)

First, shift f(x) down by 3 units

The rule is:

\(f'(x) = f(x) - 3\)

So:

\(f'(x) = x^2 - 3\)

Next, reflect f'(x) across the x-axis to get g(x)

The rule is:

\(g(x) = -f(x)\)

So, we have:

\(g(x) = -(x^2 - 3)\)

Open bracket

\(g(x) = -x^2 + 3\)

Answer:

D

Step-by-step explanation:

I figured out the hard way

There are 9444 men and 24555 females are present.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

Total students = 34000

For every 5 male students there are 13 female students.

So, the number men are

= 5/18 x 34000

= 9444

and, number of women

= 13/ 18 x 34000

= 24, 555.

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The question attached here is in other language whose translation is given below.

In a school for every 5 male students there are 13 female students. If the total number of students is 34,000, how many men and women are there?

Step-by-step explanation:

70 to 85 % of his maximum

Maximum is estimated to be 220 - age  = 220 - 42 = 178

70% of this is 125

85 % is 89  151  

I believe I would go with the third choice  116-160 bpm

=48

Multiply by 1

Add 1 1 11 11

to both sides of the equation

Answer:

The answer is 48

Step-by-step explanation:

First, add 11 to both sides

5 + 11 = 16

1/3x = 16

Next, times 16 by 3

16 times 3 = 48

Check!

1/3(48) = 16

16 - 11 = 5

X = 48

The measure of ∠1 is 41°, ∠2 is 27° and ∠3 is 63°.

Same-side exterior angles are two external angles to the parallel lines that are on the same side of the transverse line. According to the theorem, same-side exterior angles are supplementary, which means they add up to 180 degrees.

⇒∠1 + ∠2 + 22°+90° =180°

⇒∠1 + ∠2 = 180° - 112° = 68°

⇒∠1 + ∠2 = 68°

Similarly,

⇒∠3 =180°-117°=63°

⇒63°+ 90°+∠2 = 180°

⇒153°+∠2 = 180°

⇒∠2 =180°-153° =27°

⇒∠1 = 68°-27°= 41°       (since ∠1 + ∠2 = 68°)

Hence, the measure of ∠1 is 41°, ∠2 is 27° and ∠3 is 63°.

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Answer:

True

Step-by-step explanation:

It doesn't cross over one point more than once

Answer:

if i am not wrong is 119

Step-by-step explanation:

I did it like this:

I took 44 + 17= 61

And then I took 180-61= 119

Each of the five friends needs to pay £14.40 to cover the cost of the birthday person's meal.

To calculate how much each of the five friends needs to pay, we can use the concept of averages or mean.

The total cost of the meal for 6 people is £12 per person. This means that the total cost of the meal is 6 * £12 = £72.

Since the other five friends have decided to pay for the birthday person's meal, they will evenly divide the total cost of £72 among themselves.

To find the average amount each friend needs to pay, we divide the total cost by the number of friends paying, which is 5:

£72 / 5 = £14.40

Using the concept of averaging or finding the mean allows us to distribute the cost equally among the friends, ensuring fairness in sharing the expenses.

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Answer:

5/3 or 3/5

Step-by-step explanation:

If there were 5 brown desk, it will be:

4,12,36,108,304

If there were 6 white desk, it will be:

5,10,15,20,25,30

Putting them it fraction: brown/white:

5/3

If putting them in this fraction: white/brown:

3/5

Answer:

12.87  12.1  12.07  12.07

Step-by-step explanation:

Answer:

-72x - 53y + 287 = 0.

Step-by-step explanation:

To find the equation of the image of the circle, we need to reflect each point on the circle in the given line mirror.

The line mirror equation is given as 4x + 7y + 13 = 0.

The reflection of a point (x, y) in the line mirror can be found using the formula:

x' = (x - 2Ay - 2B(Ax + By + C)) / (A^2 + B^2)

y' = (y - 2Bx + 2A(Ax + By + C)) / (A^2 + B^2)

where A, B, and C are the coefficients of the line mirror equation.

For the given line mirror equation 4x + 7y + 13 = 0, we have A = 4, B = 7, and C = 13.

Now, let's find the equations of the image of the circle.

The original circle equation is x² + y² + 16x - 24y + 183 = 0.

Using the reflection formulas, we substitute the values of x and y in the circle equation to find x' and y':

x' = (x - 2Ay - 2B(Ax + By + C)) / (A^2 + B^2)

= (x - 2(4)y - 2(7)(4x + 7y + 13)) / (4^2 + 7^2)

= (x - 8y - 8(4x + 7y + 13)) / 65

= (x - 8y - 32x - 56y - 104) / 65

= (-31x - 64y - 104) / 65

y' = (y - 2Bx + 2A(Ax + By + C)) / (A^2 + B^2)

= (y - 2(7)x + 2(4)(Ax + By + C)) / (4^2 + 7^2)

= (y - 14x + 8(Ax + By + C)) / 65

= (y - 14x + 8(4x + 7y + 13)) / 65

= (57x + 35y + 104) / 65

Therefore, the equation of the image of the circle is:

(-31x - 64y - 104) / 65 + (-57x + 35y + 104) / 65 + 16x - 24y + 183 = 0

Simplifying the equation, we get:

-31x - 64y - 57x + 35y + 16x - 24y + 183 + 104 = 0

-72x - 53y + 287 = 0

So, the equation of the image of the circle is -72x - 53y + 287 = 0.

The radius of circle M is equal to 3.99 cm.

In Mathematics and Geometry, the area of a sector can be calculated by using the following formula:

Area of sector = θπr²/360

Where:

By substituting the given parameters into the area of a sector formula, we have the following;

Area of sector = θπr²/360

12.36 = 89(3.142/360) × r²

12.36 = 0.7768r²

Radius, r = √15.9114

Radius, r = 3.99 cm.

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The system of equations has infinitely many solutions.

What is a system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

Here, we have

Given:

-2x - 3y + z = 7

-x - y + 3z = -10

-2x - y - z = 13

We have to how many solutions the system of equations has.

Arranging the above equations in form of a matrix and finding the determinant, we get,

Δ = \(\left|\begin{array}{ccc}-2&-3&1\\-1&-1&3\\-2&-1&-1\end{array}\right|\)

= -2(1+3) +3(1+6) +1(1-2)

= - 4 + 21 -1 = 16

Δ₁ = \(\left|\begin{array}{ccc}7&-3&1\\-10&-1&3\\13&-1&-1\end{array}\right|\)

= 7(1+4) +3(10-39) +1(10+13)

= 35 - 87 + 23

= -29

Hence, the system of equations has infinitely many solutions.

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Answer:

Step-by-step explanation:

from the figure and the measurements it is a square, the diagonals are perpendicular and form 4 angles of 90°, so 90° is your answer.