What is the equation in slope-intercept form for the line that passes through the points (–1, 3) and (–2, –3)?

Given:

Karen earns $54.60 for working 6 hours.

Amount she earns varies directly with the  number of hours she works.

She need to work to earn an  additional $260.

To find:

Number of hours she need to work to earn an  additional $260.

Solution:

Let the amount of earnings be A and number of hours be t.

According to question,

\(A\propto t\)

\(A=kt\)     ...(i)

where, k is constant of proportionality.

Karen earns $54.60 for working 6 hours.

\(54.60=k(6)\)

Divide both sides by 6.

\(\dfrac{54.60}{6}=k\)

\(9.1=k\)

Put k=9.1 in (i).

\(A=9.1t\)

Substitute A=260 in the above equation.

\(260=9.1t\)

Divide both sides by 9.1.

\(\dfrac{260}{9.1}=t\)

\(28.5714=t\)

\(t\approx 29\)

Therefore, she need to work extra about 29 hours to earn an  additional $260.

Answer:

- 23

Step-by-step explanation:

When you see a negative number behind a minus sign, turn the minus sign into a plus sign. It's the easiest way to figure out how to solve those types of problems.

Answer:

-23

Step-by-step explanation:

-35-(-12) = -35+12 = -23

Answer:

m = -3 ; c = 1

Step-by-step explanation:

y = -3x + 1

y = mx + c

m = -3

c = 1

The length of the fence must be 618cm

The volume that it can hold is 1,909,620 cm³

First, the fence is just equal to the circumference of the cylinder, remember that the circumfernce of a circle of diameter D is:

C = П*D

Here we use П = 3, then:

C = П*206cm

C = 3*206cm = 618cm

Now the volume, for a cylinder of diameter D and height H, the volume is:

V = П*(D/2)²*H

Replacing the values that we know we will get:

V = 3*(206cm/2)²*60cm = 1,909,620 cm³

Learn more about cylinders at:

https://brainly.com/question/9554871

#SPJ1

Answer:

1 million

Step-by-step explanation:

Start counting at position 0, the rightmost position has value 10⁰ = 1

The one left to that 10¹ = 10

... and so forth ...

The 6th position has value 10⁶ = 1000000, a.k.a. one million.

The place value of 3 in 553 049 270 is 1 million.

Here the number is given as 553 049 270.

We have to find the place value of 3 in given number.

What is Place value?

Place value is describe the position or place of a digit in a number.

Now,

To find the place value of 3;

Start counting at position 0, the rightmost position has value \(10^{0}= 1\)

The position of 7, one left to 0, has value \(10^{1} = 10\)

------ and so on.

Now, position of 3 is 6th position has value \(10^{6} = 1000000\)

So, The place value of 3 in 553 049 270 is 1 million.

Learn more about Place value visit:

https://brainly.in/question/16613482

#SPJ6

If the numbers of subsets of {1, 2, 3, 4, 5, 6, 7, 8, 9} that are subsets of neither {1, 2, 3, 4, 5} nor {4, 5, 6, 7, 8, 9} is K, then the sum of digits of K is 9

Let the sets be

A =  {1, 2, 3, 4, 5, 6, 7, 8, 9}

B = {1, 2, 3, 4, 5}

C = {4, 5, 6, 7, 8, 9}

Then

B ∩ C = {4, 5}

Subsets of B ∩ C = {4}, {5}, {4,5}, {}

If we exclude the null set then the subsets remaining will be {4}, {5}, {4,5}

No. of elements in A = 9

No. of subsets of A = \(2^9\)

No. of elements in B = 5

No. of subsets of B = \(2^5\)

No. of elements in C = 6

No. of subsets of C = \(2^6\)

If we subtract the no. of subsets of B and C from the no. of subsets of A we get the no. of subsets of A that are not the subsets of B or C

But the null set will be subtracted twice

Also as the subsets of B ∩ C excluding null set will be subtracted twice

Therefore, total number of subsets of A not the subsets of B or C

\(k=2^9-2^5-2^6+1\\k=512-32-64-2\\\\k=414\)

The sum of the digits of k=9

The complete question is-

If the numbers of subsets of {1, 2, 3, 4, 5, 6, 7, 8, 9} that are subsets of neither {1, 2, 3, 4, 5} nor {4, 5, 6, 7, 8, 9} is K, then find the sum of digits of K.

learn more about sets,

https://brainly.com/question/8053622

#SPJ4

The degree of the polynomial is 14

The polynomial is given as:

y^2+7x^14-10x^2

Here, we assume that the variable of the polynomial is x

The highest power of x in the polynomial y^2+7x^14-10x^2 is 14

Hence, the degree of the polynomial is 14

Read more about polynomial at

https://brainly.com/question/4142886

#SPJ1

The value of the bond is multiplied by the factor \((1 + 0.04)\), which is the same as multiplying by 1.04. After t years, the value of the bond will be multiplied by this factor t times, giving the formula:

\(100(1.04)t\).

So, the value of the bond after t years is given by 100 • 1.04t.

A factor in mathematics is an expression or number that divides another expression or number without producing a residue. In other terms, a factor is a unit of measurement that may be multiplied by another unit of measurement to yield a specific outcome.

For example, 2 and 3 are factors of 6, because 2 multiplied by 3 equals 6. Similarly, (x + 1) and (x - 3) are factors of the expression \(x^2 - 2x - 3\), because when these factors are multiplied together, they produce the expression:

\((x + 1) \times (x - 3) = x^2 - 2x - 3\)

The bond is worth $100 initially, and it grows in value by 4% each year. This means that after one year, the value of the bond will be:

\(100 + 0.04(100) = 100(1 + 0.04) = 100(1.04)\)

In other words, the value of the bond after one year is the initial value (100) multiplied by a factor of 1.04.

Similarly, after two years, the value of the bond will be:

\(100(1.04) + 0.04(100)(1.04) = 100(1.04)^2\)

After three years, the value of the bond will be:

\(100(1.04)^2 + 0.04(100)(1.04)^2 = 100(1.04)^3\)

In general, after t years, the value of the bond will be:

\(100(1.04)t\)

To know more about factor, visit:

https://brainly.com/question/25829061

Answer:

x=-1

Step-by-step explanation:

4x+35x-15=9x-45
39x-15=9x-45
39x-9x=-45+15
30=+-30
x=-1

Answer:

\( \sf \: x = - 1\)

Step-by-step explanation:

Given equation,

→ 4x + 5(7x - 3) = 9(x - 5)

Now the value of x will be,

→ 4x + 5(7x - 3) = 9(x - 5)

→ 4x + 35x - 15 = 9x - 45

→ 39x - 15 = 9x - 45

→ 39x - 9x = -45 + 15

→ 30x = -30

→ x = -30 ÷ 30

→ [ x = -1 ]

Hence, the value of x is -1.

why are there two of these?
Answer:

53.9

Step-by-step explanation:

89% of all houses have garages and 48% have garages and pools. We try to find houses with a pool that have a garage. Let's assume that there are 100 houses in her neighborhood. then 89 of them have garages and 48 of them have garages and pools. 48 / 89 = about 0.5393. Conver this to percent and we get 53.9

Answer:

...........................................................

Step-by-step explanation:

Answer:

0.1662 = 16.62% probability that exactly 2 will stay with the same company for more than five years

Step-by-step explanation:

For each graduate, there are only two possible outcomes. Either they stay for the same company for more than five years, or they do not. Graduates are independent. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

Eight percent of all college graduates hired by companies stay with the same company for more than five years.

This means that \(p = 0.08\)

Sample of 11 college graduates:

This means that \(n = 11\)

The probability, rounded to four decimal places, that in a random sample of 11 such college graduates hired recently by companies, exactly 2 will stay with the same company for more than five years is: the absolute tolerance is +-0.0001

The tolerance means that the answer is rounded to four decimal places.

The probability is P(X = 2). So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 2) = C_{11,2}.(0.08)^{2}.(0.92)^{11} = 0.1662\)

0.1662 = 16.62% probability that exactly 2 will stay with the same company for more than five years

Answer:

\(\huge\boxed{Option \ 1}\)

Step-by-step explanation:

Since, AE = CE and BE = DE , then E is the midpoint of AC and BD. Causius can use that to show that AC and BD bisect each other which means that they both are the diagonals of a parallelogram bisecting each other. Hence, It will be proved that ABCD is a || gm.

Hope this helped!

The probabilities are given as follows:

3. P(rides bus|owns a car) = 1/3.

4. P(red|organic) = 3/5.

The probability of an event in an experiment is obtained as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.

For item 3, the outcomes are given as follows:

Hence the probability is:

P(rides bus|owns a car) = 8/24 = 1/3.

For item 4, the outcomes are given as follows:

The error was in identifying the total outcomes, and the probability is:

P(red|organic) = 18/30 = 3/5.

More can be learned about probabilities at https://brainly.com/question/14398287

#SPJ1

Answer:

Step-by-step explanation:

c 0,4 .01

\( - 5x + 2 = 10 - 9x \\ 10 + 2 = 9x + 5x \\ 12 = 15x \\ x = \frac{15}{12} = \frac{5}{4} \)

Answer: If you are solving for x then the answer would be x=2

Step-by-step explanation:

-5x+2-2=10-9x-2

-5x=-9x+8 - Add 9x to both sides of the equation

4x=8 Then Divide Both sides of the equation by 4

8/4= 2

Answer:look below

Step-by-step explanation:

4=24

6=36

8=48

10=60

Answer:

42 - 3 = 39 Is greater than 7 is

Hope this helps, even tho that's not 50 points, but i'm cool with it, I hope you get it correct

Step-by-step explanation:

Answer:

Step-by-step explanation:

5 * 2^2*5 + 2^4

5^2*2^2+2^4

answer is B

Graph A and graph D represents quadratic function and linear function respectively.

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.

In the given figure,

In option A graph parabola represents the quadratic function.

In option B graph doe's not represents the function.

In option C graph doe's not represents the function.

In option D graph straight line represents the linear function.

Therefore, option A and option D are the correct answers.

To learn more about the graph visit:

brainly.com/question/14375099.

#SPJ1

Step-by-step explanation:

n = 52

x bar = 122.31

standard deviation sd = 38.75

1. the hypothesis:

null hypothesis

h0: μ ≤ 35

alternative hypothesis

h1: μ > 35

2.

we have been given the sd of the sample but not that of the population. so what we are supposed to use here is the t test and not the z test. the following conditions have to be met.

3.

= \(\frac{122.31-35}{38.75/\sqrt{52} }\)

= 87.31/5.37

= 16.26

using the T distribution function in excel, the p value was calculated and found to be approximately equal to 0.

TDIST(16.26, 51, 1)

since p value is very small we reject the null and accept the alternate hypothesis.

4. from the result above the answer to this question is yes

(a) The probability that the top card is an ace or a king is \($\frac{2}{13}\)

(b) The probability that the top card is spades and the second card is clubs is \($\frac{1}{2652}\)

(c) The probability that the top card is spades and the second card is an ace is \($ \frac{1}{663}\)

(d) The probability that the top 3 cards are all spades is \($\frac{1}{132600}\)

(e) The probability that the top 4 cards include 3 different ranks, with one rank appears twice is \($\frac{2}{925}\)

As per the data given:

A standard deck of 52 cards has 13 ranks (ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king) and 4 suits (spades, hearts, diamonds, and clubs), such that there is exactly one card for any given rank and suit.

a) The probability that the top card is an ace or a king:

The probability that the top card is an ace \($\frac{4}{52} = \frac{1}{13}\)

The probability that the top card is an king \($\frac{4}{52}=\frac{1}{13}\)

The probability that the top card is an ace or a king is \($\frac{1}{13} +\frac{1}{13} =\frac{2}{13}\).

b) The probability that the top card is spades is \($\frac{1}{52}\)

Already a card is drawn then the probability that the second card is clubs is \($\frac{1}{51}\)

The probability that the top card is spades and the second card is clubs is \($\frac{1}{52}\times\frac{1}{51} = \frac{1}{2652}\)

c) The probability that the top card is spades is \($\frac{1}{52}\)

Already a card s drawn then the probability that the second card is an ace is \($\frac{4}{51}\)

The probability that the top card is spades and the second card is an ace  is \($\frac{1}{52}\times\frac{4}{51} = \frac{4}{2652} = \frac{1}{663}\)

d) The probability that the top 3 cards are all spades is \($\frac{1}{52}\times\frac{1}{51}\times\frac{1}{50} = \frac{1}{132600}\)

e) There are C(52, 4) ways to choose 4 cards from the deck, and the 4 ways to choose the rank that appears twice.

So, the total number of ways to choose 4 cards with 3 different ranks and one rank appearing twice is 4 C(52, 4) = 4 × 270725.

The number of ways to choose the 4 cards such that they include 3 different ranks, with one rank appearing twice is 4  C(13, 2)  C(4, 2) = 672.

Hence, the probability is \($\frac{672}{270725} =\frac{2}{925}\)

For more questions on probability

https://brainly.com/question/14219670

#SPJ4

A standard deck of 52 cards has 13 ranks (ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king) and 4 suits (spades, hearts, diamonds, and clubs), such that there is exactly one card for any given rank and suit. The deck is randomly arranged. What is the probability that

(a) the top card is an ace or a king.

(b) the top card is spades and the second card is clubs.

(c) the top card is spades and the second card is an ace.

(d) the top 3 cards are all spades.

(e) the top 4 cards include 3 different ranks, with one rank appears twice (for example, an ace of hearts, a 3 of clubs, a 3 of hearts, and a 7 of spades).

x = number of weeks which is some positive whole number

50x = amount saved after x weeks, when saving $50 per week

50x+800 = add on the 800 she already has

The expression 50x+800 is the total money saved. We set this equal to the 1150 to set up the equation we're after

The quadratic function is already written in a recognizable way:

Evaluate the function at some values to find points on the graph of f:

Plot the points (x,f(x)) on a coordinate plane:

Draw a smooth line through those points:

Answer:

x = 65.26 degrees or x = 245.26 degrees.

Step-by-step explanation:

To solve the equation 4tan(x)-7=0 for 0<=x<360, we can first isolate the tangent term by adding 7 to both sides:

4tan(x) = 7

Then, we can divide both sides by 4 to get:

tan(x) = 7/4

Now, we need to find the values of x that satisfy this equation. We can use the inverse tangent function (also known as arctan or tan^-1) to do this. Taking the inverse tangent of both sides, we get:

x = tan^-1(7/4)

Using a calculator or a table of trigonometric values, we can find the value of arctan(7/4) to be approximately 65.26 degrees (remember to use the appropriate units, either degrees or radians).

However, we need to be careful here, because the tangent function has a period of 180 degrees (or pi radians), which means that it repeats every 180 degrees. Therefore, there are actually two solutions to this equation in the given domain of 0<=x<360: one in the first quadrant (0 to 90 degrees) and one in the third quadrant (180 to 270 degrees).

To find the solution in the first quadrant, we can simply use the value we just calculated:

x = 65.26 degrees (rounded to two decimal places)

To find the solution in the third quadrant, we can add 180 degrees to the first quadrant solution:

x = 65.26 + 180 = 245.26 degrees (rounded to two decimal places)

So the solutions to the equation 4tan(x)-7=0 for 0<=x<360 are:

x = 65.26 degrees or x = 245.26 degrees.

Answer:

x > 0

Step-by-step explanation:

To solve the inequality x/1 + 5 > 5, we first need to isolate the variable on one side of the inequality.

Subtracting 5 from both sides gives:

x/1 > 0

Multiplying both sides by 1 gives:

x > 0

Therefore, the solution to the inequality is x > 0.

The required real-world problem is below that can be solved using the equation.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

A construction company is building a new housing development and wants to know how many houses they need to build to reach a certain profit margin. They know that each house costs $9 to build and they want to sell each house for $21.

If they build x number of houses, the equation to calculate their profit is:

21x - (4x + 9) = profit.

To reach a certain profit margin, the company can set that equation equal to a specific value and solve for x.

Learn more about the equation here:

brainly.com/question/10413253

#SPJ5