=
Solving a word problem on proportions using a unit rate
Ashley made $342 for 18 hours of work.
At the same rate, how many hours would she have to work to make $152?
O
hours
Х
?

Answer:

A. The triangles are similar because the ratios of the corresponding sides are the same

Step-by-step explanation:

Both ∆sloom similar in shape. Let's find out if they are actually similar.

∆TUV and ∆QRS are similar if the ratio of their corresponding sides are the same all through.

Thus:

TU = 70, QR = 25, UV = 84, RS = 30, TV = 42, QS = 15

If both ∆s are similar, then, TU/QR = UV/RS = TV/QS

TU/QR = 70/25 = 2.8

UV/RS = 84/30 = 2.8

TV/RS = 42/15 = 2.8.

Ratio of corresponding sides is the same, therefore, both triangles are similar.

Therefore, the following statement is true:

A. The triangles are similar because the ratios of the corresponding sides are the same

Notice that the two triangles not only have congruent sides as marked with the ticks, but also have a common angle which is created by the intersection of two lines. In this intersection, angles opposed by the vertex are congruent.

Therefore the two triangles are congruent because they have corresponding equal sides and congruent angle in between those sides.

Then, the theorem that we apply for congruent is the Side Angle in between and Side Theorem (SAS) which agrees with the last answer option in your list.

The y-coordinate of -3f(x-1) when x = 0 is -63

From the question, we have the following parameters that can be used in our computation:

The table of values

So, we have

-3f(x - 1)

When x = 0, we have

y = -3f(0 - 1)

This gives

y = -3f(-1)

From the table, we have

y = -3 * 21

Evaluate

y = -63

Hence, the y-coordinate is -63

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Answer:

x = 6

Step-by-step explanation:

This is a bit of a tricky equation, and it's what we call an exponential equation since it involves some exponents. The way we begin to solve these kinds of problems is make the base on each side of the equals sign the same. On one side, we have 9 as our base, and on the other side, we have 3 as our base. 9 = 3², so we can rewrite our equation as shown below:

(3²)⁴ˣ⁻¹⁰ = 3⁵ˣ⁻²

From there, we can use the exponent rule (xᵃ)ᵇ = xᵃᵇ to simplify the left side of the equation.

3²⁽⁴ˣ⁻¹⁰⁾ = 3⁵ˣ⁻²

3⁸ˣ⁻²⁰ = 3⁵ˣ⁻²

Since our bases are now the same, we can take just the exponents and turn it into a new equation as shown below:

8x - 20 = 5x - 2

Hopefully at this point, this problem becomes easy for you, but I'll show how I solved this new equation below in case it doesn't make sense.

8x - 20 = 5x - 2

8x - 20 - 5x = 5x - 2 - 5x

3x - 20 = -2

3x - 20 + 20 = -2 + 20

3x = 18

3x/3 = 18/3

x = 6

Hopefully that's helpful! Let me know if you need more help. :)

The distance between the points M=(-4, 9 ) and L=(-1. 1) in the coordinate plane is \(\sqrt{73}\).

Explain Coordinate Plane.

In a plane, a Cartesian coordinate system is a system of a coordinate that designates each point uniquely by a pair of numerical coordinate in a plane, which are the signed distances from two fixed perpendicular oriented lines to the point on the same plane, measured in the same unit of length.

Solution Explained:

Using the distance formula, we have

\(\sqrt{(x_{2} - x_{1}) ^{2} + (y_{2} - y_{1}) ^{2} }\)

Substituting the values using the values of the points

\(\sqrt{(-1 + 4) ^{2} + (1 - 9) ^{2} }\)

\(\sqrt{(3) ^{2} + (-8) ^{2} }\)

\(\sqrt{9 + 64}\)

\(\sqrt{73}\)

Hence, the distance between the two points is \(\sqrt{73}\)

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The most appropriate conclusion is: A) This is convincing evidence of an association between longer hand and longer foot.

The chi-square test is a statistical test used to determine whether there is a significant association between two categorical variables. It is used to compare observed frequencies of data to the expected frequencies to determine if they differ significantly. The test is based on the principle of comparing the difference between the observed frequencies and the expected frequencies, and then determining if this difference is statistically significant.

Here,

At the 0.05 significance level, with a chi-square statistic of 11.942 and 4 degrees of freedom, the P-value is 0.018.

Since the P-value is less than the significance level, we reject the null hypothesis of no association and conclude that there is evidence of an association between longer hand and longer foot.

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Complete question:

Imani was curious if there was a relationship between one hand being longer than the other and one foot being longer than the other for 100 randomly selected students. Here is a summary of the data and the results from a chi-square test:

The cost of 20 T-Shirt will be 2560 when cost of one t-shirt is 128.

When a selling price and profit are provided, cost price equals selling price plus profit. When the selling price and loss are disclosed, cost price equals selling price plus loss.

Profit is calculated as S.P. - C.P. If the selling price is less than the cost price, the difference between the two is the loss incurred. Loss is also equal to C.P. - S.P.

We must divide the gross profit by the entire revenue for the year, multiply by 100, and then find the gross profit margin. We must divide net income (or net profit) by the entire annual revenue before multiplying the result by 100 to get the net profit margin.

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The factorized form of \(x^3 - (y - z)^3\ is \ (x - y + z)(x^2 - xy + 2xz + yz - 2z^2).\)

The Factorization is derived from the application of a mathematical identity. As an AI language model, the information provided is generated based on existing knowledge and formulas.

The given expression is \(x^3 - (y - z)^3.\)To factorize it,  the difference of cubes, which states that a^3 - b^3 can be factorized as\((a - b)(a^2 + ab + b^2).\)

Applying this identity to our expression, we have:

\(x^3 - (y - z)^3 = (x - (y - z))((x - (y - z))^2 + (x - (y - z))(y - z) + (y - z)^2)\)

Simplifying further, we get:

\(= (x - y + z)(x^2 - 2xy + 2xz - y^2 + 2yz - z^2 + xy - y^2 + yz - z^2 + y^2 - 2yz + z^2)\\= (x - y + z)(x^2 - 2xy + xy + 2xz + yz - 2yz - y^2 + y^2 - y^2 + 2yz - 2z^2 + y^2 - z^2 + z^2)\\= (x - y + z)(x^2 - xy + 2xz + yz - 2z^2)\)

So, the factorized form of \(x^3 - (y - z)^3 \ is\ (x - y + z)(x^2 - xy + 2xz + yz - 2z^2).\)

the above factorization is derived from the application of a mathematical identity.

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The simplified expression for \($(27^{\frac{1}{2} }) ^{\frac{2}{3} }\) is equal to 3.

We can write the simplified form of the given expression using the exponent rule as -

{aˣ/aⁿ} = {aˣ a⁻ⁿ} = {aˣ ⁻ ⁿ}

Given is the expression as -

\($(27^{\frac{1}{2} }) ^{\frac{2}{3} }\)

We can simplify the expression as -

\($(27^{\frac{1}{2} }) ^{\frac{2}{3} } = (27)^{\frac{1}{2} \times \frac{2}{3} }\)

\($(27^{\frac{1}{2} }) ^{\frac{2}{3} } = 27^{\frac{1}{3} }\)

\($(27^{\frac{1}{2} }) ^{\frac{2}{3} } = (3)^{3}^{\frac{1}{3} }\)

\($(27^{\frac{1}{2} }) ^{\frac{2}{3} } = 3\)

Therefore, the simplified expression for \($(27^{\frac{1}{2} }) ^{\frac{2}{3} }\) is equal to 3.

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Answer:

1/2

Step-by-step explanation:

because Mackenzie chose two candles and we are to find the probility that he selects a polka dot candle

Answer:

Step-by-step explanation:

Gross salary = $865

Taxes imposed= $110.32

Medicare is 6%. so 6% of $865 is $51.9

and 1% social security is $8.65

so by subtracting values, the net income will be $694.13

There are no possible real values for the first term 'a' that satisfy both equations.

Let's denote the first term of the geometric progression as 'a' and the common ratio as 'r'.

The sum of the first two terms can be expressed as:

a + ar = 16

To find the sum to infinity, we can use the formula:

Sum to infinity = a / (1 - r)

Given that the sum to infinity is 25, we have:

25 = a / (1 - r)

We now have two equations:

a + ar = 16

a / (1 - r) = 25

We can solve these equations simultaneously to find the possible values of 'a'.

From the first equation, we can factor out 'a' to get:

a(1 + r) = 16

Dividing both sides of the second equation by 25, we have:

a / (1 - r) = 1

We can rearrange this equation to get:

a = 1 - r

Substituting this expression for 'a' in the first equation, we get:

(1 - r)(1 + r) = 16

Expanding the equation, we have:

1 - r^2 = 16

Rearranging the terms, we get:

r^2 = -15

Since we are dealing with a geometric progression, the common ratio 'r' must be a real number. However, we observe that r^2 = -15 has no real solutions. Therefore, there are no possible real values for the first term 'a' that satisfy both equations.

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a reasonable estimate of the probability that the next movie is an action movie is 0.139 or roughly 13.9 percent.

We may use the percentage of action movies in the total number of films shown last year to determine the likelihood that the next film presented at the Cinemania theatre is an action film:

P(action movie) equals the number of action films divided by the overall number of films aired

By entering the specified values, we obtain:

P(movie with action) = 15 / 108 = 0.139 (rounded to three decimal places)

Consequently, a conservative estimate of the likelihood that the next film to be screened at Cinemania is an action film is 0.139, or roughly 13.9 percent.

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The length of PQ is 3√5 and its slope is -2

The length of SR is 3√5 and its slope is -2

The length of SP is 5√2 and its slope is -7

The length of RQ is 5√2 and its slope is -1

So PQ ≅ SR and SP ≅ RQ. By the Perpendicular Bisector theorem, adjacent sides are perpendicular. By the selection of  side, ∠PSR, ∠SRQ, ∠RQP and ∠QPS are right angles. So, the quadrilateral is a rectangle.

To find the lengths and slopes of the sides of the quadrilateral PQRS, we apply the distance formula:

D = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)  

and the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

1. Length PQ:

Using the distance formula, the length PQ can be calculated as follows:

PQ = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((3 - 0)² + (-4 - 2)²)

  = √(3² + (-6)²)

  = √(9 + 36)

  = √45

  = 3√5

2. Length SR:

Using the distance formula, the length SR can be calculated as follows:

SR = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((1 - (-2))² + (-5 - 1)²)

  = √((1 + 2)² + (-6)²)

  = √(3² + 36)

  = √(9 + 36)

  = √45

  = 3√5

3. Length SP:

Using the distance formula, the length SP can be calculated as follows:

SP = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((1 - 0)² + (-5 - 2)²)

  = √(1² + (-7)²)

  = √(1 + 49)

  = √50

  = 5√2

4. Length RQ:

Using the distance formula, the length RQ can be calculated as follows:

RQ = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((-2 - 3)² + (1 - (-4))²)

  = √((-2 - 3)² + (1 + 4)²)

  = √((-5)² + 5²)

  = √(25 + 25)

  = √50

  = 5√2

Now, let's calculate the slopes of the sides:

1. Slope PQ:

The slope of PQ can be calculated using the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (-4 - 2) / (3 - 0)

  = -6 / 3

  = -2

2. Slope SR:

The slope of SR can be calculated using the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (-5 - 1) / (1 - (-2))

  = -6 / 3

  = -2

3. Slope SP:

The slope of SP can be calculated using the slope formula:

m =\(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (-5 - 2) / (1 - 0)

  = -7 / 1

  = -7

4. Slope RQ:

The slope of RQ can be calculated using the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (1 - (-4)) / (-2 - 3)

  = 5 / (-5)

  = -1

Therefore, the lengths and slopes of the sides of the quadrilateral PQRS are:

Length PQ: 3√5

Length SR: 3√5

Length SP: 5√2

Length RQ: 5√2

Slope PQ: -2

Slope SR: -2

Slope SP: -7

Slope RQ: -1

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Answer:

For this case we know that the medicine ball weighs 3.6 Kg and we know that there are about 2.2 pounds in every Kg.

So then we can find the amount Kg with this expression:

\( 3.6 Kg *\frac{2.2 pounds}{1 Kg} = 7.92 pounds\)

And if we round to the nearest integer we got 8 pounds and the best answer would be:

8 pounds

Step-by-step explanation:

For this case we know that the medicine ball weighs 3.6 Kg and we know that there are about 2.2 pounds in every Kg.

So then we can find the amount Kg with this expression:

\( 3.6 Kg *\frac{2.2 pounds}{1 Kg} = 7.92 pounds\)

And if we round to the nearest integer we got 8 pounds and the best answer would be:

8 pounds

Answer:8

Step-by-step explanation:round 7.92

Answer:

D

Step-by-step explanation:

You can infer to the solution of this problem by looking at the choices. Hope this helped :)

The system A has no solution.

The system B has the solution y=( 3-x )/3

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

System A:

x+3y=9..........(1)

-x-3y=9 ..........(2)

(1) => x=9-3y........(3)

Substitute (3) into (2)

(2) = >  - ( 9-3y ) - 3y = 9

          -9 + 3y - 3y = 9

          -9 =9

This is false.

So, the system has no solution.

System B:

-x-3y=-3..........(1)

x+3y=3..........(2)

(2) => x=3-3y........(3)

Substitute (3) into (1)

-(3-3y)-3y=-3

-3+3y-3y= -3

-3=-3

This is true,

So, the solution is:

x=3-3y

=> 3y= 3-x

=> y=( 3-x )/3

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There are 30 boys and 20 girls in the classroom.

Let the variable p represent the number of people. Next, we would translate the given word problem into an algebraic equation by using a ratio as follows;

Number of girls + Number of boys = Total number of people

2p + 3p = 50

5p = 50

Dividing both sides of the equation by 5, we have the following:

p = 50/5

p = 10 people.

For the number of girls, we have:

2g = 2(10)

2g = 20 girls.

For the number of boys, we have:

3g = 3(10)

3g = 30 boys.

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Answer:

Kurt 10    Courtney 10    Mark brainiest

Step-by-step explanation:

I did this too

Answer:

they each have 10 if you count     mark me brainiest, please

Step-by-step explanation:

Answer:

P=1

Step-by-step explanation:

1-6=-5

The remainder is 5 + c, which means that the expression P(x) = \(5x^4 + 7x^3 - 2x^2 - 3x + c\) divided by (x + 1) results in a quotient of\(5x^3 + 2x^2 - 4x + 4\) and a remainder of 5 + c.

To divide the polynomial P(x) = \(5x^4 + 7x^3 - 2x^2 - 3x + c\) by the binomial (x + 1), we can use polynomial long division.

Let's set up the long division:

    \(5x^3 + 2x^2 - 4x + 4\)

_______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

We start by dividing the highest degree term of the dividend (5x^4) by the divisor (x + 1), which gives us 5x^3. We then multiply this quotient by the divisor (x + 1) and subtract it from the dividend:

              \(5x^3(x + 1)\)

     _______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

- (\(5x^3 + 5x^2)\)

This leaves us with a new polynomial:\(2x^3 - 7x^2 - 3x + c\). We repeat the process by dividing the highest degree term of this polynomial (2x^3) by the divisor (x + 1), resulting in 2x^2. We then multiply this quotient by the divisor and subtract it from the polynomial:

              \(5x^3(x + 1) + 2x^2(x + 1)\)

     _______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

-\((5x^3 + 5x^2)\)

_______________________

\(2x^2 - 3x + c\)

We continue this process until we reach the constant term, resulting in the remainder of the division.

At this point, we have:

               \(5x^3(x + 1) + 2x^2(x + 1)\)

     _______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

- \((5x^3 + 5x^2)\)

_______________________

\(2x^2 - 3x + c\)

-\((2x^2 + 2x)\)

_______________________

- 5x + c

- (-5x - 5)

_______________________

5 + c

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Answer: 36

Step-by-step explanation: 12/1 =?/3 so you multiply by 3 and 3x12= 36

Answer:

After 3 minutes, 36 gallons of water comes out of the pipe.

Step-by-step explanation:

If 12 gallons come out per minute, you can simply multiply 12 gallons by 3 minutes, thus you end up with 36 gallons / 3 minutes.

Answer:

770cents

Step-by-step explanation:

If a report is 81 pages long, 12 copies will be (81 * 12)pages long

12copies = 972 pages long

If 500 pages costs $3.96 each

972 pages will cost $x

Cross multiply

500x = 972 * 3.96

500x = 3,849.12

x = 3,849.12/500

x = 7.69824

Hence the cost of the reports is $7.69824

Convert to cents;

$1 = 100cents

$7.69824 = y

y = 7.69824 * 100

y = 769.824 cents

y ≈ 770 cents (to the nearest cent.)

Hence the paper is going to cost 770cents (to the nearest cent)

Conniving these points and connecting them, we get a V- shaped graph that's reflected vertically and shifted 4 units to the left wing.

       To graph the function g( x) = - f( x 4), we need to start with the graph of the function f( x) = | x| and  also apply the given  metamorphoses.  The function f( x) = | x| represents the absolute value function, which is a V- shaped graph symmetric with respect to the y- axis.  

First, we shift the graph of f( x) = | x| horizontally by 4 units to the left by replacing x with( x 4). This results in f( x 4).  Next, we multiply the entire function by-1, which reflects the graph vertically. This gives us- f( x 4).  Combining these  metamorphoses, we've the function g( x) = - f( x 4). To graph g( x), we can  compass a many points and  also draw the graph by connecting them.

Let's start with the original graph of f( x) = | x| and apply the  metamorphoses

For f( x)  x = -3,-2,-1, 0, 1, 2, 3  

f( x) =  3, 2, 1, 0, 1, 2, 3  For

g( x) = - f( x 4)  x = -7,-6,-5,-4,-3,-2,-1  

g( x) = -3,-2,-1, 0,-1,-2,-3

conniving these points and connecting them, we get a V- shaped graph that's reflected vertically and shifted 4 units to the left wing.

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Using system of equation, the solution shows that it will take 50 weeks before Jacob and Diego will be tied in the race to complete community service hours for scouting.

As given,

let us assign the unknown quantity (number of weeks) a variable x.

Jacob plans to devote 5 hours per week from now onwards. Hence his volunteer hours will cumulate to 5x+50 as he has already completed 50 weeks.

Diego plans to devote 6 hours per week from now onwards. Hence his volunteer hours will cumulate to 6x.

For Jacob and Diego to tie in the race, their volunteer hours should be equal.

Solution of the  system of equation is given by:

6x = 5x+50

=> 6x-5x = 50

=> x = 50

Therefore, using system of equation, the solution shows that it will take 50 weeks before Jacob and Diego will be tied in the race to complete community service hours for scouting.

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Out of the 400 surveyed students, 327 were either seniors or commuters.

To find the number of students who were either seniors or commuters out of the 400 surveyed students, we need to add the number of seniors and the number of commuters while avoiding double-counting those who fall into both categories.

According to the information given:

There were 262 seniors.

There were 215 commuters.

150 of the seniors were also commuters.

To avoid double-counting, we need to subtract the number of seniors who were also commuters from the total count of seniors and commuters.

Seniors or commuters = Total seniors + Total commuters - Seniors who are also commuters

= 262 + 215 - 150

= 327

Therefore, out of the 400 surveyed students, 327 were either seniors or commuters.

It's important to note that in this calculation, we accounted for the overlap between seniors and commuters (150 students who were both seniors and commuters) to avoid counting them twice.

This ensures an accurate count of the students who fall into either category.

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Answer: Perpendicular

Step-by-step explanation:

Given are two equations as

We have to find whether these two are parallel or perpendicular or neither

For this first we have to find the slope of these two lines

I line slope = 1

II line slope =-1

Since slopes are not equal, the lines are not parallel.

Let us check product of these slopes.  IF product =-1 the lines are perpendicular

We find that product =

Hence two lines are perpendicular

Answer:

C. 6.67

Step-by-step explanation:

Given

Reserve Ratio (RR) = 15%

Required

Determine the simple deposit multiplier

Simple deposit multiplier (M) is calculated by taking the inverse of RR.

The following formula applies:

\(M = \frac{1}{RR}\)

Substitute 15% for RR

\(M = \frac{1}{15\%}\)

Convert 15% to decimal

\(M = \frac{1}{0.15}\)

\(M=6.67\)

Hence, option C answers the question

The values of the variables are;

x = 7

y = -9

From the information given, we have that;

5x−y=44

−3x−y=−12

Using the elimination method of solving simultaneous equations

Subtract equation (2) from equation (1), we get;

5x - y - (-3x - y) = 44 - (-12)

Now, expand the bracket

5x - y+ 3x + y = 56

collect the like terms

5x + 3x = 56

add the terms

8x = 56

Make 'x' the subject of formula

x= 7

Now, substitute the value of x in equation (2)

-3x - y = -12

-3(7) - y = -12

expand the bracket

-21 - y= - 12

collect like terms

-y = 9

y = -9

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Answer:

A

Step-by-step explanation:

The reason it's A is because to make the ratio 1:1 you need to have a whole number you can't have half a pencil or pen, so what you need to do is add 22 and 96 and divide you should get 59, but if you add 23 to 96 and divide you get 59.5 and you can't have half a pencil (you can but that's not what were looking for). So in problems like this add and then divide by 2 and choose whole numbers because you can't have half in ratios cause that won't give the correct answer.

Answer:

C = 24

Step-by-step explanation:

just trust me i got it wrong thinking it was A= 22