Paige can sort her toys in 6 fewer hours that Madison can. When they work together, it
takes them only 4 hours to sort the toys. How long would it take for each of them to sort
the toys alone?

Answer:

a=4

Step-by-step explanation:

we fill in b to find a

a=2(3a-5)-10

a=6a-10-10

a=6a-20

+20  +20

a+20=6a

-a.    -a

20=5a

/5. /5

4=a

hopes this helps

The composition function  for the given function f(x) and g(x) is,

f(g(x)) = 6x^2 - 10x - 21.

What is composition of function?

The mathematical operation known as "function composition" takes two functions, f and g, and creates a function, h = g o f, such that h(x) = g. This operation involves applying the function g to the outcome of applying the function f to x.

Given:

f(x) = 2x - 7

g(x) = 3x^2 - 5x - 7

We have to find the composition function f(g(x)).

[tex]f(g(x)) = f(3x^2- 5x - 7)[/tex]

Plug x = 3x^2 - 5x - 7 in f(x).

[tex]f(g(x)) = 2(3x^2 - 5x - 7) - 7\\f(g(x)) = 6x^2 - 10x - 14 - 7\\f(g(x)) = 6x^2 - 10x - 21[/tex]

Hence, the composition function  for the given function f(x) and g(x) is, f(g(x)) = 6x^2 - 10x - 21.

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Coordinates of the point C after dilation with a scale factor of 5, centered at the origin will be: C'(10, 5)

Given that,

The point C

C(2, 1)

We have to find what are the coordinates of the point D after a dilation with a scale factor of 5, centered at the origin.

We know that,

The point C

The size of the coordinates of the picture of point P will be 5 times larger than the original coordinates of point C in a dilatation with a scale factor of 5.

The following is the scale factor 5 rule of dilation:

(x, y)  →  (5x, 5y)

C(2, 1)  →  (5x, 5y) = (5(2), 5(1)) = C'(10, 5)

Therefore, coordinates of the point C after dilation with a scale factor of 5, centered at the origin will be: C'(10, 5)

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Answer:

Step-by-step explanation:

what

Equation that represents Jada’s take-home earnings in dollars E = 12.20(h)-7.15

The equation that represents the situation is h=6.82 hours.

An equation, a formula that is express the equality of two expressions. The equation is representing direct proportion is , by the commenting them with in the equal sign .

As per the given question

Pay hour = $12.20 per hour

Bus fare = $7.15

1.Equation:

Assume that

She has work for "h" hours

Total earning = E

So, E = 12.20(h) - 7.15

If, Total earning = E = $90.45

So, E = 12.20(h) - 7.15

90.45 = 12.20(h) - 7.15

h = 6.82 hours

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Answer: t = 11

Step-by-step explanation:

f(11)= 5(11) -7

f(11) = 55 - 7

f(11) = 48

Answer:

f(11) = 48

Step-by-step explanation:

f(t) = 5t-7

we have to find out what t is

5t - 7 =48

    +7    +7

5t = 55

  /5   /5

t = 11

The statements that Adriano mixed 19/24 pound of butter with 3/16 pound of honey he ay that he ued 16/8 pound of butter than honey  is not reasonable.

A mixture is a substance made of two or more additional chemical compounds or substances that do not chemically combine. It is actually the physical blending of two or more substances so that they can still be distinguished from one another when combined as solutions, suspensions, or colloids. Physical means can be used to separate them. The different components in any mixture are not created through any sort of chemical transformation. As a result, each component's unique properties are unaltered.

A mixture's constituent parts also do not combine chemically to form new material, in contrast to a compound. Instead, they just combine while retaining their individual traits. because there are variable quantities of the components

Ratio 19/24 is nearby ¾

Ratio 3/16 is nearby ¼

And ratio 16/8 is nearby 2

So, that his statements is not reasonable.

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a) Corey's percentage increase in pay per hour is 14.2%.

b) When Dele invests $6,000 for 4 years at 3% per annum compound interest, the value of his investment (future value) at the end of 4 years is $15,757.12.

c) The worth of the car at the end of 2020 is $11,812.50, depreciating by 14% per annum.

a. Corey's original pay per hour = £12.36

Corey's new pay per hour = $14.11

Increase in pay = £1.75 (£14.11 - £12.36)

Percentage increase in pay = 14.2% (£1.75/£12.36 x 100)

b. Principal investment = $14,000

Investment period = 4 years

Compound interest rate = 3%

Compounding terms = Annually

The future value (FV) in 4 years:

N (# of periods) = 4 years

I/Y (Interest per year) = 3%

PV (Present Value) = $14,000

PMT (Periodic Payment) = $0

Results:

FV = $15,757.12

Total Interest = $1,757.12

c. Value of a car at the end of 2017 = $17,500

Depreciation rate per annum = 14%

Depreciation period = 3 years (Dec. 31, 2017 - Dece. 2020)

Value of the car at the end of 2020 = $11,812.50 ($17,500 x 1.14⁻³)

Thus, the car will reduce (depreciate) in value every year by 14%, making its value to be $11,812.50 at the end of 2020.

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Answer:

A. (3,-1)

Step-by-step explanation:

A reflection of y = x would be:

[tex](x,y)\rightarrow(y,x)[/tex]

Therefore:

[tex](-1, 3) \rightarrow (3, -1)[/tex]

The correct option should be A.

Hope this helps.

Answer:

7

Step-by-step explanation:

Answer: y= 1/2x+2

Step-by-step explanation:

Using the y=mx+b formula you simply find the slope between the two points considered on a graph

Hope this helps you

The expression that is equivalent to the given algebraic expression is; negative 14 over 18 times t minus 5 over 8

We are given the algebraic expression as;

-(10/9)t + (1/8) - [(-6/18)t + (3/4)]

Factorize out 1/72 to get;

(1/72)(-80t + 9 + 24t - 54)

= (1/72)(-45 - 56t)

= (-14/18)t - 5/8

We have used some basic mathematical operations in the expression, it gives us negative 14 over 18 times t minus 5 over 8

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In the given trapezoid, the angle ∠ HMA is 120°.

A closed polygon or geometry with four sides, four corners, and four angles is called a trapezium. Each pair of a trapezium's opposing sides is parallel to the other.

In the given trapezoid AMHT,

The angle H = 60°.

To find the angle ∠ HMA,

Since, the sum of angle MHT and angle HMA is equal to 180°.

∠ HMA + ∠ MHT = 180°

∠ HMA + 60 = 180

∠ HMA = 120

The required angle ∠ HMA is 120°.

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Answer:

318.75 miles

Step-by-step explanation:

Answer:

x = 11

Explanation:

It looks like the total distance between points I and K is -3 + x. Since I to J and J to K is also the total distance, I to K is also equal to 6 + 2x - 20. You can represent this in an equation and solve for x.

-3 + x = 6 + 2x - 20

-3 + x = 2x - 14

- 3 = x - 14

11 = x

After a comparison of females and males on the number of hours of a day that the subject watched the TV.

The hypotheses of a significance test to analyze whether the population means differ for females and males would be as follows:

(a) H0: μ1 = μ2 (the population means are equal for females and males)

Ha: μ1 ≠ μ2 (the population means are not equal for females and males)

(b) In order to conduct the significance test, we would need to calculate the t-statistic and the P-value. However, the question does not provide the necessary information to do so (e.g. sample means, standard deviations, sample sizes). Without this information, we cannot conduct the significance test and interpret the P-value(c) Without conducting the significance test, we cannot conclude anything about whether there is a gender difference in TV watching.

(d) Similarly, without conducting the significance test and calculating the confidence interval, we cannot determine whether the confidence interval would contain 0 or not.

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Postulates, corollaries, and common notions are the three main types of reasoning we will use for reasons in the right- hand of column.

A two-column geometric proof consists of a list of statements, and the reasons that we know those statements are true. The statements are listed in a column on the left, and the reasons for which the statements can be made are listed in the right column.

Postulates, corollaries, and common notions are the three main types of reasoning we will use for reasons in the right- hand of column.

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Answer:

[tex]\huge\boxed{\sf c=\frac{ad}{e-b}}[/tex]

Step-by-step explanation:

[tex]\displaystyle b + \frac{ad}{c} = e[/tex]

Subtract b to both sides

[tex]\displaystyle \frac{ad}{c} = e-b[/tex]

Multiply c to both sides

[tex]ad=c(e-b)[/tex]

Divide (e - b) to both sides

[tex]\displaystyle \frac{ad}{e-b} = c\\\\\boxed{c=\frac{ad}{e-b} }[/tex]

[tex]\rule[225]{225}{2}[/tex]

The best triangle congruent theorem for the image is Angle-Angle-Side (AAS)

Two triangles are congruent if they have exactly the same three sides and exactly the same three angles.

From triangle ABC,

<BAC is given

<ABC=90⁰

<BCA is not given

Also, in triangle ACD,

<ACD is given

<CDA =90⁰

<DAC is not given

Therefore <BAC=<ACD (given)

<CDA=<ABC=90

<DAC=<BCA (not given)

Therefore,  ΔABC=ΔACD (AAS)

In conclusion, The two triangles are congruent with SSA theorem.

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The break even point is at 500 baskets. The company must sell 500 baskets a month, at which point their revenue of $10,000 will cover their total costs of $10,000.

What is break even point?

In economics, business, and particularly cost accounting, the break-even point is the point at which total cost and total revenue are equal, or "even." Although opportunity costs have been paid and capital has received the risk-adjusted, expected return, there is no net loss or gain, and one has "broken even."

In this case we could probably solve the problem from the graph itself, but we can also solve it algebraically by setting the equations equal:

[tex]\begin{gathered}R(n)=C(n) \\20 n=6000+8 n\end{gathered}[/tex]

Subtract 8n from both sides:

[tex]12 n=6000[/tex]

Divide:[tex]n=\frac{6000}{12}=500[/tex]

Evaluate either function at this input: [tex]R(500)=C(500)=10,000[/tex]

The break even point is at 500 baskets. The company must sell 500 baskets a month, at which point their revenue of $10,000 will cover their total costs of $10,000.

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The other information that must prove by the triangle is that ∠A ≅ ∠X.

How do you understand "ABC" and "DEF"?

The triangles are congruent if their included sides are congruent and two of their angles match two of the other triangle's angles. applying labels Triangle ABC is congruent to triangle DEF if, in triangles ABC and DEF, angle A = angle D, angle B = angle E, and angle AB = DE.

By SAS or Side-Angle-Side Postulate, the corresponding two sides and it's included angles should be congruent.

Therefore, based on the illustration, the included angle for ∆ABC is ∠A while the included angle for ∆XYZ is ∠X.

Therefore, the other information that must prove by the triangle is that ∠A ≅ ∠X.

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Answer:

B. none of other works. Only hue rate of change of Function F is higher than Function G

By using Pythagoras theorem, Kyle run for the distance of 210 m.

What is the Pythagorean theorem ?

According to Pythagoras's Theorem, the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides.

                                  Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides.

The given length of the field is 84 m.

And, the width is 35 m.

Now, the diagonal of the field can be calculated using Pythagoras theorem as below,

Diagonal = √((84)² +(35)²)

              = 91

Then, the total length is found by summing the length, width and the diagonal as below,

= 84 + 35 + 91

= 210

Hence, Kyle run for the distance of 210 m.

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Answer: 12 pack.

Step-by-step explanation: 25.20 divided by 12 shows us that each gatorade costs 2.1 dollars. Now add the 3 gatorade worth to 25.2. You get 31.5 which is less than 33, showing that 12 pack is more worth as you pay less for 15 aswell.

The probability that the engineer has to test at least 5 computers in order to find 2 defective ones is 0.985.

Given :

A quality control engineer tests the quality of produced computers. suppose that 5% of computers have defects, and defects occur independently of each other.

So the probability of getting 0 defective computers out of 4 is :

= ( 1 - 0.05 )^4

= 0.95^4

= 0.814.

The probability of getting exactly 1 defective computer out of 4 is :

= 0.05 * ( 1 - 0.05 )^3 * 4! / ( 1! ( 4 - 1 )!)

= 0.05 * 0.95^3 * 24/ ( 1!3! )

= 0.05 * 0.857375 * 24/6

= 0.171.

So the probability of getting only 0 or 1 defective computers out of the 1st 4 is :

= 0.814 + 0.171

= 0.985

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The calculations for the slope-intercept forms of the equations are (1) m=-[tex]\frac{3}{4}[/tex],B=2  (2)m=1, B=5  (3) m=-1, B=6

How to use the Slope -intercept form?

Slope of a line is a number that describes both the direction and the steepness of the line.

The intercept of a line is defined as the point at which it intersects the y-axis in a graph.

The equation of a line is expressed as follows;

Y=MX+B

Where M=slope and B=intercept

From the equations:

(1) y<[tex]\frac{-3x}{4}[/tex]+2

Applying the equation of slope-intercept form,

m=[tex]\frac{-3}{4} , B=2[/tex]

(2) Y[tex]\leq 5[/tex]

Applying the equation: Y=MX+B

m=1,  B=5

(3) x+y>6

Applying the formula: Y=MX+B

Re-arrange the equation

y>-x+6(1)

⇒ m=-1, B=6

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Answer:

(-4,-7)

Step-by-step explanation:

8x - 3y = -11

2x - 5y = 27

8x - 3y = -11

4(2x - 5y) = 27 (4)

8x - 3y = -11

8x - 20y =108

8x - 8x = 0

-3y - (-20y) = 17y

- 11 - 108 = -119

17y = -119

17/17 y = -119/17

y = - 7

2x - 5(-7) = 27

2x + 35 = 27

2x = 27 - 35

2x = - 8

2/2 x = -8/2

x = -4

Together, Tony and Ted caught 78.29 pounds + 59.36 pounds = 137.65 pounds of fish when they went fishing.

Addition is a mathematical process that combines two or more numbers or units to form a sum. One of the four fundamental operations of mathematics, along with addition, subtraction, multiplication, and division, it is generally represented by the plus sign (+). The fundamental idea of addition is one that is taught to children at a young age and is utilized frequently in both mathematics and daily life. For instance, when shopping, one may tally up the costs of several goods to get the overall expense. In algebra, adding is used to solve problems and make statements simpler. Finding side lengths and shape areas are both important aspects of geometry. In general, adding is flexible. for example,Tony and ted went fishing. and we got to calculate the total fishes caught by them.

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The total no: of pages needed are 18 pages

A fundamental idea behind the unitary method is using the value of one unit to determine the values of additional units. Study up on the unitary method. With an increase in units, the value of additional units rises.

The general unitary group, also known as the group of unitary similitudes, is simply the product of the unitary group and the group of all positive multiples of the identity matrix. It includes all matrices A such that AA is a nonzero multiple of the identity matrix.

According to the question:-

The no: of pages needed for 6 letters = 6

The no: of pages needed for the other 6 letters= 6*2

                                                                              =12

Total no: of pages are 18

Hence, the total no: of pages are 18

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In a Kite ABCD the diagonals AC and BD can be proved perpendicular by linear pair perpendicular theorem.

What is linear pair perpendicular theorem?

This theorem states that if two straight lines intersect at a point, and the linear pair of angles they form have an equal measure, then the two lines are perpendicular to each other.

According to the given question:

ABCD is a Kite        //Given

AB=BC                     //Given

BE=BE                    //Common side, reflexive property of equality

∠ABE ≅ ∠CBE      // in a kite the axis of symmetry bisects the angles at  

                                      those corners

△ABE≅△CBE      //Side-Angle-Side postulate

∠AEB ≅ ∠CEB      //Corresponding angles in congruent triangles (CPCTC)

AC⊥BD     //Linear Pair Perpendicular Theorem

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Answer:

B. For 5 students, the cost will be the same, and the cost will be $70

Step-by-step explanation:

Look at the graph and see where the two linear plots intersect.

This point of intersection is at the x value of 5 and y value of 70: (5, 70)

Since the x-axis represents the number of students and y axis the total cost, the answer is B