The sum of two numbers is 57 and the difference is 3. What are the numbers?

The solution to the products of exponents is as follows;

1) -24a³b⁷

2) 15a⁵b¹⁵

3) -10d⁴ + 17sd² - 6s²

4) 6x³ - 33x² + 45x - 6

5) 21x⁷y¹¹

6) 8y⁴ + 25y³ + 60y² + 10y + 7

7) 20s³ + 50s² + 32s + 6

The Product of Powers Property of exponents states that when we multiply two powers with the same base, we add the exponents.

1) (3a²b⁴) * (-8ab³)

= -24a³b⁷

2) (3a²b⁷) * (5a³b⁸)

= 15a⁵b¹⁵

3) (-2d² + s)(5d² - 6s)

Expanding the bracket to get;

(-10d⁴ + 5sd² + 12sd² - 6s²)

= -10d⁴ + 17sd² - 6s²

4) (3x - 6) * (2x² - 7x + 1)

= 6x³ - 33x² + 45x - 6

5) (7x²y³) * (3x⁵y⁸)

= 21x⁷y¹¹

6) (y² + 3y + 7) * (8y² + y + 1)

= 8y⁴ + 25y³ + 60y² + 10y + 7

7) (4s + 2) * (5s² + 10s + 3)

= 20s³ + 50s² + 32s + 6

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Distributive property of real numbers illustrated by the equation. -2(x 4)=-2x-8

The equation -2(x 4)=-2x-8 is an example of the distributive property of real numbers. This property states that when a number is multiplied by a group of numbers that are being added together, the number can be distributed to each of the terms in the group. To rewrite this equation as -2x + (-2)(-4) = -2x - 8, the number -2 is allocated to each of the terms in the group (x and -4) in this equation.Simplifying further, we get -2x - 8 = -2x - 8.

-2(x 4) = -2x - 8

Distribute -2 to each term in the group

-2x + (-2)(-4) = -2x - 8

Simplify

-2x - 8 = -2x – 8

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The probability of men whose height falls between 70 and 73 inches is  0.273. Therefore, the percent of men whose height falls between 70 and 73 inches is 27.3%. Therefore, the solution is 27.3%.

The standard deviation is a quantity that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability.

We are informed that the heights of men in the U.S are normally distributed with a mean of 70 inches and a standard deviation of 3 inches. We need to determine the percent of men whose height falls between 70 and 73 inches. We would first evaluate the probability that the height of a randomly selected individual would fall between 70 and 73 inches;

This can be done in stat-crunch;

Click Stat, highlight on Calculators then click Normal

In the pop-up window that appears click Between

Enter the given values of mean and standard deviation; 70 and 3 respectively

Enter the values 70 and 73 in the next set of boxes in that order

Finally, click on compute;

Stat-Crunch returns a probability of 0.273. Therefore, the percent of men whose height falls between 70 and 73 inches is 27.3%. Therefore, the solution is 27.3%.

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The perimeter of the object is the sum of the lengths of all the sides

which is 302 units.

Perimeter is the sum of the lengths of all the sides of a planar two-dimensional figure.

In the case of a circle, we call it perimeter circumference it is the distance around the circle.

Given, A figure has side lengths EF = 71, FD = 80, ED = 74, IG = 40, and

HG = 37.

Now the perimeter of this figure is the sum of the lengths of all the sides which is,

= (EF + FD + ED + IG + HG).

= (71 + 80 + 74 + 40 + 37).

= 302 units.

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Answer:

Below

Step-by-step explanation:

m = slope = rise / run

m = 5 for this equation

rise /run = 5

15 / run = 5

run = 3

Answer:

B

Step-by-step explanation:

5.21 x 10^19 + 3.149 x 10^17

10^17(5.21 x 10^2 + 3.149)

10^17(521 + 3.149)

10^17(524.149)

5.24149 x 10^17 x 10^2

5.24149 x 10^(17+2)

5.24149 x 10^19

Answer: b. 5.24149 × 1019

Step-by-step explanation: I took the test

As per the sign system of the Cartesian plane coordinates of A' will be (x,-y).

The cartesian plane is defined in mathematics as a two-dimensional coordinate plane formed by the intersection of the x- and y-axes. The origin is the point where the x- and y-axes intersect perpendicularly.

Quadrant one (QI) is the top right fourth of the coordinate plane, where all coordinates are positive. Quadrant two (QII) is the coordinate plane's top left fourth. Quadrant three (QIII) is the fourth from the bottom left. Quadrant four (QIV) is the fourth from the bottom right.

Given:

The direction of rotation = clockwise, (from the first quadrant to forth quadrant then third quadrant, and so on)

Angle of rotation = 90° about the origin

According to the question, let's take our start point as A(x, y)

So, A( x, y) will lie in the first quadrant.

After 90° rotation about the origin A' will lies in fourth quadrant.

As per the sign system of the Cartesian plane coordinates of A' will be (x,-y).

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The value of the variable x is -2

An algebraic expression can be defined as an expression made up of terms, variables, coefficient, factors and constants.

These expressions are also made up of arithmetic or mathematical operations, which includes;

From the information given, we have;

2 ^ (x + 3) * 3 ^ (x + 4) = 18

Now, let's find the factors of 18 in 2's and 3's, we have;

2 ^ (x + 3) * 3 ^ (x + 4) = 2^1 × 3^ 2

Collect the common factors, we get;

x+ 3 + x + 4 = 1 + 2

collect like terms

2x = 3 - 7

2x = -4

make 'x' the subject of formula

x = - 2

Hence, the value is -2

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Answer:

1. Scalene Triangle

2. 135 degrees

3. 80 degrees

I don't have much time for the rest, i'm sryyyyy

I hope i could helppp :3

Answer:

The cake cost $6.00

Step-by-step explanation:

Let c = the cost of the cake

Let t =  the cost of the tea

c = 2t

c + 5t = 21  Substitute 2t for c

2t + 5t = 21  Combine like terms

7t = 21  Divide both sides by 7

[tex]\frac{7t}{7}[/tex] = [tex]\frac{21}{7}[/tex]

t = 3  

A cup of tea costs $3.00

c = 2t  Substitute 3 for t

c = 2(3)

c = 6

A cake costs $6.00

Answer:

Cake: £6

Step-by-step explanation:

1c = 2t             Eq. 1

1c + 5t = 21      Eq. 2

c = cost of a cake

t = cost of a cup of tea

Replacing Eq. 1 in Eq 2:

2t + 5t = 21

7t = 21

t = 21/7

t = 3

From Eq. 1:

c = 2t

c = 2*3

c = 6

Check:

From Eq. 2:

c + 5t = 21

6 + 5*3 = 21

6 + 15 = 21

Answer:

7.7

Step-by-step explanation:

I got this by subtracting 13.3 - 5.6

The length of the other leg of the triangle is 11.7 inches

Now, According to the question:

We have the right triangle

The length of the right triangle is 24 inches

The length of the hypotenuse is 26.7 inches

To find the length of the other leg of the triangle

We know that the Pythagorean theorem.

The Pythagorean theorem states that the sum of the squares of the two legs is equal to the hypotenuse squared.

Let the length of the other leg of the triangle be 'x'

According to the information:

[tex]24^2 + x^2 = 26.7^2[/tex]

576 + [tex]x^{2}[/tex] = 712.89

[tex]x^{2}[/tex] = 712.89 - 576

[tex]x^{2}[/tex] = 136.89

x = [tex]\sqrt{136.89}[/tex]

x = 11.7

Hence, The length of the other leg of the triangle is 11.7 inches.

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The area expression as products is 7 * (8 + 6)

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

Area = 54 + 42

Express 54 as a product of 7 and 8

So, we have the following representation

Area = 7 * 8 + 42

Express 42 as a product of 7 and 6

So, we have the following representation

Area = 7 * 8 + 7 * 6

Factor out 7

This gives

Area = 7 * (8 + 6)

Hence, the expression using GCF is 7  * (8 + 6)

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Answer:

D

Step-by-step explanation:

multiply by 8 and add 5.

so,

we need to do this for every unit value and see, if the result is the same as the listed output value.

5 -> 5×8 + 5 = 45

6 -> 6×8 + 5 = 53

7 -> 7×8 + 5 = 61

8 - > 8×8 + 5 = 69

9 -> 9×8 + 5 = 77

10 -> 10×8 + 5 = 85

so, D is the correct answer.

Spanish is a Romance language of the Indo-European language family that emerged from the Iberian peninsula's colloquial Latin. It is now a worldwide language with around 500 million native speakers, primarily in the Americas and Spain. Twenty nations have Spanish as their official language.

These numbers in Spanish are:

1. 49: cuarenta y nueve

2. 97: noventa y siete

3. 113: ciento trece

4. 632: seiscientos treinta y dos

5. 1.781: mil setecientos ochenta y uno

6. 3.558: tres mil quinientos cincuenta y ocho

7. 1.006.015: un millon seis mil quince

8. 67.224.370: sesenta y siete millones doscientos veinte y cuatro mil trescientos setenta

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Answer:

49: cuarenta y nueve

2. 97: noventa y siete

3. 113: ciento trece

4. 632: seiscientos treinta y dos

5. 1.781: mil setecientos ochenta y uno

6. 3.558: tres mil quinientos cincuenta y ocho

7. 1.006.015: un millon seis mil quince

8. 67.224.370: sesenta y siete millones doscientos veinte y cuatro mil trescientos setenta

Step-by-step explanation:

Answer:

A and D

Step-by-step explanation:

so sorry im in school

x+y=4

 -y.  -y

x=4-y

4-y-y=2

4-2y=2

-4      -4

-2y= -2

/-2.   /-2

y=1

x+1=4

  -1 -1

x=3

so A and D is correct

Answer:

y = 1/4x - 4

Step-by-step explanation:

4x + y = 3

y = -4x + 3

Perpendicular slope = 1/4

y = 1/4x + b

-3 = 1/4(4) + b

-3 = 1 + b

b = -4

y = 1/4x - 4

The length of the line segment with endpoints P(2, 1, -4) and Q(-1, 5, 3) is 8.60 units

To find the length of a line segment with endpoints P(x1, y1, z1) and Q(x2, y2, z2) in three-dimensional space, we can use the distance formula:

length = √((x2 - x1)² + (y2 - y1)² + (z2 - z1)²)

Substituting the coordinates of P and Q into the formula, we get:

length = √((-1 - 2))²  + (5 - 1))²  + (3 - (-4)))² )

          = √((-3))²  + (4))²  + (7))² )

         = √(9 + 16 + 49)

         = √(74)

        = 8.60 units

Therefore, the length of the line segment is 8.60 units

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0.117 Or 11.7% chance of n should the player choose in order to maximize the probability of winning a prize.

The probability of precisely x successes on n further trials in an experiment with two potential outcomes is referred to as the binomial probability (commonly called a binomial experiment).

When a procedure is performed a certain number of times (for example, in a group of patients), the result for each patient can either be a success or a failure, the binomial distribution model enables us to calculate the probability of witnessing a defined number of "successes."

The probability of winning a prize remains the same for. n = 10 or n=20 or n = 100; the probabilities are the same.

Given that,

p = 0.5, So, q = 1 - 0.5 = 0.5.

If 70% of 'n' games are won then 30% of n games must be lost.

Let n = 10.

Therefore, P ( x = 3) = [tex]^{10}C_3p^7q^3[/tex]

or, P ( x = 3) = [tex]^{10}C_3(0.5)^7(0.5)^3[/tex]

or, P (x = 3) = 120×0.0078×0.125.

or, P (x = 3) = 0.117 Or 11.7% chance.

Now, Changing the value won't have any effect as all the 'n's are multiple of 10 and we'll have same probability.

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Answer:

  30°

Step-by-step explanation:

You want the angle of elevation to a point 2900 feet up that is 5800 feet distant on a straight line.

The sine of the angle is the ratio of the height to the straight-line distance.

  sin(θ) = h/d = 2900/5800 = 1/2

  θ = arcsin(1/2) = 30°

The angle of elevation is 30° from the base to the top.

Answer: When doing a problem like this I always draw an example so I can see it. If you do that you see a right triangle with the hypothenuse, 2500 feet, is the distance from the top to the base. The opposite side is 1250 feet. Then remember  sine= o/h, (opposite side over hypothenuse). So divide 1250/2500 and you get .5  Now take your calculator and use "inv" or sin-1 button to get the answer of the angle. x = 30

sinθ 1250/2500 = 1/2; θ = sin-1(1/2) = 30°

Step-by-step explanation:

Answer:

B=20

C = 40  

These are the answers

Santiago creates a playlist of Latin dance music. The playlist contains bachata, salsa, and mambo tracks, as shown in the table. Santiago puts the playlist on shuffle mode. What is the probability that the first track he hears is a salsa track?

Answer:8/20

Step-by-step explanation:i did the quiz and it is correct

Observing the provided figure and using the transformation rule of geometry, The required transformation to map figure H onto figure I is reflection along y=x axis.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

In a mirror line, reflection is a type of transformation that reverses the shape so that each point is at the same distance from the mirror line as its reflected point.

Figure H

Mapped onto figure I

The required transformation:

reflection along y=x.

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For 10 days that bag will last when Mr. Eder's buys 6 pound bag of dog food, using kg to pound conversion and simple basic arithmetic operation.

How to convert kg to pound ?

We know that 1 Kg = 2.20 pound.

The dog is to eat 1/4 * 2.20 = 0.55 pound food

Weight of bag brought by him = 6 pound

The basic operations are :

Addition : (+) To get sum of two or more values

e.g. a = 3, b = 5

Addition = 3+5

              = 8

Subtraction : (-) The result of subtraction is the “difference”

e.g. Subtraction of a and b = a-b

                                             = 3-5

                                            = -2.

Multiplication : (*) The result of multiplication is the “product”

e.g. Multiplication of a and b = 3*4

                                                = 12

Division : (/) The result of division is the “quotient”

e.g. Division of 4 and 2 is = 4/2

                                           = 2.

so, the number of days bag can be used = 6/0.55

                                                                     = 10.90

So, the bag can be used for complete 10 days.

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The correct option regarding whether the two functions are inverse functions is given as follows:

B. No, because the composition does not result in an answer of x.

Two functions are inverses of each other if the composition of these two function has a result of x.

From the image given at the end of the answer, the two functions in this problem are defined as follows:

Their composition is given as follows:

[tex](G \circ F)(x) = G(\sqrt{x} + 4)[/tex]

[tex](G \circ F)(x) = (\sqrt{x} + 4)^2 - 4[/tex]

[tex](G \circ F)(x) = x + 8\sqrt{x} + 16 - 4[/tex]

[tex](G \circ F)(x) = x + 8\sqrt{x} + 12[/tex]

The composition does not result in x, hence the two functions are not inverses and the correct statement is given by statement B.

The problem is given by the image shown at the end of the answer.

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The solution is

a) The compound interest for the second period is $ 2.01 and the amount after the second period is $ 404.01

b) The compound interest for the first period is $ 114.125 and the amount is $ 18,374.125

The compound interest for the second period is $ 114.83828125 and the amount after second period is $ 18,488.96

What is Compound Interest?

Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.

The formula for calculating Compound Interest is

A = P ( 1 + r/n )ⁿᵇ

where A = Final Amount

P = Principal

r = rate of interest

n = number of times interest is applied

b = number of time periods elapsed

Given data ,

a)

Let the principal be P = amount after first period =  $ 402

Now , the rate of interest r = 6 %

The compound interest is calculated by compounding monthly

Now , the interest for the second period = ( PRT / 100 x 12 )

Substituting the values in the equation , we get

The interest for the second period = ( 402 x 6 x 1 ) / 1200

The interest for the second period = $ 2.01

The amount after the second period = amount after first period +  interest for the second period

The amount after the second period = 402 + 2.01

The amount after the second period = $ 404.01

b)

Let the principal be P = $ 18260

The rate of interest r = 2.5 %

The compound interest is calculated by compounding quarterly

Now , the interest for the first period = ( PRT / 4 x 100 )

Substituting the values in the equation , we get

The interest for the first period = ( 18260 x 2.5 ) / 400

The interest for the first period = 45650 / 400

The interest for the first period = $ 114.125

The amount for the first period = 18260 + 114.125

The amount for the first period = $ 18,374.125

Now , the principal for the second period = interest + amount of first period

The principal for the second period = $ 18,374.125

The rate of interest = 2.5 %

The interest for the second period = ( PRT / 4 x 100 )

Substituting the values in the equation , we get

The interest for the second period = ( 18374.125 x 2.5 ) / 400

The interest for the second period = 45935.3125 / 400

The interest for the second period = $ 114.83828125

The amount for the second period = 18,374.125+ 114.84

The amount for the second period = $ 18,488.96

Hence , the amount and interest is calculated

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If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle. Explanation is given.

Lines that cross the angle under investigation are known as angle bisectors. To "bisect" is to split into two sections of equal size. Therefore, the bisected halves divide the considered angle in half.

According to the angle bisector theorem;

An angle bisector divides the opposing side of a triangle into two portions that are proportionate to the other two sides, according to the angle bisector theorem.

a point is equally far from both sides of an angle if it is on the angle's bisector.

According to the inverse of the angle bisector theorem, a point is on the angle's bisector if it is both in the interior of the angle and equally far from its sides.

The explanation with diagram is given in the image.

Therefore, If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.

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When she uses 5 bags of coffee every day at her café, half of a bag of coffee lasts for 10 days.

Multiplication is the inverse of division. If 3 groups of 4 add up to 12, 12 split into 3 equal groups adds up to 4 in each group in division. The basic purpose of splitting is to determine how many equal groups develop or how many people are in each group when distributing equally. Division is a basic operation that divides an integer. It's best to imagine of it as a group of things being distributed among a group of individuals, as in the preceding example.

Here,

number of bags needed in a day=5

number of days 1/2 bag last,

=5÷1/2

=10 days

Half of bag of coffee last for 10 days when she uses 5 bags of coffee every day in her café.

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Answer:

1/64

Step-by-step explanation:

1/8 x 1/8 = 1/64