what is the answer and how do you get the answer​

The number of cup of lemon juice is 105 cups and number of cup of apple juice is 50 cups.

A system of equations is a set or collection of equations that you deal with all together at once. For a system to have a unique solution, the number of equations must equal the number of unknowns.

For the given situation,

Peter sold a cup of lemon juice = $1.25

Peter sold a cup of apple juice =  $2.50

Total number of cups sold = 155 cups

Total amount = $256

Let number of cup of lemon juice be x and

let number of cup of apple juice be y

The equations for the above statements are

[tex]x + y = 155 ------- (1)\\1.25x +2.50y = 256 ------- (2)[/tex]

From equation 1,

⇒ [tex]x=155-y[/tex]

Now substitute x in equation 2,

⇒ [tex]1.25(155-y)+2.50y=256[/tex]

⇒ [tex]193.75-1.25y+2.50y=256[/tex]

⇒ [tex]1.25y=256-193.75[/tex]

⇒ [tex]1.25y=62.25\\[/tex]

⇒ [tex]y=\frac{62.25}{1.25}[/tex]

⇒ [tex]y=49.8[/tex] ≈ [tex]50[/tex]

Now substitute y in equation 1,

⇒ [tex]x=155-50[/tex]

⇒ [tex]x=105[/tex]

Hence we can conclude that the number of cup of lemon juice is 105 cups and number of cup of apple juice is 50 cups.

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Answer:

Step-by-step explanation:

Prime factorize 8 and 64

8 = 2* 2 * 2 = 2³

64 = 2*2*2 *2*2*2 = 2⁶

2*8*64 = 2* 2³ *2⁶ = 2¹⁺³⁺⁶ = 2¹⁰

In exponent multiplication, if base are same, then add the exponents.

Answer:

1/2×d1×d2

=1/2× (4+4)(6+3)

=36

Answer:

see explanation

Step-by-step explanation:

To verify cos²A + sin²A = 1 with A = 90° , then

cos²90° + sin²90°

= (0)² + (1)²

= 0 + 1

= 1

Answer:

The lengths of the other sides would be 10, as well.

Step-by-step explanation:

Since we already know two of the three angles, we can subtract to find the other angle. The interior angles of a triangle will always add up to 180°. We have 60° and 60°, giving us 120°. 180 - 120 is equal to 60°, so that's the missing angle. Because all of the angles are the same, this is an equilateral triangle, which means the sides also have to be the same length. If one of the sides is 10, all of the sides are 10.

The triangle with sides 10 , 10 and 10 and all angles at 60° is an equilateral triangle

An equilateral triangle is a triangle in which all three sides have the same length.

Let the triangle be ΔABC , and

∠A = ∠B = ∠C = 60° and AB = BC = CA

Given data ,

Let the triangle be represented as ΔABC

Let the side length of the triangle be AB = 10

Now , the measure of ∠ABC = 60°

And , the measure of ∠BAC = 60°

So , the total sum of all the angles in a triangle = 180°

And , the measure of ∠ACB = 180° - ( 60° + 60° ) = 60°

Therefore , all the angles of the triangle are 60°

So , it is an equilateral triangle

And , the measure of side lengths of the triangle is 10

Therefore , AB = BC = CA = 10

Hence , it is an equilateral triangle

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Answer:  no

Step-by-step explanationn.  .......................................................w:eorkeok,feoferkeorkoe

Answer:

b

Step-by-step explanation:

[tex]\frac{x^4}{x^7} =x^4 \times x^{-7} =x^{4-7} =x^{-3}[/tex]

Answer:

5:15 simplified as 1:3

Step-by-step explanation:

Given:

30-hour review course average a score of 620 on that exam.

70-hour review course average a score of 749.

To find:

The linear equation which fits this data, and use this equation to predict an average score for persons taking a 57-hour review course.

Solution:

Let x be the number of hours of review course and y be the average score on that exam.

30-hour review course average a score of 620 on that exam. So, the linear function passes through the point (30,620).

70-hour review course average a score of 749. So, the linear function passes through the point (70,749).

The linear function passes through the points (30,620) and (70,749). So, the linear equation is:

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

[tex]y-620=\dfrac{749-620}{70-30}(x-30)[/tex]

[tex]y-620=\dfrac{129}{40}(x-30)[/tex]

[tex]y-620=\dfrac{129}{40}(x)-\dfrac{129}{40}(30)[/tex]

[tex]y-620=\dfrac{129}{40}(x)-\dfrac{387}{4}[/tex]

Adding 620 on both sides, we get

[tex]y=\dfrac{129}{40}x-\dfrac{387}{4}+620[/tex]

[tex]y=\dfrac{129}{40}x+\dfrac{2480-387}{4}[/tex]

[tex]y=\dfrac{129}{40}x+\dfrac{2093}{4}[/tex]

We need to find the y-value for [tex]x=57[/tex].

[tex]y=\dfrac{129}{40}(57)+\dfrac{2093}{4}[/tex]

[tex]y=183.825+523.25[/tex]

[tex]y=707.075[/tex]

[tex]y\approx 707.1[/tex]

Therefore, the required linear equation for the given situation is [tex]y=\dfrac{129}{40}x+\dfrac{2093}{4}[/tex] and the average score for persons taking a 57-hour review course is 707.1.

Answer:

Yes, the data provides convincing evidence that men and women have different average BF%s

Step-by-step explanation:

The given parameters are;

The number of the subjects ages 20 to 80 = 13,601

The body fat percentage, BF%, for the 6,580 men, [tex]\overline x_1[/tex] = 23.9

The body fat percentage, BF%, for the 7,021 women, [tex]\overline x_2[/tex] = 35.0

The standard error for the difference between the average men and women = 0.144

The null hypothesis, H₀; [tex]\overline x_1[/tex] = [tex]\overline x_2[/tex]

The alternative hypothesis, Hₐ; [tex]\overline x_1[/tex] ≠ [tex]\overline x_2[/tex]

The test statistic = (35.0 - 23.9)/(0.114) = 97.368

Therefore, given that the z-test is larger than the critical-z, we reject the null hypothesis, H₀, therefore, there is convincing statistical evidence to suggest that men and women have different body average BF%

Answer:

The expressions that give the value of y are A - 3B and (1/3)A - B

The solution is (27/13, -60/13)

Step-by-step explanation:

We can see both equation A and equation B.

Equation A: 2x + (1/4)y = 3

Equation B: (2/3)x - y = 6

To find the value of y, we have to solve both equations A and equation B simultaneously. This is done by multiplying equation B by 3 and subtracting from equation A (A - 3B) to get:

(13/4)y = -15

y = -60/13

you can also get y by dividing equation A by 3 and subtracting equation B (1/3A - B)

Put y = -60/13 in equation A to get x:

2x + (1/4)(-60/13) = 3

2x = 3 + 15/13

2x = 54/13

x = 27/13

The solution is (27/13, -60/13)

Answer:

{0,-3,-9,5,7}

Step-by-step explanation:

range = all y values

function =(x,y)

so all the second values are ranges

Answer:

1452628383763637£838

Answer:

B

Step-by-step explanation:

Step-by-step explanation:

here's the answer to your question

Answer:

p = 0

Step-by-step explanation:

1 - 4p - 2p = 1 - 5p

-6p + 1 = -5p + 1

-p + 1 = 1

-p = 0

p = 0

Answer:

50.265

Step-by-step explanation:

Area is radius square times pi. Radius is half of diameter .Diameter is 8 inches. Radius is 4 inches. 4 squared is 16. 16 times pi is 50.265

Answer:

In order:

Distributive Property

Subtraction Property of Equality

Division Property of Equality or Reciprocal Property

Step-by-step explanation:

Answer:

(B)

Step-by-step explanation:

Can't explain lol, but that's the answer

Answer:

C

Step-by-step explanation:

[tex]4(x + 3) \leqslant 44 \\ \\ 4x + 12 \leqslant 44 \\ 4x \leqslant 44 - 12 \\ 4x \leqslant 32 \\ 4x \div 4 \leqslant 32 \div 4 \\ x \leqslant 8[/tex]

Answer:

HCF = 6

Step-by-step explanation:

Listing the factors of each number

18 is 1, 2, 3, 6, 9, 18

30 is 1, 2, 3, 5, 6, 10, 15, 30

36 is 1, 2, 3, 4, 6, 9, 12, 18, 36

common factors are 1, 2, 3, 6

the HCF is 6

Answer:

A: The y-intercept of f(x) is equal to the x-intercept of g(x)

Step-by-step explanation:

From the equation of f(x) given, we have;

f(x) = -4(1.09)^(x)

Now,the y-Intercept will be the point where x = 0.

Thus;

f(0) = -4(1.09)^(0)

f(0) = -4

Now,from the table given for g(x), we can see that at x = 0,g(x) = -4.

Thus,it means that the y-intercept of f(x) is equal to the x-intercept of g(x)

five I think I am not sure

Answer:

A.

Step-by-step explanation:

A.-6r+6

Answer:

80°

Step-by-step explanation:

Triangle ABC and CYZ are similar so the angles would also be same

Answer:

54°

Step-by-step explanation:

Here :-

Measure of 6 :-

Answer:

m<6 = m<2 = 54º

Step-by-step explanation:

13x + 9 + 5x + 9 = 180

18x + 18 = 180

18x = 180 - 18

18x = 162

x = 162 / 18

x = 9

13x + 9

13(9) + 9

126

180 - 126

54

m<6 = m<2 = 54º

Answer:

Step-by-step explanation:

(cos 4a*cos 2a+sin 4a*sin 2a)/sin 4a

=[cos (4a-2a)]/sin 4a

=(cos 2a)/sin 4a

=(cos 2a) /(2 sin 2a cos 2a)

=1/(2 sin 2a)

=1/2 csc 2a

Answer:

4/9 of an hour (26.666 minutes)

Step-by-step explanation:

4 * x * 40/60 = 1

x * 160/60 = 1

x=60/160 = 6/16 = 3/8 (this is the rate for one worker)

~~~~~~~~~~~~~~~~

6 * (3/8) * x = 1

x = 4/9

Step-by-step explanation:

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