Colette bought 1/4 of a pound of green grapes and 1/8 of a pound of red grapes. How much more did the green grapes weigh than the red grapes?

Maria's current age is 15 and Susy's current age is 5.

We have,

Let's denote Maria's current age as M and Susy's current age as S.

We can use the given information to set up a system of equations and solve for their ages.

According to the first statement, "When I have the age that you are, your age will be 2 times that I have," we can write the equation:

M + S = 2(M - S)

Expanding and simplifying:

M + S = 2M - 2S

S + 2S = 2M - M

3S = M

According to the second statement, "When I was 10 years old, you were the age that I am," we can write the equation:

M - 10 = S

Now we have a system of equations:

3S = M

M - 10 = S

To solve the system, we can substitute the value of M from the first equation into the second equation:

3S - 10 = S

Simplifying:

2S = 10

S = 5

Substituting the value of S back into the first equation:

3(5) = M

M = 15

Therefore,

Maria's current age is 15 and Susy's current age is 5.

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The complete question:

Maria tells Susy: "When I have the age that you are, your age will be 2 times that I have and you know that when I was 10 years old, you were the age that I am".

How much do the current ages of both?

Answer:

the second one

Step-by-step explanation:

We can see that the fence is made by a rectangle and a trapezoid

A1 is the area of the rectangle and A2 is the area of the trapezoid

Given:

The expression is:

\(p^3\cdot p^2\cdot p\)

To find:

The value of the given expression.

Solution:

We have,

\(p^3\cdot p^2\cdot p\)

According to the product property of exponents,

\(a^m\cdot a^n=a^{m+n}\)

Using the product property of exponents, we get

\(p^3\cdot p^2\cdot p=p^{3+2+1}\)

\(p^3\cdot p^2\cdot p=p^{6}\)

Therefore, the value of given expression is \(p^6\).

Answer:

0.75 or... 3/4 of a cup

Step-by-step explanation:

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Answer:

13.50 (12 servings)

Step-by-step explanation:

Step 1: Multiply the whole number by the denominator:

13 × 2 = 26

Step 2: Add the product you got in Step 1 to the numerator:

26 + 1 = 27

Step 3: Divide the sum from Step 2 by the denominator:

27 ÷ 2 = 13.5

That's it folks! The answer to 13 1/2 in decimal form is displayed below:

13 1/2 =

Answer: To complete the square, we need to add and subtract the square of half the coefficient of x:

x^2 - 4x = 2

x^2 - 4x + 4 = 2 + 4 (adding and subtracting 4)

(x - 2)^2 = 6

Now we take the square root of both sides:

x - 2 = ±√6

Adding 2 to both sides gives:

x = 2 ± √6

So the solutions are:

x = 2 + √6, 2 - √6

Step-by-step explanation:

Answer:

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Answer:

The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 30°. Find the height of the tower.

A Let tower be AB

Let point be C

Distance of point C from foot of tower = 30m Hence,

BC = 30m

Angle of elevation = 30°

So < ACB = 30°

Since tower is vertical,

< ABC = 90°

Answer:

u = 7

Step-by-step explanation:

Answer:

13.8

Step-by-step explanation:

Area of square = πr²

=22/7 × 4²

=50.2

Area of square = l²

=8²

= 64

Area of shape is 64 - 50.2 = 13.8

Answer:

The answer is 13.8

Step-by-step explanation:

Yes

Answer:

10 : ( 6 * 3 ) - 5

3 * ( 6 - 5 )

( 6 * 5 ) - 3

11 : Prt A : C, 4 + ( 8 + 6 ) ÷ 2

Prt B : 11 singers had solos

12 : 7 + 4 * 3 = 19

9 + ( 45 ÷ 9 ) = 14

34 - 8 + 7 = 33

13 : ( 15 * 2 ) + 6

14 : ( 42 - 6 ) ÷ 3

Kamal puts 12 books on each shelf.

Hope this helps!

Step-by-step explanation:

C : 4 + 14 ÷ 2 = 4 + 7 = 11

Yes, an acute triangle less than 90 degrees

what is acute triangle?

An acute angled triangle is one in which all of the angles are fewer than 90 degrees. One such illustration of an acute angled triangle is the one below.

Hence the triangle less than 90 degrees is acute angle

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Answer:

2.34 pounds

Step-by-step explanation:

21.06/9=2.34

Answer:

2.34 pounds

Step-by-step explanation:

answer is 21.06/9 = 2.34

Answer:

perimeter is the total length of all the sides. So 2x+2x+10 =4x+10=2x+5

Explanation:

I'm assuming you meant to write 1/5 instead of 1:5

Add up all the fractions

1/4 + 3/8 + 1/10 + 1/5

20/80 + 30/80 + 8/80 + 16/80

(20+30+8+16)/80

74/80

37/40

He spends 37/40 of his income on rent, foot, clothes, insurance and other items combined.

Subtract this from 1 to find the fraction of his income he saves

1 - 37/40

40/40 - 37/40

(40-37)/40

3/40

He saves 3/40 of his monthly income.

(3/40)*8480 = 636 dollars is the amount saved every month.

The perimeter of the trapezoid in this problem is given as follows:

A. 23.2.

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

The bases of the trapezoid in this problem are given as follows:

The lateral segments are given as follows:

Hence the perimeter is given as follows:

P = 6 + 10 + 2 x 3.6

P = 23.2 units.

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The option that is a representation that shows y as a function of x is the graph in option 2. The answer is B.

A function is any relation or table of values which may be represented in a graph that has only one possible y value that is assigned to each x-value.

The first option is not a function because x-value 0 has two corresponding y-values, 4 and 9.

In the third option, we also have two y-values, 5 and -5, that is assigned to one x-value, 0. So, it is not a function.

The graph in option 2 represents y as a function of x, because no two y-values is assigned to the same x-value.

The answer is: B.

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Answer:

~

Step-by-step explanation:

To make it easier to graph using a translation, we can rewrite the given equation as:

y - 5 = √√4x + 16

This is obtained by subtracting 5 from both sides of the equation.

The graph of the original equation y = √√4x+16 +5 can be obtained by taking the graph of y = √√4x + 16 and shifting it upwards by 5 units. The graph of y = √√4x + 16 is a square root function that has a vertical stretch of 2, a horizontal compression of 4, and a vertical translation of 16 units upwards. So the graph of the given equation y = √√4x+16 +5 will be the same as the graph of y = √√4x + 16, but shifted upwards by 5 units.

Answer:

21.3 m

Step-by-step explanation:

Para un rectangulo de lado L y ancho W, el area está dada por:

A = L*W

Veremos que la opción correcta es B: 1, 2 y 4.

En la imagen podemos ver que el largo del rectangulo es 2*y

Y el ancho del rectangulo es 2*x

Entonces, el area será:

A = (2*y)*(2*x)

Podemos ver que esto es la expresión 2, por lo que ya sabemos que esa es correcta.

Para encontrar las otras correctas, solo reescribimos lo que tenemos arriba:

A = 2*y*2*x = 2*(2*x*y) = 2*x*y + 2*x*y

Esto es lo que tenemos en la expresión 4.

A su vez, podemos separar uno de esos terminos como:

A = 2*x*y + 2*x*y = (x*y + x*y) + 2*x*y = x*y + x*y + 2*x*y

Esto es lo que tenemos en la expresión 1.

finalmente podemos ver que la opción correcta es B: 1, 2 y 4.

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Answer:

Exact Form:

x = 6 + 3 square root sign 10, 6 - 3 sqaure root sign 10

Decimal Form:

x = 15.48683298...-3.48683298 ...

Step-by-step explanation:

Answer:

x=13

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    (2*x+14)-((3*x+1))=0

1.1      Solve  :    -x+13 = 0

Subtract  13  from both sides of the equation :

                     -x = -13

Multiply both sides of the equation by (-1) :  x = 13

Answer:

x = -0.4

Step-by-step explanation:

We have the equation:

-9x + 0.4 = 4

First, the operation to move all the constants to the right side is subtraction since we would have to subtract 0.4 from each side, let's see this:

\(-9x+0.4=4\\-9x+0.4-0.4=4-0.4\\-9x=3.6\)

Now, we have all the constants on the right side of the equation.

Now, the operation we need to perform to isolate the variable is division (since the x has a -9 that is being multiplied by x) we need to do the opposite operation:

\(-9x=3.6\\\frac{-9x}{-9} =\frac{3.6}{-9} \\x=-0.4\)

Answer:

1.) Which operation must be performed to move all the constants to the right side of the equation?

✔ Subtract 0.4 (C)

2.) Then, which operation must be performed to isolate the variable?

✔ Divide by -9 on both sides.  (D)

3.) The solution to the equation is x =

✔ -0.4   (B)

Step-by-step explanation:

I hope this helps!! Have a wonderful day!! :))

The mean score of a random student (YY) is 574.5. the standard deviation of the random student's score (YY) is 8.

Given:

- Each correct question is worth 10 points.

- Every student receives an additional 555 bonus points.

Let's calculate the mean and standard deviation of YY:

Mean of YY:

The mean score, denoted as μY, can be calculated using the mean of XX (μX) and the scoring scheme:

μY = μX * 10 + 555

Substituting the value of μX from the given information:

μY = 1.95 * 10 + 555

μY = 19.5 + 555

μY = 574.5

Therefore, the mean score of a random student (YY) is 574.5.

Standard Deviation of YY:

The standard deviation of YY, denoted as σY, can be calculated using the standard deviation of XX (σX) and the scoring scheme:

σY = σX * 10

Substituting the value of σX from the given information:

σY = 0.8 * 10

σY = 8

Therefore, the standard deviation of the random student's score (YY) is 8.

Complete question: Mr. Gupta gave his students a quiz with three questions on it. Let X represent the number of questions

that a randomly chosen student answered correctly. Here is the probability distribution of X along with

summary statistics:

0

1

2

2.

3

X = # correct

P(X)

0.05

0.20

0.50

0.25

Mean: Hex = 1.95

Standard deviation: Ox 0.8

Mr. Gupta decides to score the tests by giving 10 points for each correct question. He also plans to give

every student 5 additional bonus points. Let Y represent a random student's score.

What are the mean and standard deviation of Y?

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For the midpoint, you have to add each individual X coordinate and Y coordinate, and divide them by 2.

So:

The midpoint will be in 1, - 1/2

Answer:

38.81 pounds

Step-by-step explanation:

Considering the definition of right rectangular prism and its volume,  the total weight of the contents is 38.81 pounds.

Right rectangular prism

A right rectangular prism (or cuboid) is a polyhedron whose surface is formed by two equal and parallel rectangles called bases and by four lateral faces that are also parallel rectangles and equal two to two.

Volume of right rectangular prism

To calculate the volume of the rectangular prism, it is necessary to find the product of its dimensions, or of the three edges that converge at a certain vertex.

That is, to calculate the volume of a rectangular prism, multiply its 3 dimensions: length×width×height.

Volume of the container

In this case, you know that:

the dimensions of the container built are 7.5 ft by 11.5 ft by 3 ft.

the container is entirely full and, on average, its contents weigh 0.15 pounds per cubic foot.

So, the volume of the container is calculated as:

7.5 ft× 11.5 ft× 3 ft= 258.75 ft³

Then, the total weight of the contents is calculated as:

258.75 ft³×  0.15 pounds per cubic foot= 38.8125 pounds≅ 38.81 pounds

Finally, the total weight of the contents is 38.81 pounds.

Using the confidence interval interpretation, it is found that you would expect that there is a 95% probability of the confidence interval containing the population mean.

It means that we are x% confident that the population parameter(mean/proportion/standard deviation) is between a and b.

Hence, in this problem, the 95% confidence interval means that there is a 95% probability of the confidence interval containing the population mean.

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