marisa made a fruit salad . she used 1 cup of green grapes and 3 red grapes. she used twice as many cups of blueberries as cups of grapes
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The similar triangles for this problem are given as follows:

RST and VUT.

Then the measure VT is given as follows:

VT = 5.4 units.

Similar triangles are triangles that share these two features listed as follows:

Hence the similar triangles for this problem are given as follows:

RST and VUT.

The proportional relationship for the side lengths is given as follows:

6/14 = (x + 2)/(4x - 1).

Applying cross multiplication, the value of x is obtained as follows:

14(x + 2) = 6(4x - 1)

14x + 28 = 24x - 6

10x = 3.4

x = 3.4.

Then the length VT is given as follows:

VT = 3.4 + 2

VT = 5.4 units.

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Answer:

3/8 or 3:8

Step-by-step explanation:

pink : not pink

6 : 16

Think of it as a fraction. Simplify it in the same way.

6/16 simplifies to 3/8

So the pink:notpink ratio is 3/8 or 3:8

Answer:

1/2 cup of sugar

Step-by-step explanation:

She needs to multiply 1/8 cup of sugar by 4 to make the entire recipe since 18 cup of sugar is only good for a fourth of the recipe.

So, we are writing a function. c(x) is the manufacturing costs, and x is the amount of bikes manufactured. The y-intercept is 1908 because when no bikes are manufactured it still costs 1908 to run the factory. The slope is 75 because it costs $75 to create a bike. So, y = mx + b, where m is the slope and b is the y-intercept is:

c(x) = 75x + 1908

The absolute value function for this problem is given as follows:

y = |x - 4| - 6.

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

The coordinates of the vertex of the function are given as follows:

(4, -6).

The slope of 1 determines the leading coefficient a as follows:

a = 1.

Hence the function is given as follows:

y = |x - 4| - 6.

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Answer:

4.28%

Step-by-step explanation:

We Know

Last year you earned $72,400

This year you earned $75,500

What was the rate of change in your earnings since last year?

We Take

(75,500 ÷ 72,400) x 100 ≈ 104.28%

Then We Take

104.28 - 100 = 4.28%

So, the earning increased by about 4.28%.

the length of side a is 91 ft (rounded to the nearest whole foot) and the length of side b is 132 ft (rounded to the nearest whole foot). The area of the triangle is approximately 6007 sq ft.

Given: The hypotenuse of the right triangle,

c = 159 ft; angle A = 34°

We know that, in a right-angled triangle:

\($$\sin\theta=\frac{\text{opposite}}\)

\({\text{hypotenuse}}$$$$\cos\theta=\frac{\text{adjacent}}\)

\({\text{hypotenuse}}$$\)

We know the value of the hypotenuse and angle A. Using trigonometric ratios, we can find the length of sides in the right triangle.We will use the following formulas:

\($$\sin\theta=\frac{\text{opposite}}\)

\({\text{hypotenuse}}$$$$\cos\theta=\frac{\text{adjacent}}\)

\({\text{hypotenuse}}$$$$\tan\theta=\frac{\text{opposite}}\)

\({\text{adjacent}}$$\) Length of side a is:

\($$\begin{aligned} \sin A &=\frac{a}{c}\\ a &=c \sin A\\ &= 159\sin 34°\\ &= 91.4 \text{ ft} \end{aligned}$$Length of side b is:$$\begin{aligned} \cos A &=\frac{b}{c}\\ b &=c \cos A\\ &= 159\cos 34°\\ &= 131.5 \text{ ft} \end{aligned}$$\)

Now, we have the values of all sides of the right triangle. We can calculate the area of the triangle by using the formula for the area of a right triangle:

\($$\text{Area} = \frac{1}{2}ab$$\)

Putting the values of a and b:

\($$\begin{aligned} \text{Area} &=\frac{1}{2}ab\\ &=\frac{1}{2}(91.4)(131.5)\\ &= 6006.55 \approx 6007 \text{ sq ft}\end{aligned}$$\)

Therefore, the length of side a is 91 ft (rounded to the nearest whole foot) and the length of side b is 132 ft (rounded to the nearest whole foot). The area of the triangle is approximately 6007 sq ft.

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Answer:

1) 5m

2) 0.25tan

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

For the second step, \(\angle T\cong\angle R\) by Alternate Interior Angles. The rest of the steps appear to be correct.

Answer:

h = 14 units

Step-by-step explanation:

area of parallelogram = bh

plug everything in: 84 = (6)h

h = 84/6 = 14

Answer:

6 games

Step-by-step explanation:

Before the last game, Jonas had 88 points

In the last game, Jonas scored 23 points

Total points scored in the season = points before last game + point on last game

Total points of the season = 88 + 23

Total points of the season = 111 Points

Further ahead, we're told Jonas had a season average of 18.5 points. This means that he scored an average of 18.5 points in all the games in played in the season, each. We're then required to find the number of games he played.

To find the number of games he played, we divide the total number of points he scored in a season by the average points he scored in a game. Something like this

Number of games played = total points scored / average points scored

Number of games played = 111 / 18.5

Number of games played = 6.

Therefore, Jonas played 6 games during the season

For the unit rate, you are looking for how much one unit of something costs. Looking at the table, you'll see that 3 bottles of fragrance A costs $78. What you want to figure out is how much one bottle costs.

You can do this by taking the price and dividing it by how many there are.

78 ÷ 3 = $26

156 ÷ 6 = $26

234 ÷ 9 = $26

You can see that each bottle of fragrance A costs $26.

Now looking at the graph, you'll see that the line only lines up perfectly at 2 points: (1, 24) and (2, 48). This tells us that for each bottle of fragrance B, it costs $24.

Comparing the two, fragrance A will have the greatest unit rate.

The true statement is (c) that He could draw a diagram of a rectangle with dimensions x – 1 and x – 6 and then show the area is equivalent to the sum of x^2, –x, –6x, and 6.

factorization is the method of breaking a number into smaller numbers that multiplied together will give that original form.

The expression is given as:

\(x^{2} -7x + 6\)

Expand;

\(x^{2} -6x - x +6\)

Factorize;

x(x-1) - 6 (x- 1)

Factor out x - 6

(x - 6) (x- 1)

This means that the factors of \(x^{2} -7x + 6\) are x - 1 and x - 6

Hence, the true statement is (c) that He could draw a diagram of a rectangle with dimensions x – 1 and x – 6 and then show the area is equivalent to the sum of x^2, –x, –6x, and 6.

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Answer: Answer is C

Step-by-step explanation:

Answer:

let's call the entire length of the foot race we are looking for:  d

for distance.

We can then rewrite this problem as:

One-third of  d

is 5 miles. What is  d .

When dealing with fractions in this way the word "of" means to multiply. So we can write this problem in algebraic form as:

1 3 × d = 5

We can multiply each side of the equation by  

3  to solve for  d

while keeping the equation balanced:

3 × 1 3 × d = 3 × 5

3 3 × d = 15  1 × d = 15 d = 15

The length of the race is 15 miles.

Step-by-step explanation:

hope this helps

Answer:

40,779

Step-by-step explanation:

i took the k12 test

Answer:

1.43 ounces

Step-by-step explanation:

384 / 60 = 6.4

7.83 - 6.4 = 1.43

The solution of the system is then given by:

x = t[1 -1 1 0.5 0.5 0.33] + s[0 -2 1 1 -2 1]

This is the general solution of the system in the form of a sum of scalar multiples of fixed column vectors.

The system of linear equations can be written in matrix form as:

[1 0 1 2 1 3 | 1]

[2 1 2 4 0 10| 5]

[3 1 3 6 6 15| 8]

where the augmented matrix is [A | B].

To solve the system using the method of specifying appropriate free variables, we first convert the coefficient matrix into reduced row echelon form using Gaussian elimination.

In reduced row echelon form, the first non-zero element of each row (known as the leading entry) is 1, and the leading entries of lower rows are to the right of the leading entries of higher rows.

Applying Gaussian elimination to the coefficient matrix, we get:

[1 0 1 2 1 3 | 1]

[0 1 0 2 -2 7| 0]

[0 0 0 0 0 0| 0]

We can see that there are two non-zero rows, indicating that the system has two independent equations.

We can choose two of the variables to be free variables, and express the other variables in terms of the free ones.

Let's choose x1 and x3 as the free variables.

We can find x2 as follows:

x2 = -x1 - 2x3 + 7

And we can find x4, x5 and x6 as follows:

x4 = (1 - x1 - x3)/2

x5 = 1 - x1 - 2x3 + 2x4

x6 = (1 - x1 - x3 - 2x4)/3

So the general solution of the system can be expressed as a sum of scalar multiples of fixed column vectors:

x1 = t

x2 = -t - 2s + 7

x3 = s

x4 = (1 - t - s)/2

x5 = 1 - t - 2s + (1 - t - s)/2

x6 = (1 - t - s)/3

where t and s are scalars.

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Answer:

Yes. Her sample is unrepresentative of the population in her community.

Step-by-step explanation:

a) Data and Calculations:

Population                Study  Census %     Representative       Over/Under

                               Sample                           Sample              Representation

Whites                       300        48%           288 (48% * 600)         12

African Americans      80         12%             72 (12% * 600)           8

Latinos                       100         18%           108 (18% * 600)           (8)

Asians                         40          9%             54 (9% * 600)           (14)

Others                        80         13%             78 (13% * 600)            2

Total                         600      100%          600                                0

b) There is selection bias in her sample. A representative sample of 600 is the subset of a population that seeks to accurately reflect the characteristics of the larger group.   When the sample for each category does not accurately represent the characteristics or attributes of the population categories, then it is unrepresentative.

Sampling is the collection of randomly chosen data from the entire population to come to an end conclusion about the variable to be determined or known.

Yes, the sample is unrepresentative of the entire population.

The reason for the sample being unrepresentative of the entire population in her community is that the selected sample is deviating a lot from the population count.

As per the computation, there is selection bias in her sample. This is because the representative sample is 600 that represents the entire population and reflects the characteristics of the larger group.

The sample becomes unrepresentative when the sample chosen does not accurately represent the true attributes of the population.

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Solving for 'x' in the equation gives x = d/ cr

The subject of formula can be defined as the variable written in terms of other variables in a given expression or equation.

It is  known as the variable that is worked out in an equation or expression.

It is also described as the letter written on its own on one side of the equality sign.

Example:

The variables 'x' in the equation x = b + z is the subject of formula as it is the letter written on its own on one side of the equality sign.

Given the equation;

xc = d/r ,

To make 'x' the subject of formula, we need to divide both sides by the coefficient of x which is c

We have;

xc/c = d/ r/ c

Divide through

x = d/ cr

Thus, solving for 'x' in the equation gives x = d/ cr

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Answer:

1the answer for this is easy it is 4.4

Answer:

If we used the quadratic formula to solve the equation we can say:

-b = -5

b² - 4ac = 13

2a = 2

Solving the first and last equations we get b = 5 and a = 1. Substituting these values into the second equation we get:

25 - 4c = 13

Solving this we get c = 3 so the answer is x² + 5x + 3.

0.9758 is the decay factor of the model

Given that:

The value of the U.S. dollar over time v(t) can be modeled by the following formula:

v(t) = 1.36(0.9758)^t , where t is the number of years since 2000

The form of the exponential decay models is f(t) = ab^t

where,

a is the initial value, b is the decay factor and t is the time

Comparing  f(t) = ab^t with v(t) = 1.36(0.9758)^t :

a = 1.36

b = 0.9758

Therefore, the decay factor is 0.9758

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The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Answer:

3, 245 is less than 8, 407

Step-by-step explanation:

3, 245 < 8, 407

40 dollars per day imk if I'm wrong

The vertical displacement is of 2 units down, the correct option is B.

Remember that for a function f(x), a vertical displacement of N units is written in general form as:

g(x) = f(x) + N

If N > 0, the translation is upwards.

if N < 0, the translation is downwards.

Here we assume that we start with the parent cosine function:

y = cos(x)

And the transformed function is:

y = -2 - cos(x - π)

So we have some transformations, but the vertical translation is of 2 units down. So the correct option is B.

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Answer:

4×(x+8)=25.

use the 4 to multiply the numbers in the bracket.

which is 4x+32=25.

then collect like terms which is...

4x=25-32...

4x=-7.

x=-7/4= -1.75 or -1 whole number 3/4.

The factors of the polynomial function f(x) must be x, x + 6  and x + 3

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

The graph (see attachment)

On the graph, we have the zeros of the function to be

x = -6, x = -3 and x = 0

Set the equations to 0

So, we have the following representation

x + 6 = 0, x + 3 = 0 and x = 0

This means that the factors are

x, x + 6  and x + 3

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The 60% of the 60 equals 36 after expressed in the fraction of 100, so the answer is 60%.

It is defined as the ratio of two numbers expressed in the fraction of 100 parts. It is the measure to compare two data, the % sign is used to express the percentage.

Let's suppose the x% of 60 equals 36

So,

x% of 60 = 36

60x/100 = 36

6x/10 = 36

x/10 = 6

x = 60%

Thus, the 60% of the 60 equals 36 after expressed in the fraction of 100, so the answer is 60%.

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Answer:

30 hour

Step-by-step explanation:

girls time

12 20 hour

8 x(let)

now,

12/8=x/20

12×20=8×x

240=8x

x=240/8

x=30,,