The seventeen students on the Math Team want to raise $500 to buy practice books. They have already raised $234.63. If each student raises the same amount, how much more money must each student raise?

The fraction that Brian can iron in a minute is 5/81.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. It should be noted that in a simple fraction, the numerator as well as the denominator are both integers. On the other hand, a fraction appears in the numerator or the denominator of a complex fraction.

Here, set up a proportion (shirt ironed/minutes = shirt ironed/minutes). I'll convert 3 3/5 to an improper fraction as well to set it up.

(2/9) / (18/5) = x / 1

Cross multiply

2/9 = (18/5)x

Multiply both sides by 5/81 to solve for x.

x = 10/162

In this case, it should be noted that we can reduce 10/162 to the lowest term. This will be 5/81

The clothes that Brian can iron will be 5/81.

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Complete question

Brian irons 2/9 of his shirt in 3 3/5 minutes. If Brian irons at a constant speed how much of his shirt does he iron in a minute

Depends on the specific data and coefficients of the quadratic regression model used.

The coefficient of determination, denoted as R-squared (R2), is used to calculate the percentage of variation in productivity explained by the quadratic regression model. R-squared is a statistical measure that represents the proportion of the variance explained by an independent variable or variables in a regression model for a dependent variable.

R-squared is calculated by comparing the total sum of squares (TSS) and the residual sum of squares (RSS):

TSS = Σ(y - ȳ)^2

RSS = (y - - x - b*x2)2.

where y is the actual productivity value, is the mean of the productivity values, x is the independent variable, and b are the quadratic regression model coefficients.

R-squared can be calculated using the formula:

R2 = 1 minus (RSS/TSS)

We can then convert R-squared to a percentage to get the percentage of variation in productivity explained by the quadratic regression model.

As a result, the answer to this question is dependent on the specific data and quadratic regression model coefficients used.

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To find the equation that Stacey can use to determine the number of customers she needs to make exactly $25, we need to break down the information given. Stacey earns $15 each week, which is a fixed amount. Additionally, she earns $0.50 for each customer on her paper route, so the amount she earns from the number of customers can vary.

To represent this situation algebraically, we can use the equation:

$15 + $0.50x = $25

In this equation, "$15" represents the fixed amount Stacey earns each week, "$0.50" represents the additional amount she earns per customer, and "x" represents the number of customers she needs to make exactly $25.

Simplifying the equation, we have:

$0.50x = $25 - $15
$0.50x = $10

To isolate x, we divide both sides of the equation by $0.50:

x = $10 ÷ $0.50
x = 20

Therefore, Stacey needs 20 customers to make exactly $25 each week.

In conclusion, the equation Stacey can use to find x, the number of customers she needs to make exactly $25, is $15 + $0.50x = $25. By solving this equation, we find that she needs 20 customers.

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Answer: (-16)-(-20)= 4

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The big triangle and small triangles are similar so their corresponding sides are in proportion.

x/15 = 15/9

x= 15*15/9

x=25

Answer:

170.25

Step-by-step explanation:

Answer:

t = 60

Step-by-step explanation:

Using the rule of exponents

\((a^m)^{n}\) = \(a^{mn}\) , then

\((j^{-12}) ^{-5}\)

= \(j^{(-12(-5))}\)

= \(j^{60}\)

Then t = 60

Answer:

Step-by-step explanation:

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The actual distance between the basketball court and the pool is 37.5 feet

Distance refers to the amount of space between two objects or points. It is a measure of how far apart two things are from each other.

The scale of the model is 3 inches = 5 feet. This means that every 3 inches on the model represents 5 feet in actual size. We are given that the distance between the basketball court and the pool on the model is 22.5 inches. To find the actual distance between these areas, we need to use the scale.

We can start by setting up a proportion using the scale. We know that 3 inches on the model represents 5 feet in actual size. Therefore, we can say that:

3 inches / 5 feet = 22.5 inches / x

We are trying to solve for x, which represents the actual distance between the basketball court and the pool. To solve for x, we can cross-multiply and simplify the equation:

3 inches x x = 5 feet x 22.5 inches

3x = 112.5

x = 37.5 feet

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Complete Question:

The scale of the model of a recreational facility is 3 inches = 5 feet. If the basketball court is 22.5 inches from the pool in the model, what is the actual distance between the basketball court and the pool?

Binomial distribution with n=50, p=0.5: We can use normal approximation with mean = np = 25 and standard deviation = sqrt(npq) = 2.5.

To use normal approximation for a binomial distribution, the following conditions should be met:

The sample size n is large (n > 30)

The probability of success p is not too close to 0 or 1

Binomial distribution with n=100, p=0.1: We can use normal approximation with mean = np = 10 and standard deviation = sqrt(npq) = 3.

Binomial distribution with n=100, p=0.5: We can use normal approximation with mean = np = 50 and standard deviation = sqrt(npq) = 5.

Binomial distribution with n=50, p=0.1: Since np = 5 < 10, normal approximation is not appropriate.

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The quarts of water needed for 9 quarts of grape juice is 18 quarts of water .

The amount of grape juice needed for 15 / 4 quarts of water is 1 7/8.

The amount of water needed for 100 quarts is  66 2/3 quarts.

The amount of grape juice needed for 100 quarts is 33 1/3 quarts.

The first step is to determine the ratio between the ingredients needed for sparking grape juice.

Ratio of sparking water to grape juice - 1 1/2 : 2/4

When expressed in its simplest form, the ratio becomes - 1 1/2 : 1.2

This means that there are twice the amount of water is needed for 1 quart of grape juice.

Quarts of sparking water needed for 9 quarts of grape juice = 9 x 2 = 18 quarts of sparking water

Grape juice needed for 15/4 quarts of sparking water = 15 / 4 ÷ 2

15 / 4 x 1/2 = 15 / 8 = 1 7/8

Let a represent the quarts of grape juice that would be used to make 100 quarts of punch.

Let a represent the quarts of sparking water that would be used to make 100 quarts of punch.

a + 2a = 100

3a = 100

a = 100 / 3

a = 33 1/3

Quarts of sparking water needed = 100 - 331/3 = 66 2/3 quarts

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The number of shares of each girl will be R200, R300, and R700.

Given that:

Ratio, 2:3:7

When two objects are equal, a statement is said to be proportional.

The equation for the share of 3 girls is given as,

2x + 3x + 7x = 1200

Simplify the equation, then we have

2x + 3x + 7x = 1200

12x = 1200

x = 1200 / 12

x = 100

The shares of each girl are calculated as,

2x = 2 × 100 = 200

3x = 3 × 100 = 300

7x = 7 × 100 = 700

Thus, the number of shares of each girl will be R200, R300, and R700.

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(g ◦ f)(x) = 49x^2 - 70x + 26.

To find (f ◦ g)(x), we need to substitute g(x) into f(x).

First, let's find g(x):

g(x) = x^2 - 4x + 5

Now, substitute g(x) into f(x):

f(g(x)) = 7(g(x)) - 3
        = 7(x^2 - 4x + 5) - 3
        = 7x^2 - 28x + 35 - 3
        = 7x^2 - 28x + 32

So, (f ◦ g)(x) = 7x^2 - 28x + 32.

To find (g ◦ f)(x), we need to substitute f(x) into g(x).

First, let's find f(x):

f(x) = 7x - 3

Now, substitute f(x) into g(x):

g(f(x)) = (f(x))^2 - 4(f(x)) + 5
        = (7x - 3)^2 - 4(7x - 3) + 5
        = (49x^2 - 42x + 9) - (28x - 12) + 5
        = 49x^2 - 42x + 9 - 28x + 12 + 5
        = 49x^2 - 70x + 26

So, (g ◦ f)(x) = 49x^2 - 70x + 26.

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Answer:

check: 50+160+130+20 = 360

50:160 = 5 : 16

Step-by-step explanation:et the smaller of the unknown angles be 5x and the larger of the two be 16x

so 130+20+5x+16x = 360

21x = 210

x = 10

so the two missing angles are 50° and 160°

check: 50+160+130+20 = 360

50:160 = 5 : 16

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &155000\\ r=rate\to 25\%\to \frac{25}{100}\dotfill &0.25\\ t=hours\dotfill &6\\ \end{cases} \\\\\\ A=155000(1 + 0.25)^{6}\implies A=155000(1.25)^6\implies A\approx 591278\)

The volume of the solid is π/3.

The regions bounded by the curve x = y - y^3 in the first quadrant and the y-axis are to be revolved around the x-axis and the line y = 1, respectively.

The solids generated by revolving the region in the first quadrant bounded by the curve x=y-y3 and the y-axis about the x-axis are obtained by using disk method.

Therefore, the volume of the solid is:

V = ∫[a, b] π(R^2 - r^2)dx Where,R = radius of outer curve = yandr = radius of inner curve = 0a = 0andb = 1∫[a, b] π(R^2 - r^2)dx= π∫[0, 1] (y)^2 - (0)^2 dy= π∫[0, 1] y^2 dy= π [y³/3] [0, 1]= π/3

The volume of the solid is π/3.The solids generated by revolving the region in the first quadrant bounded by the curve x=y-y3 and the y-axis about the line y = 1 can be obtained by using the washer method.

Therefore, the volume of the solid is:

V = ∫[a, b] π(R^2 - r^2)dx Where,R = radius of outer curve = y - 1andr = radius of inner curve = 0a = 0andb = 1∫[a, b] π(R^2 - r^2)dx= π∫[0, 1] (y - 1)^2 - (0)^2 dy= π∫[0, 1] y^2 - 2y + 1 dy= π [y³/3 - y² + y] [0, 1]= π/3

The volume of the solid is π/3.

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The simplification of the expression −10x - 7x⁴ in the reduced factor form is equal to -1x ( 10 + 7x³ ).

The expression is equal to,

−10x - 7x⁴

From both the terms of the given expression '-1' is the common factor we get,

−10x - 7x⁴

= ( -1 ) ( 10x + 7x⁴ )

Now take variable 'x' common from both the terms of the expressions we get,

= ( -1 × x  ) ( 10 + 7x³ )

= -1x ( 10 + 7x³ )

Now nothing is act as common factor in the given expression we have,

Therefore, the simplified factor of the expression −10x - 7x⁴ is equal to -1x ( 10 + 7x³ ).

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The above question is incomplete, the complete question is:

Factor the expression completely.

−10x - 7x⁴

====================================================

Explanation:

This is a visual example of the pythagorean theorem. We add the areas of the two squares to get

13+29.25 = 42.25

Then we apply the square root to this to get the value of x, which is the hypotenuse of the right triangle

x = sqrt(42.25) = 6.5

---------

Side note: if you're curious about finding the other lengths of the triangle, apply the square root to those areas. The blue area 29.25 will lead to a side length of approximately sqrt(29.25) = 5.4083269; the red square will follow the same idea.

Answer:

Step-by-step explanation:

area of a square=a²

A=29.25

a=side=√29.25 first square

second square =a=√13

find x(c)

right triangle: a²+b²=c²

(√29.25 )²+(√13)²=c²

29.25+13=c²

c=√(29.25+13)=6.5 unit

Answer:

Hope this helps sorry I'm in class right now

Step-by-step explanation:

Using synthetic division:

-2 | 6    15     5

      __-12__-6

     6     3      -1

Quotient = 6x + 3

Remainder = -1

The Number of ways that four people can be seated on the bench so that john is not next to paul is 12

In mathematics, An arrangement of things or items in a specific sequence is known as a permutation. One should think about both the selection and the arrangement while dealing with permutation. In permutations, ordering is crucially important.

The arrangement of n items in r ways is given by

Here we have

4 people (John, Paul, George, and Ringo) are seated in a row on a bench

Here total No of ways that 4 can be seated = 4 × 3 × 2 × 1 = 24

The number of ways of seating the four people so that john is next to paul is 12

Then the number of ways the four people on the bench so that john is not next to paul can find as given below

= Total No of ways, 4 can be seated - No of ways that john next to paul  

= 24 - 12 = 12        

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Answer:

What is

Step-by-step explanation:

What is it

Answer:

Ascending: 6.0123, 6.0321, 6.321, 6.331, 60.123

Descending: 60.123, 6.331, 6.321, 6.0321, 6.0123

The required measure of side y = 8

Given : Triangle TUV and triangle XWV are similar

Thus \(\frac{UV}{VW} = \frac{6}{21}\)

this is further equal to \(\frac{2}{7}\)

Thus the ratio UV : VW = 2 : 7

this implies that the ratio TV : VX should also be equal to the ratio of UV : VW = 2 : 7 because of cpst or also called corresponding parts of similar triangles.

Given  UV : VW = 2 : 7

thus TV : VX = \(\frac{y}{28 }\) which on equation will give y as 8

because \(\frac{8}{28}\) when divided by 4 will give us the required ratio that is 2 : 7

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The steps to solve a quadratic formula include:

In algebra, a quadratic equation is a equation that can be rearranged in standard form as where x represents an unknown, and a, b, and c represent known numbers, where a ≠ 0.

A quadratic equation is an equation that could be written as ax² + bx + c = 0

when a 0. The factoring method is illustrated:

To solve a quadratic equation by factoring, put all terms on one side of the equal sign, leaving zero on the other side.

Set each factor equal to zero.

Solve each of these equations.

Check by inserting your answer in the original equation.

Example 1

Solve x² – 6 x = 16.

Following the steps,

x² – 6 x = 16 becomes x² – 8x + 2x – 16 = 0

Factor.

( x – 8)( x + 2) = 0

Therefore, x = 8 and -2.

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According to the given statement  the surface area a of the box is S1= 2× x ×(h+4).

An object's surface area is the total area that all of its surfaces occupy. The formulas we will learn in this post make it simple to determine the various surface areas that various 3D shapes in geometry have.

Vol = W*L*H = 100

Vol = X*(X+4)*H = 100

H = 100/(X^2 + 4X)S

A = 2*(X*(X+4) + X*H + H*(X+4))

Let h = the height× x ×(h+4)=100

h=100/x^{2} +4x

The top and bottom surfaces are:

S1= 2× x ×(h+4)

The following are the front as well as back areas:

S2= 2× (x+4)× h

The area for the sides is:

S3= 2x × h

Choose a value for x to check this as one method.

x=9x+ 4=13

h=100/x^{2} +4

h=100/81+4

h=100/117

According to the given statement  the surface area a of the box is S1= 2× x ×(h+4).

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Total number of I/Os: Read (200) + Write (200) = 400 I/Os
Sorted runs after 1st merge step: 4
Sorted runs after 2nd merge step: Not applicable, as the file is sorted after the 1st merge step.

(a) With 5 memory buffers available to sort a file consisting of 200 blocks:

1.Divide the 200 blocks into 40 equally sized runs (200 / 5 = 40), each with 5 blocks.
2. Perform 1st merge step, using 4 buffers for input and 1 for output. Merge 2 runs at a time: 40 runs / 2 = 20 sorted runs.
3. Perform 2nd merge step, again using 4 buffers for input and 1 for output. Merge 2 runs at a time: 20 runs / 2 = 10 sorted runs.

Total number of I/Os: Read (200) + Write (200) = 400 I/Os
Sorted runs after 1st merge step: 20
Sorted runs after 2nd merge step: 10

(b) With 8 memory buffers available to sort a file consisting of 200 blocks:

1. Divide the 200 blocks into 25 equally sized runs (200 / 8 = 25), each with 8 blocks.
2. Perform 1st merge step, using 7 buffers for input and 1 for output. Merge 7 runs at a time: 25 runs / 7 ≈ 3.57 => 4 sorted runs (3 runs with 8 blocks each, and 1 run with 5 blocks).
3. Perform 2nd merge step, not required as the file is already sorted after the 1st merge step.

Total number of I/Os: Read (200) + Write (200) = 400 I/Os
Sorted runs after 1st merge step: 4
Sorted runs after 2nd merge step: Not applicable, as the file is sorted after the 1st merge step.

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Answer:

2 or C

Explanation:

X intercept is where the line passes through the x-axis at, in this case it is (2,0)