the ratio of the number of students playing basketball to soccer at a local middle school is 5:2. what percent of the students at the middle school play soccer?(round to the nearest percent)

The missing value in the expression A = -2(x-9)² + ? is 162, which represents the maximum area of the storage bin.

A perfect Square is defined as an integer multiplied by itself to generate a perfect square, which is a positive integer. Perfect squares are just numbers that are the products of integers multiplied by themselves.

To complete the perfect square, we need to factor out the coefficient of the squared term (-2) from the expression:

A = -2x² + 36x

A = -2(x² - 18x)

Next, we need to add and subtract the square of half the coefficient of the x-term (-18/2 = -9) inside the parentheses:

A = -2(x² - 18x + (-9)² - (-9)²)

Simplifying the expression inside the parentheses, we get:

A = -2[(x - 9)² - 81]

Distributing the -2, we get:

A = -2(x - 9)² + 162

Therefore, the missing value in the expression is 162.

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The values 6, 4 and 12 are the measures of PR, PQ and RI respectively.

The given diagram is a triangle and the expression to be used based on the theorem is expressed as:

TP/TQ = PR+3/15

3/5 =  PR+3/15

5(PR +3)= 3(15)
5(PR + 3) = 45

PR + 3 = 9

PR = 9 - 3

PR = 6

For the measure of PQ

PQ^2 = 5^2 - 3^2

PQ^2 = 25 - 9

PQ = 4

Determine the measure of RI

3/PQ = TR/RI
3/4 = 9/RI

1/4 = 3/RI
RI = 12

Hence the measure of PR, PQ and RI are 6, 4, and 12 respectively

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The total area of the two circles will be 168316.9 square feet.

The circle is defined as a two-dimensional figure having a fixed point and the number of the points is traced around the curved path at an equal distance from the fixed point. The overall figure is called a circle.

The area of the circle is calculated by the formula:-

Area = πr²

Given that the south side of the highway needed to be compacted in order to create two circles of various sizes for a specific four-leaf clover. The two circles on the north side of the road have a 128-foot radius, whereas the two on the south side have a 102-foot radius.

The total area will be calculated as:-

Area = 2 x π x 128² + 2 x π x 102²

Area = 102943.25 + 65370.25

Area = 168316.9 square feet

Hence, the total area will be 168316.9 square feet.

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Answer:

5,144,079

Step-by-step explanation:

[tex]\displaystyle CI=\mu\pm z\biggr(\frac{\sigma}{\sqrt{n}}\biggr)\\\\CI_{99.5\%}=\mu\pm2.807\biggr(\frac{80.8}{\sqrt{n}}\biggr)\\\\0.1=2.807\biggr(\frac{80.8}{\sqrt{n}}\biggr)\\\\0.1\sqrt{n}=226.8056\\\\\sqrt{n}=2268.056\\\\n=5144078.01914\\\\n=5144079[/tex]

Thus, you would need a sample size of 5,144,079 to be 99.5% confident that the true population mean is ±0.1 away from it with a population standard deviation of 80.8 (aka. our margin of error).

Answer:

Step-by-step explanation:

Since Joe bought six bunches of seedless black grapes for $15, the cost per bunch of grapes is $15 / 6 = $2.50.

Since Anjali has $7.50, she can buy $7.50 / $2.50 = 3 bunches of seedless black grapes.

14. The mean of  the Zoo-venir Stand sales is of 23.9, representing the quotient between the sum of all the amounts and the number of observations.

15. The range of the Zoo-venir Stand sales is of 30, representing the difference between the highest number and the lowest number.

Considering the key format of the stem-and-leaf plot, the observations are given as follows:

12, 13, 13, 13, 14, 15, 15, 16, 17, 20, 21, 21, 22, 22, 23, 24, 25, 25, 25, 26, 27, 27, 28, 29, 29, 32, 34, 34, 37, 41, 42.

The mean is given by the sum of all observations divided by the number of observations, hence it's value is of: 23.9.

The range is the difference between the highest observation and the lowest observation, hence it is of:

42 - 12 = 30.

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The expression for the average number of people (8x³ +70x² +145x+182)/(2x + 13)

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

The total number of people, f(x) = 8x³ +70x² +145x+182

Number of free books = 2x + 13

To determine the average number of people that download each of the free books,

We need to divide the total number of people that register by the number of free books available.

So, we have

Expression = (8x³ +70x² +145x+182)/(2x + 13)

Hence, the expression is (8x³ +70x² +145x+182)/(2x + 13)

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The number 7.787887888 is option (C) not a rational number, it has a pattern which is predictable, but not repeating

The given number is 7.787887888

The rational numbers is a number that can be expressed as the p/q format, where p and q are integers and p will not be equal to zero. So the rational number is the ratio of the two integers.

Here the given number is 7.787887888.

So this is an non terminating number

But here we can see that there is a pattern which is predictable but its not repeating

Therefore, it is not a rational number ,but it has a pattern which is predictable, but not repeating

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The table that represents a linear relationship that is also proportional is; Table 2

A proportional relationship is defined as one where there is multiplying or dividing between the two numbers. A linear relationship can be a proportional one (for example y = 2x is proportional), but usually a linear equation has a proportional component plus some constant number (for example y = 2x + 3).

Table 1:

The proportions are;

-3/2, 0/3, 3/4

They are not equal and so not proportional

Table 2:

The proportions are;

-2/4 and -1/2

They are equal and so are proportional

Table 3:

The proportions are;

0/-2, 1/1 and 2/4

They are not equal and so not proportional.

Table 4:

The proportions are;

-4/0, 0/1 and 4/2

They are not equal and so not proportional.

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a)

The total number of possible 3​-card poker hands is 22100

b)

The number of possible black flushes is 2600

c)

The probability of being dealt a black flush is 0.1176

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Number of cards = 52

Number of cards in hand = 3

Combination formula.

[tex]^nC_r[/tex] = n! / r! (n -r)!

a)

The total number of possible 3​-card poker hands.

= [tex]^{52}C_3[/tex]

= (52 x 51 x 50) / (3 x 2)

= 22100

b.

Number of black cards (spades and clubs) = 13 + 13 = 26

The number of possible black flushes.

= [tex]^{26}C_3[/tex]

= (26 x 25 x 24) / (3 x 2)

= 2600

c.

The probability of being dealt a black flush.

From (a) and (b)

= 2600/22100

= 0.1176

Thus,

The total number of possible 3​-card poker hands = 22100

The number of possible black flushes = 2600

The probability of being dealt a black flush = 0.1176

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The required description of the given piecewise linear relations is graphed, as follows:

f(x) = 1 if [-3, -1); f(x) = 2 if [-1, 1); and f(x) = 3 if [1, 3).

A piecewise-defined function (also known as a piecewise function or a hybrid function) is a function defined by multiple sub-functions, each of which applies to a different interval of the main function's domain (a sub-domain).

The graph of the piecewise linear relations is given in the question, as shown

f(x) = 1 if [-3, -1)

This the sub-function define between the interval  [-3, -1).

f(x) = 2 if [-1, 1)

This the sub-function define between the interval [-1, 1).

f(x) = 3 if [1, 3)

This the sub-function define between the interval  [1, 3).

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(a) Conversion of 15 minutes and r minutes into hours, 0.25 hours & r/60 hours.

(b) An equation in terms of t and solution of it,  S = 0.04r miles and  r = 10

(c) Alex's average speed for the whole journey is, 3.33 mph

The distance covered by the object is equal to the product of the speed at which the object is moving and time taken for covering the distance.

Distance = Time × Speed

(a) 15 minutes is equal to 0.25 hours (15/60) and r minutes is equal to r/60 hours.

(b) Let's use the formula:

distance = speed x time for both jogging and walking.

Distance traveled while jogging = 4 mph x 0.25 hours

                                                     = 1 mile

Distance traveled while walking = 2.4 mph x (r/60) hours

                                                     = 0.04r miles

Total distance traveled = 1 mile + 0.04r miles

                                      = 1.4 miles

Solving for r, we get:

0.04r = 0.4

r = 10

So, Alex walked for 10 minutes.

(c) Total time taken = 15 minutes + 10 minutes

                                = 25 minutes

                                = 0.42 hours

Total distance traveled = 1.4 miles

Average speed = Total distance / Total time

                          = 1.4 miles / 0.42 hours

                          = 3.33 mph (rounded to two decimal places).

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Answer:

(a) 275ft²

(b) 3 gallons

(c) $73.50

Step-by-step explanation:

(a)

The shape of the wall consists of a triangle and a rectangle, so to find the wall's area we find the area of the triangle and rectangle and add them together:

Area of triangle = 0.5*base*height = 0.5*22*5 = 55ft²

Area of rectangle = base*height = 22*10 = 220ft²

So the area of the wall = 55ft²+220ft²=275ft²

(b)

To find how many gallons it would take, you divide the area by the amount of are one gallon covers: 275 / 105 = 2.619

Rounded up, this is 3 gallons

(c)

Since we're buying 3 gallons and each costs $24.50, we multiply 3 by the price to find the total: 3*24.5 = $73.50

Answer:

(a) 275ft?

(b) 3 gallons

(c) $73.50

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The evaluation of the cubic function represented by the graph can be presented as follows;

a. The equation of the function, S = a·t³ + b·t² + c·t + d, indicates that the equation is a cubic equation

b. i. d = -5

ii. The three equations are;

a + b + c = 8...(1)

8·a + 4·b + 2·c = 4...(2)

27·a + 9·b + 3·c = 0...(3)

iii. a = 2, b = -12, and c = 18

c. The student is expected to be in debt for 2 years, 4 months and 3 days

A cubic function is a degree three polynomial that can be expressed in the form; f(x) = a·x³ + b·x² + c·x + d.

The specified function can be presented as follows;

S = a·t³ + b·t² + c·t + d

a. A feature of the graph that indicates that a cubic equation is the appropriate model, is the largest power of the input time variable t in the function is 3, which is the same as the power of a cubic function.

b. i. The value of d can be found by plugging in t = 0, in the function; S = a·t³ + b·t² + c·t + d

From the table in the question, we get;

At t = 0, S = -5

Therefore;

S = a×0³ + b×0² + c×0 + d = -5

d = -5

The value of d = -5

b. ii. The simultaneous equations can be obtained by plugging in the values of t from the table into the function for S as follows;

S = a·t³ + b·t² + c·t + d

S = a·t³ + b·t² + c·t - 5

When t = 1, we get;

S = a·1³ + b·1² + c·1 - 5 = 3

a + b + c - 5 = 3

a + b + c = 3 + 5 = 8

When t = 2, we get;

S = a·2³ + b·2² + c·2 - 5 = 3

8·a + 4·b + 2·c - 5 = -1

8·a + 4·b + 2·c = -1 + 5 = 4

When t = 3, we get;

S = a·3³ + b·3² + c·3 - 5 = 3

27·a + 9·b + 3·c - 5 = -5

27·a + 9·b + 3·c = -5 + 5 = 0

iii. Solving the system of equations using a graphing calculator, indicates that we get;

c. Plugging in the values into the specified equation, we get;

S = 2·t³ - 12·t² + 18·t - 5

The solution of the above equation can be found as follows;

2·t³ - 12·t² + 18·t - 5 = 0

Based on an online tool, the Newton Raphson method indicates that a solution of the equation is; t ≈ 0.35821, which indicates that a factor of the equation, 2·t³ - 12·t² + 18·t - 5 = 0 is; (x - 0.35821)

(2·t³ - 12·t² + 18·t - 5) ÷ (x - 0.35821) ≈ 2·t² - 11.28356·t + 13.95804

The other solutions are therefore;

t ≈ 1.83, and t ≈ 3.81

The student is expected to be in debt at time t = 0, and from the graph, cross the x-axis out of depth first at time, t ≈ 0.35821 of a year

The student will be in dept again between t ≈ 1.83 and t ≈ 3.81

The total time the student is expected to be in debt is therefore;

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(a) When q = 0 or q = 1, we get p = 0.5, but for other values of q, the optimal value of p is different.

(b) When q = 1, the expected score is 1, which is the maximum possible score.

(c) The optimal value of p also depends on the value of q in this case.

a) The expected score of the meteorologist can be expressed as the weighted average of the two possible scores, where the weights are the probabilities of it raining or not raining:

Expected score = p(1 - (1 - q)^2) + (1 - p)(1 - q^2)

To maximize the expected score, we need to differentiate it with respect to p, set the derivative equal to zero, and solve for p. This gives:

2q(1 - q) = 1 - 2p

Solving for p, we get:

p = (1 - 2q + 2q^2) / 2

So the optimal value of p depends on the value of q. When q = 0 or q = 1, we get p = 0.5, but for other values of q, the optimal value of p is different.

b) If the meteorologist chooses p = q, then the expected score simplifies to:

Expected score = q(1 - (1 - q)^2) + (1 - q)(1 - q^2)

= q^3 + (1 - 2q)q^2 + (1 - q)

To find the maximum expected score, we can take the derivative of this expression with respect to q, set it equal to zero, and solve for q. This gives:

3q^2 - 4q + 1 = 0

This quadratic equation has two roots: q = 1/3 and q = 1. When q = 1, the expected score is 1, which is the maximum possible score. When q = 1/3, the expected score is (8/27), which is the maximum score for any value of q between 0 and 1.

c) If the payoffs are {1 - (1 - p)^2, 1 - 1.1p^2}, then the expected score of the meteorologist is:

Expected score = p(1 - (1 - q)^2) + (1 - p)(1 - 1.1q^2)

To maximize this expected score, we can differentiate it with respect to p, set the derivative equal to zero, and solve for p. This gives:

2.2q^2 - 2q + 1 = 2p

Solving for p, we get:

p = (2.2q^2 - 2q + 1) / 2

So, in this scenario, the value of q also affects the ideal value of p.

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[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{25\% of 79600}}{\left( \cfrac{25}{100} \right)79600}\implies \text{\LARGE 19900}[/tex]

Answer:

you are to use patagorious theory

Using their unit rates, the 12-ounce bottle costs lesser per ounce than the 8-ounce bottle of stay clean shampoo.

The unit rate is the cost per unit.

The unit rate is computed as the quotient of the total cost and the number of units.

The cost of a 12-ounce bottle of stay clean shampoo = $8

The unit rate per ounce of the 12-ounce bottle = $0.67 ($8/12)

The cost of an 8-ounce bottle of stay clean shampoo = $6

The unit rate per ounce of the 8-ounce bottle = $0.75 ($6/8)

Thus, comparing the unit rate of the 12-ounce bottle with the 8-ounce bottle, we can conclude that it costs more per ounce to buy the 8-ounce bottle than the 12-ounce bottle.

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Step-by-step explanation:

for z -> 3 (3z - 2) -> (3×3 - 2) = 7

Answer: 3

Step-by-step explanation:

Took the test

Answer:

Step-by-step explanation:

The correct answer is D. m∠6 + m∠7 = 180°.

When a transversal cuts two parallel lines, corresponding angles are equal and alternate interior angles are supplementary. This means that the sum of alternate interior angles is equal to 180°. In this diagram, ∠6 and ∠7 are alternate interior angles, so it is necessarily true that m∠6 + m∠7 = 180°.

The other options are not necessarily true. Option A states that m∠1 = m∠7, but this is only true if the two lines being cut by the transversal are perpendicular. Option B states that m∠3 = m∠6, but this is only true if the two lines being cut by the transversal are parallel. Option C states that m∠5 + m∠8 = 90°, but this is only true if the two lines being cut by the transversal are perpendicular.

Just ten more days and I'll be in London!

Answer:

Just ten more days and I'll be in London!

a).The function1 changes at greater rate of 45.

b). At x = 1; the function1 = 45 and function2 = 50.

c).The functions are equal to 90 at x = 2.

A function in the equation form "y = mx + c" represents a straight line in a two-dimensional coordinate system. "y" and "x" are variables representing the coordinates of points on the line, "m" is the slope of the line, and "c" is the y-intercept, which is the point at which the line crosses the y-axis.

The slope "m" represents the rate at which the line rises or falls as x increases. The y-intercept "c" determines the location of the line along the y-axis. This equation is known as the slope-intercept form of a linear equation.

For the function1, when y = 0 and x = 0, we can solve for c and m as follows:

0 = 0m + c

c = 0

when y = 90 and x = 2;

90 = 2m + 0

m = 45

Hence, the function1 with y = 45x changes at a greater rate of 45.

At x = 1:

for function1;

y = 45(1) + 0 = 45

for function2;

y = 40(1) + 10 = 50.

At the point when x = 2:

for function1;

y = 45(2) + 0 = 90

for function2;

y = 40(2) + 10 = 90.

Therefore, the function1 changes at greater rate of 45. At x = 1; the function1 = 45 and function2 = 50. The functions are equal to 90at x = 2.

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In these triangles, the largest angle and the largest side have been measured. This means that the two smaller sides and the two smaller angles are proportional to each other. This is known as the triangle inequality, which states that the sum of any two sides of a triangle must be greater than the third side. This means that the two smaller angles and the two smaller sides of the triangle must add up to be larger than the largest angle or side.

The Triangle Inequality states that the sum of any two sides of a triangle must be greater than the third side. This means that two other inequalities can be written:

a > |c - b| and b > |c - a|,

where |x| is the absolute value of x. This means that the length of each side must be greater than the difference between the other two sides

Answer: B

Step-by-step explanation:

Answer:

Step-by-step explanation:

ax+bx=c

x(a+b)=c

x(a+b)/(a+b)=c/(a+b)

x=c/(a+b)

Answer:

[tex]x=\dfrac{c}{a+b}[/tex]

Step-by-step explanation:

To make x the subject of the equation ax + bx = c, rearrange the equation using algebraic operations to isolate a single x-variable.

Given equation:

[tex]ax + bx = c[/tex]

Factor out x from the left side of the equation:

[tex]x(a+b)=c[/tex]

Divide both sides of the equation by (a + b):

[tex]\dfrac{x(a+b)}{(a+b)}=\dfrac{c}{(a+b)}[/tex]

Simplify:

[tex]x=\dfrac{c}{a+b}[/tex]

It looks like 1) adjacent angles.

The equation of inverse of f is f-1(x) = √(x/2)

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

f(x) = 2x^2

Express as an equation

so, we have the following representation

y = 2x^2

Swap x and y

so, we have the following representation

x = 2y^2

Divide by 2

y^2 = x/2

Take the square roots

y = √(x/2)

Hence, the inverse is f-1(x) = √(x/2)

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