What is the ratio of the number of students who sometimes watch sports to the total number of students surveyed?

Answer:

A.

Step-by-step explanation:

In the attached file

The expression becomes: p^(1/2) = p^(1/2 * 1) = p^(1/2) Now we can simplify p^(1/2) as p^1/2 which equals the square root of p.

The property of exponents that must be applied to the expression p^(1/2) to derive p as the result is the Power of a Power Property.

The Power of a Power Property states that when a power is raised to another power, the exponents are multiplied.

For instance, consider the expression p^(1/2). We can apply the Power of a Power Property to this expression as follows: p^(1/2) = (p^(1/2))^1 By applying the Power of a Power Property, the exponent (1/2) is multiplied by the exponent 1, giving a result of 1/2.

Therefore, the expression becomes: p^(1/2) = p^(1/2 * 1) = p^(1/2)Now we can simplify p^(1/2) as p^1/2 which equals the square root of p.

So we have derived p as the result using the Power of a Power Property.

In summary, we must apply the Power of a Power Property to the expression p^(1/2) to derive p as the result.

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Answer:

3

Step-by-step explanation:

annie has 3 left. 5-2=3

Answer:

it depends

Step-by-step explanation:

if your talking about Annie then she has THREE apples.

if your talking about the person she gave the apples to, then that person has TWO apples.

All sides of a rhombus have equal measures, so TU = 8. Since a rhombus is a parallelogram, and the diagonals of a parallelogram bisect each other, WU = 10. The diagonals of a rhombus are also perpendicular, meaning they form right angles. Using the Pythagorean theorem, you can find the length of TX. (TX)^2 + (WX)^2 = (WT)^2. Substituting in known values, (TX)^2 + 25 = 64. Solving gives you TX = the square root of 39. TV is double the length of TX, so TV = 2 times the square root of 39.

Using a calculator, the trigonometric ratio of sin 98 is approximately 0.9848.

One of the trigonometric ratio we have in mathematics is the sine ratio. We can use calculator to find the sine of an angle without making use of tables. To do this on your calculator, enter the sine function followed by the degree of the angle you want to find its sine. You will get your answer.

Using a calculator, we can find the sine of 98 degrees as follows:

sin 98° ≈ 0.9848

Rounding this to four decimal places, we get:

sin 98° ≈ 0.9848

Therefore, sin 98° is approximately equal to 0.9848.

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Answer:

f(−10) =  ⇒ -19

f(2) =  ⇒ 4

f(−5) =  ⇒ -9

f(−1) =  ⇒ 1

f(8) =  ⇒ -5

Step-by-step explanation:

Answer:

\(\frac{f(x) - f(a)}{x - a}=\frac{-1}{xa}\)

Step-by-step explanation:

Given

\(f(x) = \frac{1}{x}\)

Required

Evaluate \(\frac{f(x) - f(a)}{x - a}\)

We have:

\(f(x) = \frac{1}{x}\)

Next, we calculate f(a)

Substitute a for x in \(f(x) = \frac{1}{x}\)

\(f(a) = \frac{1}{a}\)

Substitute values for f(x) and f(a) in \(\frac{f(x) - f(a)}{x - a}\)

\(\frac{\frac{1}{x} - \frac{1}{a}}{x - a}\)

Take LCM of the numerator

\(\frac{\frac{a - x}{xa} }{x - a}\)

Split:

\(\frac{a - x}{xa} /{x - a}\)

Convert / to *

\(\frac{a - x}{xa} *\frac{1}{x - a}\)

Express a - x as -(x-a)

\(\frac{-(x - a)}{xa} *\frac{1}{x - a}\)

Divide numerator and denominator by x - a

\(\frac{-1}{xa} *\frac{1}{1}\)

\(\frac{-1}{xa}\)

Hence:

\(\frac{f(x) - f(a)}{x - a}=\frac{-1}{xa}\)

The area of the shape in the figure is calculated to be 180 m²

The area of the shape in the figure can be solved by breaking the shape into three rectangles, calculating the area of each rectangle and adding up

Area of rectangle is calculated by the formula

= length *  width

Area of the first rectangle

= 4 * 16

= 64

Area of the second rectangle

= (16 - 4) * (12 - 4 - 5)

= 12 * 3

= 36

Area of the third rectangle

= 16 * 5

= 80

Adding up

= 80 * 36 * 64

= 180 m²

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Answer:

----------------------

If the system of linear equations has infinitely many solutions, it means the two lines overlap.

In other words, each point of one of the lines also belongs to the second line.

Choices a, b, c  give us one or no solutions and therefore not the answer.

Choice d is reflecting the infinitely many solutions and hence is the correct one.

The slope of a line parallel to 2y= 6x+8 is 3.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

In Mathematics and Geometry, parallel lines are two (2) lines that are always the same (equal) distance apart and never meet. Therefore, two (2) lines are parallel under the following conditions:

m₁ = m₂

By making y the subject of formula, we have:

2y = 6x + 8

y = 3x + 4

Therefore, the slope is 3.

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By rounding to 1 significant figure 542.04 × 1.88 equal to 1019.0352

is 1019.

We round off numbers to make them easier to remember and it also keeps their value approximately to the place it has been rounded off.

To round off any number to any place we'll look for the digit next to that place and if it is equal to or greater than 5 we'll add one to the previous digit and make all the digits after it zeroes and if the digit is less than 5 we do not add one to the preceding digit and simply make all the digit after it to zeroes.

Given we have to round off 542.04×1.88 = 1019.0352.

Now rounding off to one significant digit means we should have only one digit after the decimal place and the second digit after the decimal place is 3 which is less than 5.

∴ 1019.0352 rounded off to one significant digit is 1019.

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Answer:

10

Step-by-step explanation:

Answer:

10 apples

Step-by-step explanation:

20% of 50 = 10

10 apples

Answer:

$15500

Step-by-step explanation:

10^3 x 12 = 12,000

10^2 x 35 = 3,500

12,000 + 3,500 = 15,500

The solution to given linear inequality, 6(x1.5) + 30 < 48, is x < 2

From the question, we are to solve the given linear inequality

The given linear inequality is

6(x1.5) + 30 < 48

First, we will write this inequality properly.

The inequality can be properly written as

6(1.5x) + 30 < 48

Now, we will solve the linear inequality

6(1.5x) + 30 < 48

Subtract 30 from both sides of the equation

6(1.5x) + 30 - 30 < 48 - 30

6(1.5x) < 18

Divide both sides of the inequality by 6

6(1.5x)/6 < 18/6

(1.5x) < 3
1.5x < 3

Divide both sides of the inequality by 1.5

1.5x/1.5 < 3/1.5

x < 2

Hence, the solution is x < 2

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Answer:

10x 8 is 80 so it will be 30+80

The contractor has a maximum of 29 hours (rounded down) to complete the job while keeping the total cost under $2000.

To find the number of hours the contractor has for the job while keeping the total cost under $2000, we can use the given cost model equation: C = 43H + 750.

Since the owner wants the total cost to be under $2000, we can set up the inequality:

43H + 750 < 2000

Now, let's solve this inequality for H, the number of hours:

43H < 2000 - 750

43H < 1250

Dividing both sides of the inequality by 43:

H < 1250/43

To determine the maximum number of hours the contractor has for the job, we need to round down the result to the nearest whole number since the contractor cannot work a fraction of an hour.

Using a calculator, we find that 1250 divided by 43 is approximately 29.07. Rounding down to the nearest whole number, we get:

H < 29

Using the cost model equation C = 43H + 750, where C represents the total cost and H represents the number of hours, we set up the inequality 43H + 750 < 2000 to satisfy the owner's requirement of a total cost under $2000.

By solving the inequality and rounding down to the nearest whole number, we find that the contractor has a maximum of 29 hours to complete the job within the specified cost limit.

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Step-by-step explanation:

a)

The given fraction is positive.

Positive divided by positive is positive.

Negative divided by negative is positive.

Answer: -7/-8

b)

The given fraction is negative.

Positive divided by negative is negative.

Negative divided by negative is negative.

Answer: 5/-2, -5/2

#a

#b

That be x and y

So

So

from eq(1)

Put in second one

Put in third one

Take it positive

Answer:

(a) (i)  Factorize \(\sf 4p-6pq+9q-6\)

Rewrite by swapping the order of the first two terms:

⇒ -6pq + 4p + 9q - 6

Factorize the first two terms and the last two terms separately:

⇒ -2p(3q - 2) + 3(3q - 2)

Factor out the common term (3q - 2):

⇒ (3q - 2)(-2p + 3)

(ii)

Square of the binomial: \((a+b)^2=a^2+2ab+b^2\)

Rewrite \(9.9\) as \(10 - 0.1\)

Therefore, \(a = 10\) and \(b = -0.1\)

Also, remember that multiplying a number by 0.1 is the same as dividing it by 10.  (when dividing a decimal number by 10, simply move the decimal point 1 place to the left).

\(\begin{aligned}\implies 9.9^2 & =(10-0.1)^2\\ & =10^2-2 \cdot 10 \cdot 0.1+0.1^2\\& = 100-\dfrac{2 \cdot 10}{10}+\dfrac{0.1}{10}\\& =100-2+0.01\\ & =98 + 0.01\\ & = 98.01\end{aligned}\)

(b) (i)

Let x = number of motor bicycles

Let y = number of cars

Given:

⇒ x + y = 15

Given:

⇒ 2x + 4y = 64

(ii)  Rewrite   x + y = 15  to make x the subject:

⇒ x = 15 - y

Substitute into 2x + 4y = 64  and solve for y:

⇒ 2(15 - y) + 4y = 64

⇒ 30 - 2y + 4y = 64

⇒ 30 + 2y = 64

⇒ 2y = 34

⇒ y = 17 cars

Substitute found value of y into  x = 15 - y  to find x:

⇒ x = 15 - 17 = -2 motorbikes

**There must be an error in the question, as with the given information, the number of motorbikes is -2, which is impossible.**

Here are the possible combinations of number of motorbikes (M) and number of cars (C) whose sum of tires is 64.  As you can see, there is no combination that sums to 15 vehicles:

0 M +  16 C = 16 vehicles

2 M +  15 C = 17 vehicles

4 M +  14 C = 18 vehicles

6 M +  13 C = 19 vehicles

8 M +  12 C = 20 vehicles

10 M +  11 C = 21 vehicles

12 M +  10 C = 22 vehicles

14 M +  9 C = 23 vehicles

16 M +  8 C = 24 vehicles

18 M +  7 C = 25 vehicles

20 M +  6 C = 26 vehicles

22 M +  5 C = 27 vehicles

24 M +  4 C = 28 vehicles

26 M +  3 C = 29 vehicles

28 M +  2 C = 30 vehicles

30 M +  1 C = 31 vehicles

32 M +  0 C = 32 vehicles

The given statement is a reasonable probability model because it fulfills the 4 conditions of binomial distribution.

The conditions for binomial distribution are;

1: The number of observations n must be fixed.

2: Each observation must be independent.

3: Each observation must represent one of two outcomes ("success" or "failure").

4: The probability of "success" p must be the same for each outcome.

Now, we are given the statement;

Joey buys a Virginia lottery ticket every week. x is the number of times in a year that he wins a prize.

From that statement, we can tell that the number of observations is fixed at 52 weeks since a year is made up of 52 weeks.

Secondly, we can say that there could be success by winning a price or failure by not winning the price.

Each weekly observation is independent.

The probability is the same for each outcome.

Thus, we conclude that since it fulfills all the four conditions then it is a binomial model.

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The original dimensions of the piece of metal were 15 inches by 20 inches.

To solve this problem, we can use the given information to set up an equation. Let's assume that the width of the rectangular piece of metal is x inches. According to the problem, the length of the piece of metal is 5 inches longer than its width, so the length would be (x+5) inches.

When squares with sides 1 inch long are cut from the four corners, the width and length of the resulting box will be reduced by 2 inches each. Therefore, the width of the box will be (x-2) inches and the length will be ((x+5)-2) inches, which simplifies to (x+3) inches.

The height of the box will be 1 inch since the flaps are folded upward.
Now, let's calculate the volume of the box using the formula Volume = length * width * height.

Substituting the values, we have:

234 = (x+3)(x-2)(1)

Simplifying the equation, we get:

234 = x^2 + x - 6

Rearranging the equation, we have:

x^2 + x - 240 = 0

Now, we can solve this quadratic equation either by factoring or by using the quadratic formula. Let's use factoring to find the values of x.

Factoring the equation, we have:
(x+16)(x-15) = 0
Setting each factor equal to zero, we get:
x+16 = 0 or x-15 = 0
Solving for x, we have:
x = -16 or x = 15
Since the width cannot be negative, we take x = 15 as the valid solution.
Therefore, the original dimensions of the piece of metal were 15 inches in width and (15+5) = 20 inches in length.

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Answer:

true

Step-by-step explanation:

6(6(13x-2)

36(13x-2)

468x-72

please mark brainliest :D

Answer:

True

Step-by-step explanation:

Given functions:

\(\begin{cases}f(x)=3x-7\\g(x)=13x-2\\h(x)=6x\end{cases}\)

\(h(h(g(x)))\) is a composite function.  

Composite functions are when the output of one function is used as the input of another.

Therefore, the given composite function means to substitute the function g(x) in place of the x in function h(x), then substitute this in place of the x in function h(x).

Step 1

Substitute the function g(x) in place of the x in function h(x):

\(\begin{aligned}h(x) & = 6x\\\implies h(g(x)) & =6(g(x))\\& = 6(13x-2)\\ & = 78x-12\\\end{aligned}\)

Step 2

Now substitute the above in place of the x in function h(x):

\(\begin{aligned}h(x) & = 6x\\\implies h \left(h(g(x))\right) & =6(h(g(x)))\\& = 6(78x-12)\\& = 468x-72\end{aligned}\)

Therefore, the statement is true.

To carry out the composite function in one step:

\(\begin{aligned}h(x) &=6x\\\implies h(h(g(x))) & = 6\:(h(g(x)))\\& = 6(6(g(x)))\\& = 6( 6(13x-2))\\& = 6(78x-12)\\& = 468x-72\end{aligned}\)

Answer:

Step-by-step explanation:

For starters, rational numbers are any numbers that has the capability to be written as a fraction.

For example, 0.5 is a decimal, and can also be written in form of a fraction, as 1/2

A recurring decimal can be written as a fraction. For example, we have 0.167 which can be written as 1/6

In the example, for the decimal 0.36425, we find the place value of the last digit. The last digit here is 5 placed in the hundred-thousandths place. On simplifying further into a fraction, we have 36425/100000.

au = -10 + 4(11 - 1)

Ok

The first term is -10

What is the common difference (11 - 1)

What term are you calculating? 11 - (-10) = 11 + 10 = 21

Answer:  (2,-1).

Step-by-step explanation:

The given system of equations is

\(3x+2y=4\)

\(-x+3y=-5\)

For \(3x+2y=4\), table of values is

x :   0        1         2

y :   2      0.5      -1

For \(-x+3y=-5\), table of values is

x :   -1        2         5

y :   -2       -1         0

Plot these points on a coordinate plane and connect them be straight lines as shown below.

Form the graph it is clear that the lines intersect each other at (2,-1).

Therefore, the solution of given system of equations is (2,-1).

Answer:

1. 60  2. 65  3. 115  4. 55  5. 120  6. 60

Step-by-step explanation:

Hope it helps!

The fraction of the class that is sophomores is \(35/43\).

The fraction of the class that is sophomores, divide the number of sophomores by the total number of students in the class.

Number of sophomores = 35

Total number of students = 43

Fraction of sophomores = (Number of sophomores)/(Total number of students Fraction of sophomores)

Fraction of sophomores  \(= 35 / 43\)

Therefore, the fraction of the class that are sophomores is = \(35/43\).

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the answer is c

3.3 x10 restu power minus 3