A total of 433 were sold for the school play. They were either adult tickets or students tickets. They were 67 fewer student ticket sold than adult tickets.

It would cost approximately $52.18 to drive from Statesville, NC to Washington, DC with a car that gets 29 miles per gallon on the interstate, considering a gas cost of $3.89 per gallon.

To calculate the time it would take to drive from Statesville, NC to Washington, DC, we can divide the distance of 389 miles by the average speed of 65 mph.

Time = Distance / Speed

Time = 389 miles / 65 mph

Time ≈ 5.98 hours

Therefore, it would take approximately 5.98 hours to drive from Statesville, NC to Washington, DC on interstates with an average speed of 65 mph.

To calculate the cost of driving to Washington, DC, we need to know the number of gallons of gas required for the trip. We can find this by dividing the distance by the car's mileage, which is 29 miles per gallon.

Number of gallons = Distance / Mileage

Number of gallons = 389 miles / 29 miles per gallon

Number of gallons ≈ 13.41 gallons

The cost of gas can be calculated by multiplying the number of gallons by the cost per gallon, which is $3.89.

Cost = Number of gallons * Cost per gallon

Cost ≈ 13.41 gallons * $3.89/gallon

Cost ≈ $52.18

Therefore, it would cost approximately $52.18 to drive from Statesville, NC to Washington, DC with a car that gets 29 miles per gallon on the interstate, considering a gas cost of $3.89 per gallon.

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Answer:

Step-by-step explanation:

Answer:

how  to find the mean: add all your values together then divide them by how many numbers u added

example:

5,7,9,9,10

add= 40

divide by 5, we have 5 values = 8

A student attempted to use similar triangles to determine the missing side length suggested by x , leading to the value of x being 2.

A closed triangle is a two-dimensional object with three angles and three straight sides. By joining three non-collinear lines, it is created. A triangle's three sides always add up to 180 degrees. In a right triangle, the hypotenuse, which is the longest edge, is located on the side opposite the largest angle. Triangles can be categorized as equilateral, isosceles, scalene, acute, right, and obtuse depending on the length of their sides and the size of their angles. In geometry and trigonometry, triangles are frequently used to analyze shapes and angles.

given

6/3 = 4/x

3*6x/3 = 4*3

= 6x /6 = 12/6

= x =2

A student attempted to use similar triangles to determine the missing side length suggested by x , leading to the value of x being 2.

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The value of the expression is -7.

We have,

-2 (3y + 7) = 28

(given)

-6y - 14 = 28

(distributive property)

-6 - 14 + 14 = 28 + 14

(addition property of equality)

-6y = 42

(simplifying)

-6y/-6 = 42/-6

(Division property of equality)

y = -7

Thus,

The value of the expression is -7.

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Therefore, it must contain one person from each class, 2,100committees are possible; if for any mixture of the classes, 20475 committees are possible; and, if exactly for  two seniors, 6300 committees are possible.

Permutations and combinations differ in that permutations are used when the order of arrangement matters, whilst combinations are used when it doesn't.

A, B, and C, for instance, can be combined in six different ways to form the letters ABC, ACB, BAC, BCA, CAB, and CBA. Only three letter combinations exist, though: ABC, ACB, and BCA.

Combinations and permutations can be used to find a solution to this issue.

(A) One member from each class must be chosen for this step. As a result, we must choose a senior, junior, sophomore, and freshman. There are many methods to do this, including:

(10 pick 1)× (7 pick 1)× (6 choose 1) ×(2100) (5 select 1)

= 10  ×7 × 6  5

=2100

(b) We can choose any combination of classes for this section. As a result, out of a total of 28, we must choose four people. There are many methods to do this, including:

(28!)/(4!×((4) (28-4)!) = 20475

(c) From the remaining pupils, we must choose exactly two seniors and two more individuals for this section. 

Consequently, we must choose two seniors from among the ten seniors and two individuals from among the remaining 18 students. There are many methods to do this, including:

  (10 choose 2) * (18 choose 2) = (10!)/(2!*(10-2)!) * (18!)/(2!*(18-2)!) = 6300

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F and G are inverse if both of them satisfy the condition h(x)=x. f(g(x))=g(f(x))=x, as we discovered. The argument f(x) and g(x) are inverse functions is thus established.

If f (x) and g (x) are inverse functions, it can be determined using one of two ways. For more information, see the explanation.

Explanation:

Instance 1

Inverse functions of both functions can be found using the first method.

Example.

Inverse of f (x) = x + 7 is what we're looking for.

We attempt to determine x using the equation y = x + 7.

y = x + 7

Inferring that g (x) is the inverse of f (x) from the fact that x = y 7

Finding g (x inverse )'s is now necessary.

g( x ) = x − 7

y = x − 7

x = y + 7

As a result, we discovered that f (x) is the inverse function of g (x).

f and g are equal if g is inverse of f and vice versa.

The second approach entails locating the compound functions f ( g ( x ) ) and g ( f ( x ) ). In this case, f and g are inverse if they are both h (x ) = x.

Example:

f ( g ( x ) =  [ x − 7 ] + 7

G ( x ) placed as x is the expression in brackets.

f ( g ( x ) ) = x − 7  + 7 = x

g (f ( x ) =  [ x + 7 ] − 7

f ( x ) inserted as x is the expression in brackets.

g ( f ( x ) ) = x + 7 − 7 = x

The equation f ( g ( x ) ) = g ( f ( x ) ) = x was what we discovered. The argument f (x) and g (x) are inverse functions is thus established.

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Answer:

Step-by-step explanation:

If within the year 2014, the population p of the rabbits m months after January 2014 is modeled by the equation p = 0.05(m-1.5)(m-8.5) and the population reach 10,000 some time in February, to determine the time, given as months after January 1 2014, that the rabbit population reach ten thousand, we will substitute p = 10 into the modeled equation and get the value of m as shown;

\(p = 0.05(m-1.5)(m-8.5)+10 \\substitute \ p = 10\\\\ 10 = 0.05(m-1.5)(m-8.5)+10\\\\10-10 = 0.05(m-1.5)(m-8.5)\\\\0 = 0.05(m-1.5)(m-8.5)\\\\0/0.05 = (m-1.5)(m-8.5)\\\\0 = (m-1.5)(m-8.5)\\ (m-1.5)(m-8.5) = 0\\ m-1.5 = 0 \ and \ m-8.5 = 0\\m = 1.5 \ and \ 8.5\\\)

Hence the population of the rabbit reach 10,000 after 1.5 months and 8.5 months

Answer:

I think it is p= $60

Answer:

5,129

Step-by-step explanation:

Answer:

C. 5129

Step-by-step explanation:

5.129 x \(10^{3}\)

you will move the decimal to the right 3 times.

Answer:

0.0023

Step-by-step explanation:

Attached is a filled-in place value chart with the info for answering this question and a blank one for any further questions!

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Answer:

(3×25)÷5=15

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Answer:

15

Step-by-step explanation:

first, you add all the marbles 25 x 3 = 75 then you divide by 5 which you get 15

The constant of proportionality in the equation is 5/4

The constant connecting two given numbers in what is known in a proportional relationship is the constant of proportionality.

The constant of proportionality may also be referred to as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.

In the problem, y = 5/4x

The constant term 5/4 as used in the equation is used t multiply the input x values to get the out put y values

The term helps in relating x to y

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Answer:

\(\bar x = 34.7\)

Step-by-step explanation:

Given

\(\begin{array}{cc}{Age} & {Fatalities} & {11 - 20} & {340} & {21-30} & {1527} & {31-40} & {866} & {41-50} & {693} & {51-60} & {423} & {61-70} & {123} \ \end{array}\)

Required

Calculate the mean

The given data is a grouped data. So, we need to calculate the class mid -point first.

This is done by calculating the average of the class intervals.

So, we have:

\(\begin{array}{ccc}{Age} & {Fatalities} & {x} & {11 - 20} & {340} & {15.5} & {21-30} & {1527} &{25.5}& {31-40} & {866} & {35.5} & {41-50} & {693} & {45.5} & {51-60} & {423} & {55.5} & {61-70} & {123} & {65.5}\ \end{array}\)

For 11 - 20, the midpoint is: \(x =\frac{1}{2}(11+20) = \frac{1}{2}*31=15.5\)

For 21 - 30, the midpoint is: \(x =\frac{1}{2}(21+30) = \frac{1}{2}*51=25.5\)

.....

For 61 - 70, the midpoint is: \(x =\frac{1}{2}(61+70) = \frac{1}{2}*131=65.5\)

The mean is then calculated as:

\(\bar x = \frac{\sum fx}{\sum f}\)

\(\bar x = \frac{(15.5 * 340) + (25.5 * 1527) + (35.5 * 866) + (45.5 * 693) + (55.5 * 423) + (65.5 * 123)}{340 + 1527 + 866 + 693 + 423 + 123}\)

\(\bar x = \frac{138016}{3972}\)

\(\bar x = 34.7472306143\)

\(\bar x = 34.7\) --- approximated

The mean is approximately 34.7

Answer:

The remainder is 11.

Step-by-step explanation:

We are given the polynomial:

\(f(x) = x^3 + x^2 - 9x + 23\)

And we want to find its remainder when the polynomial is divided by:

\(x + 4\)

We can use the Polynomial Remainder Theorem. According to the PRT, if we divide a polynomial P(x) by a binomial in the form (x - a), the remainder will be given by P(a).

In this case, our binomial is (x + 4) or (x - (-4)). Hence, a = -4.

Then the remainder will be f(-4):

\(\displaystyle \begin{aligned}f(-4) &= (-4)^3 + (-4)^2 - 9(-4) + 23 \\ &= 11 \end{aligned}\)

In conclusion, the remainder of the operation is 11.

Answer:

0

Step-by-step explanation:

=> m = 3 -3/7+5

=> m = 0/12

=> m = 0

Answer:

I think it is $59.5

Step-by-step explanation:

Hope this helped have an amazing day!

By the Mean Value Theorem, there exists a number c in (1, 7) such that ƒ'(c) = 2/c and 2/c = ln7 / 6, and c ≈ 0.909.

The Mean Value Theorem (MVT) states that if a function ƒ(x) is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists a number c in (a, b) such that:

ƒ'(c) = [ ƒ(b) - ƒ(a) ] / (b - a)

ƒ(x) = 2lnx - 8 is continuous on the closed interval [1, 7], since it is the sum and composition of continuous functions.

ƒ(x) = 2lnx - 8 is differentiable on the open interval (1, 7), since its derivative ƒ'(x) = 2/x is defined and continuous on (1, 7).

Therefore, the Mean Value Theorem can be applied to ƒ(x) on [1, 7]. To find the value of c, we need to solve the equation:

ƒ'(c) = [ ƒ(b) - ƒ(a) ] / (b - a)

Substituting the given values, we get:

2/c = [ 2ln7 - 2ln1 ] / (7 - 1)

2/c = ln7

c = 2 / ln7

c ≈ 0.909

Therefore, by the Mean Value Theorem, there exists a number c in (1, 7) such that ƒ'(c) = 2/c and 2/c = ln7 / 6, and c ≈ 0.909.

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Answer:

-3.3

Step-by-step explanation:

You look at the point and count

Answer:

1/3

Step-by-step explanation:

This problem would be 1/2 x 2/3. The answer would be 1x2 over 2x3.

The Emily soccer team has the higher ratio of wins to losses.

Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.

The ratio of a and b is denoted as a : b.

Given that,

Ratio of win to loss of Emily soccer team = 9 : 12

Ratio of win to loss of Grant soccer team = 10 : 15

9 : 12 = 9 / 12 = (9 × 5) / (12 × 5) = 45 / 60

10 : 15 = 10 / 15 = (10 × 4) / (15 × 4) = 40 / 60

If 60 games are losses, then 45 games are wins for Emily soccer team.

If 60 games are losses, then 40 games are wins for Grant soccer team.

Higher ratio is for Emily soccer team.

Hence higher ratio of wins to losses is for Emily soccer team.  

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The approximate distance around the outside of the circular field is the circumference = 172.7 feet and the correct option is B.

To calculate the circumference of a circle, multiply the diameter of the circle with π (pi). The circumference can also be calculated by multiplying 2×radius with pi (π = 3.14).

We shall derive the approximate distance around the outside of the circular field by calculating for the circumference as follows:

Radius of the circular feild = 27.5

circumference of the circular feild = 2 × 27.5 feet × 3.14

circumference of the circular feild = 55 feet × 3.14

circumference of the circular feild = 172.7 feet.

Therefore, the approximate distance around the outside of the circular field is derived as the circumference which is equal to 172.7 feet.

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Answer:

Step-by-step explanation:

Typically yes you need to know

Mean

Median

Mode

and Range

Mean = average, add all numbers then divide by how many

Median = midpoint, middle number.  Be sure to list numbers from small to large if there are 2 middle numbers (this happens when there are an even amount), take the average of the 2 middle numbers

Mode = numbers that occurs the most in the list of numbers

Range = This is the largest number minus the smallest number.  

9514 1404 393

Answer:

Step-by-step explanation:

(a) As you might imagine, the disposition of apples in inventory will be one of "sold" or "discarded". (They could also be "stolen", but we'll call that "discarded", since they're not sold.) Then the inventory turnover T is the sum of numbers sold and discarded:

  T = s + d

__

(b) The value of d for Friday will be ...

  d = T -s = 34848 -29837 = 5,011 . . . value of d for Friday

Answer:

I don't think so

Step-by-step explanation:

if the s has to be more than or equal to then s would have to equal 8 or more

1) The three main trigonometric ratios of the given triangle are:

sin B = 5/9.43

cos B = 8/9.43

tan B = 5/8

2) The measure of angle A is: ∠A = 39.6°

3) The length of side x is: x = 39.5 mm

The six trigonometric ratios of a right angle triangle are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

cot x = 1/tan x

sec x = 1/cos x

cosec x = 1/sin x

1) The three main trigonometric ratios of the given triangle are:

sin B = 5/9.43

cos B = 8/9.43

tan B = 5/8

2) The measure of angle A is gotten from:

∠A = cos⁻¹ (47/61)

∠A = 39.6°

3) The length of side x using trigonometric ratios is:

21/x = tan 28

x = 21/tan 28

x = 39.5 mm

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using SOH CAH TOA

Tan 85.144 =h/130

h=tan 85.144*130

h=1530.19 fr

The rate of interest is 73%.

What is the annual rate?

The term annual percentage rate of charge refers to the interest rate for an entire year rather than just a monthly fee or rate as applied on a loan, mortgage loan, credit card, etc. It can also be referred to as a nominal APR or an effective APR. It is an annual rate of a finance charge.

Given that 1 dollar to grow to X dollars in 2 years is given by the formula X = (1+r) ².

A dollar to triple in 2 years.

Thus putting X = 3 in X = (1+r) ²

3 = (1+r) ²

Take square root on both sides:

√3 = 1 + r

Subtract 1 from both sides:

r = √3 - 1

r = 0.73

r = 73%

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Answer:

a=2x-b

Step-by-step explanation:

\(x=\frac{a+b}{2}\\\\\frac{a+b}{2} = x\\ a+b = 2x\\a= 2x-b\\\)