Judy purchased a carpet for $173.95 and a table set for $88.08. She received a 18% discount but had to pay 8% sales tax. What is the total price?

Answer:

24 miles per gallon

Step-by-step explanation:

The flour and sugar coral that will be use to make the cookies is 2 1/4 cups.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this situation, Tucker is making cookies the recipe called for 1/3/4 cups of flour and 1/2cup of sugar.

The flour and sugar coral that will be use to make the cookies will be:

= 1 3/4 + 1/2

= 2 1/4

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Answer:

14

Step-by-step explanation:

Answer:

The answer is 14

Step-by-step explanation:

2×2 - 3(-3) + 1

4 + 9 + 1

14

The three pairs are (AB = 6, BC = 6) (AB = 4, AC = 4√2) and (BC = 2√2, AC = 4). So, First option, Option 5. and Option 6 are correct answers.

Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.

The formula for a 30-60-90 triangle is this:

1) Side opposite to 30 will be value a.

2) Side opposite to 60 will be value a√3

3) Hypotenuse will be 2a.

AB is opposite of the angle with 30 degree measurement.

BC is opposite of the angle with 60 degree measurement.

The sides of an isosceles right triangle are in the ratio,

1:1:√2

where √2 is the hypotenuse.

For the example, BC = 2√2, then AC = 2√2  x √2 = 4.

Therefore, the three pairs are;

1. (AB = 6, BC = 6)

5. (AB = 4, AC = 4√2)

6.(BC = 2√2, AC = 4).

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Answer:

(230.21 ; 233.13)

Step-by-step explanation:

Given the data :

230.66, 233.05, 232.58, 229.48, 232.58

To calculate the 90% CI

WE obtain the mean and standard deviation of the sample data :

Mean of sample, ΣX /n = 1158.35/5 = 231.67

The standard deviation of the sample, s = 1.531 (Using calculator).

(The 90% Tcritical value, 2 sided, df = 4) = 2.132

The confidence interval, CI :

Mean ± Tcritical * s/√n

C.I = 231.67 ± (2.132 * (1.531/√5)

C. I = 231.67 ± 1.4597

(231.67 - 1.4597) ; (231.67 + 1.4597)

(230.21 ; 233.13)

The value of the statement the quantity 32 minus 16 multiplied by 9 is

- 112.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

The given statement is the quantity 32 minus 16 multiplied by 9.

The numerical form of the statement is,

= (32 - 16×9).

First, we'll multiply according to PEMDAS rule.

= (32 - 144).

= - 112.

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The value of the statement the quantity 32 minus 16 multiplied by 9 is

- 112.

We have,

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

The given statement is the quantity 32 minus 16 multiplied by 9.

The numerical form of the statement is,

= (32 - 16×9).

First, we'll multiply according to PEMDAS rule.

= (32 - 144).

= - 112.

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Answer:

It is not a polynomial. It is a trinomial. Polynomials have 4 or more terms

Answer:

it is a not polynomial.

Step-by-step explanation:

In particular, for an expression to be a polynomial term, it must contain no square roots of variables, no fractional or negative powers on the variables,

Answer:Well, we already see that the number of girls is greater than the number of boys, to find the result of girls, just do the division that is 30:2= 15 and boys is 30:3= 10

i hope i have helped you

Step-by-step explanation:

Answer:

8 boys, 22 girls

To solve, you must isolate the variable. This means moving the variable and it's coefficient to the other side of the equation with only the same variable on the same side with all the constants on the other side.

If you multiply, divide, add, subtract, square root, exponent both sides of the equation by the same value, that end value stays the same.

Q)

Lets set the amount of boys to x.

The amount of girls is 3x-2 as the amount of boy is x.

Set up an equation.

x+3x-2 = 30

30 is the amount of members.

Add 2 on both sides.

x+3x+2-2=30+2

Simplify by combining like terms.

4x = 32

Divide 8 on both sides.

\(\frac{4x}{4} =\frac{32}{4}\)

x = 8

There are 8 boys in the class.

Plug back into the equation or subtract from 30 to solve for the amount of girls.

30 - 8 = 22

8(3) - 2 = 22

To find the distance between points A and B, we can use trigonometry and the given information.

Let's label the distance between A and B as "d". We know that point C is 94.4 meters away from point A. From angle A, we have the measure of 72°, and from angle C, we have the measure of 30°.

Using trigonometry, we can use the tangent function to find the value of "d".

tan(72°) = d / 94.4

To solve for "d", we can rearrange the equation:

d = tan(72°) * 94.4

Using a calculator, we can evaluate the expression:

d ≈ 4.345 * 94.4

d ≈ 408.932

Therefore, the distance between points A and B is approximately 408.932 meters.

The probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

To find the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts, we need to use the concept of the Central Limit Theorem.

In this case, we know that the mean voltage of a single battery is 15 volts and the standard deviation is 0.2 volts. When batteries are connected in series, their voltages add up.

The combined voltage of four batteries connected in series is the sum of their individual voltages. The mean of the combined voltage will be 4 times the mean of a single battery, which is 4 * 15 = 60 volts.

The standard deviation of the combined voltage will be the square root of the sum of the variances of the individual batteries. Since the batteries are connected in series, the variance of the combined voltage will be 4 times the variance of a single battery, which is 4 * (0.2)^2 = 0.16.

Now, we need to calculate the probability that the combined voltage of four batteries is 60.8 or more volts. We can use a standard normal distribution to calculate this probability.

First, we need to standardize the value of 60.8 using the formula:

Z = (X - μ) / σ

Where X is the value we want to standardize, μ is the mean, and σ is the standard deviation.

In this case, the standardized value is:

Z = (60.8 - 60) / sqrt(0.16)

Z = 0.8 / 0.4

Z = 2

Next, we can use a standard normal distribution table or calculator to find the probability associated with a Z-score of 2. The probability of obtaining a Z-score of 2 or more is approximately 0.0228.

Therefore, the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

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Answer:

B

Step-by-step explanation:

To answer this question, we need to find the area of the rectangle with sides 14 cm and 9 cm, and, then, we need to subtract from this area, the area of the semicircle with radius = 7 cm (that is, 14 cm /2 = 7 cm).

Therefore, we have:

1. Find the area of the rectangle:

2. Find the area of the semicircle:

The area of a circle is given by:

Therefore, for a semicircle, we have:

Then, we need to subtract this value from the obtained in calculating the area of the rectangle:

From the question, the answer is option D, 49.07 cm squared.

Answer: 540

Step-by-step explanation:

Given: A polling company reported that 53​% of 1018 surveyed adults said that rising gas prices are "quite annoying."

To find: The exact value of 53​% of 1018.

\(53\%\text{ of }1018 = \dfrac{53}{100}\times1018\)  [we divide a percentage by 100 to convert it into a fraction of decimal]

\(=\dfrac{53954}{100}=539.54\\\\\approx540\)

Hence, the 540  adults said that rising gas prices are "quite annoying."

Thus, the exact value = 540

There are 56 numbers of schedules that are possible for Hannah.

Basically, A permutation is an arrangement of items in a specific direction or sequence. One should consider both the selection and the arrangement while dealing with permutation. In permutations, ordering is crucially important. The permutation is seen as an ordered combination, in other words.

Given Hannah, a roller coaster enthusiast has decided to ride 2 of the world's 8 most famous roller coasters this year.

total roller coasters = 8

since Hannah wants to ride 2 roller coasters,

that can be completed in a certain manner, after completing the first one she will go for the next,

total number of possibilities is calculated by permutation,

ⁿPₓ = n!/(n - x)!

n = 8,  x = 2

⁸P₂ = 8!/(8 - 2)!

⁸P₂ = 8*7*6!/6!

⁸P₂ = 56

Hence there are 56 different schedules are possible.

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2nd X..

I hope that this is correct

The solution of the equation 4x - 3  = 5 is not extraneous .

Extraneous solutions are values that we get when solving equations that aren't really solutions to the equation.

Therefore, let's solve the equation to know whether it is extraneous solution.

Hence,

4x - 3  = 5

add 3 to both sides of the equation

4x - 3 + 3 = 5 + 3

4x = 8

divide both sides of the equation by 4

4x / 4 = 8 / 4

x = 2

Therefore, it is not extraneous solution.

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Answer: -36

Step-by-step explanation: a negative and a negative give a positive so -36/-3=12

(to check your answer you can also always just multiply the two numbers ex: 12 x -3= -36)

Answer:

Step-by-step explanation:

Hello, just apply the instructions as below.

\(3(x-2)^2(x+5)^3\)

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

4.61x10^5

Step-by-step explanation:

You want the first number to be between 0 and 10, not equaling either. So you move the decimal place to the left. Then, you write the second half, which is that you multiply it by ten to the power of however many digits you moved to the left for, which is 5.

Answer: f < 9

Step-by-step explanation:

first, cross multiply 2 and 2:

f - 5 < 4

f < 9

Answer:

f < 9

Step-by-step explanation:

=> (f-5)/2 < 2

multiplying both sides by 2

=> 2(f-5)/2 < 2×2

=> f-5 < 4

adding 5 to both sides

=> f-5+5 < 4+5

=> f < 9

The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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Answer:

pretty sure it's 360 :)

Step-by-step explanation:

...

Area = ( 1/2 × 4 × 3 ) + ( 1/2 × 5 × 6 )

Area = 6 + 15

Area = 21 ft^2

Answer:

C

Step-by-step explanation:

the answer is c

Answer:

Jenell began with $80.

Step-by-step explanation:

see image. I did this with one variable and with two, depending on what math you are studying. You only need to work through one side of the solution shown. See image.

Answer:

P(x)=\((40000)( 0.98)^x\)

A=40000    B=0.98
P(7)= 34700

Step-by-step explanation:

Notice the population can be modeled as:

P(x)=\(A B^x\)

For X=0 P(0)=40000=A (Initial population)
So A=40000
For x=1 (one year after) P=39200

\(39200=40000 B^1\)
solving for B
\(B=\frac{39200}{40000} =0.98\)
So B=0.98

So the population can be modeled as

P(x)=\((40000)( 0.98)^x\)

Now at 7 years:

P(7)=\((40000)( 0.98)^7\)= 34725.02133
Needs to be rounded to the nearest hundred
This is 34700 bonobos (7 years after the study began)

Answer:

12$

Step-by-step explanation:

Answer:

$1.20 per pound

Step-by-step explanation:

The reason for this answer is because you divide 10 by 10 so its 1 pound and whatever you do to the bottom you do to the top so you divide 12 by 10 which equals 1.2 aka $1.20