Solve the two-step equation. − 2 3 x – 21 4 = 27 4

Answer:

C) 52 in^3

Step-by-step explanation:

The first is to determine the formula of the volume of the box, which would be the following:

 V = height * length * width

Knowing that we have a rectangular piece we will determine the maximum volume, we will double a distance x (which will be the height) in the width and length of the piece, therefore as it is on both sides, the length and width are defined from the Following way:

length = 10 - 2 * x

width = 8 - 2 * x

height = x

Now we calculate the volume:

V = x * (10-2 * x) * (8-2 * x)

To determine the maximum volume we will give values to x in order to see how it behaves:

Let x = 2.5

V = (5) * (3) * (2.5) = 37.5

Let x = 2

V = (6) * (4) * (2) = 48

Let x = 1.5

V = (7) * (5) * (1.5) = 52.5

Let x = 1

V = (8) * (6) * (1) = 48

Let x = 0.5

V = (9) * (7) * (0.5) = 31.5

It can be seen that the greatest volume is obtained when the height is equal to 1.5 and its volume is 52.5 in ^ 3

Answer: 38 mph

Step-by-step explanation:

Add. 10 plis 28 is 38.

Answer: 19 miles

Step-by-step explanation:

Distance = speed × time

Biking at 10 mph, it takes Kristen 1/2 hour to reach the train station to go to work. This means that the distance covered on her way to the train station is

0.5 × 10 = 5 miles

Kristen then takes the train to work, and it takes another 1/2 hour for her to get to work when the train travels 28 mph. Distance covered by the train is

0.5 × 28 = 14 miles

Therefore, the distance that Kristen travels to work is

14 + 5 = 19 miles

Answer:

496

Step-by-step explanation:

I am assuming that there are options lacking. The average score, due to the Law Of Big Numbers, using a big enough sample will be close to the mean of the random variable. Thus the mean of the average scores will be close to 496 if the process is done many times.

The mean of the average scores will be close to the population mean of 496.

The mean of the average scores will be close to the population mean, which is 496. The Central Limit Theorem states that as the sample size increases, the sample mean approaches the population mean. In this case, since we are choosing an SRS of 100 students, the mean of the average scores will be close to the population mean of 496.

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Answer:

It depends on what negative number it is. For example -23 is 23 units or whatever to 0.

Step-by-step explanation:

Answer:

p=2

Step-by-step explanation:

Use the slope formula

(p-(-1))/(6-9)=-1

(p+1)/-3=-1

p+1=3

p=2

Answer:

Step-by-step explanation:

Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis represent

change in the value of y = y2 - y1

Change in value of x = x2 -x1

y2 = final value of y

y 1 = initial value of y

x2 = final value of x

x1 = initial value of x

The line passes through (9,-1) and (6,p) and the slope is 1

y2 = p

y1 = - 1

x2 = 6

x1 = 9

Therefore,

(p - - 1)/(6 - 9) = - 1

(p + 1)/- 3 = - 1

(p + 1) = - 1 × - 3

p + 1 = 3

p = 3 - 1

p = 2

Answer:

The answer to your question is QG = 55.8 ft

Step-by-step explanation:

Data

QG = x

Process

1.- Find T

The sum of the internal angles in a triangle equals 180°

          G  +  Q  +  T  = 180

-Solve for T

            T  =  180 - G  -  Q

- Substitution

            T = 180 - 41 - 67

-Simplification

             T = 72°

2.- Use the law of sines to find QG

              QG / sin T = GT / sin Q

-Solve for QG

              QG = GT sinT / sin Q

-Substitution

              QG = 54 sin 72 / sin 67

- Simplification

              QG = 54 (0.951)/0.921

-Result

             QG = 55.8 ft        

Answer:

Step-by-step explanation:

Considering the given triangle QGT, to determine QG, we would apply the sine rule. It is expressed as

a/SinA = b/SinB = c/SinC

Where a, b and c are the length of each side of the triangle and angle A, Angle B and angle C are the corresponding angles of the triangle. Likening it to the given triangle, the expression becomes

QG/SinT = GT/SinQ = QT/SinG

The sum of the angles in a triangle is 180°. It means that

T = 180 - (41 + 67) = 72°

Therefore

QG/Sin72 = 54/Sin 67

Cross multiplying, it becomes

QGSin67 = 54Sin72

0.921QG = 54 × 0.951

0.921QG = 51.354

QG = 51.354/0.921

QG = 55.8 ft

Answer:

[tex](f - g)(x) = {x}^{3} - 6 {x}^{2} + 18x - 10[/tex]

Step-by-step explanation:

The given functions are:

[tex]f(x) = {x}^{3} - 2 {x}^{2} + 12x - 6[/tex]

and

[tex]g(x) = 4 {x}^{2} - 6x + 4[/tex]

We want to find

[tex](f - g)(x)[/tex]

Recall that:

[tex](f - g)(x) = f(x) - g(x)[/tex]

This implies that:

[tex](f - g)(x) = {x}^{3} - 2 {x}^{2} + 12x - 6 - (4 {x}^{2} - 6x + 4)[/tex]

[tex](f - g)(x) = {x}^{3} - 2 {x}^{2} + 12x - 6 - 4 {x}^{2} + 6x - 4[/tex]

We combine similar terms to get:

[tex](f - g)(x) = {x}^{3} - 6 {x}^{2} + 18x - 10[/tex]

Answer:

Solution given:

f(x)=x3−2x2+12x−6

g(x)=4x2−6x+4

now

(f-g)(x)=f(x)-f(g)=x3−2x2+12x−6-4x²+6x-4

=x³-6x²+18x-10

Answer:

Step-by-step explanation:

Let x represent the constant amount by which the length and width of the garden is increased.

Tyler has a rectangular garden that measures 10 m wide by 13 m long. He wants to increase the area to 208 m² by increasing the width and length by the same amount. This means that the new length of the garden would be (13 + 2x) cm and the new width of the garden would be (10 + 2x) cm. Therefore,

(13 + 2x)(10 + 2x) = 208

130 + 26x + 20x + 4x² -208 = 0

4x² + 46x - 208 - 130 = 0

4x² + 46x - 78 = 0

Dividing through by 2, it becomes

2x² + 23x - 39 = 0

2x² + 26x - 3x - 39 = 0

2x(x + 13) - 3(x + 13) = 0

2x - 3 = 0 or x + 13 = 0

x = 3/2 or x = - 13

Since the value of x cannot be negative, then

x = 3/2 = 1.5 m

The length of the new garden is

13 + 1.5 = 14.5 m

Answer:

34.8 liters

Step-by-step explanation:

He has 35.8 liters.

He uses 28.6 liters.

Now that tanks has 35.8 liters - 28.6 liters = 7.2 liters

The capacity of the tank is 42 liters, and he has only 7.2 liters.

The fill up will be 42 liters - 7.2 liters = 34.8 liters

Answer: he bought 34.8 liters of gas.

Step-by-step explanation:

Let x represent the number of liters of gas that Alberto bought.

At the beginning of the week, Alberto's car has 35.8 liters of gasoline in its tank. He uses 28.6 liters of gasoline during the week. This means that the number of liters of gas left would be

35.8 - 28.6 = 7.2

Then he completely fills the tank with gas. If the gas tank of Alberto's car holds a total of 42 liters of gas., it means that

x + 7.2 = 42

x = 42 - 7.2

x = 34.8 liters

Answer: B 8/5 hr

Step-by-step explanation:

One maid can clean the house in 2 hours. This means that the rate at which she cleans the house per hour is 1/2

Another maid can do the job in 8 hours. This means that the rate at which the other maid cleans the house per hour is 1/8

If they work together, they would work simultaneously and their individual rates are additive. This means that their combined working rate would be

1/2 + 1/8 = 5/8

Assuming it takes t hours for both of them to clean the room working together, the working rate per hour would be 1/t. Therefore,

5/8 = 1/t

t = 8/5 hour

Option B is correct. Working together, the two maids can clean the house in 8/5 hours.

Let's assume that the combined rate of both maids working together is x house cleaned per hour. We can set up the equation:

1 maid's rate + another maid's rate = combined rate

1/2 + 1/8 = x

Solving for x:

4/8 + 1/8 = x

5/8 = x

The combined rate of the maids working together is 5/8 house cleaned per hour. To find how long it will take them to clean the house together, we can set up the equation:

(5/8) house per hour = 1 house

Let t be the time it takes them to clean the house together. We can write the equation:

(5/8) * t = 1

Solving for t:

t = 1 / (5/8)

t = 8/5 hours.

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Answer:

Mixed mode expression

Step-by-step explanation:

Mixed mode expression is an expression that contains or have operands that have different data types.

In this case, she has to generate values that have type equal to the operands in this situation.

Answer:

The answer to this question is N(0.50,0.091), just took a quiz with same question.

Step-by-step explanation:

Answer: the amount of interest earned is $44.7

Step-by-step explanation:

The formula for determining simple interest is expressed as

I = PRT/100

Where

I represents interest paid on the amount deposited.

P represents the principal or amount deposited.

R represents interest rate

T represents the duration in years.

From the information given,

P = $1295

R = 7%

T = 180 day. Assuming there are 365 days in a year. Converting 180 days to years, it becomes

180/365 = 0.49315 year

Therefore,

I = (1295 × 7 × 0.49315)/100 = $840,

I = $44.7

The equation for the resale value of the stereo is V = V0 * e^(-kt), where V0 is the initial value, V is the resale value at time t, and k is the decay constant. Using the given resale value after 4 years, we can solve for k and substitute it back into the equation to find the resale value of the stereo as a function of time.

To find an equation giving the resale value of the stereo as a function of time, we can use the formula for exponential decay: V = V0 * e^(-kt). V0 represents the initial value, V represents the resale value at time t, and k is the decay constant. The given resale value after 4 years is $275, so we can substitute these values into the equation: 275 = 1300 * e^(-4k). To solve for k, divide both sides by 1300 and take the natural logarithm of both sides: ln(275/1300) = -4k. Calculate the logarithm and solve for k to get the decay constant. Finally, substitute the value of k into the equation to get the complete equation for the resale value of the stereo.

Explanation:

The sample mean is not always equal to the population mean but if we take more and more number of samples from the population then the mean of the sample would become equal to the population mean.

The Central Limit Theorem states that we can have a normal distribution of sample means even if the original population doesn't follow normal distribution, But we have to take a lot of samples.

Suppose a population doesn't follow normal distribution and is very skewed then we can still have sampling distribution that is completely normal if we take a lot of samples.

Answer: A cereal with 0 grams of sugar has a rating of about 57

Step-by-step explanation:

The equation modelling the taste rating of a cereal, y, in a survey, where x is the number of grams of sugar per serving is expressed as

yˆ=2.391x + 57.420

This is a straight line graph represented in the slope intercept form which is expressed as

y = mx + c

Where

m represents the slope of the straight line

c represents the y intercept. The y intercept is the point at which x = 0.

From the given equation, the y intercept is 57.420

It means that a cereal with 0 grams of sugar has a rating of about 57

Mrs. Mathewson can serve orange juice to 4 guests. The solution was found by first converting the fractions to the same denominator, then dividing the total orange juice by the amount per guest, and taking into account that you can't serve fractions of a guest.

The problem presented here is a basic division problem that requires you to divide the total amount of orange juice by the amount served to each guest. Mrs. Mathewson has 7/8 quarts of orange juice and she would like to serve each guest 3/16 quarts of orange juice.

Firstly, we'll convert both fractions to the same denominator for simplicity. As 8 is a multiple of 16, we can leave the second fraction as it is (3/16) and change the first fraction to 14/16 (which is the same as 7/8). Now, we divide 14 by 3 which gives us roughly 4.6.

This result means Mrs. Mathewson can serve orange juice to 4 guests with a bit left over. As we can't serve a fraction of a guest, it means she can only serve 4 whole guests.

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Mrs. Mathewson can serve orange juice to 14 guests.

To determine how many guests Mrs. Mathewson can serve orange juice, we need to find the quotient of the total amount of orange juice and the amount per guest. Given that there are 7/8 quarts of orange juice and Mrs. Mathewson wants to serve 3/16 quarts per guest, we divide the total amount by the amount per guest: (7/8) ÷ (3/16) = (7/8) × (16/3) = 14 guests.

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Answer:

34 = -2

Step-by-step explanation:

20 = 7 x (5-3) = 34

(8-6) - 4 = -2

So the  answer is 34 = -2

The equation 20+7 • (5-3) = (8-6) - 4, when evaluated using the order of operations, gives the result 34 = -2, which indicates that the original equation is not balanced.

Let's evaluate the expression 20+7 • (5-3) = (8-6) - 4 using the order of operations, which can be remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

First, we solve the expressions in parentheses: 7 • (5-3) = 7 • 2 = 14 and  (8-6) - 4 = 2 - 4 = -2.

Then we perform the addition: 20 + 14 = 34. At this point, we have 34 = -2, which is not correct. Therefore, the original equation is not balanced.

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This is the formula to solve for the vertex.

Example Question:

Find the vertex of y = -0.5x^2 + 100x

-b/2a = -100/2(-0.5) = -100/-1 = 100

The x coordinate of the vertex is 100.

Best of Luck!

P.S. this is 1000th question i've answered :)

The outward pressure created by nuclear fusion within the core of stars, like the Sun, counteracts the force of gravity, preventing them from collapsing under their own self-gravity. This delicate balance sustains the stability and longevity of stars.

The correct answer is D. The outward pressure created by nuclear fusion.

Explanation: Stars, including the Sun, are massive celestial objects formed primarily of hydrogen and helium gas. In their cores, the extreme temperatures and pressures enable nuclear fusion reactions to occur, converting hydrogen into helium and releasing tremendous amounts of energy. This energy generates an outward pressure that counteracts the inward force of gravity, maintaining the star's equilibrium and preventing it from collapsing under its own self-gravity. This balance between gravitational forces pulling inward and outward pressure pushing outward due to nuclear fusion is what keeps stars, like the Sun, stable and prevents them from collapsing.

Answer:

7

Step-by-step explanation:

(x+3)/(x+8) = 2/3

3x + 9 = 2x + 16

x = 7

Answer: the angle of elevation from the person on the ground to the top of the volcano is 87.7°

Step-by-step explanation:

The person, his angle of elevation and his distance from the foot of the mountain forms a right angle triangle.

The altitude of the mountain represents the opposite side of the right angle triangle.

The distance of the person from the base of the volcano represents the opposite side of the right angle triangle.

To determine the angle of elevation from the person on the ground to the top of the volcano, we would apply the tangent trigonometric ratio.

Tan θ, = opposite side/adjacent side. Therefore,

Tan θ = 3000/120 = 25

θ = Tan^-1(25)

θ = 87.7° to the nearest tenth.

Answer:

2,880 tons of sand

Step-by-step explanation:

In this question, we are asked to calculate the amount of tons of sand required to produce a certain amount of tarry materials if a certain amount of sand had produce an amount of tarry materials.

We work as follows:

First, we write the relation that 144,000 tons of sand produces 125,000 barrels of tarry material, then x of tons would produce 2,500 barrels of tarry materials

To find c, we cross multiply:

x * 125,000 = 2,500 * 144,000

x = (2,500 * 144,000)/125,000

x = 2,880

Answer:

P ( X < 4 ) = 0.3015

Step-by-step explanation:

Given:

- The ratings for current lives on a scale 0 - 10 were normally distributed with parameters mean (u) and standard deviation (s).

                                   u = 5.3

                                   s = 2.5

Find:

Find the probability that a randomly selected study​ participant's response was less than 4.

Solution:

- Declare a random variable X that follows a normally distribution with parameters u and s, mean and standard deviation respectively.

                                  X~N( 5.3 , 2.5 )

- To determine the probability of the rating to be less than 4 for a randomly selected study participant's response we have:

                                  P ( X < 4 )

- Compute the Z-score value for the limit given:

                                  P ( Z < (4 - 5.3) / 2.5 )

                                  P ( Z < -0.52 )

- Use the Z-Table to calculate the above probability as follows:

                                  P ( Z < -0.52 ) = 0.3015

- Hence, the required probability is equivalent to Z-score value probability:

                                    P ( X < 4 ) = P ( Z < -0.52 ) = 0.3015

The probability that a randomly selected study participant's response was less than 4 is 0.3015.

To find the probability that a randomly selected study participant's response was less than 4, we can use the properties of the normal distribution. Given that the mean is 5.3 and the standard deviation is 2.5, we can standardize the value 4 using the z-score formula: z = (X - µ) / σ, where X is the value of interest, µ is the mean, and σ is the standard deviation. Once we find the z-score, we look up this value in the standard normal distribution table (Z-table) or use a calculator to find the probability.

The probability that a randomly selected study participant's response was less than 4 is therefore 0.3015, or 30.15% when converted into percentage form.

Answer:

(a)His monthly Interest Rate=0.8%

(b)Annual Interest Rate = 9.6%

(c)[tex]500(1.008)^m[/tex]

Step-by-step explanation:

For a Principal P invested at a yearly rate r, compounded m times in t years

Amount at Compound Interest= [tex]P(1+\frac{r}{m})^{mt}[/tex]

Comparing with Jerry's equation y=388 (1.008)

(a)His monthly Interest Rate= 0.008=0.8%

(b)Annual Interest Rate= Monthly Interest Rate X 12 =0.8 X 12 = 9.6%

(c)If I invest $500 at the same rate of return,

Total Money after m months

= [tex]P(1+\frac{r}{m})^{mt}[/tex][tex]=500(1+0.008)^{m}[/tex][tex]=500(1.008)^m[/tex]

Final answer:

Jerry's monthly interest rate is 0.8%, and his annual interest rate is approximately 9.96%. An investment of $500 in the same account would grow according to the equation [tex]y = 500(1.008)^{m}[/tex], where m represents the months invested.

Explanation:

Jerry says he's got his money in a great account that compounds interest monthly. The equation [tex]y=388(1.008)^{m}[/tex] represents how much money he has at the end of the month. The monthly interest rate is found in the equation inside the parentheses, 1.008, which means the monthly interest rate is 0.8% (since 1.008 is equal to 1 plus 0.008 or 1 + 0.8/100). To find the annual interest rate, we need to use the compounding formula, which for monthly compounding can be simplified to [tex](1 + monthly interest rate)^{12} - 1[/tex]. so, [tex](1.008)^{12}- 1[/tex] gives an annual rate of approximately 9.96%.

To write an equation representing your total money if you invest $500 in an account with the same rate of return, we use the formula [tex]y = P(1 + r)^{m}[/tex], where P is the principal amount ($500), r is the monthly interest rate (0.008), and m represents the number of months the money has been invested. Therefore, the equation is [tex]y = 500(1.008)^{m}[/tex].

Answer:

The answers to the question are as follows

a). Please see the examples of bit strings of length 5 and 6 that are palindromes in the following explanation.

b). The number of even length palindromes is [tex]26^{\frac{n}{2} }[/tex]

The number of odd length palindromes is [tex]26^{\frac{n+1}{2} }[/tex]

c). The number of  ternary string palindromes of length n is 702.

Step-by-step explanation:

a). Examples of bit strings of length 5 and 6 that are palindromes are

Bit strings of length 5                                 Bit strings of length 6

Kayak                                                           Hannah

Level                                                            Redder

Civic                                                             Terret

Madam                                                         Kakkak

Solos                                                            degged

Tenet

Rotor

Minim

Radar

Refer

Terret

b). When n is even, we have a choice of any of the 26 characters for the first letter, similarly, we can choose any character for the second, and so on up till the n/2 th position after which subsequent letters depend on the letter chosen before the half point following the definition of a palindrome.

Therefore we have n/2 independent choices with repetition therefore we have [tex]26^{\frac{n}{2} }[/tex] palindromes of even length with or without meaning in the alphabet

On the other hand, when n is odd, we are free to chose any letter up to the middle letter as before this means we have [tex]\frac{n-1}{2} +1 = \frac{n+1}{2}[/tex] free choices

Therefore the number of odd length palindromes are [tex]26^{\frac{n+1}{2} }[/tex]

c). For a ternary string palindrome, we have 26 letters for the first position, and also 26 for the second, while the third is the same as the first which is one option.

Where n = 2 we have 26 ways of selecting the first and second letters which are equal

Therefore the number of  ternary string palindromes of length n  are 26×26 + 26 = 702

Bit string palindromes of length 5 and 6 are strings that are the same forward and backward, like '10101' or '100001'. The number of palindromic bit strings of length n is 2 raised to the floor of n/2, and the number of ternary string palindromes of length n is 3 raised to the floor of n/2.

A palindrome is a string that remains the same when reversed. Examples of bit string palindromes of length 5 include '10001', '01110', '10101', '01010'. For length 6, examples could be '100001', '011110', '101101', '010010'.

In general, to calculate the number of palindromic bit strings for any given length, the first half of the string can be anything (2 ⌊n/2⌋ possibilities), and the second half must mirror the first. Thus there are 2 ⌊n/2⌋ bit string palindromes of length n.

For ternary palindromes (strings composed of the digits 0, 1, and 2), use the same logic but switch the base to 3. Thus there are 3 ⌊n/2⌋ ternary string palindromes of length n.

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Answer:

The decimal and fraction equivalent to the percentage of the vote maria received is 0.55 and  [tex]\frac{11}{20}[/tex] .

Step-by-step explanation:

Given:

Maria received 55% of the vote in a student council election.

Now, to find the decimal and fraction of the percentage of the vote maria received.

Percentage of vote Maria received = 55%.

So, the fraction and decimal of the percentage in its simplest form:

[tex]\frac{55}{100}[/tex]

On simplifying it:

[tex]=\frac{11}{20}[/tex].

Thus, the fraction is [tex]\frac{11}{20} .[/tex]

[tex]\frac{11}{20}[/tex]

[tex]=0.55.[/tex]

Hence in the decimal is [tex]0.55.[/tex]

Therefore, the decimal and fraction equivalent to the percentage of the vote maria received is 0.55 and  [tex]\frac{11}{20}[/tex] .

Answer: its 25 because you're adding the whole line from P to R, so 12.5 + 12.5 is 25

Step-by-step explanation:

P to T is 12.5

T to R is 12.5

Add those together

12.5 + 12.5 gives you 25

Answer:

25 in.

Step-by-step explanation:

In a rectangle the diagonals bisect each other.

Therefore PT = TR = ST = TQ = 12.5 in.

PR = PT + TR = 12.5 + 12.5

= 25 in.

Answer:

-429/629

Step-by-step explanation:

Use angle difference formula:

sin(x − y) = sin x cos y − sin y cos x

Assuming x and y are in the first quadrant:

sin(x − y) = sin x cos y − √(1 − cos²y)√(1 − sin²x)

Plugging in values:

sin(x − y) = (8/17) (12/37) − √(1 − (12/37)²)√(1 − (8/17)²)

sin(x − y) = (8/17) (12/37) − (35/37)(15/17)

sin(x − y) = -429/629