Find the value of variable x. If your answer is not an integer, write it in simplest radical form with the denominator rationalized.

Answer:

Option (c)

Chuy will save more than he needs and will meet his goal in less than 27 week.

Step-by-step explanation:

Given that, Chuy wants to buy a new television. The television cost is $1,350.

He decides to save the same amount of money each week.

After 8 weeks he saved $440.

Each week he saved [tex]=\$\frac{440}{8}[/tex]

                                 =$ 55

If he saved $55 each week.

At the end of 27 week he will save = $(27×55)

                                                          =$1485

Therefore he will save $1485 at the end of 27th week.

The saved money is more than the cost price of the television.

Therefore Chuy will meet his goal in less than 27 weeks.

Answer:

the awnser is the 27 week one

Step-by-step explanation:

Answer:

The answer to your question is 34°

Step-by-step explanation:

Data

m∠1 = 34°

m∠2 = 116°

m∠3 = ?

Process

1.- If lines l and m are parallel then angles 1 and 3 are interior alternate angles.

2.- Interior alternate angle measure the same.

3.-  m∠1 = m∠3

4.- m∠3 = 34°

5.- Another information given is not necessary to answer this question.

Answer: 34°

Step-by-step explanation:

There may be another way to do it; angle 1 is equal to 34°, angle one and the supplement of 3(we will call it angle 4) are supplementary. So if angle 1 equals 34, angle 4 = 180-34 (which equals 146). since angles 3 and 4 are supplementary, angle 3; would equal 180 - 146 (which equals 34).

Have a nice day! Good luck with the exam.

Answer:

[tex]2\dfrac{2}{3}[/tex] cups of flour

Step-by-step explanation:

Each batch uses 2/3 cup of flour.

If Eduardo makes 4 batches, he is going to need [tex]4X\frac{2}{3}[/tex] cups of flour.

[tex]4 X \dfrac{2}{3}=\dfrac{8}{3}=2\dfrac{2}{3}[/tex]

Eduardo is going to need [tex]2\dfrac{2}{3}[/tex] cups of flour.

Final answer:

Eduardo will need 2 2/3 cups of flour for 4 batches.

Explanation:

To find the total cups of flour Eduardo needs for 4 batches:

Amount of flour for 1 batch: 2/3 cup

Total cups for 4 batches: (2/3 cup) x 4 = 8/3 cups = 2 2/3 cups

So, Eduardo will need 2 2/3 cups of flour for 4 batches.

Answer:

Eli used 1.25 pounds of butter to make mashed potato.            

Step-by-step explanation:

We are given the following in the question:

Amount of potato used by Eli = 12.5 pounds

Amount of butter used =

[tex]\dfrac{1}{10}(\text{Amount of potato used})[/tex]

Thus, pounds of butter used by Eli is:

[tex]\dfrac{1}{2}\times 12.5\\\\=1.25[/tex]

Thus, Eli used 1.25 pounds of butter to make mashed potato.

The length of the segment is 6.63 inches

Explanation:

Given that the radius of the circle is 12 inches.

The center of the circle to the endpoint and the midpoint of the chord forms a right angled triangle.

The hypotenuse is 12 inches.

One of the sides is [tex]\frac{20}{2}=10[/tex]

Applying the Pythagorean theorem, we have,

[tex]a^2+b^2=c^2[/tex]

Where [tex]a=x, b=10[/tex] and [tex]c=12[/tex]

Thus, we have,

[tex]x^{2} +10^2=12^2[/tex]

Simplifying, we get,

[tex]x^{2} =144-100[/tex]

[tex]x^{2} =44[/tex]

Taking square root on both sides of the equation, we have,

[tex]x=6.63[/tex]

Thus, the length of the line segment is 6.63 inches.

Answer: the total area where roses will be planted is 1520 feet²

Step-by-step explanation:

The formula for determining the area of a parallelogram is expressed as

Area = base × height

From the information given,

Base = 20 + 40 = 60 feet

Height = 38 feet

Area of the rose garden = 60 × 38 = 2280 feet²

The formula for determining the area of a rectangle is expressed as

Area = length × width

From the information given,

Length = 38 feet

Width = 20 feet

Area of the rectangular walkway is

20 × 38 = 760 feet²

Therefore, the total area where roses will be planted is

2280 - 760 = 1520 feet²

Answer:

0, 1 , 2, 3, 4, 5, 6, 7, 8, 9, A, B, 10, 11, 12, 13, 14, 15, 16, 17, 18

Step-By-Step Explanation:

i will go from 0 to 20:

0: 0

1: 1

2: 2

3: 3

4: 4

5: 5

6: 6

7: 7

8: 8

9: 9

10: A (10 is another 'digit')

11: B

12: 10 (12 = 1*12^1 + 0* 12^0)

13: 11 (13 = 1*12^1 + 1*12^0)

14: 12 (14 = 1*12^1 + 2*12^0)

15: 13

16: 14

17: 15

18: 16

19: 17

20: 18

Just remember to use the notation A and B after the digit nine, for example

22: 1A

23: 1B

24: 20

In other words, the answer is 0, 1 , 2, 3, 4, 5, 6, 7, 8, 9, A, B, 10, 11, 12, 13, 14, 15, 16, 17, 18

The first twenty counting numbers in base twelve are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, 10, 11, 12, 13, 14, 15, 16, and 17.

In base twelve, the counting numbers are represented using the digits 0, 1, 2, 9, A, and B. The first twenty counting numbers in base twelve are:

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Answer:

0.875

Step-by-step explanation:

This is a binomial distribution because a child can be either a boy or a girl. We denote the probability of being a boy as p and being a girl as q. Both are mutually exclusive. The questions both are equally likely. Hence, p = q = 0.5.

The event of having at least a boy is the complement of the event of having no boy. Now the probability of having no boy is the the probability of all children being girls. This is given by

[tex]P(3G) = 0.5\times0.5\times0.5 = 0.125[/tex]

Then, the probability of at least 1 boy, by the law of complements, is

[tex]P(\ge1B) = 1 - P(3G) = 1 - 0.125 = 0.875[/tex]

Answer:

The probability of having at least one is a boy = 0.875

Step-by-step explanation:

Let B represent boy and G represent Girl.

For a couple having three children with the probability of having a boy or a girl is the same, they are 8 possible outcomes which are [BBB, BBG, BGG, BGB, GGG, GGB, GBG, GBB] = 8

BBB means having a boy followed by a boy followed by a boy while BGB means having a boy followed by a girl followed by a boy.

The probability of having at least one is a boy, it can be [ BBB BBG BGG BGB GGB GBG GBB] = 7  

Probability is the ratio number of favorable outcomes to the total number of possible outcomes.

Therefore, The probability of having at least one is a boy = 7/8 = 0.875

Answer:

17.6 feet

Step-by-step explanation:

If Diana walks forward and her angle looking to the top of the building changes to 40°, how much closer is she to the building? Round the answer to the nearest tenth of a foot.

Let x be the distance between the building and Diana,

Tan theta = opposite / adjacent side

then tan 37 = 130/x

 [tex]tan(37)=\frac{130}{x} \\xtan(37)= 130\\x=\frac{130}{tan(37)} =172.5 feet[/tex]

Let y be  distance between the building and Diana after moving forward,

[tex]tan(40)=\frac{130}{y} \\ytan(40)= 130\\y=\frac{130}{tan(40)} =154.9 feet[/tex]

now find the distance by subtracting to find how much closer she is to the building

[tex]172.5 - 154.9 = 17.6 ft[/tex]

Answer:

The -15°C temperature of the ice in their snow cones mean that the temperature of that ice is 15° below the freezing point of water.

Step-by-step explanation:

It is explained that Celsius scale was calibrated based on water. The scientists use 0°C to represent the freezing point of water and subsequently use positive numbers to indicate temperatures above the freezing point of water and negative numbers to indicate temperatures lower than the freezing point of water.

So, a temperature of -15°C simply means that the temperature is 15° lower than the freezing point of water.

Hope this Helps!!!

Answer:

Its A

Step-by-step explanation:

The expression that does not belong with the other three is −58+(−34) because it results in a more negative value compared to the other expressions.

The expression that does not belong with the other three is −58+(−34).

−58−34 and −34+58 are both addition expressions, while −34−58 is a subtraction expression. These three expressions involve adding or subtracting two numbers.

However, −58+(−34) is different because it involves adding a negative number to another negative number, which results in a more negative value. The other three expressions all result in a positive value.

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Answer:

  check your math

Step-by-step explanation:

The first subtraction was correct:

  36 -7 3/4 = 28 1/4

The second subtraction needs to be revisited.

  28 1/4 -6 2/4 = 27 5/4 -6 2/4 = 21 3/4

__

You can do what you did, but you need to pay attention to the signs.

  28 1/4 -6 2/4 = (28 -6) +(1/4 -2/4) = 22 - 1/4 = 21 3/4

The result of subtracting 2/4 from 1/4 is -1/4, not +1/4.

_____

The length of the first cut piece was 21 3/4 inches.

Answer:

21 ¾ inches

Step-by-step explanation:

36 - 6½ - 7¾

36 - (6½ + 7¾)

36 - (6 + 7 + ½ + ¾)

36 - (13 + [2+3]/4) lcm:4

36 - (13 + 5/4)

36 - (13 + 1 + ¼)

36 - 14 - ¼

22 - ¼

21¾ inches

Answer:

It is likewise significant on the grounds that it causes you decide if your business has enough cash to run or to grow it in future. Thus budget and cash flow spreadsheet is an absolute necessity in a simulation to grow.

Step-by-step explanation:

Cash flow spreadsheet alludes to the announcement of planned cash inflows and outflows. Budget cash flow spreadsheet is utilized to assess the momentary cash necessity and it can likewise be utilized to distinguish where the most extreme cash is going out and from where is the greatest inflow.

Answer:the mode is b

Step-by-step explanation:

B

Answer: 31

Step-by-step explanation:

the mode is the number that appears the most, in that case it would be 31. i also just did this in a quiz 2 seconds ago and was right.

Answer:

Therefore, the probability is P=0.000142.

Step-by-step explanation:

We have a weighted coin which lands on Heads with probability 0.17. You decide to toss it 5 times.

We calculate the  probability that the total number of times the coin lands on Heads. We get:

[tex]P=0.17^5\\\\P=0.000142[/tex]

Therefore, the probability is P=0.000142.

The answer involves using the binomial distribution to calculate the probabilities of getting different numbers of heads when tossing a weighted coin five times. The outcome of interest is the sum of probabilities of getting 0, 1, or 4 heads, as these are not prime numbers, unlike 2, 3, and 5.

The probability of a weighted coin landing on heads is given as 0.17. When tossing this coin 5 times, there are several outcomes, but we're interested in the probability that the total number of heads is not a prime number. To address the question, we need to calculate the binomial probabilities for obtaining 0, 1, 2, 3, 4, or 5 heads, since these cover all possible outcomes.

Then, we need to identify which of these are prime numbers, and which are not. Prime numbers within our range are 2, 3, and 5. Therefore, we want the probabilities of getting 0, 1, or 4 heads. These probabilities can be computed using the binomial probability formula:

P(X = k) = (n choose k) * (p^k) * ((1-p)^(n-k))

Where 'n' is the number of trials, 'k' is the number of successes (heads in this case), 'p' is the probability of getting a head on a single toss, and 'n choose k' is the binomial coefficient.

The probability of getting a total number of heads that is not a prime number is the sum of the probabilities of getting 0, 1, or 4 heads.

Answer:

The answers to the question are;

(a) 0.042 to three decimal places.

(b) 0.115 to three decimal places.

(c) μ = 8.25, σ = 1.44 to two decimal places.

Step-by-step explanation:

To solve the question, we note that this is a binomial distribution problem

(a) The probability that all 11 will be available is given by

P(11) = ₁₁C₁₁ × 0.75¹¹×0.25¹¹⁻¹¹ = 0.0422

(b) Probability of 6 or less success = P(6) + P(5) +P(4) +P(3) + P(2) + P(1) +P(0)

P(6)  = ₁₁C₆ × 0.75⁶×0.25⁵ = 0.080299

P(5) = ₁₁C₅ × 0.75⁵×0.25⁶ = 0.026766

P(4) = ₁₁C₄ × 0.75⁴×0.25⁷ = 0.063729

P(3) = ₁₁C₃ × 0.75³×0.25⁸ = 0.001062

P(2) = ₁₁C₂ × 0.75²×0.25⁹ = 0.0001180

P(1) = ₁₁C₁ × 0.75¹×0.25¹⁰ = 0.000007867

P(0) = ₁₁C₀ × 0.75⁰×0.25¹¹ = 0.00000002384

Therefore P(6) + P(5) +P(4) +P(3) + P(2) + P(1) +P(0) = 0.11462

Which is 0.115 to three decimal places

(c) The expected number of those available to serve on the jury =

Probability of success = n·p = 11×0.75 = 8.25

μ = 8.25

The standard deviation,σ [tex]=\sqrt{npq}[/tex] =[tex]\sqrt{11*0.75*0.25}[/tex] = 1.43614 ≅ 1.44 to two decimal places

The probability of everyone being available for jury duty can be calculated by multiplying the individual probabilities. More complex probabilities, such as the chance of more than 5 not being available, can be determined using a binomial distribution or a normal approximation. The expected number and standard deviation are calculated from these probabilities.

The probability of different outcomes for jury duty service can be calculated based on known probabilities and using principles of statistics. If 25% of those called find an excuse to avoid it, that means 75% are available. We can use that data to find the probability of all 11 individuals being available, or more than 5 being unavailable.

a) Probability that all 11 will be available: The probability would be (0.75)^11 = 0.042. Because all events are independent, we multiply the individual probabilities.

b) Probability that 5 or more will not be available: You would use a binomial distribution or a normal approximation to a binomial distribution to find this probability (0.115).

c) Expected number and standard deviation: The expected number of people available to serve would be the total people called multiplied by the probability of being available (11*0.75) = 8.25 people. The standard deviation, which is a bit more complex to compute, would be about 1.436 people.

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Answer:

Step-by-step explanation:

I think your question is lack of information, so here is my addition for it:

Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. Assume a production process produces items with a mean weight of 10 ounces. Calculate the probability of a defect and the expected number of defects for a 1000-unit production run in the following situations.

a,The process standard deviation is .15, and the process control is set at plus or minus one standard deviation. Units with weights less than 9.85 or greater than 10.15 ounces will be classified as defects.

My answer:

As we know that

μ = 10

σ = 0.15

The standarlized score is the value z decrease by the mean and then divided by the standard deviation.

Z = (x- μ) / σ = [tex]\frac{9.85 -10}{0,15}[/tex] ≈-1

Z = (x- μ) / σ = [tex]\frac{10.15 -10}{0.15}[/tex] ≈1

Determine the corresponding probability using the table 1 of the appendix

P (x<9.85 or x>10.15) = P(z < -1.00 or z > 1.00) = 2P9z<-1.00) = 2*0.1587 = 0.3714

She probability of a defect and the expected number of defects for a 1000-unit production = 0.3714 *100% = 37.14%

Final answer:

The answer explains how to calculate the probability of defects in a production process with a specific mean weight using the normal distribution and standard deviations.

Explanation:

Probability

In a production process where the mean weight of items is 10 ounces, the probability of defects can be calculated using the normal distribution. For instance, in a scenario with a 10% defect rate, drawing a random sample of 100 items can help determine the number of defective items expected based on standard deviations.

Expected Number of Defects

Utilizing the 68-95-99.7 empirical rule, one can assess the number of defects in a sample of products. Additionally, standard deviations are useful in determining the probability of defects to ensure product quality and calibration needs in manufacturing processes.

Answer:

1) $1966.62

2) $1968.12

3) $1968.88

Step-by-step explanation:

1) 1500 × (1 + .034/4)³²

= 1966.618592

2) 1500 × (1 + .034/12)⁹⁶

= 1968.123402

3) 1500 × (e^(8×0.0314))

= 1968.880502

Answer:

1968.880502

Step-by-step explanation:

Final answer:

The trigonometric functions and their inverse functions are related to each other because they undo each other's actions. Inverse trigonometric functions give the angle whose trigonometric ratio is a given value. The domains and ranges of inverse trigonometric functions are restricted to ensure that they are well-defined.

Explanation:

The trigonometric functions and their inverse functions are related to each other because they undo the actions of the other function. Let's take the sine function as an example. The sine function takes an angle as input and gives the ratio of the opposite side to the hypotenuse as output. Its inverse function, arcsine, takes a ratio as input and gives the angle whose sine is that ratio as output.

These comparisons make sense in the light of the definition of the inverse of a function because an inverse function undoes the action of the original function. In the case of trigonometric functions, they represent a ratio between the sides of a right-angled triangle, and their inverses give the corresponding angle.

The domains and ranges of the inverse trigonometric functions make sense in relation to their parent functions because they are restricted to a specific range to ensure that the inverse function is well-defined. For example, the domain of arcsine function is [-1, 1] because the output of sine function is always between -1 and 1. By restricting the domain, we can ensure that the inverse function is a one-to-one mapping and has a well-defined output for each input.

Answer:

4/3*π*[tex]100^{3}[/tex]

Step-by-step explanation:

water level rises to the 200 mL mark, it means the ball diameter is 200, and the radius is: 100

So the  voulume of the ball is: 4/3*π*[tex]r^{3}[/tex]

= 4/3*π*[tex]100^{3}[/tex]

Hope it will find you well.

Answer:

0.57 yr  

Step-by-step explanation:

To find the doubling time with continuous compounding, we should look at the formula:

[tex]FV = PVe^{rt}[/tex]

FV = future value, and

PV = present value

If FV is twice the PV, we can calculate the doubling time, t

[tex]\begin{array}{rcl}2 & = & e^{rt}\\\ln 2 & = & rt\\t & = & \dfrac{\ln 2}{r} \\\end{array}[/tex]

1. David's doubling time

[tex]\begin{array}{rcl}t & = & \dfrac{\ln 2}{0.06125}\\\\& = & \textbf{11.317 yr}\\\end{array}[/tex]

2. Violet's doubling time

The formula for interest compounded periodically is

[tex]FV = PV\left (1 + \dfrac{r}{n} \right )^{nt}[/tex]

where

n = the number of payments per year

[tex]\begin{array}{rcl}9600 & = & 4800\left (1 + \dfrac{0.065}{4} \right )^{4t}\\\\2 &= & (1 + 0.01625 )^{4t}\\& = & 1.01625^{4t}\\\ln 2& = & 4 (\ln 1.01625)\times t \\& = & 0.064478t\\t& = & \dfrac{\ln 2}{0.064478}\\\\& = & \textbf{10.750 yr}\\\end{array}[/tex]

3. David's doubling time vs Violet's

11.317 - 10.750 = 0.57 yr

It would take 0.57 yr longer for David's money to double than Violet's.

The average rate of change of f over intervals of x from x = 3 to  = 3.5 is - 159.

Given that the function is,

f (x) = - 5x³

Used the formula for the average rate of change of function f at interval [a, b] is,

f' (x) = [ f (b) - f (a) ] / (b - a)

Here, f (x) = - 5x³

At x = 3;

f (3) = - 5 × 3³

= - 135

At x = 3.5;

f (3.5) = - 5 × (3.5)³

= - 214.4

Hence, the average rate of change of f over intervals of x from x = 3 to  = 3.5 is,

f ' (x) = [- 214.5 - (- 135)] / (3.5 - 3)

f ' (x) = [- 79.5] / 0.5

f ' (x) = - 159

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Final answer:

The average rate of change of the function f(x) = -5[tex]x^3[/tex] from x = 3 to x = 3.5 is -158.75.

Explanation:

The average rate of change (ARoC) can be determined using the formula:

ARoC = (f(x2) - f(x1)) / (x2 - x1)

In this case, the given function is f(x) = -5x^3. To find the ARoC from x = 3 to x = 3.5, substitute these values into the formula:

ARoC = (-5[tex](3.5)^3 - (-5(3)^3)[/tex]) / (3.5 - 3)

Simplifying the equation gives:

ARoC = (-5(42.875) - (-5(27))) / (0.5)

ARoC = (-214.375 + 135) / 0.5

ARoC = -79.375 / 0.5

ARoC = -158.75

Therefore, the average rate of change of f(x) from x = 3 to x = 3.5 is -158.75.

Answer: Osvoldo did not meet his goal.

Step-by-step explanation:

If he ate 220 grams of carbohydrates today and 55 grams were from whole grains, it means that the percentage of the carbohydrates he ate today that came from whole grains is

55/220 × 100 = 25%

Since he has a goal of getting at least 30% percent of his grams of carbohydrates each day from whole grains, then he did not meet his goal because 25% is lesser than 30% and he needs 30% or more

Answer:  The number of girls in the auditorium is represented by the algebraic expression y=(4x +72) /5

Step-by-step explanation:

Hi, to answer this question we have to analyze the information given:

So, the total number of boys is:

x + 18  

Number of girls = y

Number of boys / number of girls = 5/4

(x+18) /y = 5/4

Solving for "y"

4 (x +18) =5 y

4x +72 = 5y

(4x +72) /5 = y

The number of girls in the auditorium is represented by the algebraic expression y=(4x +72) /5

Answer:

y = mx + b

Hope I helped!!! :)

~Nuha

Answer:

Please see the attached pictures for full solution.

First problem: let [tex]b[/tex] and [tex]h[/tex] be the base and height of the rectangle, respectively. We know that [tex]b=11+h[/tex] (the base if 11 longer than the height), and that [tex]2(b+h)=58[/tex] (the perimeter is 58 centimeters).

So, we have the system

[tex]\begin{cases}b=11+h\\2(b+h)=58\end{cases}\iff\begin{cases}b=11+h\\b+h=29\end{cases}[/tex]

Use the first equation to substitute into the second:

[tex]b+h=11+h+h=2h+11=29 \iff 2h=18 \iff h=9[/tex]

And since the base is 11 centimeters longer, we have

[tex]b=11+h=11+9=20[/tex]

Second problem: Let [tex]m,n,o[/tex] be the number of cards owned by Mark, Norm and Oscar, respectively. We know that:

[tex]m+n+o=810[/tex] (they have 810 cards in total)

[tex]n=m+30[/tex] (Norm has 30 more than Mark)

[tex]o=2m[/tex] (Oscar has twice as much as Mark)

The second and third equation express [tex]n[/tex] and [tex]o[/tex] in terms of [tex]m[/tex], and substituting those expressions in the first equation we have

[tex]m+n+o=m+(m+30)+2m=810 \iff 4m+30=810 \iff 4m=780 \iff m=195[/tex]

And then we can use again the second and third equations:

[tex]n=m+30=195+30=225[/tex]

[tex]o=2m=2\cdot 195=390[/tex]

Final answer:

The maximum height attained by the rocket is 134 meters.

Explanation:

To find the maximum height attained by the rocket, we can use the kinematic equation:

Final velocity squared = Initial velocity squared + 2 * acceleration * distance

First, convert the initial velocity from feet per second to meters per second. Then, plug in the values into the equation:

0² = (8.8 m/s²) * H + (288 ft/s)²

Solve for H, which represents the maximum height attained:

H = (288 ft/s)² / (2 * g)

Finally, convert the maximum height from feet to meters:

H = (288 ft/s)² / (2 * 8.8 m/s²) = 134 m

Answer:

a) The marginal cost function is given by

C'(x) = 4 + 0.04x + 0.0003x² (in dollars)

b) C'(70) = $8.27

Step-by-step explanation:

C(x) = 1000 + 4x + 0.02x² + 0.0001x³

a) Marginal cost is usually defined as the cost of producing one extra unit of product. It expresses how much the total cost is changing with respect to number of units of product.

Mathematically,

MC = (dC/dx) = C'(x)

For this question,

C'(x) = 4 + 0.04x + 0.0003x²

b) C'(70) means the marginal cost at x = 70 units, that is, how much the total cost is changing after the production of 70 units; the cost of producing one extra unit of product after producing 70 units.

C'(x) = 4 + 0.04x + 0.0003x²

C'(70) = 4 + 0.04(70) + 0.0003(70²)

C'(70) = $8.27

Hope this helps!