Find the value of each variable.
105°
86°
106°/2°

Answer:

I don’

think so

Step-by-step explanation:

Answer:

680 sq. units

Step-by-step explanation:

Multiply the height (17) by the length (40) which gets us 680. This is because if you "move" the triangle on the left of 17, to the right, you complete a rectangle, which can be easily solved.

Hope this helps!

:)

Answer:

$148.00

Step-by-step explanation:

y is the total amount of money the electrician will charge.

x is the hours they work

$68 is the materials cost

y = $68 + 40(x)

It should all equal y since y is the total cost for the electricians service. You plug in 2 in place of x since it took them 2 hours.

y = 68 + 40(2)

y = 68 + 80

y = 148

Answer:

line of best fit: y = -2.9114x + 46.569

Step-by-step explanation:

Plugging in your table into Excel, it turns out that y = -2.9114x + 46.569  provides a better fit of the data points into the line.  Please see the attached image for details.

Hope this helps.

The rate at which the wage earners and rural households should save is 21%.

Given that:

Depreciation (δ) = 0.03

Capital output ratio (c) = 3

Profit share of income (π/Y) = 0.5

Savings out of capital income (sπ) = 25% = 0.25

We know that the modified Harrod-Domar growth model is given as:

c(g+δ) = (sπ - sW)(Yπ) + sW

We can rearrange the above equation to find the value of savings out of wage income as follows:

sW = c(g+δ - sπ(Yπ))/ (sπ - π/Y)

Plugging in the given values:

sW = 3(0.04 + 0.03 - 0.25(0.5))/ (0.25 - 0.5)

On solving the above equation, we get:

sW = 0.21 or 21%

Hence, the rate at which the wage earners and rural households should save is 21%. Therefore, the required answer is 21%.

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a. The probability of success (hitting the target) is constant for each trial (88% or 0.88).

b. The probability of hitting the 6th target is:

P(X = 1) = C(1, 1) * 0.88^1 * (1 - 0.88)^(1 - 1) = 0.88

c. Using the binomial probability formula as before, with p = 0.88 and n = 3:

P(X = 1) = C(3, 1) * 0.88^1 * (1 - 0.88)^(3 - 1)

P(X = 2) = C(3, 2) * 0.88^2 * (1 - 0.88)^(3 - 2)

P(X = 3) = C(3, 3) * 0.88^3 * (1 - 0.88)^(3 - 3)

a) The three characteristics of this scenario that indicate we are working with Bernoulli trials are:

The experiment consists of a fixed number of trials (eight shots).

Each trial (shot) has two possible outcomes: hitting the target or missing the target.

The probability of success (hitting the target) is constant for each trial (88% or 0.88).

b) To find the probability of hitting the 6th target (considered as a single trial), we can use the binomial probability formula:

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

where:

P(X = k) is the probability of getting exactly k successes,

C(n, k) is the binomial coefficient or number of ways to choose k successes out of n trials,

p is the probability of success in a single trial, and

n is the total number of trials.

In this case, k = 1 (hitting the target once), p = 0.88, and n = 1. Therefore, the probability of hitting the 6th target is:

P(X = 1) = C(1, 1) * 0.88^1 * (1 - 0.88)^(1 - 1) = 0.88

c) To find the probability that the first time hitting the target is not until the 4th shot, we need to consider the complementary event. The complementary event is hitting the target before the 4th shot.

P(not hitting until the 4th shot) = P(hitting on the 4th shot or later) = 1 - P(hitting on or before the 3rd shot)

The probability of hitting on or before the 3rd shot is the sum of the probabilities of hitting on the 1st, 2nd, and 3rd shots:

P(hitting on or before the 3rd shot) = P(X ≤ 3) = P(X = 1) + P(X = 2) + P(X = 3)

Using the binomial probability formula as before, with p = 0.88 and n = 3:

P(X = 1) = C(3, 1) * 0.88^1 * (1 - 0.88)^(3 - 1)

P(X = 2) = C(3, 2) * 0.88^2 * (1 - 0.88)^(3 - 2)

P(X = 3) = C(3, 3) * 0.88^3 * (1 - 0.88)^(3 - 3)

Calculate these probabilities and sum them up to find P(hitting on or before the 3rd shot), and then subtract from 1 to find the desired probability.

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The longest poster that can fit in the box must have dimensions of 10 inches (height) by 20 inches (length) by 12 inches (width).

To find the longest poster that can fit in the box, we need to determine the longest dimension of the box itself. Since the box is 10 inches high, the longest poster that can fit in the box must have a height of no more than 10 inches.

Now, we need to consider the other two dimensions of the box. The box is 20 inches long and 12 inches wide, so the longest poster that can fit in the box must have a length of no more than 20 inches and a width of no more than 12 inches.

As for why we can only fit one maximum-length poster in the box but we can fit multiple 22-inch posters in the same box, it's because the length and width of the box are larger than the length and width of the 22-inch poster.

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Explanation:

The general cosine template is

y = A*cos(B(t - C)) + D

where in this case

We only really need to worry about the B value. To get the period T, we do the following

T = 2pi/B

T = (2pi)/(pi/4)

T = 2pi * (4/pi)

T = 8

Note how the pi terms canceled. The period is 8 seconds, which is the length of one full cycle. This is the time it takes for the pendulum to do one full swing (eg: start at the right, swing to the left all the way, then swing back to the right again).

The result of 8 we got has nothing to do with the D = 8 value (this D value could be any other number and T = 8 would still be the case as long as B doesn't change of course).

Answer:

5,750

Step-by-step explanation:

if he has 10 of each then you can multiply each bag by 10 and then multiply the amount of bags to the amount the coin is worth

The given fractions have equal value, so Liam is correct.

Equivalent fractions are defined as fractions that have different numerators and denominators but the same value. For example, 2/4 and 3/6 are equivalent fractions because they are both equal to 1/2. A fraction is part of a whole. Equivalent fractions represent the same part of a whole.  

Liam is claiming that the fraction -(5/12) is equivalent to 5/-12.

Thus, we can say that:

The fraction  -(5/12) can be described as the opposite of a positive number divided by a positive number. A positive number divided by a positive number always results in a positive quotient and its' opposite is always negative.

The fraction 5/-12 can be described as a positive number divided by a negative number which always results in a negative quotient

The fractions have equal value, so Liam is correct

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Answer:

9300$

Step-by-step explanation:

Answer:

x=3

Step-by-step explanation:

i just know

Answer:

Cole bought 7 pants and 9 shirts.

Step-by-step explanation:

Let p represent the number of pants and s represent the number of shirts.

Then using the provided data two equations can be formed.

p + s = 12...(i)

22p + 16s = 234...(ii)

Solve (i) and (ii) simultaneously.

Multiply (i) by 16 and subtract the resultant equation from (ii) as follows:

16p + 16s = 192

-22p - 16s = -234

-6p = -42

p = 7

Substitute p = 7 in (i) and solve for s as follows:

p + s = 16

7 + s = 16

s = 9

Thus, Cole bought 7 pants and 9 shirts.

the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis is  8π

y = x^2 and x = 2

=> y = 4

Volume = [int 0 to 4] π x^2 dy

= [int 0 to 4] π y dy

= 8π

In mathematics, "volume" is a mathematical quantity that describes the three-dimensional space occupied by an object or closed surface. Volume units are cubic units such as m3, cm3, and in3. Volume is sometimes called capacity.

Volume is a measure of the volume contained in an object. For example, if 100ml of water fills the rim of the cup, the capacity is said to be 100ml. Volume can also be defined as the amount of space occupied by a three-dimensional object.

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Answer:a) The 12 o'clock position: Al and Betty are 35 feet above the ground when they are at the 12 o'clock position on the Ferris wheel.

b) The 9 o'clock position: Al and Betty are 5 feet above the ground when they are at the 9 o'clock position on the Ferris wheel.

c) The 6 o'clock position: Al and Betty are 20 feet above the ground when they are at the 6 o'clock position on the Ferris wheel.

d) The 8 o'clock position: Al and Betty are 5 feet above the ground when they are at the 8 o'clock position on the Ferris wheel.

e) 10 seconds after passing the 11 o'clock position: Al and Betty are 35 feet above the ground when they are 10 seconds after passing the 11 o'clock position on the Ferris wheel.

2) Al and Betty are 30 feet above the ground when they are at the 2 o'clock position on the Ferris wheel.

Step-by-step explanation:

Answer:

12(+2)

Step-by-step explanation:

12x+24

12(x+2)

Answer: By the addition property of equality, AC2 plus AB2 = BC multiplied by DC plus AB2.

Answer:

31°F

Step-by-step explanation:

image is attached

Answer:

C. y= 105(1+0.05)^x

Step-by-step explanation:

y = a(1 + r)t    the formula

The acutal width of the picnic area by using proportion if the scale used is 3 inches : 2 yards will be 60 yards.

Let the actual width of the picnic area be x yards.

According to the given question.

Laura measured a picnic area near the river and made a scale drawing.

The scale she used was 3 inches : 2 yards.

⇒ The scale is 3 inches : 2 yards

The width of the picnic area in the drawing is 90 inches.

As we know that, a proportion is a fraction of a total amount, and the measures are related using a rule of three.

Thereofore, the acutal width of the picnic area by using proportion if the scale used is 3 inches : 2 yards is given by

3inches : 2 yards = 90inches : x

⇒ 3x = 180

⇒ x = 60yards

The acutal width of the picnic area by using proportion if the scale used is 3 inches : 2 yards will be 60 yards.

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Answer:

A) first term is 23 the second term is 37

B) 8

C) y-x. x-y, x+y

Step-by-step explanation:

Answer:

5x + 6

Step-by-step explanation:

first multiply 1/2 by 10x, that's 5x. then multiply 1/2 by 12, that's 6

Answer:

5x + 6

Step-by-step explanation:

\( \frac{1}{2} (10x + 12) \\ = (\frac{1}{2} \times 10x) + (\frac{1}{2} \times 12) \\ = \frac{10x}{2} + \frac{12}{2} \\ = 5x + 6\)

Jhon will take 6 hours to compete the same work

Men and work :

             This question is based on the concept of men and work

given,

John and Jane together can clean the house in 2 hours 24 minutes

                               = 120 + 24

                               = 144 minutes

Let,

          Jane can complete the work alone in x minutes

then,

        Jhon will take (x+120) minutes to complete the same work alone

According to question,

                                    \(\frac{1}{x} +\frac{1}{x+120} = \frac{1}{144}\)

                                     \(\frac{x+120+x}{x(x+120)} =\frac{1}{144}\)

                               144(2x+120) = x(x+120)

                      288x + 17280= \(x^{2}\) + 120x

                         \(x^{2}\) - 168x -17280 = 0

                          (x + 72) (x-240) =0

                             x= -72 and x =240

x can not be negative, so x =240 minute =4 hours

 Jane can complete the work alone in 240minutes = 4 hours

Jhon will take (x+120) minutes to complete the same work

                    x+120

                = 240 + 120

               = 360 minutes = 6 hours

Hence,

           Jhon will take 6 hours to compete the same work

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\(7x + 12 = 9x - 6\)

\(7x + 12 - 7x = 9x - 6 - 7x\)

\(12 = 2x - 6\)

\(12 - 6 = 2x -6 - 6\)

\(6 = 2x - 12\)

\(6 + 12 = 2x\)

\(18 = 2x\)

\(18 \div 2 = x\)

\(9 = \bold{ x}\)

In pythagoras, c is the hypotenuse. That is AC. Where a is AB and b is BC.

\( {c}^{2} = {a}^{2} + {b}^{2} \)

\( {(6 x + 5)}^{2} = {(7x + 12)}^{2} + {BC}^{2} \)

\( {((6 \times 9) + 5)}^{2} = {((7 \times 9)}^{2} + 12)^{2} +{BC}^{2} \)

\( {(54 + 5)}^{2} = {(63 + 12)}^{2} + {BC}^{2} \)

\( {59}^{2} = {75}^{2} + {BC}^{2} \)

\(3481 = 5625 + {BC}^{2} \)

\(3481 - 5625 = {BC}^{2} \)

\( - 2144 = {BC}^{2} \)

\( \sqrt{ - 2144} = BC\)

Answer:

Belt = $34

wallt = $22

Step-by-step explanation:

The company sold 66 wallets and 83 belts for a total of $4,274 the previous month and sold 66 wallets and 86 belts for a total of $4,376 this month.

Let w represent wallets and b represent belts:

66w + 83b = $4,274

66w + 86b = $4,376

66w + 86b - 66w + 83b = $4,376 - $4,274

3b = $102

b = $34 this is the price for a belt.

To find the price of a wallet we need to replace b with 34 in the equation:

34×83 + 66w = $4,274

2,822 + 66w = $4,274

66w = $1,452

w = $22

Answer:

(3.2, 12)

Step-by-step explanation:

Total cost for gas = $12

Cost per gallon = $3.75

Letting total cost of gas be y and number of gallons be x, maximum number of gallons of gas he can buy would be ;

Total cost of gas/ cost per gallon = 12 / 3.75 = 3.2 gallons

Therefore , the coordinate pair (x, y) = (3.2, 12)

Answer:

\(53 = 110 \left(\dfrac{1}{2}\right)^{\dfrac{x}{6}}\)

Step-by-step explanation:

The decay of a radioactive substance can be modeled using the half-life formula:

\(\large{\boxed{N(t)=N_0\left(\dfrac{1}{2}\right)^{\frac{t}{t_\frac{1}{2}}}}}\)

where:

In this case, the initial amount of substance is N₀ = 110 grams and the half-life is t_{1/2} = 6 days.

To find the number of days, x, required for the substance to decay to 53 grams, we can set N(t) = 53 and t = x.

Therefore, the equation that can be used to determine the number of days, x, required for the substance to decay to 53 grams is:

\(\boxed{53 = 110 \left(\dfrac{1}{2}\right)^{\dfrac{x}{6}}}\)

\(\hrulefill\)

To solve the equation, divide both sides by 110:

\(\left(\dfrac{1}{2}\right)^{\dfrac{x}{6}}=\dfrac{53}{110}\)

Take natural logarithms of both sides:

\(\ln \left(\dfrac{1}{2}\right)^{\dfrac{x}{6}}=\ln \dfrac{53}{110}\)

\(\textsf{Apply the power law:} \quad \ln x^n=n \ln x\)

\(\dfrac{x}{6}\ln \left(\dfrac{1}{2}\right)=\ln \left(\dfrac {53}{110}\right)\)

Multiply both sides by 6:

\(x\ln \left(\dfrac{1}{2}\right)=6\ln \left(\dfrac{53}{110}\right)\)

Divide both sides by ln(1/2):

\(x=\dfrac{6\ln \left(\dfrac{53}{110}\right)}{\ln \left(\dfrac{1}{2}\right)}\)

Evaluate:

\(x=6.32063555...\)

Therefore, the number of days required for the substance to decay to 53 grams is approximately 6.32 days, as calculated using the half-life formula.

The scenario for test statistic is estimated z-score to make inferences about the population mean which is unknown.

x is the sample mean = 11

μ is the population mean = unknown

σ is the population standard deviation = 5

And n is the sample size= 1,166

Assuming a normal distribution for the number of alcoholic beverages consumed per week,

Use a z-test to calculate the test statistic.

The formula for the z-score is,

z = (x - μ) / (σ / √(n))

Since the population mean is unknown,

Not possible to calculate the exact z-score,

Calculate an estimated z-score using the sample mean,

z = (x - μ) / (σ / sqrt(n))

z = (11 - μ) / (5 / sqrt(1166))

z ≈ (11 - μ) / 0.146

Therefore, need to know the population mean μ for the z-score in the calculated test statistic.

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