Solve each system of equations. 2c + 6d = 14 7 7 3 3 + 1/2 c = -2

Answer:

x = -7

Step-by-step explanation:

4(2x + 14) = 0

Isolate the variable (x)

2x + 14 = 0 ÷ 4

2x + 14 = 0

2x = 0 - 14

2x = -14

x = -14 ÷ 2

x = -7

The volume of the display case is 2161 1/8 cubic inches.To find the volume of a rectangular prism-shaped display case, we multiply its length, width, and height.

Given that the display case is 30 1/2 inches wide, 10 1/2 inches long, and 32 1/4 inches tall, we can calculate the volume as follows:

Volume = Length * Width * Height

Using the given measurements:

Volume = 10 1/2 inches * 30 1/2 inches * 32 1/4 inches

To simplify the calculation, we can convert the mixed numbers to improper fractions:

Volume = (21/2) inches * (61/2) inches * (129/4) inches

Next, we multiply the fractions:

Volume = (21/2) * (61/2) * (129/4) = 17289/8

The resulting fraction, 17289/8, is an improper fraction. To convert it back to mixed number form:

Volume = 2161 1/8 in³.

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Answer:

probability that a player wins after playing the game once = 5/9

Step-by-step explanation:

To solve this, we will find the probability of the opposite event which in this case, it's probability of not winning and subtract it from 1.

Since, we are told that there are 2 fair six sided die thrown at the same time and that he receives a five or a one on either die ;

Probability of not winning, P(not win) = 4/6.

Thus;

P(winning) = 1 - ((4/6) × (4/6))

P(winning) = 1 - 4/9 = 5/9

A company pays $5,000 for equipment. The book value of the equipment at the end of Year 2 will be $4,000.

The book value of an asset can be calculated by subtracting the accumulated depreciation from the initial cost of the asset.

Given:

Initial cost of the equipment = $5,000

Annual depreciation = $500

After Year 1, the accumulated depreciation would be $500.

So, the book value at the end of Year 1 would be:

Book value at the end of Year 1 = Initial cost - Accumulated depreciation

Book value at the end of Year 1 = $5,000 - $500 = $4,500

After Year 2, the accumulated depreciation would be $500 + $500 = $1,000 (since depreciation is $500 per year).

So, the book value at the end of Year 2 would be:

Book value at the end of Year 2 = Initial cost - Accumulated depreciation

Book value at the end of Year 2 = $5,000 - $1,000 = $4,000

Therefore, the book value of the equipment at the end of Year 2 is $4,000. Hence, the correct answer is option a. $4,000.

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The exact solution of this equation involves solving a quadratic equation, which may not result in a simple integer value for x.

To find the point (x, y) on the function f(x) = 6 - 7x that is closest to the point (-10, -4), we need to minimize the distance between the two points.

The distance between two points (x1, y1) and (x2, y2) is given by the formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

In this case, we want to minimize the distance between the point (-10, -4) and any point on the function f(x) = 6 - 7x. So we can set up the distance equation:

d = sqrt((-10 - x)^2 + (-4 - (6 - 7x))^2)

To find the point (x, y) that minimizes the distance, we can find the value of x that minimizes the distance equation. Let's differentiate the distance equation with respect to x and set it equal to zero to find the critical point:

d' = 0

Differentiating and simplifying the equation, we get:

(-10 - x) + (-4 - (6 - 7x))(-7) = 0

Solving this equation will give us the value of x at the closest point. Plugging this x-value into the function f(x) = 6 - 7x will give us the corresponding y-value.

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Answer:

201.5

Step-by-step explanation:

806/4=201.5

this is the answer

Answer:

201.5

Step-by-step explanation:

The researchers are investigating the perception of three-dimensional shapes on computer screens and specifically examining the components of a square figure or cube necessary for viewers to perceive details of the shape. They vary the stimuli to include fully rendered cubes, cubes with incomplete sides, and cubes with missing corner information. Four participants are recruited for an intense study, and their accuracy rates are measured across the three figure conditions. The trials are presented in different orders for each participant using a random-numbers table to determine unique sequences.

In this study, the researchers are interested in understanding how viewers perceive details of three-dimensional shapes on computer screens. They manipulate the stimuli by presenting fully rendered cubes, cubes with incomplete sides, and cubes with missing corner information. By varying these components, the researchers aim to identify which elements are necessary for viewers to accurately perceive the shape.

Four participants are recruited for an intense study, indicating a small sample size. While a larger sample size would generally be preferred for generalizability, intense studies often involve fewer participants due to the time and resource constraints associated with conducting a large number of trials. This approach allows for in-depth analysis of individual participant performance.

The participants are trained on how to detect subtle deformations in the shapes, which suggests that the study aims to assess their ability to perceive and discriminate fine details. After the training, the participants' accuracy rates are measured across the three different figure conditions, likely reported as a percentage of correctly identified shape details.

To minimize potential biases, the trials are presented in different orders for each participant, using a random-numbers table to determine unique sequences. This randomization helps control for order effects, where the order of presenting stimuli can influence participants' responses.

The researchers in this study are investigating the perception of three-dimensional shapes on computer screens. By manipulating the components of square figures or cubes, they aim to determine which elements are necessary for viewers to perceive shape details accurately. The study involves four participants, an intense study design, and measures accuracy rates across different figure conditions. The use of randomization in trial presentation helps mitigate potential order effects.

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Answer:

f − 1  ( x )  =  x  +  12

Step-by-step explanation:

To find the inverse, interchange the variables and solve for  

y .

I hope this helps.

Answer: f^-1(x) = x + 12.

Step-by-step explanation:

1. Make f(x) = y.

y = x - 12

2. Switch the x and y variables:

x = y - 12

3. Solve for y by adding 12 on both sides:

x + 12 = y

4. Change y into f^-1(x):

f^1(x) = x + 12

I hope this is helpful! :)

Step-by-step explanation:

v = u + at

v-u = at

a = (v -u)/t

When t = 4, u=10, v=50

a = (50-10)/4

a= 40/4

a = 10

Using the binomial distribution, it is found that she should expect it to land on 3 9 times.

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The expected value of the binomial distribution is:

E(X) = np

In this problem:

Then, the expected value is given by:

E(X) = np = 36 x 0.25 = 9.

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The amount that Sarah's parent owe the bank now, will be the value of the loan which is $76, 800.

The amount owed to a bank is the money that one either borrowed from the bank, or owes the bank for services such as overdraft or maintenance fees.

In this case, the amount of Sarah's parents will owe to the bank is the amount that they took as a loan which is $76, 800. The money in their account is still there's unless they default on paying off the loan.

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Answer:

92*.15=13.8   Add the $13.8 to the $92 and you get $105.8

Step-by-step explanation:

The missing factor in the second equation is 1, and the completed equation is: -24y + (-5) = -4(6y + 5/4)

We know that the GCF of -24y and -20 is 4. To find the missing factor in each equation, we can divide both terms by the GCF of 4.

For the first equation, we have:

-24y = 4 * (-6y)

Dividing both sides by 4, we get:

-6y = -24/4

Simplifying, we get:

-6y = -6

Therefore, the missing factor in the first equation is -1, and the completed equation is:

-24y + 20 = -4(6y - 5)

For the second equation, we have:

-20 = 4 * (-5)

Dividing both sides by 4, we get:

-5 = -20/4

Simplifying, we get:

-5 = -5/1

Therefore, the missing factor in the second equation is 1, and the completed equation is:

-24y + (-5) = -4(6y + 5/4)

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Answer:

Here is the answer hope it helps:)

Answer:

0.25

Step-by-step explanation:

0.25 x 24 = 6

Answer:

\(a) \: 421 {mm}^{2} \: = 0.000421 {m}^{2} \)

\(b) \: 9.3 {kg}^{2} \: = 9,300,000 {g}^{2} \)

\(c) \: 25 {kl}^{2} \: = \: 25,000,000 {g}^{2} \)

\(d) \: 1439 {m}^{2} = 0.001439 {k m}^{2} \)

Joaquin will need 1 and two fifths cups to make his famous chocolate chip cookies for his friend's birthday party

To solve this problem we will use a rule of three with the problem information:

5 people-------- 1/4 cup of butter

28 people -------- x

Applying the rule of three we get:

x = ( 28 people * 1/4 cup of butter) / 5 people

x = 1,4 cup of butter

x = 1 + 2/5 cup of butter = 1 and two fifths cups

It describes the proportionality of 3 known data and an unknown data. When you have more than 3 known facts that are involved in the proportionality, it is known as a compound rule. The rule of three is also known as a direct proportions.

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Answer:

f(-8) = -2

Step-by-step explanation:

The equation of the function is given as;

F(x) = x/4

To get F(-8), we simply substitute-8 for x

Thus we have

F(-8) = -8/4 = -2

Answer:

f(-8) = -2

Step-by-step explanation:

took the test on edge

Answer:

see below

Step-by-step explanation:

TMN = TRS = 60 because they are similar triangles

Answer:

∠1 = 52

∠2 = 128

∠4 = 128

Step-by-step explanation:

∠3 and ∠1 are vertical angles

As we now vertical angles are congruent

So if ∠3 = 52°, then ∠1 also equals 52°

∠3 and ∠4 are supplementary angles

supplementary angles add up to equal 180

Thus, ∠3 + ∠4 = 180

If ∠3 = 52°

Then 52 + ∠4 = 180

180 - 52 = 128

Hence, ∠4 = 128

∠4 and ∠2 are vertical angles

Like stated previously vertical angles are congruent

So if ∠4 = 128 then ∠2 also equals 128

For the month ended, the cost of goods sold was $600.

Cost of goods sold (COGS) is a crucial accounting formula that calculates the expenses incurred when a company sells its products or services. Therefore, $600 represents the cost of items sold for the just finished month.

A measurement of the cost of products sold throughout the accounting period is the cost of goods sold (COGS). It is computed by adding the ending inventory after deducting the beginning inventory from the cost of the products bought during the accounting period.

The following formula is used to determine Dig the Dogs, Inc.'s cost of goods sold for the just ended month: Starting inventory is zero, and the cost of the goods was $900. $300 is the ending inventory.

Beginning Inventory = 0

Cost of Goods Purchased = $900

Ending Inventory = $300 .

COGS = Beginning Inventory + Cost of Goods Purchased - Ending Inventory  COGS = 0 + 900 - 300   = $600

Therefore, the cost of goods sold for the month ended is $600.

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The correlation coefficient between X and Y is approximately -0.483.

We must first determine the mean and standard deviation for both X and Y in order to calculate the correlation coefficient between X and Y.

X has a mean of:

(-5 + 1 + 2 + 11)/4 = 2.25 is the mean of X.

Y has a mean of:

average of Y = (5 + 3 - 3 + 0)/4 = 1.

The value of X's standard deviation is

s_X = sqrt([(-5 - 2.25)^2 + (1 - 2.25)^2 + (2 - 2.25)^2 + (11 - 2.25)^2]/3) = 5.1478

The value of Y's standard deviation is

s_Y = sqrt([(5 - 1)^2 + (3 - 1)^2 + (-3 - 1)^2 + (0 - 1)^2]/3) = 3.7712

After that, we can figure out the correlation between X and Y:

cov(X, Y) = [(-5 - 2.25) × (5 - 1) + (1 - 2.25) × (3 - 1) + (2 - 2.25) × (-3 - 1) + (11 - 2.25) × (0 - 1)]/3 = -7.25

We can finally determine the correlation coefficient:

r = cov(X, Y)/(s X, s Y)=-7.25/(5.1478 3.7712)=-0.483

Thus, roughly -0.483 is the correlation coefficient between X and Y.

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As we know 1 kilometer = 39370.079 inches

and, 8.39 kilometer = 330,315 inches.

Kilometers: - It is a unit of length in the international system of units (SI) equal to one thousand meters. It is now the measurement unit used for expressing distances between geographical places on land in most of the world.

Inches: - It is a unit of length in the British imperial and united states customary system of measurement. It is equal 1/36 yard or 1/12 of a foot.

To convert a kilometer measurement to an inch measurement, multiply the length by the conversion ratio.

Since 01 kilometer = 39,370.07874 inches,

We can use this simple formula to convert:

          inches = kilometers × 39,370.079

Now, according to the question:

inches = 8.39 × 39370.079

inches = 33.315

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Answer:

110.09174

Step-by-step explanation:

120yd/1.09meters per yard=110.09174...

The answer needs to be rounded to whatever decimal place is called for.

Domain of the function is,  (0, ∞).

Range of the function is, (-∞, ∞).

x - intercept of the function is, (1, 0).

Vertical asymptote of the function is,  None.

What is domain and range?

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x).

A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

First to find the domain of the function,

Since, all input values shown on the x-axis make up a graph's domain.

We can see that values of x values are from 0 to ∞.

Hence, the domain is (0, ∞).

Now to find the range.

Since, the y-axis on a graph represents the possible output values, or range.

The y - axis having the values from -∞ to ∞.

Hence, the range of the function is, (-∞, ∞).

x - intercept is the point where function crosses the x - axis.

Here function crosses x - axis at (1, 0).

Hence, the x - intercept is (1, 0).

A graph's vertical asymptote is the vertical line at x = a where the graph trends toward positive or negative infinity as the inputs go closer to a.

So, the vertical asymptote is x = 0.

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Answer: 9

Step-by-step explanation:

Let the consecutive odd numbers be y, y+2 and y+4.

Five times the smallest of three consecutive odd integers is seven more than twice the largest. Find the largest integer can be expressed as:

5y = 2(y+4) + 7

5y = 2y + 8 + 7

5y = 2y + 15

5y - 2y = 15

y = 3

The smallest odd number is 5

The largest integer will be:

= y + 4

= 5+4

= 9

Answer:

Step-by-step explanation:

p

Answer:

The proof consists of two columns, where the first column contains a numbered chronological list of steps, called Statements, leading to the desired conclusion. The second column contains the justifications, called Reasons, to support each step in the proof.

Step-by-step explanation: