Carmine mixes 2. 8 pounds of cashews with almonds to make a trail mix. He divides the trail mix into 5 equal portions. Each portion weighs 1. 5 pounds. Which equation and solution shows the total amount of almonds he used in the mixture?

Answer:

The car is 13 years old

Step-by-step explanation:

Lets say Car is x and the Truck is y, so the trucks age = x + 3 = y

    Lets find the value of the Car or x

x + 3 = 1/2(x + 7)------- >

first we will divide x by 1/2 and 7 by 1/2, So...

x + 3 = (x / 1/2 + 7 / 1/2)------- >

x + 3 = 1/2x + 3.5------->

next Isolate variable x,

x + 1/2x = 3 + 3.5

1/2x = 6.5, So...

x = 13 and in turn, y = 13 + 3

:)

Answer:

-249/28

Step-by-step explanation:

Answer:

Given the equation,  −6y + 7= ​24x + 25, you'll have to transform this equation into its slope-intercept form, y = mx + b:

−6y + 7 = 24x + 25

Subtract 7 from both sides:

−6y + 7 − 7 = 24x + 25 − 7

−6y = 24x + 18

Divide both sides by −6:

\(\frac{-6y}{-6} = \frac{24x + 18}{-6}\)

y = -4x - 3 ← This is the slope-intercept form, where m = slope and b = y-intercept.

Next, you need to find at least two points to plot on your graph. We can do this by using the y-intercept, (0, -3). Using the slope, -4 and the y-intercept (0, -3):

Start at (0, -3) then go 4 units down (because it is a negative slope) and 1 unit to the right. Your next point should be (1, -7). You can connect those two points and create a line.    

The attached screenshot shows the graph of the linear equation, y = -4x - 3.

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Answer:

\(\frac{1}{2^5}\)

Step-by-step explanation:

The equation the represents the situation is x / 12 = 6, and the number of songs that he downloaded is 72

Consider the total number of songs that Oliver downloaded as x

The given statement is "The number of song Oliver has downloaded this year, divided by 12, is equal to 6

The equation will be

x / 12 = 6

The equation is defined as the mathematical statement that shows the relationship between one expression and another expression. The equation consist of variables, numbers and mathematical operator

The equation is

x / 12 = 6

Solve the equation

x = 6 × 12

= 72 songs

Therefore, he downloaded 72 songs this year

The complete question is

The number of song Oliver has downloaded this year, divided by 12, is equal to 6. What is an equation that represent this situation, and how many song has Oliver downloaded?

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So, the formula that we're going to use is:

Compound interest

A = P(1 + r/n)ⁿˣ

Where

A = amount

P = principal = $100

r = rate = 8% = 8 / 100 = 0.08

x = time

In this case, n=4 since it is being compounded quarterly, so:

The answer is $126.82.

The Law of Large Numbers is a fundamental concept in probability theory and statistics stating the number of trials of a random event increases, the average of the outcomes approaches the expected value of the event. It's better to use 500 trials.

In other words, as we repeat an experiment a large number of times, the proportion of times that a certain outcome occurs will converge to its probability of occurrence. This is an important concept in statistical inference, as it helps to ensure that the results of a sample are representative of the population from which it was drawn.

Now, if you were using the relative frequency of an event to estimate the probability of the event, it would be better to use 500 trials rather than 100 trials. The reason is that the larger the number of trials, the more accurate the estimate of the probability is likely to be.

Using a larger sample size reduces the impact of random variation and provides a more precise estimate of the true probability. The Law of Large Numbers tells us that as the sample size increases, the relative frequency of the event should converge to the true probability, so a larger sample size will generally give a more reliable estimate

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The unknown angles of the right angle triangle is 45 degrees.  

A right angle triangle is a triangle with one angle equals to 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, the right triangle has two angle measurements that are equal to each other. The third angle is 90 degrees.

Therefore, let's find the angles measure x, the two other equal angles.

Hence,

x + x + 90 = 180

2x + 90 = 180

subtract 90 from both sides of the equation

2x + 90 = 180

2x + 90 - 90 = 180 - 90

2x = 90

divide both sides by 2

x = 90 / 2

x = 45 degrees

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Answer:

59/12

Step-by-step explanation:

2 1/4=9/4

9/4+8/3=27/12+32/12=59/12

This is not a function. The input 7 in set A maps to outputs -1 and -3 at the same time in set B, which is why we don't have a function.

For a function to be possible, each input must map to exactly one output only.

LCL and UCL values of both scenarios are (158.61,161.39),(69.65,70.35) respectively.

To calculate the lower confidence limit (LCL) and upper confidence limit (UCL) for each given scenario, you'll need to use the following formula:

LCL = X - (z * (sigma / √n))
UCL = X+ (z * (sigma / √n))

where X is the sample mean, n is the sample size, sigma is the population standard deviation, and z is the z-score corresponding to the desired confidence level (1 - alpha).

First Scenario:
X = 160, n = 436, sigma = 30, alpha = 0.01

1. Find the z-score for the given alpha (0.01).
For a two-tailed test, look up the z-score for 1 - (alpha / 2) = 1 - 0.005 = 0.995.
The corresponding z-score is 2.576.

2. Calculate LCL and UCL.
LCL = 160 - (2.576 * (30 / √436)) ≈ 158.61
UCL = 160 + (2.576 * (30 / √436)) ≈ 161.39

First Scenario Result:
LCL = 158.61
UCL = 161.39

Second Scenario:
X= 70, n = 323, sigma = 4, alpha = 0.05

1. Find the z-score for the given alpha (0.05).
For a two-tailed test, look up the z-score for 1 - (alpha / 2) = 1 - 0.025 = 0.975.
The corresponding z-score is 1.96.

2. Calculate LCL and UCL.
LCL = 70 - (1.96 * (4 / √323)) ≈ 69.65
UCL = 70 + (1.96 * (4 / √323)) ≈ 70.35

Second Scenario Result:
LCL = 69.65
UCL = 70.35

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Answer:

−y−1=3

Step-by-step explanation:

Which equation can be used to find the solution of (1/4)^y+1=64?

This can be solved by power of indices

(1/4)^(y+1)=64

(4^-1)^(y + 1)= 4^3

Note

(x^a)^b = x^ab

Hence:

4^(-1)(y + 1)= 4^3

4^-y - 1 = 4^3

Divide both sides by 4

−y−1=3

Hence, the equation that can be used to find the solution of (1/4)^y+1=64 is

−y−1=3

Answer:

-y-1=3

Step-by-step explanation:

took the test and got it correct

The graph that represents the situation is required.

What is graph?

A graph is a structure that resembles a set of items in discrete mathematics, more especially in graph theory, in which certain pairs of the objects are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.

Graphs are a popular tool for graphically illuminating data connections. A graph serves the objective of presenting facts that are either too many or complex to be fully expressed in the text while taking up less room.

Here the  X- axis denotes the number of hours and

Y- axis denotes the pounds of ice.

The given ordered pair is

\(\left(\frac{1}{2}, 1 \frac{1}{2}\right)=(0.5,1.5)\)

At zero hours the ice produced will be zero so, the third and fourth options are incorrect.

The only graph where the line passes through (0.5,1.5).

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Answer:

85

Step-by-step explanation:

According to the empirical rule, approximately 95% of the data is expected to fall within ±2 standard deviations of the mean.

The empirical rule, also known as the 68-95-99.7 rule, is a guideline based on the normal distribution. It states that for a normal distribution, about 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and about 99.7% falls within three standard deviations.

To calculate the percentage of funds expected to be within ±2 standard deviations of the mean, we can use the properties of the normal distribution. Since the empirical rule tells us that about 95% falls within this range, we can conclude that approximately 95% of the funds are expected to be within ±2 standard deviations of the mean.

This means that if we have a large dataset that follows a normal distribution, we can expect the majority of the values to fall within this range. It provides a useful estimate of the spread of data around the mean and helps us understand the distribution's characteristics.

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Answer:

So the formula of area of the circle A=πr2. The answer is 153.86.

Step-by-step explanation:

You first divide 14/2=7 then do 7^2 which equals 49 lastly multiplying 3.14 X 49. So how is the radius 7 because half of a diameter is a radius.Therfore the answer is 153.86.

The length of the diagonal side is 82, or answer (d) in its simplest radical form.

The Pythagorean Theorem must be utilized in order to determine the length of the diagonal side of a square with a length of 8 feet. You can use the formula a2 + b2 = c2, where a and b are the sides of the triangle and c is the hypotenuse, since the diagonal side of the square is. Because a and b are both 8 feet, you can use those numbers to solve for c:

82 + 82 = c2 64 + 64 = c2 128 = c2 The length of the diagonal side is 82, or answer d in its simplest radical form.

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Answer:

y = 2x - 7

Step-by-step explanation:

y = 2x - 3

Gradient of line w = 2

Gradient of line d = 2

i.e line w and d are parallel.

Equation of line d is:

y - (-1) = 2(x - 4)

y + 1 = 2x - 8

y = 2x - 7

The dimensions that maximize the area of the pen are approximately 91.46 meters for the side perpendicular to the barn and 155.09 meters for the side parallel to the barn.

We have two triangular pens built against a barn, and we have a total of 400 meters of fencing to use for the three sides and the diagonal dividing fence. To maximize the area of the pen, we need to find the lengths of the sides.

Let's use x to represent the length of the side perpendicular to the barn and y to represent the length of the side parallel to the barn. The diagonal dividing fence has a length given by the formula √(x² + y²).

The sum of the lengths of the two triangular pens and the diagonal dividing fence must equal the total length of fencing, which is 400 meters. This can be expressed as:

x + y + √(x² + y²). = 400.

We can solve for x in terms of y:

x = 400 - y - √(x² + y²).

The area of the pen is given by A = 0.5xy. By substituting the expression for x in terms of y and simplifying, we obtain:

A = 0.5y(400 - 2y - √((400 - y)² + y²)).

To find the values of x and y that maximize A, we take the derivative of A with respect to y, set it equal to zero, and solve for y. After solving, we find that y is approximately 155.09 meters.

Substituting this value of y into the equation for x, we get x is approximately 91.46 meters.

Therefore, the area of the pen is maximized when the side perpendicular to the barn is about 91.46 meters long and the side parallel to the barn is about 155.09 meters long.

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Answer:

4 toothpicks.

Step-by-step explanation:

We have been given that Kiley had a piece of bamboo skewer that measured 14 3/5 inches long. She wanted to cut it into toothpicks that were each 3 1/5 inches long.

To find the number of toothpicks that Kiley can make from bamboo skewer, we need to divide the length of skewer by length of each toothpick.

Total number of toothpicks = 14 3/5 ÷ 3 1/5

First of all, we will convert our given mixed fractions into improper fractions as:

Total number of toothpicks = 73/5 ÷ 16/5

Dividing a fraction by another fraction is same as multiplying the 1st fraction by the reciprocal of 2nd fraction.

Total number of toothpicks = 73/5 x 5/16

Total number of toothpicks = 73/16

Total number of toothpicks = 4.5625

Therefore, Kiley can make 4 toothpicks.

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Percent of land planted with wheat  is 50% of total land.

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

Given,

a farmer planted

320 acres of one variety of wheat

160 acres of a second variety of wheat.

He also planted 40 acres of milo,

and he has 440 acres that will lie fallow

Total land farmer has = 320 + 160 + 40 + 440 = 960 acres

Land planted with wheat = 320 + 160 = 480 acres

Percentage of land with wheat

= (land planted with wheat/ total land)× 100

= 480/960 × 100

= 0.5 × 100

= 50%

Hence, 50% of total land is planted with wheat.

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Teresa needs to buy two new tires for her mountain bike.

With a budget of $120, she will likely spend within $25 of that amount.

To help her find the best deal, Teresa should first research what type of mountain bike tire she needs. She can look at the bike's current tires to determine the size, or she can look up the bike model and size online. She should then research prices at a variety of local bike shops and online retailers to compare costs.

Once she finds the best price, Teresa should look for discounts and coupon codes that she can use to reduce the cost of her tires. She should also make sure she is aware of any extra costs, such as shipping and taxes.

With some research and savvy shopping, Teresa should be able to find two mountain bike tires that fit within her budget of $120 and that will keep her bike running smoothly.

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Answer:

1/18

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

Answer:

\(area = (6 + 2y) \times (8 + 2y)\)

Step-by-step explanation:

when we visualize this problem, we see that for each dimension, we add 2y to its size. for width, we add y for the left and right sides of the frame, and for height, we add y for the top and bottom parts.

this gives us the dimensions of the frame in terms of the dimensions of the picture and y:

the frame is (6+2y) by (8+2y)

the area of a rectangle is calculated by multiplying its side-lengths, so we get:

\(area = (6 + 2y) \times (8 + 2y)\)

In 2012, 8 percentage of high school seniors sampled had used lad sometime during their life.

LSD use among secondary school understudies is a specific concern. In excess of 8% of secondary school seniors in the United States utilized the medication something like once in the course of their life, and almost 4% involved the medication in the previous year, as per the University of Michigan's Monitoring the Future Survey. In spite of the fact that by the 1980s LSD use had extraordinarily declined, it made a resurgence during the 1990s, basically among teens. An overview led by Monitoring the Future Study discovered that 13.6 percent of 1997's secondary school seniors had tried different things with LSD no less than once contrasted with just 7.2 percent in 1986.

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Answer:

56 square units

Step-by-step explanation:

I'd recomend using something like "Desmos" to plot the points so then you can see the points and the rectangle. Then count the length and width. For the this rectangle the length was 8 and the width was 7, multiply these and you get the answer of 56 sqaure units.

The formula for the final velocity,\(v_{f}\) , in terms of initial velocity, vi, acceleration, a, and time, t is given by \(V_{f}=at+V_{i}\)

A =\((V_{f}-V_{i} )/t\)  You can put \(1\) under A and then cross multiply.

\(at =V_{f} -V_{i}\)

Get \(V_{f}\)  by adding  \(V_{i}\) in both sides of the equation.

\(at+V_{i} =V_{f}\)

                                                OR

The final speed \(V_{f}\) in terms of other parameters is given by the relation \(V_{f}\)\(=at+V_{i}\)

How to calculate the acceleration of an object?

Mathematically, acceleration is calculated using this formula:

\(a=(V_{f}-V_{i} )/t\)

Where:

Making \(V_{f}\) the subject of the formula, we have:

\(at =V_{f} -V_{i}\)

\(V_{f} =V_{i} +at\)

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It is true that the indexed variables (members) of an array must be integers.

The indexed variables or members of an array must be integers. This is because arrays are data structures that store elements in a contiguous block of memory, and each element is accessed using an index. Indexing allows us to uniquely identify and retrieve specific elements within the array. In most programming languages, including C, C++, Java, and Python, array indices are integers and must be whole numbers (positive or negative) without any fractions or decimals. Attempting to use non-integer values as indices would result in a compilation error or unexpected behavior.

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