Ella is trying to determine the side lengths of a triangle. She knows that the longest
side is three times longer than the shortest side. The medium side is ten more than
twice the shortest side. If the perimeter is 142 cm, how long is each side?

Answer:

Step-by-step explanation:

4 - 5= -1  same as 4 + -5

19 - (-6) = 25  subtracting a negative is the same as adding a positive becuase of the two negative signs.

-5 - 4 = -5 + -4 = -9

-10 - 12 = -10 + -12 = -22

-8 -(-7) - again two negatives make a positive ity becomes

-8 + 7 = -1

-12 - 10 - same as adding a negative becomes -12 + -10 = -22

The requried total change to Rob's funds as an integer is -$50, indicating that he spent more than he received and his funds decreased by $50.

Let's break down the different transactions and calculate the total change to Rob's funds:

Bought 5 rabbits for $10 each: 5 x $10 = $50 spent
Returned 2 rabbits: 2 x $10 = $20 received
Found 2 twenty dollars bills: 2 x $20 = $40 received
Bought 2 desks for $30 each: 2 x $30 = $60 spent

To calculate the total change to Rob's funds, we can add up the amounts received and subtract the amounts spent:
$20 + $40 - $50 - $60 = $-50

Therefore, the total change to Rob's funds as an integer is -$50, indicating that he spent more than he received and his funds decreased by $50.

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True. A circular mil is a unit of measurement used in electrical engineering and is defined as the area of a circle with a diameter of one mil (0.001 inch) which is equivalent to a circumference of one mil.

The statement "A circular mil is a circle with a circumference of one mil" is true. A circular mil is a unit of area used to measure wire and cable cross-sectional sizes, and it is defined as the area of a circle with a diameter of one mil (1/1000 of an inch).

Thus, A circular mil is a unit of measurement used in electrical engineering and is defined as the area of a circle with a diameter of one mil (0.001 inch) which is equivalent to a circumference of one mil.

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Answer: B

Step-by-step explanation:

When you distribute the number to the equation you want to be able to eliminate a variable when you add.

a. not right you get 2x for your first term if you added it to the next equation you get 4x which does not eliminate x

b. is right, you get -2x +2x = 0 this is what you want

c. not right, you get -2x but added to the first  -2x+x [tex]\neq[/tex] 0

d. not right -4x +x [tex]\neq[/tex] 0

The median of the scores of the 13 players would be = 8. That is option B.

The total number of players that score 7 = 4

The total number of players that score 8 = 3

The total number of players that score 9 = 5

The total number of players that score 10 = 1

The scores = 7,7,7,7,,8,8, 8 ,9,9,9,9,9,10

The median score is 8.

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Answer:

D. The number of multiple-choice questions plus the number of

short-answer questions is 15.

The number of hours that the grade 7 student spends studying can be found to be 2 hours.

We are told that the grade 7 student gets 4 hours of free time after school and from that time, they spend 1 / 2 of it studying.

This means that the number of hours spent by the grade 7 student in studying can be found by the formula:

= Free time x proportion of time spent studying

= 4 hours x 1 / 2

= 4 / 2

= 2 hours

In conclusion, the grade seven student spent 2 hours studying.

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The full question is:

A typical grade 7 student is reported to have about 4 hours of free time after school on weekdays. They spend 1 / 2 of this time studying.

How many hours does the grade 7 students spend in studying?

1. The cost for 100 shares at the 52-Week Low is $52.28 (option a).

2. The amount received if you sold your 100 shares at the High on August 16 is $67.20 (option d).

3. Your net gain or net loss after the sale of your 100 shares was $1492 Net Gain. (option d)

4. If you sold stock for $3200 and your broker earns 2% of that as his fee, Then the amount did the broker receive was $64. (option a).

To calculate the cost of 100 shares at the 52-Week Low, we need to multiply the low price per share by the number of shares. Therefore, the cost for 100 shares at the 52-Week Low can be calculated as follows:

Cost = 100 x 52-Week Low price per share

Out of the options given, the correct answer is A. $5228, assuming that the 52-Week Low price per share is $52.28.

To calculate the amount received from selling 100 shares at the High on August 16, we need to multiply the high price per share by the number of shares. Therefore, the amount received can be calculated as follows:

Amount Received = 100 x High price per share

Out of the options given, the correct answer is D. $6720, assuming that the high price per share on August 16 was $67.20.

To calculate the net gain or loss after the sale of 100 shares, we need to subtract the cost of buying the shares from the amount received from selling them. Therefore, the net gain/loss can be calculated as follows:

Net Gain/Loss = Amount Received - Cost

Using the numbers from the previous questions, we can calculate the net gain/loss as follows:

Net Gain/Loss = $6720 - $5228

Net Gain/Loss = $1492

Therefore, the correct answer is D. $1492 Net Gain.

To calculate the amount received by the broker as a fee for selling stock for $3200, we need to multiply the selling price by the broker's commission rate, which is given as 2%. Therefore, the broker's fee can be calculated as follows:

Broker's Fee = Selling Price x Commission Rate

Using the numbers from the question, we can calculate the broker's fee as follows:

Broker's Fee = $3200 x 0.02

Broker's Fee = $64

Therefore, the correct answer is A. $64.

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The volume of the given figure is 29070 cubic centimeter.

The dimensions of the given 3D figure is Length of cuboid=45 cm, breadth of cuboid=17 cm and the height of cuboid = 20 cm.

Height of rectangular prism is 18 cm.

Volume of cuboid = Length×Breadth×Height

= 45 × 17 × 20

= 15300 cubic centimeter

Now, volume of rectangular prism = Area of Base ×Height

= 45×17×18

= 13770 cubic centimeter

Total volume = 15300 + 13770

= 29070 cubic centimeter

Therefore, the volume of the given figure is 29070 cubic centimeter.

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The best point estimate for the mean monthly car payment for all residents of the local apartment complex is 631

The best point estimate for the mean monthly car payment for all residents of the local apartment complex is simply the sample mean, which is $631. This is because the sample mean is an unbiased estimator of the population mean, meaning that on average, it will give us an accurate estimate of the true population mean.

To explain this in mathematical terms, let's use X to represent the monthly car payment for an individual resident of the apartment complex. We have a sample of n=97 residents, and we can calculate the sample mean as follows:

[tex]$\bar{X} = \frac{1}{n} \sum_{i=1}^{n} X_i$[/tex]

In this case, we know that [tex]\bar{X} = $631,[/tex] so this is our point estimate for the population mean:

[tex]$\mu \approx \bar{X} = 631$[/tex]

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If the interior angle's of the right-triangle are 60°, 90° and 30°, then length of side"A" is 9.24cm and side"B" is 8 cm.

In a "right-triangle", the "Sine" of an angle is defined as the length of the opposite side divided by the length of the hypotenuse,

The "Cosine" of an angle is defined as the length of the adjacent side divided by the length of the hypotenuse.

The hypotenuse (opposite the right angle) is "A".

The base (adjacent to the 60° angle) is "B".

The height (opposite the 60° angle) is given as 8 cm.

Using the 60° angle and height, we can find the length of the base :

⇒ Sin(60°) = (opposite-side)/(hypotenuse),

⇒ Sin(60°) = 8/A,

⇒ A = 8/Sin(60°),

⇒ A ≈ 9.24 cm

Using the 30° angle and base, we can find the length of the height as:

⇒ Cos(30°) = (adjacent-side)/(hypotenuse),

⇒ Cos(30°) = B/A,

⇒ B = A × Cos(30°),

⇒ B = 9.24 × Cos(30°),

⇒ B ≈ 8.00 cm

Therefore, the length of side "A" is 9.24 cm and side "B" is 8.00 cm.

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The given question is incomplete, the complete question is

Find the length of the lettered sides "A" and "B" of a right angle triangle if the angle of the interior is 60°, 90° and 30°. And the height is 8cm and the hypotenuse is given as "A" and the base is given as "B".

The probability of the match finishing in two sets is higher than the probability of the match finishing in three sets, so if you were to bet on the outcome, you would bet on it finishing in two sets.

P(win in 2 sets) = P(win 1st set) * P(win 2nd set)

P(win in 2 sets) = 0.5 * 0.5

P(win in 2 sets) = 0.25 or 25%

The probability of winning three sets in a best-of-three tennis match is:

P(win in 3 sets) = P(win 1st set) * P(lose 2nd set) * P(win 3rd set)

P(win in 3 sets) = 0.5 * 0.5 * 0.5

P(win in 3 sets) = 0.125 or 12.5%

As a result, the liability of the match ending in two sets is lesser than the probability of the match ending in three sets,  therefore if you were to  go on the  outgrowth, you would  go on the match ending in two sets. It's  pivotal to note,  still, that this presupposes a constant chance of winning a set, which may not be the case in practise.

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Answer:

3/5

Step-by-step explanation:

cause it is

To evaluate P(2), we plug in n=2 into the inequality 2^n < (n+1)!. This gives us 2^2 < (2+1)! which simplifies to 4 < 6. Therefore, P(2) is true.

To show the inductive step for k≥2, we assume that P(k) is true, i.e. 2^k < (k+1)!. We need to show that P(k+1) is also true, i.e. 2^(k+1) < (k+2)!.

Starting with P(k), we can multiply both sides by 2 to get 2^(k+1) < 2(k+1)!. Now we just need to show that 2(k+1)! < (k+2)!, which simplifies to 2 < (k+2)/(k+1). This is true for all k≥1, so P(k+1) is also true.

Therefore, we have shown that if P(k) is true for some integer k≥2, then P(k+1) is also true. This completes the inductive step.
(a) P(2) is given by the inequality 2^(n+1) < (n+1)!. When n = 2, the inequality becomes 2^(2+1) < (2+1)!, which simplifies to 2^3 < 3!, or 8 < 6. This is not true, so P(2) is false.

(b) P(k) is the inequality 2^(k+1) < (k+1)!. In the inductive step, we need to show that if k is any integer with k ≥ 2 and if P(k) is true, then P(k+1) is also true. This means that if 2^(k+1) < (k+1)!, we need to show that 2^(k+2) < (k+2)!.

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A machine learning model overfits when it becomes overly complicated and begins to memorize the training data rather than learning broad patterns that can be applied to fresh data. In other words, the model performs worse on the validation or test set because it cannot generalize to new data due to how well it fits the training data.

Assume, for instance, that we train a convolutional neural network (CNN) on the 2,000 training images in the cats vs. dogs dataset and obtain high accuracy on the training set. However, the accuracy drastically declines when we test the model on the 2,000 test photographs. This is a symptom of overfitting and indicates that the model cannot generalize to new data since it has learned the specific features of the training set too well. We can employ strategies like regularisation, dropout, and early halting, as well as increasing the volume of training data, to avoid overfitting.

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Answer:

B) KL = 9.36

Step-by-step explanation:

It looks like the triangle JKL is scaled to a factor of 1.2 because with the first angle XY at 8.7 and the first angle JK at 10.44, this is 10.44/8.7 = 1.2.

Therefore, multiply the rest of the angles by the scale factor to get:

JL: 8.2 * 1.2 = 9.84

KL: 7.8 * 1.2 = 9.36

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Answer:

The ratio of green apples to red apples is 6:7.

Step-by-step explanation:

The ratio of all apples in the basket to red apples is 13:7 (since there are 13 total apples and 6 of them are green, leaving 13-6=7 red apples).

The number of constant terms in the expression x³ ± 6x ± 8 is 1.

Given expression is,

x³ ± 6x ± 8

Constant terms are terms which consists of only the numerical values and not includes any variables.

Here the variable is x.

The terms x³ and 6x includes variables.

So the only term which is a constant is 8.

So there is only 1 constant term.

Hence the number of terms in the expression which are constants is only 1, which is 8.

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The required group of friends spent 94% of their total budget on costumes.

To evaluate the percentage of the total budget that was spent on costumes, we can use the formula:
Percentage = (amount spent / total budget) x 100%

In this case, the amount spent on costumes was $658, and the total budget was $700. Substituting these values into the formula, we get:

percentage = (658 / 700) x 100%

Simplifying the fraction, we get:

percentage = 0.94 x 100%

Converting the decimal to a percentage, we get:

percentage = 94%

Thus, the group of friends spent 94% of their total budget on costumes.

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Answer:

The correct answer is C. 20 in. To calculate the area of the triangle, we can use the formula A = 1/2 bh. The base of the triangle is 10 in and the height is 8 in, so the area is 1/2 x 10 x 8 = 40 in^2. Since the triangle is a right triangle, the area is half of 40 in^2, which is 20 in^2

Spencer will have spent 56 minutes on the phone in total while routing 28 phone calls.

If Spencer spent 10 minutes while routing 5 phone calls, the unit rate of time spent on the phone per phone call is;

10 minutes ÷ 5 phone calls = 2 minutes/phone call

Therefore, the unit rate tells us that Spencer spent an average of 2 minutes on the phone for each of the 5 phone calls he routed.

To find how much time Spencer will spend on the phone in total while routing 28 phone calls, we can use the unit rate as a conversion factor;

Total time on the phone = (Number of phone calls) x (Time per phone call)

Total time on the phone = 28 phone calls x (2 minutes/phone call)

Total time on the phone = 56 minutes

Therefore, Spencer will have spent 56 minutes on the phone.

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The focus of the parabola y=5x²+5 would be (0 , 5.05)

Since All points in a plane that are equally spaced out from a given point and a given line make up a parabola. The line is the directrix, and the point is the parabola's focus.

The stanard form of the parabola is y = 1/4p ( x - h)²+ k

Where, (h,k) is the vertex of parabola

(h , k + p) is the focus of the parabola

Given equation to the standard form;

y=5x²+5

y = 5 (x - 0)² + 5

Therefore, we have h = 0

1/4p = 5

p = 1/20

k = 5

Now, the focus = (h , k + p)

= (0 , 5 + 1/20)

(0 , 5.05)

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The total amount the teacher has in the account at the end of two years is $7,935.94.

To calculate the total amount the teacher has in the account at the end of two years, we can use the formula for compound interest

A = P(1 + r/n)^(nt)

Where

A = the total amount the teacher has in the account at the end of two years

P = the principal amount (the initial amount the teacher deposited), which is $7500 in this case

r = the annual interest rate, which is 2.5% expressed as a decimal, or 0.025

n = the number of times the interest is compounded per year, which is once per year in this case

t = the time in years, which is 2 years in this case

Substituting the values, we get

A = $7500(1 + 0.025/1)²

A = $7500(1.025)²

A = $7,935.94

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Answer:

Step-by-step explanation:

To calculate the rate of inflation, we can use the inflation rate formula:

inflation rate = ((new price - old price) / old price) x 100%

Using the given information, we have:

old price = $64.99

new price = $150.00

inflation rate = ((150.00 - 64.99) / 64.99) x 100%

inflation rate = (85.01 / 64.99) x 100%

inflation rate = 130.81%

Rounding the inflation rate to the nearest whole number, we get:

inflation rate ≈ 131%

Therefore, the rate of inflation from 1985 to today for a pair of Jordans is approximately 131%.

If you have a probability between 0 and 0.5, the word you could used to describe the numerical value is Less likely

From the question, we have the following parameters that can be used in our computation:

Probability value = between 0 and 0.5

As a general rule

Probability values between 0 and 0.5 are unlikely or less likely

This is because of the following grading system of probability values

Using the above as a guide, we have the following:

The word to use is (d) less likely

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There is a 97.91% chance that at least 74 students out of 130 randomly selected students would prefer a boy.

To find the probability that at least 74 students would prefer a boy out of 130 randomly selected students, we need to use the binomial probability formula:

P(X >= k) = 1 - P(X < k)

Where:

P(X >= k) is the probability that the number of students who prefer a boy is greater than or equal to k

P(X < k) is the probability that the number of students who prefer a boy is less than k

In this case, k = 74, n = 130, and the probability of success (i.e., preferring a boy) is p = 0.45 (based on the results of the poll).

To calculate P(X < 74), we can use a binomial distribution calculator or a statistical software program. The result is 0.0209.

Therefore, the probability that at least 74 students would prefer a boy is:

P(X >= 74) = 1 - P(X < 74)

P(X >= 74) = 1 - 0.0209

P(X >= 74) = 0.9791

In terms of percentage = 0.9791 x 100 = 97.91%

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Answer: Option B and Option C

I hope this helps :)

Step-by-step explanation:

Option B and Option C are functions because all the first terms in their ordered pairs are different.

The value of x and y can be found using the Pythagorean Theorem and the law of sines;

x = 3·√(17)

y ≈ 7.37

The Pythagorean Theorem states that the square of the length of the longest side of a right triangle (the hypotenuse side) is equivalent to the sum of the squares of the other two sides of the right triangle

The value of y can be obtained from the law of sines as follows;

5/(sin(36°)) = y/(sin(60))

y = (sin(60)) × 5/(sin(36°))

(sin(36°)) = √((10 - 2·√5))/4

(sin(60)) = √(3)/2

y = (sin(60)) × 5/(sin(36°)) = √(3)/2 × 5 × 4/√((10 - 2·√5)) = 10·√(3)/√((10 - 2·√5)) ≈ 7.37

The value of x can be found using the Pythagorean Theorem as follows;

x² = 12² + 3² = 144 + 9 = 153

x = √153 = 3·√(17)

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The value of both variables is equal to 23.

The angle measures are 45 degrees and 135 degrees respectively.

In Mathematics and Geometry, a supplementary angle simply refers to two (2) angles or arc whose sum is equal to 180 degrees.

Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can reasonably infer and logically deduce that the sum of the given angles are supplementary angles:

(2x - 1)° + (4x + 43)° = 180°

By rearranging and collecting like-terms, the value of y is given by:

6x + 42 = 180

6x = 180 - 42

x = 138/6 = 23

(2x - 1)° = 2(23) - 1 = 45°

(4x + 43)° = 4(23) + 43 = 135

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