one of the bases of a trapezoid has length , and the height of the trapezoid is . if the area of the trapezoid is , then how long is the other base of the trapezoid?

Answer:

False

Step-by-step explanation:

68% falls between the first standard deviation from the mean.

plus minus two would fall under 95%

Answer:

6 gallons

Step-by-step explanation:

32/4=8

48/8=6

Answer: 6

Step-by-step explanation: If 4 gallons can take you 32 miles, divide 4 into 32 to get 8. That means 8 miles is 1 gallon. Now just do 48/8 to get 6.

Answer:

ab - bc = 6

Step-by-step explanation:

COMPUTATION:

ab - bc = ?

(2 x -3) - (-3 x 4) = ?

(-6) - (-3 x 4) = ?

(-6) - (-12) = ?

-6 + 12 = 6

Hope this helps!

Answer:

D: 3x – 5 and 2x + 4y = 8

Step-by-step explanation:

I used desmos calculator

The sides of the quadrilateral arranged from longest to shortest are CD, AB, DA, and BC.

We have,

To arrange the length of the sides of the quadrilateral from longest to shortest, we need to calculate the length of each side of the quadrilateral using the distance formula:

Distance Formula:

If (x1, y1) and (x2, y2) are two points in a plane, then the distance between them is given by:

d = √((x2 - x1)² + (y2 - y1)²)

Using the distance formula, we can calculate the length of each side of the quadrilateral as follows:

AB = √((4 - (-5))² + (5 - 5)²) = 9

BC = √((2 - 4)² + (0 - 5)²) = √(29)

CD = √((-5 - 2)² + (-2 - 0)²) = √(74)

DA = √((-5 - (-5))² + (5 - (-2))²) = 7

Therefore,

The sides of the quadrilateral arranged from longest to shortest are CD, AB, DA, and BC.

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Functions (c) L(1) = C1 + AC and (d) L(1) = C°1 are linear operators on R^n, while functions (a), (b), and (e) do not satisfy the properties of linearity and therefore are not linear operators.

a) L(A) = 1 - 1: This function is not a linear operator because it does not preserve scalar multiplication. Multiplying A by a scalar c would yield L(cA) = c - c, which is not equal to cL(A) = c(1 - 1) = 0.

b) L(A) = 1 + 17: Similar to the previous case, this function is not linear since it fails to preserve scalar multiplication. Multiplying A by a scalar c would result in L(cA) = c + 17, which is not equal to cL(A) = c(1 + 17) = c + 17c.

c) L(1) = C1 + AC: This function is a linear operator since it satisfies both the preservation of addition and scalar multiplication properties. Adding matrices A and B and multiplying the result by scalar c will yield L(A + B) = C(1) + AC + C(1) + BC = L(A) + L(B), and L(cA) = C(1) + cAC = cL(A).

d) L(1) = C°1: This function is a linear operator since it satisfies the properties of linearity. Addition and scalar multiplication are preserved, and L(cA) = C(0)1 = c(C(0)1) = cL(A).

e) L(1) = 1?C: This function is not a linear operator as it does not preserve scalar multiplication. Multiplying A by a scalar c would give L(cA) = 1?(cC), which is not equal to cL(A) = c(1?C).

In summary, functions (c) L(1) = C1 + AC and (d) L(1) = C°1 are linear operators on R^n, while functions (a), (b), and (e) do not satisfy the properties of linearity and therefore are not linear operators.

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The quotient is x^2 - (4/3)x + (1/9)x and the remainder is (2/3)x^3 - (11/9)x^2 + (49/9)x + 3.

To find the quotient and remainder when dividing 6x^4 - 6x^3 + 5x + 3 by 6x^2 + 2x + 4, we can use polynomial long division.

               _____________________________

   6x^2 + 2x + 4 | 6x^4 - 6x^3 + 5x + 3

To start, we divide the highest degree term of the dividend by the highest degree term of the divisor. In this case, it is (6x^4 / 6x^2) = x^2.

                     x^2

               _____________________________

   6x^2 + 2x + 4 | 6x^4 - 6x^3 + 5x + 3

Next, we multiply the entire divisor by x^2 and subtract it from the dividend:

               x^2(6x^2 + 2x + 4)

             = 6x^4 + 2x^3 + 4x^2

              _____________________________

   6x^2 + 2x + 4 | 6x^4 - 6x^3 + 5x + 3

             - (6x^4 + 2x^3 + 4x^2)

             = -8x^3 + x + 3

Now, we repeat the process with the new dividend -8x^3 + x + 3.

Dividing the highest degree term of the new dividend by the highest degree term of the divisor, we have (-8x^3 / 6x^2) = -(4/3)x.

                   x^2 - (4/3)x

               _____________________________

   6x^2 + 2x + 4 | 6x^4 - 6x^3 + 5x + 3

             - (6x^4 + 2x^3 + 4x^2)

             = -8x^3 + x + 3

Multiplying the entire divisor by -(4/3)x and subtracting it from the new dividend:

               (-(4/3)x)(6x^2 + 2x + 4)

             = -(8/3)x^3 - (8/3)x^2 - (16/3)x

              _____________________________

   6x^2 + 2x + 4 | 6x^4 - 6x^3 + 5x + 3

             - (6x^4 + 2x^3 + 4x^2)

             = -8x^3 + x + 3

             - (-(8/3)x^3 - (8/3)x^2 - (16/3)x)

             = (2/3)x^3 - (4/3)x^2 + (16/3)x + 3

We repeat the process with the new dividend (2/3)x^3 - (4/3)x^2 + (16/3)x + 3.

Dividing the highest degree term of the new dividend by the highest degree term of the divisor, we have ((2/3)x^3 / 6x^2) = (1/9)x.

                   x^2 - (4/3)x + (1/9)x

               _____________________________

   6x^2 + 2x + 4 | 6x^4 - 6x^3 + 5x + 3

             - (6x^4 +

2x^3 + 4x^2)

             = -8x^3 + x + 3

             - (-(8/3)x^3 - (8/3)x^2 - (16/3)x)

             = (2/3)x^3 - (4/3)x^2 + (16/3)x + 3

             - ((1/9)x^2 - (4/9)x + (1/9)x)

             = (2/3)x^3 - (11/9)x^2 + (49/9)x + 3

We have now completed the division process. The quotient is given by x^2 - (4/3)x + (1/9)x and the remainder is (2/3)x^3 - (11/9)x^2 + (49/9)x + 3.

Therefore, the quotient is x^2 - (4/3)x + (1/9)x and the remainder is (2/3)x^3 - (11/9)x^2 + (49/9)x + 3.

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Answer:

²,2.5,2.5+10,25.0

may it help you

Answer:

19.26

Step-by-step explanation:

You multiply the cost of the backpack by 1.tax percent.

Answer:

C

Step-by-step explanation:

Answer:

The answer would be £198

principal (p) = 2200

Rate (R) = 0.5%

Time (T) = 18

Interest(I) = ?

Now,

or, Interest. = P×T×R/100

or, Interest = 2200×18×0.5/100

or, Interest = 19800/100

Hence, Interest = 198

Given a Math exam with 7 short answer questions and Peter intending to answer three of them, there are a total of 35 different combinations of short answer questions he can choose.

To determine the number of combinations, we can use the concept of combinations in combinatorics. The formula for combinations is given by:

C(n, r) = n! / (r! * (n - r)!)

Where:

C(n, r) represents the number of combinations of choosing r items from a set of n items.

n! denotes the factorial of n, which is the product of all positive integers up to n.

In this case, Peter wants to answer three out of the seven questions, so we can calculate it as:

C(7, 3) = 7! / (3! * (7 - 3)!) = 7! / (3! * 4!)

Simplifying further:

7! = 7 * 6 * 5 * 4 * 3 * 2 * 1

3! = 3 * 2 * 1

4! = 4 * 3 * 2 * 1

C(7, 3) = (7 * 6 * 5 * 4 * 3 * 2 * 1) / [(3 * 2 * 1) * (4 * 3 * 2 * 1)]

After canceling out common terms, we get:

C(7, 3) = 7 * 6 * 5 / (3 * 2 * 1) = 35

Therefore, there are 35 different combinations of short answer questions Peter can choose to answer.

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9514 1404 393

Answer:

  350 km/h

Step-by-step explanation:

Speed = distance/time

speed = (700 km)/(2 h) = 350 km/h

We can be 99.7% confident that the true proportion of individuals with schizophrenia in the population lies between 0.44 and 0.62.

In our schizophrenia model, the rough 99.7% certainty stretch can be determined utilizing the point gauge and standard blunder of the extent. With a point gauge of 0.53 and a standard blunder of 0.03, we can involve the equation for a certainty stretch, which is point gauge ± z* (standard mistake), where z* is the z-score related with the ideal certainty level.

For a 99.7% certainty stretch, the z-score is roughly 3. Consequently, the certainty span would be:

0.53 ± 3(0.03) = (0.44, 0.62)

This implies that we can be 99.7% certain that the genuine extent of people with schizophrenia in the populace lies somewhere in the range of 0.44 and 0.62.

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Answer:

LOL

Step-by-step explanation:

giggles

In the given triangle ΔOPQ, the measure of ∠Q is 75.5°.

In the given triangle ΔOPQ o = 5. 2 inches, p = 8. 4 inches and q=8. 7 inches where o is the side opposite to ∠O, p is the side opposite to ∠P, and q is the side opposite to ∠Q. Using the law of cosine c^2 = a^2 + b^2 – 2abcosƟ where Ɵ is the angle opposite c. Hence

q^2 = o^2 + p^2 – 2(o)(p) cos Q

8.7^2 = 5.2^2 + 8.4^2 – 2(5.2)(8.4)cos Q

75.69 = 27.04 + 70.56 – 87.36cos Q

-21.91 = -87.36cos Q

Cos Q = 0.251

Q = 75.5°

Hence, ∠Q is 75.5°.

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Answer: $20

Step-by-step explanation:

First, the earnings per share will be:

= $600 mill / 100 mill shares

= $6 per share

Since the retention ratio is 20%, it means that the payout ratio = 100% - 20% = 80%.

Therefore, the dividend per share will be:

=$6 × 80%

= $6 × 0.8

=$4.80

We will calculate then calculate market price as:

Dividend yield =Dividend per share / Market price

0.04 =$4.80 / Market price

Market price =$4.80 / 0.04

Market price = $120

The price earnings ratio will be:

= Market price / EPS

= $120 / $6

= $20

Answer:

=15

Step-by-step explanation:

1/2(24)+1/3(9)

=12+1/3(9)

=12+3

=15

Answer: The answer should be 15.

Step-by-step explanation: 1/2*24+ 1/3*4

                                                   12 + 3=15

Answer:

24/100

Step-by-step explanation:

Simplest fractional form of 0.24 repeating will be 6/25.

Fractions: A number in p/q form where q must not be zero is termed as fractions.

Given, that number 0.24 is repeating in nature.

So, to convert 0.24 from decimal to fraction .

Remove the decimal by dividing the whole number by 100 as decimal is two places behind.

0.24 = \(\frac{24}{100}\)

Simplify the fractional form,

GCF of 24 and 100 = 4

So divide 24 and 100 by 4,

Therefore the required fraction is ,

= \(\frac{6}{25}\)

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Answer:

8411.67 m³

Step-by-step explanation:

The volume of a pyramid is one third its height times the area of its base. The Louvre pyramid has a height of 20.6 meters and a square base with sides of 35 meters. Find its volume, rounded to the nearest hundredth. Include units in your answer.

Volume of a pyramid is given as:

1/3 × Height × Area of it's base

= 1/3 × 20.6m × (35 m)²

= 8411.6666667 m³

Approximately = 8411.67 m³

Therefore, the volume of the pyramid = 8411.67 m³

Answer:

4

Step-by-step explanation:

use pemdas.

4+4-4x4/4

4+4-16/4

4+4-4

8-4

4

All of the answer options are correct (option d). If each person increased their score by 5 points, the interquartile range could remain unchanged, the median score would increase by 5 points, and the third quartile would increase.

If each person's exam score is increased by 5 points, several changes can be observed. Firstly, the interquartile range (the range between the first and third quartiles) could remain unchanged if the scores within that range also increase uniformly. Secondly, the median score, which represents the middle value of the data, would increase by 5 points. This is because the median is affected by the overall shift in scores. Lastly, the third quartile, which represents the boundary for the upper 25% of the scores, would increase as well, indicating a shift in the higher range of scores. These changes depend on the specific distribution and initial values of the scores.

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Complete Question:

The exam scores (out of 100 points) for all students taking an introductory statistics course are used to construct the following boxplot:

If each person increased his or her score by 5 points, then

a. All of the answer options are correct.

b. the interquartile range would remain unchanged.

c. the median score would increase by 5 points.

d. the third quartile would increase

Answer:

Her proportion does not have corresponding parts in the same position.

Step-by-step explanation:

Sharon is drawing up a plan for building a reduced Eiffel Tower on her backyard patio. She has room to make a base of 5 feet. Her work is shown below.

What was Sharon’s error in finding the missing height measurement for her reduced tower?

Her proportion does not have corresponding parts in the same position.

For cross products, she needed to multiply 1050(328) and 5(x).

She needed to divide both sides by 1640, instead of 1050.

She needed to round down to 1.5 feet.

Height : base = 1,050 : 328

She has room to make a base of 5 feet.

Height : base = x : 5

1,050 : 328 = x : 5

1,050 / 328 = x / 5

Cross product

1,050 * 5 = 328 * x

5,250 = 328x

Divide both sides by 328

x = 5250 / 328

= 16.006

Approximately 16

Sharon's error:

Her proportion does not have corresponding parts in the same position.

Answer:

A

Step-by-step explanation:

The radius of convergence of the series \sum_{k=1}^{\infty} \frac{k ! x^{2 k}}{k^{k}} is e. The ratio test states that for a series of the form \sum_{k=1}^{\infty} a_k x^k, the series converges when lim_{k->\infty} |a_{k+1}/a_k| < 1. In this case, we have a_k = \frac{k ! x^{2 k}}{k^{k}}.

The ratio test states that the series converges if lim_{k->\infty} |a_{k+1}/a_k| < 1, and diverges if lim_{k->\infty} |a_{k+1}/a_k| > 1. In this case,

|a_{k+1}/a_k| = |x^2| = x^2

The series converges when x^2 < 1, which means -1 < x < 1. The radius of convergence is therefore the distance from 1 to -1, which is e.

To see this, let's consider the values of the series for x = -1, 0, and 1. When x = -1, the series becomes

\sum_{k=1}^{\infty} \frac{k ! (-1)^{2 k}}{k^{k}} = \sum_{k=1}^{\infty} \frac{k !}{k^{k}}

This is the alternating harmonic series, which is known to converge. When x = 0, the series becomes

\sum_{k=1}^{\infty} \frac{k ! 0^{2 k}}{k^{k}} = \sum_{k=1}^{\infty} \frac{k !}{k^{k}}

This is the harmonic series, which is known to diverge. When x = 1, the series becomes

\sum_{k=1}^{\infty} \frac{k ! 1^{2 k}}{k^{k}} = \sum_{k=1}^{\infty} \frac{k !}{k^{k}}

This is again the alternating harmonic series, which is known to converge. Therefore, the series converges when -1 < x < 1, and the radius of convergence is e.

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Answer:

72

Step-by-step explanation:

First find the discount

10% of 80

.10 * 80

8

Subtract this amount from the bill

80 -8 = 72

The customer will pay 72

The current in the circuit will be equal to (10 - 3j)/(4 + j) when the voltage is 10 - 3j and impedance is 4 + j.  

When put in an electromagnetic field, charged matter experiences a force due to the fundamental property of electric charge. Positive or negative electrical ions are possible.

When two charge are in opposition to one another, they repel one another. The term "neutral" refers to an object has no net charge.

As per the given information in the question,

Voltage, E = 10 - 3j

Impedance, Z = 4 + j

Then, the value of current will be,

E = IZ

I = E/Z

I = (10 - 3j)/(4 + j)

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Answer:

There are four kings in a standard deck of 52 cards, so the probability of drawing a king is 4/52 or 1/13.

Since we know that the card drawn is a king, there are now only four possible cards that could have been drawn: the king of spades, the king of hearts, the king of clubs, and the king of diamonds.

Out of these four possibilities, only one of them is the king of diamonds. Therefore, the probability that the card is a king of diamonds, given that the card drawn is a king, is 1/4.

In other words, the conditional probability of drawing the king of diamonds given that a king has been drawn is:

P(king of diamonds | king) = P(king of diamonds and king) / P(king) = 1/52 / 4/52 = 1/4

Hope this helps! If not, I'm sorry. Feel free to ask for help from me! :]