Determine the length of AC and DE, and the value of x.

Given:

a.) A person had 14,000 infested in two accounts.

b.) One paying 9% simple interest.

c.) One paying 10% simple interest.

Let,

x = the amount invested at 9% simple interest

y = the amount invested at 10% simple interest

1.) We know the total amount of money invested is $14,000. We get,

x + y = 14,000

2.) We know that the total interest for the year for the two accounts is $1432. We get,

0.09*x + 0.1*y = 1,339

Let's equate the two equations,

x = 14,000 - y (Substitute for x)

0.09*(14,000 - y) + 0.1*y = 1,339

1,260 - 0.09y + 0.1y = 1,339

0.1y - 0.09y = 1,339 - 1,260

0.01y = 79

0.01y/0.01 = 79/0.01

y = 7,900

Therefore, $7,900 was invested at the rate of 10% simple interest.

Let's determine x, substituting y = 7,900 in x + y = 14,000.

x + y = 14,000

x + 7,900 = 14,000

x = 14,000 - 7,900

x = 6,100

Therefore, $6,100 was invested at the rate of 9% simple interest.

Answer:

the answer is D

Step-by-step explanation:

y>4 : the shaded region is above the line

y>x : the shaded region is above the line

Answer: how do you do the question what the

Step-by-step explanation:

The values of the given expression having exponent with negative fractional base i.e. \(-2^{(3/2)^2}\\\) is evaluated out to be 16/9.

First, we need to simplify the expression inside the parentheses using the rule that says "exponents with negative fractional base can be rewritten as a fraction with positive numerator."

\(-2^{(3/2)^2}\) = (-2)² × (2/3)²

Now, we can simplify the expression  further by solving the exponent of (-2)² and (2/3)²:

(-2)² × (2/3)² = 4 × 4/9 = 16/9

Therefore, the value of the given expression \(-2^{(3/2)^2}\\\)  is 16/9.

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The question is :

What is the value of the expression \(-2^{(3/2)^2}\) ?

The particular solution is y(t) = 5 cos(2t) - 3 sin(2t), which is obtained by using the initial value conditions y(0) = 5, y'(0) = -6.

To solve the initial-value problem

y'' + 4y = 0, y(0) = 5, y'(0) = -6, the general solution of the differential equation is first determined.

The characteristic equation for this second-order homogeneous linear differential equation is r^2 + 4 = 0.The solution of this characteristic equation is:r = ±2i.Using the general solution formula for the differential equation, the general solution is: y(t) = c1 cos(2t) + c2 sin(2t).To obtain the particular solution, the initial conditions are used:

y(0) = 5,

y'(0) = -6.

Using

y(0) = 5:c1 cos(2(0)) + c2 sin(2(0))

= 5c1 = 5.

Using y'(0) = -6:-2c1 sin(2(0)) + 2c2 cos(2(0)) = -6c2 = -3.

The particular solution is thus:y(t) = 5 cos(2t) - 3 sin(2t).

The general solution for the differential equation \

y'' + 4y = 0, y(0) = 5, y'(0) = -6 is y(t) = c1 cos(2t) + c2 sin(2t).

Here, r^2 + 4 = 0 is the characteristic equation for this second-order homogeneous linear differential equation. It has the solution r = ±2i. The particular solution is y(t) = 5 cos(2t) - 3 sin(2t), which is obtained by using the initial conditions y(0) = 5, y'(0) = -6.

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Answer:

The original length is 9 cm and the original width 5 cm

Step-by-step explanation:

The area of  a rectangle A is given as the product of its' length L and width W.

Given that the width of a rectangle is 4cm less than the length then

W = L - 4

If each dimension were increased by 3cm, then the new

Length

= L + 3

Width

= W + 3

the width of the new rectangle formed would be 2/3 the length of the new rectangle

W + 3 = 2/3(L + 3)

3W + 9 = 2L + 6

3W = 2L +6 - 9

3W = 2L - 3

Recall that W = L - 4

3(L - 4) = 2L - 3

3L - 12 = 2L - 3

3L - 2L = 12 - 3

L = 9 cm

W = 9 - 4

= 5 cm

The hypothesis is given as

H0:  μd< 0

H1: μd > 0

The null hypothesis is given as

H0:  μd< 0

H1: μd > 0

SWe have to find the value of s

we would use this formula s = sqrt [ (Σ(di - d)^2 / (n - 1) ]

This gives us  3.454

Next we have to determine the standard error

s / √(n)

3.454/2.8284

= 1.22

Degree of freedom = 8 - 1

= 7

t = (x1 - x2) - D / S.E

=  1.025

Find t critical at 0.10

= 1.895

P-value = 0.1697

d. Given that p value is greater thatn 0.1 we fail to reject the null hypothesis.

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When 293 college students are randomly selected and surveyed, it is found that 114 own a car. The upper limit for the 90% confidence interval for the percentage of all college students who own a car is 46.3%.

The given problem is an example of confidence intervals in statistics. The formula for finding the confidence interval in percentage is given below:

Confidence Interval in Percentage = P ± Z Score x √ (PQ/n)

where

P = Sample proportion

Q = 1 - P

n = Sample Size

Z Score is obtained from the Z-Table where the confidence level is given.

To obtain the upper limit, the following formula should be used:

Upper Limit of the Confidence Interval = P + Z Score x √ (PQ/n)

Substitute the given values of the question into the formula:

P = 114/293 = 0.3891

Q = 1 - 0.3891 = 0.6109

n = 293

The upper limit for the 90% confidence interval is given by the Z-Table at 1.645:

Upper Limit of the Confidence Interval = 0.3891 + 1.645 x √ [(0.3891 x 0.6109)/293]

≈ 0.3891 + 1.645 x 0.0467

≈ 0.3891 + 0.07701

≈ 0.4661 = 46.3%

Therefore, the answer is 46.3%.

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The probability that exactly one of the three jewels chosen at random is a ruby is 0.4503 or approximately 0.45.

To find the probability that exactly one of the three jewels chosen at random is a ruby, we can use the binomial probability formula:

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

where:

n is the number of trials (in this case, n = 3)

k is the number of successful trials (in this case, k = 1)

p is the probability of success (in this case, p = 0.33)

Using this formula, we can plug in the values and calculate the probability:

P(X = 1) = (3 choose 1) * (0.33)^1 * (1-0.33)^(3-1)

= 3 * 0.33 * 0.4489

= 0.4503

This means that if we were to repeat this experiment many times (i.e., randomly selecting three jewels), we would expect to get one ruby in the set of three jewels about 45% of the time.

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Answer: where is the question??

what do you need help with?

Answer:  B 9:21

Step-by-step explanation:

9 reduces to three and 21 reduced to 7

Correct option is A. Passage 2 strongly challenges the point of view in

Passage 1.

The idea that women should be equal strongly challenges the notion that men and women should have separate roles and rights. 3

And then, if we look at answer B, the answer is the passage, two conclusions drawn, 35  alternative conclusions from the evidence presented in paragraph 1. 36 So the answer  B would be incorrect. 37 If you mention something with evidence, it will appear more often in a scientific passage than in a historical passage like this.

2 So  if we look at answer choice C, it says paragraph 3 to better explain the proposition presented in paragraph one, which would show that the passage is,  would agree with each other. . This is why C is incorrect.

5 And then if we look at D, he says he put it back in different words,

8 ​​And obviously he's not. Answer D is therefore incorrect.

9 And a, the fact that paragraph two challenges strongly.

Passage 1

"half the human race is excluded by the other half from any participation in government; that they are native by birth but foreign by law in the very land

where they were born; and that they are

Line

5

property-owners yet have no direct influence or representation: are all political phenomena apparently impossible to explain on abstract principle. But on another level of ideas, the question changes and maybe easily resolved. The purpose of

10

all these institutions must be the happiness of the

.........................................................

85

In this style, argue tyrants of every denomination, from the weak king to the weak father of a family; they are all eager to crush reason; yet always assert that they usurp its throne only to be

useful. Do you not act a similar part, when you force all women, by denying them civil and political rights, to remain immured "

Passage 2 -

"Contending for the rights of woman, my main argument is built on this simple principle, that if she be not prepared by education to become the companion of man, she will stop the progress of 45 knowledge and virtue; for truth must be common to all, or it will be inefficacious with respect to its influence on general practice.

...............................................

open before you when you observed, "that to see one half of the human race excluded by the other from all participation of government, was a political phenomenon that, according to abstract

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The value of the expression 9 + 3 × 5² - 10 × 6 following the rules of PEMDAS is 24.

9 + 3 × 5² - 10 × 6

Based on the operation of PEMDAS

So,

9 + 3 × 5² - 10 × 6

Solve the exponent

= 9 + 3 × 25 - 10 × 6

Solve the multiplication

= 9 + 75 - 60

Add

= 84 - 60

= 24

Ultimately, 24 is the solution to the given expression.

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The major assumption in factor analysis (but not PCA) is that the observed variables are caused by a smaller number of underlying, unobserved (latent) variables, which are called factors.

Factor analysis and principal component analysis (PCA) are both techniques used for data reduction and dimensionality reduction. However, they differ in their assumptions and goals.

In factor analysis, the focus is on identifying the underlying latent variables (called factors) that explain the observed correlations among a set of variables. The major assumption in factor analysis is that the observed variables are caused by a smaller number of underlying factors. These factors cannot be directly measured, but are inferred from patterns of correlations among the observed variables. The goal of factor analysis is to extract these factors and to estimate how much each factor contributes to each observed variable.

In contrast, PCA is a technique that focuses on finding a linear combination of the original variables that explain the maximum amount of variance in the data. The major assumption in PCA is that the observed variables are not caused by any underlying factors, but are simply linearly related to each other. The goal of PCA is to find a set of orthogonal (uncorrelated) principal components that capture the maximum amount of variance in the data.

Therefore, the major assumption in factor analysis (but not PCA) is that there are underlying latent variables (factors) that cause the observed correlations among the variables.

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Answer:

90 degrees.

Step-by-step explanation:

They right ray point is on the 90 degree number and left ray is on zero so we find the difference.

90-0=90

so it measures 90 degrees.

Answer:

<ba=180 <bc=90

Step-by-step explanation:

The evaluation of the segment formed by the parallel lines using Thales Theorem also known as the triangle proportionality theorem are;

8. \(\overline {ST}\) is parallel to \(\overline{PR}\)

9. \(\overline{ST}\) is parallel to \(\overline{PR}\)

10. \(\overline{ST}\) is not parallel to \(\overline{PR}\)

11. x = 57.6

12. x = 25.8

13. x = 11

14. x = 10

15. x = 5

16. x = 17

Thales Theorem also known as the triangle proportionality theorem states that a parallel line to a side of a triangle that intersects the other two sides of the triangle, divides the two sides in the same proportion.

8. The ratio of the sides the segment \(\overline{ST}\) divides the sides QR and QP of the triangle ΔPQR into are; 7/11.2 = 10/16 = 0.625

Therefore; according to the Thales theorem, \(\overline{ST}\) ║ \(\overline{PR}\)

9. The ratio of the sides the parallel side to the base divides the other two sides are;

33/41.8 = 15/19

45/(102 - 45) = 45/57 = 15/19

Therefore, \(\overline{ST}\) and \(\overline{PR}\) bisects \(\overline{QP}\) and \(\overline{QR}\) into equal proportions and therefore, \(\overline{ST}\) ║ \(\overline{PR}\)

10. The ratio of the sides the segment \(\overline{ST}\)  bisects the other two sides are;

24/57 and 19/38

24/57 ≠ 19/38, therefore \(\overline{ST}\) ∦ \(\overline{PR}\)

Second part; To solve for x

11. x/30 = 48/25

x = (48/25) × 30 = 57.6

x = 57.6

12. x/34.4 = (49 - 28)/28

x = 34.4 × (49 - 28)/28 = 25.8

x = 25.8

13. (2·x + 6)/52.5 = 32/60

(2·x + 6) = 52.5 × (32/60)

x = (52.5 × (32/60)) - 6)/2 = 11

x = 11

14. (x - 3)/21 = (x - 1)/27

27·x - 27 × 3 = 21·x - 21

27·x - 81 = 21·x - 21

6·x = 60

x = 60 ÷ 6 = 10

x = 10

15. (35 - 20)/20 = (4·x - 2)/(7·x - 11)

15/20 = (4·x - 2)/(7·x - 11)

15 × (7·x - 11) = 20 × (4·x - 2)

105·x - 165 = 80·x - 40

105·x - 80·x = 165 - 40 = 125

25·x = 125

x = 125/25 = 5

x = 5

16. (x - 3)/35 = 4/(x - 7)

(x - 3) × (x - 7) = 35 × 4 = 140

x² - 10·x + 21 = 140

x² - 10·x - 119 = 0

(x - 17) × (x + 7) = 0

x = 17 or x = -7

Therefore, the possible value of x is 17

x = 17

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Answer:

it will be 45 percent or 65

Step-by-step explanation:

Answer:

Increase by 3.

Step-by-step explanation:

4 x 21 = 84

84 x 2 = 168

Begin to try numbers.

5 x 22 = 110

6 x 23 = 138

7 x 24 = 168

7 - 4 = 3

24 - 21 = 3

Increase each side by 3 ft. for a total dimension of 7 ft. x 24 ft.

(i) For function f(x) = x² - 2x + 2 over interval [-1, 2]: f(-1) = 5, f(2) = 2.

(ii) For function f(x) = x² + x over interval [0, 1]: f(0) = 0, f(1) = 2.

(iii) For function f(x) = 1/x² over interval [1, 2]: f(1) = 1, f(2) = 1/4.

To find the value of the function at the end-points of the interval, we substitute the values of the endpoints into the given functions.

Part (a) : f(x) = x² - 2x + 2; [-1, 2]

At x = -1:

f(-1) = (-1)² - 2(-1) + 2 = 1 + 2 + 2 = 5,

At x = 2:

f(2) = (2)² - 2(2) + 2 = 4 - 4 + 2 = 2,

So, values of function at the endpoints of the interval [-1, 2] are f(-1) = 5 and f(2) = 2.

Part (b) : f(x) = x² + x; [0, 1]

At x = 0:

f(0) = (0)² + 0 = 0.

At x = 1:

f(1) = (1)² + 1 = 1 + 1 = 2.

So, values of function at the endpoints of the interval [0, 1] are f(0) = 0 and f(1) = 2.

Part (c) : f(x) = 1/x²; [1, 2]

At x = 1:

f(1) = 1/(1)² = 1/1 = 1.

At x = 2:

f(2) = 1/(2)² = 1/4.

Therefore, the values of the function at the endpoints of the interval [1, 2] are f(1) = 1 and f(2) = 1/4.

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The given question is incomplete, the complete question is

Find the value of the function at the end points of the interval.

f(x) = x² - 2x + 2;   [-1, 2]

f(x) = x² + x;   [0,1]

f(x) = 1/x² ;    [1,2]

Answer:

The mistake he made was not distributing the 1/4 to all the terms in the parentheses. It should've instead become 1/4x + 3, which would then lead to a different answer

Answer:

He forgot to divide 12 by 4.

Step-by-step explanation:

1/4(x + 12) = 2

1/4(x) + 1/4(12) = 2

x/4 + 12/4 = 2

x/4 + 3 = 2

x/4 = -1

x = -1/4

Answer:

A 0.85

Step-by-step explanation:

half the original line

Answer:

0.85 ft

Step-by-step explanation:

Divide the length of the circle by 2 because the radius of a circle is half of the circles length

This is our rectangle:

We know that the area of a rectangle is it's length times it's width:

The problem says that one side is 12ft longer than 3 times the other side, so if a is the shorter side:

And we know that the area is 135ft². If we replace this and the expression for b into the equation for the area we can clear a and then find b:

Note that we got a 2 degree equation. We can solve it this way:

In our equation we have that A=3, B=12 and C=135 (and instead of x we have a):

One of these results will be negative, but since a is the size of the side of a rectangle we don't want a negative number, so we'll keep the positive result:

So we got that side a = 5 feet

Then we find b with the expression:

Side b = 27 feet

To find out how much the Guilderian trader must pay for the same 50 flop barrel of pickles, we need to calculate the cost per gulp and then multiply it by the number of gulps in the barrel.

Given that the Guilderian trader initially exchanged 25 gulps for the 50 flop barrel of pickles, we can determine the cost per gulp by dividing the total cost (50 flops) by the number of gulps (25).  Cost per gulp = 50 flops / 25 gulps = 2 flops/gulp . Since the gulp depreciates to 0.5 flops per gulp, the Guilderian trader must pay 0.5 flops per gulp for the same barrel of pickles.

Therefore, the Guilderian trader must pay 0.5 flops/gulp * 25 gulps = 12.5 flops for the 50 flop barrel of pickles. For the Florish trader, we need to calculate the cost per flop and then multiply it by the number of flops in the crate.

Given that the Florish trader initially exchanged 40 flops for the 20 gulp crate of apples, we can determine the cost per flop by dividing the total cost (40 flops) by the number of flops (20).

Cost per flop = 40 flops / 20 flops

= 2 flops/flop .

Therefore, the Florish trader must pay 2 flops per flop for the same crate of apples.

The Guilderian trader must pay 12.5 flops for the same 50 flop barrel of pickles, and the Florish trader must pay 2 flops for the same 20 gulp crate of apples.

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Answer:

34650 dollars by next year

Step-by-step explanation:

Answer:

Step-by-step explanation31500x.10. 3150. 31500+3150. 34650. 34650/12 2887.50. 31500/12. : 2625. Difference per month 262.50

Answer: A

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

If the drive in can only hold 72 cars, the n is all positive integers less than or equal to 72

Answer:

1/6

Step-by-step explanation:

you can just add the exponents because the number is the same so 9 +5 = 14

so now you can divide top and bottom by 6^14 and your left with 1/6

Answer:

10 Inches

Step-by-step explanation:

Remember the radius is always half the diameter. So, r * 2 = d. Plug those in...

5 * 2 = 10.

Therefore, the answer is 10 inches.