what is the length of side s of the square shown below ​

Answer:

5^-2

Step-by-step explanation:

5^3 * 5^-5

~Use exponent rule [ x^y * x^z = x^y+z ]

5^3+(-5)

~Simplify

5^-2

Best of Luck!

Answer:

f(x) = cos x

cos 0= 1

cos pi = -1

cos pi/2 = 0

Answer:

x = -2

y = 4

Step-by-step explanation:

6x-5y=-32

-7x+8y=46

Solve for x in the first equation.

6x = -32 + 5y

x = (-32 + 5y) /6

x = 5/6y - 16/3

Put x as 5/6y - 16/3 in the second equation and solve for y.

-7(5/6y - 16/3) +8y = 46

-35/6y+112/3 +8y = 46

13/6y + 112/3 = 46

13/6y = 46 - 112/3

13/6y = 26/3

y = 26/3 × 6/13

y = 4

Put y as 4 in the first equation and solve for x.

6x-5(4)=-32

6x-20 = -32

6x = -32+20

6x = -12

x = -12/6

x = -2

The formula predicting the number of US billionaires in any given year (t) is:f(t) = 17.2t - 34,129. We can assume a linear growth model on the based of given information.

The given data states that in the year 1985, there were 13 US billionaires. Whereas in 1990, there were 99 US billionaires. We have to find out the formula that predicts the number of US billionaires in any given year (t).

The yearly increase remains constant, so we can consider the formula for the linear function.f(t) = mt + b

where

t is the year and f(t) is the number of US billionaires in that year (t).

m is the slope of the line and b is the y-intercept.

The slope of the line is given by the formula:m = (y₂ - y₁) / (x₂ - x₁)

Let's plug in the given values to find the slope of the line.m = (99 - 13) / (1990 - 1985)m = 86 / 5m = 17.2 .The y-intercept of the line can be found by substituting the values of t and f(t) from any of the given points into the equation of the line.

Let's use the point (1985, 13).f(t) = mt + b => f(1985) =17.2(1985) + b => f(1985) = 34,142 + b =>b = 13 - 34,142 & b = -34,129.

The formula predicting the number of US billionaires in any given year (t) is:f(t) = 17.2t - 34,129

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Answer: y = 1

y = 2x+7 x = -3

y = 2(-3) + 7

y = 1

1. AABBCCDD: The probability of this happening is \(1/16\), since each parent would need to contribute a dominant allele for each gene.

2. AABBCcDD:  This genotype can be produced in two ways:

a) If both parents are homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D.

The probability of this happening is  = 1/128.

b) If one parent is homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A and B, homozygous dominant for C, and heterozygous for D.

3. The probability of this happening is 1/32.

AaBbCcDd : The probability of this happening is  1/256.

4. aaBBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D. The probability of this happening is  1/128.

b) If one parent is homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A, homozygous dominant for B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is  1/32.

To solve this problem, we need to use the principles of probability and Punnett squares.

For a tetrahybrid cross, we need to consider the four genes independently and combine the probabilities of each gene's alleles.

Assuming that A, B, C, and D are dominant alleles, and a, b, c, and d are recessive alleles, we can create a Punnett square for each gene, which would look like this:

A  |  A  |  a  |  a  

---|-----|-----|----

B  |  B  |  b  |  b  

---|-----|-----|----

C  |  C  |  c  |  c  

---|-----|-----|----

D  |  D  |  d  |  d  

Each box in the Punnett square represents a possible combination of alleles from the two parents.

For example, the top-left box represents offspring that inherit an A allele from the mother and an A allele from the father.

We can use these Punnett squares to calculate the probabilities of each genotype in the F2 offspring.

AABBCCDD - This genotype can only be produced if both parents are homozygous dominant for all four genes.

The probability of this happening is \((1/2)^4 = 1/16\) , since each parent would need to contribute a dominant allele for each gene.

AABBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D.

The probability of this happening is\((1/2)^4 * 1/2 * (1/2)^3 = 1/128\)

b) If one parent is homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A and B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is\(2 * (1/2)^4 * 1/2 * 1/2 * 1/2 = 1/32\)

AaBbCcDd - This genotype can be produced in 16 ways, since each gene can be inherited in two different ways (dominant or recessive).

The probability of this happening is \((1/2)^8 = 1/256.\)

aaBBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D. The probability of this happening is\((1/2)^4 * 1/2 * (1/2)^3 = 1/128.\)

b) If one parent is homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A, homozygous dominant for B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is \(2 * (1/2)^4 * 1/2 * 1/2 * 1/2 = 1/32.\)

Note that we have assumed independent assortment of the four genes, which means that the inheritance of one gene does not affect the inheritance of another gene.

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A. By the Unique Representation Theorem, for each x in V, there exists a unique set of scalars C1, Cn such that x = C1b1 + ... + Cnbn.

By the Unique Representation Theorem, for any vector x in V, there exists a unique set of scalars C1, Cn such that x can be expressed as a linear combination of the basis vectors b1, ..., bn. This means that any vector in V can be uniquely represented using the basis B.

In other words, the basis B spans the vector space V, and any vector in V can be written as a linear combination of the basis vectors. The coefficients C1, Cn represent the weights or scalars that determine the combination of basis vectors needed to obtain the given vector x.

The statement A is true because it reflects the Unique Representation Theorem. It states that for each vector x in V, there exists a unique set of scalars C1, Cn such that x can be expressed as a linear combination of the basis vectors C1b1 + ... + Cnbn.

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You are given the expected number of people who drop out due to relapse and those who move out of the study area, along with their respective standard deviations. Since the numbers are supposed to be independent, you can simply add the expected values to find the expected number of people who will drop out due to either reason.

Step 1: Note the expected number of people dropping out due to relapse, which is 10.
Step 2: Note the expected number of people dropping out due to moving away, which is 6.
Step 3: Add the expected values from Steps 1 and 2: 10 + 6 = 16.

The expected number of people who will drop out due to either relapse or moving away is 16. Therefore, the correct answer from the group of choices is 16.

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Answer:

a

Step-by-step explanation:

The answer is OC. Minimum: -12.48; maximum: 64.48.

The minimum usual value - 20 and the maximum usual value y + 20 for the given values of n and p, n = 100; p = 0.26 are found below.

Minimum usual value = np - z * sqrt(np(1 - p)) = 100 × 0.26 - 1.645 × sqrt(100 × 0.26 × (1 - 0.26))= 26 - 1.645 × sqrt(100 × 0.26 × 0.74) = 26 - 1.645 × sqrt(19.1808) = 26 - 1.645 × 4.3810 = 26 - 7.2101 = 18.79 ≈ 18.80

Maximum usual value = np + z * sqrt(np(1 - p)) = 100 × 0.26 + 1.645 × sqrt(100 × 0.26 × (1 - 0.26))= 26 + 1.645 × sqrt(100 × 0.26 × 0.74) = 26 + 1.645 × sqrt(19.1808) = 26 + 7.2101 = 33.21 ≈ 33.22

Therefore, the minimum usual value - 20 is 18.80 - 20 = -1.20.The maximum usual value y + 20 is 33.22 + 20 = 53.22.

Hence, the answer is OC. Minimum: -12.48; maximum: 64.48.

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Answer:

PERIOD POOOOOOOOOOOOOOO

Step-by-step explanation:

If the function is continuous function and ∫0 to 8 f(u) du = 6, the value of ∫ 1 to 3 xf(x² - 1) dx is B) 3.

Given ∫0 to 8 f(u) du = 6 and we need to find the value of ∫ 1 to 3 xf(x² - 1) dx

We can say, u = x² - 1

Differentiating both sides

du = 2x dx

dx = du/2x

When x = 1,

         u = 1² - 1 = 0

and when x = 3

         u = 3² - 1 = 8

So, ∫ 1 to 3 xf(x² - 1) dx can be written as

           ∫ 1 to 3 xf(x² - 1) dx = ∫ 0 to 8 xf(u)  du/2x

                                          = 1/2∫ 0 to 8 f(u) du

It is given that ∫0 to 8 f(u) du = 6

So, ∫ 1 to 3 xf(x² - 1) dx = 1/2 x 6 = 3

Hence, the value of ∫ 1 to 3 xf(x² - 1) dx is 3.

The question is incomplete. The complete question is

" The function f is continuous and ∫0 to 8 f(u) du=6. What is the value ∫ 1 to 3 xf(x² - 1) dx? (A) 3/2 (B) 3 (C) 6 (D) 12 (E) 24 "

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The function equality that represents the point where f(x) = g(x) is; A: f(0) = g(0) and f(2) = g(2)

From the question, the curved red line represents g(x) while the straight blue line represents f(x).

Now, the equality of functions f(x) = g(x)  is represented as a common function between their curves. Thus, we will just need to find a common point for both. This is;

f(x) has points (0, 4) and (2, 0).

g(x) has points (0,4) and (2,0).

It is pertinent to note that both functions have the same y-value for x=0 and x = 2. Thus, we can say that;

f(2) = g(2) and f(0) = g(0)

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Answer:

Step-by-step explanation:

Los movimientos bancarios de Santiago se representan matemáticamente teniendo en cuenta que consignar es sumar y retirar el restar. Por lo tanto podes expresar los movimientos bancarios de la siguiente manera:

Al realizar la sumatoria se obtiene:

 +300.000 - 120.000 - 95.000 + 80.000 = + 165.000

En la semana Santiago obtiene en su cuenta bancaria $165.000

The Fundamental Theorem of Calculus states that if a function f is continuous on the closed interval [a,b] and F is the antiderivative of f on [a,b], then the definite integral of f from a to b is equal to F(b) - F(a).

For the first question, we can use the Fundamental Theorem of Calculus and the Chain Rule to find the derivative:

ddx∫x−1(3t5−t)30dt = (3x5-x)/30

For the second question, we can use Part 2 of the Fundamental Theorem of Calculus:

d/da ∫a^3 (7t^2 + 6) dt = 7a^6 + 6a^3

Then, we can use the Chain Rule to find the derivative of the function with respect to t:

d/dt (7a^6 + 6a^3) = 42a^5(da/dt) + 18a^2(da/dt)

Since the problem gives us da/dt = 20, we can substitute to find:

d/dt (7a^6 + 6a^3) = 8400a^5 + 3600a^2

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Answer:

\(q = 22\)

Step-by-step explanation:

The angle measure of a straight line is (180) degrees As given in the picture, line (AC) is a straight line, thus its angle measure is (180) degrees. Angles (ABD) and (DBC) make up line (AC). Therefore, one can conclude that the sum of angles (ABD) and (DBC) is (180) degrees. Form an equation, simplify and use inverse operations to solve for the unknown parameter (q).

\((<ABD) + (<DBC) = (AC)\)

Substitute for the angle measures,

\((7q-46)+(3q+6)=180\)

Simplify,

\(10q-40=180\)

Inverse operations,

\(10q-40=180\\\\10q = 220\\\\q = 22\)

Answer:

need pts

Step-by-step explanation:

The rate of the square increasing when the area is 16 cm² is 64 cm²/s. The result is obtained by using basic derivative rules.

The rate of a square increasing can be counted by the derivative of the area of the square as a function of time.

dA/dt = 2s ds/dt

Where s is side length.

If each side of a square is increasing at a rate of 8 cm/s, what is the rate of the square increasing when the area is 16 cm²?

We have the side of the square as the function of time.

ds/dt = 8 cm/s

When the area is 16 cm², the side length is

A = s²

16 = s²

s = √16

s = 4 cm

The rate of the square increasing is

dA/dt = 2s ds/dt

dA/dt = 2 × 4 × 8

dA/dt = 64 cm²/s

Hence, the rate of the square increasing when the area is 16 cm² is 64 cm²/s.

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Answer: 12 dimes

Step-by-step explanation: 12 quarters = 3.00

five nickels = 3.25

12 dimes = 4.45

13 pennies = 4.58

Answer:

the data set seems wrong, since for every 4twix bars, she had 2 pieces of jolly ranchers; so ratio 4 twix bars : 2 ranchers is to be use but it wouldn't work, it can only work for the first 30 candies ( 20twix bars and 10 ranchers) so the last 2 candies( if following the ratio will be 4/3 for the twix bars and 2/3 for the ranchers)

One disadvantage of a certificate of deposit (CD) is that you may have to pay a penalty if you withdraw your money before the agreed-upon maturity date. This penalty serves as a deterrent for early withdrawals and can reduce the overall return on your investment.

When you invest in a certificate of deposit, you commit to keeping your money in the account for a fixed period known as the maturity period. If you withdraw your funds before this maturity date, you are likely to incur a penalty fee. The penalty amount can vary depending on the terms and conditions set by the financial institution offering the CD.

This penalty is imposed to discourage premature withdrawals and compensate for the bank's loss of interest income.

The penalty for early withdrawal can have a negative impact on the overall return on your investment. It reduces the amount of interest you will earn and may even result in a partial loss of the principal amount.

Therefore, it is important to carefully consider the maturity period and your financial needs before investing in a certificate of deposit to avoid potential penalties and ensure the best possible return on your investment.

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\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

Profit made when we spend $ 2000 on advertising is ~

Refer to attachment for solution ~

On solving the provided question, we can say that - by doing the equation we have 70 adult tickets were sold. and 130 children's tickets were sold.

An algebraic equation of the form y=mx+b, where m denotes the slope and b the y-intercept, is known as a linear equation. When y and x are variables, the aforementioned is referred to as a "linear equation in two variables." Bivariate linear equations are defined as linear equations with two variables. 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples of linear equations.

Total: $610, quantity: 200, adult: $5, number of children: x, child: $2

Price:\(5x + 2y = 610\)

Quantity: 200 when x plus y.

\(2(x + y = 200) 2x - 2y = -400 1(5x + 2y = 610) 5x + 2y = 610\\3x + 0 = 210\\ x = 70.\)

In either the Cost or Quantity equation, substitute "x = 70":

\(x + y = 200 70 + y = 200 y = 130\)

70 adult tickets were sold.

130 children's tickets were sold.

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Answer:

.09

Step-by-step explanation:

Using conditional probability, it is found that the probability that a randomly selected customer will get the classic wash and vacuum their car is:

B) 0.09

Conditional Probability

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which

In this problem:

Then:

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

\(P(A \cap B) = P(B|A)P(A)\)

\(P(A \cap B) = 0.25(0.35)\)

\(P(A \cap B) = 0.0875\(

Close to 0.09, hence option B.

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Answer:

the 0.28 company

Step-by-step explanation:

0.28 is smaller than 0.3 and 0.28 still costs the same amount of money as 0.3

Company A requires a greater monthly income since its ideal debt-to-income ratio (0.3) results in a higher portion of income allocated to the mortgage payment compared to Company B's ideal ratio of 0.28.

Company A's ideal metric for the debt-to-income ratio is 0.3, which means the monthly mortgage payment should be 30% of the total monthly income. Similarly, Company B's ideal metric is 0.28, which means the monthly mortgage payment should be 28% of the total monthly income.

Since the target mortgage payment is the same for both companies, the company with the smaller ideal metric (0.28 for Company B) requires a greater monthly income to meet that target. This is because a smaller ratio (0.28) of the mortgage payment to the total income implies that the mortgage payment is a larger portion of the income, requiring a higher income to maintain the same payment amount.

In other words, Company B's requirement of keeping the debt-to-income ratio lower means that the mortgage payment should be a smaller fraction of the total monthly income. As a result, to keep the mortgage payment constant, a higher income is needed to achieve the smaller debt-to-income ratio of 0.28 compared to Company A's debt-to-income ratio of 0.3.

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Since the cost of digging up the chest ($5000) is higher than the total amount of money that can be obtained from the chest ($760.60), it would not be worth the effort to dig up the chest.

Based on the given information, let's calculate the values step by step:

a) Volume of the large sea chest in mL:

V = lwh = (30 in) * (18.5 in) * (19.5 in) = 10935 in³

Since there are 16.39 mL in 1 in³, we can convert the volume to mL:

Volume in mL = 10935 in³ * 16.39 mL/in³ = 179,296.65 mL

b) Amount of metal that can be held by the large sea chest:

To determine the volume of the chest in cubic centimeters:

Volume in cubic cm = (30 in) * (2.54 cm/in) * (18.5 in) * (2.54 cm/in) * (19.5 in) * (2.54 cm/in) = 13,911.72 cubic cm

The metal has a density of 7.874 g/cm³, so the mass of the metal that can be held by the chest is:

Mass of metal = Volume x Density = 13,911.72 cubic cm * 7.874 g/cm³ = 109,502.01 g

c) Conversion of mass to pounds:

Since 1 lb is equal to 453.59 g, we can convert the mass of the metal to pounds:

Mass of metal in lb = 109,502.01 g / 453.59 g/lb = 241.45 lb

d) Total amount of money obtained from the chest:

The current price of the metal is $3.15/lb, so we can calculate the total amount:

Total amount = Price per lb x Mass of metal = $3.15/lb * 241.45 lb = $760.60

e) Cost of digging up the chest:

The cost of digging up the chest is given as $5000.

Conclusion:

Since the cost of digging up the chest ($5000) is higher than the total amount of money that can be obtained from the chest ($760.60), it would not be worth the effort to dig up the chest.

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At the water slides, there are a total of 37 temporary employees and 37 permanent employees. To determine the percentage of employees who are temporary,  50% of the employees at the water slides are temporary employees.

The total number of employees at the water slides is the sum of temporary and permanent employees: 37 temporary + 37 permanent = 74 employees.
To find the percentage of temporary employees, we divide the number of temporary employees by the total number of employees and multiply by 100:
Percentage of temporary employees = (Number of temporary employees / Total number of employees) * 100
Plugging in the values:
Percentage of temporary employees = (37 / 74) * 100
Calculating this expression gives us:
Percentage of temporary employees = 0.5 * 100 = 50%
Therefore, 50% of the employees at the water slides are temporary employees.

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A rigid transformation is a rigid motion of a geometric object on a plane

The correct response is; Yes, the transformation is a rigid motion

Reason:

A rigid transformation or rigid motion is a motion in which the distance between pairs of corresponding points on the image and the preimage are equal

Therefore, given that the side lengths of the square, are each of length 3, such that the size of the preimage and the image are equal, and therefore, the distances between corresponding pairs of points on the image and the preimage, are equal, the transformation is a rigid motion

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Answer:

The answer is YES, it is a rigid motion.

Reason:

Because a rigid motion is one that does not change the shape or size, when you rotate a shape, you are only changing its orientation. The distance between any two points is also the same.