On Monday's math homework. Jeremiah solved 2 more problems correctly on Tuesday's math homework. If on Monday and Tuesday, he solved a total of 16 problems correctly, how many problems did he solve each day?

Answer: 25 cats and 15 dogs

Step-by-step explanation:

If the ratio of cats to dogs is 4:5 and the amount of cats is 20, you can evenly distribute this product by multiplying 5 on each side, meaning there would be 20 cats and 25 dogs.

For the group of animals that has just arrived, the amount of cats went up by 1.25% and the amount of dogs went down by 1.67%. To figure out the new total of animals, you are going to have to divide or multiply both sides of the ratio depending if they increased or decreased.

So in the ratio 5:3, you would multiply 20 and 1.25 to get 25, and divide 25 and 1.67 to get 15. Your final answer should be 25:15

The solution for the linear equation is:

a = 1/4.

I believe we have the linear equation:

(a + 2)/3 = 3/4

To solve this, we need to isolate the variable a in one of the sides of the linear equation, to do so, we can start by multiplying both sides by 3.

3*(a + 2)/3 = 3*(3/4)

a + 2= 9/4

Now we can subtract 2 in both sideS:

a + 2 - 2 = 9/4 - 2

a = 9/4 - 8/4 = 1/4

a = 1/4

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A Negative correlation coefficient means that as one variable increases, the other decreases (i.e., an inverse relationship).

Answer:

  (b)  Yes, they are congruent

Step-by-step explanation:

Given two triangles with a side length marked as 5 units, you want to know whether they are congruent. One triangle has marked angles 65° and 67° with the angle opposite the marked side being unmarked. The other triangle has angles marked 65° and 48°, with the latter being opposite the marked side.

In each case, the sum of angles is 180°, so the measure of the third angle is the value that makes that be the sum of all angles.

Triangle 1:

The third angle is 180° -65° -67° = 48°.

Triangle 2:

The third angle is 180° -65° -48° = 67°.

The measures of the angles in each triangle are 48°, 65°, and 67°. Since the angles are the same, the triangles are similar.

In each case, the marked side is opposite the smallest angle. This means we can claim congruence using either the ASA or AAS postulates.

Yes, they are congruent.

Answer:

D

Step-by-step explanation:

Since all the points were shifted the same way, I'll just use point A and point A'.

Point A starts at (3,5) and A' is at (5,2)

If the subract the x coordinates: 5-3=2

Then subtract the y coordinates: 2-5=-3

The 2 is positive, so it is 2 units to the right (the positive x direction) and -3 is negative so 3 units down (negative y direction)

The amount needed for retirement, rounded to the nearest cent, is option b. $398,407.85.

To determine the amount needed for retirement, we can use the present value formula for an annuity. In this case, we want to calculate the present value of the monthly withdrawals of $2,154 for 30 years, with a monthly interest rate of 5.1%.

First, we need to convert the interest rate to a monthly decimal rate. We divide 5.1% by 100 to get 0.051, and then divide it by 12 to get 0.00425.

Next, we use the formula: PV = PMT * (1 - (1 + r)^(-n)) / r, where PV is the present value, PMT is the monthly withdrawal amount, r is the monthly interest rate, and n is the total number of withdrawals.

Plugging in the values, we have:

PV = $2,154 * (1 - (1 + 0.00425)^(-12*30)) / 0.00425

Using a calculator, we find that PV is approximately $398,407.85.

Therefore, the amount needed for retirement, rounded to the nearest cent, is option b. $398,407.85. This amount will allow the individual to make monthly withdrawals of $2,154 for 30 years from an account paying 5.1% compounded monthly.

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The converse of the statement "If a figure is a square, its diagonals divide it into isosceles triangles" would be:

"If a figure's diagonals divide it into isosceles triangles, then the figure is a square."

The converse statement is not necessarily true. While it is true that in a square, the diagonals divide it into isosceles triangles, the converse does not hold. There are other shapes, such as rectangles and rhombuses, whose diagonals also divide them into isosceles triangles, but they are not squares. Therefore, the converse of the statement is not always true.

Therefore, the converse of the given statement is not true. The existence of diagonals dividing a figure into isosceles triangles does not guarantee that the figure is a square. It is possible for other shapes to exhibit this property as well.

In conclusion, the converse statement does not hold for all figures. It is important to note that the converse of a true statement is not always true, and separate analysis is required to determine the validity of the converse in specific cases.

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The indefinite integral of x√(x-9) dx is \((2/5)(x-9)^{(5/2)} + 2(x-9)^{(3/2)} + C\), where C is the constant of integration.

To find the indefinite integral of ∫x√(x-9) dx, we can use the substitution method.

Let u = x - 9, then du = dx.

Substituting these values into the integral, we have:

∫x√(x-9) dx = ∫(u + 9)√u du

Expanding the expression, we get:

∫(u√u + 9√u) du

Now we can integrate each term separately:

∫u√u du = ∫ \(u^{(3/2)}\) du = \((2/5)u^{(5/2)} + C1\)

∫9√u du = 9∫ \(u^{(1/2} du\) = \(9(2/3)u^{(3/2) }+ C2\)

Combining the results and substituting back u = x - 9, we have:

∫x√(x-9) dx = \((2/5)(x-9)^{(5/2)} + 9(2/3)(x-9)^{(3/2) }+ C\)

Simplifying further, we get:

∫x√(x-9) dx = \((2/5)(x-9)^{(5/2) }+ (6/3)(x-9)^{(3/2)} + C\)

                  = \((2/5)(x-9)^{(5/2)} + 2(x-9)^{(3/2)} + C\)

Therefore, the indefinite integral of x√(x-9) dx is\((2/5)(x-9)^{(5/2)} + 2(x-9)^{(3/2)} + C\), where C is the constant of integration.

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Answer:

A / B = X / Y       proportionate fractions

For a proportion to hold the ratios must be equal or

A Y = B X

Looking at B    5 / 15 = 4 / 12    

Both equal 1/3   and 5 * 12 = 15 " 4

Answer:

4x - 3.4xy

Step-by-step explanation:

x(4 - 3.4y)

4x - 3.4xy

Answer:

26

Step-by-step explanation:

a) The probability of a very good poker player earning a profit (more than $0) after playing 40 hands in $100/$200 Texas Hold'em can be calculated using the normal distribution and the given mean ($1) and standard deviation ($31). b) The proportion of the time a very good poker player can expect to earn at least $500 after playing 100 hands in $100/$200 Texas Hold'em can be calculated using the normal distribution and the given mean ($1) and standard deviation ($31).

To compute these probabilities, we need to make some assumptions and use probability distribution calculations based on the given information.

a) To determine the probability of a profit after playing 40 hands, we can use the concept of the normal distribution. We need to calculate the z-score using the formula: z = (x - μ) / σ, where x is the desired profit, μ is the expected profit per hand, and σ is the standard deviation. In this case, x = $0, μ = $1, and σ = $31.

Once we have the z-score, we can use a standard normal distribution table or calculator to find the corresponding probability.

b) Similarly, to find the proportion of the time a player can expect to earn at least $500 after playing 100 hands, we need to calculate the z-score for x = $500, using the same formula as in part (a). Then, we can use the standard normal distribution table or calculator to find the corresponding proportion.

c) To determine the probability of earning a profit during a 14-hour session, we need to calculate the number of hands played, which is 20 hands per hour multiplied by 14 hours. Let's denote it as N. Then, we can calculate the mean profit for the 14-hour session by multiplying the expected profit per hand ($1) by N.

The standard deviation for the session can be calculated by multiplying the standard deviation per hand ($31) by the square root of N. Finally, we can use the normal distribution and the same z-score calculation as in part (a) to find the probability.

Please note that the above calculations assume that the profits from each hand are independent and follow a normal distribution. Real poker outcomes may deviate from these assumptions.

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The rule that best describes the transformation that was applied to circle q to create circle q' is a dilation.

A dilation is a transformation that stretches or shrinks a figure by a certain scale factor, while preserving its shape. In this case, circle q was transformed into circle q' by either stretching or shrinking it, resulting in a circle that is either larger or smaller than the original circle. Since the shape of the circle remained the same, we can conclude that a dilation was the transformation that was applied.

To fully understand the transformation that was applied to circle q, we need to look at the properties of dilations. A dilation is a type of transformation that changes the size of a figure, but not its shape. It is performed by multiplying the coordinates of each point by a scale factor, which can be greater than 1 to stretch the figure, or less than 1 to shrink it. To determine if a dilation was applied to circle q, we can compare its properties to those of circle q'. First, we can look at the radii of the two circles. If circle q' is larger or smaller than circle q by a certain factor, this would indicate that a dilation was used. We can also examine the center of dilation, which is the point around which the figure is stretched or shrunk. If the center of circle q' is the same as that of circle q, this would suggest that a dilation was performed.

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Answer: y = -3x - 4

Step-by-step explanation:

Slope intercept form would be y = mx + b. To get your equation to this form you would need to isolate for y as shown:

3x + y = -4

y = -3x - 4 <-- Here I subtracted both sides by 3x

Answer:

A rectangle is a quadrilateral in which all angles are right angles. A rectangle is a parallelogram, so its opposite sides are equal. The diagonals of a rectangle are equal and bisect each other.

The control limits for the x chart for a sample of size 10,

a-Develop the control limits for the $\oveline x$ chart for samples of size 10, 20, and 30

UCL = 359.48

LCL = 340.51

b. What happens to the control limits as the sample size is increased

The control limits for the x chart for a sample of size 20,

UCL = 356.71

LCL = 343.29

c-What happens when a Type I error is made

The control limits for the x chart for a sample of size 30,

UCL = 355.47

d- What happens when a Type II error is made? e. What is the probability of a Type I error for samples of size 10, 20, and 30

LCL = 344.52

Possibility is referred to as probability. This branch of mathematics deals with the occurrence of a random event.

The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events.

Probability generally refers to the degree to which something is likely to occur.

This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is.

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The solution to the system of equations is x = 8/3 and y = 41/43.

To find the solution for the given system of equations, we can use the method of substitution or elimination. Let's use the method of elimination:

Given equations:

3x + 2y = 22 ---(1)

-x + 15y = 21 ---(2)

To eliminate one variable, we can multiply equation (2) by 3 and equation (1) by -1, then add the resulting equations:

-3x + 45y = 63 ---(3) (multiplying equation (2) by 3)

-3x - 2y = -22 ---(4) (multiplying equation (1) by -1)

Adding equations (3) and (4) eliminates the x variable:

43y = 41

Dividing both sides by 43 gives us:

y = 41/43

Now we can substitute this value of y into either equation (1) or (2). Let's use equation (1):

3x + 2(41/43) = 22

Multiplying both sides by 43 to eliminate the fraction:

129x + 82 = 946

Subtracting 82 from both sides:

129x = 864

Dividing both sides by 129:

x = 864/129

Simplifying:

x = 8/3

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Answer:

221

Step-by-step explanation:

Answer:

the answer you already chose is correct

The purchase price of the computer is $41,000.

We know that,

   1 year = 12 months

 5 year =( 12 * 5 ) months

  ∴5 year = 60 months

According to the question,

The company rented a computer for $800 a month.

The company had purchased the computer and paid a $100 maintenance charge.

The company would have saved $1000.

Purchase price=(800×60)- [(5×12 month×100)+1,000]

Apply BODMAS Rule,

⇒Purchase price=48,000-[60 * 100+1,000)

⇒Purchase price=48,000-[6,000+1,000)

⇒Purchase price=48,000-7,000 ( using subtraction)

⇒Purchase price=41,000

So, the purchase price of the computer is $41,000.

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The standard error of the sample mean is 1.21.

Given;

Suppose a diet regimen for men results in an average weight loss of between 13. 4 and 18. 3 pounds, according to a 95% confidence interval. These findings were based on a group of 42 men who were classified as overweight at the beginning of the four-month trial.

A 95% confidence interval for a population mean is (13.4, 18.3)

Upper limit = 18.3

Lower limit = 13.4

Since population SD is unknown, this interval is constructed using the t distribution.

n = 42

c = 0.95

∴ α = 1 - c = 1 - 0.95 = 0.05

α/2 = 0.025

Also, d.f = n - 1 = 42 - 1 = 41

∴ ta/2.d.f =  ta/2.n-1  =  t0.025,41  =  2.02 . . . . use t table

Now,

The margin of error = (Upper limit - Lower limit)/2

                                 = (18.3 - 13.4)/2

                                 = 2.45

But,

Margin of error = ta/2.d.f-  * (s / \sqrt{} n)

Margin of error = ta/2.d.f-  * Standard error

2.45 = 2.02 * Standard error

Standard error = 1.2129

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The style of jazz from the late 1950s and 1960s that matches the description you provided is known as "Cool Jazz" or "West Coast Jazz."

Cool Jazz emerged as a response to the energetic and complex bebop style that dominated the 1940s and early 1950s. It aimed to create a more relaxed, understated, and melodic approach to jazz. Cool Jazz musicians focused on creating a laid-back and serene atmosphere with their music.

One of the key features of Cool Jazz was the emphasis on a calm and controlled presentation. Musicians played with a more restrained and subtle energy, showcasing a less aggressive and fiery style compared to bebop. The improvisations were still virtuosic and skillful but were executed with a sense of effortlessness and ease.

Prominent figures associated with Cool Jazz include trumpeter Miles Davis, pianist Dave Brubeck, saxophonist Paul Desmond, and guitarist Wes Montgomery. Albums such as Miles Davis' "Kind of Blue," Dave Brubeck's "Time Out," and Paul Desmond's "Take Ten" are considered quintessential examples of the Cool Jazz sound.

Overall, Cool Jazz was characterized by its relaxed and sophisticated approach, showcasing intricate improvisations with a smooth and elegant delivery.

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Answer:

1) 2 should be added with 12 only and not with 6x as 6x and 2 are not like terms.

2) When adding polynomials, You should add only like terms.

Step-by-step explanation:

The steps done are:

Step 1: y-2=6x+12

Step 2: Add 2 on both sides

y-2+2=6x+12+2

Answer : y=8x+14

1) What mistake did I made?

You made a mistake in step 2,

When adding polynomials, you add only like terms. i.e

y-2+2=6x+12+2

y=6x+14

2 should be added with 12 only and not with 6x as 6x and 2 are not like terms.

2) Suggestion to avoid Such mistake in the future.

When adding polynomials, You should add only like terms.

Like terms are those that have same degree of variables i,e

2x and 3x, 2x^2 and 3x^2, 2 and 3 they all are like terms.

You can add 2x and 3x but can't add 2x and 2x^2 as they are not like terms.

So, while solving polynomials always add like terms.

To determine if there has been a change in the distribution of motivations for using a credit card among college students, a survey of 425 students was conducted.

The alternate hypothesis states that the distribution of motivations differs from the old survey. The critical value and rejection region need to be determined to test this hypothesis.

To test if there has been a change in the distribution of motivations, the null hypothesis assumes that the distribution remains the same as in the old survey, while the alternate hypothesis suggests a difference. In this case, the alternate hypothesis is that the distribution of motivations differs from the old survey.

To determine the critical value and rejection region, the significance level (α) needs to be specified. In this case, α is given as -0.005. However, it seems there may be some confusion in the provided information, as a negative significance level is not possible. The significance level should typically be a positive value between 0 and 1.

Without a valid significance level, it is not possible to determine the critical value and rejection region for hypothesis testing. The critical value is typically obtained from a statistical table or calculated based on the significance level and the degrees of freedom.

In conclusion, without a valid significance level, it is not possible to determine the critical value and rejection region to test the hypothesis regarding the change in the distribution of motivations for credit card usage among college students.

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The answer is option 2 and option 6

Answer:

2 and 6 are correct

Step-by-step explanation:

The probability of a random patient being alcoholic with elevated cholesterol levels is 55/80, or 0.6875. The probability of a random patient being nonalcoholic is 320/400, or 0.8. Lastly, the probability of a random patient being nonalcoholic with Non elevated cholesterol levels is 248/400, or 0.62.

To calculate the probability of a random patient being alcoholic with elevated cholesterol levels, we must first determine the total number of patients with elevated cholesterol levels. This can be done by adding the number of alcoholic patients (55) with elevated cholesterol levels to the number of nonalcoholic patients (72) with elevated cholesterol levels.

The result is a total of 127 patients with elevated cholesterol levels. This means that out of 400 patients, 55 of them were alcoholic and had elevated cholesterol levels. Therefore, the probability of a random patient being alcoholic with elevated cholesterol levels is 55/400, or 0.6875.

The probability of a random patient being nonalcoholic is equal to the total number of nonalcoholic patients (320) divided by the total number of patients (400). This yields a probability of 0.8.

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Answer:

We know that at 6:00 they are 180 degrees from each other. Every minute, the hour hand moves 1/2 of a degree, and the minute hand moves 6 degrees. So in 48 minutes, the hour hand moves 24 degrees and the minute hand moves 288 degrees. 288-180-24=84. So, 84 degrees.

Answer : A=abs((30*6) - (5.5*48)), solve for A A = 84 Degrees.

Step-by-step explanation:

Answer:

B. 1/2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Functions

Step-by-step explanation:

Step 1: Define

Identify

f(x) = 4(2)ˣ

Step 2: Evaluate

Answer: 0.4

Step-by-step explanation: Simplify the expression

The length of AB which is a diameter of the circle is equal 52 m using the Pythagoras rule.

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

The hypotenuse of the right triangle ADC is a radius and twice the length of the radius is that of the diameter so;

radius = √(10² + 24²)

radius = √(100 + 576)

radius = √676

radius = 26

diameter AB = 2 × 26 = 52m

Therefore, the length of AB which is a diameter of the circle is equal 52 m using the Pythagoras rule.

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