PLZ HELP Kate is three years older than her sister. In two years Kate will be twice older. How old is Kate's sister now?

7.68 pounds of honey remains after the bears ate 0.32 pounds.

What is a initial amount mean?

When referring to any Capital Appreciation Bond, Original Amount refers to the Bond's Accrued Value as of the date of issuance.

To find how much honey remains, we need to subtract the amount eaten by the bears from the initial amount produced:

Remaining honey = Initial honey - Honey eaten by bears

Remaining honey = 8 pounds - 0.32 pounds

Remaining honey = 7.68 pounds

Therefore, 7.68 pounds of honey remains after the bears ate 0.32 pounds.

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Answer:

x=14.02

Step-by-step explanation:

Use b=\(\sqrt{c^2-a^2}\) to solve for the missing side in the triangle. You will get a rounded answer of 8.49. Then you multiply that by 2 and subtract that value from 31. Then that will be your answer.

(a) The point estimate for Bernie's sample is 0.58.

(b)The margin of error for Bernie's winning bets, given a 99% confidence level, is approximately 0.124.

(a) The point estimate for Bernie's sample is simply the proportion of wins in his sample.

Point estimate = Number of wins / Sample size

                        = 58 / 100

                        = 0.58

So, the point estimate for Bernie's sample is 0.58.

(b) To compute the margin of error for Bernie's winning bets,

we need to use the confidence level and the sample size.

Given that the confidence level is 99%,

we can determine the corresponding critical value from the standard normal distribution.

The critical value for a 99% confidence level can be found using a standard normal distribution table or technology.

It is ≈ 2.576.

The margin of error (ME) is then calculated as the product of the critical value and the standard error (SE).

Standard error (SE) = √((point estimate × (1 - point estimate)) / sample size)

⇒SE = √((0.58 × (1 - 0.58)) / 100) ≈ 0.048

Margin of error (ME) = Critical value × Standard error

⇒ ME ≈ 2.576 × 0.048 ≈ 0.124

The margin of error for Bernie's winning bets, given a 99% confidence level, is approximately 0.124.

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Answer:

9.333

Step-by-step explanation:

\(19. \: cross \: multiplying \\ 6a = 7 \times 8 \\ 6a = 56 \\ \frac{6a}{6} = \frac{56}{6 } \\ a =9.333\)

25. Cross multiplying

nx1 =0.19x12

n=2.28

Answer:

\(\Large \boxed{{19. \ a \approx 9.33}} \\ \\ \Large \boxed{25. \ n=2.28}\)

Step-by-step explanation:

(19)

\(\displaystyle \frac{6}{8} =\frac{7}{a}\)

Cross multiply.

\((6)(a)= (7)(8)\)

\(6a=56\)

Divide both sides by 6.

\(\displaystyle a = \frac{56}{6}=\frac{28}{3}\)

\(a \approx 9.33\)

(25)

\(\displaystyle \frac{1}{0.19} =\frac{12}{n}\)

Cross multiply.

\((1)(n)=(0.19)(12)\)

\(n=2.28\)

Answer:

14 minutes

Step-by-step explanation:

We take

63 / 6 = 10.5 words per minute

So, Nachelle can text 10.5 words per minute.

At this rate, how many minutes would it take her to text 147 words?

We take

147 / 10.5 = 14 minutes

So, at this rate, it would take her 14 minutes to text 147 words.

This means that there are 10 different possible results. Thus, there are 10 different possible values may result.

Let's consider two positive even integers less than (not necessarily distinct). When the sum of these two numbers is added to their product, how many different https://brainly.com/question/30241588https://brainly.com/question/30241588values may result?

Solution:The product of two even numbers will be even.

The sum of two even numbers will also be even. When we add an even number and an even number, the result is always even, and

even + even = even.

However, if we sum two different even numbers with their product, the result is always an odd number.

Even * Even = Even, and

even + even = even.

Even + Odd = Odd.

Therefore, we must find all possible sums of two even numbers. And then, we must determine how many of those sums are even.

Consider the following

:2 + 2 = 4, which is even

.2 + 4 = 6, which is even.

2 + 6 = 8, which is even.

2 + 8 = 10, which is even.

4 + 4 = 8, which is even.

4 + 6 = 10, which is even.

4 + 8 = 12, which is even.

6 + 6 = 12, which is even.

6 + 8 = 14, which is even.

8 + 8 = 16, which is even.

Only even numbers resulted from adding two even numbers. This means that there are 10 different possible results.

Thus, there are 10 different possible values may result.

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The sum of two positive even integers is always an even number, and their product is also an even number. When we add an even number to another even number, the result will always be an even number.

Let's consider two positive even integers, A and B. Since they are positive even integers, they can be expressed as 2x and 2y, where x and y are positive integers.

The sum of A and B is 2x + 2y = 2(x + y), which is always an even number.

The product of A and B is (2x)(2y) = 4xy, which is also an even number.

When we add the sum of A and B to their product, we get an expression:

(2x + 2y) + (4xy) = 2(x + y) + 4xy = 2[(x + y) + 2xy].

Let's define a new positive integer, Z = (x + y) + 2xy.

Now, we can see that the expression (2x + 2y) + (4xy) is equal to 2Z, which is always an even number.

Since the expression is always an even number, there are no different possible values that can result from the sum of two positive even integers less than Z.

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The one-sided limit as x approaches 1 from the left is 6.

To find the indicated one-sided limit as x approaches 1 from the left, we substitute values of x that are slightly less than 1 into the function and observe the behavior.

\(lim_{x - > 1^-} (8x - 2)\)

As x approaches 1 from the left, the expression 8x - 2 approaches:

8(1) - 2 = 8 - 2 = 6

Therefore, the one-sided limit as x approaches 1 from the left is 6. The limit represents the value that the function approaches as the input approaches a particular value. In this case, as x gets closer to 1, the function 8x - 2 gets closer to 6.

The complete question is:

Find the indicated one-sided limit, if it exists. (If an answer does not exist, enter DNE.)

\(lim_{x - > 1^-} (8x - 2)\)

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The interval estimate becomes narrower.

An interval estimate is the use of sample data to calculate an interval of possible (or probable) values ​​of an unknown population parameter, as opposed to a point estimate, which is a single number.

Estimation is a method of drawing conclusions about an unknown population parameter from a sample. An estimate is a statistic that is used to calculate the value of a parameter that is not defined. Intervals are statistical estimation approaches that use survey data to generate ranges of values ​​that are likely to contain the population value of interest. Point estimates, on the other hand, are single-valued estimates of the population value. Confidence intervals are the most familiar of the various forms of statistical intervals. Certain types of analysis and scenarios, on the other hand, require the use of different scopes that provide different details.

Hence in interval estimation, as the sample size becomes larger, the interval estimate becomes narrower.

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The z-score corresponds to 0.275 is -0.63.

The specific number of skateboards corresponding to the z-score from part (a) is 20,468.

We have,

(a)

To find the z-score corresponding to a specific percentage of days, we can use the standard normal distribution table or a calculator.

In this case, we are given that 45% of the days had a production of skateboards less than the specific value.

Since the standard normal distribution is symmetrical, we can find the z-score corresponding to 45% by finding the z-score that corresponds to

(1 - 0.45) / 2 = 0.275, which is the area to the left of the z-score.

Using the standard normal distribution table or a calculator,

We find that the z-score corresponds to 0.275 is:

= -0.63.

(b)

To find the specific number of skateboards corresponding to the z-score, we can use the formula:

x = μ + zσ

where x is the specific number of skateboards, μ is the mean (20,500), z is the z-score (-0.63), and σ is the standard deviation (55).

Substituting the values.

x = 20,500 + (-0.63) x 55

x = 20,468.35

Rounding to the nearest whole number,

x = 20,468.

Therefore,

The z-score corresponds to 0.275 is -0.63.

The specific number of skateboards corresponding to the z-score from part (a) is 20,468.

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Answer:

Please look at the image

From the info 2 jars with 106 sprinkles each, we know 1 jar would have 53 sprinkles.

1 jar has 53 sprinkles.

6 jars have 318 sprinkles because:

6 × 53 = 318

13 jars have 689 sprinkles because:

13 × 53 = 689

- Events A, B, C, and D are exhaustive.
- Events A and B, B and D are not mutually exclusive.
- Events A and C, C and D, A and D are mutually exclusive.

To determine whether the events are exhaustive or mutually exclusive, we need to understand the definitions of these terms:
1. Exhaustive events: Events are considered exhaustive if the union of all the events covers the entire sample space S. In other words, there are no outcomes in the sample space that are not included in any of the events.
2. Mutually exclusive events: Events are considered mutually exclusive if they have no outcomes in common. In other words, the events cannot occur simultaneously.
Now let's analyze the given events:
A = {1, 2, 4}
B = {1, 2, 4, 5, 6}
C = {5, 6}
D = {2, 3, 6}
To determine if the events are exhaustive, we need to check if their union covers the entire sample space S.
The union of A, B, C, and D is {1, 2, 3, 4, 5, 6}, which covers the entire sample space S. Therefore, the events A, B, C, and D are exhaustive.

To determine if the events are mutually exclusive, we need to check if any outcomes are shared between the events.
The outcomes 1, 2, and 4 are shared between events A and B. Therefore, events A and B are not mutually exclusive.
The outcomes 2 and 6 are shared between events B and D. Therefore, events B and D are not mutually exclusive.
No outcomes are shared between events A and C, C and D, or A and D. Therefore, events A and C, C and D, and A and D are mutually exclusive.

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Answer:

srat

Step-by-step explanation:hehe i really dont know

The rate of population growth is proportional to the logarithm of the ratio of the carrying capacity to the current population.

The Gompertz function is a solution of the differential equation:

dP/dt = c ln(K/P) P

where P(t) is the population at time t, c is a constant, and K is the carrying capacity, i.e., the maximum population that can be sustained by the available resources.

To solve this differential equation, we can use separation of variables:

dP/P ln(K/P) = c dt

Integrating both sides, we get:

∫ dP/P ln(K/P) = ∫ c dt

Integrating the left-hand side requires a substitution. Let u = ln(K/P), then du/dP = -1/P and the integral becomes:

-∫ du/u = -ln|u| = -ln|ln(K/P)|

The right-hand side is just:

c t + C

where C is an arbitrary constant of integration.

Putting these together, we get:

-ln|ln(K/P)| = ct + C

Taking the exponential of both sides, we get:

|ln(K/P)| = e^(-ct-C)

Using the absolute value is unnecessary, since ln(K/P) is always positive, so we can drop the absolute value and write:

ln(K/P) = e^(-ct-C)

Solving for P, we get:

P = K e^(-e^(-ct-C))

This is the Gompertz function, which gives the population as a function of time, under the assumption that the rate of population growth is proportional to the logarithm of the ratio of the carrying capacity to the current population.

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Answer:

  a = 1/2

Step-by-step explanation:

You want the solution to 3 +0.5(4a +8) = 9 −2a.

It usually works well to start by simplifying the equation. That is, you eliminate parentheses, combine like terms.

  3 +0.5(4a) +0.5(8) = 9 -2a

  3 + 2a +4 = 9 -2a

  7 +4a = 9 . . . . . . . . . add 2a

  4a = 2 . . . . . . . . . subtract 7

  a = 0.5 . . . . . . divide by 4

The value of a is 1/2.

__

Additional comment

The attached calculator output shows this value of 'a' satisfies the equation.

Answer: 234 inches

Step-by-step explanation:

The billboard is 6 meters long and we are given the conversion factor for centimeters to inches.

To convert the length to inches therefore, convert the length from meters to centimeters first:

1 meter = 100 cm

6 meters would therefore be:

= 6 * 100

= 600 cm

1 cm = 0.39 inches so 600 cm is:

= 600 * 0.39

= 234 inches

Answer: 4a + 16

Step-by-step explanation:

After calculating the unit rate for coffee we can infer that she bought 5 pounds of coffee.

A rate in mathematics is the ratio of two related variables stated in different units. If one of these variables is written as a single unit in the denominator of the ratio and it is assumed that this quantity can be changed on a regular basis (i.e., is a variable and the independent), the ratio's numerator indicates the corresponding rate of change in another (dependent) variable.

A rate is commonly referred to as an output-input ratio or a benefit-cost ratio. Miles per hour, for example, is the output (or profit) in terms of miles travelled from a few hours of travelling somewhere (a cost in time) (at this velocity).

Money on the gift card = $80

Amount left after buying coffee = $ (80-43.70) = $ 36.30

Unit rate of coffee =$ 7.26

Now we have to divide the total amount of money by the unit rate to calculate the amount of coffee bought.

amount of coffee bought = $(36.30 ÷ 7.26) = 5 pounds

Hence she bought 5 pounds of coffee.

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we estimate that g^-1(4) is approximately 0.8.

To find g^-1(4), we need to find the value of x that satisfies the equation g(x) = 4, where g(x) = 3 + x + e^x.

So, we start by setting g(x) equal to 4 and solving for x:

3 + x + e^x = 4

Subtracting 3 from both sides, we get:

x + e^x = 1

We cannot solve this equation for x algebraically, so we need to use numerical methods to approximate the solution. One common method is to use the graph of the function g(x) and its inverse g^-1(x) to estimate the value of g^-1(4).

First, we graph the function g(x) and look for the point on the curve where the y-coordinate is 4:

Graph of g(x) = 3 + x + e^x

From the graph, we can see that there is a point on the curve where the y-coordinate is close to 4, which is approximately x = 0.5.

Next, we look at the graph of the inverse function g^-1(x), which is simply the reflection of the curve of g(x) across the line y = x:

Graph of g^-1(x)

From the graph, we can see that the point on the curve of g^-1(x) that corresponds to the point (0.5, 4) on the curve of g(x) is approximately g^-1(4) = 0.8.

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To convert the rate of water flow from meters per minute to kilometers per hour, we need to multiply by a conversion factor. Since there are 60 minutes in an hour and 1000 meters in a kilometer, the conversion factor is (60/1000).

So, the rate of flow in km/h is (300 * 60/1000) = 18 km/h.

Therefore, the correct answer is option b) 18.

To find the ratio of 1 liter to 350 ml, we need to convert both measurements to the same unit. Since 1 liter is equal to 1000 ml, the ratio becomes:

1 liter : 1000 ml

To simplify the ratio, we divide both sides by 50:

(1 liter / 50) : (1000 ml / 50)

Therefore, the correct ratio is option a) 20:7.

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Answer:

2√5

Step-by-step explanation:

d = √(x2 - x1)² + (y2 - y1)²

= √[1 - (-1)]² + [3 - (-1)]

= √(2)² + (4)²

= √(4) + (16)

= √20

= 2√5

The evaluated probabilities for the given question are 0.20 for the men who asked for promotion, 0.59 for the men who received the promotion when asked, and  0.118 for men who asked for promotion and received.under the condition that from the men interviewed  20% had asked for a promotion and 59% of the men who had asked for a promotion and  received.
Then,
P(man asked for a promotion)
= 20/100
= 0.20

P(man received promotion, given he asked for one)
= 59/100
= 0.59

P(man asked for promotion and received )
= P(man asked for a promotion) x P(man received promotion, given he asked for one)
= 0.20 x 0.59
= 0.118
Probability is considered as  the percentage of an event taking place in a specific time frame, in a given place. It is said to be a great aid in the horizons of science and mathematics.


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Answer:

A dilation by 2 and a rotation about the origin at 90 degrees counter-clockwise

Step-by-step explanation:

Already taken geometry.

If f(x)=2x²-5x-3 g(x)=2x²+5x+2 then (f/g)(x) = (x - 3) / (x + 2).

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.

To find (f/g)(x), we need to divide f(x) by g(x) as follows:

f(x) = 2x² - 5x - 3

g(x) = 2x² + 5x + 2

f(x) / g(x) = (2x² - 5x - 3) / (2x² + 5x + 2)

To simplify this expression, we can factor the numerator and denominator:

f(x) / g(x) = [(2x + 1)(x - 3)] / [(2x + 1)(x + 2)]

Now, we can cancel out the common factor of (2x + 1) from both the numerator and denominator:

f(x) / g(x) = (x - 3) / (x + 2)

Therefore, (f/g)(x) = (x - 3) / (x + 2).

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Answer:

53 degrees

Step-by-step explanation:

If the two lines intersected by a transversal are parallel then the same side interior angle should add up to 180 degrees.

180-127 = 53 degrees

the solution to the system of equations is x = 2 and y = 1.

To solve the system of equations by substitution, we will solve one equation for one variable and substitute it into the other equation.

Given the system of equations:

1) y = 6x - 11

2) -2x - 3y = -7

Step 1: Solve equation (1) for y.

  y = 6x - 11

Step 2: Substitute the value of y from equation (1) into equation (2).

  -2x - 3(6x - 11) = -7

Step 3: Simplify and solve for x.

  -2x - 18x + 33 = -7

  -20x + 33 = -7

  -20x = -7 - 33

  -20x = -40

  x = (-40)/(-20)

  x = 2

Step 4: Substitute the value of x into equation (1) to find y.

  y = 6(2) - 11

  y = 12 - 11

  y = 1

Therefore, the solution to the system of equations is x = 2 and y = 1.

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The solution to the system of equations y = 6x - 11 and -2x - 3y = -7 is x = 2 and y = 1. This is achieved by substituting y into the second equation, simplifying, and solving for x, then substituting x back into the first equation to solve for y.

To solve the system of equations y = 6x - 11 and -2x - 3y = -7 by substitution, we start by substituting the equation y = 6x - 11 into the second equation in place of y, giving us -2x - 3(6x - 11) = -7. Next, simplify the equation by distributing the -3 inside the parentheses to get -2x - 18x + 33 = -7. Combine like terms to get -20x + 33 = -7. Subtract 33 from both sides to obtain -20x = -40, and finally, divide by -20 to find x = 2.

Once we find the solution for x, we substitute it back into the first equation y = 6x - 11. Substituting 2 in place of x gives y = 6*2 - 11, which simplifies to y = 1.

Therefore, the solution to the system of equations is x = 2 and y = 1.

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For the given question, we will find the value of x

As shown, there is a right angle triangle

The opposite side to the angle 2.5° = x

The adjacent side to the angle 2.5° = 5 ft

Using the tan function:

Using the cross product, the value of x will be:

the answer will be in inches, so we will convert ft to in

so, as 1 foot = 12 inches

Rounding to the nearest tenth

so, the answer will be x = 2.6 in

The average rate of water usage over the interval 0 < t < 5 is approximately 446.86 gallons per hour.

To find the average rate of water usage, we need to calculate the total amount of water used over the given interval and divide it by the length of the interval. The average rate is the ratio of the total water usage to the duration.

The integral of the rate function W(t) over the interval [0, 5] gives us the total amount of water used:

∫[0,5] 16te^t dt = [16te^t - 16e^t] evaluated from t = 0 to t = 5 = (16(5e^5 - e^5) - 16e^5) - (16(0 - 1) - 16) = 16(5e^5 - 1) - 16e^5 + 16 = 80e^5 - 16e^5 + 16 = 64e^5 + 16.

The length of the interval is 5 - 0 = 5.

Dividing the total amount of water used by the interval length:

Average rate = (64e^5 + 16) / 5 ≈ 446.86 gallons per hour.

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