Four years ago, Peter was three times as old as sylvia. In 5 years, the sum of their ages will be 38. What are their ages now

Answer:2 48,39=87

Step-by-step explanation:

Answer:

DV

DE

VE

Step-by-step explanation:

Answer:

2x + 35 = 8x + 5

6x = 30, so x = 5

The answer is:

Work/explanation:

Our equation is

\(\sf{2x+35=8x+5}\)

Subtract 2x from each side

\(\sf{35=6x+5}\)

Flip

\(\sf{6x+5=35}\)

Subtract 5 from each side

\(\sf{6x=30}\)

Divide each side by 6

\(\sf{x=5}\)

Answer:

x=6

Step-by-step explanation:

Did it ask you to solve for x?

19x-4=110

19x=110+4

19x=114

x=114÷19

x=6

A data set's attributes are enumerated through descriptive statistics. You can use inferential statistics to test a hypothesis or determine whether your data can be applied to a larger population.

Descriptive statistics concentrate on describing the features of a dataset that are readily evident (a population or sample). In contrast, inferential statistics concentrate on drawing conclusions or generalisations from a sample of data in a larger dataset.

The information from a research sample is described and condensed using descriptive statistics. We can draw conclusions about the larger population from which we drew our sample using inferential statistics.

The area of statistics known as descriptive statistics is focused on providing a description of the population being studied. A type of statistics known as inferential statistics concentrates on inferring information about the population from sample analysis and observation.

Hence we get the required answer.

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such pair of equation that have only one pair of solutions which satisfy both equation is linear equation

Answer:

Change in temperature was 12 degrees

Step-by-step explanation:

If you start with five degrees and end into negative 7 degrees, you can find the result within two steps

5 degrees minus 5 = 0 degrees

then, 0 degrees minus 7 = -7 degrees

Because you subtracted 5 from five, and 7 from seven, you add those two values together

7 + 5 = 12 degrees

So the change in temperature was 12 degrees

Hope this helps!

Answer:

You can

Step-by-step explanation:

To see if multiple ratios are proportional, you could write them as fractions, reduce them, and compare them.

Answer:

To tell if a table values are proportional, the x and the y value should have a common factor. When the numbers are all divided by their common factor, the points should all be equal to each other.

The solution to the equation and to the nearest tenth is:

x = 4.3

x = 0.3

To solve for x in this equation, we will use the quadratic formula as the equation is the quadratic type. In this equation:

\(x = -b±\sqrt{b^{2} - 4ac} /2a\\x = 9±\sqrt{-9^{2} - 4(2*2} /2*2\\x = 9±\sqrt{81 - 16}/4\\\)

So, x = 9 ± √65/4

x = 9 + 8/4

x = 17/4

x = 4.26 and approximately, 4.3 to the nearest tenth.

Also,

x =  9 - 8/4

x = 1/4

x = 0.25

x = 0.3 So, the two values of x to the nearest tenth are 4.3 and 0.3

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Answer:

5/8

Step-by-step explanation:

Find the rational number half way between 1/2 and 3/4

First add 1/2 and 3/4

1/2 + 3/4 = 2/4 + 3/4 = 5/4

Next, divide this sum by 2

5/4 divided by 2/1 = 5/4 * 1/2 = 5/8

5/8 is half from 1/2 and 3/4

1/2 < 5/8 > 3/4

The grade point average received by hector is 3.75.

Your grade point average (GPA) is calculated by dividing the total number of credits you have earned in high school by the sum of all of your course grades. The majority of colleges and secondary schools use a 4.0 scale to report grades. A perfect score, or an A, is a 4.0.

The unit value for each course in which a student obtains one of the grades mentioned above is multiplied by the grade point total for that grade to determine the GPA. Then, divide the sum of these products by the sum of the units. The cumulative GPA is calculated by dividing the total grade points by the total number of units.

3 a and one is B received by Hector.

The A = 4.0, B = 3.0, C = 2.0, D = 1.0 is given by college

We have GPA= A+A+A+B/4

GPA=4+4+4+3/4

GPA= 15/4

GPA=3.75

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Complete question

Hector Ramirez received three A's and one B in his college courses. What is his grade point average? Assume each course is three credits. A = 4.0, B = 3.0, C = 2.0, D = 1.0

Answer: $96,220

Step-by-step explanation:

From the questionwe are we informed that Daniel is a very good television salesperson and that his annual sales average at $187,400 and his commission on sales is 30% while his annual base salary is $40,000.

His annual gross income will be his annual base salary plus commission annually. This will be:

= $40,000 + (30% × $187,400)

= $40,000 + (0.3 × $187,400)

= $40,000 + $56,220

= $96,220

The interval (-U(ₙ), a=U(ₙ)) is a (1 - a) level confidence interval for 0, where U(ₙ) represents the maximum value among U₁, U₂, ..., Uₙ, and a = U(ₙ) represents the upper bound of the interval.

What is the confidence interval?

A confidence interval is a range of values that is likely to contain the true value of an unknown population parameter, such as the population mean or population proportion. It is based on a sample from the population and the level of confidence chosen by the researcher.

To show that the interval (-U(ₙ), a=U(ₙ)) is a (1 - a) level confidence interval for 0, we need to demonstrate that it has the property that the probability that 0 is contained within the interval is equal to (1 - a).

Let's proceed with the proof:

Since U(1) is the minimum value among U₁, U₂, ..., Uₙ, we have:

P(U(1) > a) = P(min{U₁, U₂, ..., Uₙ} > a)

This is equivalent to all of the observations U₁, U₂, ..., Uₙ being greater than a:

P(U(1) > a) = P(U₁ > a, U₂ > a, ..., Uₙ > a)

Since the observations U₁, U₂, ..., Uₙ are independent and identically distributed from Uniform(0, θ), where θ > 0 is unknown, we have:

P(U(₁) > a) = P(U₁ > a) * P(U₂ > a) * ... * P(Uₙ > a)

Since each Ui is from Uniform(0, θ), the probability that Ui > a is given by:

P(Ui > a) = 1 - P(Ui ≤ a) = 1 - a/θ

Therefore, we can write:

P(U(₁) > a) = (1 - a/θ)ⁿ

Now, let's consider U(n), which is the maximum value among U₁, U₂, ..., Uₙ:

P(U(ₙ) ≤ a) = P(max{U₁, U₂, ..., Uₙ} ≤ a)

This is equivalent to all of the observations U₁, U₂, ..., Uₙ being less than or equal to a:

P(U(ₙ) ≤ a) = P(U₁ ≤ a, U₂ ≤ a, ..., Uₙ ≤ a)

Using the same reasoning as before, the probability that Ui ≤ a is given by:

P(Ui ≤ a) = a/θ

Therefore, we can write:

P(U(ₙ) ≤ a) = (a/θ)ⁿ

Now, let's compute the probability that 0 is contained within the interval (-U(ₙ), a=U(ₙ)):

P(-U(ₙ) ≤ 0 ≤ a=U(ₙ)) = P(Uₙ) ≥ 0 ≥ -U(ₙ)) = P(U(ₙ) ≥ 0) = 1 - P(U(ₙ) < 0)

Since U(ₙ) follows a Uniform(0, θ) distribution, the probability that U(ₙ) < 0 is 0.

Therefore, we have:

P(-U(ₙ) ≤ 0 ≤ a=U(ₙ)) = 1 - P(U(ₙ) < 0) = 1 - 0 = 1

Hence, the probability that 0 is contained within the interval (-U(ₙ), a=U(ₙ)) is 1.

To complete the proof, we need to show that the probability that 0 is contained outside this interval is equal to a:

P(0 ≤ -U(ₙ) or a=U(ₙ)) = P(U(ₙ) ≤ 0 or a ≤ U(ₙ)) = P(U(ₙ) ≤ 0) + P(a ≤ U(ₙ))

Since U(ₙ) follows a Uniform(0, θ) distribution:

P(U(ₙ) ≤ 0) = 0 (since U(n) is always positive)

P(a ≤ U(ₙ)) = (a/θ)ⁿ

Therefore, we have:

P(0 ≤ -U(ₙ) or a=U(ₙ)) = P(U(ₙ) ≤ 0) + P(a ≤ U(ₙ)) = 0 + (a/θ)ⁿ

Since we want to show that this probability is equal to a, we need to equate it to a:

(a/θ)ⁿ = a

Taking the n-th root of both sides, we have:

(a/θ) = √[a]

Simplifying further, we get:

θ = a/√[a]

Therefore, the value of θ that satisfies this equation is θ = a/√[a].

Now, let's compute the confidence level associated with the interval (-U(ₙ), a=U(ₙ)).

The confidence level is defined as 1 minus the probability that the interval does not contain the true value of 0:

Confidence level = 1 - P(0 ≤ -U(ₙ) or a=U(ₙ))

= 1 - (a/θ)ⁿ

= 1 - (a/(a/√[a]))ⁿ

= 1 - (√[a])ⁿ

= 1 - aⁿ

We know that the confidence level should be equal to (1 - a) since it is a (1 - a) level confidence interval. Equating the two, we have:

1 - aⁿ = 1 - a

Simplifying, we get:

aⁿ = a

Since a is in the range (0, 1), we can conclude that this equation holds for any a in that range.

Therefore, the interval (-U(ₙ), a=U(ₙ)) is a (1 - a) level confidence interval for 0, where U(ₙ) represents the maximum value among U₁, U₂, ..., Uₙ and a = U(ₙ) represents the upper bound of the interval.

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Answer: false

Step-by-step explanation:

1. FALSE. If X and Y are independent, then P(X=x, Y=y) = P(X=x)*P(Y=y). So, the value is not 0 in general. In fact, it holds value if at least one of P(X=x) and P(Y=y) posses value 0. 2. TRUE. An event and its complement event constitutes the total s

True, for any two random variables x and y, -1 < p < 1.

The value p represents the correlation coefficient between two random variables x and y. The correlation coefficient measures the strength and direction of the linear relationship between the variables. The range of p is between -1 and 1. If p is closer to -1, it implies that there is a strong negative correlation between x and y, meaning that as x increases, y decreases. If p is closer to 1, it implies that there is a strong positive correlation between x and y, meaning that as x increases, y also increases. If p is 0, it implies that there is no correlation between x and y.

Therefore, for any two random variables x and y, -1 < p < 1, as the correlation coefficient p must fall within this range.

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Let's assume that the length of the rectangle is x cm.

According to the problem, the width is 1/2 of the length. Therefore, the width is 1/2 x cm, or (1/2)*x cm.

The area of the rectangle is given as 388 square centimeters.

We know that the formula for the area of a rectangle is:

Area = Length x Width

So, we can plug in the values we have:

388 = x * (1/2)*x

Simplifying this equation:

776 = x^2

Taking the square root of both sides:

x = √776 ≈ 27.87 cm

Therefore, the length of the rectangle is approximately 27.87 cm, and the width is (1/2)*x, or approximately 13.94 cm.

So the dimensions of the rectangle are approximately 27.87 cm by 13.94 cm.

The 14.9% increase in Sylvia's lead lathe tech's hourly wage of $18.50 results in a $2.75 per hour increase. Assuming the lead lathe tech works 2,080 hours per year, the additional cost to Sylvia's annual wages budget would be approximately $5,720, excluding benefits or taxes.

First, we need to find the percentage increase in the lead lathe tech's hourly wage. The increase requested is $2.75, which is 14.9% of the current wage rate ($18.50). To calculate the percentage increase, we divide the increase by the current wage rate and multiply by 100: ($2.75 / $18.50) * 100 ≈ 14.9%.

To determine the additional cost to Sylvia's annual wages budget, we need to know the total number of hours worked by the lead lathe tech in a year. Let's assume the lead lathe tech works 40 hours per week and there are 52 weeks in a year, resulting in a total of 2,080 hours.

To calculate the annual cost of the wage increase, we multiply the hourly increase ($2.75) by the total number of hours worked (2,080): $2.75 * 2,080 ≈ $5,720.

Therefore, the 14.9% increase in the lead lathe tech's hourly wage will cost Sylvia an additional $5,720 in her annual wages budget, excluding benefits or taxes.

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Answer:

1) A = 48 sq units  2) 42 sq units

Step-by-step explanation:

The formula to find the area of a trapezoid of a trapezoid is A = 1/2(b1+b2)h.

So for number 1, it is stated that the height of each unit is 2. Now let's substitute the variables in the formula with the actual bases and heights. I got A = 1/2(8+4)8, A=6*8, A=48 sq units.

For number 2, each unit also has a height of 2. Let's substitute the variables in the formula again. And we get A = 1/2(10+4)6, A = 7*6, A = 42 sq units.

This is how you find the areas of the trapezoids!

To determine the number of suppliers Witt Input Devices should use, we need to consider the probability of a "super-event" and the marginal cost of managing additional suppliers.

With a 3% probability of a total shutdown and an estimated cost of $400,000, along with a 5% "unique-event" risk per supplier, the company should aim to balance the costs and risks to make an informed decision on the number of suppliers.

Phillip Witt wants to create a portfolio of local suppliers for his keyboards. He faces the risk of "super-events" that could shut down all suppliers simultaneously for at least two weeks. The probability of such an event occurring is 3% per year, which would result in an estimated cost of $400,000 for the company.

Additionally, each individual supplier carries a "unique-event" risk of 5%. To mitigate the risks, Witt Input Devices needs to determine the optimal number of suppliers to use. However, it is stated that up to three nearly identical local suppliers are available.

To make a decision, the company needs to balance the costs and risks. Each additional supplier incurs a marginal cost of $15,000 per year. The company should evaluate the trade-off between the cost of managing additional suppliers and the risk reduction achieved by having multiple suppliers.

Considering these factors, Witt Input Devices should analyze the costs and benefits of each additional supplier and select the number of suppliers that provides an optimal balance between risk mitigation and cost management.

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Answer:

The answer is C x<18 indirectly saying 5<18 the other options has no match for it

Answer:

15 boys

Step-by-step explanation:

Whatever number one side of the ratio is multiplied by, the other side has to be multiplied by that same number. So, we have to find the number that 4 is multiplied by to get 20. We can represent this as an equation, where the unknown number is x:

4x = 20

Divide both sides of the equation by 4 to find the value of x:

x = 5

4 was multiplied by 5 to get 20.

To find the number of boys, multiply 3 by 5:

3 * 5 = 15

If there are 20 girls, there will be 15 boys.

The expected standard deviation of stock A's returns, based on the information presented in the table, is approximately 23.57%.

To calculate the expected standard deviation of stock A's returns, we first need to calculate the variance. The variance is the average of the squared deviations from the expected return, weighted by the probabilities of each outcome.

Given the information provided:

Outcome Probability Stock A Return

Good 16% 65.00%

Medium 51% 17.00%

Let's calculate the expected return first:

Expected Return = (Probability of Good × Stock A Return in Good) + (Probability of Medium × Stock A Return in Medium)

= (0.16 × 65.00%) + (0.51 × 17.00%)

= 10.40% + 8.67%

= 19.07%

Next, we calculate the squared deviations from the expected return for each outcome:

Deviation from Expected Return in Good = Stock A Return in Good - Expected Return

= 65.00% - 19.07%

= 45.93%

Deviation from Expected Return in Medium = Stock A Return in Medium - Expected Return

= 17.00% - 19.07%

= -2.07%

Now, we calculate the variance:

Variance = (Probability of Good × Squared Deviation in Good) + (Probability of Medium × Squared Deviation in Medium)

= (0.16 × (45.93%^2)) + (0.51 × (-2.07%^2))

= (0.16 × 0.2110) + (0.51 × 0.0428)

= 0.0338 + 0.0218

= 0.0556

Finally, we calculate the standard deviation, which is the square root of the variance:

Standard Deviation = √Variance

= √0.0556

= 0.2357 or approximately 23.57%

Therefore, the expected standard deviation of stock A's returns, based on the information presented in the table, is approximately 23.57%.

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Answer:

The monomial is second degree.

Step-by-step explanation:

The degree of a monomial is the sum of all the exponents of its variables.

The given monomial only has one variable, k, raised to the second power.

In conclusion, the degree is two, and the expression is a second degree monomial.

yes I pretty sure this is right......

1 - According to the conjugate zeros theorem if a complex number is the root of a polynomial its conjugate is a root as well.

2 - So the conjugates of i, -7i would be

-i, 7i, so

-i , 7i would ALSO be roots of the polynomial according to the conjugates zeros theorem and those are the two roots we were missing.

Answer:

$43,500

Step-by-step explanation:

10 percent increase of $29,000

10% = 0.10

29,000*0.10 = 2,900

So 2,900 a year

so 2,900*5 = 14,500

Then add

29,000+14,500 = 43,500

Answer:

The sea lion dives 24 feet.

Step-by-step explanation:

A seal (S) dives 15 feet.

A sea lion (SL) dives 6 feet less than 2 times the seal's dive.  That can be expressed as:

SL = 2S -6

Since we know S = 15, we can say:

SL = 2*(15) - 6

SL = 24 feet

The sea lion dives 24 feet.

Answer: -3 AND 7

Step-by-step explanation: very important to include the and, as it that point could be to the right or left of (3,1)

It is true that the existence of two local maxima does not guarantee the presence of a local minimum. It is possible for a function to have multiple local maxima and no local minimum.

For example, consider the function f(x,y) = x^4 - 4x^2 + y^2. This function has two local maxima at (2,0) and (-2,0), but no local minimum. Therefore, the statement "if f(x,y) has two local maximal, then f must have a local minimum" is false. The presence or absence of local maxima and minima depends on the behavior of the function in the immediate vicinity of a point, and cannot be determined solely based on the number of local maxima. It is possible for a function to have an infinite number of local maxima and minima, or none at all. Therefore, it is important to carefully analyze the behavior of a function in order to determine the presence or absence of local extrema.

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(a)The amount of water in the tank is increasing.

(b)Evaluate  \(\int\limits^{18}_0(W(t) - R(t)) dt\) to get the number of gallons of water in the tank at t = 18.

(c)Solve part (b) to get the absolute minimum from the critical points.

(d)The equation can be set up as   \(\int\limits^k_{18}-R(t) dt = 1200\) and solve this equation to find the value of k.

What is the absolute value of a number?

The absolute value of a number is its distance from zero on the number line. It represents the magnitude or size of a real number without considering its sign.

To solve the given problems, we need to integrate the given rates of water flow to determine the amount of water in the tank at various times. Let's go through each part step by step:

a)To determine if the amount of water in the tank is increasing at time t = 15, we need to compare the rate of water being pumped in with the rate of water being removed.

At t = 15, the rate of water being pumped in is given by \(W(t) = 95Vt sin^2(\frac{t}{6})\) gallons per hour. The rate of water being removed is \(R(t) = 275 sin^2(\frac{1}{3})\) gallons per hour.

Evaluate both rates at t = 15 and compare them. If the rate of water being pumped in is greater than the rate of water being removed, then the amount of water in the tank is increasing. Otherwise, it is decreasing.

b) To find the number of gallons of water in the tank at time t = 18, we need to integrate the net rate of water flow from t = 0 to t = 18. The net rate of water flow is given by the difference between the rate of water being pumped in and the rate of water being removed. So the integral to find the total amount of water in the tank at t = 18 is:

\(\int\limits^{18}_0(W(t) - R(t)) dt\)

Evaluate this integral to get the number of gallons of water in the tank at t = 18.

c)To find the time t when the amount of water in the tank is at an absolute minimum, we need to find the minimum of the function that represents the total amount of water in the tank. The total amount of water in the tank is obtained by integrating the net rate of water flow over the interval [0, 18] as mentioned in part b. Find the critical points and determine the absolute minimum from those points.

d. For t > 18, no water is pumped into the tank, but water continues to be removed at the rate R(t) until the tank becomes empty. To find the value of k, we need to set up an equation involving an integral expression that represents the remaining water in the tank after time t = 18. This equation will represent the condition for the tank to become empty.

The equation can be set up as:

\(\int\limits^k_{18}-R(t) dt = 1200\)

Here, k represents the time at which the tank becomes empty, and the integral represents the cumulative removal of water from t = 18 to t = k. Solve this equation to find the value of k.

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