Theee siblings - Dave, Kave, and Sarah-commithed themselves to volunteer 190 hours for a hometoss charify to build new housing. Sarah wotked 25 hours more than Dave. Kaie worked 15 hours fewer than Dave. How mary hours did each of these siblings volunteer? Number of hour Dave worked = hourn. Number of hours Kate woked = hours. Number at hours 5 arah woned = hours

Answer:56.66 mi/h

Step-by-step explanation:

210 + 130 / 3.5 + 2.5 = 340 / 6

Divide by 6 and you get 56.66

Rounding to the nearest tenth 56.7 mi/h

Answer:

78kg

Step-by-step explanation:

76×5= 380kg

380-72-74-75-81= 78kg

Answer:

Hypotenuse^2 = Opposite^2 + Adjacent^2

Step-by-step explanation:

Here,

      Hypotenuse = 4

      Opposite = 3

find Adjacent side(x).

So,

Hypotenuse^2 = Opposite^2 + Adjacent^2

=> 4^2 = 3^2 + x^2

=> 16-9 = x^2

=> x^2 = 7

∴ x = √7

Hope this helps!!

The estimated probability of passing the true/false test with random guesses is approximately 0.0384 or 3.84%.

To estimate the probability of passing a true/false test of 20 questions with a minimum passing grade of 70% when all responses are random guesses, we can use the normal approximation to the binomial distribution.

In this case, each question has two possible outcomes (true or false), and the probability of guessing the correct answer is 0.5 since the responses are random. With 20 questions, we can consider this as a binomial distribution with n = 20 and p = 0.5.

To apply the normal approximation, we need to calculate the mean (μ) and the standard deviation (σ) of the binomial distribution:

μ = n * p = 20 * 0.5 = 10

σ = √(n * p * (1 - p)) = √(20 * 0.5 * 0.5) = √5 ≈ 2.236

Now, we want to find the probability of passing, which means answering at least 70% of the questions correctly. Since the test has 20 questions, we need to find the probability of getting 14 or more correct answers.

We can now use the normal distribution with the calculated mean and standard deviation to estimate this probability. Since the distribution is continuous, we need to use continuity correction by subtracting 0.5 from the lower bound:

P(X ≥ 14) ≈ P(Z ≥ (14 - 0.5 - 10) / 2.236)

         ≈ P(Z ≥ 1.77)

Using a standard normal distribution table or a calculator, we can find the probability associated with Z ≥ 1.77. From the table, this probability is approximately 0.0384.

Therefore, the estimated probability of passing the true/false test with random guesses is approximately 0.0384 or 3.84%.

Learn more about probability here

https://brainly.com/question/25839839

#SPJ11

The solution to the given differential equation 2xy(dy/dx) = y², with the initial condition y(2) = 3, is y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\).

To solve the given differential equation

2xy(dy/dx) = y²

We will use separation of variables and integrate to find the solution.

Start with the given equation

2xy(dy/dx) = y²

Divide both sides by y²:

(2x/y) dy = dx

Integrate both sides:

∫(2x/y) dy = ∫dx

Integrating the left side requires a substitution. Let u = y², then du = 2y dy:

∫(2x/u) du = ∫dx

2∫(x/u) du = ∫dx

2 ln|u| = x + C

Replacing u with y²:

2 ln|y²| = x + C

Using the properties of logarithms:

ln|y⁴| = x + C

Exponentiating both sides:

|y⁴| = \(e^{x + C}\)

Since the absolute value is taken, we can remove it and incorporate the constant of integration

y⁴ = \(e^{x + C}\)

Simplifying, let A = \(e^C:\)

y^4 = A * eˣ

Taking the fourth root of both sides:

y = (A * eˣ\()^{1/4}\)

Now we can incorporate the initial condition y(2) = 3

3 = (A * e²\()^{1/4}\)

Cubing both sides:

27 = A * e²

Solving for A:

A = 27 / e²

Finally, substituting A back into the solution

y = ((27 / e²) * eˣ\()^{1/4}\)

Simplifying further

y = (27 *  e⁽ˣ⁻²⁾\()^{1/4}\)

Therefore, the solution to the given differential equation with the initial condition y(2) = 3 is

y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\)

To know more about differential equation:

https://brainly.com/question/2273154

#SPJ4

The required white effective interest rate is 0.71% more than his nominal interest rate.

Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.

Here,

White Effective interest R,
\(R=(1+i/m)^m)-1\\R=(1+0.1362/4)^4)-1\\R =0.1433*100=\)
R = 14.33 percent

So

Difference in interest = 14.33%-13.62%
                                    =0.71%

Thus, the required white effective interest rate is 0.71% more than his nominal interest rate.

Learn more about compound interest here:

https://brainly.com/question/14295570

#SPJ1

Answer:

Sure! The perimeter of a rectangle is calculated by adding the lengths of all four sides. Since the length of the rectangle is given as (5x²y) and the width is given as (3x²y), we can calculate the perimeter as follows:

Perimeter = 2 * Length + 2 * Width = 2 * (5x²y) + 2 * (3x²y) = 10x²y + 6x²y = 16x²y

So, the perimeter of this rectangle is 16x²y.

Step-by-step explanation:

Answer:

Hi! A piecewise function is a function defined by multiple sub-functions, or pieces of different functions over different intervals. Piecewise definition is a way of expressing the function and is not actually integral to the function itself.

f(x) = |x - 2| is an absolute value function. As a piecewise function, it's written like this:

f(x) = {x - 2, x ≥ 2

        {-x + 2, x < 2

Hope this helps! Have a great day.

Answer: The operation preformed is multiplication.

Step-by-step explanation: When you have a integer that is raised to a power, you must evaluate that integer first. For example, if you are asked to solve 2^3 + 4^7, you must first multiply. 2^3= 8 and 4^7= 16,384 then we must add these two products together to get 16,392.

How to find the product of to the power number: 8^3. We take eight and times it by it's self 3 times to get 512.

Hope this helps!

Answer:

29.8

Step-by-step explanation:

a^2+b^2=c^2

a^2+7^2=11^2

a = h = 8.5

A= 1/2*b*h

A= 1/2*8.5*7

A=29.8

Answer:

A) The area of parallelogram 1 is 4 square units greater than the area of parallelogram 2.

The area of parallelogram 1 is 2 square units greater than the area of parallelogram. Option 2 is correct.

The space filled by a flat form or the surface of an item is known as the area.

The number of unit squares that cover the surface of a closed-form is the figure's area. Square centimeters and other similar units are used to measure area.

A₁ is the area of parallelogram 1

A₁ is the area of parallelogram 2

l₁ is the distance between the points (2,6),(0,2)

l₂ is the distance between the points (4,0)(0,2)

b₁ is the distance between the points (2,0),(0,-2)

b₂ is the distance between the points (2,6),(4,-6)

A₁ =  l₁ × b₁

A₁=4.47 ×4.47

A₁  = 19.89 sq.unit

A₂=l₂×b₂

A₂=2.82 × 6.342

A₂=17.88 sq.unit

A₁-A₂ = 19.89 sq.unit - 17.88  sq.unit'

A₁-A₂= 2.01

The area of parallelogram 1 is 2 square units greater than the area of a parallelogram.

Hence,option 2 is correct.

To learn more about the area, refer to the link;

https://brainly.com/question/11952845

#SPJ2

Answer:

I believe its a: steve needs to increase the total cost from $300.00 to $500.00.

Step-by-step explanation:

Answer:

A. because it doesn't change as it is going up, up, up, and so on.

Answer:

What is the long Division rhyme to help you solve?

What is the long Division rhyme to help you solve?

Step-by-step explanation:

Answer:

-40X-3=120

Step-by-step explanation:

20 characters

If a business had sales of $4,000,000, and a margin of safety of 25%, the break-even point was is c. $1,000,000.

The margin of safety is the difference between the actual or expected sales and the break-even point. In this case, if the margin of safety is 25%, it means that the business is generating sales that are 25% higher than the break-even point.

To calculate the break-even point, we can use the following formula:

Break-even point = Fixed costs / Contribution margin ratio

The contribution margin ratio is the difference between the sales price and variable costs, divided by the sales price. We don't have enough information to calculate it directly, but we can use the margin of safety to estimate it.

If the margin of safety is 25%, it means that the contribution margin ratio is 25% of the sales price. So, the variable costs must be 75% of the sales price, and the contribution margin ratio is 25%/100% = 0.25.

We know that the sales are $4,000,000, but we don't know the fixed costs. However, we can use the break-even formula to solve for it:

$1,000,000 = Fixed costs / 0.25

Fixed costs = $250,000

Therefore, the break-even point is $250,000 / 0.25 = $1,000,000.

Based on the given information, the break-even point for the business with sales of $4,000,000 and a margin of safety of 25% is $1,000,000.

To know more about sales visit:

https://brainly.com/question/29436143

#SPJ11

Answer:

the answer is 2x²-6x-36

Answer:

1) solve x+1/x = 5

\( \frac{x + 1}{x} = 5\)

\(x + 1 = 5x\)

\(x - 5x = - 1\)

\( - 4x = - 1\)

\(x = \frac{ -1}{ - 4} \)

\(x = \frac{1}{4} \)

2) solve x³+1/x³

\(x {}^{3} + \frac{1}{x {}^{3} } \)

substitute x = 1/4 into the expression

\(( \frac{1}{4} ) {}^{3} + \frac{1}{( \frac{1}{4}) {}^{3} } \)

\( \frac{1}{64} + \frac{1}{ \frac{1}{64} } \)

\( \frac{1}{64} + \frac{64 \times 1}{1} \)

\( \frac{1}{64} + 64\)

\( \frac{4097}{64} \: or \: 64.02\)

The value of expression |2x+5| - 8y is -89 when x = -6 and y =12

Expression is a combination of numbers, variables and Operators.

The given expression is mod two x plus 5 minus eight y.

|2x+5| - 8y

This expression has addition, subtraction and multiplication operators.

Given value of x is minus six and y is equal to twelve.

x=-6 and y=12

plug in values of x and y in expression

|2(-6)+5|-8(12)

|-12+5|-96

|-7|-96

The value in mod will be always taken as positive

7-96

-89

Hence the value of expression |2x+5| - 8y is -89 when x = -6 and y =12.

To learn more on Expressions click:

https://brainly.com/question/14083225

#SPJ1

Yes, the new method for detecting avobenzone in sunscreen is valid/accurate at a 95% confidence level.

The standard reference material provided by the FDA contains 0.250 mg of avobenzone per gram of sunscreen. The working group analyzed the standard and obtained measurements of avobenzone content in six samples, which were found to be 0.256, 0.279, 0.328, 0.305, 0.312, and 0.230 µg/g.

To determine the validity and accuracy of the new detection method, we need to assess if the measurements obtained from the samples are within an acceptable range of the known avobenzone content provided by the standard.

At a 95% confidence level, we can calculate a confidence interval to evaluate the accuracy of the new method. The confidence interval is a range within which we can reasonably expect the true avobenzone content of the sunscreen samples to fall. If the known avobenzone content provided by the standard falls within this confidence interval, it indicates that the new method is valid and accurate.

By performing the necessary calculations, we can determine the confidence interval. Comparing the range of the measurements obtained from the samples (0.230 to 0.328 µg/g) with the known avobenzone content provided by the standard (0.250 mg/g), we find that the measurements overlap with the known value. Therefore, we can conclude that the new method is valid/accurate for the detection of avobenzone in sunscreen at a 95% confidence level.

Learn more about Confidence intervals

brainly.com/question/32546207

#SPJ11

Answer:

Side a is that side opposite to the hyp and b is the short side and c is the hyp

So a/b is 24/x

we need b

We find b=10

so 24/10 and we simply to 12/5

The null hypothesis for this scenario would be that the percentage of residents in favor of the construction of a new community is less than or equal to 46%.

And the alternative hypothesis would be that the percentage of residents in favor of the construction is greater than 46%. The mayor would need to conduct a hypothesis test to determine if there is sufficient evidence at the 0.01 level to support the claim.

This test would involve collecting data from a sample of the town's residents and determining if the sample proportion greater than or equal to the 46% claimed by the mayor. If the sample proportion is significantly greater than 46%, then the mayor's claim can be supported at the 0.01 level.

For more questions like Residents click the link below:

https://brainly.com/question/14467291

#SPJ4

To create a stemplot, we first need to separate the data into "stems" and "leaves." Each stem represents the first digit(s) of each data point, while each leaf represents the last digit(s). For example, if the data point is 12.3, the stem would be 12 and the leaf would be 3.

To make a stemplot, the data should be arranged in increasing order, and then separated into stems and leaves.

However, you can use the data given and arrange it in increasing order and separate it into stems and leaves to make a stemplot. A stemplot is a good way to check if the data follow a normal distribution quite closely, the more the data is spread out and the more symmetric it is, the more likely it is to follow a normal distribution.

Also, it is important to mention that from the given data, it is not possible to conclude if the percent change in this population has standard deviation of 2.5%. This parameter can only be estimated from a sample if it follows a normal distribution which is not clear from the given data.

Learn more about Stemplot here:

https://brainly.com/question/29174445

#SPJ4

Answer:

Domain:  (-∞, 1) ∪ (1, ∞)

Range:  (-∞, -2) ∪ (2, ∞)

Yes, it's a function.

Step-by-step explanation:

Information

The domain of a function is the set of all possible input values (x-values).

From inspection of the given graph:

Therefore, the domain is all values of x except x = 1:

The range of a function is the set of all possible output values (y-values).

From inspection of the given graph:

Therefore, the range is all values of y except between -2 and 2:

A function is a special type of relationship where each input (x-value) is related to exactly one output (y-value).

From inspection of the graph, as the two points where x = 1 are not included, each value in the range (y-values) corresponds to exactly one value in the domain, and so it is a one-to-one function.

cos^-1(3/4) = arccos(3/4) ≈ 0.7227
tan^-1(1/3) = arctan(1/3) ≈ 0.3218
sin(0.4009)  ≈ 0.3898   (using a calculator)
Therefore, the exact value of the expression sin(cos^-1(3/4) − tan^-1(1/3)) is approximately 0.3898.

To find the exact value of the expression sin(cos^-1(3/4) - tan^-1(1/3)), we will use the angle subtraction formula for sine:
sin(A - B) = sin(A)cos(B) - cos(A)sin(B)

Here, A = cos^-1(3/4) and B = tan^-1(1/3).
First, find the sine and cosine of A:
cos(A) = 3/4
Since sin^2(A) + cos^2(A) = 1, we get:
sin^2(A) = 1 - (3/4)^2 = 7/16
sin(A) = √(7/16)

Next, find the sine and cosine of B:
tan(B) = 1/3
Since tan^2(B) + 1 = sec^2(B) (or 1/cos^2(B)), we get:
cos^2(B) = 1 / (1 + (1/3)^2) = 9/10
cos(B) = √(9/10)
And since sin(B) = tan(B) * cos(B),
sin(B) = (1/3) × √(9/10) = √(3/10)

Now, use the angle subtraction formula:
sin(A - B) = sin(A)cos(B) - cos(A)sin(B)
= (√(7/16)) × (√(9/10)) - (3/4) × (√(3/10))
= (3√(7/40)) - (√(9/40))

= sin(cos^-1(3/4) − tan^-1(1/3))
= sin(0.7227 - 0.3218)   (substituting values)
= sin(0.4009)   (simplifying)
≈ 0.3898   (using calculator)

The exact value of the expression sin(cos^-1(3/4) - tan^-1(1/3)) is (3√(7/40)) - (√(9/40)) is ≈ 0.3898 .

Learn more about Expression:

brainly.com/question/14083225

#SPJ11

Answer:

(3x^2 - 1)(3x^2 + 1)(9x^4 + 1).

Step-by-step explanation:

Using the identity for the difference of 2 squares;

a^2 - b^2 = (a - b)(a + b)  

we put a^2 = 81x^8 and b^2 = 1  giving

a = 9x^4 and b = 1, so:

81x^8 − 1 =   (9x^4 - 1)(9x^4 + 1)

Applying the difference of 2 squares to 9x^4 - 1:

= (3x^2 - 1)(3x^2 + 1)(9x^4 + 1).

Answer:

The answer is (3x^2 - 1)(3x^2 + 1)(9x^4 + 1).

Step-by-step explanation:

Step-by-step explanation:

Break it up into two trapezoids as shown

area = trap1 + trap2

      = 2 *   (7+3) / 2   + 3 *  ( 7 + 3) / 2 = 10 + 15 = 25 units^2

Answer:

m=4+8p/n

Step-by-step explanation:

Start with mn-8p=4

add 8p to both sides to get:

mn=4+8p

divide both sides by n to get:

m=4+8p/n

Answer:

26.3 grams

Step-by-step explanation:

36% = 36/100 = 0.36

73 * 0.36 = 26.28 grams ≈ 26.3 grams

Answer:

i think 26.3 grams

Step-by-step explanation:

0.36×73 = 26.28

When rounded to the nearest tenth, 26.28 should be equal to 26.3

So Dante's the chocolate bar contains 26.3 grams of cocoa.