Andre and Noah started tracking their savings at the same time. Andre started with $15 and deposits $5 per week. Noah started with $2.50 and deposits $7.50 per week. (ill give brainiest and extra 50 points)

Therefore, the maximum blood pressure of 200 mmHg occurs at approximately 0.524 seconds, and the minimum blood pressure of 120 mmHg occurs at approximately 1.571 seconds within the time interval 0 ≤ t ≤ 0.75.

To find the maximum and minimum values of the blood pressure function p(t), we need to examine the behavior of the sinusoidal term, -40sin(3t), within the given time interval. The function is a sine wave with an amplitude of 40 and a period of 2π/3. This means that the maximum value occurs at the peak of the sine wave (amplitude + offset), and the minimum value occurs at the trough (amplitude - offset).

The maximum blood pressure corresponds to the peak of the sine wave, which is 40 + 160 = 200 mmHg. To find the time at which this occurs, we set the argument of the sine function, 3t, equal to π/2 (since the peak of the sine wave is π/2 radians). Solving for t gives t = (π/2) / 3 = π/6 ≈ 0.524 seconds.

Similarly, the minimum blood pressure corresponds to the trough of the sine wave, which is -40 + 160 = 120 mmHg. Setting the argument of the sine function equal to 3π/2 (the trough of the sine wave), we find t = (3π/2) / 3 = π/2 ≈ 1.571 seconds.

Therefore, the maximum blood pressure of 200 mmHg occurs at approximately 0.524 seconds, and the minimum blood pressure of 120 mmHg occurs at approximately 1.571 seconds within the time interval 0 ≤ t ≤ 0.75.

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It is true that +10 and -10, are 10 units from 0 on the number line

from the question, we have the following parameters that can be used in our computation:

Numbers = +10 and -10

The number of units of these numbers from 0 is calculated as

Units = |0 - Number|

So, we have

Units = |0 - 10| = 10

Units = |0 + 10| = 10

This means that the number of units is 10

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Explanation

In the question, we are given that the difference of three times a number and six is nine. Using the variable x, we can write the equation as:

Answer 1:

We can then solve the equation below;

Answer 2: x=5

Answer:

a. $5,037.50

Step-by-step explanation:

Area = length × width

25 × 13 = 325 sq. ft

It costs $15.50 to carpet an area of 1 sq. foot.

For 325 sq. ft of area, it will cost

15.50 × 325 = 5037.5

It will cost $5,037.50 to carpet the rectangular room.

Option A is the correct answer.

A rectangle is a 2-D shape with length and width.

The length and width are different.

If the length and width are not different then it is a square.

The area of a rectangle is given as:

Area = Length x width

We have,

The area of the rectangular room is:

= 25 ft x 13 ft

= 325 sq ft

Multiplying by the cost per square foot:

= 325 sq ft x $15.50/sq ft

= $5,037.50

Therefore,

It will cost $5,037.50.

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Answer: 2.36

Step-by-step explanation:

Using the μ=∑[x⋅P(X=x)

U will need to do

2/11 because you have 2 labeled 1

3/11 because you have 3 labeled 2

6/11 because you have 6 labeled 3

Then you will do:

1 x 2/11 = 0.18

2 x 3/11 = 0.5454 = 0.55

3 x 6/11 = 1.63

Then add them all together to find the μ

0.18 + 0.55 + 1.63 = 2.36

Hope that helps, plz put a good rating

Answer:

C. 8485.3 meters

Step-by-step explanation:

Think of the sailboat’s path as a 45-45-90 right triangle.

The hypotenuse is the 6000 meter distance.

In this way the leg will be the hypotenuse divided by √2.

So 6000/√2 or 4242.64 meters.

Remember that the sailboat has to turn and head back toward its goal and travel another 4242.64 meters.

Thus, your answer is 4242.64 x 2 = 8485.28 meters or 8485.3 meters.

In this exercise we have to use the knowledge of triangles to calculate the distance that one of the sides has:

Letter C

Some information given in the statement about the triangle:

So performing the calculation we have:

\(6000\sqrt{2}=4242.64 \\4242.64 * 2 = 8485.28\)

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After considering the given data we conclude that Taylor series is \(f(z) = 1/z^2(1-cos(z)) = 1/z^2 - 1/2! + (z^2/4!) - (z^4/6!) + ...\)
To present  that the function f(z) = 1/z^2(1-cos(z)) is entire, we need to express it as a Taylor series.
The Taylor series of f(z) can be evaluated by first elaborating (1-cos(z)) as a power series and then applying division using  z². The power series of (1-cos(z)) is:
\(1 - cos(z) = 1 - (z^2/2!) + (z^4/4!) - (z^6/6!) + ...\)
Applying divison using z², we get:
\((1 - cos(z))/z^2 = 1/z^2 - (1/2!)(z^2/ z^2) + (1/4!)(z^4/ z^2) - (1/6!)(z^6/ z^2) + ...\)
Applying simplification , we get:
\((1 - cos(z))/z^2 = 1/z^2 - 1/2! + (z^2/4!) - (z^4/6!) + ...\)
Therefore, the Taylor series of f(z) is:
\(f(z) = 1/z^2(1-cos(z)) = 1/z^2 - 1/2! + (z^2/4!) - (z^4/6!) + ...\)
Since the Taylor series of f(z) converges for all z, except possibly at z = 0, and the function is defined to be 1/2 at z = 0, we can conclude that f(z) is entire.
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The complete question is
By expressing it as a Taylor series, show that the following function is entire: f(z)= 1 z² (1-cos z) if z≠ 0& 1/2  if z = 0

The solution to the inequality is y ≤ -8. This means that any value of y that is less than or equal to -8 will satisfy the original inequality.

To solve the inequality y + 7 ≤ -1, we need to isolate the variable y on one side of the inequality sign.

Starting with the given inequality:

y + 7 ≤ -1

We can begin by subtracting 7 from both sides of the inequality:

y + 7 - 7 ≤ -1 - 7

y ≤ -8

The solution to the inequality is y ≤ -8. This means that any value of y that is less than or equal to -8 will satisfy the original inequality.

In the context of a number line, all values to the left of -8, including -8 itself, will make the inequality true. For example, -10, -9, -8, -8.5, and any other value less than -8 will satisfy the inequality. However, any value greater than -8 will not satisfy the inequality.

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The following question may be like this:

What is a solution of the inequality shown below? y+7≤-1

The annual percentage rate, APR, for the loan is about 5.486%

The annual percentage rate is the cost of a loan or interest on an investment per year during the loan term or period.

Price of the car = $35,000.00

The down payment = 20% of $35,000 = $7,000

The installment loan details include;

The number of installment = 48 monthly installment

The amount paid each month = $651

The total payment, A= 48 × 651 = 31248

The equal monthly installment (EMI) formula is presented as follows;

\(EMI = P\cdot \frac{r\cdot (1+r)^n}{(1+r)^n -1}\)

Where;

EMI = The equal monthly installment paid = $651

P = The principal amount of the loan

r = The interest rate

n = Number of payments to be made = 48

The principal is therefore;

P = $35,000.00 - $7,000.00 = $28,000.00

Therefore;

The

\(651 = 28000\times \frac{r\cdot (1+r)^{48}}{(1+r)^{48} -1}\)

Using an online calculator and by trial and error, or by graphing we get;

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Answer:

y - 5 = (3/2)(x - 8)  POINT SLOPE FORM or y = (3/2)x -7   SLOPE INTERCEPT FORM

Step-by-step explanation:

y - y1 = m( x - x1 )   POINT-SLOPE FORM

y - 5 = (3/2)(x - 8)  POINT SLOPE FORM

OR

y - 5 = (3/2)x - (3/2)*8

y - 5 = (3/2)x - 12

y = (3/2)x -7   SLOPE INTERCEPT FORM

Answer:

Step-by-step explanation:

28

Answer:

Below in bold.

Step-by-step explanation:

The angle in a regular octagon =  180 - (360/8) = 135.

Using trigonometry  sin (135/2) = k/2 / EF

sin 67.5 = k / 2EF

2EF = k / sin 67.5

EF = k / 2 sin 67.5 = k/1.8478

Perimeter of octagon = 8 * k/1.8478

= 4.33k to the nearest hundredth.

Answer:

\(y = - \frac{5}{4} x - \frac{1}{2} \)

Step-by-step explanation:

Slope-intercept form: y= mx +c, where m is the slope and c is the y-intercept.

\(\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }\)

Slope

\( = \frac{ - 3 - \frac{1}{8} }{2 - ( - \frac{1}{2}) } \)

\( = - \frac{5}{4} \)

Substitute the value of m into the equation:

\(y = - \frac{5}{4} x + c\)

To find the value of c, substitute a pair of coordinates the line passes through into the equation.

When x= 2, y= -3,

\( - 3 = - \frac{5}{4} (2) + c\)

\( - 3 = - \frac{5}{2} + c\)

\(c = - 3 + \frac{5}{2} \)

\(c = - \frac{1}{2} \)

Thus, the equation of the line is \(y = - \frac{5}{4} x - \frac{1}{2} \).

Answer:

the age of father is 42

Step-by-step explanation:

let the age of father be x then,

By the question,

or, 2÷7 of x = 12

or, (2÷7) × x = 12

or, x = 12 × (7÷ 2)

x = 42

Answer:

i believe it is 20

Step-by-step explanation:

to find the diameter you just deveide the circumference by pi thats it and i got 20.0101433

so i believe its 20

hope this helped :)

The given argument is invalid. It says that if one person has more gray hair in their beard than another person, then they have a higher percentage of gray hair in their beard.

The argument is invalid because it is possible for one person to have a higher percentage of gray hair in their beard but a lower number of gray hairs in total.One possible counterexample by model is:Suppose Plato has 200 hairs in his beard and 50 of them are gray. So, 1/4 of his hairs are gray. Now, let's suppose Aristotle has 400 hairs in his beard, and 300 of them are gray. So, 3/4 of his hairs are gray. Even though Plato has fewer gray hairs than Aristotle, his percentage of gray hairs is more significant (1/4) than Aristotle's (3/4).

Therefore, the given argument is invalid since Aristotle's beard contains more gray hairs in quantity, but Plato has a higher percentage of gray hair in his beard.

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After solving the given expression we get  a = b = 12 and q = r = 24.

A fractiοn is a numerical quantity that represents a part οf a whοle οr a ratiο between twο quantities. It is written as a tοp number (numeratοr) οver a bοttοm number (denοminatοr), separated by a hοrizοntal line.

Tο subtract 2/3 - 1/4, we need tο find a cοmmοn denοminatοr fοr the twο fractiοns. The smallest cοmmοn denοminatοr is 12, sο we'll cοnvert each fractiοn tο an equivalent fractiοn with a denοminatοr οf 12:

2/3 = 8/12 (multiply bοth numeratοr and denοminatοr by 4)

1/4 = 3/12 (multiply bοth numeratοr and denοminatοr by 3)

Nοw we can subtract the twο fractiοns:

8/12 - 3/12 = 5/12

Sο 2/3 - 1/4 = 5/12.

Tο express the result as a fractiοn in the fοrm x/y, we can simply use the answer we fοund: x = 5, y = 12, sο:

2/3 - 1/4 = 5/12 = 5/12

Similarly, tο express the result as a fractiοn in the fοrm a/b, we need tο find anοther equivalent fractiοn with a cοmmοn denοminatοr. We can use 24 as a cοmmοn denοminatοr this time:

2/3 = 16/24 (multiply bοth numeratοr and denοminatοr by 8)

1/4 = 6/24 (multiply bοth numeratοr and denοminatοr by 6)

Nοw we can subtract the twο fractiοns:

16/24 - 6/24 = 10/24

Sο 2/3 - 1/4 = 10/24.

Tο express the result as a fractiοn in the fοrm a/b, we can simplify the fractiοn by dividing bοth numeratοr and denοminatοr by their greatest cοmmοn factοr, which is 2:

10/24 = (10 ÷ 2) / (24 ÷ 2) = 5/12

Sο we get a=b=12 and q=r=24.

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The new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees are approximately (4.993, 2.048).

To find the new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees, we can use the rotation formula:

x' = x * cos(theta) - y * sin(theta)

y' = x * sin(theta) + y * cos(theta)

Where (x, y) are the original coordinates, (x', y') are the new coordinates after rotation, and theta is the angle of rotation in radians.

Converting the angle of rotation from degrees to radians:

theta = 5 degrees * (pi/180) ≈ 0.08727 radians

Plugging in the values into the rotation formula:

x' = 5 * cos(0.08727) - 2 * sin(0.08727)

y' = 5 * sin(0.08727) + 2 * cos(0.08727)

Evaluating the trigonometric functions and simplifying:

x' ≈ 4.993

y' ≈ 2.048

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Answer:

2 + sqrt(3)

Step-by-step explanation:

Roots that contain square roots come in pairs

If there is a root that is a- sqrt(b), there is a root that is a+ sqrt(b)

2 -sqrt(3) means there is a root 2 + sqrt(3)

The correct rule describing the composition of Transformations is: R0,2 ∘ T0,10 ∘ R0,270°

The rule that describes the composition of transformations mapping rectangle PQRS to P''Q''R''S'', we need to analyze the given coordinates and determine the sequence of transformations.

Let's compare the coordinates of the corresponding points:

P (−3, −5) ↔ P'' (−5, 5)

Q (−2, −5) ↔ Q'' (−5, 4)

R (−2, −1) ↔ R'' (−1, 4)

S (−3, −1) ↔ S'' (−1, 5)

From the comparison, we can observe the following transformations:

1. Translation: The x-coordinate of P'' is obtained by subtracting 2 from the x-coordinate of P. The y-coordinate of P'' is obtained by adding 10 to the y-coordinate of P. This suggests a translation of (−2, 10).

2. Reflection: The x-coordinate of Q'' is obtained by reflecting the x-coordinate of Q across the y-axis. The y-coordinate of Q'' remains the same. This indicates a reflection across the y-axis.

3. Rotation: The coordinates of R'' and S'' are obtained by rotating R and S 270 degrees counterclockwise about the origin (0, 0).

Now, let's determine the composition of transformations:

The sequence of transformations that maps rectangle PQRS to P''Q''R''S'' is as follows:

1. Translation by (−2, 10)

2. Reflection across the y-axis

3. Rotation of 270 degrees counterclockwise about the origin

Therefore, the correct rule describing the composition of transformations is:R0,2 ∘ T0,10 ∘ R0,270°

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We are required 1.5 half cups to form the required fraction of a cup.

The upper part of a fraction is numerator and the lower part is denominator.

We are told to make 3/4 of a cup from1/2 of cup so let the number of times we need half of a cup be x

So

1/2 * x=3/4

x=3/2 which means 1.5

So we need 1.5 times the half cup to make 3/4 of a cup.

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In order to calculate the z-scores for the given Confidence Interval (CI) levels, we need to use the Z-table. It is also known as the standard normal distribution table. Here are the z-scores for the given Confidence Interval levels:1. 68% CI: The confidence interval corresponds to 1 standard deviation on each side of the mean.

Thus, the z-score for the 68% \(CI is ±1.00.2. 85% CI\): The confidence interval corresponds to 1.44 standard deviations on each side of the mean.

We can calculate the z-score using the following formula:\(z = invNorm((1 + 0.85)/2)z = invNorm(0.925)z ≈ ±1.44\)Note that invNorm is the inverse normal cumulative distribution function (CDF) which tells us the z-score given a certain area under the curve.3. 99% CI: The confidence interval corresponds to 2.58 standard deviations on each side of the mean. We can calculate the z-score using the following formula:\(z = invNorm((1 + 0.99)/2)z = invNorm(0.995)z ≈ ±2.58\)

Note that in general, to calculate the z-score for a CI level of (100 - α)% where α is the level of significance, we can use the following formula:\(z = invNorm((1 + α/100)/2)\) Hope this helps!

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Answer:

4

Step-by-step explanation:

Answer:

Opposite sides are congruent (AB = DC).

Opposite angels are congruent (D = B).

Consecutive angles are supplementary (A + D = 180°).

If one angle is right, then all angles are right.

The diagonals of a parallelogram bisect each other.

Each diagonal of a parallelogram separates it into two congruent triangles.

Step-by-step explanation:

Total contribution margin is an accounting metric that evaluates how well a company's sales income covers its variable expenses. The company's total contribution margin can be found using the formula: Total Contribution Margin = Total Revenue - Total Variable Costs.

1. Determine the total revenue: This is the amount of money the company makes from selling its products or services. You can find this by multiplying the selling price of each product by the number of units sold.

2. Determine the total variable costs: These are the costs that change depending on the level of production or sales. Examples of variable costs include raw materials, direct labor, and shipping costs. Calculate the variable cost for each product by multiplying the variable cost per unit by the number of units produced or sold.

3. Subtract the total variable costs from the total revenue to find the total contribution margin. This value represents the amount of money the company has remaining after covering its variable costs, which can be used to cover fixed costs and contribute to profit.

So, to calculate the company's total contribution margin, use the formula: Total Contribution Margin = Total Revenue - Total Variable Costs, and follow the steps above.

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Answer: 80g

Step-by-step explanation:

we can write an equation for the weight of chocolate; 360-(2/5)x=248

when we solve that equation, we get x=280

since the total weight is 360, we can minus 280 from it to get the weight of the box

360-280=80

Answer: 4:5

Step-by-step explanation: The lowest form

Answer:

Step-by-step explanation:

4:5