You saved $3 during Week 1, $6 during Week 2, $12 during Week 3, and $21 during Week 4. If the pattern continues, how much money will you save during Weeks 8 and 9 combined?

The minimum value of the function is -5 and the maximum value of the function is 15.

The minimum and maximum value of the given trigonometric function f(x)=10sin(2/5x)+5 can be determined by analyzing the amplitude and period of the sine function. The amplitude of the sine function is 10, which means that the maximum value of the function is 10+5=15 and the minimum value is -10+5=-5.

The period of the sine function is given by 2π/2/5=5π. This means that the function completes one full cycle every 5π units. To find the minimum and maximum values of the function, we need to evaluate it at the critical points of the function, which occur at intervals of 5π.

At x=0, the function has a value of 5+10sin(0)=15, which is the maximum value of the function. At x=5π/2, the function has a value of 5+10sin(2π/5)=5, which is the minimum value of the function.

At x=[tex]5π[/tex], the function has a value of 5+10sin(4π/5)=-5, which is the maximum value of the function. At x=15π/2, the function has a value of 5+10sin(6π/5) =5, which is the minimum value of the function.

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Answer:

d

Step-by-step explanation:

so b = 4

and the slope is rise over run = 5/2

Answer:

D) [tex]y=\frac{5}{2}x+4[/tex]

Step-by-step explanation:

The line equation of a line is:

[tex]y=mx+b[/tex] with m being the slope and b being the y-intercept.

We can see from the graph that the y-intercept is 4, as that's where the line intercepts the y-axis, and when x=0.

To find the slope, we first need to pick 2 points: (0,4) and (2,9).

The formula for slope is:

[tex]\frac{rise}{run}[/tex]

The rise is how many units you go up/down from one point to another.  The run is how many units you go left/right from one point to another.
We can see that we go up 5 units and we go right 2 units.  This means our slope is 5/2.

The completed line equation is:

[tex]y=\frac{5}{2}x+4[/tex], which means D is the correct option.

Hope this helps! :)

The length of the third board the builders will add to create a right triangle, according to the Pythagorean Theorem is about 8.72 ft

Pythagorean Theorem is the relationship between the lengths of the three sides of a right triangle. The theorem states that the square of the length of the hypotenuse is equivalent to the sum of the square of the other two sides of the right triangle.

The specified dimensions of the ramp are;

Length of one side of the ramp = 20 ft

Length of the other side of the ramp = 18 ft

The shape of the triangle the builders would like to create = A right triangle

Let x represent the length of the third board, and let the 20 ft board represent the hypotenuse side. Pythagorean Theorem indicates that we get;

20² = 18² + x²

20² - 18² = x²

x² = 20² - 18² = 76

x = √(76) = 2·√(19) ≈ 8.72

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Answer:

Step-by-step explanation:

Total of rides from Tyler's house to Cousin's house and Cousin's house to Tyler's house = 1.8km = 1800m

So, the distance from Tyler's house to his cousin's house is

= 1800m ÷ 2 = 900m

a) If the supplement of an angle is 30 degrees more than the measure of the angle, the measure of the angle is 75 degrees.

b) If the supplement of an angle is 12 degrees less than twice the measure of the angle, the measure of the angle is 64 degrees.

a) Let x be the measure of the angle. The supplement of the angle is 180-x. According to the problem, the supplement of the angle is 30 degrees more than the measure of the angle. This can be written as:

180 - x = x + 30

Solving for x, we get:

2x = 150

x = 75

b) Let x be the measure of the angle. The supplement of the angle is 180-x. According to the problem, the supplement of the angle is 12 degrees less than twice the measure of the angle. This can be written as:

180 - x = 2x - 12

Solving for x, we get:

3x = 192

x = 64

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Point 5 is located on the x-axis (horizontal one)

On a general coordinate axis we have two axes.

The vertical one is called the y-axis, and here we put the outputs.

The horizontal one is called the x-axis, here we put the inputs.

Here we can see that point 5 (P5) is located on the horizontal axis, then the correct option is the first one, x-axis.

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The E is enclosed by the planes z = 0 and z = x + y + 5

Why will E is enclosed by the planes z = 0?

The evaluate the triple integral ∫∫∫_E eˣ dV, where E is enclosed by the planes z = 0 and z = x + y + 5, and by the cylinders x² + y² = 4 and x² + y² = 9,

Follow these steps:

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The fraction is 1/6. Option D

First, we need to know the conversion factor the parameters.

Then, we have that';

1 liter = 1000 milliliter

10 milliliters (ml) = 1 centiliter (cl)

10 centiliters =  1 deciliter (dl) = 100 milliliters

1 liter =  1000 milliliters

1 milliliter =  1 cubic centimeter

1 liter =  1000 cubic centimeters

Then, we can say that;

If 1 liter = 1000ml

Then 2 4/8 = 400ml

2.4 liters is equal to 2.4 x 1000= 2400 milliliters.

400/2400

Simplify the fraction;

4/24

Divide the values, we get;

1/6

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The ordered pairs of the system of inequalities are (1, 0) and (0, -5)

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

6x - y > -3

4x + 3y < 4

The above expression is a system of linear inequality

That implies that we graph the inequalites in the system on the same plane and write out ordered pairs from the region that represent the solution of the system

Next, we plot the graph

See attachment for the graph of the inequality

The ordered pairs are (1, 0), (0, -5) and other pairs

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The population is 38, and the sample is 5 students.

. The population for this problem is the entire soccer team, which consists of 38 members.

b. The sample for this problem is the group of 5 students who are selected by the coach to represent the team in the Homecoming Parade.

c. One method for selecting a random sample of 5 students from the team is to use a random number generator to choose 5 numbers between 1 and 38, representing the 38 team members. The coach can then select the students who correspond to the chosen numbers. Another method is to write the names of all 38 team members on identical slips of paper, place the slips in a container, mix them up, and then randomly select 5 slips to determine the students who will participate in the parade. It is important to ensure that the selection method is truly random to avoid any bias or non-representativeness in the sample.

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The probability that Morgan will catch the train to Agon is 0.578.

To catch the train to Agon, one of the following conditions must be met:

The train to Bewford is not late and the train to Agon is not late.

The train to Bewford is not late and the train to Agon is late.

The probability of the first condition is:

(0.76) x (0.65) = 0.494

The probability of the second condition is:

(0.24) x (0.35) = 0.084

Therefore, the probability that Morgan will catch the train to Agon is:

0.494 + 0.084 = 0.578 (to three decimal places)

So the probability that Morgan will catch the train to Agon is 0.578.

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The correct answer is (D) 2,205.

To calculate the number of different combinations of tag codes, we need to consider the possible options for each position in the code.

For the first and third positions (consonants), we have 21 options for each position since there are 21 consonants in the English language.

For the middle position (vowel), we have 5 options since there are 5 vowels in the English language.

Therefore, the total number of different combinations is calculated by multiplying the number of options for each position:

21 (consonant options) * 5 (vowel options) * 21 (consonant options) = 2,205

Therefore, the correct answer is (D) 2,205.

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If the S&P stock index fell by an average of 8% each day, we can model the

data using exponential decay. Let P represent the initial value of the S&P

stock index and t represent the number of days. Then, the equation for the

S&P stock index after t days is:

[tex]P(t) = P * (0.92)^t[/tex]

Here, 0.92 represents the daily decay factor, which is derived from

subtracting 8% from 100% (100% - 8% = 92%). As each day passes, the

value of P(t) decreases exponentially by a factor of 0.92.

It's important to note that this equation assumes that the S&P stock index

falls by exactly 8% each day, which may not be a realistic scenario in real

life. Additionally, this equation only models the decay of the S&P stock

index value and does not take into account any external factors that may

affect its value.

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The sample mean difference from these 24 pairs of siblings is 1.79 inches.

To find the sample mean difference from these 24 pairs of siblings, you can use the given 95% confidence interval for the mean difference in heights, which is (-0.76, 4.34).

The sample mean difference is the midpoint of the confidence interval. To calculate this, add the lower bound (-0.76) and the upper bound (4.34) of the confidence interval, and then divide by 2:

(-0.76 + 4.34) / 2 = 3.58 / 2 = 1.79 inches

So, the sample mean difference from these 24 pairs of siblings is 1.79 inches.

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In the circle, the measure of p is 34 (option 3).

First, we know that angle MBC is an exterior angle to triangle PBC. Therefore, the measure of angle PBC is equal to the sum of angles MBC and MCB, which is 100 + (1/2)(angle MCP) = 100 + (1/2)(angle MQP).

Similarly, angle MCD is an exterior angle to triangle PCD. Therefore, the measure of angle PDC is equal to the sum of angles MCD and MDC, which is 62 + (1/2)(angle MPQ) = 62 + (1/2)(angle MQP).

Since angle PBC and angle PDC are both subtended by the same arc BC, they are equal. Therefore, we can set the expressions for these angles equal to each other and solve for angle MQP:

100 + (1/2)(angle MQP) = 62 + (1/2)(angle MQP)

38 = (1/2)(angle MQP)

angle MQP = 76 degrees

Finally, we can use the fact that angles MPQ and MQP form a linear pair, so they add up to 180 degrees. Therefore, angle MPQ is 180 - 76 = 104 degrees.

Since angle MPQ is an exterior angle to triangle PAB, we can use the exterior angle theorem to find the measure of angle P, as follows:

angle P = angle MPQ + angle PAB = 104 + 100 = 204 degrees

However, angles in a circle cannot be greater than 180 degrees, so we need to subtract 180 from angle P to get the actual measure of angle P:

angle P = 214 - 180 = 34 degrees

Therefore, the answer is option (3).

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The number of servings did Pablo make is (B) 26.

Unit conversion is the process of converting a value expressed in one unit of measurement to another unit of measurement that represents the same quantity but is expressed in a different unit.

The given quantities are in different units, so we need to convert them to a common unit to determine the number of servings. For this, we need to convert quarts and gallons to fluid ounces.

Here we have

Pablo mixed 2 1/2 quarts of fruit juice with 1 gallon of seltzer.  

Each serving is 8 fluid ounces

Let's first convert the quantities to the same units.

=> 1 gallon = 4 quarts

Total amount of liquid = 2 1/2 + 4 = 6 1/2 quarts

Now, let's find how many 8-ounce servings are in 6 1/2 quarts:

=> 1 quart = 32 fluid ounces

=> 6 1/2 quarts = 6.5 x 32 = 208 fluid ounces

Given that, 1 serving = 8 fluid ounces

Number of servings = 208/8 = 26

Therefore,

The number of servings did Pablo make is (B) 26.

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Complete Question:

Pablo mixed 2 1 /2 quarts of fruit juice with 1 gallon of seltzer. If each serving is 8 fluid ounces, how many servings did Pablo make?

A: 20    B: 26     C: 32    D: 36

Linda contributed $3,355.56 to social security in 2003.

The Social Security tax is a payroll tax that is deducted from employees' paychecks to help fund the Social Security program, which provides retirement, disability, and survivor benefits to eligible individuals.

The Social Security tax rate is typically 6.2% for employees and employers, and the maximum amount of taxable earnings is determined each year by the Social Security Administration (SSA).

In 2003, the maximum taxable earnings was $87,000. This means that any earnings above $87,000 were not subject to Social Security taxes.

To calculate Linda's contribution to social security in 2003, we will use the given social security tax rate of 6.2% and her income of $54,122.

Convert the tax rate percentage to a decimal by dividing by 100.
6.2% / 100 = 0.062

Multiply Linda's income by the decimal tax rate.
$54,122 * 0.062 = $3,355.56

Linda contributed $3,355.56 to social security in 2003.

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The slope of the graph is the same positive value that is 0.75.

Hence the correct option is (1).

We know that the equation of a straight line with slope 'm' and y intercept 'c' is given by,

y = mx + c

Here the model equation

c = 0.75h, where c is the total cost to buy hotdogs

h is the number of hotdogs bought

And 0.75 is the price of one hotdog

Now we can clearly say that c = 0.75h will make a straight line coordinate plane.

Now comparing the equation with slope intercept equation of straight line we get,

m = 0.75 and c = 0

So the slope of the line represented by model equation = 0.75 which is a positive number.

y intercept  = 0.

We know that the slope of one particular straight line on cartesian plane is unique.

So, the slope of the graph is the same positive value.

Hence the correct option is (1).

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Answer:

Sure, here's the solution to the word problem:

Jack has $10 in his lunch account and plans to spend $2 a week on snacks. To find out how long it will take his lunch account to reach zero, we can divide the total amount of money in his account by the amount he spends each week.

```

$10 / $2 = 5 weeks

```

Therefore, it will take Jack 5 weeks to spend all of the money in his lunch account.

Here's another way to solve the problem:

We can also set up an equation to represent the situation. Let x be the number of weeks it takes Jack's lunch account to reach zero. We know that Jack starts with $10 and spends $2 each week, so we can write the equation:

```

$10 - $2x = 0

```

Solving for x, we get:

```

x = 5

```

Therefore, it will take Jack 5 weeks to spend all of the money in his lunch account.

Answer:

in 5 weeks he will have 0$ in his account

Step-by-step explanation:

In circle P, if m(QR) = 80 , and m(QRT) = 39 , m(QPR) = 39 and m(PT) = 78

Based on the information given, we know that:

- m(QR) = 80 (this is the measure of arc QR)
- m(QRT) = 39 (this is the measure of angle QRT)

To find the other measures, we can use the following formulas:

- The measure of a central angle is equal to the measure of its intercepted arc
- The measure of an inscribed angle is half the measure of its intercepted arc

Using these formulas, we can find the measure of angle QPR and the measure of arc PT as follows:

- m(QPR) = m(QRT) = 39 (since angle QRT and angle QPR intercept the same arc QR)
- m(PT) = 2 * m(QRT) = 78 (since angle QRT and angle PQT intercept the same arc PT, and the measure of an inscribed angle is half the measure of its intercepted arc)

So the final answers are:

- m(QR) = 80
- m(QRT) = 39
- m(QPR) = 39
- m(PT) = 78

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A 20-ounce smoothie from Blender Splendor contains 8 ounces of fruit juice.

To find out how many ounces of fruit juice are in a 20-ounce smoothie from Blender Splendor, given that 40% of the smoothie is fruit juice, follow these steps:

1. Convert the percentage to a decimal: 40% = 0.40
2. Multiply the total ounces of the smoothie by the decimal: 20 ounces * 0.40 = 8 ounces

Your answer: A 20-ounce smoothie from Blender Splendor contains 8 ounces of fruit juice.

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Answer:

Sure, I can help you with that!

To find the area of a regular pentagon, we can use the formula:

Area = (1/2) x apothem x perimeter

where apothem is the distance from the center of the pentagon to the midpoint of any side, and perimeter is the total length of all the sides.

So, to find the area of your pentagon, we can first calculate the perimeter:

Perimeter = 5 x side

Perimeter = 5 x 10.6

Perimeter = 53

Now, we can plug in the values for apothem and perimeter into the formula:

Area = (1/2) x apothem x perimeter

Area = (1/2) x 7.3 x 53

Area = 193.45

Therefore, the area of your pentagon is approximately 193.45 square units.

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Answer:

x = 0.35

Step-by-step explanation:

We Know

x · 10 = 3 1/2

Find the missing number.

3 1/2 = 7/2 = 3.5

x · 10 = 3.5

x = 0.35

So, the answer is 0.35.

The required answer to the algebraic fraction [ {(5)/(6)}a + 4 {(1)/(4)}a ] is [ {(11)/(6)}a ] .

We can simplify this algebraic fraction problem by simple rule of fraction addition and with application LCM rule as,

{(5)/(6)}a + 4 {(1)/(4)}a

= {(5)/(6)}a + (1)a

= [{ (5)+ (6) }/(6)]a

= {(11)/(6)}a

The LCM (or, Least Common Multiple) rule is used for the two algebraic fraction here as the value that is divisible by the two given numbers in the denominator of the algebraic fractions. Then by rule, the numerators are multiplied by the factor of LCM of the denominator and then the numerators are added.

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It will take the population 10.5 years to reach 25,000

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

Inital population, a = 15000

Rate of increase, r = 5%

Using the above as a guide, we have the following:

The function of the situation is

f(x) = a * (1 + r)ˣ

So, we have

f(x) = 15000 * (1 + 5%)ˣ

When it reaches 25000, we have

15000 * (1 + 5%)ˣ = 25000

Divide both sides by 15000

(1 + 5%)ˣ = 1.67

Take the logarithm of both sides

x = log(1.67)/log(1 + 5%)

Evaluate

x = 10.5

Hence, the number of years is 10.5

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Nora would have to pay a total of $5 + $0.75s in a month when she downloaded "s" songs.

The cost for downloading 30 songs would be:

$0.75 per song × 30 songs = $22.50

Therefore, Nora would have to pay a total of $5 + $22.50 = $27.50 in a month when she downloaded 30 songs.

If she downloaded "s" songs, the cost would be:

$0.75 per song × s songs = $0.75s

Therefore, Nora would have to pay a total of $5 + $0.75s in a month when she downloaded "s" songs.

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Y-component of the vector as shown in the diagram is 67.84 m in the direction of the negative y-axis.

Vector is a quantity that has both magnitude and direction.

Examples a vectors are

To find the Y-component of the vector, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the y component is 67.84 m.

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The area of the facade measuring 30' across and 20' in height is 300 square feet.

The front facade of an A-frame house is a triangular shape, with a base of 30 feet and a height of 20 feet. To calculate the area of the facade, we need to use the formula for the area of a triangle, which is 1/2 times the base times the height = 1/2 * b * h, where b is the base and h is the height.

In this case, the base is 30 feet and the height is 20 feet, so we can plug those values into the formula:

Area = 1/2 x 30 x 20

Simplifying the multiplication, we get:

Area = 300 square feet

Therefore, the area of the front facade of the A-frame house is 300 square feet.

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Each game of skee ball requires 2 tokens and each game of pinball requires 2 tokens.

Let the number of tokens required for each game of skee ball be x and for each game of pinball be y.

From the given information, we can form two equations:

10x + 8y = 44    ... (1)

3x + 8y = 30      ... (2)

Multiplying equation (2) by 3, we get:

9x + 24y = 90     ... (3)

Subtracting equation (1) from equation (3), we get:

- x + 16y = 46

Solving for x, we get:

x = 16y - 46

Substituting this value of x in equation (2), we get:

3(16y - 46) + 8y = 30

Simplifying and solving for y, we get:

y = 2

Substituting this value of y in equation (1), we get:

10x + 8(2) = 44

Solving for x, we get:

x = 2

Therefore, each game of skee ball requires 2 tokens and each game of pinball requires 2 tokens.

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