A sample of maximum pressure from 12 trials with a stamping machine yielded a mean of 7.2 thousand psi and a standard deviation of 1.2 thousand psi. The histogram of the sample data is approximately normal. Calculate a 90% confidence interval.

Using compound interest, we can find that at age 59 retirement option 1 will be better than retirement option 2.

Compound interest is computed on the principal and the accrued interest for a given time period. The interest that has accumulated on the principal over time is added to it, and the combined amount acts as the new principal for the subsequent time period. Once more, the interest for the following period is calculated using the total cumulative principal amount.

Compound interest is the term used to describe the method of computing interest employed in all financial and business transactions globally. The benefit of compounding is that it is consistently better than or comparable to other strategies, such simple interest.

At age 59,

Option 1 = 30000 × 34

= $1020000

Option 2 = 15000 (1+12/408) ^34

= 15000 × (1.02) ^34

= 15000 × 1.9606

= $29409.

So, when you retire at 59, option 1 is better than option 2.

At age 69,

Option 1 = 30000 × 44

= $1,320,000

Option 2 = 15000 (1+12/528) ^44

= 15000 × (1.02) ^44

= 15000 × 2.390

= $35,850.

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At age 59, retirement option 1 will outperform retirement option 2, according to compound interest.

On the principal and the interest that has accrued over a specific length of time, compound interest is calculated. The principal is increased by the interest that has accrued on it over time, and the combined sum serves as the new principal for the term that follows. Once more, the entire cumulative principal amount is used to determine the interest for the upcoming period.

The term "compound interest" refers to the technique of calculating interest used in all financial and commercial transactions worldwide. Compounding has the advantage of constantly outperforming or being on par with other approaches, like simple interest.

At age 59,

Option 1:

= 30000 × 34

= $1020000

Option 2:

[tex]=15000(\frac{1+12}{408} )^{34} \\\\=15000\times 1.02^{34}[/tex]

= 15000 × 1.9606

= $29409.

So, when you retire at 59, option 1 is better than option 2.

At age 69,

Option 1:

= 30000 × 44

= $1,320,000

Option 2:

[tex]=15000(\frac{1+12}{528} )^{44} \\\\=15000\times 1.02^{44}[/tex]

= 15000 × 2.390

= $35,850.

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Answer:

------------------------------

Angle with the measure of 130° forms a vertical angle pair with the sum of x and 107° angle.

Since vertical angles are congruent we have:

The two angles, x and 2x together form a right angle, since they form a linear pair with another angle, marked as right angle. Therefore, x and 2x are complementary angles:

Answer:

7s

Step-by-step explanation:

The steps that should be taken to evaluate the order of operations given are:

To solve with PEMDAS, you first need to solve what is in the brackets in the order of operations given which is 8÷2 (1+3) - 2^3.

= 8÷2 (1+3) - 2^3

= 8÷2 x 4 - 2^3

Then solve for the exponents :

= 8÷2 x 4 - 2^3

= 8÷2 x 4 - 8

Then because the division comes first, you solve for that:

= 8÷2 x 4 - 8

= 4 x 4 - 8

You then solve for the multiplication as this takes precedence over subtraction:

= 4 x 4 - 8

= 16 - 8

Then solve the subtraction:

= 16 - 8

= 8

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The number of ounces in solution A= 16, and the number of ounces in the solution B = 104

let x be the number of ounces of solution A

let y be the number of ounces of solution B

x+y=120

Substitute the value of y,

y=120-x

Solution A is 70% salt and B is 95% salt,

then

0.7x+.95y=.75(120)

0.7x+.95y=90

multiply both sides of the equation by 100 to remove the decimal points,

70x+95y=900

70x+95(120-x)=900

70x+1140-95x=900

-15x=900-1140

15x=240

x=16

and y=120-16

y=104

The number of ounces in solution A= 16

and the number of ounces in solution B = 104

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Answer:

A) -3

Step-by-step explanation:

To remove the radical on the left side of the equation, cube both sides of the equation.

[tex]\sqrt[3]{4x + 4}^{3}[/tex] = (-2)³

Simplify each side of the equation.

4x + 4 = -8

4x = -12

x = -3

So, the answer is A) -3

Yes, 5:10 and 15:30 are equivalent ratios because they simplify to the same ratio of 1:2.

Ratios represent the relationship between two or more quantities or values. When two ratios have the same simplified form, they are considered equivalent because they represent the same relationship between the quantities being compared.

In the given example, the ratios 5:10 and 15:30 can be simplified to the same ratio of 1:2. This means that both ratios represent the same relationship between the quantities being compared. Specifically, both ratios represent a comparison between two quantities where the second quantity is twice as large as the first quantity.

To simplify a ratio, we divide both the numerator and denominator by their greatest common factor (GCF). The GCF is the largest number that divides evenly into both the numerator and denominator. In this case, the GCF of 5 and 10 is 5, and the GCF of 15 and 30 is 15. Dividing both ratios by their respective GCFs results in a simplified ratio of 1:2 for both ratios.

Therefore, 5:10 and 15:30 are equivalent ratios because they represent the same relationship between quantities, and have the same simplified form.

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Total area of garden after adding rectangular piece will be 55 ft² i.e. B.

What exactly is a rectangle?

A rectangle is a two-dimensional geometric shape that is characterized by having four sides and four right angles. Opposite sides of a rectangle are parallel and equal in length, while opposite angles are equal. The area of a rectangle can be calculated by multiplying its length by its width, while its perimeter is the sum of the lengths of all its sides. Rectangles are commonly used in many fields, such as architecture, engineering, and mathematics.

Now,

The rectangle has a length of |-21 - (-23)| = 2 and a width of |7 - 12| = 5. Therefore, the area of the new rectangular piece is 2 x 5 = 10 square feet.

Adding this to the area of the existing garden gives a total area of 45 + 10 = 55 square feet.

Therefore, the answer is (B) 55 ft².

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The ratio means that for every 2 motor boats, there are 3 sail boats. 6 sail boats must also enter so that the ratio remains the same. A possible missing information will be the total number of ships in the armada.

A ratio is a mathematical expression that represents the relationship between two quantities or numbers. It is a comparison of two numbers, often written in the form of a fraction or with a colon. Ratios are used to express how much of one thing there is in relation to another.

1. a. The ratio of motor boats to sail boats can be written in three ways:

As a fraction: 2/3

With a colon: 2:3

With the word "to": 2 to 3

This ratio means that for every 2 motor boats, there are 3 sail boats. Alternatively, it can be interpreted as for every 3 sail boats, there are 2 motor boats. The ratio does not specify the total number of boats, only the relative proportion of motor boats to sail boats.

b. To keep the ratio between motor boats and sail boats the same, we need to maintain the same ratio of motor boats to sail boats.

Currently, the ratio of motor boats to sail boats is 2:3.

Let x be the number of sail boats needed to maintain the ratio.

After x sail boats enter, the total number of boats will be 2 + x motor boats and 3 + x sail boats.

The ratio of motor boats to sail boats will still be 2:3, so we can write,

[tex]\frac{(2 + x)}{(3 + x)}[/tex] = [tex]\frac{2}{3}[/tex]

Cross-multiplying, we get,

2(3 + x) = 3(2 + x)

6 + 2x = 6 + 3x

x = 6

Therefore, 6 sail boats must also enter so that the ratio remains the same.

2. To find the total number of galleons and galleys in the Spanish armada, we need at least one additional piece of information. The ratio of 5:1 tells us that for every 5 galleons, there is 1 galley. However, we don't know the total number of galleons and galleys in the armada.

One possible missing information that could help us find the total number of galleons and galleys is the total number of ships in the armada. If we knew the total number of ships, we could find the number of galleons and galleys in the armada.

For example, let's say the total number of ships in the armada is 100. And let number of galleons = a and number of galleys = b. Then,

a + b = 100

[tex]\frac{a}{b}[/tex] = 5/1

b = a/5

Substituting this expression into the first equation, we get:

a+ (a/5) = 100

(6a/5) = 100

a = 500/6 ≈ 83.33

Then b = (1/5)(83.33) = 16.67

However, since we cannot have a fractional part of a ship, we can round up or down to get whole numbers. Therefore, we can conclude that the Spanish armada had approximately 83 galleons and 17 galleys, based on the given ratio of 5:1.

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The new set B = {1, 2, 3, 5, 7}, and the intersection of A, B, and C would be D = {2}.

Intersection is the point at which two sets of data meet. It is the common point or element that exists in both sets.

The intersection of the three sets A, B, and C is the set of elements that are common to all three sets.

In this case, the intersection of A, B, and C is the null set, denoted as ∅. This means that there are no elements that are common to all three sets.

To make the intersection set D = {2}, one of the sets must contain the element 2.

In this case, set A already contains the element 2, so it is sufficient to add the element 2 to one of the other sets, either set B or set C.

Let's say we add the element 2 to set B. The new set would be B = {1, 2, 3, 5, 7}, and the intersection of A, B, and C would be D = {2}.

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Step-by-step explanation:

The probability of Meikel wearing khakis and sandals is

3 ÷ 12 which will give us

1/4

Therefore, we can't calculate the difference in blood pressure between the control and treatment groups. Difference in means: 244.9 - 226.5 = 18.4 mg/dL.

by the question.

The question appears to be incomplete. It asks for the "difference," but it doesn't specify what difference it's referring to. Based on the information provided, I can provide some possible interpretations and calculations:

Difference in cholesterol levels before and after treatment:

Since all patients started with a cholesterol level of 245 mg/dL, we can't calculate the difference in cholesterol levels before and after treatment. We don't have any data on the patients' cholesterol levels after treatment.

Difference in average cholesterol levels between the control and treatment groups:

Control group mean: (241+243+242+245+250+248+246+245+242+247)/10 = 244.9 mg/dL

Treatment group mean: (230+225+220+218+224+240+232+221+235+224)/10 = 226.5 mg/dL

Difference in means: 244.9 - 226.5 = 18.4 mg/dL

Difference in average blood pressure between the control and treatment groups:

The prompt states that the experiment tested whether the cholesterol medication lowers the overall blood pressure for male patients, but it doesn't provide any data on blood pressure.

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Answer:

Step-by-step explanation:

-8^2 and (-2)^3 are exponents so it should be solved first

-8^2 = -64 and (-2)^3 = -8

(-64)/(-8)

64/8

8

8

To solve this expression, we need to follow the order of operations, which is PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction) from left to right:

First, we need to simplify the exponents: -8^2 means -1 times 8 squared, which is -1 times 64 or -64. (-2)^3 means -2 multiplied by itself three times, which is -2 x -2 x -2 or -8.

Next, we need to perform the division and multiplication, again from left to right: -64 ÷ -8 equals 8.

Therefore, the final answer to the expression -8^2÷(-2)^3 is 8.

After simplifying the given expression we can write answer using positive exponent [tex]7^3 * 6^30[/tex].

What is expression?

In mathematics, an expression is a combination of numbers, variables, and symbols that are grouped together to represent a mathematical relationship or quantity. It can be a single term, or a combination of terms separated by mathematical operations such as addition, subtraction, multiplication, and division.

When we raise a power to another power, we need to multiply the exponents. So we can simplify the expression as follows:

[tex]7^3(6^6)^5 = 7^3 * 6^(6*5) = 7^3 * 6^30[/tex]

so we write the answer using positive exponents as:

[tex]7^3 * 6^30[/tex]

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Rewriting the absolute value problems gives us: y = |x − 3| + |x + 2| − |x − 5| = 3 - x + x + 2 - (5 - x) = x

The absolute value is simply defined as the distance from zero.

The equation we are to rewrite is:

y = |x − 3| + |x + 2| − |x − 5|, if -2 < x < 3  

Modulus value means that it always gives positive value. Thus:

if x < a, then |x - a| is positive when |x - a | = a -x, which is positive as a is larger than x.

and if x >a, then |x-a| is positive when |x-a| = x - a, which is positive as a is smaller than x.

Applying the same,

For  -2 < x < 3,

|x - 3 | = 3 - x, as x <3

| x + 2 | = | x - (-2)| = x - (-2) = x+2 as x> -2

| x - 5 | = 5 -x , as x < 5

Therefore, y = |x − 3| + |x + 2| − |x − 5| = 3 - x + x + 2 - (5 - x) = x

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an expression for height h in terms of radius r, h=r/4

The quantity of space a three-dimensional solid shape takes up is measured by its volume. Although it is hard to conceive in any shape, it may be likened to shapes. A compass box, for instance, has a bigger volume than an eraser inserted inside of it.

Volume of Sphere=4/3πr³

Volume of Cone=1/3πR²h

Given:

R=4r

4/3πr³=1/3πR²h

4r³=R²h

4r³=(4r)²h

r=4h

an expression for height h in terms of radius r, h=r/4.

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The maximum number of homes that can be placed on the street is 11.

first we need to divide the total length of the street by the width of each home.

The length of the street is 345 feet and the width of each home is 30 feet. Therefore, the number of homes that can be placed on the street is:

345 feet / 30 feet per home = 11.5 homes

Since we cannot have a fraction of a home, we need to round down to the nearest whole number.

Therefore, the maximum number of homes that can be placed on the street is 11.

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In conclusion MN is approximately 8.73.

How to solve?

In triangle MNK, we know that MN = NK and the angle between them is 110 degrees. Let's call the third angle in this triangle A.

We also know that MK = 5.

Since the sum of the angles in a triangle is always 180 degrees, we can find angle A:

A + 110 + A = 180

2A = 70

A = 35

Now we can use the Law of Sines to find MN:

MN/sin(110) = MK/sin(A)

MN/sin(110) = 5/sin(35)

MN = 5×sin(110)/sin(35)

MN ≈ 8.73

Therefore, MN is approximately 8.73.

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Complete Quedtion:

In triangle AMNK, we have MN = NK, angle M/N = 110 degrees, and MK = 5. What is the length of MN?

The coordinates of vertex A' are (1, 1)

The coordinates of vertex B' are (2, 3).

The coordinates of vertex C' are (2, 1).

In Geometry, a reflection over or across the x-axis is represented or modeled by the following transformation rule (x, y) → (x, -y). This ultimately implies that, a reflection over or across the x-axis would maintain the same x-coordinate (x-value) while the sign of the y-coordinate (y-value) changes from positive to negative or negative to positive as the case may be.

In this exercise, you are required to apply a reflection over the x-axis, a rotation of 90° clockwise about the origin, and finally reflected across the line y = x as shown in the transformation table below;

Original vertex   Reflection (x-axis)   Rotated 90° clockwise   Line y = x

A (1, 1)           →             (1, -1)          →              (-1, -1)           →             (1, 1)

B (2, 3)          →            (2, -3)        →              (-3, -2)         →             (2, 3)

C (2, 1)          →            (2, -1)         →              (-1, -2)         →              (2, 1)

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After answering the prοvided questiοn, we can cοnclude that As a result, the sοlutiοn tο the inequality is p greater than 32.

In mathematics, an inequality is a nοn-equal relatiοnship between twο expressiοns οr values. As a result, imbalance leads tο inequality. In mathematics, an inequality cοnnects twο values that are nοt equal. Inequality is nοt the same as equality. When twο values are nοt equal, the nοt equal sign is cοmmοnly used ().

Different inequalities, nο matter hοw small οr large, are used tο cοntrast values. Many simple inequalities can be sοlved by mοdifying the twο sides until οnly the variables remain. Hοwever, a number οf factοrs cοntribute tο inequality: Negative values are divided οr added οn bοth sides. Exchange left and right.

We must isοlate the variable p οn οne side οf the inequality sign in οrder tο sοlve it.

-16 negative οne-half p

When bοth sides οf the inequality are multiplied by -2 (and the inequality sign is reversed because we are multiplying by a negative number), we get:

p > 32

As a result, the sοlutiοn tο the inequality is p greater than 32.

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Amount Due at Maturity a. $102,000, b. $30,100, c. $62,620, d. $42,930, e. $40,700.

Interest is the cost of borrowing money, typically expressed as a percentage of the borrowed amount, called the principal. It is the amount charged by a lender to a borrower for the use of money over a certain period of time. Interest can also refer to the amount earned on money that is invested, such as in a savings account or a bond. The rate of interest depends on factors such as the level of risk associated with the loan, the length of the loan period, and the market rate of interest at the time of borrowing. The amount of interest paid or earned can be calculated using various formulas, including simple interest and compound interest.

To determine the due date and amount of interest due at maturity for each note, we can use the following formula:

Interest = Principal x Rate x Time

where Principal is the face amount of the note, Rate is the annual interest rate, and Time is the time in years (based on a 360-day year).

a. January 5, $100,000, 6%, 120 days

Due Date: May 5

Time: 120/360 = 1/3 year

Interest = $100,000 x 0.06 x 1/3 = $2,000

Amount Due at Maturity = Principal + Interest = $100,000 + $2,000 = $102,000

b. February 15, $30,000, 4%, 30 days

Due Date: March 17 (assuming non-leap year)

Time: 30/360 = 1/12 year

Interest = $30,000 x 0.04 x 1/12 = $100

Amount Due at Maturity = Principal + Interest = $30,000 + $100 = $30,100

c. May 19, $62,000, 8%, 45 days

Due Date: July 3

Time: 45/360 = 1/8 year

Interest = $62,000 x 0.08 x 1/8 = $620

Amount Due at Maturity = Principal + Interest = $62,000 + $620 = $62,620

d. August 20, $42,400, 5%, 90 days

Due Date: November 18

Time: 90/360 = 1/4 year

Interest = $42,400 x 0.05 x 1/4 = $530

Amount Due at Maturity = Principal + Interest = $42,400 + $530 = $42,930

e. October 19, $40,000, 7%, 90 days

Due Date: January 17

Time: 90/360 = 1/4 year

Interest = $40,000 x 0.07 x 1/4 = $700

Amount Due at Maturity = Principal + Interest = $40,000 + $700 = $40,700

Therefore, the due date and amount of interest due at maturity for each note are as follows:

a. Due Date: May 5, Interest: $2,000, Amount Due: $102,000

b. Due Date: March 17, Interest: $100, Amount Due: $30,100

c. Due Date: July 3, Interest: $620, Amount Due: $62,620

d. Due Date: November 18, Interest: $530, Amount Due: $42,930

e. Due Date: January 17, Interest: $700, Amount Due: $40,700

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Answer: The regular tube is the better buy

Step-by-step explanation: $2.50/3.2 ounces equals $.78 per ounce. $1.00/1.2 ounces equals $.83 per ounce. Therefore, the regular tube is the better buy.

First, 90 + 90 = 180

Second, 320 - 180 = 140

Third, 140 / 2 = 70.

|                                90 * 70 = 6,300
|
|
| 90
|
|____________

         70

21. The trainer raised the end of the treadmill from the floor by 0.62 ft or 7.4 in.

22. The ramp needs to be 1.19 ft tall at the highest point.

23. The springboard is 6.21 in long.

Trigonometric ratio is the ratio of two sides of a right triangle to each other, or the ratio of the sine, cosine, or tangent of an angle in a right triangle.

21: Incline = 7°

Length of walking surface = 5 ft

We need to calculate the change in height of the treadmill.

Let x be the height of the end of the treadmill from the floor.

We can use the trigonometric ratio, tangent (tan), to solve the problem.

tan(7°) = Opposite/Adjacent

=> x/5 = tan(7°)

=> x = 5tan(7°)

=> x = 5×0.124

=> x = 0.62 ft

22: Angle = 20°

Length of board = 3.5 ft

We need to calculate the height of the ramp at the highest point.

Let y be the height of the ramp at the highest point.

We can use the trigonometric ratio, sine (sin), to solve the problem.

sin(20°) = Opposite/Hypotenuse

=> y/3.5 = sin(20°)

=> y = 3.5sin(20°)

=> y = 3.5×0.342

=> y = 1.19 ft

23: Angle = 14.5°

Length of springboard coils = 6 in

We need to calculate the length of the springboard.

Let z be the length of the springboard.

We can use the trigonometric ratio, cosine (cos), to solve the problem.

cos(14.5°) = Adjacent/Hypotenuse

=> 6/z = cos(14.5°)

=> z = 6/cos(14.5°)

=> z = 6/0.966

=> z = 6.21 in

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If Fran and Jill made a new years resolution to ride bikes.  it will take 3 weeks for Fran and Jill to have ridden the same number of miles..

Let's assume that it takes "x" number of weeks for Fran and Jill to ride the same number of miles.

In the first week, Fran rides 40 miles, and Jill rides 70 miles.

In the "x"th week, Fran will have ridden a total of 40 + 55x miles.

In the "x"th week, Jill will have ridden a total of 70 + 45x miles.

For Fran and Jill to ride the same number of miles in "x" weeks, we need to solve the following equation:

40 + 55x = 70 + 45x

Simplifying this equation, we get:

10x = 30

x = 3

Therefore, it will take 3 weeks for Fran and Jill to have ridden the same number of miles.

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Answer: The answer is C.

Step-by-step explanation:

The equation that could represent a rational function is answer C.

I hope this helped! A brainilist would be amazing! <3

Step-by-step explanation:

r = 250   ( thousand)   and   r = 180 + 35 log4 (x)    <====base 4 LOG

    sooooo     250 = 180 + 35 log4(x)       find 'x' thousands

                      (250 -180)/35 = log4 (x)

                        2 = log4(x)         these are exponents of 4 ...anti log base 4:

                      4^2 = 4^(log4 x)

                       16   = x          

                     But x is thousands of $ (per the question info)

                                     so  $ 16 000

Answer:

The number of times the tire will have to turn in travelling the length of the street is 30.9 times.

To determine the number of times the tire will have to turn in travelling the length of the street, we will first calculate the circumference of the tire.  

Since the tire is circular, the circumference of the tire can be calculated from the formula for calculating the circumference of a circle.

The circumference of a circle is given by

C = πd

Where C is the circumference and d is the diameter

From the question d = 1.7m and π = 3.14

∴ C = 3.14 × 1.7

C = 5.338 m

Therefore, the circumference of the tire is 5.338 m

Now, for the number of times the tire will have to turn in travelling the length of the street, we will divide the length of the street by the circumference of the tire.

Number of times the tire will have to turn = Length of the street ÷ Circumference of the tire

Number of times the tire will have to turn = 165 m ÷ 5.338 m

Number of times the tire will have to turn = 30.91045 times

Number of times the tire will have to turn ≅ 30.9 times

Hence,  the number of times the tire will have to turn in travelling the length of the street is 30.9 times

Answer:

7:22

Step-by-step explanation:

Given: 2 hours and 22 minutes

5:00 + 2 hours

5 + 2 = 7

7:00 + 22 minutes

7:22