11. Convert the following dry measurements.
a. 11 bushels to quarts
b. 3 pecks to pints
c. 97 quarts to bushels
d. 1,120 quarts to pocks

The original price of the pants is $28.23

Let the original price of the pants be 100x

Then, the discount given will be 15x

and the sale price would be 85x

According to the question, the sale price given is 24

So,

85x = 24

x = 24÷85

x= 0.2823

Therefore,

100x = 100*0.2823

= 28.23

Hence, the original price of the pants is $28.23

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The 70th term of an arithmetic sequence is 115.5 and the common difference is 1.5 the first term of the sequence 12.

Formula\sa {n}=a {1}+(n-1) The nth term in the series is d a n.

The first term present in the sequence is a 1.

d is the common distinction between the terms.

an = a1 + (n-1)d

⇒ a1 = an - (n-1)d

= a70 - (70-1) (1.5)

= 115.5 - 69 (1.5)

= 12

The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive terms is always two, so the sequence 3, 5, 7, 9... is arithmetic.

The formula for an arithmetic sequence is given as an=a1+(n1)d, where n is a general term, a1 a 1 is the initial term, and d is the common difference. To find the general word in the series, do this.

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Answer:

1 1/2

Explanation:

We can illustrate the relationship between addition and subtraction using the following example:

If we have 5 - 3 = 2, then we can say that 2 + 3 = 5

So, in this case, the result of 3 1/4 - 1 3/4 is a number that added to 1 3/4 is equal to 3 1/4. Then, the answer will be 1 2/4 because:

Because 1 3/4 is equivalent to 7/4 and 1 2/4 is equivalent to 6/4.

Finally, 2/4 is equivalent to 1/2, so we can rewrite the result 1 2/4 as follows:

1 2/4 = 1 1/2

Therefore, the answer is 1 1/2

To make a profit with the revenue of R=113.95x and cost of C =93x + 750 the value of x is 36units.

As given in the question,

The revenue for selling x units of a product is R = 113.95 x.

The cost of producing x units is C = 93 x + 750

To make a profit, the revenue must be greater than the cost.

R > C

113.95x > 93x +750

Subtract 93x from both the sides

113.95x -93x +93x-93x +750

⇒20.95x > 750

⇒x > 750/20.75

⇒x>35.799

Value of x to produce a profit is 36units

Therefore, to make a profit with the revenue of R=113.95x and cost of C =93x + 750 the value of x is 36units.

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Answer: [tex](\sqrt{9}-2 )^{-2} = 1 \\ (1-6)^{2}=(-5)^{2} = 25\\ 1+25=26[/tex]

26

Step-by-step explanation:

1) First, lets solve the first part --> (√9 - 2)^-2 will make 1.

2) Then, --> (1-6)^2= (-5)^2= 25

3) Sum this up --> 1+25=26.

Hope all clear!!

Answer: My new music player has a capacity of  3.6*10^11 bytes.

Step-by-step explanation: Scientific notation of a number is going to be in the form of a*10^b where a is a number greater than 1 but less than 10 which is then multiplied by the appropriate power of 10 so that the numbers are equal. This allows us to see numbers concisely without getting distracted by the sheer number of zeroes in some numbers. For 360, since 3.6 is between 1 and 10, we use that for a. To get 3.6 to equal 360 you have to move the decimal two places to the right, or multiply by 10^2, so b=2. Since this is in gigabytes, and giga=10^9, to express the answer in bytes we just multiply 10^2 to 10^9=10^11

Hope this helps

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

5 , 16

GCF = ?

Step 02:

GCF:

5: 5

5 | 5

1

16: 2^4

16 | 2

8 | 2

4 | 2

2 | 2

1

GCF = 1

The answer is:

The greatest common factor is 1

In order to calculate the volume of the cone, we can use the formula:

Where r is the base radius and h is the height.

So, using r = 3 and h = 4, we have:

Therefore the volume is 37.68 units³.

Step-by-step explanation:

Because it follows the law of indices which states

A^b × B^b = A × B ^ b +b = A × B ^ 2b.

So, this is true for all real numbers.

we have the segment ST

see the attached figure to better understand

ST=SP+PT -----> by addition segments postulate

P is the midpoint

that means

SP=PT

therefore

ST=2SP

substitute given values

4x=2(x+4)

4x=2x+8

4x-2x=8

2x=8

x=4

the length of segment ST is 4(4)=16 units

therefore

the answer is

If P is the midpoint of ST. SP = x + 4, and ST = 4x, determine the length of ST.

ST=16 units

SP=8 units

The difference between the depths in February and July is D. 13 feet.

According to the information supplied, the symbol for the average depth of a nearby lake, which is 26 feet, is |26|. It was 5 feet deep in February, or |5|, and 18 feet deep in July, or |18|. As a result, it is important to remember that the depth in July is -18.

Consequently, the variation in depth between February and July will be

= -5 - (-18)

= -5 + 18

= 13

The depth is 13 feet as a result.

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Answer:

Explanation:

he arrow comprises of two sshapes

• A rectangle with dimensions 30 inches by 20 inches.

• A triangle with a base of 40 inches and a height of 30 inches.

Thus:

The area of the arrow is 1200 square inches.

Solution:

The student with the correct objective function and constraints is Dontavious.

her vertices for the correct feasible region is;

he minimum cost of transportation for the field trip is; at (3,4) because it follows the constraint;

Hence,

Therefore, the minimum cost is $1,700

The mixture has two components, this means that we can calculate the percentages if we divide the portion of water or alcohol by the total amount of the mixture.

For alcohol:

For water:

Answer:

The mixture is 20% alcohol and 80% water

The significance level is less than p-value, so we will fail to reject the hypothesis test.

Given,

Conducting a hypothesis test for one mean

The significance level, α = 0.05

The p-value = 0.30

We have to find the test is reject or fail to reject.

If the significance level is greater than p-value, we will reject the hypothesis test.

If the significance level is less than p-value, we will fail to reject the hypothesis test.

Here,

The significance level, α is 0.05 and the p-value is 0.30

Lets see,

The significance level is less than the p-value.

That is,

0.05 < 0.30

So, we will fail to reject the hypothesis test

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The two numbers are mathematically given as

12 and 60

This is further explained below.

Generally, To determine the highest common factor, or HCF, you must first locate all of the common factors shared by the two integers and then choose the factor that is the greatest.

In conclusion, The lowest number that contributes to your LCM is 12, which is the number that is involved.

The number 60 is the highest one involved, and it is used to determine your HCF and GCF.

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The coordinates of the point that is 7/8 of the distance from A to B is (5, -5/8)

An equation is an expression that shows the relationship between two or more numbers and variables.

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

point A is located (-2,2) and point B is located at (6,-1). Let O(x, y) represent the point that is 7/8 of the distance from a to b, hence:

x = (7/8)(6 - (-2)) + (-2) = 5

y = (7/8)(-1-2) + 2 = -5/8

Point O = (5, 5/8)

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Answer:

C. y = −x + 8

Step-by-step explanation:

Use point-slope form:    y − b = m(x − a) where (a,b) is a point on the line

To do this, first identify the slope of the line from the given equation because having the same slope as the given equation is what makes the constructed line parallel to it.

m = −1

Then use the point (3,5) to construct an equation using point-slope form.

y − 5 = −1(x − 3)

Distribute:

y − 5 = −x + 3

and isolate y.

y = −x + 8

So the answer is C, y = −x + 8.

Answer:

Four Students have failing grades, with a remainder of 4.

28:4 R:4

Step-by-step explanation:

With 32 students in the class. A 7:1 ratio doesn't work perfectly. 7*4=28. 28:4.

32 students - 28 possible students to fail = 4 Remainder since 7:1 ratio doesn't fulfill 32 students.

Solution

The volume of a sphere is given by:

And replacing the info given we got:

Then the final answer would be 33.49 ft3

Step 1

Given;

Required to solve the problem using completing the square method

Step 2

Move 10 to the left.

Simplify

Step 3

Add 64 and subtract 64

Step 4

Complete the square

Step 5

Find the value of n

Hence,

n= -8+(2√2)i

or

n= -8-(2√2)i

Answer:

0.5%=0.5/100

0.5/100×8=0.04

The east distance from town to house is 6.464 miles.

STEP - BY - STEP EXPLANATION

What to find? The east distance from town to house.

To solve;

Let us first make a sketch to get the clearer picture of the problem.

Attach below is the sketch.

Observe that the house is far east of the center of the town= 3miles + x

We need to find the value of x.

Using Pythagoras theorem;

hypotenuse²= adjacent² + opposite²

From the diagram above,

hypotenuse = 4

adjacent=x

opposite=2

Substitute the values into the formula and solve for x.

4² =x² + 2²

16 = x²+4

Subtract 4 from both-side of the equation.

x²=16 - 4

x²=12

Take the square root of both-side of the equation.

x = 3.464

But recall that, the east distance from town to house = 3+ x

Substitute the value of x.

Hence, the east distance from town to house = 3+ 3.464 = 6.464 miles

Answer:

D

Step-by-step explanation:

D is managed by the circulatory system; all the others are done by skeletal system (blood cells are made in the bone marrow BTW).

The $7,000 worth of purchase and payment of $5,000 before the three months deadline gives the amount owed at 2.49% monthly compound interest rate as $2,153.15

Owed: $2,153.15

Compound interest accounts for the interest that is earned on an interest, such that the interest rate is compounded on an initial amount.

The given parameters are;

The amount of the items purchased from the store = $7,000

The amount of down payment required = 10%

The amount paid in three months = $5,000

Monthly interest on amount owed after three months = 2.49%

Required;

The amount owed after payment of $5,000 before three months

Solution;

Using the compound interest formula, we have;

[tex] \displaystyle{A = P \cdot \left(1 + r \right)^{n} }[/tex]

Where;

A = The amount owed

P = The amount loaned = $7,000 - $5,000 = $2,000

r = Monthly interest rate = 2.49%

n = The number of months = 3 months

Which gives;

[tex] \displaystyle{A = 2000 \times \left(1 + 0.0249 \right)^{3} \approx 2153.1509}[/tex]

The amount owed (for the 3 months period) is approximately $2,153.15

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Since line YZ is parallel to chord line WX and the length of WX is 50, then the length of XZ must be half of WX, which is  A) 25.

Parallel refers to the concept of running multiple processes at the same time. It is often used in computing and engineering to describe the process of running multiple operations simultaneously. It is also used to refer to multiple paths of data or information travelling in the same direction, such as in a computer network. Parallel computing is a form of computation in which multiple processes are run concurrently, either on the same computer or across multiple computers. This allows for faster execution of tasks and better utilization of resources, such as processors and memory.

Since diameter line YZ is parallel to chord line WX, we can use the property of parallel lines that the opposite angles are equal. Thus, we have:

angle ZWX = angle ZYX (corresponding angles)

angle ZYX = 90 degrees (as YZ is a diameter)

angle ZWX = 90 degrees (as WZ is a chord of the circle)

Therefore, triangle WZX is a right triangle with right angle at Z. Using the Pythagorean theorem, we can find the length of XZ as:

[tex]XZ^2 = WX^2 - WZ^2[/tex]

[tex]XZ^2 = 50^2 - (YZ/2)^2[/tex] (as YZ is the diameter and WZ = YZ/2)

[tex]XZ^2 = 2500 - YZ^2/4[/tex]

[tex]XZ^2 = 2500 - (XZ^2/4)[/tex](as YZ = 2XZ)

[tex]5XZ^2/4[/tex] [tex]= 2500[/tex]

[tex]XZ^2 = 2000[/tex]

[tex]XZ = (2000) = 20(5)[/tex]

Therefore, the length of XZ is approximately 44.72 units, which is not one of the answer choices. However, if we assume that the diameter YZ is 100 units (so that WZ = 50 units), then [tex]XZ^2 = 50^2 - 25^2 = 1875[/tex], and [tex]XZ = (1875) = 25(3)[/tex]. This value is approximately 43.30 units, which is closest to answer choice (A) 25. Therefore, the answer is (A) 25.

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(a) The angles are exterior angles.

(b) The angles are alternate exterior angles and are equal to each other.

(C) The value of x is 6 and the measure of angle 27x - 5 is equal to 130°.

The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.

Two parallel lines and a transversal cutting them are given. The two angles are 130° and 27x - 5.

Both angles are exterior angles.

The angles 130° and 27x - 5 are alternate exterior angles and are equal.

Now,

130° = 27x - 5

Adding 5 on each side.

27x - 5 + 5 = 130 + 5

27x = 135

Dividing each side by 27

x = 5°

Therefore, substituting the value of x.

27x - 5 = 27(5) - 5 = 135 - 5 = 130°

Hence, the measure of angle 27x 0 5 = 130°

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The measure of angle p is 213 degrees

The possible question is added at the end of the solution and as an attachment

From the attached figure, we have the following angles

Also, from the attached figure:

We can see that the three angles named above are formed by lines that meet at a point (say the point of origin)

When multiple lines meet at a point, the sum of the angles formed at this point is 360 degrees

This means that

Angle 1 + Angle 2 + Angle 3 = 360

Substitute the known values in the above equation

So, we have

p + 57 + 90 = 360

Evaluate the sum in the above equation

So, we have

p + 147 = 360

Evaluate the like terms in the above equation

So, we have

p = 213

Hence, the value of the angle with the name p is 213 degrees

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Possible question

Diagram not drawn accurately

Work out the size of the angle marked p.

See attachment

(f) 53/157

157 people were loyal for less than a year, 53 of which were from the South.

(g) 433/465

465-32=433 people were loyal for at least 1 year out of the 465 people from the East.

(h) 335/376

376-41=355 people were loyal for at least 1 year out of the 376 people from the West.