Sydney has a loyalty card good for a discount at her local hardware store. The item she wants to buy is priced at $21, before discount and tax. After the discount, and before tax, the price is $20. 79. What is the percent discount?

Answer :

solution in the pic

300 milligrams is 0.3 grams of protein.

A conversion factor is a number that is used to multiply or divide one set of units into another. If a conversion is required, it must be done using the correct conversion factor to get an identical value. For instance, 12 inches equals one foot when converting between inches and feet.

To convert a value or expression between two different forms. • Measurement: converting between different units, for as from inches to millimeters or liters to gallons. For instance, change 12 inches to millimeters. 304.8 millimeters are equal to 12 inches multiplied by the inch-to-millimeter ratio of 25.4.

Given Data

100 grams of honey  contains about 0.3 grams of protein.

1 gram = 1000 milligrams

To find milligrams in protein:

0.3 grams multiplied by 1000

0.3(1000)

300

300 milligrams is 0.3 grams of protein.

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Answer:

J. x = 1

Step-by-step explanation:

Write an equation based on the image of the scales.

3x + 6 = 9

Subtract 6.

3x = 3

Divide by 3.

x = 1

If you haven't learned to solve equations yet, the same thought process can be used with the scale image. The scales are balanced. To keep them balanced, remove 6 of the pieces marked "1" from BOTH sides of the scale. Then the scale will have three x's on one side and three "1"'s on the other side. So each x has to be one "1".

Answer:

George must run the last half mile at a speed of 6 miles per hour in order to arrive at school just as school begins today

Step-by-step explanation:

Here, we are interested in calculating the number of hours George must walk to arrive at school the normal time he arrives given that his speed is different from what it used to be.

Let’s first start at looking at how many hours he take per day on a normal day, all things being equal.

Mathematically;

time = distance/speed

He walks 1 mile at 3 miles per hour.

Thus, the total amount of time he spend each normal day would be;

time = 1/3 hour or 20 minutes

Now, let’s look at his split journey today. What we know is that by adding the times taken for each side of the journey, he would arrive at the school the normal time he arrives given that he left home at the time he used to.

Let the unknown speed be x miles/hour

Mathematically;

We shall be using the formula for time by dividing the distance by the speed

1/3 = 1/2/(2) + 1/2/x

1/3 = 1/4 + 1/2x

1/2x = 1/3 - 1/4

1/2x = (4-3)/12

1/2x = 1/12

2x = 12

x = 12/2

x = 6 miles per hour

The statement "the sum of the percent frequencies for all classes in a frequency distribution will always equal" is True.

The sum of the percent frequencies for all classes in a frequency distribution will always equal 100%. This is because the percent frequency for each class is calculated by dividing the frequency of that class by the total number of observations and then multiplying by 100. Therefore, when we add up all the percent frequencies for all the classes, we get the total percentage of observations, which must be 100%.

In a frequency distribution, percent frequencies are calculated by dividing the frequency of each class by the total number of observations and then multiplying by 100. Since all observations are accounted for in the distribution, the sum of the percent frequencies for all classes will always equal 100%.

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For f(4), it's 15. For determining x, it's 9.

For f(4), juet plug in 4 to x. 4(4) equals 16, minus 1 is 15.

For getting 35, we need to determine x. If you plug in 9 for f(x), 4(9) equals 36, minus 1 is 35.

The equation that shows an example of the associative property of addition is:

\(\((-7+i)+7i = -7 + (i+7i)\)\)

According to the associative property of addition, the grouping of numbers being added does not affect the result. In this equation, we can see that both sides of the equation represent the addition of three terms:

\(\((-7+i)\), \(7i\),\)  and  \(\(i\).\)  The equation shows that we can group the terms in different ways without changing the sum.

The equation  \(\((-7+i)+7i = -7 + (i+7i)\)\)  demonstrates the associative property by grouping  \(\((-7+i)\)\) and  \(\(7i\)\)  together on the left side of the equation, and  \(\(-7\)\) and  \(\((i+7i)\)\)  together on the right side of the equation. Both sides yield the same result, emphasizing the associative nature of addition.

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Answer: 6

Step-by-step explanation:

4+(x-3) = 2x-5

x+1 = 2x-5

x=6

A. Null hypothesis: The mean age of pine trees in Colorado is 30 years.

Alternative hypothesis: The mean age of pine trees in Colorado is greater than 30 years.

B. Null hypothesis: The mean age of people in the United States is 75 years.

Alternative hypothesis: The mean age of people in the United States is greater than 75 years.

C. Null hypothesis: The mean weight of trout in Lake Standard error is 3.4 pounds.

Alternative hypothesis: The mean weight of trout in Lake Standard error is different from 3.4 pounds.

D. Null hypothesis: The mean length of Acme Caterpillar Farm's award-winning caterpillars is 8 centimeters.

Alternative hypothesis: The mean length of Acme Caterpillar Farm's award-winning caterpillars is shorter than 8 centimeters.

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The given statement is 1. Always true

2. Always true

3. Always true

4. Sometimes true

5. Never true

Statement 1: A line and a point are always coplanar.

Answer: Always true.

Reason: This statement is always true because a line and a point can always be found on the same plane. In Euclidean geometry, a plane is a flat surface that extends infinitely in all directions, and any two points on the plane can be connected by a straight line. Therefore, a line and a point will always lie on the same plane.

Statement 2: Congruent angles form vertical angles.

Answer: Always true.

Reason: Vertical angles are formed by the intersection of two lines. When two angles are congruent, it means they have the same measure. If two angles have the same measure and are formed by the intersection of two lines, then they are vertical angles. Therefore, congruent angles always form vertical angles.

Statement 3: Linear pairs that are congruent are right angles.

Answer: Always true.

Reason: A linear pair consists of two adjacent angles that share a common side and form a straight line. If the two angles of a linear pair are congruent, it means they have the same measure. In Euclidean geometry, a straight angle measures 180 degrees. If two angles in a linear pair are congruent and their measures add up to 180 degrees, then each angle must measure 90 degrees, which is the measure of a right angle. Therefore, linear pairs that are congruent are always right angles.

Statement 4: The sum of angles that form a linear pair is less than 180 degrees.

Answer: Sometimes true.

Reason: The sum of angles that form a linear pair is always equal to 180 degrees, not less than 180 degrees. This is based on the definition of a linear pair, which states that the two angles in a linear pair are supplementary, meaning their measures add up to 180 degrees. However, if the statement said "less than or equal to 180 degrees," then it would be always true.

Statement 5: Vertical angles are complementary.

Answer: Never true.

Reason: Vertical angles are not complementary. Complementary angles are two angles that add up to 90 degrees. Vertical angles, on the other hand, are a pair of non-adjacent angles formed by the intersection of two lines. They do not necessarily have any specific relationship to each other in terms of their angle measures. Therefore, vertical angles are not complementary by definition.

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The truth of each statement depends on the properties of angles and theorems that support them. A line and a point are always coplanar, congruent angles can sometimes form vertical angles, congruent linear pairs are not always right angles, the sum of angles that form a linear pair is always 180 degrees, and vertical angles are never complementary.

To determine the truth of each statement, we need to consider the properties of angles and theorems that support them.

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you can either graph this or plug in values.

\(f(x)=3+\frac{1}{3}x\)

\(f(-1)=3+\frac{1}{3}(-1)\\\\f(-1)=3-\frac{1}{3}\\\\f(-1)=2\ \frac{2}{3}\\\\f(0)=3\\\\f(1)=3\ \frac{1}{3}\)

\(\therefore\) we can conclude that this function is linear.

Also here is a graph

Answer:

\(\left \{ {{6x+4y=76} \atop {x+y=16}} \right.\)

Step-by-step explanation:

1) if (according to the condition) the amount of quilting is 'x' and the amount of sateen is 'y', then the price of the quilting fabric is 6*x and the price of then sateen fabric is 4*y;

2) the 76$ she spends can be written as 6x+4y=76;

3) total of 16 yards can be written as x+y=16;

4) finally, the required system is:

\(\left \{ {{6x+4y=76} \atop {x+y=16}} \right.\)

A system of equations is a collection of two or more equations with a same set of unknowns. 4x+6y=76, x+y=16 are required system of equations.

A system of equations is a collection of two or more equations with a same set of unknowns.

According to the condition the amount of quilting is 'x' and the amount of sateen is 'y', then the price of the quilting fabric is 4x and the price of then sateen fabric is 6y;

the 76$ she spends can be written as 4x+6y=76;

Total of 16 yards can be written as x+y=16;

So the required system of Equations is:

4x+6y=76

x+y=16

Hence Option C is correct. 4x+6y=76, x+y=16.

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Answer:

Step-by-step explanation:

it’s 10 i think I tried :)

The whole number closest to √22 is 5.

The square root of 22 is:

= √22

= 4.69

The whole number that it is closest to will depend on the first decimal point.

If it is 5 or above then it will be closest to 5.

If it is 4 and below, then it is closest to 4.

The first decimal point is 6 so √22 is closer to 5.

In conclusion, the square root of 22 is closer to 5.

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The garden has a length of x + 8 units and a width of x - 4 units. This can be represented by:

Therefore, the area is given by:

The probability of getting one head and one tail on either coin, is 2/4 or 1/2. The Option A.

To get probability of getting one head and one tail, we have to consider all possible outcomes when flipping a penny and a dime.

Possible outcomes when flipping a penny and a dime:

Penny: Heads, Dime: Heads

Penny: Heads, Dime: Tails

Penny: Tails, Dime: Heads

Penny: Tails, Dime: Tails

Out of four possible outcomes, there are two outcomes where we get one head and one tail:

(2) Penny: Heads, Dime: Tails

(3) Penny: Tails, Dime: Heads.

So, he probability of getting one head and one tail, on either coin, is 2 out of 4.

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Answer:

The solution set is where the 2 lines intersect.

Step-by-step explanation:

Answer:

2.5 and -0.75

Step-by-step explanation:

i think i could be wrong x

Graphs aren't mandatory, but they may help visual learners see why an equation works a certain way. Also, they are a visual tool to quickly find a solution to a problem. Furthermore, they help with presentations to quickly convey an idea to someone (who may not be well versed in mathematics).

For example, if you save $10 a week and already have $50 in a savings account, then the equation you graph is y = 10x+50. Here x is the number of weeks and y is the amount saved.

Now let's say you want to find out how many weeks it would take to have $90 total. You could use guess and check to get the answer. Or you could use algebra and the substitution property. The visual way would be to graph y = 10x+50 and y = 90 together to note how the two lines intersect at (4, 90) to indicate it will take x = 4 weeks to have y = 90 total.

Answer:

a. the number is even or less than 12

Step-by-step explanation:

why ?

let's look at the logic of the statements :

a.

the number is even

true for 2, 4, 6, 8, 10

false for 3, 5, 7, 9

so, false in general.

but there is an "or" condition, which makes the true/false status of the first condition irrelevant, as false or true is always true, and false or false is always false.

and this "or" condition says "less than 12". that is true for all given numbers.

so, false or true = true is or result here.

b.

"neither prime nor composite" means "not prime and not composite". what else would there be ? this could only be true for an empty set of numbers. so, it is false here.

c.

"the number is greater than 2" is false for 2 and therefore false for the entire sample space (even though it is true for most of the numbers. but it is not true for all).

d.

"the number is not divisible by 5" is false for 5 and 10.

so, the same principles of c. apply.

Answer: answer above me is correct

The values of the missing sides are;

a.  x = 35. 6 degrees

b. x = 15

c. x = 22. 7 ft

d. x = 31. 7 degrees

To determine the values, we have;

a. Using the tangent identity;

tan x = 5/7

Divide the values

tan x = 0. 7143

x = 35. 6 degrees

b. Using the Pythagorean theorem

x² = 9² + 12²

find the square

x² = 225

x = 15

c. Using the sine identity

sin 29= 11/x

cross multiply the values

x = 11/0. 4848

x = 22. 7 ft

d. sin x = 3.1/5.9

sin x = 0. 5254

x = 31. 7 degrees

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If this claim is true then one percent of response times take at least \(38.077\) minutes.

In the given question,

A fire department in a rural county reports that its response time to fires is approximately normally distributed with a mean of 22 minutes and a standard deviation of 6.9 minutes.

We have to assuming that the claim is true and finding that one percent of response times take at least how many minutes.

From the question,

Mean \(\mu=22\) minutes

Standard deviation \(\sigma=6.9\) minutes.

Since the given percentage is \(1\%\) and percentage means division of \(100\) so we can write \(1\%=1/100=0.01\)

So the one percent of response times take at least how many minutes is

\(P(x\geq a)=0.01\)

\(P(x\geq \frac{a-\mu}{\sigma})=0.01\)

As we know the all values. SO putting the values in the formula

\(P(x\geq \frac{a-22}{6.9})=0.01\dots\dots\)Equation 1

From the z table

\(P(z\geq 2.33)=0.01\dots\dots\)Equation 2

Now from Equation 1 and Equation 2

\(\frac{a-22}{6.9}=2.33\)

Multiply by \(6.9\) on both side

\(\frac{a-22}{6.9}\times6.9=2.33\times6.9\)

Simplifying

\(a-22=2.33\times6.9\)

\(a-22=16.077\)

Add \(22\) on both side

\(a-22+22=16.077+22\)

\(a=38.077\)

Hence, if this claim is true then one percent of response times take at least \(38.077\) minutes.

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The probability of getting a value of χ2 less than or equal to 7.267 when ν = 10 is 0.05. Therefore, the correct option is: (b) ν = 10 : p ( χ 2 ≤ 7.267 )

To find the probabilities, we need to use the chi-squared distribution. The chi-squared distribution is a probability distribution that is used to test whether an observed distribution differs significantly from an expected distribution. It is commonly used in hypothesis testing and confidence interval estimation.

(a) For ν = 30 and p ( χ 2 ≥ 18.493 ), we can use a chi-squared table or a calculator to find the probability. Using a calculator, we get:

P(χ2 ≥ 18.493) = 0.0775

Therefore, the probability of getting a value of χ2 greater than or equal to 18.493 when ν = 30 is 0.0775.

(b) For ν = 10 and p ( χ 2 ≤ 7.267 ), we can use a chi-squared table or a calculator to find the probability. Using a calculator, we get:

P(χ2 ≤ 7.267) = 0.05

Therefore, the probability of getting a value of χ2 less than or equal to 7.267 when ν = 10 is 0.05.

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Answer:

Step-by-step explanation:

According to the midsegment theorem, the length of each side of the formed triangle is the half the parallel side of DEF.

So the perimeter is:

\(P= \dfrac{1}{2} (d + e + f)\)

\(P= \dfrac{1}{2} (12 + 16 + 20)\)

\(P= \dfrac{1}{2} (48)\)

\(P=\cancel{ \dfrac{1}{2} (48)}\)

\(\sf\red{P= 24}\)

ANSWER:

(c) y = 5

STEP-BY-STEP EXPLANATION:

We can calculate the value of y when x is equal to 1 graphically just like this:

Also by means of the equation:

The probability best prediction for the number of times that Ellen will draw a blue marble is 200.

Number of blue marbles: 222

Number of red marbles: 333

Total number of marbles: 555

Probability of drawing a blue marble:

222/555

= 0.4

Number of times drawing a blue marble:

300300300 x 0.4

= 120,120,120

Rounded to nearest whole number:

120,120

Ellen has a bag with 333 red marbles and 222 blue marbles in it. She is going to randomly draw a marble from the bag 300300300 times, putting the marble back in the bag after each draw. The best prediction for the number of times that Ellen will draw a blue marble is 200. This prediction is based on the fact that there are more red marbles than blue marbles in the bag. To calculate this, we first need to determine the probability of drawing a blue marble; there are 222 blue marbles out of 555 total marbles, so the probability is

222/555

= 0.4.

Multiplying this by the total number of draws (300300300) gives us 120,120,120. Rounding this to the nearest whole number gives us our prediction of 200 times.

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Answer:

= x - 2

Step-by-step explanation:

algebraically is:

x - 2

...

The sum of the infinite terms of a G.P. is (aᵣ / (1 - r))

A geometric progression (G.P.) is a sequence where each term is obtained by multiplying the preceding term by a constant ratio. The general term of a G.P. is given by the formula aₙ = aᵣ(r)^(n-1), where aᵣ is the first term and r is the common ratio.

The sum of infinite terms of a G.P. can be calculated using the formula Sₙ = a(1 - rⁿ) / (1 - r), where Sₙ is the sum of the first n terms of the G.P., a is the first term, and r is the common ratio.

As n approaches infinity, rⁿ approaches zero if the value of r is less than one. Hence, we can write the formula for the sum of infinite terms of a G.P. as S = a / (1 - r), provided that the value of r is less than one.

Therefore, the main answer can be written as the sum of the infinite terms of a G.P. is (aᵣ / (1 - r)), where aᵣ is the first term, and r is the common ratio.

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To determine how many pieces of the press must be purchased, we need to consider the production rate, operating hours, efficiency, and scrap rate.

Number of units processed per day = 10,000

Machine efficiency = 95%

Punching operation time = 10 seconds

Number of shifts per day = 2

Number of hours per shift = 8

To calculate the required number of presses, we can use the following formula:

Number of presses = (Number of units processed per day / (Machine efficiency * Number of shifts * Number of hours)) * (Punching operation time / 3600)

Number of presses = (10,000 / (0.95 * 2 * 8)) * (10 / 3600) = 52.08

Therefore, approximately 52 presses would be needed to meet the production requirements.

If the press has a scrap rate of 10%, we need to consider the effect of scrapped units on the required number of presses.

Number of scrapped units per day = 10,000 * 0.10 = 1,000

Number of units that can be reworked = 1,000 * 0.70 = 700

To modify the formula for the new scenario, we subtract the reworked units from the total units processed per day:

Number of units processed per day (after rework) = 10,000 - 700 = 9,300

Number of presses (after considering scrap and rework) = (9,300 / (0.95 * 2 * 8)) * (10 / 3600) = 48.48

Therefore, approximately 48 presses would be needed when considering the scrap rate and rework capability.

The new answer is different from Exercise 11 because the scrap rate reduces the effective production rate, resulting in a lower requirement for punch presses. By accounting for scrap and rework, the company can optimize its resource allocation and production planning to meet the desired output while considering the potential loss due to scrap.

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You have approximately 4 green apples out of the total 10 apples from the ratio of 3:5.

If there are 3:5 green apples out of a total of 10 apples, we can calculate the number of green apples by dividing the total number of apples into parts according to the given ratio.

First, let's determine the parts corresponding to the green apples. The total ratio of parts is 3 + 5 = 8 parts.

To find the number of green apples, we divide the number of parts representing green apples (3 parts) by the total number of parts (8 parts) and multiply it by the total number of apples (10 apples):

Number of green apples = (3 parts / 8 parts) * 10 apples

Number of green apples = (3/8) * 10

Number of green apples = 30/8

Simplifying the expression, we find:

Number of green apples ≈ 3.75

Since we cannot have a fraction of an apple, we need to round the value. In this case, if we consider the nearest whole number, the result is 4.

Therefore, you have approximately 4 green apples out of the total 10 apples.

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Based on the given values, the future value of the ordinary annuity would be approximately 1,278,524,283.54

Let's calculate the future value of the ordinary annuity using the provided values.

Given:

B = 1537 (starting amount)

E = 7 (interest rate)

D = 37 (compounding periods per year)

C = 537 (number of payments)

First, we need to convert the annual interest rate to a quarterly rate. Since the interest is compounded quarterly, we divide the annual rate by 4. So, the quarterly interest rate (r) is 7%/4 = 1.75%.

Next, we calculate the total number of compounding periods (n) by multiplying the compounding periods per year (D) by the number of payments (C). Therefore, n = D * C = 37 * 537 = 19,749.

Now, we can use the formula for the future value of an ordinary annuity:

FV = P * ((1 + r)^n - 1) / r

Substituting the values, we have:

FV = 1537 * ((1 + 0.0175)^19,749 - 1) / 0.0175

Therefore, based on the given values, the future value of the ordinary annuity would be approximately 1,278,524,283.54.

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