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Ming split her pops equally between four of her friends then bought 9 more.

Write an expression to show the number of pops she started with, p

Answer:

its 3.45 x 10^5

Step-by-step explanation:

The solution of the given expression will be 3.84 x 10⁻².

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is 3.99 x 10⁻² - 1.5 x 10⁻³. The expression will be solved as below:-

E = 3.99 x 10⁻² - 1.5 x 10⁻³

E = ( 3.99 x 0.15 ) x 10⁻²

E = 3.85 x 10⁻²

Therefore, the solution of the expression is 10⁻².

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Part A

Each triangle shown is a 45-45-90 triangle. The numbers refer to the angle measures. These types of triangles are known as isosceles right triangles.

The two legs of these triangles are the same length. So for this specific triangle, the two legs are 28 units each.

The hypotenuse can be found using the pythagorean theorem

\(a^2+b^2 = c^2\\\\c = \sqrt{a^2+b^2}\\\\m = \sqrt{28^2+28^2}\\\\m = \sqrt{2*28^2}\\\\m = \sqrt{2}*\sqrt{28^2}\\\\m = \sqrt{2}*28\\\\m = 28\sqrt{2}\\\\\)

We can avoid using the pythagorean theorem by remembering the rule that the hypotenuse is exactly sqrt(2) times that of either leg length.

\(\text{hypotenuse} = \text{leg}*\sqrt{2}\)

This shortcut only applies to 45-45-90 triangles.

Answer:  \(m = 28\sqrt{2}\)

=============================================================

Part B

Again we can use the pythagorean theorem to find the missing variable.

\(a^2+b^2 = c^2\\\\t^2+t^2 = 24^2\\\\2t^2 = 576\\\\t^2 = 576/2\\\\t^2 = 288\\\\t = \sqrt{288}\\\\t = \sqrt{144*2}\\\\t = \sqrt{144}*\sqrt{2}\\\\t = 12\sqrt{2}\\\\\)

Or we could follow the steps like this

\(\text{hypotenuse} = \text{leg}*\sqrt{2}\\\\\text{leg} = \frac{\text{hypotenuse}}{\sqrt{2}}\\\\\text{t} = \frac{24}{\sqrt{2}}\\\\\text{t} = \frac{24\sqrt{2}}{\sqrt{2}*\sqrt{2}}\\\\\text{t} = \frac{24\sqrt{2}}{2}\\\\t = 12\sqrt{2}\\\\\)

The second set of steps only apply for 45-45-90 triangles.

Answer: \(t = 12\sqrt{2}\\\\\)

=============================================================

Part C

Like mentioned earlier, the two leg lengths are the same.

Therefore, \(b = \frac{9\sqrt{2}}{2}\)

=============================================================

Part D

Multiply the leg lengths by the factor sqrt(2) to determine the hypotenuse

\(\text{hypotenuse} = \text{leg}*\sqrt{2}\\\\\text{J} = 30\sqrt{2}*\sqrt{2}\\\\\text{J} = 30*2\\\\\text{J} = 60\\\\\)

Or you could use the pythagorean theorem as an alternative route.

The solution to the equation is x = 7.

What is the linear equation in one variable?

A linear equation in one variable is an equation of the form ax + b = 0, where a and b are constants and x is the variable. The general form of a linear equation in one variable is ax + b = 0, where a and b are constants and x is the variable. The graph of a linear equation in one variable is a straight line.

The first step in solving the equation 2x - 4 = 10 using algebra tiles would be to add 4 to both sides of the equation to get 2x = 14. The next step would be to divide both sides of the equation by 2 to get x = 7.

Hence, the solution to the equation is x = 7.

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Answer: 39

Step-by-step explanation:

30-8=22

22/2=11

11+2=13

13 times 3 =39

Answer:

8n-5

Step-by-step explanation:

Find the difference between the numbers, +8 so 8n then subtract the diffference from the first number so 3 - 8= -5

The expression will be 8n - 5

Answer:

$8.91

Step-by-step explanation:

Multiply $4.95 times 0.80 ( convert 80% to a decimal ) and that will equal 3.96 .

Then , since you're marking it up , you're gonna add the 3.96 to 4.95 which will equal $8.91 .

:)

Andy would pay $23.94 more in finance charges compared to Brett, given their respective APRs, average daily balances, and monthly percentage rates.

To calculate the monthly percentage rate (MPR) from the given annual percentage rate (APR), we divide the APR by 12.

For Brett:

APR = 12.6%

MPR = 12.6% / 12 = 1.05%

For Andy:

APR = 16.2%

MPR = 16.2% / 12 = 1.35%

Next, we can calculate the finance charge for each individual using the formula: finance charge = average daily balance * MPR.

For Brett:

Finance charge = $7,980 * 1.05% = $83.79

For Andy:

Finance charge = $7,980 * 1.35% = $107.73

To find the difference in the finance charges between Andy and Brett, we subtract Brett's finance charge from Andy's finance charge:

Difference = $107.73 - $83.79 = $23.94

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Ending Inventory Cost and Cost of Goods Sold using different inventory methods:

FIFO Method:

Ending Inventory Cost: $11,920

Cost of Goods Sold: $15,068

LIFO Method:

Ending Inventory Cost: $11,996

Cost of Goods Sold: $15,123

Weighted Average Cost Method:

Ending Inventory Cost: $11,974

Cost of Goods Sold: $15,087

Using the FIFO (First-In, First-Out) method, the cost of the ending inventory is determined by assuming that the oldest units (those acquired first) are sold last. In this case, the cost of the ending inventory is calculated by taking the cost of the most recent purchases (70 units at $142 per unit) plus the cost of the remaining 10 units from the March 10 purchase.

This totals to $11,920. The cost of goods sold is calculated by taking the cost of the units sold (50 units from the Jan. 1 inventory at $124 per unit, 60 units from the March 10 purchase at $132 per unit, and 20 units from the August 30 purchase at $138 per unit), which totals to $15,068.

Using the LIFO (Last-In, First-Out) method, the cost of the ending inventory is determined by assuming that the most recent units (those acquired last) are sold first. In this case, the cost of the ending inventory is calculated by taking the cost of the remaining 10 units from the December 12 purchase, which amounts to $1,420, plus the cost of the 70 units from the August 30 purchase, which amounts to $10,576.

This totals to $11,996. The cost of goods sold is calculated by taking the cost of the units sold (50 units from the Jan. 1 inventory, 60 units from the March 10 purchase, and 20 units from the August 30 purchase), which totals to $15,123.

Using the Weighted Average Cost method, the cost of the ending inventory is determined by calculating the weighted average cost per unit based on all the purchases. In this case, the total cost of all the purchases is $46,360, and the total number of units is 200.

Therefore, the weighted average cost per unit is $231.80. Multiplying this by the 80 units in the physical inventory at December 31 gives a total cost of $11,974 for the ending inventory. The cost of goods sold is calculated by taking the cost of the units sold (50 units from the Jan. 1 inventory, 60 units from the March 10 purchase, and 20 units from the August 30 purchase), which totals to $15,087.

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The expressions 1 and 4 are having values less than 1.

Given are the expressions, we need to solve them,

1) -7 · 1/2 - 4

= -7/2-4

= -7-8 / 2

= -15/2

= -7.5 < 1

2) -7 · (1/2 - 4)

= -7 · -7/2

= 49/2

= 24.5 > 1

3) -7 · 1/2 · (- 4)

= -14/2 · (- 4)

= 56/2

= 28 > 1

4) -7 + 1/2 · (- 4)

= -7 -4/2

= -7 -2

= -9 < 1

5) -7 ÷ 1/2 · (- 4)

= -7 × 2 × -4

= -14 × -4

= 56 > 1

Hence, the expressions 1 and 4 are having values less than 1.

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The volume of the figure with two rectangular prisms would be 1, 728 ft ³

.

To find the volume of the figure with the two rectangular prisms, you can find the volume of the individual rectangular prisms and then add them up.

Volume of rectangular prism 1:

= Length x Width x Height

= 19 x 12 x 6

= 1, 368 ft ³

Volume of rectangle prism 2:

= Length x Width x Height

= 10 x 12 x 3

= 360 ft ³

The volume of the entire figure is then :

= 1, 368 + 360

= 1, 728 ft ³

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Answer:

12.5pages

Step-by-step explanation:

50pages ×6hours=300 and then we divide by 8 to get 37.5(the number of pages printed by david in 6 hours)

subtract 37.5 from 50 to find the number of pages printed by andy

Answer:

x is 44 because

3x+4+x=180

4x=180-4

4x=176

x=44

Answer:

sohcahtoa

sine=opposite/hypotenuse

cosine=adjacent/hypotenuse

tangent=opposite/adjacent

I don't know what else to say

A) The algebraic expression will be 12d + 7 = 91

B) He drives 7 miles per day to work.

For 11 days straight, Ms. Chung drove the same distance every day going to and coming from work.

The distance she drove on Saturday was; 0.9 miles.

The number of miles she drives per day:

84 miles/12

= 7 miles per day

Let the number of miles she travels be day = d

12d + 7 = 91 miles

12d + 7 = 91

12d = 91 - 7

12d = 84

d = 84/12

d = 7 miles per day

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Answer:

It will ALWAYS be true!

Step-by-step explanation:

Inputting any real or imaginary numbers such as i or e, (which are also known as complex numbers), and when put in the place of x will ALWAYS equal one another. You could put 1, 2, 3, etc. all the way up to infinity and still get the two equations equal to each other.

Hope this helped!

Answer:

Step-byHow do I calculate the mean?

The mean can be calculated only for numeric variables, no matter if they are discrete or continuous. It's obtained by simply dividing the sum of all values in a data set by the number of value

-step explanation:

46+57+66+63+49+52+61+68= 462/8 the total number of observation

the answer 57

All sides of a rhombus have equal measures, so TU = 8. Since a rhombus is a parallelogram, and the diagonals of a parallelogram bisect each other, WU = 10. The diagonals of a rhombus are also perpendicular, meaning they form right angles. Using the Pythagorean theorem, you can find the length of TX. (TX)^2 + (WX)^2 = (WT)^2. Substituting in known values, (TX)^2 + 25 = 64. Solving gives you TX = the square root of 39. TV is double the length of TX, so TV = 2 times the square root of 39.

The effect that does NOT relate to one's driving ability is breathalyzer test results indicating a high BAC. Option B.

While the breathalyzer test measures the blood alcohol concentration (BAC), it is a method used to determine the level of alcohol in a person's system and is commonly used in assessing impairment for driving under the influence.

Therefore, it directly relates to one's driving ability and is not excluded from the effects on driving ability caused by a BAC of .2 percent.

On the other hand, options, lack of coordination, impaired gross motor skills, and impaired reactions all directly relate to one's driving ability as they affect the physical and cognitive abilities necessary for safe and efficient driving.

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Answer:

0.9851 = 98.51% probability that the person is actually infected.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which

P(B|A) is the probability of event B happening, given that A happened.

\(P(A \cap B)\) is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Positive test

Event B: Infected

Probability of a positive test:

99% of 25%(People have the disease).

0.5% of 100 - 25 = 75%(People do not have the disease). So

\(P(A) = 0.99*0.25 + 0.005*0.75 = 0.25125\)

Probability of a positive test and being infected:

99% of 25%, so:

\(P(A \cap B) = 0.99*0.25 = 0.2475\)

What is the probability that the person is actually infected?

\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.2475}{0.25125} = 0.9851\)

0.9851 = 98.51% probability that the person is actually infected.

Answer:

The juice bar can sell 3 more cups of the passion juice than the berry juice (last one)

Step-by-step explanation:

Passion: 768/16=48

Berry: 810/18=45

passion can fill 48 cups while berry can fill 45 cups, so passion fills +3

:)

Area of the plot = 193 sq.yd.  , Option B is the correct answer.

Area is the space occupied by a flat surface or an object .

It is measured in square units

It has wide daily life importance like in the question mentioned , a plot will be measured in area of the space.

It is given that

A developer buys an empty lot to build a small house.

area of the lot = ?

The figure is incomplete and the complete figure is attached with the answer.

To determine the area the figure needs to be divided into triangles and rectangles as shown in the figure

Area of the first triangle = (1/2) * base * height

By Calculation

base = 17 unit and height = 10 unit

= (1/2) * 17 * 10

= 17*5

=85 sq.unit

Area of the second triangle = (1/2)* 9* 8

=36 sq. unit

Area of the rectangle = base * height

base = 9 unit and height = 7 unit

Area = 9*7= 63 sq.unit

Area of the last triangle = (1/2) * 2*9

= 9 unit

The area of the plot = 85+36+63+9

Area of the plot = 193 sq.yd.

Therefore , Option B is the correct answer.

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Answer:

Step-by-step explanation:

Area of the plot = 193 sq.yd.  , Option B is the correct answer.

What is Area ?

Area is the space occupied by a flat surface or an object .

It is measured in square units

It has wide daily life importance like in the question mentioned , a plot will be measured in area of the space.

It is given that

A developer buys an empty lot to build a small house.

area of the lot = ?

The figure is incomplete and the complete figure is attached with the answer.

To determine the area the figure needs to be divided into triangles and rectangles as shown in the figure

Area of the first triangle = (1/2) * base * height

By Calculation

base = 17 unit and height = 10 unit

= (1/2) * 17 * 10

= 17*5

=85 sq.unit

Area of the second triangle = (1/2)* 9* 8

=36 sq. unit

Area of the rectangle = base * height

base = 9 unit and height = 7 unit

Area = 9*7= 63 sq.unit

Area of the last triangle = (1/2) * 2*9

= 9 unit

The area of the plot = 85+36+63+9

Area of the plot = 193 sq.yd.

Therefore , Option B is the correct answer.

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Flint is starting a business. Before starting to sell anything, he bought fixtures for £1,200, a van for £6,000 and an inventory of goods for £2,800. Although he has paid in full for the fixtures and the van, he still owes £1,600 for some of the inventory. B. Rub lent him £2,500. After the above, Flint has £200 in the business bank account and £175 cash in hand. Total capital is £10,375

What do you mean by capital?

Any employed financial asset might be considered capital. A company's capital is represented on its balance sheet as the earnings from its ongoing operations. The money in a bank account, the proceeds from the sale of stock shares, and the proceeds from the sale of bonds are a few examples.

A factory and its equipment, intellectual property like patents, or the financial assets of a company or a person are all examples of things that provide value or benefit to their owners and fall within the broad definition of capital.

Fixtures= £1,200, van= £6,000, inventory of goods= £2,800, cash =£375

So, Total assets= £10,375

Payable=  £1,600, loan from Rub= £2,500, Balancing figure= £6,275

Total liabilities= £10,375

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Solution,

Change in water level is \(1\dfrac{1}{2}\ \text{inches}=\dfrac{3}{2}\ \text{inches}\)

The water level of a lake fell by \(1\dfrac{1}{2}\)  inches  during a \(1\dfrac{2}{3}\ \text{or}\ \dfrac{5}{3}\)week-long dry spell.

Average rate at which the water level changed  every week is given by :

\(R=\dfrac{1\dfrac{1}{2}}{1\dfrac{2}{3}}\\\\R=\dfrac{\dfrac{3}{2}}{\dfrac{5}{3}}\\\\R=\dfrac{3}{2}\times \dfrac{3}{5}\\R=\dfrac{9}{10}\\\\R=0.9\)

Hence, the average rate is 0.9 every week.

The equation for the proportion, p, of consumers who shop with coupons is: p = C/N where C is the number of consumers who use coupons and N is the total number of consumers asked.

An equation is a mathematical statement that indicates the equality of two expressions. It consists of two expressions separated by an equal sign (=). The expression on the left side of the equal sign is equivalent to the expression on the right side. Equations can have one or more variables, which are usually represented by letters such as x, y, or z. The goal in solving an equation is to determine the value(s) of the variable(s) that make the equation true. This involves manipulating the expressions on both sides of the equal sign using algebraic operations such as addition, subtraction, multiplication, and division, to isolate the variable on one side of the equation. Equations are used in many areas of mathematics and science to represent relationships between variables and to solve problems. They are also used in various fields such as engineering, physics, and economics to model real-world situations and make predictions based on mathematical analysis.

Here,

This equation represents the ratio of the number of consumers who use coupons to the total number of consumers. It is commonly used in statistics and market research to measure the prevalence of a certain behavior or preference among a population. By calculating the proportion of consumers who use coupons, businesses can make informed decisions about their pricing strategies, promotions, and advertising campaigns.

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The cups of each ingredient we will need are

Flour = 21 cups

Water = 9 cups

Sugar = 6 cups

Butter = 3 cups

What is proportion?

In general, the term "proportion" refers to a part, share, or amount that is compared to a whole. According to the definition of proportion, two ratios are in proportion when they are equal. Two ratios or fractions are equal when an equation or a declaration to that effect is utilized.

Given that, a recipe requires ingredients of Flour, Water, Sugar, and Butter in the ratio 7:3:2:1 respectively

Also, given that after mixing all the ingredients we got 39 cups of batter.

Let the number of ingredients be 7x, 3x, 2x, and x cups.

The total will be 7x + 3x + 2x + x = 13x cups = 39 cups

13x = 39

x = 3

7x = 21

3x = 9

2x = 6

x = 3

Therefore, the required ingredients are Flour, Water, Sugar, and Butter 21, 9, 6, and 3 cups respectively.

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If Q is an orthogonal matrix with an eigenvalue λ1 = 1, then x, the eigenvector corresponding to λ1, is also an eigenvector of QT with an eigenvalue λ2 = λ1 * (QT * x).

To show that x is also an eigenvector of QT, we need to demonstrate that QT * x is a scalar multiple of x.

Given that Q is an orthogonal matrix, we know that QT * Q = I, where I is the identity matrix. This implies that Q * QT = I as well.

Let's denote x as the eigenvector corresponding to the eigenvalue λ1 This means that Q * x = λ1 * x.

Now, let's consider QT * x. We can multiply both sides of the equation Q * x = λ1 * x by QT:

QT * (Q * x) = QT * (λ1 * x)

Applying the associative property of matrix multiplication, we have:

(QT * Q) * x = λ1 * (QT * x)

Using the fact that Q * QT = I, we can simplify further:

I * x = λ1 * (QT * x)

Since I * x equals x, we have:

x = λ1 * (QT * x)

Now, notice that λ1 * (QT * x) is a scalar multiple of x, where the scalar is λ1. Therefore, we can rewrite the equation as:

x = λ2 * x

where λ2 = λ1 * (QT * x).

This shows that x is indeed an eigenvector of QT, with the eigenvalue λ2 = λ1 * (QT * x).

In conclusion, if Q is an orthogonal matrix with an eigenvalue λ1 = 1, then x, the eigenvector corresponding to λ1, is also an eigenvector of QT with an eigenvalue λ2 = λ1 * (QT * x).

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Step-by-step explanation:

-6 (3 - 8r) = 18

-18+48r = 18

48r = 18 + 18

48r = 36

r = 36/48

r = ¾

Answer:

y=2x-3

Step-by-step explanation: