What is the slope of the line that passes through the points
(4, -3) and (8, -2)?

Answer:You will need to buy 1/2 a pound of cashews and 1/2 a pound of peanuts

Set D ∈ {76, 90, 92, 94, 96}

Sets are groups of clearly defined objects or elements in mathematics. A set is denoted by a capital letter, and the cardinal number of a set is enclosed in a curly bracket to indicate how many members there are in a finite set.

As per the given data:

Set D consists of positive two-digit even numbers greater than 74 without the digit 8 in them.

For writing set D in the roster form:

For greater than 74:

{76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98}

Without the digit 8:

{76, 90, 92, 94, 96}

Hence, Set D ∈ {76, 90, 92, 94, 96}

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The coordinates of the point on the directed line segment from (-7, 9) to (3, -1) that partitions the segment into a ratio of 2 to 3 are (-3, 5).

To find the coordinates of the point that divides the directed line segment from (-7, 9) to (3, -1) into a ratio of 2 to 3, we can use the section formula.

Let's label the coordinates of the desired point as (x, y). According to the section formula, the x-coordinate of the point is given by:

x = (2 * 3 + 3 * (-7)) / (2 + 3) = (6 - 21) / 5 = -15 / 5 = -3

Similarly, the y-coordinate of the point is given by:

y = (2 * (-1) + 3 * 9) / (2 + 3) = (-2 + 27) / 5 = 25 / 5 = 5

Therefore, the coordinates of the point that divides the line segment in a ratio of 2 to 3 are (-3, 5).

To understand this conceptually, consider the line segment as a distance from the starting point (-7, 9) to the ending point (3, -1). The ratio of 2 to 3 means that the desired point is two-thirds of the way from the starting point and one-third of the way from the ending point. By calculating the x and y coordinates using the section formula, we find that the desired point is located at (-3, 5).

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Answer: Let x be the number of bottles of lemonade and y be the number of juice boxes.

The cost of x bottles of lemonade is 2x dollars.

The cost of y juice boxes is 0.5y dollars.

The total cost of the drinks is the sum of the cost of the bottles of lemonade and the cost of the juice boxes:

2x + 0.5y ≤ 100

So the correct inequality that models this situation is:

(3) 2x + 0.50y ≤ 100

Therefore, Peter can spend no more than $100 on drinks, which includes the cost of the bottles of lemonade and the juice boxes.

Step-by-step explanation:

Answer:

part A - 256 stickers

part B - 8 stickers each

Step-by-step explanation:

hope this helps

Answer:

a) 256

b) 8

Step-by-step explanation:

a) as it says in the question, each box contains 64 stickers. Mrs Kim bought 4 boxes , so she has 4 times more than a single box (64 stickers)

The calculation is simple: 64 x 4, which equals 256

b) If there are 256 stickers all-together and she has 32 people to share them equally with, you have to divide 256 by 32 to see how many stickers each person will get:

256 ÷ 32 = 8

Answer:

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

The total cost is the cost for a can of gas plus rental cost per number of hours.

So the total cost is:

The value of matrix A is \(A =\left[\begin{array}{cc}0&4\\-8&12\end{array}\right]\)

The given parameters are:

\(\lambda_1 = 4\) at \(v_1 = \left[\begin{array}{c}1&1\end{array}\right]\)

\(\lambda_2 = 8\) at \(v_2 = \left[\begin{array}{c}1&2\end{array}\right]\)

The matrix A is calculated using:

A = S ∧ S⁻¹

Where:

\(S = \left[\begin{array}{cc}v_1&v_2\end{array}\right]\)

\(\lambda = \left[\begin{array}{cc}\lambda_1&0\\0&\lambda_2\end{array}\right]\)

\(\lambda =\left[\begin{array}{cc}4&0\\0&8\end{array}\right]\)

Next, we have:

\(S = \left[\begin{array}{cc}v_1&v_2\end{array}\right]\)

This gives

\(S =\left[\begin{array}{cc}1&1\\1&2\end{array}\right]\)

Calculate the determinant of S

|S| = 1 * 2 - 1 * 1

|S| = 1

So, the inverse of S is:

\(S^{-1} = \frac{1}{1} * \left[\begin{array}{cc}2&-1\\-1&1\end{array}\right]\\\)

Evaluate

\(S^{-1} = \left[\begin{array}{cc}2&-1\\-1&1\end{array}\right]\\\)

Recall that:

A = S ∧ S⁻¹

So, we have:

\(A =\left[\begin{array}{cc}1&1\\1&2\end{array}\right] * \left[\begin{array}{cc}4&0\\0&8\end{array}\right] * \left[\begin{array}{cc}2&-1\\-1&1\end{array}\right]\)

Multiply the first two matrices

\(A =\left[\begin{array}{cc}1 * 4 + 1 * 0&1 * 0 + 1 * 8\\1 * 4 + 2 * 0&1 * 0 + 2 * 8\end{array}\right] * \left[\begin{array}{cc}2&-1\\-1&1\end{array}\right]\)

Evaluate

\(A =\left[\begin{array}{cc}4&8\\4&16\end{array}\right] * \left[\begin{array}{cc}2&-1\\-1&1\end{array}\right]\)

Evaluate the product

\(A =\left[\begin{array}{cc}4*2+8*-1&4 * -1 + 8 * 1\\4 * 2 + 16 * -1&4 * -1 + 16 * 1\end{array}\right]\)

Evaluate

\(A =\left[\begin{array}{cc}0&4\\-8&12\end{array}\right]\)

Hence, the value of matrix A is \(A =\left[\begin{array}{cc}0&4\\-8&12\end{array}\right]\)

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The area of the shaded region is 73.5 cm square.

Supposing that there is no direct formula available for deriving the area, we can derive the area of that region by dividing it into smaller pieces, whose area can be known directly. Then summing all those pieces' area gives us the area of the main big region.

We are given the dimension of the shaded region.

Length = 15 cm

Breadth = 7 cm

The area of the trapezium is

Area = 1/2(sum of non parallel sides)height

Area = 1/2 (12 + 9) 7

Area = 1/2 x 21 x 7

Area = 73.5

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Answer:

n=4

Step-by-step explanation:

The Dividend per Shareholder in 2017 is $20.

As, Dividend per Shareholder = Profit / Number of Shareholders

Since the number of shareholders is assumed to have remained unchanged during the period 2017-2020, we can calculate the dividend per shareholder in 2017 using the profit value for that year.

Based on the given table, the profit for 2017 is $7,000.

Dividend per Shareholder in 2017

7000/x = 15500 / 44.29

7000/x = 349.966

x = 7000/349.966

x= 20.01

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Answer:  $1.40

Work Shown:

x = cost before markup

1.45x = cost after the 45% markup

1.45x = 2.03

x = (2.03)/(1.45)

x = 1.40

Answer:

3 and 4!!

hope this helps!!!

1. 80 people attended only the FSU-Butler game.

2. 165. Since it's not possible to have negative number of people, the answer is 0.

3. 210 people attended at least two of these games.

4. 340 people attended the Marist and Butler games, but not the North Carolina State game.

5. 365 people attended the North Carolina State or the Butler game

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Answer:

24 : 15 : 20

Step-by-step explanation:

express ratios in fractional form and express b and c in terms of a

\(\frac{a}{b}\) = \(\frac{8}{5}\) ( cross- multiply )

8b = 5a ( divide both sides by 8 )

b = \(\frac{5}{8}\) a

also

\(\frac{b}{c}\) = \(\frac{3}{4}\) ( cross- multiply )

3c = 4b ( divide both sides by 3 )

c = \(\frac{4}{3}\) b = \(\frac{4}{3}\) × \(\frac{5}{8}\) a = \(\frac{5}{6}\) a

Then

a : b : c

= a : \(\frac{5}{8}\) a : \(\frac{5}{6}\) a ( multiply each part by 24, the LCM of 8 and 6 )

= 24a : 15a : 20a ( divide each part by a )

= 24 : 15 : 20 ← in simplest form

Answer:

the answer should be C.

Step-by-step explanation:

When two straight lines intersect each other at 90˚ or are perpendicular to each other at the intersection, they form the right angle. A right angle is represented by the symbol ∟.

Jupiter's model diameter will be 280 mm, if the real diameter is 142,984km?.

Proportion can be referred to as a part, share, or number considered in comparative relation to a whole. Proportion is defined as when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

real diameter : model diameter

12,756 : 25

142,984 : x

where x is the model diameter of jupiter

x = (25 x 142,984) / 12,756

x = 280 mm

Therefore, the model diameter of Jupiter is 280mm

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The fare for a 500-mile trip is 164.

The equation provided in the question is known as a linear equation. A linear equation is an equation that has a single variable that is raised to the power of one.

The general form of a linear equation is:

y = mx + b

Where:

In the equation used to calculate the fare, y=0.28x+24, 0.28 is the variable cost and 24 is the fixed cost.

Cost of a 500-mile trip = y=0.28(500) +24

y = 140 + 24

y = 164

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The probability that the student got an 'A' given they are male is approximately 0.12 or 12%.

To find the probability that a student got an 'A' given they are male, we need to use Bayes' theorem:

P(A | Male) = P(Male | A) × P(A) / P(Male)

We can find the values of the terms in the formula using the information given in the table:

P(Male) = (25/54) = 0.46 (the proportion of all students who are male)

P(A) = (17/54) = 0.31 (the proportion of all students who got an 'A')

P(Male | A) = (3/17) = 0.18 (the proportion of all students who are male and got an 'A')

Therefore, plugging these values into the formula:

P(A | Male) = 0.18 × 0.31 / 0.46

P(A | Male) ≈ 0.12

So the probability that the student got an 'A' given they are male is approximately 0.12 or 12%.

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Answer:

it's 60

Step-by-step explanation:

i say that because that triangle equals to 180

so 93+30 is 123 so u -123 from 180 and it gives u 60.

The expression that is equivalent to StartRoot \(8 x^7 y^8\) EndRoot is (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2.

To understand why this is the case, let's break down each expression and simplify them step by step:

StartRoot \(8 x^7 y^8\) EndRoot:

We can rewrite 8 as \(2^3\), and since the square root can be split over multiplication, we have StartRoot \((2^3) x^7 y^8\) EndRoot. Applying the exponent rule for square roots, we get StartRoot \(2^3\) EndRoot StartRoot \(x^7\) EndRoot StartRoot \(y^8\) EndRoot.

Simplifying further, we have 2 StartRoot \(2 x^3 y^4\) EndRoot StartRoot \(2^2\) EndRoot StartRoot \(x^2\) EndRoot StartRoot \(y^4\) EndRoot. Finally, we obtain 2 \(x^3 y^4\) StartRoot 2 x EndRoot, which is the expression in question.

(\(2 x y^2\) StartRoot 8 x^3 EndRoot)^2:

Expanding the expression inside the parentheses, we have \(2 x y^2\)StartRoot \((2^3) x^3\) EndRoot. Applying the exponent rule for square roots, we get \(2 x y^2\) StartRoot \(2^3\) EndRoot StartRoot \(x^3\) EndRoot.

Simplifying further, we have \(2 x y^2\) StartRoot 2 x EndRoot. Squaring the entire expression, we obtain (\(2 x y^2\) StartRoot 2 x EndRoot)^2.

Therefore, the expression (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2 is equivalent to StartRoot \(8 x^7 y^8\) EndRoot.

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Answer: The usual dose for an 18-month-old weighing 21 pounds is 48 mg of ibuprofen.

Step-by-step explanation: To find the usual dose of ibuprofen for a child, we need to follow these steps:

Therefore, the usual dose for an 18-month-old weighing 21 pounds is 48 mg of ibuprofen. Hope this helps, and have a great day! =)

As per the histogram the mean of data set to be larger than the median

The infant mortality rate is an important measure of the health of a country, as it reflects the number of deaths of infants under the age of one year per 1,000 live births.

The histogram below shows the distribution of estimated infant death rates for 222 countries in 2012.

The median of a data set is the value that separates the lower half of the data from the upper half. It can be estimated from the histogram by finding the middle value of the data set, or the point at which half of the data points fall below it and half fall above it.

In the histogram, the median is estimated to be around 25, as there are roughly equal numbers of countries with infant mortality rates below and above this value.

The first quartile (Q1) is the value that separates the lowest 25% of the data from the rest of the data, while the third quartile (Q3) separates the top 25% of the data from the rest. In the histogram, Q1 is estimated to be around 10 and Q3 is estimated to be around 40.

It is common for the mean of a data set to be larger or smaller than the median, depending on the distribution of the data. In the case of the infant mortality rate histogram, it is possible that the mean may be larger than the median, as the data is likely to be skewed towards higher values due to outliers.

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Step-by-step explanation:

step 1. x + 51 + 39 + 127 = 360 (1 revolution is 360°)

step 2. x + 90 + 127 = 360

step 3. x + 127 = 270. (subtract 90 on both sides)

step 4. x = 143° (subtract 127 on both sides)

The amount of dry ingredients used in the cake recipe is approximately 7 cups.

We have,

3 ½ cups of flour, 2 ⅔ cups of sugar, and 1 ¾ cups of cocoa.

Now, first convert all quantity in same unit.

3 ½ cups of flour

= 3 cups + 0.5 cups

= 3 cups and 8 ounces.

and, 2 ⅔ cups of sugar

= 2 cups + 0.67 cups,

= 2 cups and 10.72 ounces.

and, 1 ¾ cups of cocoa

=1 cup + 0.75 cups

= 1 cup and 12 ounces.

So, the total amount

= 3 cups and 8 ounces + 2 cups and 10.72 ounces + 1 cup and 12 ounces = 6 cups and 14.72 ounces

= 7 cups

Therefore, the amount of dry ingredients used in the cake recipe is approximately 7 cups.

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\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 9000\\ P=\textit{original amount deposited}\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &4 \end{cases}\)

\(9000 = P\left(1+\frac{0.04}{4}\right)^{4\cdot 4} \implies 9000=P(1.01)^{16} \\\\\\ \cfrac{9000}{(1.01)^{16}}=P\implies \boxed{7675.39\approx P}\)

Answer:

  (b)  22 in

Step-by-step explanation:

You want the perimeter of a rectangle with side lengths 4 inches and 7 inches.

The perimeter of a rectangle is the sum of the lengths of its sides. Your rectangle has two sides that are 4 inches, and two sides that are 7 inches. The perimeter is the sum of these lengths:

  P = 4 in + 4 in + 7 in + 7 in

  P = 22 in

The perimeter of the rectangle is 22 inches.

__

Additional comment

We can save a math operation by recognizing the sum can be arranged to ...

  P = (4 in +7 in) +(4 in +7 in) = 2(4 in +7 in)

This is evaluated using one sum and one product, rather than the three sums we need if we simply add the lengths of the four sides.

This is why the usual formula for the perimeter of a rectangle is ...

  P = 2(L +W)

Answer: $19.26  which is rounded to $19

Step-by-step explanation:

To get the answer shown above you must add 18 + 7%. We're adding both because the question provided asks to find the total cost.