(no. 7) Write an equation in point-slope form for the line that has a slope of 1/3 and passes through (–2, 8).

Answer:

x + 5y ≤ 30

Step-by-step explanation:

The intervals of each behavior of the function are given as follows:

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The cost of gas is proportional to the volume of gas because a constant rate of $3.15 to 1 gallon of gas.

From the given table;

The volume of the first gas Layla bought = 3 gallons.

The cost of the 3 gallons = 9.45

Therefore the cost of 1 gallon = ?

That is:

3 gallons = $9.45

1 gallon = X

Make X the subject of formula:

X = 9.45/3 = $3.15

Therefore, the cost of 11 gallons of gas would be = 11×3.15 = $34.65. This is because the cost of 1 gallon would be = $3.15.

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Using the inequality rule we know that 11 is greater than -11, (11 > -11).

Mathematical expressions with inequalities are those in which the two sides are not equal.

Contrary to equations, we compare two values in inequality.

Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Two expressions in inequality aren't always equal, which is denoted by the symbols >, <, ≤, or ≥.

So, let's say the inequality equation looks like this: A

Right now, A is valued at

Let p be used to representing the initial number.

P equals 11, so

Let q be used to representing the second number.

Q has a value of -11.

-11 and 11 are both numbers that are greater than zero.

Then, 11 > -11 ... (1)

A has a value of 11 > -11.

Therefore, using the inequality rule we know that 11 is greater than -11, (11 > -11).

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Correct question:
Is 11 greater than, equal to, or less than -11?

Answer: Carat

Step-by-step explanation:

It is given that 1 atomic unit is equivalent to

\(8.3\times 10^{-24}\ \text{carat}\) and \(1.66\times 10^{-21}\ mg\)

Express carat and milligram in the atomic mass unit, that is

\(1\ \text{amu}\equiv 8.3\times 10^{-24}\ \text{carat}\\1\ \text{carat}\equiv \dfrac{1}{8.3\times 10^{-24}}=1.204\times 10^{23}\ amu\)

For milligram

\(1\ \text{amu}\equiv 1.66\times 10^{-21}\ mg\\1\ mg\equiv \dfrac{1}{1.66\times 10^{-21}}=6.02\times 10^{20}\ \text{amu}\)

clearly, carat is greater than milligram

Step-by-step explanation:

Area of the trapezoid = height x average of bases

                 area = 4 x (8+13)/2) = 42 in^2

Area of triangle  = 1/2 base * height   = 1/2 (13-8) * 4 = 10 in^2

Answer:

A. A reflection over the line x = 6

Step-by-step explanation:

You can see in the picture if you follow the line every edge has the same

Number x=6

Answer:

15x + 24y <= 120

Step-by-step explanation:

It takes 15 minutes per oil change, 15x

It takes 24 minutes per tire change, 24y

In at most 120 minutes, so it must be less than or equal to the time available.

Answer:

24

Step-by-step explanation:

For the denominators (2, 8, 6, 1) the least common multiple ( LCM ) is 24. Therefore, the least common denominator ( LCD ) is 24.

Answer: 1

Step-by-step explanation:thats what i got

The radius of the gear should be approximately 2.8644 inches.It is important to note that when making calculations involving units, we need to make sure that all units are consistent and convert them when necessary. In this case, we converted the answer from feet to inches to match the given unit.

To find the radius of the gear that will pull a chain at 60 ft/min when rotating at 40 rev/min, we can use the formula:

chain speed = 2 x pi x radius x rotational speed

where pi is a mathematical constant approximately equal to 3.14.

We know that the chain speed is 60 ft/min and the rotational speed is 40 rev/min, so we can substitute those values into the formula:

60 = 2 x 3.14 x radius x 40

Simplifying the equation, we get:

radius = 60 / (2 x 3.14 x 40)

radius = 0.2387 ft

To convert feet to inches, we can multiply the answer by 12:

radius = 0.2387 x 12 = 2.8644 inches.

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The domain value that corresponds to a range value of 4 is,

⇒ x = 1/2

Given that;

Function is,

y = 4x + 2

Since, the equation equal to the range value:

4 = 4x + 2

Then, we can solve for "x":

4 - 2 = 4x

2 = 4x

x = 1/2

Now that we have the value of "x", we can find the corresponding value of "y" by substituting it into the given equation:

y = 4x + 2

y = 4(1/2) + 2

y = 4 + 2

y = 6

Therefore, the domain value that corresponds to a range value of 4 is,

⇒  x = 1/2

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Answer:

p=1/8     q=3/4

Step-by-step explanation:

-2p+7q=5

-6p+35q=51/2

cancel out a variable

(-5)(-2p+7q=5)

-6p+35q=51/2

10p-35q=-25

-6p+35q=51/2  =

4p=1/2

4p/4=1/2  /4

p=1/8

substitute p=1/8 into one of the equation to find q

-2p+7q=5

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

-1/4+7q=5

7q=5+1/4

7q=21/4

q= 21/4  /7

q=3/4

The probability that both players show rock in the first round is 1/9 or 0.1111 (rounded to four decimal places).

In rock, paper, scissors there are three possible outcomes for each player: rock, paper, or scissors. Assuming both players choose randomly and independently of each other, each player has a 1/3 chance of showing rock in the first round.

To find the probability that both players show rock in the first round, we can use the multiplication rule of probability for independent events. The multiplication rule states that the probability of the intersection of two independent events is the product of their probabilities.

Therefore, the probability that both players show rock in the first round can be calculated as follows:

P(both show rock) = P(player 1 shows rock) x P(player 2 shows rock) P(both show rock) = 1/3 x 1/3 P(both show rock) = 1/9

So the probability that both players show rock in the first round is 1/9 or approximately 0.111.

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The volume of the sphere is approximately 3431.82 cubic miles.

To find the volume of a sphere, we need the radius of the sphere. The length of a great circle is the circumference of the sphere, which is related to the radius by the formula C = 2πr, where C is the circumference and r is the radius.

In this case, we are given that the length of the great circle is 60 miles. We can use this information to find the radius of the sphere.

C = 2πr

60 = 2πr

Divide both sides of the equation by 2π:

r = 60 / (2π)

r = 30 / π

Now that we have the radius, we can use the formula for the volume of a sphere:

V = (4/3)πr³

V = (4/3)π(30/π)³

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)(27000/π²)

V = (4/3)(27000/9.87) (approximating π to 3.14)

V ≈ 3431.82 cubic miles

Therefore, the volume of the sphere is approximately 3431.82 cubic miles.

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Question

You are given the great circle of a sphere is a length of 60 miles. What is the volume of the sphere?

Answer:

NO

Step-by-step explanation:

substitute x=3  into the equation

2(3)+3

=9

Therefore x=3 is not a solution

Answer:

No, it is not a solution.

Step-by-step explanation:

x = 3

8 = 2x + 3

8 = 2 (3) + 3

8 = 6 + 3

8 ≠ 9

1) The independent variable is ''Day'' shown in x - axis.

2) Days shows on x - axis are incorrectly arranged.

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

We have to given that;

The graph is shown in graph.

On the graph;

Day is shown in x - axis.

And, Earnings shown in y - axis.

Now, We know that;

The independent variable is shown in x - axis.

Hence, The independent variable is Day.

And, One wrong thing in graph is,

Days shows on x - axis are incorrectly arranged.

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answer:

74

Step-by-step explanation:

The sample size for the given confidence interval is 96.

A range of estimates for an unknown parameter is called a confidence interval (CI). A confidence level calculates a confidence interval; The most common confidence level is 95 percent. The confidence level is the percentage of corresponding CIs that contains the actual value of the parameter over time.

Given confidence of margin is at 95%

E = 0.1 = margin of error

95% confidence interval of Z = 1.96

sample size = n, which is given by

n = (Z/E)²(p)(1 - p)

n = (1.96/0.1)²(0.5)(0.5)

n = 96.04 = 96 approx

Hence, the sample size is 96.

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How to get that answer:

If order mattered, then there would be 8*7*6 = 336 different permutations of sauces. I started with 8 and counted down by 1 until three slots were filled.

That 336 value would be the answer if order mattered; however, it does not matter. For any grouping of three, there are 3*2*1 = 6 ways to order that specific group. This indicates the 336 is too large by a factor of 6.

To fix this, we divide by 6 and we get 336/6 = 56

There are 56 ways to pick the 3 brands from the 8 overall brands to choose from.

Answer:

(48, 3), (80, 5), (160, 10)

Answer:

X = 1.3

Step-by-step explanation:

Answer:

I think you need to know the value of X to get this answer.

Step-by-step explanation:

(a) To meet the desired 20g protein and 80g carbohydrate intake, prepare 4 servings of Pork & Beans and combine with 15 slices of "lite" rye bread.

(b) Bread: A/4 slices, Beans: B/21 - (A/4) * (12/21) servings.

(a) To prepare a meal of "beans-on-toast" that supplies 20 grams of protein and 80 grams of carbohydrates, you can use the following combination:

- Servings of Campbell's Pork & Beans: 4 servings.

- Slices of "lite" rye bread: 15 slices.

By using 4 servings of Campbell's Pork & Beans, you will obtain a total of 20 grams of protein (5 grams per serving) and 84 grams of carbohydrates (21 grams per serving).

Combining this with 15 slices of "lite" rye bread will contribute an additional 60 grams of carbohydrates (12 grams per slice) and 4 grams of protein (4 grams per slice). Thus, your meal will meet the desired nutritional requirements of 20 grams of protein and 80 grams of carbohydrates.

(b) The formula to determine the number of slices of bread and servings of Pork & Beans needed to meet specific protein and carbohydrate requirements is as follows:

- Number of slices of bread (Bread): A divided by 4.

- Number of servings of Pork & Beans (Beans): (B divided by 21) minus ((A divided by 4) multiplied by (12 divided by 21)).

Using this formula, you can calculate the appropriate quantities of bread and beans based on the desired protein (A) and carbohydrate (B) values.

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Answer:

  -1.9

Step-by-step explanation:

The opposite of the opposite is the original number, -1.9.

It is located at -1.9 on the number line.

Answer:

a

Step-by-step explanation:

Analyze the different intervals at which the function takes the values provided by the graph. Pay special attention on the circles, whether they are filled up or not.

From the graph, notice that the function takes the value of 3 when x is equal to -4, -2 or any number between them. Therefore, the condition is:

If x is greater (but not equal) than -2 and lower or equal to 3, the function takes the value of 5. Therefore:

Finally, the function takes the value of -3 whenever x is greater (but not equal) to 3 and less than or equal to 5. Then:

Since our assumption holds for all values between 6 and k, and we have shown it also holds for k+1, we can conclude by strong induction that it is possible to cut a square into n smaller squares for any n ≥ 6.

To prove this using strong induction, we will first establish a base case and then prove that if the statement holds true for any value k, then it also holds true for k+1.
Base Case: n = 6
Divide the square into four equal smaller squares by drawing two lines, one vertical and one horizontal, each passing through the center.

Then, divide one of these smaller squares into two equal rectangles by drawing a line parallel to the side.

We have now divided the original square into 6 smaller squares.
Inductive Step:
Assume the statement is true for all values n = 6, 7, ..., k,

where k ≥ 6.

We want to prove that the statement is true for n = k+1.
Consider a square that is divided into k smaller squares.

We will show that it is possible to divide this square into k+1 smaller squares.

Choose one of the k squares and label it S.

If S is a rectangle, divide it into two smaller squares by drawing a line parallel to the shorter side.

If S is a square, divide it into two equal rectangles by drawing a line through the center parallel to a side.
In either case, we have replaced one of the original k squares with two smaller squares, resulting in a total of k+1 squares.

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The required two column proof is explained below.

A midpoint is a point which divides a line segment into two equal parts. Thus it can be referred to as the middle point of the line segment.

The two column proof for the information is given as:

M is the midpoint of CD    (Given)

CD = CM + MD   (addition property of a line segment)

CM = MD  (definition of a midpoint)

So that;

5x – 2 = 3x + 2    (Definition of midpoint)#

Then,

5x - 3x = 2 + 2 (collecting like terms)

2x = 4

x = 2

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Answer: Sam was 2.5 Km far from his house

Step-by-step explanation:

Sam's parents gave him a map to reach his house.

As per Map Sam was =1.5cm from his home.

To find actual distance from house

If we consider actual distance  of sam house =X

We have,

If each 3 cm on scale drawing equals 5 km

We know on map 3cm  = 5Km

If 1.5 cm = X Km

We need to cross multiple

 3X =1.5 × 5

 3X = 7.5

X= 7.5÷3

X= 2.5 Km

Sam was 2.5 Km far from his house.

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If the dilation is centered at the origin, determine the vertices of polygon A′B′C′D′ are: D. A′(−2.4, 3.6), B′(−1.2, 1.2), C′(2.4, −1.2), D′(2.4, 2.4).

In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.

Next, we would have to dilate the coordinates of the preimage by using a scale factor of 3/5 centered at the origin as follows:

Ordered pair A (-4, 6) → Ordered pair A' (-4 × 3/5, 6 × 3/5) = Ordered pair A' (-2.4, 3.6).

Ordered pair B (-2, 2) → Ordered pair B' (-2 × 3/5, 2 × 3/5) = Ordered pair B' (-1.2, 1.2).

Ordered pair C (4, -2) → Ordered pair C' (4 × 3/5, -2 × 3/5) = Ordered pair C' (2.4, -1.2).

Ordered pair D (4, 4) → Ordered pair D' (4 × 3/5, 4 × 3/5) = Ordered pair D' (2.4, 2.4).

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