Luis uses 1.6 liters of gasoline each hour he spends mowing lawns. How much gas does he use in 5.8 hours?


can someone please help me? I'm really not a fan of the subject math, and I'm currently struggling and my math grade isn't good at the moment AND grade book closes next week friday :(

Answer:

slope=3 and put points on (1,3) and (2,6) to graph

Step-by-step explanation:

Answer:

The slope is 3

Plot these two points on the graph: (1,3) and (4,12)

Step-by-step explanation:

Slope = y2-y1/x2-x1

Let's find two ordered pairs

(1,3)     (2,6)

x1y1     x2y2

6-3/2-1 = 3/1 = 3

The slope is 3

To graph, plot these two points on the graph:

(1,3) and (4,12)

Be sure you connect them

Hope this helps :)

If a sample of seven infants is randomly selected and their weights at birth are recorded as 23.1, 29.1, 30.1, 30.1, 27.1, 34.1, and 34.1 pounds. Then the sample standard deviation is  127.88

Standard Deviation: It gives the error of a given experiment. It shows how the much the mean value is deviate from the original value

x=(mean)=23.1+29.1+30.1+30.1+27.1+34.1+34.1/7 = 29.671

x²= (mean)²=880.368

(mean²)=23.1²+29.1²+30.1²+30.1²+27.1²+34.1²+34.1²/7

           = 533.61+846.81+906.01+906.01+1162.81+1162.81/7

           =120636.25/7

           =17233.75

Standard deviation=\(\sqrt{(mean^2)-(mean)^2}\)

                              =√16353.382

                              =127.88

Therefore the If a sample of seven infants is randomly selected and their weights at birth are recorded as 23.1, 29.1, 30.1, 30.1, 27.1, 34.1, and 34.1 pounds. Then the sample standard deviation is  127.88

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Answers in bold:

S9 = 2

i = 20

R = -2

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

Explanation:

\(S_0 = 20\) is the initial term because your teacher mentioned \(A_0 = I\) as the initial term.

Then R = -2 is the common difference because we subtract 2 from each term to get the next term. In other words, we add -2 to each term to get the next term.

Here is the scratch work for computing terms S1 through S4.

\(\begin{array}{|l|l|}\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{1} = S_{1-1} - 2 & S_{2} = S_{2-1} - 2\\S_{1} = S_{0} - 2 & S_{2} = S_{1} - 2\\S_{1} = 20 - 2 & S_{2} = 18 - 2\\S_{1} = 18 & S_{2} = 16\\\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{3} = S_{3-1} - 2 & S_{4} = S_{4-1} - 2\\S_{3} = S_{2} - 2 & S_{4} = S_{3} - 2\\S_{3} = 16 - 2 & S_{4} = 14 - 2\\S_{3} = 14 & S_{4} = 12\\\cline{1-2}\end{array}\)

Then here is S5 though S8

\(\begin{array}{|l|l|}\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{5} = S_{5-1} - 2 & S_{6} = S_{6-1} - 2\\S_{5} = S_{4} - 2 & S_{6} = S_{5} - 2\\S_{5} = 12 - 2 & S_{6} = 10 - 2\\S_{5} = 10 & S_{6} = 8\\\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{7} = S_{7-1} - 2 & S_{8} = S_{8-1} - 2\\S_{7} = S_{6} - 2 & S_{8} = S_{7} - 2\\S_{7} = 8 - 2 & S_{8} = 6 - 2\\S_{7} = 6 & S_{8} = 4\\\cline{1-2}\end{array}\)

And finally we arrive at S9.

\(S_{n} = S_{n-1} - 2\\\\S_{9} = S_{9-1} - 2\\\\S_{9} = S_{8} - 2\\\\S_{9} = 4 - 2\\\\S_{9} = 2\\\\\)

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

Because we have an arithmetic sequence, there is a shortcut.

\(a_n\) represents the nth term

S9 refers to the 10th term because we started at index 0. So we plug n = 10 into the arithmetic sequence formula below.

\(a_n = a_1 + d(n-1)\\\\a_n = 20 + (-2)(n-1)\\\\a_n = 20 - 2(n-1)\\\\a_{10} = 20 - 2(10-1)\\\\a_{10} = 20 - 2(9)\\\\a_{10} = 20 - 18\\\\a_{10} = 2\\\\\)

In other words, we start with 20 and subtract off 9 copies of 2 to arrive at 20-2*9 = 20-18 = 2, which helps see a faster way why \(S_9 = 2\)

In the next 10 years there will be 398 racoons in the state park

The annual increase in the population size is defined as a sum of differences: the difference between births less deaths and the difference between immigrants less emigrants, in a given country, territory or geographic area at a given year.

Using the formula

p(t) = p(o) e^ kt

k = 3.5/100 = 0.035

t = 10 years

p(t) = 280 e^ 0.035 ×10

p(t) = 280e^0.35

p(t) = 280 × 1.42

p(t) = 398( nearest whole number)

therefore be after 10 years there will be 398 racoons in the state park.

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The given system of equations is:

\(\displaystyle\sf \begin{align}2x - y &= -4\\3x - 2y &= -6\end{align}\)

To solve this system, we can use the method of elimination or substitution. Let's use the method of elimination:

First, we'll multiply the first equation by 2 to make the coefficients of \(\displaystyle\sf y\) in both equations equal:

\(\displaystyle\sf \begin{align}4x - 2y &= -8\\3x - 2y &= -6\end{align}\)

Now, we can subtract the second equation from the first equation to eliminate the variable \(\displaystyle\sf y\):

\(\displaystyle\sf (4x - 2y) - (3x - 2y) = -8 - (-6)\)

Simplifying the expression:

\(\displaystyle\sf x = -2\)

Now that we have found the value of \(\displaystyle\sf x\), we can substitute it back into either of the original equations to solve for \(\displaystyle\sf y\). Let's substitute it into the first equation:

\(\displaystyle\sf 2(-2) - y = -4\)

Simplifying the expression:

\(\displaystyle\sf -4 - y = -4\)

Solving for \(\displaystyle\sf y\):

\(\displaystyle\sf -y = 0\)

\(\displaystyle\sf y = 0\)

Hence, the solution to the system of equations is \(\displaystyle\sf x = -2\) and \(\displaystyle\sf y = 0\).

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♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

The average rate of change, in simplest form, is -2/5.

What is average rate ?

Divide the change in y-values by the change in x-values to determine the average rate of change. Identifying changes in quantifiable parameters like average speed or average velocity calls for the knowledge of the average rate of change.

The rate of change of the function is its gradient or slope.

The formula for calculating the gradient of a function is expressed as:

\(m=\frac{d y}{d x}=\frac{y_2-y_1}{x_2-x_1}$$\)

Using the coordinate points from the table (0,41) and (15,35)

Substitute the coordinate into the expression:

\($$\begin{aligned}& m=\frac{35-41}{15-0} \\& m=\frac{-6}{15} \\& m=\frac{-2}{5}\end{aligned}$$\)

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Answer:

90

Step-by-step explanation:

To find how many 18-inch pieces of ribbon there are in 1620 inches, simply divide 1620 by 18.

1620/18 = 90

For the original question, we know that each roll of ribbon is 9 feet long. To convert to inches, multiply 9 by 12.

9*12 = 108

Now, to find how many 18-inch pieces of ribbon there are in 108 inches,  divide 108 by 18.

108/18 = 6

Since we have 15 rolls of ribbon, multiply 6 by 15.

6*15 = 90

∴ The dressmaker can cut ninety 18-inch pieces from 15 rolls or ribbon.

Answer:

A) - 54.48

Step-by-step explanation:

Just plug it into the calculator like this;  (-68.1) x 0.8, which equals -54.48.

the answer is negative because you multiplied a positive # and a negative #.

Answer:

(x + 9) (x - 7)

Step-by-step explanation:

when we put x + 9 = 0 then x = -9 as it's the root of the fuction.

same thing here: x - 7 = 0 then x = 7

Answer:

0

Step-by-step explanation:

The total number of events is

45+37+52+94+72 = 300

P(purple) = purple/total

               = 0/300

                 =0

Answer:

C; multiply 4 to both sides

Step-by-step explanation:

When you want to solve for a variable, you always want to isolate it.

So, to move 4, we have divide:

\(\frac{A}{4}\) = \(\frac{4r}{4}\).

The 4 in 4r is "one'd" out, and now we have 1r, or simply r.

Now, we have r = A/4

Answer:

(a) 13 824cm³

(b) 452.16cm³

(c) 13 371.84cm³

Step-by-step explanation:

Formulas (For easier reference):

Volume of cubic box = length³

Volume of ball = \(\pi\) × radius²

Radius = \(\frac{diameter}{2}\)

We just have to put in the formulas.

Volume of box = 24³

                         = 13 824cm³

Volume of ball = 3.14 × (\(\frac{24}{2}\))²

                        = 3.14 × 144

                        = 452.16cm³

Remaining space = 13 824cm³ - 452.16cm³

                             = 13 371.84cm³

Answer:

F     n= -5.4

U     p = 45

Step-by-step explanation:

-5.2 + n = -10.6

n = -5.4

7 = - 38 + p

p = 45

Answer:

F.-5.2+n=-10.6

n=-10.6+5.2

n=-5.4

u.7=-38+p

p=38+7

p=45

Explanation:

Amount = 28.97

coupo

To show that (βa)^(-1) = 1/β A^(-1), we can use the definition of the inverse of a matrix.

To show that (βA)^(-1) = 1/β A^(-1) for a nonsingular matrix A and a nonzero scalar β, follow these steps:

1. Let's consider a nonsingular matrix A and a nonzero scalar β.
2. Multiply both sides of the equation by (βA).

On the left side, we have:
(βA)(βA)^(-1)

On the right side, we have:
(βA)(1/β A^(-1))

3. Apply the property of inverse matrices:

(βA)(βA)^(-1) = I, where I is the identity matrix.

4. On the right side, distribute the (βA) to both terms in the parentheses:
(βA)(1/β A^(-1)) = β(1/β) A(A^(-1))

5. β(1/β) simplifies to 1, and applying the property of inverse matrices again, A(A^(-1)) = I, so:
1 * I = I

Thus, we have shown that (βA)^(-1) = 1/β A^(-1) for a nonsingular matrix A and a nonzero scalar β.

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3.40 and 15

Step-by-step explanation:

3 for 1.50 means 1 is 50 cents each.

5 oranges for 3 dollars mean each one is 60 cents.

So this equation is 4(.60)+2(.50)

=3.40

For the swimming problem,

divide the 2 and 5 and you should get 2.5.

Multiply 2.5 by 6 to get 15.

Here are the answers for the missing blanks

(2.5, 1) (5, 2) (7.5, 3) (10, 4) (12.5, 5)

The answer is  True, the percentile rank identifies the percentile of a particular value within a set of data.

The percentile rank is a measure that identifies the percentage of scores in a distribution that are equal to or lower than a given score. It is calculated by dividing the number of scores that are equal to or lower than the given score by the total number of scores in the distribution, and multiplying the result by 100 to obtain a percentage. The percentile rank can be used to compare individual scores to the rest of the distribution, and can provide useful information about the relative standing of a score within a particular group or population. Therefore, it is true that the percentile rank identifies the percentile of a particular value within a set of data.

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Answer:

46

add all the number together and divide by how many there is

Answer: 0 bottles of Brand X and 10 bottles of Brand Y

(please let me know if I read the question wrong and I will do my best to fix it)

Step-by-step explanation:

This problem can be solved using linear programming. Let x be the number of Brand X bottles and y be the number of Brand Y bottles. The objective is to minimize the cost, given by:

Cost = 25x + 15y

Subject to the following constraints, which represent the minimum nutrient requirements:

3x + 9y ≥ 30 (Nutrient A)

3x + 2y ≥ 16 (Nutrient B)

7x + 2y ≥ 24 (Nutrient C)

x ≥ 0, y ≥ 0 (Non-negativity constraint)

We can solve this system of inequalities graphically by finding the feasible region and the corner points.

Nutrient A constraint (3x + 9y ≥ 30):

Divide the inequality by 3:

x + 3y ≥ 10

Nutrient B constraint (3x + 2y ≥ 16):

Divide the inequality by 2:

1.5x + y ≥ 8

y ≥ 8 - 1.5x

Nutrient C constraint (7x + 2y ≥ 24):

Divide the inequality by 2:

3.5x + y ≥ 12

y ≥ 12 - 3.5x

Now we will graph the inequalities on the xy-plane:

y ≥ 10 - x/3

y ≥ 8 - 1.5x

y ≥ 12 - 3.5x

The feasible region is the area where all three inequalities are satisfied. It's a triangular region with corner points A(0,10), B(4,4), and C(8/3, 2).

Now we need to find the cost at each corner point:

Cost A (0, 10) = 25(0) + 15(10) = $150

Cost B (4, 4) = 25(4) + 15(4) = $160

Cost C (8/3, 2) = 25(8/3) + 15(2) ≈ $153.33

The minimum cost is $150, which occurs when 0 bottles of Brand X and 10 bottles of Brand Y are used. So, the public aquarium should add 0 bottles of Brand X and 10 bottles of Brand Y to satisfy the needs of the reef tank at the minimum possible cost.

Answer:

-64x^6

Step-by-step explanation:

The value of a = -2 and b = 3.

What is a system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

Here, we have

Given: 3a - 5b = -26, a + 2b = 6

We have to solve this equation.

3a - 5b = -26...(1)

a + 2b = 6...(2)

Now we multiply equation (1) by 2 and equation (2) by 5 and we get

6a - 10b = -52....(3)

5a + 10b = 30....(4)

After solving equations (3) and (4), we get

11a = -22

a = -2

Now we put the value of 'a' in equation(3) and we get

6(-2) - 10b = -52

-10b = -52 + 12

-10b =  -30

b = 3

Hence, the value of a = -2 and b = 3.

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Answer:

The answer is C

BC=EF

Step-by-step explanation:

A statement which is necessary to prove that the two (2) triangles are congruent by the SAS criterion is: C. BC = EF.

A triangle can be defined as a two-dimensional (2D) geometric shape that has three (3) sides, three (3) angles and three (3) vertices.

Based on the side, angle, side (SAS) criterion, a statement which is necessary to prove that the two (2) triangles are congruent is that side BC must be equal to side EF because angle ABC is equal to angle DFE.

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Concept

Name the sides and apply the Pythagoras theorem to find the third side.

Opposite = 12 cm

Hypotenuse = 14 cm

Adjacent = m

Next,

Substituting opposite and hypotenuse to get the adjacent.

Find the square root of both sides

Final answer

Other leg = 7.2 cm

Answer:

see below

Step-by-step explanation:

a) They could be congruent because having the same angles doesn't necessarily mean that they are congruent.

b) These triangles are  congruent by ASA because using the sum of angles in a triangle they have the same angles and one congruent side.

Answer:

a) F

b) C

Step-by-step explanation:

Brainliest please?

For a) it only tells you all the angles, which makes them similar triangles, but none of the sides are given, so it cannot be determined whether they are congruent.

For b) it is not to scale and using a little subtraction, you can quickly use the fact that there are 180 degrees in a triangle, you can determine that the 2 triangles have the same angles, with the side with 9.2 cm between 58 and 68 degree vertices on both triangles, making the 2 triangles congruent by ASA.

QED

The relationship between distance and travel time. It is not excessively strong or weak. In other words, the rate of change in journey time is moderate and constant with respect to distance.

positive negative moderate weak linear nonlinear relationship between distance and travel time can be described as follows:•

           Positive• Linear• Moderate

   Explain as we move from point A to point B, the distance covered and the travel time it takes to get there are positively correlated. As the distance increases, the travel time required to reach the destination also increases, resulting in a positive correlation.

          The relationship between distance and travel time is linear because the rate at which distance is covered remains constant, resulting in a straight-line relationship on a graph. It means that if distance doubles, the travel time will also double, indicating a linear relationship.

Hence, the linear relationship is also referred to as a direct relationship. On a graph, the line that represents the relationship between distance and travel time is moderate. This implies that the slope of the line is neither too steep nor too gentle.

               Thus, it is neither too strong nor too weak. In other words, the rate of change in travel time is consistent as distance changes, making it moderate.

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Answer:

1/10

Step-by-step explanation:

0.01 as a fraction is 1/100

now we take the square root of 1, which is 1 and

we take the square root of 100, which is 10 to get

the answer of 1/10

Answer:

80.2

Step-by-step explanation:

Answer:80.2

Step-by-step explanation:

i did the test so yeh edg 2023