Write the equations 1.-reflect across x axis-up 3 units-left 4 units

The mass of one art book is 0.8 kg, and the mass of one biology book is 0.6 kg

Let's denote the mass of one art book by "a" and the mass of one biology book by "b".

From the given information, we have two equations:

6a + 4b = 7.2 (equation 1)

2a + 3b = 3.4 (equation 2)

We can solve for "a" and "b" by using any method of solving linear equations, such as substitution or elimination.

Here, we'll use elimination method. Multiplying equation 2 by 3 and subtracting it from equation 1 multiplied by 2, we get:

12a + 8b - (6a + 9b) = 14.4 - 10.2

6a - b = 4.2 (equation 3)

Multiplying equation 2 by 2, we get:

4a + 6b = 6.8 (equation 4)

Multiplying equation 3 by 6, we get:

36a - 6b = 25.2 (equation 5)

Adding equations 4 and 5, we get:

40a = 32

a = 0.8 kg

Substituting this value of "a" in equation 2, we get:

2(0.8) + 3b = 3.4

1.6 + 3b = 3.4

3b = 1.8

b = 0.6 kg

Therefore, the mass of one art book is 0.8 kg, and the mass of one biology book is 0.6 kg.

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Answer:

The formula that is used to calculate the surface area of a triangular prism is, Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area) = (S1 + S2+ S3)L + bh; where 'b' is the bottom edge of the base triangle, 'h' is the height of the base triangle, L is the length of the prism and S1, S2 and S3 ...

Answer:

22/27

Step-by-step explanation:

There are 27 students and 11 play basketball and 13 play basketball and 5 play neither.

I realized a problem is that 11+13+5≠27, so I assumed some people play both sports.

If 5 don't play either sport, then 22 play Baseball or basketball.

22/27 play baseball or basketball,

So the probability is 22/27.

This may not be correct because of the problem mentioned earlier or there is something wrong with the problem, but hopefully, I helped.

Answer: 10.4

Step-by-step explanation:

(10x - 4) ÷ 5 = 20

             * 5    * 5

10x - 4 = 100

     + 4    + 4

10x = 104

/ 10   / 10

x = 10.4

Answer:

800, 8000

Step-by-step explanation:

8*10=80*10=800, 8*10=80*100=8000

Im not exactly sure as to what the question you are asking or what lesson this is from but I hope this helped being the closest and only way I could answer this, terribly sorry if this wasn't the correct solution

Answer: 0.0135

0.0009563758

0.00835

The expression or equation to represent the number of hat each shelter will receive is h = 1600 / 4

Algebraic expressions are the mathematical statement that we get when operations such as addition, subtraction, multiplication, division, etc. are operated upon on variables and constants.

To represent the amount each local shelter will receive, we can write an expression for that while the variable is present

The number of hats can be found by dividing the total number of hats collected by the number of local shelters.

Estimating the number of hats

1596 ≅ 1600

Number of hats (h) = 1600 / 4

h = 400

Each local shelter will receive 400 hats

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9514 1404 393

Answer:

  y = -2x +2

Step-by-step explanation:

The slope is the y-change divided by the x-change:

  m = (y2 -y1)/(x2 -x1)

  m = (0 -2)/(1 -0) = -2

The y-intercept is the y-value when x=0: b = 2.

The slope-intercept equation is ...

  y = mx +b

  y = -2x +2

The sum that Mahesh borrowed was Rs. 22,800, the interest that Mahesh has to pay was Rs. 6,492, the interest that Rakesh has to pay was Rs. 7,550, and the percentage by which Rakesh pays more interest than Mahesh was 16.3%.

a) Sum borrowed by Mahesh

Let us suppose that the principal sum borrowed by Mahesh from the bank at 9% per annum is Rs. x.

Hence, we can write that

Simple Interest = (P × R × T )/ 100

= (x × 9 × 3)/100

= 27x/100

Therefore, the amount that Mahesh has to pay after 3 years, including the interest, is

A = P + SI

= x + 27x/100

= 127x/100

Again, Mahesh invests the same amount of Rs. x to Rakesh at 10% per annum, which is compounded annually, for three years.

Hence, the total amount after three years that Rakesh has to pay Mahesh is:

Amount after 3 years = x (1 + R/100)³

= x (1 + 10/100)³ = 1.331 x

Therefore, Mahesh made a profit of Rs. 7,550 by investing Rs. x at 10% per annum, compounded annually, for three years.

Hence, we can write that

Compound Interest = Amount - Principal

CI = 1.331x - x = 0.331x

Therefore, 0.331x = Rs. 7,550=>

x = Rs. 22,800

Thus, Mahesh borrowed Rs. 22,800 from the bank.

b) Interest that Mahesh has to pay

Interest = P × R × T/100

= Rs. 22,800 × 9 × 3/100 = Rs. 6,492

Therefore, Mahesh has to pay Rs. 6,492 as interest.

c) Interest that Rakesh has to pay

The total amount that Rakesh has to pay to Mahesh is Rs. 30,350 [= (22,800 + 7,550)].

Therefore, interest that Rakesh has to pay = Total Amount - Principal

= Rs. 30,350 - Rs. 22,800 = Rs. 7,550

Therefore, Rakesh has to pay Rs. 7,550 as interest.

d) Percentage by which Rakesh pays more interest than Mahesh

Let us calculate the percentage difference between the interest paid by Rakesh and the interest paid by Mahesh.

Thus, the percentage difference can be calculated as

% Difference = (|Interest paid by Rakesh - Interest paid by Mahesh|/ Interest paid by Mahesh) × 100

% Difference = (|7,550 - 6,492|/6,492) × 100

% Difference = 16.3%

Therefore, Rakesh pays more interest than Mahesh by 16.3%.

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In a graph of a rectangular hyperbola, the X- axis and the y -axis are the asymptotes of the function.

A rectangular hyperbola is a type of conic section that has two branches, and each of these two branches of the hyperbola is shaped like a rectangle. The graph of the hyperbola is as if the graph was formed by 4 U letters.

The asymptotes of a hyperbola are the lines that the two branches approach as they extend indefinitely in either direction.

In the case of a rectangular hyperbola, these lines are perpendicular to each other and intersect at the center of the hyperbola.

Thus, in this special case, the x-axis and x-axis of the graph are the asymptotes of the rectangular hyperbola.

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A human-factors expert recommends that there be at least 9 square feet of floor space in a college classroom for every student in the class. The minimum floor space that 18 students require is 162 square feet.

What do you mean by human factor?

Environmental, organizational, and job elements as well as human and individual qualities that have an impact on behavior at work and could jeopardize health and safety are referred to as "human factors."

9ft²=1student

xft²=18 students

   9ft²            xft²

_______=_________

1student   18 students

Cross multiply

1x=162

divide both sides by 1

x=162ft²

Hence the correct answer is 162ft²

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The solution is Option A.

The values of x that makes the inequality equation x² + 5x > 6 is -6 < x < 1

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

x² + 5x > 6   be equation (1)

Now , on simplifying the equation , we get

Subtracting 6 on both sides of the equation , we get

x² + 5x - 6 > 0

On factorizing the equation , we get

x² + 6x - x - 6 > 0

Taking the common terms in the equation , we get

x ( x + 6 ) - 1 ( x + 6 ) > 0

( x - 1 ) ( x + 6 ) > 0

So , the values of x are

x + 6 > 0

Subtracting 6 on both sides of the equation , we get

x > -6  

And ,

x - 1 < 0

Adding 1 on both sides of the equation , we get

x < 1

So , the inequality equation is true when x < 1 and when x > -6

Hence , the inequality equation is -6 < x < 1

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Answer:

\(\text{27}\)

Step-by-step explanation:

Given that :

\(\text{Dimension of poster board} = 1 \ \text{yd} \ \text{by} \ 1 \ \text{yd}\)

\(\text{Dimension of each poster board} = \dfrac{1}{3} \ \text{yd} \ \text{by} \ \dfrac{1}{9} \ \text{yd}\)

Number of poster signs that can be cut :

\(\text{Area of poster sign} = \dfrac{1}{3} \times \dfrac{1}{9} = \dfrac{1}{27} \ \text{yard}^2\)

\(\text{Area of poster board} = 1 \ \text{yard}^2\)

Number of poster signs that can be cut :

\(\dfrac{\text{Area of poster board}}{\text{Area of poster sign}}\)

\(1 \ \text{yard}^2\div (\dfrac{1}{27} ) \ \text{yard}^2\)

\(1 \div \dfrac{1}{27}\)

\(1 \times \dfrac{27}{1}\)

\(\bold{= 27 \ poster \ signs}\)

Answer:

Step-by-step explanation:

Infinite solution

Answer: maybe a

Step-by-step explanation:

Answer:

2,260.80 cubic millimeters

Step-by-step explanation:

The figure is made up of a cylinder and a sphere which has been cut in half. The radius of each half sphere is 6 mm. What is the volume of the composite figure? Use 3.14 for Pi. Round to the nearest hundredth. A cylinder and 2 half spheres. All have a radius of 6 millimeters. The cylinder has a height of 12 millimeters. Recall the formulas V = B h and V = four-thirds pi r cubed 527.52 cubic millimeters 1,431.84 cubic millimeters 2,034.72 cubic millimeters 2,260.80 cubic millimeters

Answer:

\(Range = 11\)

\(\sigma^2 = 12.1\)

\(\sigma = 3.5\)

Step-by-step explanation:

Given

\(Data: 16,12,17,8,15,15,10,11,19,18\)

Solving (a): Range

This is calculated as:

\(Range = Highest - Least\)

Where:

\(Highest = 19\)

\(Least = 8\)

So:

\(Range = 19 - 8\)

\(Range = 11\)

Solving (b): The population variance

First, calculate the population mean using:

\(\mu = \frac{\sum x}{n}\)

So:

\(\mu = \frac{16+12+17+8+15+15+10+11+19+18}{10}\)

\(\mu = \frac{141}{10}\)

\(\mu = 14.1\)

So, the population variance is:

\(\sigma^2 = \frac{\sum(x - \mu)^2}{n}\)

\(\sigma^2 = \frac{(16 - 14.1)^2 + (12 - 14.1)^2 +............... + (19- 14.1)^2 + (18- 14.1)^2}{10}\)

\(\sigma^2 = \frac{120.9}{10}\)

\(\sigma^2 = 12.09\)

\(\sigma^2 = 12.1\) --- approximated

Solving (c): The population standard deviation.

This is calculated as:

\(\sigma = \sqrt{\sigma^2\)

\(\sigma = \sqrt{12.09\)

\(\sigma = 3.5\)

Answer: $4,998

Step-by-step explanation:

34000*1.147

38998-34000=4998

Answer:

9.1

Step-by-step explanation:

I went into my calculator and typed in \(\sqrt{82}\) and I was given:

9.055385...

So to round the nearest tenth, you look at the tenths place (which is 0) and go one number behind that (which is 5). Since the number behind the tenths place is 5 or higher, you round up to 1

Given Information:

Mean weekly salary = μ = $490

Standard deviation of weekly salary = σ = $45

Required Information:

P(X > $525) = ?

Answer:

P(X > $525) = 21.77%

Step-by-step explanation:

We want to find out the probability that a randomly selected teacher earns more than $525 a week.

\(P(X > 525) = 1 - P(X < 525)\\\\P(X > 525) = 1 - P(Z < \frac{x - \mu}{\sigma} )\\\\P(X > 525) = 1 - P(Z < \frac{525 - 490}{45} )\\\\P(X > 525) = 1 - P(Z < \frac{35}{45} )\\\\P(X > 525) = 1 - P(Z < 0.78)\\\\\)

The z-score corresponding to 0.78 from the z-table is 0.7823

\(P(X > 525) = 1 - 0.7823\\\\P(X > 525) = 0.2177\\\\P(X > 525) = 21.77 \%\)

Therefore, there is 21.77% probability that a randomly selected teacher earns more than $525 a week.

How to use z-table?

Step 1:

In the z-table, find the two-digit number on the left side corresponding to your z-score. (e.g 0.7, 2.2, 1.5 etc.)

Step 2:

Then look up at the top of z-table to find the remaining decimal point in the range of 0.00 to 0.09. (e.g. if you are looking for 0.78 then go for 0.08 column)

Step 3:

Finally, find the corresponding probability from the z-table at the intersection of step 1 and step 2.

9514 1404 393

Answer:

  40°

Step-by-step explanation:

The sum of angles in a triangle is 180°.

  (6x)° +x° +(2x)° = 180°

  9x = 180

  x = 20

  ∠B = (2·20)° = 40°

Due to the difference in their price elasticity of demand, if a per-unit excise tax of the same amount is imposed on goods X and Y, the quantity demanded for good Y will decline more than the quantity demanded for good X.

1. Consider Good X with Price Elasticity of Demand (-0.5):

The demand for good X is inelastic if the price elasticity of demand is less than zero (-0.5).

This suggests that consumers are not particularly responsive to price changes and that changes in price do not considerably affect the quantity demanded.

Excise tax effects on good X:

When good X is subject to excise tax, its price will rise. The quantity demanded won't drastically decrease because the demand is inelastic.

2. Good Y with a (-2) demand price elasticity

Demand for good Y is elastic if price elasticity of demand is -2. This shows that consumers react quickly to price fluctuations and that the amount requested fluctuates considerably as well.

Excise tax effects on good Y:

Good Y's price will rise if the excise tax is applied. The quantity needed will significantly decrease since the demand is elastic.

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The rocket's maximum height is 800 feet. It reached its maximum height at 5 seconds after launch.

To solve this problem, we need to find the vertex of the parabola represented by the equation Y= -16t^2+160t. The vertex of a parabola is the point where the parabola changes direction, from increasing to decreasing or vice versa.

The vertex of the parabola is given by the following formula:

(-b/2a, c - b^2/4a)

In this case, the value of b is 160 and the value of a is -16. Plugging these values into the formula, we get the following:

(-160/2(-16), 800 - 160^2/4(-16))

(5, 800)

Therefore, the rocket reached its maximum height at 5 seconds after launch. The maximum height is 800 feet.

The probability of Miguel selecting a tile number less than 3 from each bag -1 is 1/5 and bag-2 is 2/5.

The given tiles in bag-1 = {2, 4, 5, 8, 9}

Total number of tiles in bag-1 = 5

The number of tiles less than number 3 in the bag - 1 = 1

The probability of Miguel selecting a tile number less than 3 =

number of tiles less than 3 / total number of tiles = 1/3

The given tiles in bag-2 = {0, 1, 3, 6, 7}

Total number of tiles in bag-2 = 5

The number of tiles less than number 3 in the bag-2 = 2

The probability of Miguel selecting a tile number less than 3 =

number of tiles less than 3 / total number of tiles = 2/3

From the above analysis, we solved the problem.

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Answer:

-10 2/5

Step-by-step explanation:

2 3/5 as an improper fraction is 13/5

-4×13/5=-52/5

-52/5 as a mixed fraction is -10 2/5

Answer is -10 2/5

Answer:true

Step-by-step explanation:It’s on khan

Answer:

True

Step-by-step explanation:

A function is when each element of the domain has only one corresponding element in the range.

True

To simplify the expression (2x-3)(5x^2-2x+7), we can use the distributive property.

First, multiply 2x by each term inside the second parentheses:

2x * 5x^2 = 10x^3

2x * -2x = -4x^2

2x * 7 = 14x

Next, multiply -3 by each term inside the second parentheses:

-3 * 5x^2 = -15x^2

-3 * -2x = 6x

-3 * 7 = -21

Combine all the resulting terms:

10x^3 - 4x^2 + 14x - 15x^2 + 6x - 21

Now, combine like terms:

10x^3 - 19x^2 + 20x - 21

So, the simplified expression is 10x^3 - 19x^2 + 20x - 21.

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Answer:

Step-by-step explanation:

Based on the calculation below, the Mean Absolute Deviation (MAD) of the test scores is 0.

The mean of the 6 test scores is first calculated as follows:

Mean = Sum of the test scores / Number of test scores = (48 + 61 + 73 + 76 + 76 + 74) / 6 = 68

We can now calculate the MAD of the test scores as follows:

MAD = Sum of deviations of all the test scores from the Mean / Number of test scores = ((48 - 68) + (61 – 68) + (73 – 68) + (76 – 68) + (76 – 68) + (74 – 68)) / 6 = 0 / 6 = 0

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