What property is illustrated by this statements if a b and b = C, then a = c?​

I like to work with the slope-intercept form of the line:

x=4y-8 �> y = (1/4)x + 2 (1)

12x+y=11 �> y = -12x + 11 (2)

At the point where they intersect the two y values must be equal, so set eq(1) = eq(2):

(1/4)x + 2 = -12x + 11

( (1/4) + (48/4))x = 9

(49/4)x = 9

Ans: x = 36/49

Check: Plug in x=36/49 to eq(1) and eq(2) to make sure they produce identical y values:

(1) y = (1/4)(36/49) + 2 = (9/49) + (98/49) = 107/49

(2) y = -12(36/49) + 11 = (-432/49) + (539/49) = 107/49 (they match)

By using substitution method,

The x-coordinate of the point where the lines x=4y−8 and 12x+y=11 intersect is  \(\frac{36}{49}\).

"The substitution method is one of the algebraic methods to solve linear equations. It involves substituting the value of any one of the variables from one equation to the other equation."

We have the lines

x=4y−8 ..........................(1)

12x+y=11 .........................(2)

By using substitution method

Substitute x = 4y - 8 in equation (2)

⇒ 12(4y-8) + y = 11

⇒ 48y - 96 + y = 11

⇒ 49y = 11 + 96

⇒ y = \(\frac{107}{49}\)

Calculating the x - coordinate by substituting y value in equation (1)

x=4y−8

⇒ x = \(4(\frac{107}{49} )-8\)

⇒ x = \(\frac{428-392}{49}\)

⇒ x = \(\frac{36}{49}\)

Hence, the x-coordinate of the point where the lines x=4y−8 and 12x+y=11 intersect is  \(\frac{36}{49}\).

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The cost of the carpet will be $2,335.5.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The dimensions of the carpet are;

⇒ 15 feet by 18 feet

Now,

The area of the carpet = 15 x 18

                                   = 279 feet²

                                   = 270 / 3 yards²

                                   = 90 yards²

Since, The carpet costs = $25.95 per square yard.

Hence, The carpet cost for 90 yards² = 90 x $25.95

                                                          = $2,335.5

Thus, The cost of the carpet will be $2,335.5.

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Fitness increases with energy intake rate was an assumption varied by Lima, Valone, & Caraco (1985) in their model of squirrel food carrying

Now, According to the question:

A parameter is used to describe the entire population being studied. For example, we want to know the average length of a butterfly. This is a parameter because it is states something about the entire population of butterflies.

Fitness increases with energy intake rate varied by Lima, Valone and Caraco (1985) in their model of squirrel food carrying.

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The given question is incomplete, complete question is:

Mathematical models allow researchers to make different predictions by varying assumptions. Which of the following parameters was an assumption varied by Lima, Valone, & Caraco (1985) in their model of squirrel food carrying?

Answer:

-20% discount

Step-by-step explanation:

subtract the two numbers:

1020-1360= -340 (is a percentage reduction, so I have to subtract the larger number from the smaller one)

divide the result by the original value:

-340÷1360= -0,25

to turn it into a percentage, multiply it by 100:

-0,25×100= -25%

Hope it helps!

Answer:

there's a decrease of 25%

or

-25%

Step-by-step explanation:

100% = 1360

___% = 1020

\( \frac{1020 \times 100}{1360} = 75\)

100- 75= 25%

Keegan's error is assuming that the product of the slopes of any two sides of a triangle should be -1 for the triangle to be a right triangle.

To determine if the triangle LMN is a right triangle, Keegan should instead calculate the lengths of the three sides of the triangle and check if they satisfy the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

To correct his approach, Keegan should calculate the lengths of sides LM, MN, and NL using the coordinates of the vertices and then check if the Pythagorean theorem holds true.

If the squared length of one side is equal to the sum of the squares of the other two sides, then the triangle LMN is a right triangle.

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The equivalent expression of 4(5+y)  by distributing is 20 + 4y.

In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.).

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

In other words, two mathematical expressions are said to be equivalent if they yield the same result upon solving them.

Therefore, let's find the equivalent expression of 4(5 + y) by distributing it.

Hence,

4(5 + y)  = 20 + 4y

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Answer:

The model represents the equation "0 + x² = 1/2", which is not directly related to multiplying with fractions.

Answer:

4

Step-by-step explanation:

I'm not to sure though your answer doesn't really maker sense

Answer:

0.9225 = 92.25% probability that two or more internship trained candidates are hired.

Step-by-step explanation:

Candidates are chosen without replacement, which means that we use the hypergeometric distribution to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

Group of 13 individuals:

This means that \(N = 13\)

6 candidates are selected:

This means that \(n = 6\)

6 in trained internships:

This means that \(k = 6\)

Find the probability that two or more internship trained candidates are hired.

This is:

\(P(X \geq 2) = 1 - P(X < 2)\)

In which

\(P(X < 2) = P(X = 0) + P(X = 1)\)

So

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)

\(P(X = 0) = h(0,13,6,6) = \frac{C_{6,0}*C_{7,6}}{C_{13,6}} = 0.0041\)

\(P(X = 1) = h(1,13,6,6) = \frac{C_{6,1}*C_{7,5}}{C_{13,6}} = 0.0734\)

\(P(X < 2) = P(X = 0) + P(X = 1) = 0.0041 + 0.0734 = 0.0775\)

\(P(X \geq 2) = 1 - P(X < 2) = 1 - 0.0775 = 0.9225\)

0.9225 = 92.25% probability that two or more internship trained candidates are hired.

The person that has the winning time is Alex.

From the information given, three runners run 100 yards race. Sara runs the race in 9.25 seconds and Alex runs the race in 8.625 seconds and Tonya runs the race in 9.8 seconds.

It should be noted that in a race, the person that has the lowest time wins.

In this situation, the person with 8.625 seconds is the lowest.

Therefore, Alex wins.

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The square root of 138 lies between 11 and 12, as 11²=121 and 12²=144.

Number is a mathematical object used to count, measure, and label. Numbers are used in almost every field of mathematics and science, including algebra, calculus, geometry, physics, and computer science. Numbers can also be used to represent data, such as population, income, temperature, or time. In addition, numbers are used to represent abstract concepts, such as love, truth, beauty, and justice.

This is because the square root of a number is the number that, when multiplied by itself, produces the original number. Therefore, to find the square root of 138, we need to identify two consecutive integers such that one of them squared is smaller than 138 and the other squared is larger than 138.

To do this, we can work our way up from the integer closer to 0, in this case 11. 11 squared is 121, which is smaller than 138, so we know that the square root of 138 must be between 11 and a larger integer. Then, if we square 12, we get 144, which is larger than 138. Therefore, we can definitively say that the square root of 138 lies between 11 and 12.

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The square root of 138 lies between 11 and 12, as 11² is 121 and 12² is 144.

Number is a mathematical object used to count, measure, and label. Numbers are used in almost every field of mathematics and science, including algebra, calculus, geometry, physics, and computer science. Numbers can also be used to represent data, such as population, income, temperature, or time. In addition, numbers are used to represent abstract concepts, such as love, truth, beauty, and justice.

To calculate this, we can divide 138 by 11 and 12, and see which integer is closer to the answer.

138 divided by 11 is 12.545454545454545454545454545455.
138 divided by 12 is 11.5.

Since 11.5 is closer to the answer, the square root of 138 lies between 11 and 12.

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Answer:

3\(\frac{1}{2}\) ft

Step-by-step explanation:

7 yd x 3ft/yd = 21 ft

21 ft / 6 pieces = 3.5 ft/piece = 3'6" / piece

Answer:

$21,038.28

Step-by-step explanation:

Use the equation 15000(1.07)^5 since 1.07 equals to 7% and you are loaning more money to Tony's account for 5 years.  You should get $21,038.28 as your result.

Answer: 21286

Step-by-step explanation:

Answer:

C 532 square feet

Step-by-step explanation:

We need to calculate the surface area of the storage shed.  This includes the floor.  I did the calculations without the floor and I got 434ft, which is not one of the answers.

Length = 14ft Width = 7ft Height = 8ft

The front and back of the shed both have dimensions of 14x8

The left and right sides of the shed have dimensions of 7x8

The roof and floor have the dimensions of 14x7

2(14 x 8) + 2(7 x 8) + 2(14 x 7)

2(112) + 2(56) + 2(98)

224 + 112 + 196

532 square feet

I hope this helps.

Answer:

41, 49

Step-by-step explanation

It goes up in 8 if you work out 25-17 or 33-25.

33+8=41, 41+8=49

The height is the distance between the opposite parallel sides of the parallelogram.

Therefore, the height of the parallelogram is 4 cm.

given equations are:

Now put the value x= -3 in another equation:

By plotting graph for both equation:

The blue line for x-3y=-15

And red line for x=-3

The value of the z-score for the number 15  in a data set is 0.93.

Define z-score.

A data point's z-score, also known as a standard score, indicates how far it deviates from the mean. In practical terms, however, it's a measurement of how many standard deviations a raw number is from or above the population mean.

You can plot a z-score on a normal distribution graph. Z-scores can be anywhere between -3 and +3 standard deviations.

                     ∴  z = (x – μ) / σ

Given:

σ = 4.32

x = 15

Data set: 5, 7, 9, 11, 13, 15, 17

So, mean = 5 + 7 + 9 + 11 + 13 + 15 + 17/7

                = 77/7

            μ = 11

z = (x – μ) / σ

  = (15 - 11)/4.32

   = 4/4.32

z  = 0.93

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The sale price for the snowboard after the trade and loyalty discount of 15% and 4% will be 351.01 dollars.

The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.

Frigid Boards purchases one of its snowboards for $395 less a retail trade discount of 15% and a loyalty discount of 4%. Then the price of the snowboards will be

⇒ $ 395 × 0.85 × 0.96

⇒ $ 322.32

Its markup on selling price percentage on all snowboards is 21%, then we have

⇒ $ 322.32 × 1.21

⇒ $ 390.01

At the end of the season, any leftover snowboards are marked down by 10%, then we have

⇒ $ 390.01 × 0.90

⇒ $ 351.01

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Step-by-step explanation:

70 to 85 % of his maximum

Maximum is estimated to be 220 - age  = 220 - 42 = 178

70% of this is 125

85 % is 89  151  

I believe I would go with the third choice  116-160 bpm

Answer:

The ratio of texts sent to calls made was 8:5

For every 5 calls made there were 8 texts sent

Answer:

For every 8 calls made there were 2 texts sent.

And

For every 2 texts sent there were 8 calls made.

Answer:

A. you are correct!

Step-by-step explanation:

Answer:

3/8

Step-by-step explanation:

3/8 of 16 is 6

1/4 of 16 is 4

6+4 = 10

16-10 = 6

3/8 of 16 = 6

Answer:

27.57 degree

Step-by-step explanation:

shown in the diagram

The measurement of the smallest angle, of Δ ABC, is 27.57°

A triangle is a polygon with three edges and three vertices and three angles.

Given that, a triangle has sides 17, 29 and 16, we need to find the measurement of the smallest angle,

We know that, In any triangle, the largest side and largest angle are opposite one another, the smallest side and smallest angle are opposite one another, the mid-sized side and mid-sized angle are opposite one another. (please refer to the figure attached)

Therefore, the smallest angle, is opposite to side 16,

Using the cosine law of the triangle,

c² = a²+b²-2abcosC

C = cos⁻¹(a²+b²-c²) / 2ab

C = cos⁻¹(29²+17²-16²) / 2(29)(17)

C = cos⁻¹(874/986)

C = cos⁻¹(0.886409736)

C = 27.57°

Hence, the measurement of the smallest angle, of Δ ABC is 27.57°

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Step-by-step explanation:

look at the picture !

she has to paint actually 6 rectangles :

the 3 tops of the 3 stairs.

and the 3 vertical front boards (the front of each step of the stairs).

what is the area of these rectangles ? summing up all 6 - that is the surface area to be painted.

each top rectangle is clearly

82×19 (19 cm deep) = 1558 cm²

each front board is

82×12 (12 cm high) = 984 cm²

so, in total we have

3×1558 + 3×984 = 4674 + 2952 = 7626 cm²

as surface area to be painted.

The required distance between the points  (−1,6) and (−1,7). is 1 unit.

Given that,
using the distance formula to evaluate the distance between the points  (−1,6) and (−1,7).

Distance is defined as the object traveling at a particular speed in time from one point to another.

Here,
The distance formula is given as,
D = √[[x₂ - x₁]² + [y₂+ - y₁]²]
Substitute the values in the above equation,
D = √[[-1 + 1]² + [7 - 6]²]
D = √[0 + 1]
D = 1

Thus, the required distance between the points  (−1,6) and (−1,7). is 1 unit.

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Answer:

The 96% confidence interval for the average IQ score of all seventh-grade girls in the school is (105, 111.6).

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 31 - 1 = 30

96% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 30 degrees of freedom(y-axis) and a confidence level of \(1 - \frac{1 - 0.96}{2} = 0.98\). So we have T = 2.15

The margin of error is:

\(M = T\frac{s}{\sqrt{n}} = 2.15\frac{15}{\sqrt{31}} = 5.8\)

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 105.8 - 5.8 = 105.

The upper end of the interval is the sample mean added to M. So it is 105.8 + 5.8 = 111.6

The 96% confidence interval for the average IQ score of all seventh-grade girls in the school is (105, 111.6).

Interest is a fee charged by a lender to a borrower for the use of money or credit, usually expressed as a percentage of the amount borrowed or invested over a period of time. Brandon invested $\(4700\) at 3% interest and $\(1100\) at \(8\)% interest.  The total interest earned after one year is $229

How much was in each account?

Let x be the amount invested in the first account that pays 3% interest, and let y be the amount invested in the second account that pays 8% interest. Since the total amount invested is $5800, we have:

\(x + y = 5800\)

The amount of interest earned on the first account is 0.03x, and the amount of interest earned on the second account is 0.08y. Since the total interest earned after one year is $229, we have:

\(0.03x + 0.08y = 229\)

We now have two equations with two unknowns:

\(x + y = 5800\)

\(0.03x + 0.08y = 229\)

We can solve for x and y by using elimination or substitution method. Here, we will use the substitution method.

Solve the first equation for x:

\(x = 5800 - y\)

Substitute this expression for x into the second equation and solve for y:

\(0.03(5800 - y) + 0.08y = 229\)

\(174 - 0.03y + 0.08y = 229\)

\(0.05y = 55\)

\(y = 1100\)

Now substitute this value of y into either equation to solve for x:

\(x + 1100 = 5800\)

\(x = 4700\)

Therefore, Brandon invested $\(4700\) at 3% interest and $\(1100\) at \(8\)% interest.

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