the sum of 20 and a number divided by 5 is 25

Answer:

Step-by-step explanation:

x-y=14

x-1/3y=1/10

-y=14-x

y=-14+x

take out the factors

x-10/30y=3/30

30x-10y=3

substitute

30x-10(-14+x)=3

30x+140-10x=3-140

20x/20=-137/20

x=-6.85

y=-14+(-6.85)

y=-20.85

The two numbers are 143/20 and 423/20.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Given that, the difference between two numbers is 14.

Let the smaller number be x and the larger number be y.

Here, y-x=14 ------------(i)

If 1/3 of the larger number is subtracted from the smaller number ,the result equals 1/10.

1/3 of larger number is 1/3 y

x-y/3 =1/10 ------------(ii)

From equation (i), substitute y=14+x in equation (ii), we get

x-(14+x)/3 =1/10

10(3x-14-x)=3

30x-140-10=3

20x-140=3

20x=143

x=143/20

Substitute x=143/20 in equation (i), we get

y-143/20=14

y=14+143/20

y=(280+143)/20

y=423/20

Therefore, the two numbers are 143/20 and 423/20.

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The system of equation that could have led to the equation 9x = 27 is

7x - 2y = 15

x + y = 6

The correct option is the third option

7x - 2y = 15

x + y = 6

From the question, we are to determine the system that could have led to 9x = 27

1.

9x + 2y = 21

-9x - 2y = 21

Subtracting, we get

9x + 2y = 21

-9x - 2y = 21

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

18x + 4y = 0

2.

10x - y = 15

x + y = - 12

Subtracting, we get

10x - y = 15

x + y = - 12

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

9x -2y = 27

3.

7x - 2y = 15

x + y = 6

Here, multiply the second equation by 2

2 × [x + y = 6]

2x + 2y = 12

Now, add to the first equation

7x - 2y = 15

2x + 2y = 12

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

9x = 27

4.

4x + 3y = 24

-5x - 3y = 3

Subtracting, we get

4x + 3y = 24

-5x - 3y = 3

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

9x + 6y = 21

Hence, the system of equation that could have led to the equation 9x = 27 is

7x - 2y = 15

x + y = 6

The correct option is the third option

7x - 2y = 15

x + y = 6

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Answer:

Yes it has infinity of solutions.

Step-by-step explanation:

If you plug in certain numbers it will make the statements true.

Answer:

Infinitely many solutions.

Step-by-step explanation:

Let's solve your system by substitution.

2x+3y=−6;4x+6y=−12

Step: Solve2x+3y=−6for x:

2x+3y=−6

2x+3y+−3y=−6+−3y(Add -3y to both sides)

2x=−3y−6

2x/2 = −3y−6/2

(Divide both sides by 2)

x= −3/2y−3

Step: Substitute −3/2y−3 for x in 4x+6y=−12:

4x+6y=−12 4(−3/2y−3)+6y=−12

−12=−12(Simplify both sides of the equation)

−12+12=−12+12(Add 12 to both sides)

0=0

Answer:

Infinitely many solutions.

Fig. 2.6 alone does not provide sufficient information to calculate the percent elongation of materials. Percent elongation is a measure of the increase in length of a material after it has been subjected to a tensile load, and is calculated by dividing the increase in length by the original length and multiplying by 100.

Fig. 2.6 shows stress-strain curves for different materials, which provide information about the relationship between stress and strain for those materials. While the curve shape can provide some insight into the behavior of the material under load, it does not provide information about the original length or the change in length of the material, which are necessary to calculate percent elongation.

In order to calculate percent elongation, additional information about the material's original length and the change in length after a tensile load is required. This information can be obtained through laboratory testing or from material specifications provided by the manufacturer.

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Answer:

.0097

Step-by-step explanation:

Take the decimal and move it 3 (variable for any negative exponent) places to the left

Answer:

0.0097 is the answer.

Step-by-step explanation:

You start by counting from the decimal place. For negative exponents, you would count to the left. Three decimal places to the left of 9.7 is 0.0097.

Answer:

y= -1/3x-7

Step-by-step explanation:

Answer: equation is (y5+g(x)

Step-by-step explanation: Percent change = 56 - 32 |32| × 100% = 24 32 × 100 = 75% (increase). Where: 32 is the old value and 56 is the new value. In this case we have a positive

Answer:

3.6

Step-by-step explanation:

260% of 6

100%= 0.06

100% times 2 is 0.06 X 2= 0.12

200%= 0.12

10%= 0.6

60%= 3.6

200% + 60%=

0.12 + 3.6= 3.72

The closest to 3.72 is 3.6

So the answer is 3.6

Answer:

To find this, multiply 6 by the decimal value of the percent.

6*2.6=15.6

Final answer: 15.6

Step-by-step explanation:

Answer:

around 228 degrees

Step-by-step explanation:

Answer: 143

Step-by-step explanation:

Answer:

If four friends can eat four cakes in four days, then four friends will eat an average of one cake per day, so each friend will be able to eat 1/4 of a cake per day.

So 10 friends will eat 10/4 of cake per day, or two and a half cakes per day, so they will eat 2,5 * 10 = 25 (twenty-five) cakes per 10 days, assuming they will eat at the same rate

Step-by-step explanation:

Branily?

We have proven that if the inequality holds true for k, it also holds true for k + 1. By the principle of mathematical induction, the inequality 2^n > n^2 holds true for all n > 4.

To prove the inequality 2^n > n^2 using induction with a basis greater than 4, we will use n=5 as the basis.

Basis: n = 5
2^5 = 32 and 5^2 = 25. Since 32 > 25, the inequality holds true for n = 5.

Now, we need to assume that the inequality holds true for an arbitrary positive integer k > 4, and then prove that it holds true for k + 1.

Assume: 2^k > k^2 for k > 4.

Prove: 2^(k + 1) > (k + 1)^2

Step 1: Multiply both sides of the assumption by 2.
2 * (2^k) > 2 * (k^2)

Step 2: Simplify the left side of the inequality.
2^(k + 1) > 2k^2

Step 3: Show that 2k^2 is greater than (k + 1)^2 for k > 4.
2k^2 > (k + 1)^2
2k^2 > k^2 + 2k + 1

Step 4: Rearrange the inequality to show that it holds true for k > 4.
k^2 - 2k - 1 > 0

Since k > 4, it is clear that k^2 - 2k - 1 > 0, as the left side increases as k increases.

Therefore, we have proven that if the inequality holds true for k, it also holds true for k + 1. By the principle of mathematical induction, the inequality 2^n > n^2 holds true for all n > 4.

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Answer:

2

Step-by-step explanation:

i am not sur but 12 5 = 2?

Answer:

you need to learn how to "prime factor" numbers....

primes are 2,3,5,7,11,13,17....

they go on forever. ALL whole numbers can be "broken down" into a bunch of primes multiplied together.

take the fractions (top and bottom) and start dividing them bu the smallest prime, and going up until all the numbers multiplied make the original number...

15 = 3 * 5

24= 2 * 12 = 2 * 2 * 6 = 2* 2* * 2 * 6

thus   \(\frac{15}{24}\) = \(\frac{3 * 5 }{2* 2* 2* 3}\)  now just cancel all the SAME numbers from to to bottom

"pair them up" .... in this case only one of the threes in the bottom "takes out" one of the threes in the top

result \(\frac{5}{2*2*2 } = \frac{5}{8}\)

~~~~~~~~~~~~~~~~~~~~

\(\frac{21}{35}\)

21= 3 * 7

35= 5* 7

\(\frac{3*7}{5*7} = \frac{3}{5}\)

Step-by-step explanation:

The alternative hypothesis will be 200β₂> -0.03.

The null hypothesis of the given statement will state that decreasing the total size by 200 square feet will not decrease the price by more than three percent. On the other hand, the alternative hypothesis lines up with the research prediction, which states that decreasing the total size by 200 square feet, will decrease the price by more than three percent. Here, the negative sign indicates a decrease in price.

Therefore, the correct answer is 200β₂> -0.03.

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Graphing the equation 3x - 2y = -6 over the range x = -10 to x = 10:

To graph the equation 3x - 2y = -6, we need to rearrange it in the form y = mx + b, where m is the slope and b is the y-intercept.

3x - 2y = -6

-2y = -3x - 6

Divide both sides by -2:

y = (3/2)x + 3

Now we have the equation in slope-intercept form.

To graph the equation, we can plot a few points and draw a line through them. Let's choose some x-values from the range -10 to 10 and find the corresponding y-values.

For x = -10:

y = (3/2)(-10) + 3

y = -15 + 3

y = -12

For x = 0:

y = (3/2)(0) + 3

y = 0 + 3

y = 3

For x = 10:

y = (3/2)(10) + 3

y = 15 + 3

y = 18

Plotting these points (-10, -12), (0, 3), and (10, 18) on the graph and drawing a line through them, we get the graph of the equation 3x - 2y = -6.

Using the graphical method to solve the pair of equations:

The given equations are:

10x = 5y

-3x + y = 1

To solve these equations graphically, we need to plot their graphs on the same coordinate plane and find the point where they intersect, which represents the solution.

Rearranging the second equation in slope-intercept form:

y = 3x + 1

Now we have the equations in the form y = mx + b.

Plotting the graphs of the equations 10x = 5y and y = 3x + 1, we can find the point of intersection, which represents the solution to the system of equations.

The point of intersection is the solution to the system of equations.

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Let's put more details in the given figure to better understand the problem:

It appears that the triangle is an Isosceles Triangle. Because of this, the legs of the triangle should be congruent.

Let's determine the length of its leg using the Sine Function: Let, x = the length of the leg.

Therefore, the length of its leg is 8√2

a) The sample mean home sale amount is $660,500 and the sample median home sale amount is $582,500.

b) The new sample mean home sale amount would be $617,500 and the new sample median home sale amount would be $575,000.

c) The 20% trimmed mean home sale amount is $573,600.

d) The 15% trimmed mean home sale amount is $601,400.

In a group of numerical data, the median serves as a gauge of central tendency. When the values are ordered in order of magnitude, it is the median value in the dataset. In other words, the median is the value in the middle when a dataset has an odd number of variables. The median is the average of the two middle values when the dataset has an even number of values. Because it is unaffected by extreme numbers or outliers that can influence the mean, the median is helpful in these situations. To indicate the typical value of a dataset, it is frequently employed.

a. To calculate the sample mean, we add up all the home sale amounts and divide by the total number of homes in the sample:

(590 + 815 + 575 + 608 + 350 + 1285 + 408 + 540 + 555 + 679) / 10 = 660.5

So the sample mean home sale amount is $660,500.

To find the sample median, we first need to order the home sale amounts from lowest to highest:

350, 408, 540, 555, 575, 590, 608, 679, 815, 1285

There are 10 homes in the sample, so the median is the middle value. Since there are an even number of homes, we take the average of the two middle values:

(575 + 590) / 2 = 582.5

So the sample median home sale amount is $582,500.

b. If the 6th observation had been 985 rather than 1285, the sample mean would change as follows:

(590 + 815 + 575 + 608 + 350 + 985 + 408 + 540 + 555 + 679) / 10 = 617.5

So the new sample mean home sale amount would be $617,500.

To find the new sample median, we first need to order the home sale amounts from lowest to highest:

350, 408, 540, 555, 575, 590, 608, 679, 815, 985

There are 10 homes in the sample, so the median is the middle value. Since there are an odd number of homes, the median is simply the middle value:

575

So the new sample median home sale amount would be $575,000.

c. To calculate a 20% trimmed mean, we first need to remove the two smallest and two largest observations:

(540, 555, 575, 590, 608)

Then, we calculate the mean of the remaining observations:

(540 + 555 + 575 + 590 + 608) / 5 = 573.6

So the 20% trimmed mean home sale amount is $573,600.

d. To calculate a 15% trimmed mean, we need to remove the 1.5 smallest and 1.5 largest observations. Since we can't remove half an observation, we need to remove 1 observation from each end of the list. This gives us:

(555, 575, 590, 608, 679)

Then, we calculate the mean of the remaining observations:

(555 + 575 + 590 + 608 + 679) / 5 = 601.4

So the 15% trimmed mean home sale amount is $601,400.

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A story that can be represented using the equation y=x+1/5x is "John has an apple and he cut another apple into 5 equal parts and took on part. What's the rural fraction of apple that he has?

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

In this case, if John has an apple and he cut another apple into 5 equal parts and took on part.

This can be illustrated as:

y = x + 1/5x

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Answer:

The answer is the letter D

Step-by-step explanation:

The sum of 2t and 2 could be written as:

\(a=2t+2\)

Now, the twice of the cube of s will be:

\(b=2s^{3}\)

Finally, the quotient between a and b will be:

\(\frac{a}{b}=\frac{2t+2}{2s^{3}}\)

Therefore the answer is the letter D

I hope it helps you!

To compute the determinants of the matrices A₁, A₂, A₃, A₄, and As obtained from Ao through the specified operations, we need to apply the given operations to the matrix Ao and calculate the determinant at each step.

Given:

Ao is a 5 x 5 matrix with det(Ao) = -3.

a) A₁: Obtained from Ao by multiplying the fourth row of Ao by 2.

To compute det(A₁), we need to perform the specified operation on Ao and calculate the determinant.

A₁ = Ao (after multiplying the fourth row by 2)

det(A₁) = 2 * det(Ao) (multiplying a row by a scalar multiplies the determinant by the same scalar)

det(A₁) = 2 * (-3) = -6

b) A₂: Obtained from A₁ by swapping the first and last rows of A₁.

To compute det(A₂), we need to perform the specified operation on A₁ and calculate the determinant.

A₂ = A₁ (after swapping the first and last rows of A₁)

det(A₂) = det(A₁) (swapping rows does not change the determinant)

det(A₂) = -6

c) A₃: Obtained from A₂ by multiplying A₂ by itself.

To compute det(A₃), we need to perform the specified operation on A₂ and calculate the determinant.

A₃ = A₂ * A₂ (multiplying A₂ by itself)

det(A₃) = det(A₂) * det(A₂) (multiplying matrices multiplies their determinants)

det(A₃) = (-6) * (-6) = 36

d) A₄: Obtained from A₃ by replacing the second row with the sum of itself plus 3 times the third row.

To compute det(A₄), we need to perform the specified operation on A₃ and calculate the determinant.

A₄ = A₃ (after replacing the second row with the sum of itself plus 3 times the third row)

det(A₄) = det(A₃) (replacing rows does not change the determinant)

det(A₄) = 36

e) As: Obtained from A₄ by scaling A₄ by the number 2.

To compute det(As), we need to perform the specified operation on A₄ and calculate the determinant.

As = 2 * A₄ (scaling A₄ by 2)

det(As) = 2 * det(A₄) (scaling a matrix multiplies the determinant by the same scalar)

det(As) = 2 * 36 = 72

Therefore, the determinants of the matrices obtained through the given operations are:

det(A₁) = -6,

det(A₂) = -6,

det(A₃) = 36,

det(A₄) = 36,

det(As) = 72.

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Answer:

On friday the chef made about 0.8333 batches or 7.5/9 of a batch of ice cream.

On thursday the chef made about 0.67 batches or 2/3 of a batch of icecream

Step-by-step explanation:

Answer:

Step-by-step explanation:To find two angles between 0° and 360° that satisfy the given condition, we need to solve the equation √√3 cos0 = 2.

Let's start by isolating the cosine term:

√√3 cos0 = 2

cos0 = 2 / √√3

To find the angles, we need to find the inverse cosine (cos⁻¹) of the ratio:

cos⁻¹(2 / √√3)

Using a calculator, we find that the principal value of cos⁻¹(2 / √√3) is approximately 30°.

Now, since cosine is positive in both the first and fourth quadrants, we can add 360° to obtain the second angle:

Second angle = 30° + 360° = 390°.

Therefore, the two angles between 0° and 360° that satisfy the given condition are 30° and 390°.

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The number that satisfies the given conditions is 798. When you divide 798 by 32, the remainder is 30. Similarly, when you divide 798 by 58, the remainder is 44.

To solve this problem, we can use simultaneous equations. Let x be the number we need to find. Then, x = 32a + 30 and x = 58b + 44, where a and b are the quotients obtained on dividing x by 32 and 58. Simplifying this equation, we get 16a + 15 = 29b + 22.

Rearranging the equation, we get 16a - 29b = 7. To find a value for b where 13b + 7 is divisible by 16, we can use the least common multiple of 13 and 16, which is 176. Therefore, b = 13.

Substituting the value of b in the first equation, we get x = 58b + 44 = 798. Hence, the number we are looking for is 798.

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Answer:

5 and 35

Step-by-step explanation:

It's going up in tens so it must start from 5, therefore the one between 25 and 45 must be 35.

Answer:

x=4

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

I tried plugging it in and it worked!

Hope this helps!

In this study, weight loss would be the dependent variable, as it is being measured or observed as a result of the change in the independent variable, which is the calorie intake (1,300 calories/day).

The independent variable is the factor that is being manipulated or changed in the study, and the dependent variable is the factor that is being measured or observed as a result of that change.

Put simply, an independent variable is just what it sounds like it is. It's a separate factor that can't be affected by the others. One independent variable could be a person's age.

In research, the independent variable might be either (1) quantitative or (2) qualitative. Variables with numeric or scalar ranges are called quantitative. They can be thought of as numerical variables that provide answers to "how many?" or "how often?"

The three primary categories of research variables are the independent variable, the dependent variable, and the controlled variables. Take the case of an automobile driving along a variety of terrains.

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Answer:

x = 4.5

Step-by-step explanation:

thesetwo triangles are similar to we can create a proportion from corresponding sides as follows:

4/9 = 2/x

cross-multiply:

4x = 18

x = 4.5