2. Name the property illustrated by this equation
-5 · 1 = -5

Answer: You multiply 8 x 3/4=24/4.  Then you simplify your answer and it is 6 hours.  24/4 is division 24 divided by 4 equals 6.

Step-by-step explanation: Or, you can change 3/4 to a decimal which is .75.  Then you multiply .75 x 8 and the answer is 6.00 which is 6 hours because you do not use the zeros after the decimal point.

Answer:

2 hours

Step-by-step explanation:

You can just multiply 1/4 by 8. You're simply just adding on 1/4 8 times, and that is the same as multiplying.

Answer:

The answers are 47 &12 for "q" & "△" respectively

Given: A rhombus YWZA with XY=7 ft and XA=8 ft.

Since the diagonals of a rhombus bisect each other, therefore

As YZ and AW are the diagonals of this rhombus, its area will be:

Thus, the area of this rhombus is 112 feet squared.

Answer:

Since there are 10 boys and 6 of them equal 400Kg and the average of each boy is 60kg the remaining 4 boys should equal around 250kgs

Based on Kendall's interests and lack of skill playing baseball, a good career choice for him would be a football coach. So correct option is A.

Baseball is a bat-and-ball game that is played between two teams of nine players each. The objective of the game is to score runs by hitting a ball thrown by the opposing team and running around a series of four bases on a diamond-shaped field.

The game is typically played in nine innings, with each team taking turns at bat and in the field. The team in the field tries to prevent the other team from scoring by catching the ball and getting the opposing players out, while the team at bat tries to score runs by hitting the ball and running around the bases.

Baseball is a popular sport in many countries, particularly in the United States, where it is often referred to as "America's pastime." It has a rich history and culture, with many famous players, teams, and moments that have become part of popular culture.

Based on Kendall's interests and lack of skill playing baseball, a good career choice for him would be a football coach. Coaching allows him to be involved in the sport he enjoys and make a career out of it, without requiring him to have exceptional athletic ability. As a coach, he can use his knowledge of the sport to teach and train players, develop strategies, and lead a team to success.

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According to the information, we can infer that Mazibane must pay R3640 into the account on 30 June to have no debt.

To calculate the amount Mazibane must pay on 30 June to have no debt in the account, we need to consider the initial debt, the interest, and the previous payment.

Initial Debt:

Interest Calculation:

Previous Payment:

To determine the remaining debt on 1 June, we subtract the payment from the initial debt:

From 1 June to 30 June, a period of one month, interest is charged on the remaining debt.

To calculate the interest for one month, we use the formula:

where the principal is the remaining debt, the rate is the monthly interest rate (16%/12), and the time is the number of months (1).

To find the total debt on 30 June, we add the remaining debt on 1 June and the interest for one month:

To have no debt on 30 June, Mazibane must pay the total debt amount:

Calculating the interest and summing up the values, we find that Mazibane must pay approximately R3640 into the account on 30 June to have no debt.

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The correct step to prove that \(BC^2 = AB^2 + AC^2\) is:

By the cross product property, \(AC^2 = BC \cdot AD\).

To prove that \(BC^2 = AB^2 + AC^2\), we can use the triangle similarity and the Pythagorean theorem. Here's a step-by-step explanation:

Given triangle ABC with right angle at A and segment AD perpendicular to segment BC.

By triangle similarity, triangle ABD is similar to triangle ABC. This is because angle A is common, and angle BDA is a right angle (as AD is perpendicular to BC).

Using the proportionality of similar triangles, we can write the following ratio:

\($\frac{AB}{BC} = \frac{AD}{AB}$\)

Cross-multiplying, we get:

\($AB^2 = BC \cdot AD$\)

Similarly, using triangle similarity, triangle ACD is also similar to triangle ABC. This gives us:

\($\frac{AC}{BC} = \frac{AD}{AC}$\)

Cross-multiplying, we have:

\($AC^2 = BC \cdot AD$\)

Now, we can substitute the derived expressions into the original equation:

\($BC^2 = AB^2 + AC^2$\\$BC^2 = (BC \cdot AD) + (BC \cdot AD)$\\$BC^2 = 2 \cdot BC \cdot AD$\)

It was made possible by cross-product property.

Therefore, the correct step to prove that \(BC^2 = AB^2 + AC^2\) is:

By the cross product property, \(AC^2 = BC \cdot AD\).

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Answer:

The answer is "23, 62, and 139"

Step-by-step explanation:

In point a:

\(\to \sigma = \$0.24\\\\ \to E = \$0.10\\\\ 95\% \text{confidence level of the z}: \\\\\to \alpha = 1 - 95\% = 1 - 0.95 = 0.05\\\\\to \frac{\alpha}{2} = \frac{0.05}{2} = 0.025\\\\\to Z_{\frac{\alpha}{2}} = Z_{0.025} = 1.96\\\\\)

 Calculating the sample size:

\(\to n = (\frac{(Z_{\frac{\alpha}{2}} \times \sigma)}{E})^2\)

      \(= (\frac{(1.96 \times 0.24 )}{0.10})^2\\\\= 22.13 \approx 23\)

In point b:

\(\to \sigma = \$0.24\\\\\to E = \$0.06\\\\\to Z_{\frac{\alpha}{2}} = Z_{0.025} = 1.96\\\\\to n = (\frac{(Z_{\frac{\alpha}{2}} \times \sigma )}{E})^2\\\\\)

      \(= (\frac{(1.96 \times 0.24 )}{0.06})^2\\\\= 61.47 \approx 62\)

In point c:

\(\to \sigma = \$0.24\\\\\to E =\$0.04\\\\\to Z_{\frac{\alpha}{2}} = Z_{0.025} = 1.96\\\\\to n = (\frac{(Z_{\frac{\alpha}{2}} \times \sigma )}{E})^2\\\\\)

      \(= (\frac{(1.96\times 0.24 )}{0.04})^2 \\\\=138.30 \approx 139\)    

Answer:

NOTE: NONE OF THE OPTIONS GIVEN IS CORRECT. THIS IS THE CORRECT ANSWER.

AB = EF, BC = FG, AC = EG

Step-by-step explanation:

According to the SSS Congruence statement, for ∆ABC to be congruent to ∆EFG, all the sides of ∆ABC must be congruent to all the corresponding sides of ∆EFG.

This means that:

AB must be congruent to EF

BC must be congruent to FG

AC must be congruent to EG

Therefore, additional information is needed to prove that triangles ABC and EFG are congruent by the SSS triangle congruence theorem are:

AB = EF, BC = FG, AC = EG

NOTE: NONE OF THE OPTIONS GIVEN IS CORRECT. THIS IS THE CORRECT ANSWER.

The statement "for every positive rational number x, there exist positive integers n1, ..., nk such that x = n1/n2 + ... + nk/nk" is known as the Egyptian fraction representation theorem and is proved.

Let x be a positive rational number with numerator p and denominator q, where p and q are coprime. Let's assume that x can't be represented as a sum of positive unit fractions (i.e., fractions with numerator 1).

Then, construct a sequence of positive rational numbers x1, x2, ..., xk such that x1 = x and for each i, xi is equal to the difference between xi-1 and the largest unit fraction that is less than or equal to xi-1.

Since x is a positive rational number, it follows that xi is also a positive rational number for all i. Since x can't be represented as a sum of positive unit fractions, it follows that xi can't be represented as a sum of positive unit fractions for all i. Since the sequence x1, x2, ..., xk is constructed as the difference of two positive rational numbers, it follows that xi is a positive rational number for all i.

Since x1 = x, it follows that there exists a positive integer n such that x1 is equal to n/n + 1. But this contradicts our assumption that x can't be represented as a sum of positive unit fractions. Thus, our assumption is false, and it follows that x can be represented as a sum of positive unit fractions.

Therefore, we have proved that for every positive rational number x, there exist positive integers n1, ..., nk such that x = n1/n2 + ... + nk/nk.

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_____The given question is incomplete, the complete question is given below:

prove: let x be a positive rational number, then there exist positive integers n1, ..., nk such that x = n1/n2 + ..... + nk/nk.

A) All x- and y-intercepts include the following:

x-intercepts: none.

y-intercept: 1.

B) The equation for vertical asymptote is x = 4 and the equation for horizontal asymptote is y = 0.

C) The domain and range of f are:

Domain = [-∞, 4) U [4, ∞]

Range = [0, ∞]

In Mathematics, the x-intercept is the point at which the graph of a function crosses or touches the x-coordinate and the y-value or value of "y" is equal to zero (0).

Part A.

Based on the graph of this rational function, the x-intercept and y-intercept include the following:

x-intercept: none.

y-intercept: 1.

Part B.

An equation that represents the vertical asymptote is x = 4 while the equation represents the horizontal asymptote is y = 0 because the line does not cross those points.

Part C.

By critically observing the graph of this rational function, we can logically deduce the following domain and range:

Domain = [-∞, 4) U [4, ∞] or {x|x ≠ 4}.

Range = [0, ∞] or {y|y ≥ 0}.

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The association between the variables is strong and positive.

What are variables?

Any qualities, quantity, or number that can be gauged or tallied qualifies as a variable. A data item is another name for a variable. Examples of variables include age, sex, company income and expenses, country of birth, capital expenditures, class grades, eye color, and vehicle kind.

Here, we have

Given: A line to model the data is given by

y=12x + 41.

The equation of a straight line given by y = mx + c.  can easily make use of a regression line to ascertain the nature of the relationship between two variables as we can see in the graph shown in the question.

From the graph shown in the question, it is easy to ascertain that the association between the variables is strong and positive. The association is strong because the points lie together and positive because the plot increases linearly.

Hence, the association between the variables is strong and positive.

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A salary slip for the month of March 2023 with information given below.

Salary Slip - March 2023

Employee Details:

Name: [Employee Name]

Employee ID: [Employee ID]

Designation: [Employee Designation]

Earnings:

Basic Salary: [Basic Salary]

House Rent Allowance (HRA): [HRA]

Dearness Allowance (DA): [DA]

Incentive: [Incentive]

Total Earnings: [Total Earnings]

Deductions:

Provident Fund (PF): [PF]

Insurance: [Insurance]

Loss of Pay (LOP): [LOP]

Total Deductions: [Total Deductions]

Net Pay: [Net Pay]

Breakdown:

Basic Salary: 50% of CTC (18L) = [Basic Salary]

HRA: 20% of Basic Salary = [HRA]

DA: 12% of Basic Salary = [DA]

Incentive: 75% of target completion = [Incentive]

Total Earnings = Basic Salary + HRA + DA + Incentive = [Total Earnings]

PF: 12% of Basic Salary = [PF]

Insurance: Rs. 2500 = [Insurance]

LOP: [LOP]

Total Deductions = PF + Insurance + LOP = [Total Deductions]

Net Pay = Total Earnings - Total Deductions = [Net Pay]

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The equation showing the constant of proportionality between water in bowl and time is given as m = y / x

The constant of proportionality is the ratio that relates two given values in what is known as a proportional relationship. Other names for the constant of proportionality include the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.

Constant of proportionality is the constant value of the ratio between two proportional quantities. Two varying quantities are said to be in a relation of proportionality when, either their ratio or their product yields a constant. The value of the constant of proportionality depends on the type of proportion between the two given quantities:

In this case, since the number of time affects the number of millimeters directly, it is a direct variation.

We can also write this in form of an equation.

y = mx

m = constant of proportionality.

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Answer:

x = 4

m<AXC = 150

Step-by-step explanation:

m<1 + m<2 = m<AXC

102 + 10x + 8 = 6(6x + 1)

10x + 110 = 36x + 6

26x = 104

x = 4

m<AXC = 6(6x + 1)

m<AXC = 6(24 + 1)

m<AXC = 150

Answer: f(8) = 620.6

Step-by-step explanation:

To solve, you must first use substitution, and replace the x value in the given function, with 8.

\(f(8)=\frac{750}{1 + 74e^{-0.734(8)} }\)

Next you follow PEMDAS to solve the rest of the equation to find f(8).

What is PEMDAS?

PEMDAS is the order of operations for mathematical expressions involving more than one operation.

You solve in the following order

In this case our next step is deal with the exponents.

And by doing so, you will be multiplying -0.734 by 8

\(f(8)=\frac{750}{1 + 74e^{-5.872} }\)

And typical with exponents we would raise the number or variable given to the power of the exponent.

However we have a continuous number in this case, which is e.

What is e?

e is a mathematical constant approximately equal to 2.71828

We can now use a calculator to find what e (2.71....) is when raise to the exponent -5.872. Which results to 0.002817 (0.0028172332293320237716146943697).

When continuing to use numbers in calculators, don't use the rounded or shortened of the full number. Make sure to use the all of the numbers (given in the calculator) to its full extent to maintain accuracy.

\(f(8)=\frac{750}{1 + 74(0.002817) }\)

Now multiply 74 and 0.002817.... (use the full number to multiply (0.0028172332293320237716146943697)). The product is (0.2084752589705697590994873833578).

\(f(8)=\frac{750}{1 + 0.2084 }\)

Now lets add 1 + 0.2084.... and you get 1.2084

\(f(8)=\frac{750}{1.2084 }\)

Last you need to divide:

and you get that

f(8) = 620.6167

Now lets go back to the question, and we see that is says for you to round your answer to the nearest tenth.

so your final answer is:

f(8) = 620.6

Answer:

48,000

Step-by-step explanation:

SOLUTION: Each cubic foot holds 7.5 gallons of water. So, the amount of water required to fill the pool is 6400(7.5) = 48,000.

Answer:

4,000

Step-by-step explanation:

Rounding rule:

"4 or less, round down / keep the same."

"5 or more, round up."

Since the hundreds place has a 3, that means we round the thousands place to 4,000, because the hundreds place is lower than 5.

Answer:

m<15 = 88°

Step-by-step explanation:

Because m and n are parallel lines, that makes m<2 and m<10 corresponding angles, meaning they're equal.

So, since we're told m<2=92°, we can then say that similarly, m<10=92°.

m<10 and m<15 form a straight line, which adds to 180°. Writing this as a mathematical expression, we get:

m<10+m<15=180°

92°+m<15=180°

m<15=180°-92°=88°

The coordinates of point B are (-3, 17).

The given equation is M = I₁ + I₂ = 31 + 32.

Now let's substitute in our given values:

(-2, 2) = ((-5 + x₂) / 2, (-5 + 2 + y₂) / 2)

We will now set up two equations to solve for our two unknowns, x₂ and y₂:

Equation 1: (-5 + x₂) / 2 = -4

Multiply both sides by 2:

-5 + x₂ = -8

Add 5 to both sides:

x₂ = -3

This gives us the x-coordinate of point B.

Equation 2: (-5 + 2 + y₂) / 2 = 7

Simplify:

(-3 + y₂) / 2 = 7

Multiply both sides by 2:

-3 + y₂ = 14

Add 3 to both sides:

y₂ = 17

This gives us the y-coordinate of point B.

Therefore, the coordinates of point B are (-3, 17).

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Answer:3/9

Step-by-step explanation: 2/6=1/3. And 1/3x3=3/9

Answer:

Step-by-step explanation:

\(n^{5}= 1254\\n^{5} = 2.3.11.19\)

Therefore it is not possible that n is a perfect power of 5

           it is approximately 4.16

Answer:

n ≈ 4.165

Step-by-step explanation:

To solve this, you need to take the 5th root of both sides:

\(n^5=1,254\)

\(\sf{\sqrt[5]{n^5} =\sqrt[5]{1254}}\)

On the lhs we're only left with n as n^5 and the 5th root cancel each other out.

On the right-hand side we need to calculate:

\(n\approx4.165\)

Answer:

-8

Step-by-step explanation:

The term-to-term rule is -8.

16 - 24= -8

8 - 16 = -8

0 - 8 = -8

The arithmetic sequence is a concept of algebra and in given sequence 24, 16, 8, 0 the next term is, -8

In the arithmetic sequence  the common difference remains constant between any two consecutive terms. In this sequence we can get the next term by adding one fixed value which is known as a common difference. It is also known as arithmetic progression(AP).

Formula for any \(n^{th}\) term in AP,

T = a + (n-1)d

d = T₂-T₁

Where, a is first term , n is \(n^{th}\)  term and d is common difference

Given sequence,

24, 16, 8, 0

a = 24

n = 5

d = 16-24 = -8

T₅ = 24 +( (5-1)×(-8))

T₅ = -8

Hence,  \(5^{th}\) term of sequence is -8

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when the scale factor is 1, we have:

(side length of side opposite ∠A) / (length of hypotenuse) = sin A

When the scale factor is 1, the ratio of the side length of the side opposite ∠A to the length of the hypotenuse remains the same as in the original triangle. In a right triangle, the side opposite ∠A is referred to as the "opposite" side, and the hypotenuse is the longest side.

The ratio of the side length of the side opposite ∠A to the length of the hypotenuse is commonly known as the sine of angle A (sin A). So, when the scale factor is 1, the ratio of the side length of the side opposite ∠A to the length of the hypotenuse is equal to sin A.

In mathematical terms, when the scale factor is 1, we have:

(side length of side opposite ∠A) / (length of hypotenuse) = sin A

It's important to note that this ratio holds true for any right triangle, regardless of its size or dimensions, as long as the angle A remains the same.

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the infusion rate is 88.89 ml/hr or 88.89 gtt/min.

What is Rate?

A rate in arithmetic is a ratio that contrasts two separate values with various unit systems. For instance, if John types 50 words per minute, that means he types 50 words per minute. We are dealing with a rate because the word "per" is there. The symbol "/" can be used in place of the word "per" in issues.

When two or more similar amounts or numbers are being compared using the same units, a ratio is utilized. When referring to the ratio of one quantity "to" the second quantity in spoken language, it is frequently written with a colon.

Next, we can use the formula:

Flow rate (ml/hr) = (Volume infused ÷ Time in hours)

Flow rate (ml/hr) = (800 ml ÷ 9 hours)

Flow rate (ml/hr) = 88.89 ml/hr (rounded to two decimal places)

Finally, we can convert the flow rate from ml/hr to drops per minute (gtt/min) using the drop factor of 60 gtt/ml:

Flow rate (gtt/min) = Flow rate (ml/hr) x Drop factor (gtt/ml) ÷ 60 (min/hr)

Flow rate (gtt/min) = (88.89 ml/hr x 60 gtt/ml) ÷ 60 (min/hr)

Flow rate (gtt/min) = 88.89 gtt/min (rounded to two decimal places)

Therefore, the infusion rate is 88.89 ml/hr or 88.89 gtt/min.

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Answer:

\(\begin{array}{cc}X&P(X)\\0&0\\1&0.3333\\2&0.6667\end{array}\)

E(X)= 1.667

Step-by-step explanation:

The question asks for the probability distribution and the expected value of X.

The possible values for the number of defective cameras (X) are 0, 1 or 2.

The probability distribution for X is:

\(P(X=0)=0\)

Since there is only one camera in the box that is not defective, it is impossible for no camera to be defective when picking 2.

\(P(X=1)=\frac{1}{6}*\frac{5}{5}+\frac{5}{6}*\frac{1}{5}\\ P(X=1)=0.3333\)

\(P(X=2)=\frac{5}{6}*\frac{4}{5}\\ P(X=2) =0.6667\)

The probability distribution is:

\(\begin{array}{cc}X&P(X)\\0&0\\1&0.3333\\2&0.6667\end{array}\)

The expected value of X is:

\(E(X) = 0.3333*1+0.6667*2\\E(X) = 1.667\)

The expected value is 1.667 defective cameras.

Answer:

7^9

Step-by-step explanation:

when dividing you take away powers.

Answer:

7 to the power of 9

Step-by-step explanation:

7 by it self is 7 to the power of 1, and when you are dividing a power to subtract the power on top, so 10-1=9 and the answer is 7 to the power of 9 or 7^9

Answer:

The answer is y=-1 (answer is C).

Answer:

SIMPLIFY:

1.4x + 5x=9x

2.7y - 2y=5y

3.8 X a=8a

Step-by-step explanation:

1.4+5=9 and then just add X

2.7 - 2=5 and then just add y

3.8 X a=8a cause in the question there is no value of a

hope this help :)