The expression 4 square root of 81^3 can be rewritten as_____.

A. 81^3/4

B.81^4/3

C. 81^12

D. 81^1/12

Your answer would be a.

Answer: 3

hope this helps! :)

~Izzie

multiply 50 x tan(60) = 86.6 feet.

round your answer as needed

GCF is the greatest common factor, that divides two number and the distributive property is that when a number multiplied with each number in the bracket and then perform addition or subtraction etc.

GCF help with distributive property and it is important to use when factoring a sum of two numbers. For example we have to add fractions 2/3 and 4/9, now the GCF is 9

2/3 + 4/9

= 2(3) + 4 (1) / 9

Now 2 is the common factor, so it allow us to use the distributive property.

= 2 (3 + 2) / 9

= 2(5) /9

=10 / 9 is the answer.

Answer:

 [tex]\text{Probability}=4.3\%[/tex]

Step-by-step explanation:

Given : In a batch of 280 water purifiers, 12 were found to be defective.

To find : What is the probability that a water purifier chosen at random will be defective?  Write the probability as a percent.

Solution :

Total number of batch of purifiers = 280

Number of defective purifiers = 12

The probability that a water purifier chosen at random will be defective is given by,

[tex]\text{Probability}=\frac{\text{Favorable outcome}}{\text{Total outcome}}[/tex]

 [tex]\text{Probability}=\frac{12}{280}[/tex]

 [tex]\text{Probability}=\frac{3}{70}[/tex]

Converting into percentage,

 [tex]\text{Probability}=\frac{3}{70}\times 100[/tex]

 [tex]\text{Probability}=4.28\%[/tex]

Round to nearest tenths,

 [tex]\text{Probability}=4.3\%[/tex]

We state restrictions for rational expressions to ensure that the denominator does not equal zero, as division by zero is undefined in mathematics. The restrictions are the values of the variable that make the denominator equal to zero. We state the restrictions whenever we are simplifying, performing operations with, or solving rational expressions.

A rational expression is an expression that can be written in the form of a fraction, where the numerator and the denominator are polynomials. The denominator of a rational expression cannot be zero because division by zero is not defined in mathematics. Therefore, when working with rational expressions, it is crucial to identify the values of the variable that would make the denominator equal to zero. These values are the restrictions, or domain restrictions, for the rational expression.

For example, consider the rational expression [tex]\(\frac{1}{x-3}\)[/tex]. The denominator is[tex]\(x-3\)[/tex]. To find the restriction, we set the denominator equal to zero and solve for [tex]\(x\)[/tex]:

[tex]\[x - 3 = 0\][/tex]

[tex]\[x = 3\][/tex]

Therefore, the restriction for this rational expression is [tex]\(x \neq 3\)[/tex], meaning that [tex]\(x\)[/tex] can be any real number except 3.

We must state these restrictions whenever we perform operations such as simplifying, adding, subtracting, multiplying, or dividing rational expressions, as well as when we are solving rational equations. This ensures that the operations are valid and that the solutions to the equations do not include any undefined expressions.

In summary, stating restrictions for rational expressions is a critical step in avoiding mathematical errors and ensuring that the expressions and equations we work with are well-defined.

Answer:

(2 2/7, 5 1/3)

Step-by-step explanation:

The coordinates of point Q, lies along R(-2,4) and S(18,-6)

thus, QR and RS, that is in ratio of QR : RS = 3 : 7

Let point Q = (x,y)

Hence, QR = -2 - x; RS =  -6 - 4

Thus, QR/RS = 3/7, which is: (-2 - x)/(-6 - 4) = 3/7

7(-2 - x) = -30

-14 - 7x = -30

7x = 16

∴ x = 16/7 = 2 2/7

If x : y = 3 : 7 ( where x = 2 2/7)

Hence, (2 2/7)/y = 3/7

3y = 16

∴ y = 16/3 = 5 1/3

The coordinates  of point Q = (2 2/7, 5 1/3)

Answer:

The answer is B!!!!

The equation for the student's question is 25 - (1/5)x = 18. Solving for x involves simple algebraic manipulation, resulting in x being equal to 35.

The student's question '25 decreased by 1/5 of a number is 18' is a basic algebra problem. We could represent the unknown number as x. So the equation would be 25 - (1/5)x = 18.

To solve the equation 25 decreased by 1/5 of a number is equal to 18, we can set up the equation as 25 - (1/5)x = 18, where x is the unknown number.

To isolate x, we first subtract 25 from both sides of the equation:

- (1/5)x = -7.

Next, we can multiply both sides of the equation by -5 to eliminate the fraction:

x = (-7) * (-5) = 35.

To solve for x, first, add (1/5)x to both sides to get 25 = 18 + (1/5)x.

Then, subtract 18 from both sides to obtain 7 = (1/5)x. Finally, multiply both sides by 5 to find the value of x. Thus, x equals 35.

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divide 48 by 8%

48/0.08 = 600

check

600*0.08 = 48

x=600

Plan A = 30 +0.15x

Plan B = 16 +0.20x

30+0.15x = 16+0.20x

subtract 16 from each side

14 +0.15x = 0.20x

subtract 0.15x from each side

14=0.05x

 x = 14/0.05 = 280 minutes

280*0.15 = 42 +30 = $72

280 * 0.20 = 56 +16 = 72

 280 minutes and cost $72 each

We can solve this problem by simply using ratio and proportion. Let us call the height of the flagpole to be X. Therefore the ratio and proportion would be:

3 ft is to 4 ft and X ft is to 72 ft

3 / 4 = X / 72

X = (3 / 4) * 72

X = 54 ft

The height of the flagpole is 54 ft.

assuming it is based on a 40 hour work week, working 52 weeks per year:

35485/52 = 682.40 per week

682.40/40 = 17.06 per hour

50606/52 = 973.19 per week

973.19/40 = 24.33 per hour

 so between 17.06 & 24.33 per hour

To find the length of radius MJ, we can use right triangle trigonometry. Firstly, we can show that triangles LMJ and LKJ are right triangles. Then, we can use the given angle MLK of 61ᵒ to find the length of radius MJ, using the sine function. The equation to find MJ is MJ = rM * sin(29ᵒ).

To find the length of radius MJ, we can use right triangle trigonometry. Firstly, we can show that triangles LMJ and LKJ are right triangles. Since JL is a common tangent, it is perpendicular to the radii of the circles at points J. Therefore, angle LMJ and angle LKJ are right angles. Now, we can use the given angle MLK of 61ᵒ to find the length of radius MJ.

Let's call the radius of circle M rM and the radius of circle K rK. In triangle LMJ, we have the following relationships:

Using the sine function, we can find the length of side MJ:

sin(angle MLJ) = length of side MJ / length of side LJ

sin(-29ᵒ) = MJ / rM

Since sin(angle MLJ) = -sin(angle MJL), we can rewrite the equation as:

sin(29ᵒ) = MJ / rM

Now, we can rearrange the equation to solve for MJ:

MJ = rM * sin(29ᵒ)

Since we are not given the values of rM or rK, we cannot find the specific value of MJ. However, we can use this equation to find the length of radius MJ if we are given the values of the radii of the circles and the given angle MLK.

Remember to round the answer to the nearest hundredth as specified in the question.

The value of the expression 8x-2y over 10xy when x=4 and y=-7 is -0.1643 (rounded to four decimal places).

To evaluate the expression 8x-2y over 10xy when x=4 and y=-7, we substitute these values into the expression:

8(4)-2(-7) over 10(4)(-7)

Simplifying further,

32+14 over -280

46 over -280

Therefore, the value of the expression 8x-2y over 10xy when x=4 and y=-7 is -0.1643 (rounded to four decimal places).

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The confidence interval for a given sample value can be calculated using the following formula:

Confidence interval = Average value ± Margin of error

Which in this case the values are:

Average value = 85%

Margin of error = 12%

Therefore substituting the given values into the equation will give us:

Confidence interval = 85 ± 12

Confidence interval = 73, 97

Therefore the percentage of the residents of the town who are favour of building a new community center ranges from 73% to 97%.

Based from the given choices, only letter B 79% is within this range:

Answer:

B. 79%

Answer:

B. 79%

Step-by-step explanation:

yes

The minimum cost of producing this product is:

                                13

The function which is used to represent the cost to produce x elements is given by:

          [tex]f(x)=5x^2-70x+258[/tex]

Now, on simplifying this term we have:

[tex]f(x)=5(x^2-14x)+258\\\\i.e.\\\\f(x)=5(x^2+49-49-14x)+258\\\\i.e.\\\\f(x)=5((x-7)^2-49)+258\\\\i.e.\\\\f(x)=5(x-7)^2-5\times 49+258\\\\i.e.\\\\f(x)=5(x-7)^2-245+258\\\\i.e.\\\\f(x)=5(x-7)^2+13[/tex]

We know that:

[tex](x-7)^2\geq 0\\\\i.e.\\\\5(x-7)^2\geq 0\\\\i.e.\\\\5(x-7)^2+13\geq 13[/tex]

This means that:

[tex]f(x)\geq 13[/tex]

This means that the minimum cost of producing this product is: 13

In probability, a fraction does not need to be simplified but converting to a percentage or decimal can aid in interpretation, with percentages being fractions with a denominator of 100. (First option)

When a probability answer is written in the form of a fraction, it is important to know how to handle the result. Simplifying the fraction is not generally required, especially in Probability Topics, where the focus is on understanding the probability itself rather than the arithmetic of fractions.

However, converting the probability to a percentage is a common practice that can help with interpretation. This is done by writing the value of the percent as a fraction with a denominator of 100 and then simplifying it if possible.

Converting a fraction to a decimal is another common step, which involves dividing the numerator by the denominator. It's also important to note that for rounding answers to probability problems, the convention is to round to four decimal places.

After calculating the diagonal of the doorway to be approximately 8.944 feet using the Pythagorean theorem, it's clear that the 10-foot square piece of plywood will not fit diagonally through the door. Thus, the correct answer is option (A).

The question is whether a 10-foot square piece of plywood can fit through an 8-foot by 4-foot doorway when tilted diagonally. To determine if the plywood can fit, we need to calculate the diagonal of the doorway using the Pythagorean theorem which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as c² = a² + b² where c is the hypotenuse, and a and b are the other two sides.

Let's apply the theorem to our doorway:

Height (a) = 8 feet

Width (b) = 4 feet

Diagonal (c) = ?

We calculate the diagonal:

c² = a² + b²
c² = 8² + 4²
c² = 64 + 16
c² = 80
c = sqrt(80)
c = 8.944 feet (approx)

The diagonal of the doorway is approximately 8.944 feet, which is less than the 10 feet length of the plywood. Therefore, the correct answer is:

No, because the length of the diagonal is close to 9 feet.

The option (A) is correct.

Answer:

Option 1st is correct

[tex]f(-3) = -5[/tex]

Step-by-step explanation:

If any point [tex](x, y)[/tex] is on the graph then we can write the function as:

[tex]y= f(x)[/tex]

where

x is the independent variable and

y is the dependent variable.

As per the statement:

The point (–3, –5) is on the graph of a function.

⇒x = -3 and y = -5

By above definition we have;

[tex]f(-3) = -5[/tex]

Therefore, the equation must be true regarding the function is, [tex]f(-3) = -5[/tex]