A 118° sector of a circle has an area of 75 square centimeters. To the nearest centimeter, what is the diameter of the circle?

The number of laps it has made to a stop is 300 laps

Given the following

The rate at which the fan blows = 30rps

The time it takes to blow  = 10s

Required

number of laps it has made to a stop

Using the formula

Rate = Number of laps/time

30 = Number of laps/10

Number of laps = 30 * 10

Number of laps = 300

Hence the number of laps it has made to a stop is 300 laps

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Answer:

The expression πr2h is a monomial because it is a single term that is the product of three variables: π, r2, and h. The term "mono" means "one," and "monomial" refers to a single term in algebraic expressions.

The degree of a monomial is the sum of the exponents of its variables. In this case, the degree of the monomial is 3, because the variables π, r, and h have exponents of 1, 2, and 1 respectively. Therefore, the degree of the monomial is 1 + 2 + 1 = 3.

Answer:

About $59.66

Step-by-step explanation:

To find the amount of tax was paid, multiply 64.50 by 0.075 (because 0.075 = 7.5%). This would be 4.8375, which when rounded is 4.84. You subtract 64.50 by 4.84 to get 59.66, but because I rounded, it is about $59.66.

Answer:

60

Step-by-step explanation:

First, change the percentage to a decimal and write the equivalence of the sales tax amount. Let x be the original cost of the item.

Sales tax amount =x⋅0.075

Next, substitute the value into the equation:

Original Cost + Sales Tax Amount = Total Cost

x+0.075x=64.50

Add like terms.

1.075x=64.50

Divide both sides by 1.075 to isolate the unknown value.

x=$60

The result of the expression 20 - 6 is 14.

To solve the given expression, 20 - 6, and isolate the variable, we need to clarify whether there is an equation involved. However, in this case, the expression does not contain any variable to isolate, and it is not an equation that needs balancing. It is a straightforward arithmetic expression.

Step 1: Start with the given expression, 20 - 6.

Step 2: Evaluate the subtraction operation: 20 - 6 = 14.

Step 3: The simplified expression is now 14. However, since there is no variable present, there is no need to isolate any variable.

This means that when you subtract 6 from 20, the answer is 14. Remember that isolating a variable and balancing an equation are relevant when dealing with equations that involve variables. In this case, the expression is a simple subtraction operation, yielding a constant value of 14 as the answer.

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The number of cannonballs in illustration is 506.

Math Illustrations enables you to produce more useful geometry figures for your students in less time by fusing the constraint-based design of Geometry Expressions with simple-to-use sketching and graphing features.

The number of cannonballs in the first layer = 1² = 1

Number of cannonballs in the second layer = 2² = 4

Number of cannonballs in the third layer = 3² = 9

So, the generalized formula to count the balls is given as

= n(n + 1) (2n + 1)/ 6

Here, n= the total number of layers

Put n =11

11(11 + 1)(2(11) + 1) / 6

= 11(12)(23)/6

= 3036/6
= 506

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You can find the simple interest using the following formula:

I = PV*r*t

Where:

PV = Present value or principal = $530

r = interest rate = 6% = 0.06

t = time = 1

Replacing the data into the equation:

I = 530*0.06*1 = $31.8

Hi! So you need CE.  CD + DE = CE, and the values are 14 + 2x + 3.  That's 17 + 2x.  Is there any more given information?  I don't see what's available.  Otherwise that may be the only way you can simplify it.

Answer:

Tan(x)

Step-by-step explanation:

JUST TOOK THE TEST

tan(x) is equivalent to 1/sin2x - cos2x/sin2x. Option a is correct.

To determine equivalent 1/sin2x - cos2x/sin2x.

tan(x) is tangent of x here, tan is trigonometric operator.

Here,
= 1/sin2x - cos2x/sin2x
= (1-cos2x)/sin2x
= (2sin²x)/2sinxcosx
= sin(x)/cos(x)
= tan(x)

Thus, tan(x) is equivalent to 1/sin2x - cos2x/sin2x.

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Answer:

x=\(1.22930\)

Step-by-step explanation:

47(218 x+12 ) =−2(17 −528 x)

Simplify 47(218 x+12 ) :    327(21x+4) 327(21x+4) =−2(17 −528 x)

Multiply both sides by 7(21x+4)

327(21x+4) · 7(21x+4)=−2(17 −528 x)· 7(21x+4)

Simplify, 32=−14(17 −528 x)(21x+4)

Solve  32=−14(17 −528 x)(21x+4):    x=32+4√589105 , x=32−4√589105 x=32+4√589105 , x=32−4√589105

Answer:

x = 0.5

Step-by-step explanation:

\(\frac{4}{7}(\frac{21}{8}x + \frac{1}{2}) = -2(\frac{1}{7} - \frac{5}{28}x)\)

\(1\frac{1}{2}x + \frac{2}{7} = - \frac{2}{7} + \frac{5}{14}x\)

\(1\frac{1}{2}x - \frac{5}{14}x + \frac{2}{7} = - \frac{2}{7} + \frac{5}{14}x - \frac{5}{14}x\)

\(1\frac{1}{7}x + \frac{2}{7} = - \frac{2}{7}\)

\(1\frac{1}{7}x + \frac{2}{7} - \frac{2}{7} = - \frac{2}{7} - \frac{2}{7}\)

\(1\frac{1}{7}x = - \frac{4}{7}\)

\(\frac{1\frac{1}{7}x}{1\frac{1}{7} } = \frac{- \frac{4}{7}}{1\frac{1}{7} }\)

\(x = -\frac{1}{2}\)

Answer:

Step-by-step explanation:

B looks like it would work.

You add speeds * time when you are travelling in opposite directions.

I don't know why you would add or subtract 1 as in A and C

120 * t = 540

t = 540/120

t = 4.5 hours.

So after 4.5 hours they are 540 miles apart.

Answer:

b

Step-by-step explanation:

The exact solution of the equation 3x = 8 written as a logarithm is x = log3 8 and an approximate solution rounded to the nearest thousandth using the Change of Base Formula is x ≈ 1.893.

The equation given is 3x = 8.

Part A asks for the exact solution written as a logarithm. To solve for x, we can use logarithms. Taking the logarithm of both sides with base 3, we have:

log3(3x) = log3(8)

Using the power rule of logarithms, we get:

x log3(3) = log3(8)

Since log3(3) = 1, we have:

x = log3(8)

Therefore, the answer to Part A is (A) x = log3(8).

Part B asks for an approximate solution rounded to the nearest thousandth. We can use the change of base formula, which states that:

loga(b) = logc(b) / logc(a)

Using this formula with base 10, we get:

x = log10(8) / log10(3)

Using a calculator, we get:

x ≈ 1.892

Rounding to the nearest thousandth, we get:

x ≈ 1.892

Therefore, rounded to the nearest thousandth, the approximate solution is 1.892.

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Answer:

  B.  A point

Step-by-step explanation:

You want a description of the intersection between a plane and a cone given that the plane is parallel to the base and passes through the vertex of the cone.

The vertex of a cone is a single point. If a plane passes through that, but does not intersect the base of the cone, it will not intersect anywhere else.

The intersection is one point.

__

Additional comment

Figure f in the attachment illustrates this case.

Answer:

P(B,B) = 3/68

P(R,B) = 2/17

P(R,R) = 7/17

Step-by-step explanation:

P(B,B) = 4/17 · 3/16 = 3/68

P(R,B) = 8/17 · 4/16 = 2/17

P(R,R) = 8/17 · 7/16 = 7/17

Answer:

all are 17.67%

Step-by-step explanation:

Answer:

Solution given:

x+100=180°{linear pair}

x=180-100

x=80

Answer:

Things which are equal to the same thing are also equal to one another. If equals be added to equals, the wholes are equal. If equals be subtracted from equals, the remainders are equal. Things which coincide with one another are equal to one another.

Answer:

Step-by-step explanation:

Answer : 8$

you have 1$ left

The needed number of days at 10 degrees is given as follows:

11 days.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

For this problem, we have that when x decreases by 5, y increases by 2, hence the slope m is given as follows:

m = -2/5

m = -0.4.

Hence the time needed for a temperature of 10 degrees is given as follows:

9 + 2 = 11 days.

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Answer:

x + \(x^{2}\) = yz

Step-by-step explanation:

The expressions that are equivalent to 3^8 are:

We have to solve these out

3^8. = 6561

From the options

A. 3^2x3^4

= 9 x 81

= 729

B  3²x3^6

= 9 x 729

= 6561

C.  3^16/3^2

= 43046721/9

= 4782969

d. 3^12/3^4

= 531441 / 81

= 6561

E.  (3^4)²

= 3⁴ x 3⁴

= 3⁴⁺⁴

= 3⁸

= 6561

F. (3¹)^7

= 3⁷

= 2187

The expressions that are equivalent to 3^8 are:

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It will take approximately 28.67 years for Talwar's investment of R5,800 to grow to R26,100 at a simple interest rate of 12.2% per annum.

To calculate the number of years it will take for Talwar's investment to grow to R26,100 at a simple interest rate of 12.2% per annum, we can use the formula for simple interest:

Simple Interest = Principal × Rate × Time

Given that the principal (P) is R5,800, the rate (R) is 12.2% (or 0.122 as a decimal), and the desired amount (A) is R26,100, we need to find the time (T) it will take. Rearranging the formula, we get:

Time = (Amount - Principal) / (Principal × Rate)

Plugging in the values, we have:

Time = (R26,100 - R5,800) / (R5,800 × 0.122)

= R20,300 / R708.6

≈ 28.67 years

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The values of x is 6 and y is (-6).

An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.

Given:

-4x-5y=6............(1)

9x+7y=12..................(2)

Solving Equation (1) and (2) we get

-36 x  - 45y = 54

36x + 28y = 48

____________

         -17y= 102

              y= -6.

and, -4x -5y= 6

-4x - 5(-6) = 6

-4x + 30 = 6

-4x = 6-30

-4x = -24

x= 6

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To get the value of m x H

We will first get the value of m and then H

To get the value of m

The next is to get H

Let H be represented by [ A B C] so that

=>

=> Simplifying further

Thus,

The final step will be to find m x H

To simplify m

Therefore

Therefore

m x H will be

The answer is:

Answer: 7

Step-by-step explanation:

Since there are 42 tubes and each tray can hold 6 tubes, it will be 42/6 which is 7.

The probability that the average length of a randomly selected bundle of steel rods is greater than 168.58 cm is 0.7486

First, we need to calculate the z-score for the sample mean:

z = (x - μ) / (σ / √n)

z = (168.58 - 169) / (2.2 / √10)

z = -0.67

Next, we need to find the probability that a randomly selected bundle of steel rods will have a mean length greater than 168.58 cm. This is equivalent to finding the area under the standard normal distribution curve to the right of z = -0.67.

Using a standard normal distribution table or calculator, we find that the probability is 0.7486.

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Answer: Mr. Jay’s cost 85 cents and Mr. Tony’s costs 83 cents.

Step-by-step explanation:

you divide the price by how many seeds they sold.

Answer:

\( SE =\sqrt{\frac{p(1-p)}{n}}\)

And replacing we got:

\( SE=\sqrt{\frac{0.75*(1-0.75)}{900}}= 0.014\)

Step-by-step explanation:

For this case we have the following info given:

\( n=900\) represent the sample size selected

\(p = 0.75\) represent the population proportion

We want to find the standard error and we can use the distribution for the sample proportion and for this case since the sample size is large enough and we satisfy np>10 and n(1-p) >10 we have:

\( \hat p \sim N (p,\sqrt{\frac{p(1-p)}{n}})\)

And the standard error is given;

\( SE =\sqrt{\frac{p(1-p)}{n}}\)

And replacing we got:

\( SE= \sqrt{\frac{0.75* (1-0.75)}{900}}= 0.014\)

The value of length BC is 18.9

Cosine Rule states that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

Therefore,

c² = a² + b² - 2abcosC

To find the length BC we use cosine rule.

c² = 13² + 7² - 2(13)(7)cos140

c² = 218 - 182cos140

c² = 218-(-139.42)

c² = 218+139.2

c² = 357.2

c = √357.2

c = 18.9

Therefore, the length of BC is 18.9

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In the triangle, the value of the side BC is 18.9cm to 1 decimal place

The side BC can be found using the cosine formula, Remember that Cosine Rule states that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

The cosine formula states that

c² = a² + b² - 2abcosC

To find the length BC we use cosine rule.

c² = 13² + 7² - 2(13)(7)cos140

c² = 218 - 182cos140

c² = 218-(-139.42)

c² = 218+139.2

c² = 357.2

c = √357.2

c = 18.9

In conclusion, the value of  the length of BC is 18.9cm

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