3 + 8 + 6 + 6 + 6 = 58 + 6
How do we solve this

Answer:

14

Step-by-step explanation:

angle 90° is opposite the side x. angle 45° is opposite side 7√2.

x/sin 90 = (7√2)/sin 45

multiply both sides by sin 90 (sin 90 is = 1).

x = (7√2)/sin 45

 = 14

Answer:

B.  -414,720 x⁷y⁶

Step-by-step explanation:

To find the 4th term of the expansion of (2x - 3y²)¹⁰, we can use the binomial theorem.

The binomial theorem states that for an expression of the form (a + b)ⁿ:

\(\displaystyle (a+b)^n=\binom{n}{0}a^{n-0}b^0+\binom{n}{1}a^{n-1}b^1+...+\binom{n}{r}a^{n-r}b^r+...+\binom{n}{n}a^{n-n}b^n\\\\\\\textsf{where }\displaystyle \rm \binom{n}{r} \: = \:^{n}C_{r} = \frac{n!}{r!(n-r)!}\)

For the expression (2x - 3y²)¹⁰:

Therefore, each term in the expression can be calculated using:

\(\displaystyle \boxed{\binom{n}{r}(2x)^{10-r}(-3y^2)^r}\quad \textsf{where $r = 0$ is the first term.}\)

The 4th term is when r = 3. Therefore:

\(\begin{aligned}\displaystyle &\;\;\;\;\:\binom{10}{3}(2x)^{10-3}(-3y^2)^3\\\\&=\frac{10!}{3!(10-3)!}(2x)^7(-3y^2)^3\\\\&=\frac{10!}{3!\:7!}\cdot2^7x^7(-3)^3y^6\\\\&=120\cdot 128x^7 \cdot (-27)y^6\\\\&=-414720\:x^7y^6\\\\ \end{aligned}\)

So the 4th term of the given expansion is:

\(\boxed{-414720\:x^7y^6}\)

The mode of the data set is 7

The median is 6

the mean is 5.2

The range is 7

This is the number with the highest frequency or occurrence. This is 7

arrange based on ascending order

1, 2, 3, 4, 5, 7, 7, 7, 8, 8

median = 5 + 7 / 2

= 6

add all the numbers / total number

52 /10

= 5.2

The range = highest - lowest

= 8 - 1

= 7

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The value of the inverse function f-¹ (3) is (e) 11

From the question, we have the following parameters that can be used in our computation:

f(x) = x - 8

To calculate the inverse value at f-¹ (3)

We set the value to 3

using the above as a guide, we have the following:

x - 8 = 3

Evaluate the like terms

x = 11

Hence, the value of the inverse function is (e) 11

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Complete question

if f(x) = x - 8, what is the value of f-¹ (3)?

Using trigonometric functions, The length of perpendicular x will be 4.2 unit.

Trigonometric functions are what ?

Trigonometric functions, often known as circular functions, are simple functions that compute the angle of a triangle. These trigonometric functions establish the relationship between a triangle's angles and sides. The fundamental functions are sine, cosine, tangent, cotangent, secant, and cosecant.

Trigonometric functions are fundamentally classified by the sine, cosine, and tangent angles. The three functions cotangent, secant, and cosecant may be obtained using the fundamental functions.

Now,

Given length of hypotenuse = 6

and angles are 45°, 45° and 90°

then sin 45°=perpendicular/hypotenuse=6/x

x=6/√2

x=4.2

Hence,

          The length of perpendicular x will be 4.2 unit.

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Answer:

2144.7cm³

Step-by-step explanation:

volume =  \(\frac{4}{3}\) pi 8³

A compound event can be described for flipping a coin two times and getting at least 1 head.

Compound event is defined as the events in which there are more than one event happens together.

All the outcomes of the events sum up the probability to 1.

We have to describe a compound event where the probability is in between 50% and 80%.

That is, probability is in between 0.5 and 0.8.

That is, there is more than half of the chance to occur the event.

Suppose that we flip a coin two times.

Sample space = {HH, HT, TH, TT}

Find the probability of getting at least 1 head.

There are 3 outcomes out of 4 of getting at least 1 head.

Probability = 3/4 = 75%

Hence there is a 75% probability for getting at least 1 head when flipped a coin two times.

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Manual paid with a $10 bill and he got $2.46 as a change.

Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. Subtraction is signified by the minus sign, −.

Money spent on sandwich=$4.56 and money spent on drink=$2.98.

We need to find out how much did he spend in all.

That is, the total money spent=4.56+2.98=$7.54

He paid with a $10 bill, he gets change as 10-7.54=$2.46

Hence, he paid with a $10 bill and he got $2.46 as a change.

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We're given:

If the shop sold " \(9\dfrac{9}{10}\)  times as much milk chocolate as white chocolate", we must multiply \(9\dfrac{9}{10}\) by the amount of white chocolate sold to find the amount of milk chocolate sold.

Multiply \(9\dfrac{9}{10}\) by 9 ounces:

\(9\dfrac{9}{10}\times9\)

Convert the fraction into an improper fraction:

\(=\dfrac{99}{10}\times9\)

Multiply:

\(=\dfrac{891}{10}\)

The shop sold \(\dfrac{891}{10}\) ounces of milk chocolate.

a. The  slope of the curve at the point (4,16)   is approximately 1.165, and at the point (16,4)  is approximately -0.496.

b. The   curve has a horizontal tangent line at the points(0,0) and (3,27).

c. The   curve has a vertical tangent lineat the points (0,0) and (65/2, (65/2)³).

a. To find the   slope of the curve given by the equation x³ + y³ - 65xy = 0 at the points (4,16) and (16,4),we can differentiate the equation implicitly with respect to x and solve for dy/dx.

Differentiating the equation with respect to x, we have  -

3x² + 3y²(dy/dx) - 65y - 65x(dy/dx) = 0

To find the slope at a specific point, substitute the x and y coordinates into the equation and solve for dy/dx.

For the point (4,16)  -

3(4)² + 3(16)²(dy/dx) - 65(16) - 65(4)(dy/dx) = 0

48 + 768(dy/dx) - 1040 - 260(dy/dx) = 0

508(dy/dx) = 592

(dy/dx) = 592/508

(dy/dx) ≈ 1.165

For the point (16,4)  -

3(16)² + 3(4)²(dy/dx) - 65(4) - 65(16)(dy/dx) = 0

768 + 48(dy/dx) - 260 - 1040(dy/dx) = 0

(-992)(dy/dx) = 492

(dy/dx) = 492/(-992)

(dy/dx) ≈ -0.496

Thus, the slope of the   curve at the point (4,16) isapproximately 1.165, and at the point (16,4) is approximately -0.496.

b. To find the point where the curve has   a horizontal tangent line, we need to find the x-coordinate(s)where dy/dx equals zero.

This means   the slope is zero and the tangent line is horizontal.

From the derivative we obtained earlier  -

3x² + 3y²(dy/dx) - 65y - 65x(dy/dx) = 0

Setting dy/dx equal to zero  -

3x² - 65y = 0

Substituting y = x³/65 into the equation  -

3x² - 65(x³/65) = 0

3x² - x³ = 0

Factoring out an x²  -

x²(3 - x) = 0

This equation has two solutions  -  x = 0 and x = 3.

hence, the curve has a horizontal   tangent line at the points(0,0) and (3,27).

c. To find the point where the curve has a vertical tangent line, we need to find the x-coordinate(s)   where the derivative is undefinedor approaches infinity.

From the derivative  -

3x² + 3y²(dy/dx) - 65y - 65x(dy/dx) = 0

To find the vertical tangent line, dy/dx should be undefined or infinite. This occurs when the denominator of dy/dx is zero.

Setting the denominator equal to zero:  -

65x = 65y

x = y

Substituting this condition back into the original equation  -

x³ + x³ - 65x² = 0

2x³ - 65x² = 0

x²(2x - 65) = 0

This equation has two solutions  - x = 0 and x = 65/2.

Therefore, the curve has a vertical tangent line   at the points (0,0)

and(65/2, (65/2)³).

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Answer:

3kg = 6.614 pounds

Step-by-step explanation:

please mark me brainliest

Answer:

D. A pair of intersecting lines

Step-by-step explanation:

A conic section is a fancy name for a curve that you get when you slice a double cone with a plane. Imagine you have two ice cream cones stuck together at the tips, and you cut them with a knife. Depending on how you cut them, you can get different shapes. These shapes are called conic sections, and they include circles, ellipses, parabolas and hyperbolas. If you cut them right at the tip, you get a point. If you cut them slightly above the tip, you get a line. If you cut them at an angle, you get two lines that cross each other. That's what happened in your question. The plane cut the cone at an angle, so the curve is two intersecting lines. That means the correct answer is D. A pair of intersecting lines.

I hope this helps you ace your math question.

Answer:

Your answer would be 15

Step-by-step explanation:

The first step you are going to want to do is multiply 2 and 30

30×2=60

Then you are going to divide 60 by 12

60÷12=5

Last you wanna add the 5 and the 10

5+10=15

Answer:

Step-by-step explanation:

The given hexagon has interior angles

x,x,x, x/2, x/2, x/2 for a total of S1=4.5x.

We also know that the sum of interior angles of any polygon of n sides is

S2=180(n-2)

For a hexagon, S2 = 180(6-2) = 720°.

Equating S1 and S2

4.5x = 720

x = 720/4.5 = 160.

Therefore substitute x in the given angles to get

{160°,160°.160°,80°,80°,80°}

The equation for number of miles is 14/7 = x and she ran 2 miles each day.

Simplify the equation to bring all the variable terms to one side and the constant value to the other in order to solve linear equations with a single variable. Find the LCM (least common multiple) if there are any fractional terms, then simplify them so that the variable values are on one line and the steady terms are on the other.

Let us suppose the number of miles she ran each day = x.

Given that, Aroline ran 14 miles in 7 days.

Thus,

Total distance / Number of days = x

14/7 = x

x = 2

Hence, the equation is 14/7 = x and she ran 2 miles each day.

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Answer:

Step-by-step explanation:

The volume of this pyramid in cubic inches is 16.

Given that,

The base and height is 8 and 6.

Based on the above information, the calculation is as follows:

The volume is

= 16

The description that will show that it is safe to perform inference is that (a) Both dotplots are roughly symmetric. There are no outliers in either dotplot.

In order to use the two-sample t procedure to make inferences, certain conditions need to be met such as the sample being random and independent.

The variances for the groups in the data need to be equal which is why the presence of no outliers in either dotplot would present an safe opportunity to be able to perform inferences on the data.

In conclusion, option A is correct.

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Answer:

A

Step-by-step explanation:

(because -4 is equal to -4 and meets the condition of the top inequality, you plug in -4 into the top function)

\(g(-4)=\sqrt[3]{(-4)+5}\\\\g(-4)=\sqrt[3]{1} =1\)

Answer

x=52/5

Step-by-step explanation:

Multiply all terms by the same value to eliminate fraction denominators next

Cancel multiplied terms that are in the denominator after that you

Multiply the numbers

Answer:

3

Step-by-step explanation:

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Answer:

1. C

2. A

3. A

Step-by-step explanation:

1. It is the Symmetric Property of Congruence because the definition is literally what it says.

2. Incomplete sentences don't matter as long as you have the right stuff.

3. Step 2 is wrong because it should be Definition of Midpoint.

If Curtis is attempting to defend a step in his proof paragraph. He should apply the symmetric property of congruence so that he can demonstrate that AB=BC and that BC=AB. It's best to choose C.

It is defined as the branch of mathematics that is concerned with the size, shape, and orientation of two-dimensional figures.

A)If Curtis is trying to justify a step in his paragraph proof. Symmetric Property of Congruence that he should use as a result he can show AB=BC therefore BC=AB. Option C is correct.

B)All of the following would make a formal proof incomplete except Incomplete sentences. Option A is correct.

C)Step 2 in the proof has a flaw Because it is not a symmetric property while they show congruency because it must be a midpoint definition. Option A is correct.

Thus, if Curtis is trying to justify a step in his paragraph proof. Symmetric Property of Congruence that he should use as a result he can show AB=BC therefore BC=AB. Option C is correct.

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we have

2(w+3)-(w-1) ​

apply distributive property first term and remove the parenthesis

2w+6-w+1

combine like terms

The total cost of rents is $180.

In the given table,

The cost of skis per day  = $48

The cost of pole per day = $12

Now since given that,

Alveres rents for 3 days

Therefore,

The cost of skis for 3 days  = $48 x 3

                                             =  $144

The cost of pole for 3 days = $12 x 3

                                             = $36

To find the total cost of rental,

Adding the cost of 3 days of skis and cost of 3 days of poles,

Hence,

Total cost of rents = $144 + $36

                               = $180

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Answer:

Keith solve the equation correctly

Step-by-step explanation:

x² + 17x + 72 = 12 ( subtract 12 from both sides )

x² + 17x + 60 = 0 ← in standard form

Consider the factors of the constant term (+ 60) which sum to give the coefficient of the x- term (+ 17)

The factors are + 12 and + 5 , since

12 × 5 = 60 and 12 + 5 = 17 , then

(x + 12)(x + 5) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 12 = 0 ⇒ x = - 12

x + 5 = 0 ⇒ x = - 5

The solutions of the equation are x = - 12, x = - 5

Answer:

12 & 13

Step-by-step explanation:

trust me

Answer:

D

Step-by-step explanation:

...................

The solutions to the quadratic equation x² + 10x - 13 = 17 are x = -5 + √55 and x = -5 - √55. The correct answer is option D.

The quadratic equation is given as:

x²+10x-13 =17

Move the constant term to the right side of the equation:

x² + 10x - 13 - 17 = 0

x² + 10x - 30 = 0

Take half of the coefficient of the x-term (10) and square it: (10/2)² = 25.

Add the squared value to both sides of the equation:

x² + 10x + 25 - 30 = 25

(x + 5)² - 30 = 25

Simplify the equation:

(x + 5)² = 25 + 30

(x + 5)² = 55

Take the square root of both sides of the equation:

√((x + 5)²) = ±√55

x + 5 = ±√55

Solve for x by subtracting 5 from both sides:

x = -5 ± √55

Therefore, the solutions to the equation x² + 10x - 13 = 17 are:

x = -5 + √55 and x = -5 - √55.

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Answer:

Step-by-step explanation:

a. 1, 2, 3, 4, 5, 10, 11, 12, 13, 14, 15, 20, 21, 22, 23

b. 1, 2, 3,,4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16.

The first fifteen counting numerals for number base six are 1, 2, 3, 4, 5, 10, 11, 12, 13, 14, 15, 20, 21, 22, 23.

The first fifteen counting numerals for number base nine are 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18

A number base is the number of digits or combination of digits that a system of counting use to  represent numbers.

A base can be any whole number greater than 0

a) First fifteen counting numerals for base six

1) 1

2) 2

3) 3

4) 4

5) 5

6) 10

7) 11

8) 12

9) 13

10) 14

11) 15

12) 20

13) 21

14) 22

15) 23

b) First fifteen counting numerals for base 9

1) 1

2) 2

3) 3

4) 4

5 ) 5

6) 6

7) 7

8) 8

9 ) 10

10) 11

11) 12

12) 13

13) 14

14) 15

15) 16

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