In the triangle below, angle B measures 60° and BC is 18. What is the length of AC?

Right triangle A B C is shown. Side B C is the hypotenuse.
9 StartRoot 3 EndRoot
StartFraction 9 Over StartRoot 3 EndRoot EndFraction
9
StartFraction StartRoot 3 EndRoot Over 9 EndFraction

The method is: Find the increase and find the ratio of the increase and the old price.

The percentage increase is 20%

A percentage is defined as the ratio that can be expressed as a fraction of 100.

The method below shows how you would calculate the % increase.

First step: Find the increase:

increase = 480 - 400 = $80

Second step: Find the ratio of the increase and the old price and multiply by 100 to express in percentage:

80/400 * 100 = 20%

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Answer:

10.7

Step-by-step explanation:

Since this is a right triangle, we can use trig functions to calculate the hypotenuse.

We know the opposite side from the angle labeled 59 degrees.

sin 59 = opp side / hypotenuse

sin 59 = 9.2/x

x = 9.2/ sin 59

x = 10.733

a. The answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.

b. The answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.

a. To represent 20 longs in base seven, we need to find the fewest number of multibase blocks required.

In base seven, we have the following conversions:

1 long = 1 unit

1 flat = 10 units

1 block = 10 flats

To represent 20 longs, we can use 2 flats (each flat representing 10 units) and 0 units since there are no remaining units.

So, the fewest number of multibase blocks required would be 2 flats.

Therefore, the answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.

b. To represent 10 longs in base three, we need to find the fewest number of multibase blocks required.

In base three, we have the following conversions:

1 long = 1 unit

1 flat = 3 units

1 block = 3 flats

To represent 10 longs, we can use 3 flats (each flat representing 3 units) and 1 unit since there is one remaining unit.

So, the fewest number of multibase blocks required would be 3 flats and 1 unit.

Therefore, the answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.

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Answer:

X + 15 < 9

x < 15 - 9

x < -6

Step-by-step explanation:

Hope you got it

In 2021 a 30-second commercial during the Super Bowl cost $5.6 million and the CPI was approximately 271.4. Assuming that price changes are simply due to inflation, when the CPI was 33.4 the estimated cost of a 30-second commercial during the first Super Bowl in 1967 would be approximately $68,900.

To calculate the cost of the 30-second commercial during the first Super Bowl in 1967, we can use the concept of inflation and the Consumer Price Index (CPI).

The CPI measures the average price change of a basket of goods and services over time. By comparing the CPI values of two different years, we can estimate the relative increase in prices due to inflation.

Given data:

Cost of a 30-second commercial in 2021 = $5.6 million

CPI in 2021 = 271.4

CPI in 1967 = 33.4

To calculate the cost in 1967, we need to adjust the 2021 cost for inflation using the CPI ratio:

Cost in 1967 = (Cost in 2021) * (CPI in 1967 / CPI in 2021)

Cost in 1967 = ($5.6 million) * (33.4 / 271.4)

Cost in 1967 ≈ $0.689 million

To round the cost to the nearest hundred dollars, we can multiply the cost by 100 and round it to the nearest whole number:

Cost in 1967 ≈ $68,900

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Answer:

c. x=65

f. Alternate Exterior Angles

Step-by-step explanation:

2x+2=3x-63

2x=3x-65

-x=-65

x=65

They would be Alternate Exterior Angles because, they are 1, both on the outside of the parallel lines, and they are on different sides of the intersecting line, making them alternate. So, Alternate Exterior Angles

Answer:

To simplify the expression (a÷b)³×(b÷c)×(c÷a)³ when a=3, b=a², c=a³, we can substitute the given values and perform the calculations.

Substituting the values of a, b, and c:

a = 3

b = a² = 3² = 9

c = a³ = 3³ = 27

Now let's simplify the expression:

(a÷b)³×(b÷c)×(c÷a)³

(3÷9)³×(9÷27)×(27÷3)³

Simplifying each term:

(3÷9) = 1/3

(9÷27) = 1/3

(27÷3) = 9

Now we can substitute the simplified values back into the expression:

(1/3)³×(1/3)×9

Simplifying further:

(1/27)×(1/3)×9

1/9

Therefore, the simplified expression is 1/9.

Answer:

Step-by-step explanation:

6x5x7=210

the volume is 7m

Answer:A

Step-by-step explanation:

The items of worth $600,000,000 should be purchased in the state to meet the requirement, the correct option is A.

An equation is a mathematical statement that is formed when two algebraic expressions are equated using an equal sign.

The state has predicted to get $24 million from the state lottery,

The amount from property tax is $32 million

The amount form excise tax is $14 million

The state needs $100 million to cover its expenses

A sales tax of 5% is charged by the state

Let the total sales is $x in million dollars then the equation that can be formed is

24 + 32 +14 +(5/100 ) * x = 100

70+ (5/100 ) * x = 100

(5/100 ) * x = 100 -70

(5/100 ) * x = 30

x = 30 * 100 / 5

x = $600,000,000

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Answer:

  16x^3 +64x^2 -40x

Step-by-step explanation:

Use the distributive property. The factor outside parentheses multiplies each term inside parentheses:

  8x(2x^2 +8x -5) = (8x)(2x^2) +(8x)(8x) +(8x)(-5)

  = 16x^3 +64x^2 -40x

Answer:

2/1

Step-by-step explanation:

So you want to find a point where the line crosses a intersection near perfectly, point A (1,3) and then a second point, B (2,5)

and then you count up from point a, on the Y axis until you are even with the second point, that number is your RISE

it is 2

then you just count over to point B from that spot where you counted up. RUN TO IT

1

so it is 2/1 or just 2

((point (0,1) would have worked too))

Answer:

Step-by-step explanation:

First, we need to find the difference between the price that he sold the shares for and the price that he bought them at: (67.68-60.65) = 7.03

That means that there was a gain of $7.03 per share for Archie.

That being said, since Archie bought 100 shares, we can multiply that number by 100 to find the total gain from selling the shares:

(7.03x100)= 703

The answer then is:

Archie gained $703 from selling all of his shares.

Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

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The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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The expression -√3 sin x + cos x in the desired form k sin(x+0), where k = -1.732 and 0 = π/2. Therefore, -√3 sin x + cos x = -1.732 sin(x+π/2)

We can start by trying to write the expression in the form k sin(x+0), where k is some constant and 0 is an angle. To do this, we'll need to use some trigonometric identities.

First, note that -√3 is the same as -1.732, which is the negative square root of 3.

Next, we can use the identity sin(a+b) = sin(a)cos(b) + cos(a)sin(b) to write:

-1.732 sin(x) + cos(x)

= -1.732 sin(x) + 1 sin(x + π/2)

= sin(x + π/2) (-1.732 cos(π/2) + 1 sin(π/2))

= sin(x + π/2) (-1.7320 + 11)

= sin(x + π/2) (-1.732)

So we have expressed the expression -√3 sin x + cos x in the desired form k sin(x+0), where k = -1.732 and 0 = π/2. Therefore, -√3 sin x + cos x = -1.732 sin(x+π/2)

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Answer:

DC = 53

Step-by-step explanation:

the midsegment EF is half the sum of the bases , that is

\(\frac{AB+DC}{2}\) = EF

\(\frac{41+DC}{2}\) = 47 ( multiply both sides by 2 to clear the fraction )

41 + DC = 94 ( subtract 41 from both sides )

DC = 53

Answer:

27

Step-by-step explanation:

3(5+1+3) distribute

15+ 3+ 9 add

27

The calculated scale factor from ABC to A'B'C is 1/3

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

The triangles

From the triangles, we have the following parameters

A = (0, 3)

A' = (0, 1)

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

Scale factor of the dilation = A'/A

So, we have

Scale factor of the dilation = (0, 1)/(0, 3)

Evaluate

Scale factor of the dilation = 1/3

Hence, the scale factor of the dilation is 1/3

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By using the 68-95-99.7 Rule, the percent of scores in the data set that are expected to be below a score of 120 is 84.13%.

In Mathematics, the Empirical Rule is sometimes referred to as the 68-95-99.7 rule and it can be defined as a statistical rule which states that:

At the middle 68% of the normal distribution, we have the following standard score:

μ - σ = 108 - 12 = 96.

μ - σ = 108 + 12 = 120.

Where:

At the middle 95% of the normal distribution, we have:

μ - σ = 108 - 2(12) = 84.

μ - σ = 108 + 2(12) = 132.

At the middle 99.7% of the normal distribution, we have:

μ - σ = 108 - 3(12) = 72.

μ - σ = 108 + 3(12) = 144.

Now, we can determine the percent (P) of scores in the data set that are expected to be below a score (x) of 120;

P(x < 120) = P((x - μ)/σ < (120 - 108)/12)

P(x < 120) = P((x - μ)/σ < 12/12)

P(x < 120) = P(z < 1)

P(x < 120) = 0.8413

P(x < 120) = 84.13%

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Answer:

18.5

Step-by-step explanation:

27 rounds up to 30. 53 rounds up to 50

Answer:

19.00

Step-by-step explanation:

Answer:

Explained below

Step-by-step explanation:

A) A skewed distribution in a dataset is when the median is not equal to the mean in such a manner that the bell curve is tilted to the left or right.

B) If in a data set, there are outliers which are extremely large or extremely small in comparison to other values in that same dataset, then we can say that such a curve will be pulled towards the outlier and thus the distribution is skewed.

Also, if the curve is inclined to the left, it means there are few extreme values to the left and is is negatively skewed.

Similarly, if the curve is inclined to the right, it means there are few extreme values to the right and is positively skewed.

C) Example of a research question is;

If in a developed country where the poverty level is about 0%, if we collect the data of income of the households, we will discover majority of people with average income and very few people with extreme high levels of income. This condition means the data to is positively skewed.

Answer: 11x + 30

Step-by-step explanation: Algebraic expression is a way of use letters to express relationships between algarisms.

For this question:

Units digit = x

Tens digit = 10(x + 3)

The number in question is:

10(x + 3) + x

10x + 30 + x

To simplify, add, subtract, multipy or divide similar terms:

As x is of the first order:

10x + x + 30

11x + 30

The simplified algebraic expression is 11x + 30

Step-by-step explanation:

first, determine the coordinates values like x =9 and y=-5

so x-6 =3

Answer:Rules for rotating points about the origin

1. The point (a,b) rotated 90° counterclockwise about the origin

becomes (-b,a).

A′ (-1, 3) B′ (-2, 2) C′ (-2, 1) D′ (-1, 1)

A (a,b)-----------------A′ (-b,a)=(-1, 3)----------->A( 3,1)

B (a,b)-----------------B′ (-b,a)=(-2, 2)----------->B( 2,2)

C (a,b)-----------------C′ (-b,a)=(-2, 1)----------->C( 1,2)

D (a,b)-----------------D′ (-b,a)=(-1, 1)----------->D( 1,1)

Step-by-step explanation:

Answer:

0.104 = 104/1000

0.75 = 75/100

Chow,...!

Answer:

\(\frac{13}{125}\)

Step-by-step explanation:

\(0.104 = \frac{0.104*1000}{1*1000} = \frac{104}{1000} = \frac{104/8}{1000/8} = \frac{13}{125}\)

The time when Hank's Movers will cost less is the point when the total charges is both Movers are Equal, the time is at 3 hours

Given Data

For Acme, the expression for the total charges is

Total = 45+40x ----------1

For Hank, the expression for the total charges is

Total = 55x ----------------2

Equating both expressions we have

45+40x = 55x

collect like terms

45 = 55x-40x

45 = 15x

divide both sides by 15

x = 45/15

x = 3 hours

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Answer:

(3,-2)

Step-by-step explanation:

When looking at a graph, the way to find the solution to the system of equations is to look at the points where the two systems intersect. Where if you put in an x-value, you will get the same y-value.

Explanation:

A = set of odd numbers = {1,3,5}

B = set of factors of 12 = {1,2,3,4,6}

A U B = union of set A and set B

A U B = {1,3,5} union {1,2,3,4,6}

A U B = {1,3,5,       1,2,3,4,6}

A U B = {1,2,3,4,5,6}

The set union operation combines two sets into one bigger set. Duplicates are tossed out.

There are 6 elements in the set A U B = {1,2,3,4,5,6} out of 6 faces of the number cube.

Therefore, the probability event  A U B happens is 6/6 = 1 = 100%; i.e. it is guaranteed to happen. Each face of the number cube is either odd, a factor of 12, or both.

Side notes:

Answer:

\(\frac{5}{3}\)

Step-by-step explanation:

let blank be O

\(\frac{5}{6} +O=\frac{5}{2} \\\)

\(O=\frac{5}{2} -\frac{5}{6} =\frac{15}{6} -\frac{5}{6} =\frac{10}{6} =\frac{5}{3}\)

Answer:

when u search it one by one