Write the ratio of corresponding sides for the similar triangles and reduce the ratio to lowest terms. 2 similar triangles. Triangle 1 has side lengths 14, 21, blank. Triangle 2 has side lengths 18, 27, blank. a. StartFraction 14 Over 27 EndFraction = StartFraction 21 Over 28 EndFraction = StartFraction 14 Over 27 EndFraction b. StartFraction 14 Over 18 EndFraction = StartFraction 21 Over 27 EndFraction = StartFraction 7 Over 9 EndFraction c. StartFraction 14 Over 21 EndFraction = StartFraction 18 Over 27 EndFraction = StartFraction 2 Over 3 EndFraction d. StartFraction 27 Over 14 EndFraction = StartFraction 28 Over 21 EndFraction = StartFraction 27 Over 14 EndFraction Please select the best answer from the choices provided A B C D

Answer:

50.3

Step-by-step explanation:

75*0.33=24.75

75-24.75=50.25

50.25=50.3

answer:

a. 8 · 10^7 is 4000 times larger than 2 · 10^4

step-by-step explanation:

8 · 10^7 (or 8 X 10000000) = 80000000

2 · 10^4 (or 4 X 10000) = 20000

80000000 / 20000 = 4000

Answer:

20% coupon

Step-by-step explanation:

20% of 32.50 = 6.5

32.50 - 6.50 = 26

32.50 - 5 = 27.50

26 is less than 27.50, therefore, the 20% off coupon should be used to save him $1.50.

The standard equation of the sphere is:

x^2 + y^2 + z^2 - 18x - 4y - 10z + 46 = 0

The standard equation of a sphere is given by:

(x - a)^2 + (y - b)^2 + (z - c)^2 = r^2

where (a, b, c) is the center of the sphere and r is the radius.

In this case, the center of the sphere is given by c = (9, 2, 5) and the radius is r = 8.

Substituting these values into the standard equation of the sphere, we get:

(x - 9)^2 + (y - 2)^2 + (z - 5)^2 = 8^2

Expanding and simplifying, we get:

x^2 - 18x + 81 + y^2 - 4y + 4 + z^2 - 10z + 25 = 64

x^2 + y^2 + z^2 - 18x - 4y - 10z + 46 = 0

Therefore, the standard equation of the sphere is:

x^2 + y^2 + z^2 - 18x - 4y - 10z + 46 = 0

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Answer:

\(\dfrac{1}{729}\)

Step-by-step explanation:

\(\left(\dfrac{}{}(-3)^2\dfrac{}{}\right)^{-3}\)

First, we should evaluate inside the large parentheses:

\((-3)^2 = (-3)\cdot (-3) = 9\)

We know that a number to a positive exponent is equal to the base number multiplied by itself as many times as the exponent. For example,

\(4^3 = 4 \, \cdot\, 4\, \cdot \,4\)

       ↑1 ↑2 ↑3 times because the exponent is 3

Next, we can put the value 9 into where \((-3)^2\) was originally:

\((9)^{-3}\)

We know that a number to a negative power is equal to 1 divided by that number to the absolute value of that negative power. For example,

\(3^{-2} = \dfrac{1}{3^2} = \dfrac{1}{3\cdot 3} = \dfrac{1}{9}\)

Finally, we can apply this principle to the \(9^{-3}\):

\(9^{-3} = \dfrac{1}{9^3} = \boxed{\dfrac{1}{729}}\)

Answer:

503.8

Step-by-step explanation:

Since in the hundredth place you have a number higher than 5, we want to round the tenth digit up by one to get 503.8.

Answer:

503.8

Step-by-step explanation:

the slope is a positive one.

the equation would be y = x + 1

Answer:

y = x + 1

Step-by-step explanation:

x because the change is x is 1. And the change in y is also 1. 1/1 can be written as x.

The line crosses the y axis on 1, making it the y-intercept.

Answer:

The answer to the question is

\(4a { }^{2} - 2a\)

Have a good day

The area of the metal sheet required to make this square-shaped traffic sign is x² + 2x + 1. Then the correct option is A.

It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a square, opposite sides are parallel and all sides are equal and each angle is 90 degrees. And its diagonals are also equal and intersect at mid-point at right-angle.

A square-shaped traffic sign is shown with the length of one side labeled as x plus 1.

Side of square = x + 1

Then the area of the square will be

Area = (side of square)²

Area = (x + 1)²

Area = x² + 2x + 1

Thus, the area of the metal sheet required to make this square-shaped traffic sign is x² + 2x + 1. Then the correct option is A.

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Answer:

2

Step-by-step explanation:

find the y for x=7 in the chart

Answer:

D. Hamish earns $20 per hour, and Harry earns $26 per hour.

Step-by-step explanation:

Hamish and Harry work as plumbers. Harry earns a dollar more than 5/4 the amount Hamish earns per hour. The amount Harry earns per hour is $2 less than 7/5 the amount Hamish earns per hour. How much does each of them earn per hour?

Hamish earnings per hour = x

Harry earnings = 1 + 5/4x

The amount Harry earns per hour is $2 less than 7/5 the amount Hamish earns per hour

Harry also earns = 7/5x - 2

Equate both Harry's earnings

1 + 5/4x = 7/5x - 2

Collect like terms

1 + 2 = 7/5x - 5/4x

3 = 28x-25x/20

3 = 3/20x

Divide both sides by 3/20

x = 3 ÷ 3/20

= 3 × 20/3

x = 20

Hamish earnings per hour = x

= $20

Substitute Harry's earnings into 7/5x - 2

= 7/5 × 20 - 2

= 28 - 2

= 26

Harry's earnings = $26

D. Hamish earns $20 per hour, and Harry earns $26 per hour.

Once we have the total surface area, we will know how much burlap Dominique needs to buy to cover the flower box.

To determine how much burlap Dominique needs to buy to cover the flower box, we need to calculate the surface area of the box. Unfortunately, without the specific dimensions or a provided diagram,

I cannot give you an exact number.
However, here are the general steps to calculate the surface area of a rectangular flower box:
1. Identify the dimensions: length (L), width (W), and height (H).
2. Calculate the surface area of each face:
  - Top/Bottom: 2 x (L x W)
  - Sides: 2 x (L x H)
  - Front/Back: 2 x (W x H)
3. Add the surface areas of all faces together to get the total surface area.
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Using the simple interest formula, Mr. Solo received $26 interest.

In the given question we have to find how much interest Mr. Solo received.

The investment(P) = $325.

Interest rate(R) = 8%

Time(T) = 1 year

Finding the interest using the simple interest formula.

I = PRT/100

where I = interest

P = Principal Amount

T = Time

R = Interest Rate

Putting the value

I = 325*8*1/100

I = 26

Hence, Mr. Solo received $26 interest.

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The $1314^\text{th}$ digit past the decimal point is 2.

To find the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$, we can use long division to compute the decimal expansion of the fraction.

The long division of $\frac{5}{14}$ is as follows:

```

0.35    <-- Quotient

-----

14 | 5.00

   4.2    <-- Subtract: 5 - (14 * 0.3)

   -----

     80   <-- Bring down the 0

     70    <-- Subtract: 80 - (14 * 5)

     -----

     100   <-- Bring down the 0

      98    <-- Subtract: 100 - (14 * 7)

      -----

       20   <-- Bring down the 0

       14    <-- Subtract: 20 - (14 * 1)

       -----

        60   <-- Bring down the 0

        56    <-- Subtract: 60 - (14 * 4)

        -----

         40   <-- Bring down the 0

         28    <-- Subtract: 40 - (14 * 2)

         -----

         120   <-- Bring down the 0

         112    <-- Subtract: 120 - (14 * 8)

         -----

           80   <-- Bring down the 0

           70    <-- Subtract: 80 - (14 * 5)

           -----

           ...

```

We can see that the decimal expansion of $\frac{5}{14}$ is a repeating decimal pattern with a repeating block of digits 285714. Therefore, the $1314^\text{th}$ digit past the decimal point is the same as the $1314 \mod 6 = 0^\text{th}$ digit in the repeating block.

Since $1314 \mod 6 = 0$, the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$ is the first digit of the repeating block, which is 2.

So, the $1314^\text{th}$ digit past the decimal point is 2.

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Answer:

\(c \: (x + 5)(x - 1)\)

Answer:

x > - 3

Step-by-step explanation:

Given

- 2x + 12 < 18 ( subtract 12 from both sides )

- 2x < 6

Divide both sides by - 2, reversing the symbol as a result of dividing by a negative quantity

x > - 3

There is sufficient evidence to suggest that there is a relationship between the type of automobile owned and the gender of the individual.

1. The sample size is large enough such that

np1≥10, np2≥10, n(1−p1)≥10, and n(1−p2)≥10,

2. The samples are independent.

3. Since |z| = 3.82 > 1.645, we reject the null hypothesis.

Automobile Ownership

A study was conducted to find out whether there is a relationship between the type of automobile owned and the gender of the individual. The data are shown below:

Luxury Large Midsize Small

Men 10 17 19 24

Women 40 33 29 28

At a=0.10, the relationship between the type of automobile owned and the gender of the individual can be determined by using the critical value method with tables.In order to conduct a hypothesis test for the equality of two population proportions, we must first check if the following conditions are met or not:

1. The sample size is large enough such that

np1≥10, np2≥10, n(1−p1)≥10, and n(1−p2)≥10,

where n1 and n2 are the sample sizes, p1 and p2 are the sample proportions, and

n=n1+n2 is the total sample size.

2. The samples are independent.

3. Both populations are at least ten times larger than their respective sample sizes.Let p1 be the proportion of men who own luxury cars. Let p2 be the proportion of women who own luxury cars. Then the null hypothesis is given by,

H0: p1 = p2The alternative hypothesis is given by,

Ha: p1 ≠ p2

The level of significance is given by,

α = 0.10

Since it is a two-tailed test, the critical values of z are given by,

zα/2 = ±1.645

The test statistic is given by,

z = (p1 - p2) / √((p^(1-p^2)) * ((1/n1) + (1/n2)))

Here,

p = (x1 + x2) / (n1 + n2)

= (10 + 40) / (10 + 17 + 19 + 24 + 40 + 33 + 29 + 28)

= 50 / 200 = 0.25

Replacing the values in the formula, we get,

z = (0.10 - 0.40) / √((0.25*(1-0.25)) * ((1/94) + (1/130)))

z = -3.82

Since |z| = 3.82 > 1.645, we reject the null hypothesis.

Hence, there is sufficient evidence to suggest that there is a relationship between the type of automobile owned and the gender of the individual.
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Answer:

Angle B = 120.5°

Step-by-step explanation:

When two angles are supplementary, it means that they add up to 180°. Therefore, you can find the measure of Angle B by doing the following:

Angle B = 180 - 59.5

Angle B = 120.5°

Hope this helps

The probability  that the average scholarshi[s in the samle greater than 20,000 is (69.729, 74.271).

Let X: Marks of students and be the population average marks.

X ~ N(72, 16)

The formula for the CI for is,

CI = mean + tₐ/₂ , ₙ₋₁ s/n

= 72 ± 2.539 × 4/20

= 72 ± (2.539 × 0.8944)

= 72 ± 2.27

= 72 - 2.27 , 72 + 2.27

= (69.729, 74.241)

Therefore, the required 98% CI for the average marks of the students is (69.729, 74.271).

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Answer:

$5.5 per mile

40 miles

Step-by-step explanation:

Given :

Fixed cost = $10

Variable cost = $3

For a journey of 4 miles ;

Cost = fixed cost + Variable Cost

Cost = $10 + $3x

x = number of miles

Cost = $10 + $3(4)

Cost = $10 + $12 = $22

Average cost per mile for a journey of 4 miles

Cost / number of miles

$22 / 4 = $5.5 per mile

Minimum distance if average per mile is to be less Than 3.25

$3.25 = (10 + 3x) / x

3.25x = 10 + 3x

3.25x - 3x = 10

0.25x = 10

x = 10 / 0.25

x = 40 miles

The x-intercept and y-intercept are x-intercept = 1 and 5 and y-intercept = 5

Given that

g(x) = (x - 1)(x - 5)

Substitute 0 for x in g(0)

So, we have

g(0) = (0 - 1)(0 - 5)

Evaluate

g(0) = 5

Set g(x) = 0 for the x-intercept

So, we have

(x - 1)(x - 5) = 0

Evaluate

x-intercept = 1 and 5

The y-intercept is the same as g(0)

The domain is all set of real values

For the range, we have

g(x) = (x - 1)(x - 5)

Express in vertex form

g(x) = (x - 3)² - 4

So, the range is

g(x) ≥ -4

From g(x) = (x - 3)² - 4, the vertex is

Vertex = (3, -4)

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Answer:

C

Step-by-step explanation:

negative four raised to the sixth power divided by negative four raised to the fourth power

because  negative four raised to the fourth power divided by negative four raised to the second power = negative four raised to the second power

negative four raised to the sixth power divided by negative four raised to the fourth power also = negative four raised to the second power

The answer is A: negative four raised to the second power divided by negative four raised to the fourth power. This is obtained by applying the rules of exponents, specifically, when dividing with the same base, subtract the exponents.

This question pertains to exponents division rules. According to the rule of Power of a Power in exponents, when you divide expressions with the same base, you subtract the exponents. So if you have negative four raised to the fourth power (-4⁴) and you want to divide it by negative four raised to the second power (-4²), you subtract 2 from 4 to get an exponent of 2. This results in a negative four raised to the second power (-4²). So, the correct option from the given choices in your question is A: negative four raised to the second power divided by negative four raised to the fourth power.

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Answer:

7x² - 8x + 4

Step-by-step explanation:

f(x) - g(x)

= 5x² - 2x + 7 - (- 2x² + 6x + 3) ← distribute parenthesis by - 1

= 5x² - 2x + 7 + 2x² - 6x - 3 ← collect like terms

= 7x² - 8x + 4

Answer:

(3 3/4) : (3/4) = 5/1 = 5

Step-by-step explanation:

Hope you could understand.

If you have any query, feel free to ask.

The maximum number of edges in a directed graph without any self-loops, having a total 6 of vertices is 15.

Edge:

In geometry, an edge is a particular type of line segment that connects two vertices of a polygon, polyhedron, or higher-dimensional polyhedron. In polygons, edges are line segments of the boundary and are often called polygon sides. In a polyhedron, or more generally a polytope, an edge is a line segment where two faces (or sides of a polyhedron) meet. A line segment connecting two vertices and passing inside or outside is called a diagonal, not an edge.

Directed graph:

A directed graph is a graph. A series of objects (called nodes or knots) connected together with all edges pointing from one node to another. A directed graph is sometimes called a directed graph or directed network. In contrast, graphs whose edges are bidirectional are called undirected graphs.

The graph containing maximum number of edge in a n node undirected graph without self loop is complete graph.

The number of edges in complete graph with n node, kₙ is

n(n − 1)/ 2

Now, based on the above formula:

   n( n -1) /2

= 6( 6 - 1)/2

= 5× 6/2 = 30/2 = 15

Therefore, The maximum number of edges in a directed graph without any self-loops, having a total 6 of vertices is 15.

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Answer:

the answer for this one is A

Step-by-step explanation:

the line going side to side has the first number ( that means the number you first see in this (-0, 0)and although you don't see the 5 it's still there because you should probably know 5 is between 4 and 6

Based on the data provided, we can calculate the slope and y-intercept of the line that fits the data points.

First, let's find the slope (m) using the formula: m = (y2 - y1) / (x2 - x1). We can use the first two data points for this calculation:

m = (27 - 32) / (10 - 5) = (-5) / 5 = -1

Now, let's find the y-intercept (b) using the formula: y = mx + b. We can use the first data point (5, 32) and the slope we found:

32 = -1 * 5 + b
32 = -5 + b
b = 37

Therefore, the correct slope is -1, and the y-intercept is 37.

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