Triangle EFG, with vertices E(-2,-8), F(-4,-3), and G(-7,-5)

The largest power of 10 that is a factor of 1000! is 5^249, or 10^249.

(a) To find the largest power of 10 that is a factor of 50!, we need to count the number of factors of 5 in 50! since each factor of 5 contributes at least one factor of 10.

There are 10 multiples of 5 in 50!, namely 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50. Each of these contributes one factor of 5. There are also 2 multiples of 25 (25 and 50), each of which contributes an additional factor of 5. Therefore, the total number of factors of 5 in 50! is 10 + 2 = 12.

Since each factor of 10 contains one factor of 5 and one factor of 2, we also need to count the number of factors of 2. It is clear that there are more factors of 2 than factors of 5, so we only need to count the factors of 5. Therefore, the largest power of 10 that is a factor of 50! is 5^12, or 10^12.

(b) To find the largest power of 10 that is a factor of 1000!, we follow the same reasoning as in part (a). The number of factors of 5 in 1000! is:

⌊1000/5⌋ + ⌊1000/25⌋ + ⌊1000/125⌋ + ⌊1000/625⌋ = 200 + 40 + 8 + 1 = 249

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\(4 \frac{1}{5} + x = 4 \frac{3}{5} \\ \\ x = 4 \frac{3}{5} - 4 \frac{1}{2} \\ \\ x = \frac{2}{5} \)

Answer:

y=2x-2

Step-by-step explanation:

Isolate y :3y=6x-6

Then divide both sides by 3:

y=2x-2

the value of x can be calculated using the given data.

The properties of the triangle are: The sum of all the angles of a triangle (of all types) is equal to 180°. The sum of the length of the two sides of a triangle is greater than the length of the third side. In the same way, the difference between the two sides of a triangle is less than the length of the third side.

Given a triangle, with two known angles of 42-degree and 26-degree

Let the triangle be ABC

This is, in fact, exactly what the Law of Sines tells you:

a/sinA = b/sinB = c/sinC = m

where m is that scale factor and also the diameter of the triangle's circumcircle.

in our case,

∠A = 26°

∠B = 42°

thus,

a/sinA = b/sinB

4/sin26 = b/sin42

b = 4* (sin 42 /sin26)

b =6.12

or x = 6.1 cm

therefore, the value of x can be calculated using the given data.

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Answer:

D. \sqrt(384)

Step-by-step explanation:

All you have to do is to expand the root the way I have done. I hope you understand and rate this answer well.

Don't forget 8 is the same as root(8) * root(8) which will give root(64) and the square root of 64 is 8.

The equation in slope-intercept form is y = x - 6.

What is in slope-intercept form?

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)

The equation of the given line p is

y = 8x + 2

Comparing with the slope intercept form, slope = 8

If two lines are parallel, it means that they have the same slope. Therefore, the slope of line q passing through ( -1 , -2 ) is 8

To determine the y intercept, we would substitute m = 8, x = - 1 and

y = -2 into y = mx + c. It becomes

-2 = 8 × - 1 + c

-2 = - 8 + c

c = - 8 + 2 = -6

The equation becomes

y = x - 6

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Answer: $1.48

Step-by-step explanation:

find how much each gallon cost

1. 17.76/3=5.92

Divide by 4 because 4 quarts equal a gallon

2. 5.92/4=1.48

Therefore each quart equals $1.48,

Hope this helps!

We must complete the table of probabilities such that the probability distribution is legitimate.

Because all the possible values of the variables are 0, 3, 4, 5 and 6, the sum of the probability of each number must sum up 1:

Replacing the values of the table, we have:

From the last equation, we see that to have a legitimate probability, we must select values of P(x = 3) and P(x = 4) such that they sum up 1. One possible pair of values is:

• P(x = 3) = 0.2,

• P(x = 4) = 0.24.

Answer

One possible pair of values is:

• P(x = 3) = 0.2,

• P(x = 4) = 0.24.

Answer:

To translate a shape 1 unit left and 1 unit up, you would subtract 1 from the x-coordinates of each vertex to move left and add 1 to the y-coordinates of each vertex to move up.

If you have the coordinates of the original vertices, you can apply this translation to get the coordinates of the new vertices:

For example, let's say we have a triangle with vertices at (2, 3), (4, 1), and (1, 5). To translate this triangle 1 unit left and 1 unit up, we would subtract 1 from the x-coordinates and add 1 to the y-coordinates of each vertex:

Vertex (2, 3) becomes (2 - 1, 3 + 1) = (1, 4)

Vertex (4, 1) becomes (4 - 1, 1 + 1) = (3, 2)

Vertex (1, 5) becomes (1 - 1, 5 + 1) = (0, 6)

Therefore, the new vertices of the triangle after a translation 1 unit left and 1 unit up are (1, 4), (3, 2), and (0, 6).

Step-by-step explanation:

The length of the rectangle is 19.25 cm when it is 2 more than three times the width of 5.75 cm.

A perimeter is a closed path that encompasses, surrounds, or outlines a two-dimensional shape or length in one dimension. A circle's or an ellipse's circumference is its perimeter. There are several applications for calculating the perimeter. The length of fence required to encircle a yard or garden is known as the calculated perimeter.  

The perimeter (circumference) of a wheel/circle describes how far it can roll in one revolution.  Similarly, the amount of string wound around a spool is proportional to the perimeter of the spool; if the length of the string were exact, it would equal the perimeter.

Given that,

Perimeter = 2(l + b) = 50cm

And also given that,

l = 2 + 3b

Substituting the value of l in perimeter we get

2((2 + 3b) + b) = 50cm

2(2 + 4b) = 50cm

4 + 8b) = 50cm

8b = 50 - 4

b = 46/8

b = 5.75

Substituting the value of b in l, we get

l = 2 + 3(5.75)

l = 19.25

Therefore, the length of the rectangle is 19.25 cm when it is 2 more than three times the width of 5.75 cm.

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Answer:150%

Step-by-step explanation. (11.25-4.5)divide 4.5•100 =675divide4.5•100=1.5•100=150%

Answer:

\(\frac{200}{33} \cdot 4^{\frac{1}{5} }\)

Step-by-step explanation:

We have :

\(y = x^{\frac{6}{5} } \,\,\, and \,\,\, y = 4x^{\frac{1}{5} }\)

\(y = x^{\frac{6}{5} } = 4x^{\frac{1}{5} }\\\\\implies x^{\frac{6}{5} } = 4x^{\frac{1}{5} }\\\\\implies 4x^{\frac{1}{5} } - x^{\frac{6}{5} } = 0\\\\\implies x^{\frac{1}{5} }[4 - x] = 0\\\\\implies x^{\frac{1}{5} } = 0 \;\;\;or\;\;\;4-x=0\\\\\implies x = 0 \;\;\;or\;\;\; x = 4\)

Area between the curves:

\(\int\limits^4_0 {4x^{\frac{1}{5} }} \, dx -\int\limits^4_0 {x^{\frac{6}{5} }} \, dx \\\\=4\int\limits^4_0 {x^{\frac{1}{5} }} \, dx -\int\limits^4_0 {x^{\frac{6}{5} }} \, dx \\\\=4[\frac{x^{^{\frac{1}{5} +1}}}{\frac{1}{5} +1} ]_{_0}^{^4}-[\frac{x^{^{\frac{6}{5} +1}}}{\frac{6}{5} +1} ]_{_0}^{^4}\\\\=4[\frac{x^{^{\frac{6}{5}}}}{\frac{6}{5}} ]_{_0}^{^4} - [\frac{x^{^{\frac{11}{5}}}}{\frac{11}{5}} ]_{_0}^{^4}\\\\\)

\(= 4(\frac{5}{6})[x^{^{\frac{6}{5}}}]_{_0}^{^4} - \frac{5}{11} [x^{^{\frac{11}{5}}}]_{_0}^{^4}\\\\=\frac{10}{3}[4^{^{\frac{6}{5}}}-0^{^{\frac{6}{5}}}] -\frac{5}{11}[4^{^{\frac{11}{5}}}-0^{^{\frac{11}{5}}}] \\\\=\frac{10}{3} [4^{^{\frac{5}{5}}} * 4^{^{\frac{1}{5}}}] - \frac{5}{11} [4^{^{\frac{10}{5}}} * 4^{^{\frac{1}{5}}}]\\\\=\frac{10}{3} [4 * 4^{^{\frac{1}{5}}}] - \frac{5}{11} [4^{^{2}} * 4^{^{\frac{1}{5}}}]\\\\\)

\(= 4^{^{\frac{1}{5}}}[\frac{10*4}{3} - \frac{5*4^2}{11} ]\\\\= 4^{^{\frac{1}{5}}}[\frac{40}{3} - \frac{80}{11} ]\\\\= 4^{^{\frac{1}{5}}}[\frac{40(11) - 80(3)}{3(11)} ]\\\\= 4^{^{\frac{1}{5}}}[\frac{440 - 240}{33} ]\\\\= 4^{^{\frac{1}{5}}}[\frac{200}{33} ]\)

The amount of money that the company can expect to pay during the year the policies were written is; $25005

The probability that a person will die at age 20 = 0.001

Revenue from 52 policies = 52 * $75,000 = $3,900,000

Revenue from 477 policies = 477 * $25,000 = $11,925,000

Revenue from 918 policies = 918 * $10,000 = $9,180,000

Total revenue from all policies = $3,900,000 + $11,925,000 + $9,180,000

Total Revenue from all Policies = $25,005,000

Expected amount to pay out during the year the policies were written =  $25,005,000* 0.001 = $25,005

Thus, the company can expect to pay out $45,000 over the year after the policies were written.

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The sequence is will always have even numbers, is hence proved.

Given, the quadratic sequence is: 44:52:64:80

Sequences with a term are known as quadratic sequences. They can be distinguished by the fact that the first differences between terms are not equal but the second differences between terms are. Utilizing the term sum in an arithmetic progression formula, the sum of even numbers formula is achieved. The equation is Sum of Even Numbers Formula = n(n+1), where n is the total number of terms in the series.

The formula is: Tₙ = 2n² ₊ 2n  ₊ 40

take 2 common

Tₙ = 2(n² ₊ n  ₊ 20)

in other words n² ₊ n  ₊ 20  = y

therefore , Tₙ = 2y

which by definition makes Tₙ an even number at all times.

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Answer:

Step-by-step explanation:

Let's just say this circle has value x.

x increases by 5%, or 0.05 of x.

x + 0.05x = 1.05x

1.05x now increases by 5% again:

1.05x + 0.05(1.05x) = 1.1025x

The total increase is equal to (1.1025-1)*100 = 10.25%

Hope this helps!

Answer:

15 rides

Step-by-step explanation:

29.50 - 7 = 22.50

22.50 / 1.50 = 15

Answer:

\(m=2\)

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

Find points from graph.

Point (2, 8)

Point (-6, -8)

Step 2: Find slope m

Answer:

Step-by-step explanation:

(2.2×10^4)*(7.1×10³)

=(2.2×7.1)×10{4+3}

=15.62×10^7

=1.562×10^8

Answer:

A = $7,554.84

A = P + I where

P (principal) = $4,500.00

I (interest) = $3,054.84First, convert R as a percent to r as a decimal

r = R/100

r = 2.73/100

r = 0.0273 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 4,500.00(1 + 0.0273/12)(12)(19)

A = 4,500.00(1 + 0.002275)(228)

A = $7,554.84

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $4,500.00 at a rate of 2.73% per year compounded 12 times per year over 19 years is $7,554.84.

Step-by-step explanation:

Number of milkshake with whipped cream will be 24.

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100

Given that;

Whitney's Diner sold 96 milkshakes last week.

25% of the milkshakes had whipped cream on top.

Now,

Total number of milkshake = 96

Milkshakes with whipped cream on top = 25%

Hence, Number of milkshakes with whipped cream on top is;

= 25% of 96

= 25 / 100 x 96

= 96 / 4

= 24

Thus, Number of milkshake with whipped cream will be 24.

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Given:

The diagram of the ramp is shown in the image.

The vertical distance Rise (R) of the ramp = 3.

The horizontal distance Run (r) of the ramp = 10.

Required:

The slope(m) of the ramp.

Explanation:

The slope of the ramp is calculated by dividing the Rise by the Run.

Therefore, the slope of the ramp is,

Final Answer:

The slope (m) of the ramp is,

Option C is correct.

For the given arena's tickets sales , the round of figure of all the sales to the nearest thousand is given by :

   Events                                         Nearest thousand

As given in the question,

Rules to round of nearest thousand are:

Check the near by hundred digit :

Given is the actual ticket rates of the different events tickets sales ,round off to the nearest thousand is given by:

 Events                                         Nearest thousand

Therefore, For the given arena's tickets sales , the round of figure of all the sales to the nearest thousand is given by :

   Events                                         Nearest thousand

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Answer:

\(\dfrac{2}{3}\)

Step-by-step explanation:

Given that:

The number of observations is:

6, 10, 12

If we are to use a simple  random sampling without replacement, then we will have:

(6,10)  (6,12)  (10,12)

Here;

the sample size n = 2

The population size N = 3

For (6,10) ; The sample mean = \(\dfrac{6+10}{2}\)

= \(\dfrac{16}{2}\)

= 8

For (6,12) ; The sample mean = \(\dfrac{6+12}{2}\)

= \(\dfrac{18}{2}\)

= 9

For (10, 12) ; The sample mean = \(\dfrac{10+12}{2}\)

= \(\dfrac{22}{2}\)

= 11

The probability distribution of sample mean(x) is:

X           8           9          11

P(X=x)    \(\dfrac{1}{3}\)          \(\dfrac{1}{3}\)           \(\dfrac{1}{3}\)

Thus, the probability that the sample mean  is larger than 8 is:

P(X> 8) = P(X = 9) + P(X + 11)

P(X> 8) = \(\dfrac{1}{3}+\dfrac{1}{3}\)

P(X > 8) = \(\dfrac{1+1}{3}\)

P(X> 8) = \(\dfrac{2}{3}\)

Answer:

84days

Step-by-step explanation:

1 week = 7days =>12 weeks = 12×7 = 84days

Answer:

84 days are in 12 weeks

Step-by-step explanation:

1 week = 7 days

4 weeks = 28 days

So 28 + 28 + 28 = 84 days

Comparing the √17 and 29/7 using <, > or = , we have √17 < 29/7.

Mathematical number comparison is the process or method of comparing two numbers to determine whether one is less, bigger, or equal to the other. The comparison symbols for numbers are "=", which stands for "equal to," "=", which stands for "greater than," and " ", which stands for "less than." Comparing amounts is a technique for figuring out how much to compare units in relation to a different standard or reference unit. A common reference point is necessary for two comparing units to be compared; otherwise, they cannot be compared.

Given,

Comparing the following using <, > or = ,

Numbers:

√17 and 29/7

For √17

Simplifying,

√17 = 4.123

For 29/7

29/7 = 4.14

√17 < 29/7

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The overtime rate of pay is K10.25.

The overtime rate of pay can be calculated by multiplying the basic rate pay by the time-and-a-quarter factor. In this case, the basic rate pay is K8.20.

To determine the overtime rate of pay, we need to calculate one-quarter (1/4) of the basic rate pay, and then add that amount to the basic rate pay. One-quarter of K8.20 is calculated as (1/4) * K8.20 = K2.05.

By adding the calculated overtime amount to the basic rate pay, we get the overtime rate of pay: K8.20 + K2.05 = K10.25.

Therefore, the overtime rate of pay is K10.25.

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Answer =  A.  Aella

Step-by-step explanation: Add 60, 25, and 95 degrees because that will equal 180 which is what the triangle equals.

Answer:

t ≥ 7.4.

Step-by-step explanation:

To solve the equation 2(t - 6.7) ≥ 1.4 for t, we can follow these steps:

  2t - 2(6.7) ≥ 1.4

  2t - 13.4 ≥ 1.4

  2t - 13.4 + 13.4 ≥ 1.4 + 13.4

  2t ≥ 14.8

  (2t)/2 ≥ 14.8/2

  t ≥ 7.4