Question 5 of 10
What is the slope of the line x = 3?
Answer here

9514 1404 393

Answer:

Step-by-step explanation:

For a pair of numbers, I find it convenient to think in terms of factors unique to the number, and factors shared with the other number.

Consider the numbers 21 and 51, for example.

  21 = 3·7

  51 = 3·17

The factor 3 is shared by both numbers. The factors 7 and 17 are unique to one number or the other.

If we group these factors like this ...

  (factors unique to 1 [ shared factors ) factors unique to 2]

  = (7 [3 ) 17]

The numbers in ( ) parentheses are the factors of 21, and the numbers in [ ] brackets are the factors of 51.

The LCM (least common multiple) is the product of the factors in those brackets:

  LCM(21, 51) = 7 × 3 × 17 = 357

__

The unique factors of the numbers don't have to be prime (as in the above example); they just cannot be shared. Here's another example for the numbers 42 and 90

  (7 [ 3·2 ) 3·5 ] = (7 [ 6 ) 15] . . . . factors of (42) and [90]

Then the LCM is ...

  LCM(42, 90) = 7 × 6 × 15 = 630

_____

Additional comment

What we have called "shared factors" here is the same as the "greatest common divisor"(GCD) or "greatest common factor" (GCF).

If we divide our little diagram so it shows the product of the two numbers:

  (42)[90] = (7×6)·[6×15]

we can see that the LCM is the quotient of the product and the GCD.

  LCM(A, B) = A·B/GCD(A, B)

This is an occasionally handy relationship, as it is not difficult to find the GCD of a pair of numbers using Euclid's algorithm.

Step-by-step explanation:

the required formula is C = 2(pi)r.

Here that comes to 6.28(2 units), or 12.56 units.

Answer:

[tex]77[/tex]

Step-by-step explanation:

The troop wants to sell a minimum of 1,000 boxes, so we're looking for the smallest number of boxes they can sell and still meet the goal. Since there are 13 girls in the troop, take the ceiling (round up to the nearest whole number) of 1,000 divided by 13:

[tex]\left\lceil \frac{1,000}{13}\right\rceil=\boxed{77}[/tex]

Answer:

Last answer is correct..

Step-by-step explanation:

Thei answers in picture

Answer:

[tex]\frac{21}{8}[/tex]

Step-by-step explanation:

[tex]6\frac{1}{4}=6+\frac{1}{4}=\frac{25}{4}\\\\3\frac{5}{8}=3+\frac{5}{8}=\frac{29}{8}\\[/tex]

finally

[tex]6\frac{1}{4}-3\frac{5}{8}=\frac{25}{4}-\frac{29}{8}=\frac{21}{8}[/tex]

Answer:

for every x in the domain of f, f -1[f(x)] = x, and

for every x in the domain of f -1, f[f -1(x)] = x

Step-by-step explanation:

f(1) and f(-2) means to replace x in the equation with the number inside the parenthesis and then solve.

f(1) = (1)^2 -3(1) -f = 1 -3 -f = -2-f

f(-2) = (-2)^2 -3(-2) -f = 4 + 6 - f = 10-f

Answer:

11. C

12. A

Step-by-step explanation:

11. (10 + x + 1)(x + 1) = (x + 5)² (secant-tangent rule)

(11 + x)(x + 1) = (x + 5)(x + 5)

11(x + 1) +x(x + 1) = x(x + 5) +5(x + 5)

11x + 11 + x² + x = x² + 5x + 5x + 25

Add like terms

x² + 12x + 11 = x² + 10x + 25

Collect like terms

x² - x² + 12x - 10x = -11 + 25

2x = 14

2x/2 = 14/2

x = 7

12. (x + 8)(8) = (15 + 9)(9) (secant-secant theorem)

8x + 64 = 216

Subtract 64 from each side

8x = 216 - 64

8x = 152

8x/8 = 152/8

x = 19

Answer:

1/36

Step-by-step explanation:

you multiply 1/6 × 1/6

because the only way to get the sum of 2 is 1+1 and there is a 1/6th chance on both dice

Answer:

1/36

Step-by-step explanation:

got it right

Answer:

144 isnt it? 6x6x4 length x width x height it should be 36x4

Step-by-step explanation i dont know sorry

Answer:

x = 2

Step-by-step explanation:

Let the number be x

When we multiply a number by 6 and subtract it by 5, we would get 7.

On multiplication of number x with 6 it will be 6x.12

On subtraction of 5 it will be 6x - 5

6x - 5 = 7

6x = 7 + 5  

6x = 12

x = 12/6

x = 2

Answer:

The number is 2

Step-by-step explanation:

Let the number be n

Multiply the number by 6 = 6n

Subtract 5 from the number , 6n - 5

And we get 7

So , the expression : 6n - 5 = 7

                                6n = 7 + 5

                                6n = 12

                                  n = 2

Answer:

Step-by-step explanation:

using pythagoras theorem

a^2+b^2=c^2

7^2+KL^2=25^2

49+KL^2=625

KL^2=625-49

KL=[tex]\sqrt{576[/tex]

KL=24

take M as reference angle

using tan rule

tan M=/opposite/adjacent

tan M=KL/ML

tan M=24/7

Answer:

301

Step-by-step explanation:

Heres ow you do it,

1- 100-19= 81

2- 81+20= 101

3- 101+200= 301

Hope this helps!!! :)

Answer:

1/125

Step-by-step explanation:

(5^-2)(5^-1) = 5^-3=1/5^3=1/125

Answer:

a)15:6 b)2:3

Step-by-step explanation:

No. of used books=15-9=6

a) 15:6

b)

6:9

2:3

Answer:

The 95% confidence interval is [tex]0.231 \pm 1.96\sqrt{\frac{0.231*0.769}{432}}[/tex]

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

A random sample of 432 voters revealed that 100 are in favor of a certain bond issue.

This means that [tex]n = 432, \pi = \frac{100}{432} = 0.231[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

Confidence interval:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.231 \pm 1.96\sqrt{\frac{0.231*0.769}{432}}[/tex]

The 95% confidence interval is [tex]0.231 \pm 1.96\sqrt{\frac{0.231*0.769}{432}}[/tex]

Answer:

The missing length is 80 degrees.

Step-by-step explanation:

Every triangle is equal to 180 degrees. If you add 64 and 36, you get 100. 180-100 is equal to 80, therefor x is equal to 80.

Answer:4,1x101, 9, 4.1, 2, 0.42, 0.042

Step-by-step explanation:

Answer:

You will have saved $69,612 after five years.

Step-by-step explanation:

This can be calculated using the for formula for calculating the future value of a growing annuity as follows:

FV = C * (((1 + r)^n - (1 + g)^n) / (r - g)) ……………………………………… (1)

Where;

FW = future value or amount you will have saved after five years = ?

C = first deposit = $1,000

r = periodic monthly interest rate of = 0.4%, or 0.004

g = growth rate of contribution = 0.1%, or 0.001

n = number of months = 5 years * 12 = 60

Substituting all the values into equation (1), we have:

FV = $1,000 * (((1 + 0.004)^60 - (1 + 0.001)^60) / (0.004 - 0.001))

FV = $1,000 * 69.612001854052

FV = $69,612.00

Therefore, you will have saved $69,612 after five years.

Answer:

Step-by-step explanation:

Sample standard deviation is found by steps below.

Find the mean:

Find deviations from the mean and their squares:

Sum the squares:

Divide by N - 1 (N - number of samples):

Square root is the sample standard deviation:

Answer:

B C and F

Step-by-step explanation:

Polygons are closed shaped with straight lines

D and E have curves therefore they cannot be classified as polygons

A is not closed therefore it A is not a polygon

B, C and F are closed and use only straight lines therefore those 3 are polygons

9514 1404 393

Answer:

  center: (1/2, 6)

  radius: √5

Step-by-step explanation:

The standard form equation for a circle of radius r and center (h, k) is ...

  (x -h)^2 +(y -k)^2 = r^2

When we compare this to the given equation:

  (x -1/2)^2 +(y -6)^2 = 5

we see that h=1/2, k=6, and r^2=5.

The center is (h, k) = (1/2, 6); the radius is √5.

Answer:

11

Step-by-step explanation:

D+16/3=17 the steps?

1. D+16/3=17

Divide 16/3.

D+6 = 17

2. subtract 6 from both side.

D = 11.

Answer:

A. 2.5 pounds

B. 12.5 pounds

Step-by-step explanation:

Answer:

a 2.5 b 12.5

Step-by-step explanation:

Answer:

Hello! answer: 13

Step-by-step explanation:

12 × 12 = 144

5 × 5 = 25

144 + 25 = 169

√169 = 13

13 × 13 = 169 therefore the length of the missing side is 13 hope that helps!

Answer:

a. The minimum sample size required is of 60,025.

b. The minimum sample size required is of 20,465.

c. The minimum sample size required is 9,589.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is of:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

Question a:

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

p and q unknown means that we use [tex]\pi = 0.5[/tex], which is when the largest sample size is needed.

Margin of error: 0.004

We have to find n for which M = 0.004. So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.004 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.004\sqrt{n} = 1.96*0.5[/tex]

[tex]\sqrt{n} = \frac{1.96*0.5}{0.004}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96*0.5}{0.004})^2[/tex]

[tex]n = 60025[/tex]

The minimum sample size required is of 60,025.

b. Margin of error: 0.009, confidence level: 99%; p and q unknown

99% confidence level

So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].

Margin of error: 0.009

We have to find n for which M = 0.009. So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.009 = 2.575\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.009\sqrt{n} = 2.575*0.5[/tex]

[tex]\sqrt{n} = \frac{2.575*0.5}{0.009}[/tex]

[tex](\sqrt{n})^2 = (\frac{2.575*0.5}{0.009})^2[/tex]

[tex]n = 20464.9[/tex]

Rounding up:

The minimum sample size required is of 20,465.

c. Margin of error: 0.01; confidence level: 95%; from a prior study, p is estimated by the decimal equivalent of 52%.

Here we have [tex]\pi = 0.52[/tex].

The minimum sample size is n for which M = 0.01. So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.01 = 1.96\sqrt{\frac{0.52*0.48}{n}}[/tex]

[tex]0.01\sqrt{n} = 1.96\sqrt{0.52*0.48}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.52*0.48}}{0.01}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96\sqrt{0.52*0.48}}{0.01})^2[/tex]

[tex]n = 9588.6[/tex]

Rounding up:

The minimum sample size required is 9,589.

Answer:

37632

Step-by-step explanation:

An=A(1+12%)²