Write each expression in a simpler form that is equivalent to the given expression. Let g be a nonzero number. 1/g^1 or 1/g-1

Answer:

13 units

Step-by-step explanation:

Use the equation of a circle, (x - h)² + ( y - k )² = r², where (h, k) is the center and r is the radius.

Plug in the values and solve for r:

(5 - 0)² + (12 - 0)² = r²

25 + 144 = r²

169 = r²

13 = r

Answer:

42  headbands per dancer

Step-by-step explanation:

Selling 1260 headband

Divide by the three coaches

1260/3

420 per coach

Divide by each dancer under a coach

420/10 = 42

Each dancer must sell 42 headbands

Answer:

[tex]\mathbf{P(x>6) = 0.0265}[/tex]

Step-by-step explanation:

Given that:

A baseball player has a batting average (probability of getting on base per time at bat) of 0.215

i.e

let x to be the random variable,

consider [tex]x_1 = \left \{ {{1} \atop {0}} \right.[/tex]  to be if the baseball player has a batting average or otherwise.

Then

p(x₁ = 1) = 0.125

What is the probability that they will get on base more than 6 of the next 15 at bats

So

[tex]\mathtt{x_i \sim Binomial (n,p)}[/tex]

where; n =  15 and p = 0.125

P(x>6) = P(x ≥ 7)

[tex]P(x>6) = \sum \limits ^{15}_{x=7} ( ^{15 }_x ) \ (0.215)^x \ (1 - 0.215)^{15-x}[/tex]

[tex]P(x>6) = 1 - \sum \limits ^{6}_{x=7} ( ^{15 }_x ) \ (0.215)^x \ (1 - 0.215)^{15-x}[/tex]

[tex]P(x>6) = 1 - \sum \limits ^{6}_{x=0} ( ^{15 }_x ) \ (0.215)^x \ (1 - 0.215)^{15-x}[/tex]

[tex]P(x>6) = 1 -0.9735[/tex]

[tex]\mathbf{P(x>6) = 0.0265}[/tex]

Answer:

k = 5

Step-by-step explanation:

I will assume that your polynomial is

x^2 - 3x^2 + kx + 14

If x - a is a factor of this polynomial, then a is a root.

Use synthetic division to divide (x - 2) into x^2 - 3x^2 + kx + 14:

 2      /      1     -3     k     14

                        2     -2    2k - 4

         -------------------------------------

               1        -1    (k - 2)   2k - 10

If 2 is a root (if x - 2 is a factor), then the remainder must be zero.

Setting 2k - 10 = to zero, we get k = 5.

The value of k is 5 and the polynomial is x^2 - 3x^2 + 5x + 14

Answer:

D. The z scores are numbers without units of measurement.

Step-by-step explanation:

Z-scores are without units, or are pure numbers.

Answer:

The percentage of variation in the dependent variable explained by the variation in the independent variable is 80 %.

Step-by-step explanation:

A coefficient of correlation of 0.8 means that dependent variable changes in 0.8 when independent variable changes in a unit. Hence, the percentage of such variation ([tex]\%R[/tex]) is:

[tex]\%R = \frac{\Delta y}{\Delta x}\times 100\,\%[/tex]

Where:

[tex]\Delta x[/tex] - Change in independent variable, dimensionless.

[tex]\Delta y[/tex] - Change in dependent variable, dimensionless.

If [tex]\Delta x = 1.0[/tex] and [tex]\Delta y = 0.8[/tex], then:

[tex]\%R = 80\,\%[/tex]

The percentage of variation in the dependent variable explained by the variation in the independent variable is 80 %.

Answer:

15/2 cups: 2 1/2 cups

2 cups: 2/3 cups

2 1/2 cups: 5/6 cups

Step-by-step explanation:

Take and divide each by the smaller number

15/2 cups: 2 1/2 cups

First put in improper fraction form

15/2 : 5/2

Divide each by 5/2

15/2 ÷ 5/2  : 5/2 ÷5/2

15/2 * 2/5  : 1

3 :1   yes

1 cup: 1/4 cups

Divide each by 1/4 ( which is the same as multiplying by 4)

1*4  : 1/4 *1

4 : 1    no

2/3 cups: 1 cup

Divide each by 2/3  ( which is the same as multiplying by 3/2)

2/3 * 3/2  : 1 * 3/2

1 : 3/2   no

3 3/4 cups: 2 cups

Change to improper fraction

( 4*3+3)/4  : 2

15/4    : 2

Divide each side by 2

15/8  : 2/2

15/8   : 1    no

2 cups: 2/3 cups

Divide each side by 2/3 ( which is the same as multiplying by 3/2)

2 * 3/2 : 2/3 *3/2

3  : 1   yes

2 1/2 cups: 5/6 cups

Change to an improper fraction

( 2*2+1)/2 : 5/6

5/2  : 5/6

Divide each side by 5/6( which is the same as multiplying by 6/5)

5/2 * 6/5  : 5/6 * 6/5

3  : 1   yes

The 15/2 cups: 2 1/2 cups, 2 cups: 2/3 cups, and 2 1/2 cups: 5/6 cups have a unit rate of 3

It is defined as the comparison between two quantities that how many times the one number acquires the other number. The ratio can be presented in the fraction form or the sign : between the numbers.

For checking: 15/2 cups: 2 1/2 cups

= (15/2)/(5/2)       [2(1/2) = 5/2]

= 3

For checking:  1 cup: 1/4 cups

= 1/(1/4)

= 4

For checking: 2/3 cups: 1 cup

=(2/3)/1

= 2/3

For checking: 3 3/4 cups: 2 cups

= (15/4)(2)

= 15/8

For checking: 2 cups: 2/3 cups

= (2)/(2/3)

= 3

For checking: 2 1/2 cups: 5/6 cups

= (5/2)/(5/6)

= 3

Thus, the 15/2 cups: 2 1/2 cups, 2 cups: 2/3 cups, and 2 1/2 cups: 5/6 cups have a unit rate of 3

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Answer:

[tex]f(a) = 2a + 8[/tex]

[tex]f(x + h) = 2x + 2h + 8[/tex]

[tex]\frac{f(x + h) - f(x)}{h} = 2[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 2x + 8[/tex]

Required

[tex]f(a)[/tex]

[tex]f(x + h)[/tex]

[tex]\frac{f(x + h) - f(x)}{h}[/tex]

Solving for f(a)

Substitute a for x in the given parameter

[tex]f(x) = 2x + 8[/tex] becomes

[tex]f(a) = 2a + 8[/tex]

Solving for f(x+h)

Substitute x + h for x in the given parameter

[tex]f(x + h) = 2(x + h) + 8[/tex]

Open Bracket

[tex]f(x + h) = 2x + 2h + 8[/tex]

Solving for [tex]\frac{f(x + h) - f(x)}{h}[/tex]

Substitute 2x + 2h + 8 for f(x + h), 2x + 8 fof f(x)

[tex]\frac{f(x + h) - f(x)}{h}[/tex] becomes

[tex]\frac{2x + 2h + 8 - (2x + 8)}{h}[/tex]

Open Bracket

[tex]\frac{2x + 2h + 8 - 2x - 8}{h}[/tex]

Collect Like Terms

[tex]\frac{2x - 2x+ 2h + 8 - 8}{h}[/tex]

Evaluate the numerator

[tex]\frac{2h}{h}[/tex]

[tex]2[/tex]

Hence;

[tex]\frac{f(x + h) - f(x)}{h} = 2[/tex]

Answer:

The probability that the diagnosis is correct is 0.95249.

Step-by-step explanation:

We are given that the American Diabetes Association estimates that 8.3% of people in the United States have diabetes.

Suppose that a medical lab has developed a simple diagnostic test for diabetes that is 98% accurate for people who have the disease and 95% accurate for people who do not have it.

Let the probability that people in the United States have diabetes = P(D) = 0.083.

So, the probability that people in the United States do not have diabetes = P(D') = 1 - P(D) = 1 - 0.083 = 0.917

Also, let A = event that the diagnostic test is accurate

So, the probability that a simple diagnostic test for diabetes is accurate for people who have the disease = P(A/D) = 0.98

And the probability that a simple diagnostic test for diabetes is accurate for people who do not have the disease = P(A/D') = 0.95

Now, the probability that the diagnosis is correct is given by;

    Probability = P(D) [tex]\times[/tex] P(A/D) + P(D') [tex]\times[/tex] P(A/D')

                      = (0.083 [tex]\times[/tex] 0.98) + (0.917 [tex]\times[/tex]0.95)

                      = 0.08134 + 0.87115

                      = 0.95249

Hence, the probability that the diagnosis is correct is 0.95249.

Answer:

x = 1

Step-by-step explanation:

First, move all the variables to one side by subtracting 5x on both sides:

5x + 2 = 12x - 5

2 = 7x - 5

Add 5 to both sides:

7 = 7x

1 = x

Answer:

x=1

Step-by-step explanation:

5x + 2 =12x- 5

Subtract 5x from each side

5x-5x + 2 =12x-5x- 5

2 = 7x-5

Add 5 to each side

2+5 = 7x-5+5

7 = 7x

Divide each side by 7

7/7 = 7x/7

1 =x

Answer:

[tex]Probability = \frac{3}{7}[/tex]

Step-by-step explanation:

Given

Electrician = 6

Mechanic = 8

Required

Determine the probability of selecting an electrician

First, we need the total number of employees;

[tex]Total = n(Electrician) + n(Mechanic)[/tex]

[tex]Total = 6 + 8[/tex]

[tex]Total = 14[/tex]

Next, is to determine the required probability using the following formula;

[tex]Probability = \frac{n(Electrician)}{Total}[/tex]

[tex]Probability = \frac{6}{14}[/tex]

Divide numerator and denominator by 2

[tex]Probability = \frac{3}{7}[/tex]

Hence, the probability of selecting an electrician is 3/7

Answer:

300%

Step-by-step explanation:

1 year = 12 months

percent = part/whole * 100%

percent = 12/4 * 100% = 300%

Answer:

please can u follow me I've started following you

Answer:

C, 39.3 in²

Step-by-step explanation:

Lets first find the area of the rectangle part of the house.

To find the area of a rectangle its base × height.

So its 6×4=24 in².

Now lets find the area of the top triangle.

Area for a triangle is (base × height)/2.

The height is 3 inches, because its 7-4. While the base is 6 inches.

(6×3)/2=9 in².

To find the area of the half circle the formula, (piR²)/2.

The radius of the circle is 2 because its half of the diamter which is 4.

(pi2²)/2=6.283 in².

Now we just need to add up the area of every part,

24+9+6.283=39.283in²

Answer:

[tex]\huge\boxed{6 ( 3d + 2 )}[/tex]

Step-by-step explanation:

18d + 12

The greatest common factor is 6, So we need to factor out 6

=> 6 ( 3d + 2 ) [Distributive property has been applied and this is the simplest form]

Answer:

6(3d+2)

Step-by-step explanation:

6 is the gcd of the two terms.

The intervals would contain approximately 95% of the measurements will be (120, 280). Then the correct option is C.

The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

In numerical documentation, these realities can be communicated as follows, where Pr(X) is the likelihood capability, Χ is a perception from an ordinarily circulated irregular variable, μ (mu) is the mean of the dispersion, and σ (sigma) is its standard deviation:

The interval for 95% will be given as,

Pr(X) = μ ± 2σ

Pr(X) = 200 ± 2(40)

Pr(X) = 200 ± 80

Pr(X) = (200 - 80, 200 + 80)

Pr(X) = (120, 280)

The intervals would contain approximately 95% of the measurements will be (120, 280). Then the correct option is C.

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Answer:

Below

Step-by-step explanation:

If d is a positive number then the greatest common factor is 108d.

To get it isolate d and d^2 from the numbers.

108 divides 216. (216 = 2×108)

Then the greatest common factor of 216 and 108 is 108.

For d^2 and d we will follow the same strategy

d divides d^2 (d^2 = d*d)

Then the greatest common factor of them is d.

So the greatest common factor will be 108d if and only if d is positive. If not then 108 is the answer

Answer:

[tex]\boxed{108d}[/tex]

Step-by-step explanation:

Part 1: Find GCF of variables

The equation gives d ² and d as variables. The GCF rules for variables are:

The GCF for the variables is d.

Part 2: Find GCF of bases (Method #1)

The equation gives 108 and 216 as coefficients. To check for a GCF, use prime factorization trees to find common factors in between the values.

Key: If a number is in bold, it is marked this way because it cannot be divided further AND is a prime number!

Prime Factorization of 108

108 ⇒ 54 & 2

54 ⇒ 27 & 2

27 ⇒ 9 & 3

9 ⇒ 3 & 3

Therefore, the prime factorization of 108 is 2 * 2 * 3 * 3 * 3, or simplified as 2² * 3³.

Prime Factorization of 216

216 ⇒ 108 & 2

108 ⇒ 54 & 2

54 ⇒ 27 & 2

27 ⇒ 9 & 3

9 ⇒ 3 & 3

Therefore, the prime factorization of 216 is 2 * 2 * 2 * 3 * 3 * 3, or simplified as 2³ * 3³.

After completing the prime factorization trees, check for the common factors in between the two values.

The prime factorization of 216 is 2³ * 3³ and the prime factorization of 108 is 2² * 3³.  Follow the same rules for GCFs of variables listed above and declare that the common factor is the factor of 108.

Therefore, the greatest common factor (combining both the coefficient and the variable) is [tex]\boxed{108d}[/tex].

Part 3: Find GCF of bases (Method #2)

This is the quicker method of the two. Simply divide the two coefficients and see if the result is 2. If so, the lesser number is immediately the coefficient.

[tex]\frac{216}{108}=2[/tex]

Therefore, the coefficient of the GCF will be 108.

Then, follow the process described for variables to determine that the GCF of the variables is d.

Therefore, the GCF is [tex]\boxed{108d}[/tex].

Answer:

(i) 0.32          (ii) 0.85

(iii) 0.3412    (iv) 0.20

(v) 0.29         (vi) 0.12

Step-by-step explanation:

The data provided is as follows:

   Race                    Smoker (S)         Nonsmoker (N)             Row Total

 White(W)                    290                       560                           850

  Black(B)                     30                        120                           150

Column Total                320                       680                        1,000

(i)

Compute the value of P (S) as follows:

[tex]P(S)=\frac{n(S)}{N}=\frac{320}{1000}=0.32[/tex]

P (S) = 0.32.

(ii)

Compute the value of P (W) as follows:

[tex]P(W)=\frac{n(W)}{T}=\frac{850}{1000}=0.85[/tex]

P (W) = 0.85.

(iii)

Compute the value of P (S|W) as follows:

[tex]P(S|W)=\frac{n(S\cap W)}{n(W)}=\frac{290}{850}=0.3412[/tex]

P (S|W) = 0.3412.

(iv)

Compute the value of P (S|B) as follows:

[tex]P(S|B)=\frac{n(S\cap B)}{n(B)}=\frac{30}{150}=0.20[/tex]

P (S|W) = 0.20.

(v)

Compute the value of P (S∩W) as follows:

[tex]P(S\cap W)=\frac{n(S\cap W)}{T}=\frac{290}{1000}=0.29[/tex]

P (S∩W) = 0.29.

(vi)

Compute the value of P (N∩B) as follows:

[tex]P(N\cap B)=\frac{n(N\cap B)}{T}=\frac{120}{1000}=0.12[/tex]

P (S∩W) = 0.12.

Answer:

35%

Step-by-step explanation:

[tex]Principal = 2500\\\\Simple\:Interest = 3500\\\\Time = 4 \:years\\\\Rate = ?\\\\Rate = \frac{100 \times Simple \: Interest }{Principal \times Time}\\\\Rate = \frac{100 \times 3500}{2500 \times 4} \\\\Rate = \frac{350000}{10000}\\\\ Rate = 35 \%[/tex]

[tex]S.I = \frac{PRT}{100}\\\\ 100S.I = PRT\\\\\frac{100S.I}{PT} = \frac{PRT}{PT} \\\\\frac{100S.I}{PT} = R[/tex]

Answer:

35%

Step-by-step explanation:

I REALLY HOPE I HELPED

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JUST A RANDOM GIRL WANTING TO HELP PEOPLE!

                                PEACE!

Answer:

102 cm

Step-by-step explanation:

Answer:

0.9719

Step-by-step explanation:

Find the mean and standard deviation of the sampling distribution.

μ = 5.1

σ = 1.1 / √49 = 0.157

Find the z score.

z = (x − μ) / σ

z = (4.8 − 5.1) / 0.157

z = -1.909

Use a calculator to find the probability.

P(Z > -1.909)

= 1 − P(Z < -1.909)

= 1 − 0.0281

= 0.9719

The probability of the randomly used item mean length is greater than 4.8 inches is 0.9719

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values.

The arithmetic mean is found by adding the numbers and dividing the sum by the number of numbers in the list.

Given,

Mean = 5.1 inches

Standard deviation = 1.1 inches

Sample size = 49

New mean = 4.8

Z score = Difference in mean /(standard deviation / [tex]\sqrt{sample size}[/tex])

Z score = [tex]\frac{4.8-5.1}{1.1/\sqrt{49} }=-1.909[/tex]

Z score = -1.909

Then the probability

P(Z>-1.909)

=1-P(Z>-1.909)

=1-0.0281

=0.9719

Hence, The probability of the randomly used item mean length is greater than 4.8 inches is 0.9719

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Answer:

125π ft²

Step-by-step explanation:

1/4π(30)² - 1/4π(20)² = 125π

Answer:

Yes.

It is 1.45 x 10^-7 or 0.000000145

Hope it helps!

Answer:

It is 1.45 x 10^-7 or 0.000000145

Step-by-step explanation:

Answer: The value of x- 2y is a. [tex]\pm 3[/tex].

Step-by-step explanation:

Given:  x and y are two positive real numbers such that [tex]x^2+4y^2=17[/tex]   and [tex]xy= 2[/tex] .

Consider [tex](x-2y)^2=x^2-2(x)(2y)+(2y)^2\ \ \ [(a+b)^2=(a^2-2ab+b^2)][/tex]

[tex]=x^2-4xy+4y^2[/tex]

[tex]=x^2+4y^2-4(xy)[/tex]

Put  [tex]x^2+4y^2=17[/tex]   and [tex]xy= 2[/tex] , we get

[tex](x-2y)^2=17-4(2)=17-8=9[/tex]

[tex]\Rightarrow\ (x-2y)^2=9[/tex]

Taking square root on both sides , we get'

[tex]x-2y= \pm3[/tex]

Hence, the value of x- 2y is a. [tex]\pm 3[/tex].

Answer:

[tex]x = 2-t[/tex] and [tex]y = -5\cdot t +21[/tex]

Step-by-step explanation:

Given that [tex]y = 5\cdot x + 11[/tex] and [tex]t = 2-x[/tex], the parametric equations are obtained by algebraic means:

1) [tex]t = 2-x[/tex] Given

2) [tex]y = 5\cdot x +11[/tex] Given

3) [tex]y = 5\cdot (x\cdot 1)+11[/tex] Associative and modulative properties

4) [tex]y = 5\cdot \left[(-1)^{-1} \cdot (-1)\right]\cdot x +11[/tex] Existence of multiplicative inverse/Commutative property

5) [tex]y = [5\cdot (-1)^{-1}]\cdot [(-1)\cdot x]+11[/tex] Associative property

6) [tex]y = -5\cdot (-x)+11[/tex]  [tex]\frac{a}{-b} = -\frac{a}{b}[/tex] / [tex](-1)\cdot a = -a[/tex]

7) [tex]y = -5\cdot (-x+0)+11[/tex] Modulative property

8) [tex]y = -5\cdot [-x + 2 + (-2)]+11[/tex] Existence of additive inverse

9) [tex]y = -5 \cdot [(2-x)+(-2)]+11[/tex] Associative and commutative properties

10) [tex]y = (-5)\cdot (2-x) + (-5)\cdot (-2) +11[/tex] Distributive property

11) [tex]y = (-5)\cdot (2-x) +21[/tex] [tex](-a)\cdot (-b) = a\cdot b[/tex]

12) [tex]y = (-5)\cdot t +21[/tex] By 1)

13) [tex]y = -5\cdot t +21[/tex] [tex](-a)\cdot b = -a \cdot b[/tex]/Result

14) [tex]t+x = (2-x)+x[/tex] Compatibility with addition

15) [tex]t +(-t) +x = (2-x)+x +(-t)[/tex] Compatibility with addition

16) [tex][t+(-t)]+x= 2 + [x+(-x)]+(-t)[/tex] Associative property

17) [tex]0+x = (2 + 0) +(-t)[/tex] Associative property

18) [tex]x = 2-t[/tex] Associative and commutative properties/Definition of subtraction/Result

In consequence, the right answer is [tex]x = 2-t[/tex] and [tex]y = -5\cdot t +21[/tex].

Answer:

[tex] Perimeter = 3x + 3 [/tex]

Step-by-step explanation:

Perimeter of the given triangle in the figure is the sum of all three sides.

The expressions for the 3 sides are given as, [tex] x, (x - 3), (x + 6) [/tex].

Therefore,

[tex] Perimeter = x + (x - 3) + (x + 6) [/tex]

Simplify,

[tex] Perimeter = x + x - 3 + x + 6 [/tex]

Collect like terms

[tex] Perimeter = x + x + x - 3 + 6 [/tex]

[tex] Perimeter = 3x + 3 [/tex]

Answer:

Step-by-step explanation:

The sequence of the problem above is an arithmetic sequence

For an nth term in an arithmetic sequence

F(n) = a + ( n - 1)d

where a is the first term

n is the number of terms

d is the common difference

To find the equation first find the common difference

0.65 - 0.5 = 0.15 or 0.80 - 0.65 = 0.15

The first term is 0.5

Substitute the values into the above formula

That's

f(n) = 0.5 + (n - 1)0.15

f(n) = 0.5 + 0.15n - 0.15

The final answer is

Hope this helps you

Answer:

Step-by-step explanation:

Took the math test on edge

Answer:

Number of levels = 2

Type of design = Repeated measure

Dependent variable = Typing Speed

Step-by-step explanation:

The number of levels in an experiment simply refers to the number of experimental conditions in which participants are subjected to. In the scenario above, the number of levels is 2. Which are ; Halfway through the class and After the class is over.

The type of designed employed is REPEATED MEASURE, this is because the participants all took part in each experimental condition.

The dependent variable is TYPING SPEED, which is the variable which is measured with respect to the independent variable. Hence the observed value depends on period that is (halfway through the class or after the class is over).

Answer:

Step-by-step explanation:

Let the speed of Frank be x and speed of Gregory be y. If Gregory drives 22 miles per hour faster than Frank, then y = 22+x. SInce they they are 216miles apart after 2.25 hours,

Speed = Distance/Time

Total time travelled by them = 2.25hours

Total distance = 216 hours

Total speed = x+y = x+22+x

Substituting this parameters into the formula given to get x we will have;

x+22+x = 216/2.25

2x+22 = 96

2x = 96-22

2x = 74

x = 74/2

x = 37

Hence the speed of Frank is 37miles per hour while that of gregory is 37+22 = 59miles/hour

Answer:

Step-by-step explanation:

First you have to find the medians which is when you put the numbers in number order and find the one in the middle.

Class A: 60,65,70,70,75,80,80,85,90,90

=77.5

Class B: 75,85,85,85,90,90,90,90,95,100

=90

That the class B is more advanced, and they probably studied.

Answer: The missing number is 5.

Step-by-step explanation:

In the table we can only have numbers between 1 and 9,

The pattern that i see is:

We have sets of 3 numbers.

"the bottom number is equal to the difference between the two first numers, if the difference is negative, change the sign, if the difference is zero, there goes a 9 (the next number to zero)"

Goin from right to left we have:

9 - 6 = 3

6 - 2 = 4

4 - 9 = - 5 (is negative, so we actually use -(-5) = 5)

4 - 4 = 0 (we can not use zero, so we use the next number, 9)

3 - 3 = 0 (same as above)

? - 1 = 4

? = 4 + 1 =  5

The missing number is 5.