Savita was given a set of 250 cherries and Gail was given a set
of 350 cherries. Both were also given a set of small plastic bags.
Savita had to pack 8 cherries in a bag and Gail had to pack 12
cherries in a bag. Explain how you know who will have more
bags of cherries at the end.​

Answer:8

Step-by-step explanation:

The smallest prime is 2

cube of 2 is equal to 8

2*2*2=8

Answer:

729

Step-by-step explanation:

The second smallest prime number is 3 (preceded by 2). We have (3^2)^3=3^6=729.

Hope this helped! :)

Answer:

168 mm²

Step-by-step explanation:

Let A be the area of this shape

the kite is made of two triangles

Let A' and A" be the areas of the triangles

let's calculate A' and A" :

The area of a triangle is the product of the base and the height over 2

Let's calculate A

Answer:

option C is the right answer

c) 70 and 60

Answer:

[tex]\boxed{\sf \ \ x=-2, \ y=-3 \ \ }[/tex]

Step-by-step explanation:

Hello,

I assume that you want to solve this system of two equations

   (1) 5x - y  = -7

   (2) 4x + 2y = -14

We will multiply (1) by 2 and add to (2) so that we can eliminate the terms in y

2*(1)+(2) gives

   10x - 2y + 4x + 2y = -7*2 -14 = -14 - 14 = -28

   <=>

   14x = - 28 we can divide by 14 both parts

   x = -28/14 = -2

and then we replace x in (1)

   5*(-2)-y=-7

   -10-y=-7 add 7

   -10-y+7=0

   -3-y=0 add y

   -3 = y

which is equivalent to y = -3

do not hesitate if you have any question

Answer:

x = -2, y = -3

Step-by-step explanation:

5x - y = -7

4x + 2y = – 14

Multiply the first equation by 2

2(5x - y) = 2*-7

10x -2y = -14

Add this to the second equation to eliminate y

10x -2y = -14

4x + 2y = – 14

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

14x = -28

Divide by 14

14x/14 = -28/14

x = -2

Now find y

4x+2y = -14

4*-2 +2y = -14

-8+2y = -14

Add 8 to each side

2y = -6

Divide by 2

2y/2 = -6/2

y = -3

Answer:  D.) The second difference is constant.

Step-by-step explanation:

The rate of change of a quadratic function is a linear function. The rate of change of that is constant, so second differences of a quadratic number pattern are constant.

Answer:

D.

Step-by-step explanation:

Answer:

2 inches

Step-by-step explanation:

x= smallest

3x=largest

2x=medium

x+3x+2x=12

6x=12

x=2

so smallest is 2

largest is 6 (3x)

medium is 4 (2x)

2+6+4=12

¡Hola! ¡Ojalá esto ayude!

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

La fórmula para calcular el área de cualquier triángulo es:

base multiplicada por la altura y dividida por dos.

||

||

||

\/

Bh / 2.

Answer:

1. [tex] P(x) [/tex] ÷ [tex] Q(x) [/tex]---> [tex] \frac{-3x + 2}{3(3x - 1)} [/tex]

2. [tex] P(x) + Q(x) [/tex]---> [tex]\frac{2(6x - 1)}{(3x - 1)(-3x + 2)}[/tex]

3.  [tex] P(x) - Q(x) [/tex]---> [tex] \frac{-2(12x - 5)}{(3x - 1)(-3x + 2)} [/tex]

4. [tex] P(x)*Q(x) [/tex] --> [tex] \frac{12}{(3x - 1)(-3x + 2)} [/tex]

Step-by-step explanation:

Given that:

1. [tex] P(x) = \frac{2}{3x - 1} [/tex]

[tex] Q(x) = \frac{6}{-3x + 2} [/tex]

Thus,

[tex] P(x) [/tex] ÷ [tex] Q(x) [/tex] = [tex] \frac{2}{3x - 1} [/tex] ÷ [tex] \frac{6}{-3x + 2} [/tex]

Flip the 2nd function, Q(x), upside down to change the process to multiplication.

[tex] \frac{2}{3x - 1}*\frac{-3x + 2}{6} [/tex]

[tex] \frac{2(-3x + 2)}{6(3x - 1)} [/tex]

[tex] = \frac{-3x + 2}{3(3x - 1)} [/tex]

2. [tex] P(x) + Q(x) [/tex] = [tex] \frac{2}{3x - 1} + \frac{6}{-3x + 2} [/tex]

Make both expressions as a single fraction by finding, the common denominator, divide the common denominator by each denominator, and then multiply by the numerator. You'd have the following below:

[tex] \frac{2(-3x + 2) + 6(3x - 1)}{(3x - 1)(-3x + 2)} [/tex]

[tex] \frac{-6x + 4 + 18x - 6}{(3x - 1)(-3x + 2)} [/tex]

[tex] \frac{-6x + 18x + 4 - 6}{(3x - 1)(-3x + 2)} [/tex]

[tex] \frac{12x - 2}{(3x - 1)(-3x + 2)} [/tex]

[tex] = \frac{2(6x - 1}{(3x - 1)(-3x + 2)} [/tex]

3. [tex] P(x) - Q(x) [/tex] = [tex] \frac{2}{3x - 1} - \frac{6}{-3x + 2} [/tex]

[tex] \frac{2(-3x + 2) - 6(3x - 1)}{(3x - 1)(-3x + 2)} [/tex]

[tex] \frac{-6x + 4 - 18x + 6}{(3x - 1)(-3x + 2)} [/tex]

[tex] \frac{-6x - 18x + 4 + 6}{(3x - 1)(-3x + 2)} [/tex]

[tex] \frac{-24x + 10}{(3x - 1)(-3x + 2)} [/tex]

[tex] = \frac{-2(12x - 5}{(3x - 1)(-3x + 2)} [/tex]

4. [tex] P(x)*Q(x) = \frac{2}{3x - 1}* \frac{6}{-3x + 2} [/tex]

[tex] P(x)*Q(x) = \frac{2*6}{(3x - 1)(-3x + 2)} [/tex]

[tex] P(x)*Q(x) = \frac{12}{(3x - 1)(-3x + 2)} [/tex]

Composite functions involve combining multiple functions to form a new function

The functions are given as:

[tex]P(x) = \frac{2}{3x - 1}[/tex]

[tex]Q(x) = \frac{6}{-3x + 2}[/tex]

[tex]P(x) \div Q(x)[/tex] is calculated as follows:

[tex]P(x) \div Q(x) = \frac{2}{3x - 1} \div \frac{6}{-3x + 2}[/tex]

Express as a product

[tex]P(x) \div Q(x) = \frac{2}{3x - 1} \times \frac{-3x + 2}{6}[/tex]

Divide 2 by 6

[tex]P(x) \div Q(x) = \frac{1}{3x - 1} \times \frac{-3x + 2}{3}[/tex]

Multiply

[tex]P(x) \div Q(x) = \frac{-3x + 2}{3(3x - 1)}[/tex]

Hence, the value of [tex]P(x) \div Q(x)[/tex] is [tex]\frac{-3x + 2}{3(3x - 1)}[/tex]

P(x) + Q(x) is calculated as follows:

[tex]P(x) + Q(x) = \frac{2}{3x - 1} + \frac{6}{-3x + 2}[/tex]

Take LCM

[tex]P(x) + Q(x) = \frac{2(-3x + 2) + 6(3x - 1)}{(3x - 1)(-3x + 2)}[/tex]

Open brackets

[tex]P(x) + Q(x) = \frac{-6x + 4 + 18x - 6}{(3x - 1)(-3x + 2)}[/tex]

Collect like terms

[tex]P(x) + Q(x) = \frac{18x-6x + 4 - 6}{(3x - 1)(-3x + 2)}[/tex]

[tex]P(x) + Q(x) = \frac{12x - 2}{(3x - 1)(-3x + 2)}[/tex]

Factor out 2

[tex]P(x) + Q(x) = \frac{2(6x -1)}{(3x - 1)(-3x + 2)}[/tex]

Hence, the value of P(x) + Q(x) is [tex]\frac{2(6x -1)}{(3x - 1)(-3x + 2)}[/tex]

P(x) - Q(x) is calculated as follows:

[tex]P(x) - Q(x) = \frac{2}{3x - 1} - \frac{6}{-3x + 2}[/tex]

Take LCM

[tex]P(x) - Q(x) = \frac{2(-3x + 2) - 6(3x - 1)}{(3x - 1)(-3x + 2)}[/tex]

Open brackets

[tex]P(x) - Q(x) = \frac{-6x + 4 - 18x +6}{(3x - 1)(-3x + 2)}[/tex]

Collect like terms

[tex]P(x) - Q(x) = \frac{-18x-6x + 4 + 6}{(3x - 1)(-3x + 2)}[/tex]

[tex]P(x) - Q(x) = \frac{-24x +10}{(3x - 1)(-3x + 2)}[/tex]

Factor out -2

[tex]P(x) - Q(x) = \frac{-2(12x -5)}{(3x - 1)(-3x + 2)}[/tex]

Hence, the value of P(x) - Q(x) is [tex]\frac{-2(12x -5)}{(3x - 1)(-3x + 2)}[/tex]

P(x) * Q(x) is calculated as follows:

[tex]P(x) \times Q(x) = \frac{2}{3x - 1} \times \frac{6}{-3x + 2}[/tex]

Multiply

[tex]P(x) \times Q(x) = \frac{12}{(3x - 1)(-3x + 2)}[/tex]

Hence, the value of P(x) * Q(x) is [tex]\frac{12}{(3x - 1)(-3x + 2)}[/tex]

Read more about composite functions at:

https://brainly.com/question/10687170

Answer:

Option C

Step-by-step explanation:

The whole numbers a,b and c such that [tex]a^2+b^2 = c^2[/tex] are Pythagorean triples satisfying the Pythagorean theorem.

Answer:

C

Step-by-step explanation:

a, b, and c are side lengths of the triangle.

The three side lengths that make up a right triangle are most commonly known as Pythagorean triples.

Answer:

Null - p= 71%

Alternative - p =/ 71%

Step-by-step explanation:

The null hypothesis is always the default statement in an experiment. While the alternative hypothesis is always tested against the null hypothesis.

Null hypothesis: 71% of their readers own a personal computer- p = 71%

Alternative hypothesis: Not 71% of their readers own a personal computer - p =/ 71%

Answer:

It is a negative correlation

Step-by-step explanation:

As the x value increases the y value decreases. This causes it to be a negative.

Answer:

Let the number be x

The statement

A number is increased by five is written as

x + 5

Then it's squared

So we the final answer as

Hope this helps

Set up two equations and set equal to each other. Let number of years = x:

College A = 14100+750x

College B = 42100-1250x

Set equal:

14100 + 750x = 42100 - 1250x

Subtract 750x from both sides:

14100 = 42100 - 2000x

Subtract 42100 from both sides:

-28000 = -2000x

Divide both sides by -2000:

x = -28000 / -2000

x = 14

It will take 14 years for the schools to have the same enrollment.

Enrollment will be:

14100 + 750(14) = 14100 + 10500 = 24,600

Answer:

(a)2019 (14 years after)

(b)24,600

Step-by-step explanation:

Let the number of years =n

College A

Initial Population in 2005 = 14,100

Increase per year = 750

Therefore, the population after n years = 14,100+750n

College B

Initial Population in 2005 = 42,100

Decline per year = 1250

Therefore, the population after n years = 42,100-1250n

When the enrollments are the same

14,100+750n=42,100-1250n

1250n+750n=42100-14100

2000n=28000

n=14

Therefore, in 2019 (14 years after), the colleges will have the same​ enrollment.

Enrollment in 2019 =42,100-1250(14)

=24,600

Answer:

The range is found by subtracting the minimum data entry from the maximum data entry.

Step-by-step explanation:

The range is found by subtracting the minimum data entry from the maximum data entry.

It is easy to compute.

It uses only two entries from the data set.

Answer:

0.0668 or 6.68%

Step-by-step explanation:

Variance (V) = 10,000

Standard deviation (σ) = √V= 100

Mean score (μ) = 500

The z-score for any test score X is:

[tex]z=\frac{X-\mu}{\sigma}[/tex]

For X = 650:

[tex]z=\frac{650-500}{100}\\z=1.5[/tex]

A z-score of 1.5 is equivalent to the 93.32nd percentile of a normal distribution. Therefore, the probability that he or she will make a score of 650 or more is:

[tex]P(X\geq 650)=1-P(X\leq 650)\\P(X\geq 650)=1-0.9332\\P(X\geq 650)=0.0668=6.68\%[/tex]

The probability is 0.0668 or 6.68%

The probability that he or she will make a score of 650 or more is 0.0668.

Let X = Scores made on a certain aptitude test by nursing students

X follows normal distribution with mean = 500 and variance of 10,000.

So, standard deviation = [tex]\sqrt{10000}=100[/tex].

z score of 650 is = [tex]\frac{\left(650-500\right)}{100}=1.5[/tex].

The probability that he or she will make a score of 650 or more is:

[tex]P(X\geq 650)\\=P(z\geq 1.5)\\=1-P(z<1.5)\\=1-0.9332\\=0.0668[/tex]

Learn more: https://brainly.com/question/14109853

Answer:

The probability that no more than 70% would prefer to start their own business is 0.1423.

Step-by-step explanation:

We are given that a Gallup survey indicated that 72% of 18- to 29-year-olds, if given choice, would prefer to start their own business rather than work for someone else.

Let [tex]\hat p[/tex] = sample proportion of people who prefer to start their own business

The z-score probability distribution for the sample proportion is given by;

                               Z  =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, p = population proportion who would prefer to start their own business = 72%

            n = sample of 18-29 year-olds = 600

Now, the probability that no more than 70% would prefer to start their own business is given by = P( [tex]\hat p[/tex] [tex]\leq[/tex] 70%)

       P( [tex]\hat p[/tex] [tex]\leq[/tex] 70%) = P( [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] [tex]\leq[/tex] [tex]\frac{0.70-0.72}{\sqrt{\frac{0.70(1-0.70)}{600} } }[/tex] ) = P(Z [tex]\leq[/tex] -1.07) = 1 - P(Z < 1.07)

                                                                       = 1 - 0.8577 = 0.1423

The above probability is calculated by looking at the value of x = 1.07 in the z table which has an area of 0.8577.

Answer:

Step-by-step explanation:

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points

[tex](3;\ 9)\to x_1=3;\ y_1=9\\(1;\ 1)\to x_2=1;\ y_2=1[/tex]

Substitute:

[tex]m=\dfrac{1-9}{1-3}=\dfrac{-8}{-2}=4[/tex]

Answer:

m=4

Step-by-step explanation:

Slope can be found using the following formula:

[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

where [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] are points on the line.

We are given the points (3,9) and (1,1). Therefore,

[tex]x_{1}=3\\y_{1}=9 \\x_{2}=1\\y_{2}=1[/tex]

Substitute each value into the formula.

[tex]m=\frac{1-9}{1-3}[/tex]

Subtract in the numerator first.

[tex]m=\frac{-8}{1-3}[/tex]

Subtract in the denominator.

[tex]m=\frac{-8}{-2}[/tex]

Divide.

[tex]m=4[/tex]

The slope of the line is 4.

Answer:

1/5 cup

Step-by-step explanation:

Sugar: water

1             5

We want 1 cup water, so divide each side by 5

1/5 :  5/5

1/5 : 1

There is 1/5 cup sugar to 1 cup water

Answer:

( 6, pi/6)

Step-by-step explanation:

( 3 sqrt(3), 3)

To get r we use x^2 + y ^2 = r^2

( 3 sqrt(3) )^2 + 3^2 = r^2

9 *3 +9 = r^2

27+9 = r^2

36 = r^2

Taking the square root of each side

sqrt(36) = sqrt(r^2)

6 =r

Now we need to find theta

tan theta = y/x

tan theta = 3 / 3 sqrt(3)

tan theta = 1/ sqrt(3)

Taking the inverse tan of each side

tan ^-1 ( tan theta) = tan ^ -1 ( 1/ sqrt(3))

theta = pi /6

Answer:

Step by step explanation

Total length of pole = 21.3 m

Length of pole inside the ground = 0.2 m

Let length of pole outside the ground be X,

So, according to the Question,

[tex]x + 0.2 = 21.3[/tex]

Move constant to R.H.S and change its sign

[tex]x = 21.3 - 0.2[/tex]

Calculate the difference

[tex]x = 21.1 \: m[/tex]

Hope this helps...

Good luck on your assignment...

Answer:

The  probability is  [tex]P[ D n R] = 0.196[/tex]

Step-by-step explanation:

  From the question we are told that

     The number of Democrats is  [tex]D = 8[/tex]

       The number of republicans is  [tex]R = 8[/tex]

The  number of ways of selecting selecting two Democrats and four Republicans.

         [tex]N = \left {D} \atop {}} \right. C_2 * \left {R} \atop {}} \right. C_1[/tex]

Where C represents combination

substituting values

           [tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1[/tex]

           [tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8!}{(8-2)! 2!} * \frac{8! }{(8-4)! 1 !}[/tex]

=>        [tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8!}{(6)! 2!} * \frac{8! }{(6)! 1 !}[/tex]

=>        [tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8 * 7 * 6!}{(6)! 2!} * \frac{8*7 *6! }{(6)! 1 !}[/tex]

=>        [tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8 * 7 }{ 2*1 } * \frac{8*7 }{ 1 *1 }[/tex]

=>      [tex]N = 1568[/tex]

The total number of ways of selecting the committee of six people is  

          [tex]Z = \left {D+R} \atop {}} \right. C_6[/tex]

substituting values

           [tex]Z = \left {8+8} \atop {}} \right. C_6[/tex]

            [tex]Z= \left {16} \atop {}} \right. C_6[/tex]

substituting values

             [tex]Z= \left {16} \atop {}} \right. C_6 = \frac{16! }{(16-6) ! 6!}[/tex]

           [tex]Z= \left {16} \atop {}} \right. C_6 = \frac{16 *15 *14 * 13 * 12 * 11 * 10! }{10 ! 6!}[/tex]

           [tex]Z= \left {16} \atop {}} \right. C_6 = \frac{16 *15 *14 * 13 * 12 * 11 }{6* 5 * 4 * 3 * 2 * 1}[/tex]

           [tex]Z= \left {16} \atop {}} \right. C_6 = 8008[/tex]

The probability of selecting two Democrats and four Republicans  is  mathematically  represented as

           [tex]P[ D n R] = \frac{N}{Z}[/tex]

substituting values

           [tex]P[ D n R] = \frac{1568}{8008}[/tex]

            [tex]P[ D n R] = 0.196[/tex]

Answer: 680

Step-by-step explanation:

When order doesn't matter,then the number of combinations of choosing r things out of n = [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]

Given: Total participants = 17

From these, a group of 3 participants is to be tested under a special condition.

Number of groups of 3 participants chosen = [tex]^{17}C_3=\dfrac{17!}{3!(17-3)!}\[/tex]

[tex]^{17}C_3=\dfrac{17!}{3!(17-3)!}\\\\=\dfrac{17\times16\times15\times14!}{3\times2\times14!}\\\\=680[/tex]

Hence, there are 680 groups of 3 participants can  be chosen,.

Answer:

1/6

Step-by-step explanation:

The formula of a slope [tex]\frac{y2-y1}{x2-x1}[/tex] (change in y / change in x)

1. Substitute in the values

(x1, y1) = (4, 1[tex]\frac{2}{3}[/tex])

(x2, y2) = (-2, [tex]\frac{2}{3}[/tex])

([tex]\frac{2}{3}[/tex] - 1[tex]\frac{2}{3}[/tex]) / (-2 - 4)

2. Solve

[tex]\frac{2}{3}[/tex] - 1[tex]\frac{2}{3}[/tex] = -1

-2 - 4 = -6

slope = [tex]\frac{-1}{-6}[/tex] = [tex]\frac{1}{6}[/tex]

Step-by-step explanation:

81^x² = 27^x

(3^4)^x² = (3^3)^x

3^(4x²) = 3^(3x)

4x² = 3x

4x² − 3x = 0

x (4x − 3) = 0

x = 0 or ¾

Answer:

(a) The probability of getting someone who was not sent to prison is 0.55.

(b) If a study subject is randomly selected and it is then found that the subject entered a guilty plea, the probability that this person was not sent to prison is 0.63.

Step-by-step explanation:

We are given that in a study of pleas and prison sentences, it is found that 45% of the subjects studied were sent to prison. Among those sent to prison, 40% chose to plead guilty. Among those not sent to prison, 55% chose to plead guilty.

Let the probability that subjects studied were sent to prison = P(A) = 0.45

Let G = event that subject chose to plead guilty

So, the probability that the subjects chose to plead guilty given that they were sent to prison = P(G/A) = 0.40

and the probability that the subjects chose to plead guilty given that they were not sent to prison = P(G/A') = 0.55

(a) The probability of getting someone who was not sent to prison = 1 - Probability of getting someone who was sent to prison

      P(A') = 1 - P(A)

               = 1 - 0.45 = 0.55

(b) If a study subject is randomly selected and it is then found that the subject entered a guilty plea, the probability that this person was not sent to prison is given by = P(A'/G)

We will use Bayes' Theorem here to calculate the above probability;

    P(A'/G) =  [tex]\frac{P(A') \times P(G/A')}{P(A') \times P(G/A') +P(A) \times P(G/A)}[/tex]      

                 =  [tex]\frac{0.55 \times 0.55}{0.55\times 0.55 +0.45 \times 0.40}[/tex]

                 =  [tex]\frac{0.3025}{0.4825}[/tex]

                 =  0.63

Answer:

x = {9, -3}

Step-by-step explanation:

Or it can be shown as:

Answer:

Option (D)

Step-by-step explanation:

The given graph represents a rational function having,

1). Vertical asymptote → x = 2

2). Horizontal asymptote → y = 0

Parent function representing the rational function will be in the form of,

F(x) = [tex]\frac{1}{x^{2} }[/tex]

Since, vertical asymptote of the function is x = 2, denominator of the function will be in the form of (x - 2)².

Since, horizontal asymptote of the function is y = 0, highest exponent term in the numerator will be 0.

Therefore, numerator of the fraction will be x⁰.

The rational function given in the graph will be,

F(x) = [tex]\frac{x^{0}}{(x-2)^2}[/tex]

F(x) = [tex]\frac{1}{(x-2)^2}[/tex]

Option (D) will be the answer.

Answer:

[tex]7.5cm^2[/tex]

Step-by-step explanation:

Well using the following formula,

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

5*3 = 15

15 / 2

7.5cm^2

Answer:[tex]7.5cm^{2}[/tex]

Step-by-step explanation:

h=3

b=5

area=1/2 x b x h

1/2 x 5 x 3

area=7.5

Answer:

csc B = 13/12

Step-by-step explanation:

csc B = 1 / sin B

The sin B is

sin B = opp/ hyp  so

csc B = hyp /opp

csc B = 26 / 24

csc B = 13/12

Answer:

13/12

Step-by-step explanation:

sin θ = opposite/ hypotenuse

csc θ = 1/sinθ

csc θ  = hypotenuse/opposite

csc (B)  = 26/24

csc (B)  = 13/12