72 students choose to attend one of three after school activities: football, tennis or running.
There are 25 boys.
27 students choose football, of which 17 are girls.
18 students choose tennis.
24 girls choose running.
A student is selected at random.
What is the probability this student chose running?
Give your answer in its simplest form.

Answer:

Step-by-step explanation:

-8*3= -24+14=-10

Answer:

-12 and 2.

Step-by-step explanation:

-12*2= -24,

-12+2=-10

Answer:

5:2

Step-by-step explanation:

There are 5 apples and 2 cherries. Put them together to get 5:2.

Answer:

35.25

Step-by-step explanation:

Give the data set:

23 37 49 34 35 41 40 26 32 22 38 42

We are expected to calculate the midquartile of the given data set.

22 23 26 32 34 35 37 38 40 41 42 49

First step is to find the lower quartile which comprises of

22 23 26 32 34 35

Here the Q1 is (26+32)/2 = 58/2= 29

Second step to find the upper quartile which comprises of

37 38 40 41 42 49

Here the Q3 is (40+41) /2 = 81/2 = 41.5

Then to find the midquartile which is (Q1+Q3) /2 where Q1 is 29 and Q3 is 41.5

= (29+41.5)/2

= (70.5) /2 = 35.25

Answer:

[tex]\boxed{\sf \ \ x = 9, \ y = -5, \ z = 5 \ \ }[/tex]

Step-by-step explanation:

Hello,

   (1) 2x + 4y + z = 3

   (2) x - 2y - 3z = 4

   (3) x + y - z = -1

From (3) we can write z = x + y + 1 and we replace in (1)

2x + 4y + x + y + 1 = 3 <=> 3x + 5y = 3-1 =2

   (1') 3x + 5y = 2

and we replace in (2)

x - 2y -3(x+y+1) = 4 <=> -2x -5y -3 = 4 <=> -2x -5y = 4 + 3 = 7

   (2') -2x - 5y = 7

(1') + (2') gives

3x - 2x + 5y - 5y = 2 + 7 = 9

x = 9

we replace in (1')

3*9 + 5y = 2 <=> 27 + 5y = 2 <=> 5y = 2-27 = -25 <=> y = -25/5 = -5

y = -5

and then in (3)

9 - 5 - z = -1 <=> 4 - z = -1 <=> z = 4 + 1 = 5

z = 5

hope this helps

Answer:

work is shown and pictured

Answer:

1,000 i believe its that

Step-by-step explanation:

Answer:

A. Eric rode 2 more miles per week than Kim rode

Step-by-step explanation:

Number of miles Kim rode bicycle in 9 weeks = 135 miles

Let x be the number of miles per week.

135miles => 9 weeks

x miles => 1 week

[tex] x = \frac{135}{9} [/tex]

[tex] x = 15 [/tex]

Kim rode the bicycle 15 miles per week

Number of miles Eric rode bicycle in 6 weeks = 102 miles

Let x be the number of miles per week Eric rides the bicycle.

102 miles => 6 weeks

x miles => 1 week

[tex] x = \frac{102}{6} [/tex]

[tex] x = 17 [/tex]

Kim rode the bicycle 17 miles per week

Comparing the number of miles per week they rode, we would conclude that: "Eric rode 2 more miles per week than Kim rode".

Answer:

[tex]\large \boxed{\sf \ \ \ 49 \ \ \ }[/tex]

Step-by-step explanation:

Hello,

(fog)(1)=f(g(1))

and

g(1)=-3

so

(fog)(1)

= f(-3)

= 5 *9 - (-3) + 1

= 45 + 3 + 1

= 49

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Step-by-step explanation:

angle A = angle B( Corresponding angles)

so,

5x - 5 = 3x + 13

=> 5x - 3x = 13 + 5

=> 2x = 18

=> x = 9

angle B = 3x + 13 = (3×9) + 13 = 27 + 13 = 40

Answer:

x=9, ∠B=40

Step-by-step explanation:

In this case, ∠A≅∠B, as they are corresponding angles. Therefore, if you set up the equation to be 5x-5=3x+13,

2x=18, x=9

∠B=3(9)+13=27+13=40

Answer:

If no matter what choice of x my adversary makes, I can choose a y that makes the statement true, then the statement is true. Otherwise, it's false.

Step-by-step explanation:

According to the given situation, as we can see that the we cant find the y for the x i.e given that shows Parent (x) represented as Parent Of (x,y)

In mathematically,

Parent (x) = Parent (x,y)

This does not seems true

Therefore this statement is false

Hence, the fourth option is true

All other statements that are mentioned is false

Answer:

[tex]m<7[/tex]

Step-by-step explanation:

We can solve this inequality by isolating the variable [tex]m[/tex].

To do this, we subtract 8 from both sides of the equation.

[tex]15-8 > m+8-8[/tex]

[tex]7>m[/tex]

I always like formatting by inequalities with the variable on the left, so we just reverse the numbers and the sign.

[tex]m<7[/tex]

Hope this helped!

Answer:

Hey there!

15>m+8

15-8>m

7>m

m<7

Hope this helps :)

Answer:

a=6, b=5.5

Step-by-step explanation:

By looking at the sides of the triangles it can easily be seen that some of the sides match up. Side b is similar to the side of 11 and same with side a and the side of 3. Since one side is 16 and the other side on the smaller triangle is 8, the bigger triangle is twice as large than the smaller one. So 3 x 2 = 6 and 11 / 2 = 5.5

Answer:

Excluded value = -7

Solution = [tex] x = \frac{5}{9} [/tex]

Step-by-step Explanation:

The excluded value is the value that will make the denominator 0.

Thus,

[tex] x + 7 = 0 [/tex]

Subtract 7 from both sides

[tex] x + 7- 7 = 0 - 7 [/tex]

[tex] x = -7 [/tex]

The excluded value is -7

Solution=>

[tex] \frac{2x}{x + 7} + \frac{3x + 1}{x + 7} = \frac{1}{2} [/tex]

[tex] \frac{2x + (3x + 1)}{x + 7} = \frac{1}{2} [/tex]

[tex] \frac{5x + 1}{x + 7} = \frac{1}{2} [/tex]

Cross multiply

[tex] 2(5x + 1) = 1(x + 7) [/tex]

[tex] 10x + 2 = x + 7 [/tex]

[tex] 10x - x = -2 + 7 [/tex]

[tex] 9x = 5 [/tex]

[tex] x = \frac{5}{9} [/tex]

Answer:

z > -9

Step-by-step explanation:

Combine like factors.

18 - 5z + 6z > 3 + 6

18 - 5z + 6z > 9

18 + z > 9

Solve for z.

18 + z > 9

(18 + z) - 18 > 9 - 18

z > -9

Answer:

5 units

Step-by-step explanation:

we can identify this as an isosceles triangle because both angles are equal (= 45 deg). Hence we can also conclude that the vertical leg of the triangle must also be "s"

We an also identify this as a right triangle because we have one angle that is 90 degrees. Hence we can use the Pythagorean formula to solve this (see attached for reference)

(5√2 )² = S² + S²

(5)²(√2 )² = 2S²

(25)(2) = 2S²

25 = S²

S = √25

S = 5 units

The length of leg s in the right triangle is 5 units. Therefore, the correct answer is option D.

In the given isosceles right triangle, hypotenuse is 5√2.

We know that, sinθ=Opposite/Hypotenuse

sin45°=s/5√2

1/√2 = s/5√2

1 = s/5

s = 5

Therefore, the correct answer is option D.

Learn more about the trigonometric ratios here:

brainly.com/question/25122825.

#SPJ2

Answer:

Step-by-step explanation:

I do not understand your question very well but I think that the state of the glass of the water would be liquid and solid at the same time since the water would not freeze 100% and would be with small pieces of solid and some parts liquid, in terms of temperature, I think that at 5 minutes it would be 5 ° C and at 10 it would be 3-4 ° C the longer it is in the freezer the less its temperature will be

(All of that is my point of view)

Average temperature 30 °

So :

30 ÷ 15 = 2 °

30 ÷ 10 = 3 °

30 ÷ 5 = 6 °

Answer:

ΔV = 0.36π   in³

Step-by-step explanation:

Given that:

The radius of a sphere = 3.0

If the measurement is correct within 0.01 inches

i.e the change in the radius Δr = 0.01

The objective is to use differentials to estimate the error in the volume of sphere.

We all know that the volume of a sphere

[tex]V = \dfrac{4}{3} \pi r^3[/tex]

The differential of V with respect to r is:

[tex]\dfrac{dV}{dr }= 4 \pi r^2[/tex]

dV = 4 πr² dr

which can be re-written as:

ΔV = 4 πr² Δr

ΔV = 4 × π × (3)² × 0.01

ΔV = 0.36π   in³

Answer:

8 and 9

Step-by-step explanation:

If x is the smaller integer, and x + 1 is the larger integer, then:

(x + 1)² + 3x = 105

x² + 2x + 1 + 3x = 105

x² + 5x − 104 = 0

(x + 13) (x − 8) = 0

x = -13 or 8

Since x is positive, x = 8.  So the two integers are 8 and 9.

Answer:

its b i got it right on edge

Step-by-step explanation:

Answer:

-5+5i

Step-by-step explanation:

(2-i)(-3+i)=-6+3i+2i-i²   (i²=-1)

-6+3i+2i-(-1)

-6+3i+2i+1=-5+5i

-5+5i

Answer:

Option One:

type : linear growth

a : 120

b : 130

Option 2:

type: linear growth

d : 121

e : 133

Step-by-step explanation:

its right on EDG 2020

Option One:

type: linear growth

a: 120

b: 130

Option 2:

type: linear growth

d: 121

e: 133

Linear growth occurs with the aid of including an equal amount in each unit of time. An exponential increase happens while a preliminary population will increase by the same percent or issue over the same time increments or generations.

Linear and exponential relationships vary within the way the y-values change whilst the x-values increase with the aid of a steady quantity: In linear dating, the y-values have identical variations. In an exponential relationship, the y-values have identical ratios.

Learn more about Linear growth here: brainly.com/question/4025726

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Answer:

c ≤ -9

Step-by-step explanation:

c / -3 ≥ 3

c ≤ -9

Remember, we flip the sign of the inequality by multiplying / dividing by a negative number.

Answer:

c ≤ -9

Step-by-step explanation:

c / -3 ≥ 3

c ≤ -9

Answer:

Infinite Solution!

Step-by-step explanation:

First, We simplify the right side.

Distribute -4, -4x-20=-4x-20

Now we add +4x to both sides, now the equation stands as -20=-20

We know when the solution is same #= same #. We have infinite solution!

Answer:

  Over 2 oz. Class A-II felony

Step-by-step explanation:

One would need to carefully weigh the material.*

  0.06 kg ≈ 2.12 oz

Note that .06 kg is 1 significant figure, so this rounds to 2 oz (1 significant figure). Given the precision of the reported weight, there is insufficient precision to say the amount is actually over 2 oz.

__

If you take the numbers at face value, the suspect is in possession of over 2 oz, so will be charged with a Class A-II felony.

_____

* 2.00 ounces translates to about 0.0567 kg, which rounds to 0.06 kg.

Answer:

We conclude that the percentage of blue candies is equal to 29​%.

Step-by-step explanation:

We are given that in a random selection of 100 colored​ candies, 28​% of them are blue. The candy company claims that the percentage of blue candies is equal to 29​%.

Let p = population percentage of blue candies

So, Null Hypothesis, [tex]H_0[/tex] : p = 29%     {means that the percentage of blue candies is equal to 29​%}

Alternate Hypothesis, [tex]H_A[/tex] : p [tex]\neq[/tex] 29%     {means that the percentage of blue candies is different from 29​%}

The test statistics that will be used here is One-sample z-test for proportions;

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

where, [tex]\hat p[/tex] = sample proportion of blue coloured candies = 28%

           n = sample of colored​ candies = 100

So, the test statistics =  [tex]\frac{0.28-0.29}{\sqrt{\frac{0.29(1-0.29)}{100} } }[/tex]

                                    =  -0.22

The value of the z-test statistics is -0.22.

Also, the P-value of the test statistics is given by;

               P-value = P(Z < -0.22) = 1 - P(Z [tex]\leq[/tex] 0.22)

                            = 1 - 0.5871 = 0.4129

Now, at a 0.10 level of significance, the z table gives a critical value of -1.645 and 1.645 for the two-tailed test.

Since the value of our test statistics lies within the range of critical values of z, so we insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that the percentage of blue candies is equal to 29​%.

Answer:

5 feet

Step-by-step explanation:

To find x, we can write:

x + 4 + x = 14

2x + 4 = 14

2x = 10

x = 5 feet

Answer:

1 3/8

Step-by-step explanation:

Well to find the average or the mean we need to add all the numbers,

3/8 + 2/4 + 5/8 + 7/8 + 1 1/8 + 1 5/8 + 1 7/8 + 4

= 11

Then we divide t by the number of numbers in the set.

11 ÷ 8 = 1 3/8

Thus,

the average in the set is 1 3/8.

Hope this helps :)

Answer:

C. and D.

Step-by-step explanation:

In the word problem, the two facts to solve the problem are:

A. The wait to ride the roller coaster was 40 minutes and

B. The line of people was 100 meters long

Because the length of waiters has an effect on the time. Thus, if the line is reduced to 50 meters, then the waiting time would reduce i.e 20 minutes.

Therefore, the facts that are not required to solve the word problem are:

C. The roller coaster is the fastest ride at the fair.

D. It was Tuesday.

Answer:

The answer is

Step-by-step explanation:

From the above question the prism in the picture is a cube since all it's sides are equal

So the formula for finding the volume of a cube is

V = l³

where l is the length of one side

From the question l = 12″

Volume of the prism = 12³

= 1728″

Hope this helps you

Answer:

  $0.50

Step-by-step explanation:

Let's remove common factors from the equations.

Subtracting the first equation from the second, we find the cost of an apple:

  (2x +y) -(x +y) = 1.75 -1.25

  x = 0.50

The cost of one apple is $0.50.

Answer:

The full production costs are:

ABC = $22,900,000

PQR = $1,700,000

Step-by-step explanation:

Traditional costing method is a costing method that allocates or applies overhead based on a particular metric determined by a company. It therefore add both direct cost of production and production overheads absorbed to obtain the full cost of production.

Since production overheads in this question is absorbed on demand sales basis, the full production costs for ABC and PQR can be computed as follows:

ANZ Corporation

Computation of Full Production Costs

Particulars                                      ABC                 PQR    

Sales demand                             30,000             15,000

Cost                                                   $                        $    

Direct cost:

Direct materials cost (w.1)        1,350,000           900,000

Direct labor cost (w.2)                900,000          600,000  

Total direct cost                     22,500,000        1,500,000

Indirect cost:

Production overhead (w.3)        400,000          200,000

Full production cost            22,900,000        1,700,000

Workings:

w.1: Computation of direct material cost

Direct material cost = Direct material cost per unit * Sales demand

Therefore;

ABC Direct material cost = $45 * 30,000 = $1,350,000

PQR Direct material cost = $60 * 15,000 = $900,000

w.2: Computation of direct labor cost

Direct labor cost = Direct labor cost per unit * Sales demand

Therefore;

ABC Direct material cost = $30 * 30,000 = $900,000

PQR Direct material cost = $40 * 15,000 = $600,000

w.3: Allocation of production overhead

Production overheads allocated to a model = Production overheads * (Model's Sales Demand / Total Sales demand)

Total Sales demand = 30,000 + 15,000 = 45,000

Therefore, we have:

Production overhead allocated to ABC = $600,000 * (30,000 / 45,000) = $400,000

Production overhead allocated to PQR = $600,000 * (15,000 / 45,000) = $200,000