MATHEMATICS HIGH SCHOOL

There are 200 students in the 7th grade class at Manchester Middle School. Of these students, 22% play football and 12% play baseball. Eight students play on both teams. What is the probability that a student plays either football or baseball?

Answers

Answer 1

Answer:

Answer: There is 30% student plays either football or baseball.

Step-by-step explanation:

Since we have given that

Total number of students = 200

Percentage of students who play football = 22%

Number of students who play football n(F) is given by

$0.22* 200\n\n=44$

Percentage of students who play baseball = 12%

Number of students who play baseball n(B) is given by

$0.12* 200\n\n=24$

Number of students who play on both teams n(F∩B) = 8

According to rules, it becomes,

$n(F\cap B)=n(F)+n(B)-n(F\cap B)\n\nn(F\cap B)=44+24-8=60$

Probability that a student plays either football or baseball is given by

$(60)/(200)\n\n=0.3\n\n=30\%$

Hence, there is 30% student plays either football or baseball.

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Evaluate S5 for 300 + 150 + 75 + … and select the correct answer below. 18.75 93.75 581.25 145.3125

Answers

It's a geometric sequence.

$300, 150, 75,... \n \n a_1=300 \n r=(a_2)/(a_1)=(150)/(300)=(1)/(2) \n \n S_n=(a_1 (1-r^n))/(1-r) \n \Downarrow \n S_5=(300(1-((1)/(2))^5))/(1-(1)/(2))=(300(1-(1)/(32)))/((1)/(2))=(300 * (31)/(32))/((1)/(2))=(75 * (31)/(8))/((1)/(2))=((2325)/(8))/((1)/(2))=(2325)/(8) * 2= \n=(2325)/(4)=581 (1)/(4)=581.25$

The answer is 581.25.

we have that

$300 + 150 + 75 +...$

Let

$a1=300\n a2=150\n a3=75$

we know that

$(a2)/(a1) =(150)/(300) \n\n (a2)/(a1)=0.5 \n \n a2=a1*0.50$

$(a3)/(a2) =(75)/(150) \n\n (a3)/(a2)=0.5 \n \n a3=a2*0.50$

$a(n+1)=an*0.50$

Is a geometric sequence

Find the value of $a4$

$a(4)=a3*0.50$

$a(4)=75*0.50$

$a(4)=37.5$

Find the value of $a5$

$a(5)=a4*0.50$

$a(5)=37.5*0.50$

$a(5)=18.75$

Find $S5$

$S5=a1+a2+a3+a4+a5\n S5=300+150+75+37.5+18.75\n S5=581.25$

therefore

the answer is

$581.25$

Alternative Method

Applying the formula

$S_n=(a_1 (1-r^n))/(1-r) \n\na_1=300 \n r=(1)/(2)\n\n S_5=(300(1-((1)/(2))^5))/(1-(1)/(2))\n\n=(300(1-(1)/(32)))/((1)/(2))\n\n=(300 * (31)/(32))/((1)/(2))\n\n=(75 * (31)/(8))/((1)/(2))\n\n=((2325)/(8))/((1)/(2))\n\n=(2325)/(8) * 2\n\n=(2325)/(4)\n\n=581 (1)/(4)\n\n=581.25$

therefore

the answer is

$581.25$

Which products are negative?Choose all answers that are correct.

A.

-1 1/4 · (-2 3/4) · (-3)

B.

1/2 · (-1/4) · (1/8)

C.

8 • (–1.1) • 5

D.

–3.1 • (–4.2) • (–6) • (–1.5)

Answers

A,B,and C because in when multiplying or dividing, + and - will be negative and if they are + and + or, - and - then the answer will be positive.

all of them accept for d

What is 0.121212 expressed as the quotient of two integers in simplest form?

Answers

In simplest form it would be 0.12 repeating. To do the repeating sign you would put a line over 12.

The state university reported 1183 cases of flu in their student body for the month of January. If this was a 350% increase above the number of flu cases in the month of December, how many students had flu in December?

Answers

Let us assume the number of students having flu in December = x
Number of students having flu in the month of January = 1183
Percentage increase in the number of people having flu from the month of December to the month of January = 350%
Then we can write the equation as
350x/100 = 1183
350x = 1183 * 100
350x = 118300
x = 118300/350
= 11830/35
= 338
So the number of students that were affected by flu in the month of December was 338. This is the easiest way to get to the required answer.

Answer:

338

Step-by-step explanation:

1183/350%

= 338 people

type it in your calculator just like my equation and you'll get the answer.

△ABC is mapped to △A′B′C′ using the rule (x, y)→(−x, −y) followed by (x, y)→(x, −y) .Which statement correctly describes the relationship between △ABC and △A′B′C′ ?

A. △ABC is congruent to △A′B′C′ because the rules represent a reflection followed by a rotation, which is a sequence of rigid motions.

B. △ABC is congruent to △A′B′C′ because the rules represent a rotation followed by a reflection, which is a sequence of rigid motions.

C. △ABC is not congruent to △A′B′C′ because the rules do not represent a sequence of rigid motions.

D. △ABC is congruent to △A′B′C′ because the rules represent a reflection followed by a reflection, which is a sequence of rigid motions.

Answers

Transformation involves changing the position of a shape.

The correct statement is: (b) △ABC is congruent to △A′B′C′ because the rules represent a rotation followed by a reflection, which is a sequence of rigid motions.

The transformation rule is given as:

$\mathbf{(x,y) \to (-x,-y)}$ , then:

$\mathbf{(x,y) \to (x,-y)}$

The first transformation $\mathbf{(x,y) \to (-x,-y)}$ is 180 degrees rotation across the origin
The second transformation $\mathbf{(x,y) \to (x,-y)}$ is a reflection across the x-axis

Rotation and reflection are both rigid transformation.

Hence, the correct option is (b):

Read more about rotation and reflection at:

brainly.com/question/15577335

Answer:

B. △ABC is congruent to △A′B′C′ because the rules represent a rotation followed by a reflection, which is a sequence of rigid motions.

Step-by-step explanation:

I just took the test, good luck! Have a wonderful day! :)

Given Q = 3a + 5ac solve for a