The ratio of boys to girls in Jamal's class is 3:2. If four more girls join the class, there will be the same number of boys and girls. What is the number of boys in the class?

Answer:

x = 4

Step-by-step explanation:

x - 6 = -2

Add 6 to each side

x-6+6 = -2+6

x = 4

Answer:

[tex]x=4[/tex]

Step-by-step explanation:

[tex]x - 6 = -2[/tex]

Add 6 on both sides of the equation. The [tex]x[/tex] variable should be isolated on one side.

[tex]x - 6 +6= -2+6[/tex]

[tex]x=4[/tex]

The value of [tex]x[/tex] is 4.

Answer:

( P -2w) /2 = l

Step-by-step explanation:

P= 2W + 2l

Subtract 2W from each side

P= 2W -2W + 2l

P -2W = 2l

Divide by 2

( P -2w) /2 = l

Answer:

A. [tex]\frac{P - 2w}{2} = l[/tex]

Step-by-step explanation:

Well in,

P = 2w + 2l

to solve for l we need to single it out.

P = 2w + 2l

-2w

P - 2w = 2l

divide everything by 2

[tex]\frac{P - 2w}{2} = l[/tex]

Thus,

the answer is A.

Hope this helps :)

Answer:

= A

explanation :

A total of 32/3 strips can be derived from the ribbon.

In arithmetic, a quotient is a quantity produced by the division of two numbers. The quotient has widespread use throughout mathematics, and is commonly referred to as the integer part of a division, or as a fraction or a ratio.

Here, we have,

to determine the number of strips:

From the question, we have the following parameters

Length of a roll of ribbon = 4 meters

Also, from the question;

We have

Length of a piece of ribbon = 5/12 meter

The number of strips of ribbon is the quotient of the Length of a roll of ribbon and the Length of a piece of ribbon

This is represented as

Number of strips = Length of a roll of ribbon/Length of a piece of ribbon

So, we have

Number of strips = (4 )/(5/12)

Evaluate the quotient

Number of strips = 32/3

Hence, the number of strips is 32/3

Read more about quotients at

brainly.com/question/629998

#SPJ2

complete question:

How many strips of a ribbon can be cut from a roll of ribbon that is 4 4/9 meters long if each piece is 5/12 meters long

Answer:

[tex]\large \boxed{\ \ \dfrac{63}{5} \ \ }[/tex]

Step-by-step explanation:

Hello,

"Find the sum of the following infinite geometric series"

infinite

   We will have to find the limit of something when n tends to [tex]+\infty[/tex]

geometric series

   This is a good clue, meaning that each term of the series follows a geometric sequence. Let's check that.

The sum is something like

           [tex]\displaystyle \sum_{k=0}^{+\infty} a_k[/tex]

First of all, we need to find an expression for [tex]a_k[/tex]

First term is

   [tex]a_0=7[/tex]

Second term is

    [tex]a_1=\dfrac{4}{9}\cdot a_0=7*\boxed{\dfrac{4}{9}}=\dfrac{7*4}{9}=\dfrac{28}{9}[/tex]

Then

   [tex]a_2=\dfrac{4}{9}\cdot a_1=\dfrac{28}{9}*\boxed{\dfrac{4}{9}}=\dfrac{28*4}{9*9}=\dfrac{112}{81}[/tex]

and...

   [tex]a_3=\dfrac{4}{9}\cdot a_2=\dfrac{112}{81}*\boxed{\dfrac{4}{9}}=\dfrac{112*4}{9*81}=\dfrac{448}{729}[/tex]

Ok we are good, we can express any term for k integer

   [tex]a_k=a_0\cdot (\dfrac{4}{9})^k[/tex]

So, for n positive integer

[tex]\displaystyle \sum_{k=0}^{n} a_k=\displaystyle \sum_{k=0}^{n} 7\cdot (\dfrac{4}{9})^k=7\cdot \dfrac{1-(\dfrac{4}{9})^{n+1}}{1-\dfrac{4}{9}}=\dfrac{7*9*[1-(\dfrac{4}{9})^{n+1}]}{9-4}=\dfrac{63}{5}\cdot [1-(\dfrac{4}{9})^{n+1}}][/tex]

And the limit of that expression when n tends to [tex]+\infty[/tex] is

   [tex]\large \boxed{\ \ \dfrac{63}{5} \ \ }[/tex]

as

   [tex]\dfrac{4}{9}<1[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

Mars

Step-by-step explanation:

America

Answer:

70.59 feet

Step-by-step explanation:

There are a total of 14 parts when the wire is divided into a ratio of 1 to 13.

1. Divide 76 by 14

76 ÷ 14 = 5.43

2. Multiply the longer length of 13 parts

5.43 · 13 = 70.59

The longer length of the wire 70.59 feet

There are a total of 14 parts when the wire is divided into a ratio of 1 to 13.

1. Divide 76 by 14

76 ÷ 14 = 5.43

2. Multiply the longer length of 13 parts

5.43 · 13 = 70.59

In algebra, a decimal number can be defined as a range whose entire number part and the fractional element are separated by means of a decimal point. The dot in a decimal range is referred to as a decimal point. The digits following the decimal factor show a price smaller than one.

Learn more about Algebra here https://brainly.com/question/723406

#SPJ2

Answer:

0.992774 ≅ .993

Step-by-step explanation:

a²+b²=c²

a=x

b=3

c=3.16

x²+3²=3.16²

x²+9=9.9856

x²=.9856

x=0.992774

x≅0.993

Answer:

The overall shape of the data

Step-by-step explanation:

For us to know what shape a data is, it must fulfil 4 conditions

From the question, Ralph observed that the classmates time are symmetrical along the x-axis.

Therefore he is observing the shape of the data since one of the conditions have been fulfilled.

Thank you!

Answer:

a) How long will it take to repay the loan?

20 years

b) What amount of interest does the purchase pay?

$134,896

Step-by-step explanation:

a) How long will it take to repay the loan?

In the above question, they are asking you for the Loan duration

The Formula for Loan duration(T) =

ln (- m/(r÷n) × C - m)/In (1 + r/n)

Where:

m = monthly payments = $1395.40

C = Amount of mortgage =$200,000

r = Interest rate = 5.7% = 0.57

n = compounded quarterly = 4

T = ln (- 1395.40/(0.57÷4) × 200,000 - 1395.40)/In (1 + 0.57/4)

T = 20 years.

Therefore, it will take 20 years to repay the Loan.

b) What amount of interest does the purchase pay?

The total number of payments =

Loan duration × Number of months

Number of months = 12 months( because it is monthly payment)

Loan duration = 20 years

Total number of payments = 240 payments.

In the question, we are given the amount paid monthly payment as

$1,395.40

Total amount paid = Monthly payments × Total number of payments

= $1,395.40 × 240

= $334,896

The amount of Interest the purchase pay = $334,896 - $200,000

= $134,896

Answer:

[tex]\huge\boxed{(6;\ -31)}[/tex]

Step-by-step explanation:

Let: [tex]f(x)=ax^2+bx+c[/tex].

The coordinates of the vertex:

[tex](h;\ k)\to h=\dfrac{-b}{2a};\ k=f(h)=\dfrac{-(b^2-4ac)}{4a}[/tex]

We have

[tex]f(x)=x^2-12x+5\to a=1;\ b=-12;\ c=5[/tex]

Substitute:

[tex]h=\dfrac{-(-12)}{2(1)}=\dfrac{12}{2}=6\\\\k=f(6)=6^2-12(6)+5=36-72+5=-31[/tex]

The vertex form of an equation of a quadratic function:

[tex]f(x)=a(x-h)^2+k[/tex]

We have:

[tex]f(x)=x^2-12x+5\to a=1[/tex]

Complete to the square [tex](a\pm b)^2=a^2\pm2ab+b^2[/tex]

[tex]x^2-12x+5=x^2-\underbrace{2(x)(6)}_{12x}+5=\underbrace{x^2-2(x)(6)+6^2}_{a^2-2ab+b^2}-6^2+5\\\\=\underbrace{(x-6)^2}_{(a-b)^2}-36+5=(x-6)^2-31\\\\h=6;\ k=-31\to(6;\ -31)[/tex]

Answer:

He spends $1.20 Which means he has $4.80 remaining.

Step-by-step explanation:

1/5 of 6 is 6/1 multiplied by 1/5 and that is 6/5 or 1 1/5

1/5 of a dollar is 20 cents. he has $1.20

6-1.20=4.80.

Answer:

[tex]4.80 => Answer[/tex]

Step-by-step explanation:

Use the information given.

1/5 of 6 is equal to 6/5

6/5 = 1.2

Now subtract.

[tex]6-1.2= 4.8[/tex]

So the answer is 4.80 or 4.8

Hope this helps! :)

By: ❤️BrainlyMagic❤️

Brainliest would be appreciated!

Answer:

0.3110

Step-by-step explanation:

This is a binomial distribution with probability of success (being a chemistry major) p = 0.40.

The general formula for a binomial distribution is:

[tex]P(x=k)=\frac{n!}{(n-k)!k!}*p^k*(1-p)^{n-k}[/tex]

Where n is the sample size and k is the desired number of successes.

The probability of k=2 in a sample of n =6 is:

[tex]P(x=2)=\frac{6!}{(6-2)!2!}*0.4^2*(1-0.4)^{6-2} \\P(x=2)=\frac{6!}{(6-2)!2!}*0.4^2*(1-0.4)^{6-2}\\P(x=2)=3*5*0.4^2*0.6^4\\P(x=2)=0.3110[/tex]

The probability is 0.3110

Answer:

upper box is 0

middle box is 3 and

the downer box is 6

Step-by-step explanation:

Have a nice day

Answer: $68.4

Step-by-step explanation:

Given: Annual Premium = $110

Average insurance payout = $1600

Likelihood of having an accident= 2.6% = 0.026 [we divide perecnt by 100 to convert it into decimal]

Then, Expected value = (Annual Premium) - (Likelihood of having an accident) x (Average insurance payout )

= $110  - (0.026) x ($1600)

= $(110-41.6)

= $68.4

Hence, the company's expected value of this insurance policy : $68.4

Answer:

[tex]d \approx 5.8[/tex]

Step-by-step explanation:

Just use the distance formula.

[tex]d=\sqrt{(x_2-x_{1})^2+(y_2-y_{1})^2}[/tex]

[tex]d=\sqrt{(3-0)^2+(5-0)^2}}[/tex]

[tex]d=\sqrt{(3)^2+(5)^2}}[/tex]

[tex]d=\sqrt{9+25}[/tex]

[tex]d=\sqrt{34[/tex]

[tex]d \approx 5.8[/tex]

Answer:

Below

Step-by-step explanation:

Using the proprtionality relation:

● 8/10 =5/x

● (4*2)/(5*2) = 5/x

Simplify using 2

● 4/5 = 5/x

Multiply both sides by 5

● (4/5)*5 = (5/x)*5

● 4 = 25/x

Switch x and 4

● x= 25/4

■■■■■■■■■■■■■■■■■■■■■■■■■

Again use the proportionality relation but this time with y.

● 8/10 =7/y

8/10 = 4/5

● 4/5 = 7/y

Multiply both sides by 5

● (4/5)*5 =(7/y)*5

● 4 = 35/y

Switch 4 and y

● y = 35/4

Answer:

c) 52.8 m

Step-by-step explanation:

The radius of a conical tent, r = 5.6 m

The slant height = 12 m.

The area of the canvas required to make the tent is equal to the lateral area of the cone.

[tex]\text{Lateral Area of a Cone}= \pi r l\\=\pi \times 5.6 \times 12\\=67.2\pi$ m^2[/tex]

Since the width of the canvas = 4 m

Let the length = l

Area of the canvas = 4l

[tex]4l=67.2\pi$ m^2\\l=67.2\pi \div 4\\l=52.8 m$ (correct to 1 decimal place)[/tex]

The length of the canvas required  to make the tent is 52.8m.

Answer:

18.9 units of fencing

Step-by-step explanation:

First find the perimeter

P = 2(l+w)

P = 2( 2.5+1.28)

P = 2( 3.78)

P =7.56m

We need 2.5 units of fencing for each meter

Multiply by 2.5

7.56*2.5

18.9 units of fencing

Answer:

Julio needs to purchase 18.9 units of fencing.

Step-by-step explanation:

I meter of the perimeter accounts for 2.5 units of fencing. Respectively 2 meters account for 2 times as much, and 3 meters account for 3 times as much of 2.5 units. Therefore, if we determine the perimeter of this rectangular garden, then we can determine the units of fencing by multiplying by 2.5.

As you can see this is a 2.5 by 1.28 garden. The perimeter would be two times the supposed length, added to two times the width.

2.5 x 2 + 1.28 x 2 = 5 + 2.56 = 7.56 - this is the perimeter. The units of fencing should thus be 7.56 x 2.5 = 18.9 units, or option d.

Answer: (16.47, 17.49)

Step-by-step explanation:

Formula for confidence interval for the true mean if population stanmdard deviation is unknown:

[tex]\overline{x}\pm t_{\alpha/2}\dfrac{s}{\sqrt{n}}[/tex]

, where [tex]\overline{x}[/tex] = sample mean

n= sample size

s= sample standard deviation

[tex]t_{\alpha/2}[/tex] = Two tailed critical value.

We assume that the level of polyunsaturated fatty acid is normally distributed.

Given,

n= 6

degree of freedom = n-1 =5

[tex]\overline{x}[/tex] = 16.98

s= 0.31

significance level[tex](\alpha)[/tex] =1-0.99=0.01

Two tailed t- value for degree of freedom of 5 and significance level of 0.01 = [tex]t_{\alpha/2}=4.0317[/tex]    [by student's t-table]

Now , the 99% confidence interval for the true mean of fatty acid level is:

[tex]16.98\pm 4.0317(\dfrac{0.31}{\sqrt{6}})\\\\=16.98\pm 4.0317(0.126557)\\\\=16.98\pm 0.51024\\\\=(16.98-0.51023,\ 16.98+0.51023)\\\\=(16.46977,\ 17.49023)\approx (16.47,\ 17.49)[/tex]

Hence, a 99% confidence interval for the true mean of fatty acid level is: (16.47, 17.49)

Answer:

[tex]\large \boxed{\sf \ \ (-5,0) \ and \ (4,0) \ \ }[/tex]

Step-by-step explanation:

Hello,

We need to find the zeroes of

[tex]-0.25x^2-0.25x+5=0\\\\\text{*** multiply by -4 ***} \\ \\x^2+x-20=0\\\\\text{*** the sum of the zeroes is -1 and the product -20=-5x4 ***}\\\\x^2+5x-4x-20=x(x+5)-4(x+5)=(x+5)(x-4)=0\\\\x=4 \ or \ x=-5[/tex]

and then g(4)=0 and g(-5)=0

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:(-5,0) (4,0)

I took the test hope it helps you (:

Hey there! I'm happy to help!

First, let's find the area of the two circles that make up the top and bottom of the cylinder. To find the area of a circle, you square the radius multiply it by pi (we will use 3.14)

15.8²=249.64

249.64×3.14=783.8696

Since there are two of these circles we multiply this by 2.

783.8696×2=1567.7392

Now, for the rectangle. To make a cylinder, you take a rectangle and wrap it around the top and bottom circles. One side of this rectangle is the height of the cylinder, and the other is the circumference of the circle (one side wraps all the way around the circle, which is the circumference).

The circumference is the diameter multiplied by 3.14 (pi). The diameter is twice the radius.

15.8×2=31.6

31.6×3.14=99.224

We multiply this by the height.

99.224×4.4=436.5856

Now, we add the areas of the circles and the rectangle.

1567.7392+436.5856=2004.3 (rounded to nearest tenth)

This is closest to D. 2005.3 ft². It is probably a bit off because I used 3.14 instead of actual pi.

Have a wonderful day! :D

Answer:

The doctors can expect the middle 68 % of their knee replacement surgery patients to be between 49.75 years and 66.25 years.

Step-by-step explanation:

68 % of the knee replacement surgery patients implies that the ages lies within x = x₀ ± σ where x₀ = mean age = 58 years and σ = standard deviation = 8.25 years

So, the ages lies between x₀ + σ and x₀ - σ

So, the ages lie between 58 - 8.25 = 49.75 years

and 58 + 8.25 = 66.25 years

So the doctors can expect the middle 68 % of their knee replacement surgery patients to be between 49.75 years and 66.25 years.

Answer: C

Step-by-step explanation:

For system of equations, the solution is the point or points where the equations intersect. The point they meet signifies that they are the same at the x and y point.

Looking at the graph, we see 2 intersection points. They are (0,-8) and (4,8). Therefore, C is the correct answer.

Answer:

Yes, because the four points in the upper right corner from the same pattern as the four points in the lower left corner.

Step-by-step explanation:

The correlation coefficient for the points in the lower left corner equals zero.

The four points in the upper right corner have the same correlation coefficient because the four points in the upper right corner from the same pattern as the four points in the lower left corner.

Answer:

50 mph

Step-by-step explanation:

The total distance is 350 miles.

The total time is 3 hr + (240 mi / 60 mph) = 7 hr.

The average speed is 350 mi / 7 hr = 50 mph.

Answer:

[tex]y = kx[/tex]

Step-by-step explanation:

y is directly proportional to x.

[tex]y \propto x[/tex]

[tex]y = kx[/tex]

Where k is as the constant of proportionality.

Answer:

y = kx

Step-by-step explanation:

Y is directly proportional to x which means that

=> y ∝ x

=> y = kx

Where k is the constant of proportionality.

Answer:

Step-by-step explanation:

7/5 + 3/4 x 2/5 - 3/2

 7/5 + 3/10 - 3/2

    17/10 - 3/2

         1/5

Step-by-step explanation:

Here, the given polynomial are,

=7/5+3/4×2/5-3/2

multiplying 3/4 and 2/5

= 7/5+6/20-3/2

taking LCM and adding them.

=(7×4+6×1-3×10)/20

by simplifying it we get, the answer is 1/5.

Hope it helps..

Answer:

8

Step-by-step explanation:

you would just divide 32 by 4

4x = 32

x = 32/4

x=8

Answer:

[tex]\large\boxed{\sf \ \ \ x=8 \ \ \ }[/tex]

Step-by-step explanation:

Hello

4x=32 we can divide both parts by 4 so

   [tex]\dfrac{4x}{4}=\dfrac{32}{4}\\\\<=> x = 8[/tex]

Hope this helps