Can someone please help me with this math problem.

Can Someone Please Help Me With This Math Problem.

Answers

Answer 1

Answer:

8 + 30 ÷ 2 + 4  = 27

8 + 30 ÷ (2 + 4 ) = 13

(8 + 30) ÷ 2 + 4  = 23

Step-by-step explanation:


Related Questions

Type your answer
(1 out of 4)
What is the value of the function when x = 3 in the
piecewise function
g(x) =
3x when x > 1
- 2x when x < 1

Answers

Answer:

9

Step-by-step explanation:

The endpoints of PC are P(4, 1) and Q(4,8). Find the midpoint of PQ
A. (4, 4.5)
B. (0, -3.5)
C. (4.5, 4)
D. (6, 3.5)

Answers

Answer:

A. (4,4.5)

Step-by-step explanation:

Midpoint={x1+x2/2,y1+y2/2}

M={4+4/2,1+8/2}

M={8/2,9/2}

M={4,4.5}

What is the gradient of the graph shown? Give your answer in simplest form

Answers

Answer:

gradient = 2

line: y = 2x - 4

Step-by-step explanation:

Find the slope from the slope intercept formula

y = mx + b

b is the y intercept

b = -4 and the point is (0,-4)

So far the equation looks like this.

y = mx - 4

Use the other intercept (x intercept) to find m

x = 2

y = 0

0 = m*2 - 4                Add 4 to both sides

4 = 2m                      Divide by 2

4/2 = m

m = 2

So the gradient or slope is 2

The graph shows a line of best fit for data collected on the average temperature, in degrees Fahrenheit, during a month and the
number of inches of rainfall during that month.
у
90
801
70
Average Temp
20
10
Inches of Rain
The equation for the line of best fit is y=-3.32x +97.05.
Based on the line of best fit, what would be the prediction for the average temperature during a month with 13.25 inches of rainfall?

Answers

Answer:

53.06°F

Step-by-step explanation:

Given the equation of best fit :

y=-3.32x +97.05.

The average temperature for a month with 13.25 inches of Rainfall

Amount of Rainfall = x

Average temperature = y

To make our prediction ; put x = 13.25 in the equation and solve for y ;

y = -3.32x +97.05

Put x = 13.25

y = -3.32(13.25) +97.05

y = - 43.99 + 97.05

y = 53.06°F

ABC ∆ where Angle A =90° , AB = 12 m, AC = 9 m . Find BC ?

( Show all your workings )
best answer will marked as brainalist
dont put fake ones

Answers

Answer:

15m

Step-by-step explanation:

Use Pythagoras

Folow the steps in the image

Answer:

:] brainlist me friends

Your sample is normally distributed with a mean age of 36. The standard deviation in this sample is 4 years. You would expect:

Answers

Kindly find complete question attached below

Answer:

Kindly check explanation

Step-by-step explanation:

Given a normal distribution with ;

Mean = 36

Standard deviation = 4

According to the empirical rule :

68% of the distribution is within 1 standard deviation of the mean ;

That is ; mean ± 1(standard deviation)

68% of subjects :

36 ± 1(4) :

36 - 4 or 36 + 4

Between 32 and 40

2.)

95% of the distribution is within 2 standard deviations of the mean ;

That is ; mean ± 2(standard deviation)

95% of subjects :

36 ± 2(4) :

36 - 8 or 36 + 8

Between 28 and 44

3.)

99% is about 3 standard deviations of the mean :

That is ; mean ± 3(standard deviation)

99% of subjects :

36 ± 3(4) :

36 - 12 or 36 + 12

Between 24 and 48

If A = {x, y, z} then the number of non-empty subsets of A is ________.

a) 8 b) 5 c) 6 d) 7​

Answers

Answer:

(d) 7

Step-by-step explanation:

The total number of subsets that can be derived from a set with n elements is given by;

2ⁿ

Out of these subsets, there is one empty set. Therefore, the total number of non-empty subsets is given by;

2ⁿ - 1

Given:

A = {x, y, z}

Set A has 3 elements. This means that n = 3

Therefore, the total number of subsets that can be derived from set A is

2ⁿ = 2³ = 8

One of these 8 subsets is an empty set, therefore, the total number of non-empty subsets of A is;

2ⁿ - 1 = 2³ - 1

8 - 1 = 7

This can be checked by writing all the possible subsets of A as follows;

{x}

{y}

{z}

{x, y}

{y, z}

{x, z}

{x, y, z}

Removing the empty set ∅, the non-empty subsets of A are;

{x}

{y}

{z}

{x, y}

{y, z}

{x, z}

{x, y, z}

The following multiple regression printout can be used to predict a person's height (in inches) given his or her shoe size and gender, where gender = 1 for males and 0 for females.

Regression Analysis: Height Versus Shoe Size, Gender

Coefficients
Term Coef SE Coef T-value P-value
Constant 55.24 1.05 52.61 0.000
Shoe Size 1.164 0.13 0.000
Gender 2.574 0.489 5.26 0.000

Required:
a. Find the value of the test statistic for shoe size.
b. Is the regression coefficient of shoe size statistically significant?
c. Does the variable shoe size belong in the model?
d. Interpret the regression coefficient of Gender.

Answers

Answer:

a. 8.95

b. it is

c. yes it belongs

d. males are 2.574 taller than females on average.

Step-by-step explanation:

GIven the regression outpuit that we have in this question, the value of the t test statistics for the shoe size can be solved as

a. test statistic = 1.164/0.13

t test = 8.95

b. the regression coefficient of shoe size is 1.164, this is statistically significant

c. Yes the variable shoe size does belong to the model.

d. The regression coefficient of gender shows that on the average, while holding other variables constant, males are 2.574 inches taller than the their female counterparts.

one number is seven less than the second number. five times the first is 9 more than 6 times the second. find the numbers

Answers

Step-by-step explanation:

2nd number = x

1st number = x - 7

5 (x - 7) = 6x + 9

5x - 35 = 6x + 9

- x = 44

x = - 44

1st number = -51

2nd number = -44

Proof: 5 (-51) = 6(-44) + 9

-255 = -264 + 9

-255 = -255

hope it helps.

Also, I think that Brainly is an awesome app, but there's an app which is doing great work for me in maths, named Gauthmath. I will suggest it. Video concepts and answers from real tutors.


The circumference of a circle is 14 inches. Find the circle's radius and diameter.


Please help :)

Answers

circumference = 2(pi)(r)
14 = 2(pi)(r)
14/2pi = r
7pi = radius
diameter = 2r
diameter = 14pi

The system of equations y = negative one-fifth x minus 6 and y = –2x + 3 is shown on the graph below.


On a coordinate plane, 2 lines intersect at (5, negative 7).

According to the graph, what is the solution to this system of equations?
(5, –7)
(–7, 5)
(5, 7)
(7, 5)

Answers

Answer:

According to graph, solution is (5, –7)

Answer:

A) (5, –7)

Step-by-step explanation:

I got 100%, please brainlist

36x^2=y^2
Does the equation define y as a function of x ?

Answers

Answer:

ya the equation divides y as a function of x

The thickness X of aluminum sheets is distributed according to the probability density function f(x) = 450 (x2 - x) if 6 < x < 12 0 otherwise 5-1 Derive the cumulative distribution function F(x) for 6 < x < 12. The answer is a function of x and is NOT 1! Show the antiderivative in your solution. 5-2 What is E(X) = {the mean of all sheet thicknesses)? Show the antiderivative in your solution.

Answers

Solution :

Given :

[tex]f(x) = \left\{\begin{matrix}\frac{1}{450}(x^2-x) & \text{if } 6 < x < 12 \\ 0 & \text{otherwise}\end{matrix}\right.[/tex]

1. Cumulative distribution function

[tex]$P(X \leq x) = \int_{- \infty}^x f(x) \ dx$[/tex]

              [tex]$=\int_{- \infty}^6 f(x) dx + \int_{6}^x f(x) dx $[/tex]

             [tex]$=0+\int_6^x \frac{1}{450}(x^2-x) \ dx$[/tex]

             [tex]$=\frac{1}{450} \int_6^x (x^2-x) \ dx$[/tex]

             [tex]$=\frac{1}{450}\left[\frac{x^3}{3}-\frac{x^2}{2}\right]_6^x$[/tex]

             [tex]$=\frac{1}{450}\left[ \left( \frac{x^3}{3} - \frac{x^2}{2}\left) - \left( \frac{6^3}{3} - \frac{6^2}{2} \right) \right] $[/tex]

            [tex]$=\frac{1}{450}\left[\frac{x^3}{3} - \frac{x^2}{2} - 54 \right]$[/tex]

2.  Mean [tex]$E(x) = \int_{- \infty}^{\infty} \ x \ f(x) \ dx$[/tex]

                       [tex]$=\int_{6}^{12}x . \left( \frac{1}{450} \ (x^2-x)\right)\ dx$[/tex]

                     [tex]$=\frac{1}{450} \int_6^{12} \ (x^3 - x^2) \ dx$[/tex]

                     [tex]$=\frac{1}{450} \left[\frac{x^4}{4} - \frac{x^3}{3} \right]_6^{12} \ dx$[/tex]

                     [tex]$=\frac{1}{450} \left[ \left(\frac{(12)^4}{4} - \frac{(12)^3}{3} \right) - \left(\frac{(6)^4}{4} - \frac{(6)^3}{3} \right) $[/tex]

                     [tex]$=\frac{1}{450} [4608 - 252]$[/tex]

                    = 17.2857

Question 4*
4. Sam's goal is to exercise for 400 minutes each
week. This week, he reached 128% of his goal.
How many minutes did he exercise?

Answers

Answer: Get at least 150 minutes of moderate aerobic activity or 75 minutes of vigorous aerobic activity a week, or a combination of moderate and vigorous activity. The guidelines suggest that you spread out this exercise during the course of a week. Greater amounts of exercise will provide even greater health benefit.

Step-by-step explanation:

If Sam reached 128% of his goal to exercise each week, he would have exercised for 512 minutes.

How many minutes did Sam exercise this week?

Given the parameters:

Sam's goal is to exercise for 400 minutes each week.

This week, he reached 128% of his goal.

The number of minutes =?

To determine how many minutes Sam exercised this week, we simply calculate 128% of his goal.

Number of minutes = 128% × Sam's goal of exercise

Number of minutes = 128% × 400 minutes

Note that: 128% = 128/100

Number of minutes = 128/100 × 400 minutes

Number of minutes = 128 × 4 minutes

Number of minutes = 512 minutes

Therefore, Sam exercised for 512 minutes this week.

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A researcher believes that 9% of males smoke cigarettes. If the researcher is correct, what is the probability that the proportion of smokers in a sample of 664 males would differ from the population proportion by greater than 3%

Answers

Answer:

0.0070 = 0.70% probability that the proportion of smokers in a sample of 664 males would differ from the population proportion by greater than 3%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

A researcher believes that 9% of males smoke cigarettes.

This means that [tex]p = 0.09[/tex]

Sample of 664

This means that [tex]n = 664[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.09[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.09*0.91}{664}} = 0.011[/tex]

What is the probability that the proportion of smokers in a sample of 664 males would differ from the population proportion by greater than 3%?

Proportion below 9 - 3 = 6% or above 9 + 3 = 12%. Since the normal distribution is symmetric, these probabilities are equal, so we find one of them and multiply by 2.

Probability the proportion is below 6%

P-value of Z when X = 0.06. So

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

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.06 - 0.09}{0.011}[/tex]

[tex]Z = -2.7[/tex]

[tex]Z = -2.7[/tex] has a p-value of 0.0035

2*0.0035 = 0.0070

0.0070 = 0.70% probability that the proportion of smokers in a sample of 664 males would differ from the population proportion by greater than 3%

The following is a scatterplot of the percent of children under age 18 who are not in school or in the labor force vs. the number of juvenile violent crime arrests for each of the 50 states. The least-squares regression line has been drawn in on the plot. We would like to predict what the number of juvenile violent crime arrests would be in a state if 25% of children are not in school or in the labor force. This is called

Answers

Answer:

Extrapolation

Step-by-step explanation:

From the linear regression plot created in the picture given, se could see that Tha percentage of student covered by the the plot is just above 16%. Therefore, to predict the percentage of the number of juvenile violent crime arrests would be in a state if 25% of children are not in school or in the labor force will require us to assume that the current trend continues into the future. Hence, we use the information and indications we have at present to make prediction into the future based on the assumption that we the current trend will remain relevant and applicable. This assumption into the future based on current trend is called EXTRAPOLATION.

Help please!!
The triangles are similar by:
the SAS similarity theorem.
the ASA similarity theorem.
the AA similarity postulate.
None of the choices are correct.
the SSS similarity theorem.

Answers

I believe the SSS theorem as they both share/have side measurements (and no defined angles)

what is the y-intercept of the line shown below?

A:3/4
B:2
C:3
D:4​

Answers

The y-intercept is the y value where the blue line crosses the Y axis which is the vertical black line.

The line crosses at the number 4, so the y-intercept is 4

Answer: D. 4

Can anyone help me please? I've been trying for so long, but I can't figure out the answer to this problem. Picture attached. Thank you so much.

Answers

Answer:

C

Step-by-step explanation:

Start by simplifying what you can in each radicalfor example, the

∛(xy⁵)= y∛(xy²)

and

∛(x⁷y¹⁷)=x²y⁵∛(xy²)

So know our equation looks like

y∛(xy²)*x²y⁵∛(xy²)

Now because what's inside the radical is the same we can combine them

y⁶x²∛(xy²)²

distribute the square

so

∛(xy²)²=  ∛(x²y⁴)= y∛(x²y)

and finally,

y⁶x²*y∛(x²y)= y⁷x²∛(x²y)

this is equal to option C

What is the solution to the following inequality X/-2 > 5

Answers

Answer:

x < -10

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right  

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Step-by-step explanation:

Step 1: Define

Identify

x/-2 > 5

Step 2: Solve for x

[Multiplication Property of Equality] Multiply -2 on both sides:                     x < -10

[tex]\large {\mathsf {\red{\underbrace {\overbrace{\blue{ {\pink}{Answєr}}}}}}} \: [/tex]

x > - 10

[tex] \large \mathtt \green{Step-by-step \: explanation : }[/tex]

[tex] \small \sf \frac{x}{ - 2} > 5 \\ [/tex]

Solve for x

[tex] \small \sf \frac{x}{ - 2} > 5 \\ [/tex]

common denominator is 2

[tex]\small \sf ➪ \frac{2x}{ - 2} >2 \times 5 \\ [/tex]

[tex]\small \sf ➪ \frac{ \cancel{2}x}{ - \cancel{ 2}} >2 \times 5 \\ [/tex]

➪ - x > 2 × 5

➪ - x > 10

multiply by - 1

➪ - x × - 1 > 10 × - 1

x > - 10

Which solution finds the value of x in the triangle below?

A right triangle is shown. The hypotenuse has a length of 8. Another side has a length of x. The angle between the hypotenuse and the other side is 60 degrees.

Answers

Answer:

4

Step-by-step explanation:

Since this is a right triangle, and one of the angles measures 60 degrees, we can conclude that the last side measures 30 degrees.

We can see that this is a 30-60-90 degree triangle.

The rules of 30-60-90 degree triangles are that the side opposite the 90 degree angle, or the hypotenuse can be measured with the variable [tex]2a[/tex]. The side opposite the 30 degree angle can be measured with [tex]a[/tex], and the side opposite the 60 degree angle will be measured with [tex]a\sqrt{3}[/tex].

We can see that 8 represents [tex]2a[/tex] because it is the hypotenuse. Since the side marked [tex]x[/tex] is separated by the hypotenuse by an angle of 60 degrees, we note that side marked [tex]x[/tex] is opposite the angle measuring 30 degrees. We note that the side opposite 30 degrees is marked [tex]a[/tex], and since we already know that 8 is equal to [tex]2a[/tex], we realize that the side marked x is equal to [tex]a[/tex], or 4.

The value of x in the triangle is 4.

What is the Pythagorean theorem ?

The square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.

It is given this is a right triangle, and one of the angles measures 60 degrees, we can conclude that the last side measures 30 degrees. By the sum of all the three interior angles of a triangle is 180 degrees

The side opposite the 90 degree angle, or the hypotenuse can be measured with the variable '2a' . The side opposite the 30 degree angle can be measured with 'a' , and the side opposite the 60 degree angle will be measured with 'a√3'.

8 represents '2a' because it is the hypotenuse. Since the side marked x is separated by the hypotenuse by an angle of 60 degrees, we note that side marked x is opposite the angle measuring 30 degrees. We note that the side opposite 30 degrees is marked 'a', and since we already know that 8 is equal to '2a', we realize that the side marked x is equal to

'a' , or 4.

2a=8

a=4

x=a=4

so, the the value of x in the triangle is 4.

Learn more about the  Pythagorean theorem here:

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Enter an equation in point-slope form for the line.
Slope is −6 and (1, 1) is on the line.

Answers

Answer:

y - 1 = -6(x - 1)

General Formulas and Concepts:

Algebra I

Point-Slope Form: y - y₁ = m(x - x₁)

x₁ - x coordinate y₁ - y coordinate m - slope

Step-by-step explanation:

Step 1: Define

Identify

Point (1, 1)

Slope m = -6

Step 2: Find Equation

Substitute in variables [Point-Slope Form]:                                                     y - 1 = -6(x - 1)
y - 1= -6(x - 1) is the correct answerrrrrr

જ્યારે જહાંગીરની ઉંમર 18 વર્ષ થશે ત્યારે અકબરની ઉંમર 50 વર્ષ થર્શ.
જ્યારે અકબરની ઉંમર જહાંગીરની ઉંમર કરતા 5 ઘણી હશે ત્યારે
અકબરની ઉમર કેટલી હશે?
A) 36
B) 40
C) 44
D) 48

Answers

Answer:

C: 44

Step-by-step explanation:

what is the value of x?
what is the value of y?
type in an integer or decimal​

Answers

9514 1404 393

Answer:

x = 5.6y = 65

Step-by-step explanation:

There are a couple of relations that are applicable to these questions.

the product of segment lengths of crossed chords is the same for both chordsthe angle formed at crossed chords is the average of the intercepted arc measures

__

The segment lengths relation tells us ...

  10x = 8×7 . . . . . . products of segment lengths are equal

  x = 56/10 = 5.6 . . . . divide by 10

__

The value of y° is the average of the intercepted arcs:

  y° = (85° +45°)/2 = 65°

_____

Additional comment

This diagram does not have enough information to allow computation of z. We would need to know the intercepted arc, or the length of the secant that meets tangent z.

Which of the following numbers is rational? Assume that the decimal patterns continue.

Answers

Answer:

[tex]\sqrt{49}[/tex]

Step-by-step explanation:

Define a rational number by a number able to expressed a fraction where the denominator is not 0 or 1.

Non-terminating (never-ending) decimals cannot be expressed as a fraction and therefore are irrational. However, recall that [tex]\sqrt{49}=7[/tex], which can be expressed as a fraction (e.g. [tex]\frac{14}{2}[/tex], etc). Thus, the answer is [tex]\boxed{\sqrt{49}}[/tex].

Which expression is equivalent to -9x-1y-9/-15x5y-3?

Answers

Answer: -9x-1y-9/

Step-by-step explanation:

Answer: b

Step-by-step explanation:

I really dont like edge

Can someone give me the letter to all answers 1-4 or at least one 3

Answers

Answer:

hello there here are your answers:

1) a- 12, 18, 24, 30, 36

2) b- 31

3) a-communitive property of addition

4) a- 6a

Step-by-step explanation:

1: go through all the numbers and add 6 like 12+6=16 etc.

2: the common difference is 4 so 27+4 =31

3: communitive property because you can change the number in any order and still get the same sum

4: 6a because only 24ab has a b in it

Please Help NO LINKS

Answers

[tex]V = 864\pi[/tex]

Step-by-step explanation:

Since one of the boundaries is y = 0, we need to find the roots of the function [tex]f(x)=-2x^2+6x+36[/tex]. Using the quadratic equation, we get

[tex]x = \dfrac{-6 \pm \sqrt{36 - (4)(-2)(36)}}{-4}= -3,\:6[/tex]

But since the region is also bounded by [tex]x = 0[/tex], that means that our limits of integration are from [tex]x=0[/tex] (instead of -3) to [tex]x=6[/tex].

Now let's find the volume using the cylindrical shells method. The volume of rotation of the region is given by

[tex]\displaystyle V = \int f(x)2\pi xdx[/tex]

[tex]\:\:\:\:\:\:\:= \displaystyle \int_0^6 (-2x^2+6x+36)(2 \pi x)dx[/tex]

[tex]\:\:\:\:\:\:\:= \displaystyle 2\pi \int_0^6 (-2x^3+6x^2+36x)dx[/tex]

[tex]\:\:\:\:\:\:\:= \displaystyle 2\pi \left(-\frac{1}{2}x^4+2x^3+18x^2 \right)_0^6[/tex]

[tex]\:\:\:\:\:\:\:= 864\pi [/tex]

At one point in history, the NBA finals required that one of the two teams win at least three of five games in order to win the Championship. If one team wins the first two games, what is the probability that the same team wins the Championship, assuming that the two teams are well matched and each team is equally likely to win each game

Answers

Answer:

50% i believe

Step-by-step explanation:

because in every scenario theres 2 teams and if they are well matched it be half and half on every game assuming they're the same level of comp

A box contains 5 white balls, 3 black balls, and 2 red balls.A-What is the probability of drawing a white ball?B- How many white balls must be added to the box so that the probability of drawing a white ball is 3/4?C-How many black balls must be added to the original assortment so that the probability of drawing a white ball is 1/4?

Answers

Answer:

[tex](a)\ P(White) = \frac{1}{2}[/tex]

(b) 10 additional white balls

(c) 10 additional black balls

Step-by-step explanation:

Given

[tex]White = 5[/tex]

[tex]Black =3[/tex]

[tex]Red = 2[/tex]

Solving (a): P(White)

This is calculated as:

[tex]P(White) = \frac{White}{Total}[/tex]

[tex]P(White) = \frac{5}{5+3+2}[/tex]

[tex]P(White) = \frac{5}{10}[/tex]

[tex]P(White) = \frac{1}{2}[/tex]

Solving (b): Additional white balls, if [tex]P(White) = \frac{3}{4}[/tex]

Let the additional white balls be x

So:

[tex]P(White) = \frac{White+x}{Total+x}[/tex]

This gives:

[tex]\frac{3}{4} = \frac{5+x}{10+x}[/tex]

Cross multiply

[tex]30+3x = 20 + 4x[/tex]

Collect like terms

[tex]4x - 3x = 30 - 20[/tex]

[tex]x = 10[/tex]

Hence, 10 additional white balls must be added

Solving (c): Additional black balls, if [tex]P(White) = \frac{1}{4}[/tex]

Let the additional black balls be x

So:

[tex]P(White) = \frac{White}{Total+x}[/tex]

So, we have:

[tex]\frac{1}{4} = \frac{5}{10+x}[/tex]

Cross multiply

[tex]10+x = 5 * 4[/tex]

[tex]10+x = 20[/tex]

Collect like terms

[tex]x = 20 -10[/tex]

[tex]x = 10[/tex]

Hence, 10 additional black balls must be added

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