A bag contains 7 red and 10 white balls. In how many ways 4 balls are selected if there are more than 2 red balls? (Please solve it using counting rule; combination rule.)

Answers

Answer 1

Answer:

385 ways

Step-by-step explanation:

Given;

7 red balls

10 white balls

In how many ways can 4 balls be selected if there are more than 2 red balls.

Selecting 4 balls which must contain more than 2 red balls, will be 3 red balls and 1 white ball to make it 4 in total, or all the 4 balls selected will red balls.

= 3 red balls and 1 white ball  OR 4 red balls

= 7C₃ x 10C₁  + 7C₄

[tex]= \frac{7!}{4!3!} *\frac{10!}{9!1!} \ \ + \ \frac{7!}{3!4!} \\\\= (35*10) \ + \ 35\\\\= 350 \ + 35\\\\= 385 \ ways[/tex]

Therefore, there are 385 ways of selecting 4 balls, if there are more than 2 red balls.


Related Questions

A number cube with faces labeled from 1 to 6 will be rolled once. The number rolled will be recorded as the outcome. Give the sample space describing all possible outcomes. Then give all of the outcomes for the event of rolling the number 1, 3, or 4. If there is more than one element in the set, separate them with commas. Sample space: {} Event of rolling the number 1 3, or 4 :

Answers

Answer:

Sample space: [tex]\Omega=\{1,2,3,4,5,6\}[/tex]

Event of rolling the number 1 3, or 4 : A={1,3,4}

Step-by-step explanation:

When you roll a number cube with faces labeled from 1 to 6 once.

The possible outcomes are: 1,2,3,4,5 or 6.

Therefore, the sample space of this event is:

Sample space: [tex]\Omega=\{1,2,3,4,5,6\}[/tex]

Given the event of rolling the numbers 1, 3, or 4.

Now we are required to give the outcomes for the event of rolling number 1,3 or 4.  Let's call the event A. The set of possible outcomes for A has all the numbers 1, 3 and 4 as follows

Event of rolling the number 1 3, or 4 :A= {1,3,4}

arl rides his bicycle 120 feet in 10 seconds. How many feet does he ride in 1 minute? 2 feet 12 feet 720 feet 7,200 feet

Answers

Answer: 720 ft

Step-by-step explanation: He rides 720 feet.

if 120 feet are in 10 seconds then;

60 seconds are 60/10*120=720 feet

Answer:

720

Step-by-step explanation:

120/10 to find his feet per second which is 12 feet per second

12*60

since there are 60 seconds in a minute

= 720

Use technology to approximate the solution(s) to the system of equations to the nearest tenth of a unit. Select all that apply.
{f(x) = 2(3)^x
{g(x) = 10log(x+3)
(-1.9, 15.9)
(-2, 0.2)
(1.9, -15.9)
(2, -0.2) (1.9, 15.9)

Answers

Answer:

  closest choice: (-2, 0.2)

Step-by-step explanation:

The attached image from a graphing calculator shows the solutions (to the nearest tenth) to be ...

  (-1.9, 0.2)

  (1.0, 6.0)

The closest of the offered choices is (-2, 0.2). None are actually correct.

In the first year if ownership, a new car lose 20% of its value. If a car lost $4,200 value in the first year, how much did the car originally cost?

Answers

Answer:

21,000$

Step-by-step explanation:

part to whole method

20/100 and 4,200/

How many 20s to get to 4,200?

Jake made a rectangular garden area as shown in the figure. He wants to add 3 inches of topsoil to the entire area.
36 in
15 in
How much topsoil does Jake need to get at the nursery?
540 in.
1,080 in.
1,386 in.
1,620 in.

Answers

Answer:

1,620in

Step-by-step explanation:

LxWxH

36 x 15 x 3 = 1,620 in

Answer:

1620

Step-by-step explanation:

Which cosine function has maximum of 0.5, a minimum of -0.5, and a period of 2(pi)/3

Answers

Answer:

The answer is "[tex]\bold{y=0.5 \cos 3 \theta}[/tex]"

Step-by-step explanation:

The choices were missing the question so the answer to this question can be defined as follows:

The answer is [tex]y= 0.5 \cos 3\theta[/tex] because:

[tex]\Rightarrow -1 \leq \cos 3 \theta \leq 1\\\\\Rightarrow -0.5 \leq \cos 3 \theta \leq 0.5\\[/tex]

So, the maximum value is = 0.5 and the minimum value is = -0.5 of [tex]\frac{2\pi}{3}[/tex].

Answer:

D. y= 0.5 cos 3 theta

Step-by-step explanation:

The mean annual salary for intermediate level executives is about $74000 per year with a standard deviation of $2500. A random sample of 36 intermediate level executives is selected. What is the probability that the mean annual salary of the sample is between $71000 and $73500?

Answers

Answer:

11.51% probability that the mean annual salary of the sample is between $71000 and $73500

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 normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes 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.

In this question, we have that:

[tex]\mu = 74000, \sigma = 2500, n = 36, s = \frac{2500}{\sqrt{36}} = 416.67[/tex]

What is the probability that the mean annual salary of the sample is between $71000 and $73500?

This is the pvalue of Z when X = 73500 subtracted by the pvalue of Z when X = 71000. So

X = 73500

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

By the Central Limit Theorem

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

[tex]Z = \frac{73500 - 74000}{416.67}[/tex]

[tex]Z = -1.2[/tex]

[tex]Z = -1.2[/tex] has a pvalue of 0.1151

X = 71000

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

[tex]Z = \frac{71000 - 74000}{416.67}[/tex]

[tex]Z = -7.2[/tex]

[tex]Z = -7.2[/tex] has a pvalue of 0.

0.1151 - 0 = 0.1151

11.51% probability that the mean annual salary of the sample is between $71000 and $73500

Assuming that a cheese sandwich consists of 2 slices of bread and 3 slices of cheese, determine the number of whole cheese sandwiches that can be prepared from 32 slices of bread and 51 slices of cheese. g

Answers

Answer:

Only 16 whole sandwiches can be produced

Step-by-step explanation:

From the question, we know that we will need two slices of bread to make a full sandwich.

We can divide the number of slices of bread by two to check how many full sandwiches can be made.

Number of complete sets of bread = 32/2 = 16 sets

Similarly, we can divide the number of slices of cheese by 3 to find out the number of complete sets of cheese that will be there:

Number of complete sets of cheese = 51/3 = 17 sets

Since we have more cheese than bread, the number of whole sandwiches that can be made will be limited to the number of sets of bread available. (in this case, the ingredient smaller in quantity will be used to limit the production) which is = 16

Therefore only 16 whole sandwiches can be produced

What is the volume of a rectangular prism with a length of 12ft, a width of 10ft, and a height of 18ft?

Answers

Answer:

2160ft³

Step-by-step explanation:

V=whl=10·18·12=2160ft³

What is the value of x?

Answers

Answer:

x= 70

Step-by-step explanation:

These are supplementary angles

45+2x-5 = 180

Combine like terms

40+2x= 180

Subtract 40 from each side

40+2x-40 =180-40

2x= 140

Divide by 2

2x/2 =140/2

x = 70

From a barrel of colored marbles, you randomly select 1 blue, 2 yellow, 7 red, 6 green, and 2 purple marbles. Find the experimental probability of randomly selecting a marble that is NOT yellow.
A: 8/9

B: 9/10

C: 11/18

D: 7/9

Answers

Answer:

8/9

Step-by-step explanation:

1 blue, 2 yellow, 7 red, 6 green, and 2 purple marbles = 18 marbles

The number that are not yellow = total - yellow

P( not yellow) = number that are not yellow / total

                       = (18-2) / 18

                       = 16/18

                       =8/9

Write this number in expanded notation:178.25​

Answers

Answer:

100+70+8+0.2+0.05. is the answer

Answer:

178.25 as a fraction is 178 1/4 or 713 / 4

Step-by-step explanation:

hope it works out !!

if F (x) equals 4x + 7 which of the following is the inverse of F(x)​

Answers

Answer:

  [tex]F^{-1}(x)=\dfrac{x-7}{4}[/tex]

Step-by-step explanation:

To find the inverse function, solve for y the relation ...

  F(y) = x

  4y +7 = x

  4y = x - 7

  y = (x -7)/4 . . . . the inverse function

  [tex]\boxed{F^{-1}(x)=\dfrac{x-7}{4}}[/tex]

Answer: B

4x+7=y

Subtract 7 from both sides

4x=y-7

Divide both sides by 4

x= (y-7)/4

Switch x and y

y= (x-7)/4

So the answer is B

Calculate g(x)=f(x+1) when f(x) =4x-2

Answers

Answer:

g(x)= 2/5

Step-by-step explanation:

g(xl=f(4x-2)+1

5×-2

5x/5

x=2/5

what two numbers add to -7 and multiply to -60

Answers

Answer:

The answer would be 5 and -12

Please help me with this question!!!

Answers

Answer:

  3(cos(75°) +i·sin(75°)) and 3(cos(255°) +i·sin(255°))

Step-by-step explanation:

Using Euler's formula, this can be written as ...

  x^2 = 9·e^(i5π/6)

Then the square roots are ...

  x = (±√9)e^((i5π/6)/2) = ±3e^(i5π/12)

Of course, multiplying by -1 is the same as adding 180° to the angle.

The square roots are ...

  3(cos(75°) +i·sin(75°)) and 3(cos(255°) +i·sin(255°))

Alice studies the relationship between climate and heart disease around the world. H(t)H(t)H, left parenthesis, t, right parenthesis models the probability for the occurrence of heart disease (in percents relative to the global average) at an area where the temperature is ttt degrees Celsius. According to Alice's model, when the temperature is -5\degree\text{ C}−5° Cminus, 5, degree, start text, space, C, end text (which is the lowest temperature included in the model), the probability is 10\%10%10, percent above average. Then the probability decreases until the temperature reaches 30\degree\text{ C}30° C30, degree, start text, space, C, end text (which is the highest temperature included in the model), where the probability is 20\%20%20, percent below average. Which number type is more appropriate for the domain of HHH?

Answers

Answer:

The domain of the function H(t), is [-5, 30].

The range of the function H(t), is [(10% + average), (average - 20%)]

Step-by-step explanation:

The domain of a function is the complete set of possible values of the independent variable.

For this question, the function is H(t), with the temperature, t, serving as the independent variables and H(t) the evidently dependent variable.

The domain of a function refers to all the possible independent variable values that will give corresponding real dependent variable values.

For this question, Alice's model has the probability for the occurrence of heart disease (in percents relative to the global average) at an area, H(t) varying with the temperature of that area in degree Celsius.

At a temperature of -5°C (the lowest temperature in the model), the probability is 10% above the average.

Then, the probability decreases with increase in temperature, taking a value 20% lower than the average when the temperature is at its highest of 30°C in the model.

So, temperature ranges from -5°C to 30°C and the probability for the occurrence of heart disease ranges from 10% above the average to 20% below the average.

The domain of the function H(t), from the definition given above would therefore be [-5, 30]

And the range of the function H(t), is [(10% + average), (average - 20%)]

Hope this Helps!!!

The Real Number type is more appropriate fro the domain of H(t).

The domain of H(t) is given as  [tex]-5 \leq t \leq 30[/tex]

Given that:

The lowest temperature included in the model is -5° C

The highest temperature included in the model is 30° C

The domain of H includes the values of the temperature. Since the temperature can be non integer too, sometimes rational too, thus we use Real Number type for the domain of H(t).

The domain of H(t) will be given by the following interval on real number line:

[tex]\begin{aligned} Domain(H(t)) = [-5, 30]\\\end{aligned}[/tex]

or [tex]-5 \leq t \leq 30[/tex].

Hence, the Real Number type is more appropriate fro the domain of H(t).

The domain of H(t) is given as  [tex]-5 \leq t \leq 30[/tex].

Learn more here:

https://brainly.com/question/9463453

If 4/3 * 3/4 = 5k, then k =

Answers

Answer:

1/5

Step-by-step explanation:

switch sides, delete both common factors and your stuck with 5k=1. then you put both in a fraction and it gets you 1/5

Write the quotient in simplest form. Type answer as integer or a fraction

Answers

Answer:

[tex]-\dfrac{1}{26}[/tex]

Step-by-step explanation:

[tex]-\dfrac{12}{13}\div 24=\\\\-\dfrac{12}{13} \times \dfrac{1}{24}=\\\\-\dfrac{12}{13\times 24}=\\\\-\dfrac{1}{26}[/tex]

Hope this helps!

Which expression is equivalent to log Subscript 8 Baseline 4 a (StartFraction b minus 4 Over c Superscript 4 Baseline EndFraction)?

Answers

Answer:

[tex]\log_84+\log_8a+\log_8(b-4)-4\log_8c[/tex].

Step-by-step explanation:

The given expression is

[tex]\log_84a\left(\dfrac{b-4}{c^4}\right)[/tex]

Using the properties of logarithm, we get

[tex]\log_84+\log_8a+\log_8\left(\dfrac{b-4}{c^4}\right)[/tex]     [tex][\because \log_a mn=\log_a m+\log_a n][/tex]

[tex]\log_84+\log_8a+\log_8(b-4)-\log_8c^4[/tex]     [tex][\because \log_a \frac{m}{n}=\log_a m-\log_a n][/tex]

[tex]\log_84+\log_8a+\log_8(b-4)-4\log_8c[/tex]     [tex][\because \log_a x^n =n\log_a x][/tex]

Therefore, the required expression is [tex]\log_84+\log_8a+\log_8(b-4)-4\log_8c[/tex].

Answer:

B on edge

Step-by-step explanation:

The number of pieces of popcorn in a large movie theatre popcorn bucket is normally distributed, with a mean of 1610 and a standard deviation of 10. Approximately what percentage of buckets contain between 1600 and 1620 pieces of popcorn?

Answers

Answer:

A

Step-by-step explanation:

We know that in normal distribution, approximately 34% of bags will fall with in one standard deviation on one side. On both sides within the range of 1 standard deviation, 34 + 34 = 68 % of bags will fall.

Our range is:

1600 to 1620

1610 - 10 to 1610 + 10

So the answer is 1

That means, that 68% is the answer.

Answer:

The answer is A.

Step-by-step explanation:

Approximately 68%

Which of these levelers will make it easier to lift the object

Answers

Answer:

C

Step-by-step explanation:

Because it would have less weight to carry

To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the three treatments. You are given the results below. Treatment Observation A 20 30 25 33 B 22 26 20 28 C 40 30 28 22 The test statistic to test the null hypothesis equals _____.

Answers

Answer:

The test statistic to test the null hypothesis equals 1.059

Step-by-step explanation:

From the given information; we have:

Treatment               Observations

A                                20        30         25       33

B                                22         26        20       28

C                               40         30         28       22

The objective is to find the  test statistic to test the null hypothesis; in order to do that;we must first run through a series of some activities.

Let first compute the sum of the square;

Total sum of squares (TSS) = Treatment sum of squares [tex](T_r SS)[/tex]  +    Error sum of squares   (ESS)

where:

(TSS) = [tex]\sum \limits ^v_{i=1} \sum \limits ^{n_i}_{j-1}(yij- \overline {y}oo)^2[/tex]  with (n-1)   df

[tex](T_r SS)[/tex]   [tex]= \sum \limits ^v_{i=1} n_i( \overline yio- \overline {y}oo)^2[/tex]   with (v-1)  df

[tex](ESS) = \sum \limits ^v_{i=1} \sum \limits ^{n_i}_{j-1}(yij- \overline {y}io)^2[/tex]   with (n-v) df

where;

v= 3

[tex]n_i=[/tex]4

i = 1,2,3

n =12

[tex]y_{ij}[/tex] is the [tex]j^{th[/tex] observation for the [tex]i^{th[/tex] treatment

[tex]\overline{y}io[/tex] is the mean of the  [tex]i^{th[/tex] treatment  i = 1,2,3 ;  j = 1,2,3,4

[tex]\overline y oo[/tex]   is the overall mean

From the given data

[tex]\overline y oo = \dfrac{1}{12} \sum \limits ^3_{i=1} \sum \limits ^{4}_{j=1}(yij)^2= 27[/tex]

[tex]TSS = \dfrac{1}{12} \sum \limits ^3_{i=1} \sum \limits ^{4}_{j=1}(yij- 27)^2 = 378[/tex]

[tex]T_r SS= \sum \limits^3_{i=1}4 (\overline y io - \overline yoo)^2[/tex]

[tex]=4(27-27)^2+4(24-27)^2+4(30-27)^2 = 72[/tex]

Total sum of squares (TSS) = Treatment sum of squares [tex](T_r SS)[/tex]  +    Error sum of squares   (ESS)

(TSS) =  378 - 72

(TSS) =  306

Now; to the mean square between treatments (MSTR); we use the formula:

MSTR = TrSS/df(TrSS)

MSTR = 72/(3 - 1)

MSTR = 72/2

MSTR = 36

The mean square within treatments  (MSE) is:

MSE = ESS/df(ESS)

MSE = 306/(12-3)

MSE = 306/(9)

MSE = 34

The test statistic to test the null hypothesis is :

[tex]T = \dfrac{ \dfrac{TrSS}{\sigma^2}/(v-1) }{ \dfrac{ESS}{\sigma^2}/(n-v) } = \dfrac{MSTR}{MSE} \ \ \ \approx \ \ T(\overline {v-1}, \overline {n-v})[/tex]

[tex]T = \dfrac{36}{34}[/tex]

T = 1.059

Kortholts that fail to meet certain precise specifications must be reworked on the next day until they are within the desired specifications. A sample of one day's output of kortholts from the Melodic Kortholt Company showed the following frequencies: Plant A Plant B Row Total Specification Met 85 35 120 Specification Not Met 15 25 40 Column Total 100 60 160 Find the chi-square test statistic for a hypothesis of independence. Multiple Choice 7.22 14.22 -0.18 14.70

Answers

Answer:

The value of Chi-square test statistic for a hypothesis test of independence is 14.22.

Step-by-step explanation:

The data provided is for one day's output of Kortholt's from the Melodic Kortholt Company.

The formula to compute the chi-square test statistic for a hypothesis of independence is:

[tex]\chi^{2}=\sum {\frac{(O-E)^{2}}{E}}[/tex]

The formula to compute the expected frequencies (E) is:

[tex]E=\frac{\text{Row Total}\times \text{Column Total}}{N}[/tex]

Consider the Excel output attached.

Compute the value of Chi-square test statistic as follows:

[tex]\chi^{2}=\sum {\frac{(O-E)^{2}}{E}}[/tex]

    [tex]=1.333+2.222+4.000+6.667\\=14.222\\\approx 14.22[/tex]

Thus, the value of Chi-square test statistic for a hypothesis test of independence is 14.22.

Triangle ABC is a right triangle whose right angle is ZABC.
Find the measure of ZEBF.
ZABC and DBF are vertical angles, so they have the same
measure. Because IZABC is 90°, the sum of m2. DBE and
m2 EBF must also be 90°
Solve for x in this equation.
x + (x - 12) = 90
2x - 12 = 90
2x = 102
X51
m2 EBF = 51°

1.What is m
2.What is m
3.Explain how to find m

Answers

Answer: m is 13

m is 6

you find m by calculating!

Step-by-step explanation:

Mrs. Fields needs more chocolate chips to make cookies. The store has bags that weigh 0.45 lbs., 0.434 lbs., and 0.4 lbs. Which bag should she purchase if she wants the most chocolate chips?

Answers

Answer:

bag weigh 0.45 lbs

Step-by-step explanation:

Hypothetical Situation: A scientist notices that her bees may be avoiding a specific pollen from flower "X" despite its abundance in the area. To test to see if this behavior is reproducible and not anecdotal, she decides to provide a choice test to her bees. She does this by putting the bees in a small cage with two dishes. One with pollen from flower "X" the other is pollen from a flower that she knows her bees collect, flower "Y." She counts how many times the bees chooses Flower "X" vs Flower "Y" and collects this data.
What is experimental group?

Answers

Answer:

The experimental group in this case are the group of bees that are put in the small cage.

Step-by-step explanation:

The experimental group is the group of subjects that participate in the test. They are usually assigned to the treatments in study. In some cases there is a control group, with no assigned treatment.

In this case, the bees that she put in the cage, and they are not assigned to a particular treatment. It can be considered a control group.

Jamie needs the following items from the hardware store a drill bit that cost 4.99 nails that caused 0.46 and sandpaper that cost 0.89 how much money was spent if the sales tax rate is 6%

Answers

Answer: $5.96

Step-by-step explanation:

4.99 + 0.46 + 0.89 is what she paid, not with tax. That equals 6.34.

Applying 6% means we calculate 6% of 6.34 and then subtract it from 6.34. (Or, we can also calculate 100-6%=94% of 6.34). Either way, the answer is 5.9596, or rounded, 5.96.

Hope that helped,

-sirswagger21

Can someone please help me

Answers

Answer:

6

Step-by-step explanation:

Similar triangles. MNE is ABC but 3/4 the size. Multiply each side by 3/4 to get lengths.

x = 8 *3/4 = 6

The Employment and Training Administration reported that the U.S. mean unemployment
insurance benefit was $238 per week (The World Almanac, 2003). Aresearcher in the state
of Virginia anticipated that sample data would show evidence that the mean weekly unemployment
insurance benefit in Virginia was below the national average.
a. Develop appropriate hypotheses such that rejection of H0 will support the researcher’s
contention.
b. For a sample of 100 individuals, the sample mean weekly unemployment insurance
benefit was $231 with a sample standard deviation of $80. What is the p-value?
c. At αα = .05, what is your conclusion?
d. Repeat the preceding hypothesis test using the critical value approach.

Answers

Answer:

Step-by-step explanation:

a) We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

H0: µ = 238

For the alternative hypothesis,

H1: µ < 238

This is a left tailed test

b) Since the population standard deviation is not given, the distribution is a student's t.

Since n = 100

Degrees of freedom, df = n - 1 = 100 - 1 = 99

t = (x - µ)/(s/√n)

Where

x = sample mean = 231

µ = population mean = 238

s = samples standard deviation = 80

t = (231 - 238)/(80/√100) = - 0.88

We would determine the p value using the t test calculator. It becomes

p = 0.19

c) Since alpha, 0.05 < than the p value, 0.19, then we would fail to reject the null hypothesis. Therefore, At a 5% level of significance, the sample data showed insignificant evidence that the mean weekly unemployment insurance benefit in Virginia was below the national average.

d) Since α = 0.05, the critical value is determined from the t distribution table. Recall that this is a left tailed test. Therefore, we would find the critical value corresponding to 1 - α and reject the null hypothesis if the test statistic is less than the negative of the table value.

1 - α = 1 - 0.05 = 0.95

The negative critical value is - 1.66

Since - 0.88 is greater than - 1.66, then we would fail to reject the null hypothesis.

Other Questions
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