There are 32 pieces of building blocks in a bag: 8 each of blue, green, red, and yellow. Four pieces are chosen at random. Identify the probability that all 4 of the pieces are red. A. 6/3596 B. 6/4356 C. 7/899 D. 7/3596

Hey there! :)

Answer:

16p + 6.

Step-by-step explanation:

Add the two binomials together by combining like terms:

12p + 9 + 4p - 3

12p + 4p + 9 - 3

16p + 6.

Answer:

16p+6

Step-by-step explanation:

You combine like terms you do not multiply.

Answer:

A. (0,2) and (7,23)

Step-by-step explanation:

To solve, we set both equations equal to each other (because both equations equal y).

3x + 2 = x^2 -4x + 2

x^2 - 7x = 0

x(x-7)

so the x values are 7 and 0.

Plugging x back into the linear equation (because it’s easier)

3(7) + 2 = 23

3(0) + 2 = 2

so the answers are (7, 23) and (0,2)

Answer:

x = 5, AB=5, BC = 15

Step-by-step explanation:

AC = AB + BC (Segment Addition)

AC= 20, AB =x Bc = 3x,

20= x+3x 20=4x

x=5

AB=x, AB =5

BC=3x BC= 15

The segment addition postulate states gives the value of x as 5, given

that the sum of x and 3·x is 20.

Responses:

From the given diagram, we have;

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

[tex]\overline{BC}[/tex] = 3·x

According to segment addition postulate we have;

[tex]\overline{AB}[/tex] + [tex]\overline{BC}[/tex] = [tex]\overline{AC}[/tex] = 20 inches

Which gives;

x + 3·x = 20

Therefore;

4·x = 20

[tex]x = \dfrac{20}{4} = 5[/tex]

[tex]\mathbf{\overline{BC}}[/tex] = 3·x  

[tex]\mathbf{\overline{BC}}[/tex] = 3 × 5 = 15

Learn more about segment addition postulate here:

https://brainly.com/question/1397818

Answer: 52.8

Step-by-step explanation: it’s on khan ,

Options

Answer:

[tex](E)0.7+0.4-0.2=0.9[/tex]

Step-by-step explanation:

In probability theory

[tex]P$(A or B)=P(A)+P(B)$-$P(A and B)[/tex]

Let the event that the show had animals in it = A

P(A)=0.7

Let the event that the show aired more than 10 times =B

P(B)=0.4

P(A and B)= 0.2

[tex]P$(A or B)$=0.7+0.4-0.2=0.9[/tex]

Therefore, the equation which  shows the correct use of the addition rule to determine the probability that a randomly selected show had animals in it or aired more than 10 times is:

[tex]0.7+0.4-0.2=0.9[/tex]

The correct option is E.

Hey there! I'm happy to help!

The domain is all of the possible x-values and the range is all of the possible y-values.

Let's quickly rearrange our equation so we can plug in x to see what y is.

12x+6y=24

We subtract 12x from both sides.

6y=-12x+24

We divide both sides by six.

y= -2x+4

Since there are three domains we can plug into this equation that can give us one output, we will have three numbers in our range! Let's plug in our x-values to get our three y-values.

y=-2(-4)+4

y=12

y=-2(0)+4

y=4

y=-2(5)+4

y= -6

When writing your range, you order the numbers from least to greatest. We can write this range as {-6,4,12}

Have a wonderful day!

Answer:

The alternative hypothesis will state that there is significant difference between the mean list price of a three bedroom home and the mean list price of a four bedroom home.

[tex]H_a:\mu_1-\mu_2\neq 0[/tex]

Step-by-step explanation:

This would be an two-sample hypothesis test for the difference between two means.

As we are looking for differences, we are not testing if one population mean is bigger than the other. This will  be a two-tailed test and the alternative hypothesis will have a unequal sign.

The alternative hypothesis will state that there is significant difference between the mean list price of a three bedroom home and the mean list price of a four bedroom home.

This can be written as:

[tex]H_a:\mu_1-\mu_2\neq 0[/tex]

meaning that the population means are significantly different.

Answer:

Step-by-step explanation:

3x - 4y = -23

-x + 2y  = -19

3x - 4y = -23

-3x - 6y = -57

-10y = -80

y = 8

-x + 2(8) = -19

-x + 16 = -19

-x = -35

x = 35

(35, 8)

━━━━━━━☆☆━━━━━━━

▹ Answer

(-61, -40)

▹ Step-by-Step Explanation

3x - 4y = -23

2y - x = -19

3x - 4y = -23

x = 19 + 2y

3(19 + 2y) - 4y = -23

y = -40

x = 19 + 2 * (-40)

x = -61

(x, y) = (-61, -40)

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

Hey there!

3/4= 0.75

1/5=0.2

3/10=0.3

1/7=0.14

Thus, 1/7 is the smallest fraction.

Hope this helps :)

Answer:

1. Point estimate M (sample mean): 83.33

2. The lower bound is $73.36 and the upper bound is $93.30. One can be______% confident that the mean travel tax for all cities is between these values.

3. A. The researcher could decrease the level of confidence.

Step-by-step explanation:

A point esimate for the population mean travel tax can be done with the sample mean.

We can calculate the sample mean as:

[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{8}(67.85+78.62+70.28+84.03+79.28+87.72+101.54+97.28)\\\\\\M=\dfrac{666.6}{8}\\\\\\M=83.33\\\\\\[/tex]

2. We have to calculate a 95% confidence interval for the mean.

The sample mean is M=83.33.

The sample size is N=8.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

We calculate the sample standard deviation as:

[tex]s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{7}((67.85-83.33)^2+(78.62-83.33)^2+(70.28-83.33)^2+. . . +(97.28-83.33)^2)}\\\\\\s=\sqrt{\dfrac{994.49}{7}}\\\\\\s=\sqrt{142.07}=11.92\\\\\\[/tex]

The standard error is:

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{11.92}{\sqrt{8}}=\dfrac{11.92}{2.828}=4.214[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=8-1=7[/tex]

The t-value for a 95% confidence interval and 7 degrees of freedom is t=2.36.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=2.36 \cdot 4.214=9.97[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 83.33-9.97=73.36\\\\UL=M+t \cdot s_M = 83.33+9.97=93.30[/tex]

The 95% confidence interval for the mean travel tax is (73.36, 93.30).

We can be 95% confident that the true mean travel tax is within this interval.

3.. If we have no access to additional data, we can not decrease the standard deviation or increase the sample size.

The only way to have a narrower confidence interval is decreasing its level of confidence. With the same sample information, the lower the confidence, the narrower is the interval.

Answer:

Sphete B have a surface area of 48 square feet

Step-by-step explanation:

Two spheres of

Sphere A the smallest and sphere B the biggest has a scale factor of 1/3

Sphere A has surface area of 16 square feet.

Let's determine the surface area of sphere B.

Sphere A /sphere B = 1/3

Sphere A = 16

16/sphere B = 1/3

3*16= sphere B *1

48 = sphere B

Sphete B have a surface area of 48 square feet

Answer:

The statistic for this case would be:

[tex] z=\frac{\hat p -p_o}{\sqrt{\frac{\hat p(1-\hat p)}{n}}}[/tex]

And replacing we got:

[tex] z= \frac{0.436-0.4}{\sqrt{\frac{0.436*(1-0.436)}{700}}}= 1.92[/tex]

Step-by-step explanation:

For this case we have the following info:

[tex] n =700[/tex] represent the sample size

[tex] X= 305[/tex] represent the number of employees that earn more than 50000

[tex]\hat p=\frac{305}{700}= 0.436[/tex]

We want to test the following hypothesis:

Nul hyp. [tex] p \leq 0.4[/tex]

Alternative hyp : [tex] p>0.4[/tex]

The statistic for this case would be:

[tex] z=\frac{\hat p -p_o}{\sqrt{\frac{\hat p(1-\hat p)}{n}}}[/tex]

And replacing we got:

[tex] z= \frac{0.436-0.4}{\sqrt{\frac{0.436*(1-0.436)}{700}}}= 1.92[/tex]

And the p value would be given by:

[tex] p_v = P(z>1.922)= 0.0274[/tex]

Answer:

-4/8

Step-by-step explanation:

Using rise over run would give you -4/8. Since the rise is going downward four times the number would be negative. Since the run is going to the right 8 times it would be positive.

Answer:  the slope is -1/2

Step-by-step explanation:  The rise is -4. Easy to see from the y-intercept, 4 below the origin. The run is 8, again easy to see from the distance between the x-intercept at -8, 8 unite away from the origin.

So slope = rise/run -4/8   simplify (by LCM, 4) So you get slope = -1/2

Answer:

The solutions are a₁ = -4/19 i, a₂ = 4/19 i and a₃ = -1/4

Step-by-step explanation:

Given the equation 76a³+19a²+16a=-4, for us to solve the equation, we need to find all the factors of the polynomial function. Since the highest degree of the polynomial is 3, the polynomial will have 3 roots.

The equation can also be written as (76a³+19a²)+(16a+4) = 0

On factorizing out the common terms from each parenthesis, we will have;

19a²(4a+1)+4(4a+1) = 0

(19a²+4)(4a+1) = 0

19a²+4 = 0 and 4a+1 = 0

From the first equation;

19a²+4 = 0

19a² = -4

a² = -4/19

a = ±√-4/19

a₁ = -4/19 i, a₂ = 4/19 i (√-1 = i)

From the second equation 4a+1 = 0

4a = -1

a₃ = -1/4

Answer:

Validation

Step-by-step explanation: Validation is a term used to describe the processes involved when we compare a set of values and observations against a set standard or rules to ensure that they meet certain expectations or criteria.

Validation is meant to prove that something, a data set etc are acceptable based on known rules, the rules or standards which is used to evaluate what can be described as valid.

Answer:  y=-(4/3)*x-6

Step-by-step explanation:

The equation of any straight line is y=a*x+b  (1).

So we have to find the coefficients a and b and substitute them to the equation (1).

If the required line is perpendicular to y= (3/4)*x-2 it means that

a= -(4/3)   (we have to inverse the fraction 3/4 and put the opposite sign after that.  3/4 has the sign + in front of it  so we have to put sign -)

So the equation of required line is y= -(4/3) *x+b .

Now we have to find b.   To do that pls remember that the point (-12;10)  belongs to the required line y= -(4/3) *x+b  . That means:

10=-(4/3)*(-12)+b  => 10=16+b =>  b=-6

So substitute b in equation (1) and get:

y=-(4/3)*x-6

Answer:

[tex]0.0553 - 1.96\sqrt{\frac{0.0553(1-0.0553)}{380}}=0.0323[/tex]

[tex]0.0553 + 1.96\sqrt{\frac{0.0553(1-0.0553)}{380}}=0.0783[/tex]

Step-by-step explanation:

The info given is:

[tex] X= 21[/tex] number of students who said that they planned to work in a rural community

[tex] n= 380[/tex] represent the sample size selected

[tex]\hat p =\frac{21}{380}= 0.0553[/tex] the estimated proportion of students who said that they planned to work in a rural community

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical value would be given by:

[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]

The confidence interval for the mean is given by the following formula:  

[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]

Replpacing we got:

[tex]0.0553 - 1.96\sqrt{\frac{0.0553(1-0.0553)}{380}}=0.0323[/tex]

[tex]0.0553 + 1.96\sqrt{\frac{0.0553(1-0.0553)}{380}}=0.0783[/tex]

A mean for estimation is the minimum-maximum variation estimate's C.I. The % of pupils planning to work in a rural community alters between 0.0323 and 0.0783.

Confidence interval:

Let's [tex]p^{}[/tex] represent the sampling fraction of the people who promised to work in a rural area.

Sample size:

[tex]n = 380[/tex]

x: the large number the pupils expected to work in a rural setting

[tex]p^{} = \frac{x}{n} \\\\p^{} = \frac{21}{ 380} = 0.0553\\\\(1- \alpha)\ \ 100\%[/tex]confidence for true proportion:

[tex]( p^{}\ \pm Z_{\frac{\alpha}{2}} \times \sqrt{p^{} \times \frac{(1-p^{})}{n}} ) \\\\[/tex]

For [tex]95\%[/tex]confidence interval:

[tex]\to 1 - \alpha = 0.95[/tex]

When:

[tex]\to \alpha = 0.05[/tex]

Calculating the value of Z by using the table:

[tex]\to Z_{0.025} = 1.96[/tex]

When the  [tex]95\%[/tex] of the confidence interval:

[tex]\to (0.0553 \pm Z_{0.025} \times \sqrt{(0.0553 \times \frac{(1- 0.0553)}{380}})\\\\\to (0.0553 - Z_{0.025} \times \sqrt{(0.0553 \times \frac{(1- 0.0553)}{380})},0.0553 + Z_{0.025} \times \sqrt{(0.0553 \times \frac{(1- 0.0553)}{380}))}\\\\[/tex]

by solving the value we get:

[tex]\to ( 0.0323 , 0.0783 )[/tex]

Find out more about the Confidence interval here:

brainly.com/question/2396419

Answer:

I think its

             T

 R--------Q----------A

             U

Step-by-step explanation:

Because RA as a line bisects TU

Answer:

Step-by-step explanation:

opp=x,hyp=16

sin 51°=[tex]\frac{x}{16}[/tex]

cross multiply

sin 51° x 16 =x

0.7771 x 16=x

12.4=x

Answer:

The 99% confidence interval is = 0.37 +/- 0.070

= (0.300, 0.440)

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

p+/-z√(p(1-p)/n)

Given that;

Proportion p = 37% = 0.37

Number of samples n = 315

Confidence interval = 99%

z value(at 99% confidence) = 2.58

Substituting the values we have;

0.37 +/- 2.58√(0.37(1-0.37)/315)

0.37 +/- 2.58√(0.00074)

0.37 +/- 2.58(0.027202941017)

0.37 +/- 0.070183587825

0.37 +/- 0.070

= (0.300, 0.440)

The 99% confidence interval is = 0.37 +/- 0.070

= (0.300, 0.440)

Answer:

24 miles

Step-by-step explanation:

The area of a circle is given by: A = (pi)(r^2)

The problem gives the area as: 1,808.64 sq. mi.

So, (pi)(r^2) = 1,808.64 Solve for r. Divide both sides by pi (3.14)

r^2 = 1.808.64/3.14

r^2 = 576 Take the square root of both sides.

r = 24 Miles.

Answer:

23.99 miles

Step-by-step explanation:

The area of a circle is denoted by A = πr², where r is the radius.

Here, we know the circular area is A = 1808.64 square miles, so plug this into the formula to find r:

A = πr²

1808.64 = πr²

r² = 1808.64 / π ≈ 575.71

r = √575.71 ≈ 23.99 miles

The answer is thus 23.99 miles.

~ an aesthetics lover

Answer:

There is enough paint to cover the tank with one layer of paint.

Step-by-step explanation:

Given the cilindrical configuration of the tank and supposing that only external face must be painted, the surface area of the section (lateral wall + lid) can be calculated by the following expression:

[tex]A_{s} = 2\pi\cdot r\cdot h + \pi\cdot r^{2}[/tex]

Where [tex]r[/tex] and [tex]h[/tex] represent the radius and the height of the cube, respectively.

If [tex]r = 0.55\,m[/tex] (a diameter is two times the length of radius) and [tex]h = 1.4\,m[/tex], the intended surface area is:

[tex]A_{s} = 2\pi\cdot (0.55\,m)\cdot (1.1\,m)+\pi\cdot (0.55\,m)^{2}[/tex]

[tex]A_{s} \approx 4.751\,m^{2}[/tex]

It is known that 250 mL of paint are needed to cover a square meter of the surface area, the needed amount of paint to cover the required area is estimated by simple rule of three:

[tex]Q = \frac{4.751\,m^{2}}{1\,m^{2}}\times (250\,mL)[/tex]

[tex]Q = 1187.75\,mL\,(1.188\,L)[/tex]

In consequence, there is enough paint to cover the tank with one layer of paint.

Answer:

[tex]\large \boxed{\text{-1.8$^{\circ}$F/1000 ft}}[/tex]

Step-by-step explanation:

Identify the changes (Δ) in each consecutive pair of x-values and y-values, then calculate the corresponding values of Δy/Δx

Your working table should look like the one below.

[tex]\begin{array}{cccc}\textbf{Alt/1000 ft} & \textbf{B.p.$/^{\circ}$F} & \Delta\textbf{B. p}& \Delta\textbf{B.p/1000 ft}\\0 & 212.0 & & \\& &-0.9 & -1.8\\0.5 & 211.1 & & \\& &-0.9 & -1.8\\1.0 & 210.2 & & \\& &-1.8 & -1.8\\2.0 & 208.4 & & \\& &-1.8 & -1.8\\3.0 & 206.6 & & \\& &-1.8 & -1.8\\4.0 & 204.8 & & \\& &-0.9 & -1.8\\4.5 & 203.9 & & \\\end{array}[/tex]

[tex]\text{ The change in boiling point per thousand feet of altitude is $\large \boxed{\textbf{-1.8$^{\circ}$F/1000 ft}}$}[/tex]

Answer:

Answer:

Step-by-step explanation:

Identify the changes (Δ) in each consecutive pair of x-values and y-values, then calculate the corresponding values of Δy/Δx

Your working table should look like the one below.

Step-by-step explanation:

Answer:

The general term is

Sn = -(-2)ⁿ.3¹⁻ⁿ

step by step Explanation:

we were told to find a general term of the above sequence, what should come to mind is that the terms will follow an order....

CHECK THE ATTACHMENT FOR DETAILED EXPLANATION

Answer:

if m is supposed to be the equals (=) sign then x = 25

Step-by-step explanation:

45 = (2x-5)

+5         +5

50 = (2x)

÷2     ÷2

25 = x

Answer: 70

Step-by-step explanation:

Answer:

[tex]\boxed{Costing Price = $675}[/tex][tex]\boxed{Costing Price = $675}[/tex]Costing Price = $675

Step-by-step explanation:

Selling Price = $432

Discount = 36% of the costing price (36/100 * CP)

Then, Costing Price:

Let costing price be x

=> x - 0.36 x = 432

=> 0.64 x = 432

Dividing both sides by 0.64

=> x = $675

So, the costing Price is $675

Answer:

The 99​% confidence interval estimate of the percentage of girls born is between 85.46% and 94.54%.

Usually, babies are equally as likely to be boys or girls. Here, it is desired to increase the probability of conceiving a girl, which is achieved, considering the lower bound of the confidence interval is considerably above 50%.

Step-by-step explanation:

Confidence interval for the proportion:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 290, \pi = \frac{261}{290} = 0.9[/tex]

99% confidence level

So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.9 - 2.575\sqrt{\frac{0.9*0.1}{290}} = 0.8546[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.9 + 2.575\sqrt{\frac{0.9*0.1}{290}} = 0.9454[/tex]

Percentage:

Proportion multplied by 100.

0.8546*100 = 85.46%

0.9454*100 = 94.54%

The 99​% confidence interval estimate of the percentage of girls born is between 85.46% and 94.54%.

Based on the​ result, does the method appear to be​ effective?

Usually, babies are equally as likely to be boys or girls. Here, it is desired to increase the probability of conceiving a girl, which is achieved, considering the lower bound of the confidence interval is considerably above 50%.

Answer:

  134 degrees

Step-by-step explanation:

Right so far. To find the numerical measure of the angle, you need to use x=7 in your expression for the angle measure:

  m∠STU = -27 +23(7) = 134 . . . degrees

Answer:

Hey there!

The solutions to a system are where the lines, or graphs intersect each other.

We see that the graphs intersect at (0, -4) and (2, 0).

Thus, the solutions are (0, -4) and (2, 0).

Hope this helps :)