Find the exact solution of 3x^2+7=28

Answer:

[tex] z=\frac{65-64.2}{\frac{2.84}{\sqrt{75}}} = 2.440[/tex]

And we can find the probability using the complement rule and with the normal standard table like this:

[tex] P(Z>2.440) =1-P(Z<2.440) = 1-0.993 =0.007[/tex]

The probability that the mean height for the sample is greater than 65 inches is 0.007

Step-by-step explanation:

Let X the random variable that represent the women heights of a population, and we know the following parameters

[tex]\mu=64.2[/tex] and [tex]\sigma=2.84[/tex]

We are interested on this probability

[tex]P(X>65)[/tex]

Since the sample size selected is 75>30 we can use the centrel limit theorem and the appropiate formula to use would be the z score given by:

[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

If we find the z score for 65 inches we got:

[tex] z=\frac{65-64.2}{\frac{2.84}{\sqrt{75}}} = 2.440[/tex]

And we can find the probability using the complement rule and with the normal standard table like this:

[tex] P(Z>2.440) =1-P(Z<2.440) = 1-0.993 =0.007[/tex]

The probability that the mean height for the sample is greater than 65 inches is 0.007

Answer:

[tex]\fbox{\begin{minipage}{14em}Number of subsets: 16\\Number of proper subsets: 15\end{minipage}}[/tex]

Step-by-step explanation:

Given:

The set A = {5, 13, 17, 20}

Question:

Find the number of subsets of A

Find the number of proper subsets of A

Simple solution by counting:

Subset of A that has 0 element:

{∅} - 1 set

Subset of A that has 1 element:

{5}, {13}, {17}, {20} - 4 sets

Subset of A that has 2 elements:

{5, 13}, {5, 17}, {5, 20}, {13, 17}, {13, 20}, {17, 20} - 6 sets

Subset of A that has 3 elements:

{5, 13, 17}, {5, 13, 20}, {5, 17, 20}, {13, 17, 20} - 4 sets

Subset of A that has 4 elements:

{5, 13, 17, 20} - 1 set

In total, the number of subsets of A: N = 1 + 4 + 6 + 4 + 1 = 16

The number of proper subsets (all of subsets, except subset which is equal to original set A): N = 16 - 1 = 15

Key-point:

The counting method might be used for finding the number of subsets when the original set contains few elements.

The question is that, for a set that contains many elements, how to find out the number of subsets?

The answer is that: there is a fix formula to calculate the total number ([tex]N[/tex]) of subsets of a set containing [tex]n[/tex] elements: N = [tex]2^{n}[/tex]

With original set A = {5, 13, 17, 20}, there are 4 elements belonged to A.

=> Number of subsets of A: N = [tex]2^{4} = 16[/tex]

(same result as using counting method)

Brief proof of formula: N = [tex]2^{n}[/tex]

Each element of original set is considered in 2 status: existed or not.

If existed => fill that element in.

If not => leave empty.

For i.e.: empty subset means  that all elements are selected as not existed, subset with 1 element means that all elements are selected as not existed, except 1 element, ... and so on.

=> From the point of view of a permutation problem, for each element in original set, there are 2 ways to select: existed or not. There are [tex]n[/tex] elements in total. => There are [tex]2^n}[/tex] ways to select, or in other words, there are [tex]2^{n}[/tex] subsets.

Hope this helps!

:)

Answer:

b = 4.6 ft

h = 2.3 ft

Step-by-step explanation:

The volume of the tank is given by:

[tex]b^2*h=49[/tex]

Where 'b' is the length of the each side of the square base, and 'h' is the height of the tank.

The surface area can be written as:

[tex]A=b^2+4bh\\A=b^2+4b*({\frac{49}{b^2}})\\A=b^2+\frac{196}{b}[/tex]

The value of b for which the derivate of the expression above is zero is the value that yields the minimum surface area:

[tex]\frac{dA}{db} =0=2b-\frac{196}{b^2}\\2b^3=196\\b=4.61\ ft[/tex]

The value of h is then:

[tex]h=\frac{49}{4.61^2}\\h=2.31\ ft[/tex]

Rounded to the nearest tenth, the dimensions are b = 4.6 ft and h = 2.3 ft.

Answer:

12 inches.

Step-by-step explanation:

The height of a sphere = the length of its diameter.

Diameter = 2 * radius = 12 ins.

Answer:

Skewed to right

Step-by-step explanation:

there is no explanation, it just is, just like how 1+1 is 2

Brainleist! as you promised!

Answer:

Yeah no skewed right, like the guy said.

Answer:

{0, 1}

Step-by-step explanation:

Solving for 'x' in the inequality:

[tex]7x+3<17\\7x+3-3<17-3 \leftarrow \text{Subtraction Property of Equality}\\7x<14\\7x/7<14/7 \leftarrow \text{Division Property of Equality}\\\boxed{x<2}[/tex]

X's value has to be less than two to make the inequality true. So, {0, 1} should be the correct answer.

Answer:

I took the quiz and the answer is B

Step-by-step explanation:

Answer:

3 both ways x = 3

EXPLANATION:

plug in inputs and do a little simplifying we get

x = 6 ± √(36-36) all of that over 2

So we simplify and we get 6±sqrt(0) / 2

Then we get 6/2 = 3

x-0 = x+0

thats why there is only one answer

Answer:

The value of X is 3

Step-by-step explanation:

x²-6x+9=0

x²- 3x - 3x + 9= 0

X(x-3) -3(x-3)=0

(x-3) (x-3)=0

(x-3)²=0

(x-3)=0

x-3 = 0

X= 3

Answer:

[tex]20.25 \: m^2[/tex]

Step-by-step explanation:

Use the formula for the area of a square.

[tex]A=s^2[/tex]

Where [tex]s=4.5[/tex]

[tex]s^2\\(4.5)^2\\20.25[/tex]

The area of the square is 20.25 square meters as per the concept of the square.

To find the area of a square, we need to square the length of one of its sides. In this case, the side length is given as 4 1/2 meters.

First, we need to convert the mixed number 4 1/2 into an improper fraction. We can rewrite it as 9/2.

Next, we square the side length:

[tex]\frac{9}{2}^2 = \frac{81}{4}[/tex].

To simplify the fraction, we can divide the numerator by the denominator:

81 ÷ 4 = 20 remainders 1.

Therefore, the area of the square is 20 1/4 square meters.

However, we can simplify the mixed number further. Since 4 can be divided by 4 and 1 can be divided by 4, we have:

20 1/4

= 20 + 1/4

= 20 + 1/4

= 20 + 0.25

= 20.25.

Therefore, the area of the square is 20.25 square meters.

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Answer

The figure shows three lines that intersect at point N.

3 lines intersect. Lines G K and J M intersect at point N to form a right angle. Line H L intersects the other lines at point N. Angle H N G is 48 degrees.

Angle GNH is congruent to angle KNL. Angle MNL is complementary to angle KNL. What is the measure of angle MNL?

42°

48°

132°

138°

Step-by-step explanation:

42

The required measure of angle MNL is 42°. Option A is correct.

3 lines intersect lines G K and J M intersect at point N to form a right angle. Line H L intersects the other lines at point N. Angle H N G is 48 degrees. Angle GNH is congruent to angle KNL. Angle MNL is complementary to angle KNL. What is the measure of angle MNL is to determine

The angle can be defined as the one line inclined over another line.
unit of measure of an angle is degree and radians.

Angle GNH is congruent to angle KNL.
∠KNL = 48°
Angle MNL is complementary to angle KNL
Since angle MNK = 90°
∠MNL + ∠KNL = 90°

∠MNL = 90-48
∠MNL = 42°

Thus, the required measure of angle MNL is 42°. Option A is correct.

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The correct question is:

A circle has a radius of 45 units and is centered at (-2.4, -4.8).

What is the equation of this circle?

Answer:

Equation of the circle is;

(x + 2.4)² + (y + 4.8)² = 2304

Step-by-step explanation:

The standard equation of a circle is;

(x - a)² + (y - b)²  =  r²

where;

(a,b) is the center of the circle and r is the radius of the circle

Now, from the question, the circle is centered at (-2.4, -4.8) and the radius is 45

Thus, plugging those values into the standard form of equation of a circle, we have;

(x - (-2.4))²  +  (y - (-4.8))²  = 48²

This gives;

(x + 2.4)² + (y + 4.8)² = 2304

The difference of the equation is A = ( x² - 3x - 12 ) / ( x + 3 ) ( x - 5 ) ( x + 7 )

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let the first equation be P = x / ( x² - 2x - 15 )

Let the second equation be Q = 4 / x² + 2x - 35 )

Now , A = P - Q

On simplifying , we get

A = x / ( x² - 2x - 15 ) - 4 / x² + 2x - 35 )

Taking the LCM , we get

A = x ( x + 7 ) - 4 ( x + 3 ) / ( x + 3 ) ( x - 5 ) ( x + 7 )

A = x² + 7x - 4x + 12 / ( x + 3 ) ( x - 5 ) ( x + 7 )

A = ( x² - 3x - 12 ) / ( x + 3 ) ( x - 5 ) ( x + 7 )

Therefore , the value of A is ( x² - 3x - 12 ) / ( x + 3 ) ( x - 5 ) ( x + 7 )

Hence , the equation is A = ( x² - 3x - 12 ) / ( x + 3 ) ( x - 5 ) ( x + 7 )

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Answer:

a) P(X < 30) = 0.0392.

b) P(28 < X < 32) = 0.2760

c) P(X > 35) = 0.1190

d) P(X > 31) = 0.8810

e) At least 35.7965 mpg

Step-by-step explanation:

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.

In this question, we have that:

[tex]\mu = 33, \sigma = 1.7[/tex]

a. P(X<30)

This is the pvalue of Z when X = 30. So

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

[tex]Z = \frac{30 - 33}{1.7}[/tex]

[tex]Z = -1.76[/tex]

[tex]Z = -1.76[/tex] has a pvalue of 0.0392.

Then

P(X < 30) = 0.0392.

b) P(28 < X < 32)

This is the pvalue of Z when X = 32 subtracted by the pvalue of Z when X = 28. So

X = 32

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

[tex]Z = \frac{32 - 33}{1.7}[/tex]

[tex]Z = -0.59[/tex]

[tex]Z = -0.59[/tex] has a pvalue of 0.2776.

X = 28

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

[tex]Z = \frac{28 - 33}{1.7}[/tex]

[tex]Z = -2.94[/tex]

[tex]Z = -2.94[/tex] has a pvalue of 0.0016.

0.2776 - 0.0016 = 0.2760.

So

P(28 < X < 32) = 0.2760

c) P(X>35)

This is 1 subtracted by the pvalue of Z when X = 35. So

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

[tex]Z = \frac{35 - 33}{1.7}[/tex]

[tex]Z = 1.18[/tex]

[tex]Z = 1.18[/tex] has a pvalue of 0.8810.

1 - 0.8810 = 0.1190

So

P(X > 35) = 0.1190

d. P(X>31)

This is 1 subtracted by the pvalue of Z when X = 31. So

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

[tex]Z = \frac{31 - 33}{1.7}[/tex]

[tex]Z = -1.18[/tex]

[tex]Z = -1.18[/tex] has a pvalue of 0.1190.

1 - 0.1190 = 0.8810

So

P(X > 31) = 0.8810

e. the mileage rating that the upper 5% of cars achieve.

At least the 95th percentile.

The 95th percentile is X when Z has a pvalue of 0.95. So it is X when Z = 1.645. Then

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

[tex]1.645 = \frac{X - 33}{1.7}[/tex]

[tex]X - 33 = 1.645*1.7[/tex]

[tex]X = 35.7965[/tex]

At least 35.7965 mpg

The upper 5% of cars have a mileage rating of 35.805 mpg

Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

z = (raw score - mean) / standard deviation

Given;  mean of 33 mpg and a standard deviation of 1.7

a) For < 30:

z = (30 - 33)/1.7 = -1.76

P(x < 30) = P(z < -1.76) = 1 - 0.8413 = 0.0392

b) For < 28:

z = (28 - 33)/1.7 = -2.94

P(x < 28) = P(z < -2.94) = 0.0016

c) For > 35:

z = (35 - 33)/1.7 = 1.18

P(x > 35) = P(z > 1.18) = 1 - P(z < 1.18) = 1 - 0.8810 = 0.119

d) For > 31:

z = (31 - 33)/1.7 = -1.18

P(x > 31) = P(z > -1.18) = 1 - P(z < -1.18) = 0.8810

e) The  upper 5% of cars achieve have a z score of 1.65, hence:

1.65 = (x - 33)/1.7

x = 35.805 mpg

The upper 5% of cars have a mileage rating of 35.805 mpg

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Answer:  [tex]\bold{\dfrac{8}{17}=47.1\%}[/tex]

Step-by-step explanation:

[tex]\dfrac{\text{painter or sculptor}}{\text{total artists}}=\dfrac{6+2}{6+2+9}=\dfrac{8}{17}[/tex]

Answer:

Remember the formula for calculating volume is: Volume = Area by height. V = A X h.

For a triangle the area is calculated using the formula: Area = half of base by altitude. A = 0.5 X b X a.

So to calculate the volume of a triangular prism, the formula is: V = 0.5 X b X a X h.

Step-by-step explanation:

Answer: y

Step-by-step explanation:

Answer:

  0

Step-by-step explanation:

The x-axis corresponds to the line y = 0. All points on the x-axis have a y-value of zero.

Answer:

3 apples / 4 people

3/4

to check divide fractions

Multiply reciprocal

3/1 x 4/1

3/1 / 1/4 = 3/4

3/4 x 4 = 12/4 = 3 apples

3/4 is the answer

Hope this helps

Step-by-step explanation:

Answer:

a) Median amount of time that is spent is around 2.3, rounded to 2.

b) 4 unit time

c) Mean amount of time is bigger than the median.

Step-by-step explanation:

Find the given attachment.

Note: Complete Question, along with the diagram is added

Answer:

: 4qrs • (qr2 + 2)

Step-by-step explanation:

Step by step solution :

Step 1 :

Equation at the end of step 1 :

((22q2 • r3) • s) + 8qrs

Pulling out like terms :

3.1 Pull out like factors :

4q2r3s + 8qrs = 4qrs • (qr2 + 2)

Final result :

4qrs • (qr2 + 2)

I am really soo sorry if the answer is wrong!

Answer:

a) 0.32 = 32% probability that your bid will be accepted

b) 0.72 = 72% probability that your bid will be accepted

c) An amount in excess of $15,400.

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X lower than x is given by the following formula.

[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]

Assume that the competitor's bid x is a random variable that is uniformly distributed between $10,400 and $15,400.

This means that [tex]a = 10400, b = 15400[/tex]

a. Suppose you bid $12,000. What is the probability that your bid will be accepted (to 2 decimals)?

You will win if the competitor bids less than 12000. So

[tex]P(X \leq 12000) = \frac{12000 - 10400}{15400 - 10400} = 0.32[/tex]

0.32 = 32% probability that your bid will be accepted

b. Suppose you bid $14,000. What is the probability that your bid will be accepted?

You will win if the competitor bids less than 14000. So

[tex]P(X \leq 14000) = \frac{14000 - 10400}{15400 - 10400} = 0.72[/tex]

0.72 = 72% probability that your bid will be accepted

c. What amount should you bid to maximize the probability that you get the property (in dollars)?

His bid is uniformly distributed between $10,400 and $15,400.

So, to maximize the probability that you get the property, you should bid an amount in excess of $15,400.

Answer:

P = 4878

Step-by-step explanation:

So we'll use the formula

A = p(1+r/n)^ (nt)

A = 1000000

P is the unknown

R = 4.2

N = 13

T = 13

1000000= p ( 1+ 0.42/13)^ 169

1000000 = p (1.032)^169

1000000= p 205

P = 4878

Answer:

hes lyin prolly

Step-by-step explanation:

Answer:

[tex]68.04-1.959\frac{35.74}{\sqrt{250}}=63.618[/tex]    

[tex]68.04+1.959\frac{35.74}{\sqrt{250}}=72.461[/tex]    

And the best option for this case would be

Step-by-step explanation:

Information given

[tex]\bar X=68.04[/tex] represent the sample mean

[tex]\mu[/tex] population mean

s=35.74 represent the sample standard deviation

n=250 represent the sample size  

Confidence interval

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

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

The degrees of freedom are given by:

[tex]df=n-1=250-1=249[/tex]

The Confidence level is 0.95 or 95%, and the significance [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and the critical value for this case woud be [tex]t_{\alpha/2}=1.956[/tex]

And replacing we got:

[tex]68.04-1.959\frac{35.74}{\sqrt{250}}=63.618[/tex]    

[tex]68.04+1.959\frac{35.74}{\sqrt{250}}=72.461[/tex]    

And the best option for this case would be

Answer:

1) [tex] E(M) = 14*0.3 + 10*0.4 + 19*0.3 = 13.9 \%[/tex]

2) [tex]E(J)= 22*0.3 + 4*0.4 + 12*0.3 = 11.8 \%[/tex]

3) [tex] E(M^2) = 14^2*0.3 + 10^2*0.4 + 19^2*0.3 = 207.1 [/tex]

And the variance would be given by:

[tex]Var (M)= E(M^2) -[E(M)]^2 = 207.1 -(13.9^2)= 13.89[/tex]

And the deviation would be:

[tex] Sd(M) = \sqrt{13.89}= 3.73[/tex]

4) [tex] E(J^2) = 22^2*0.3 + 4^2*0.4 + 12^2*0.3 =194.8 [/tex]

And the variance would be given by:

[tex]Var (J)= E(J^2) -[E(J)]^2 = 194.8 -(11.8^2)= 55.56[/tex]

And the deviation would be:

[tex] Sd(M) = \sqrt{55.56}= 7.45[/tex]

Step-by-step explanation:

For this case we have the following distributions given:

Probability  M   J

0.3           14%  22%

0.4           10%    4%

0.3           19%    12%

Part 1

The expected value is given by this formula:

[tex] E(X)=\sum_{i=1}^n X_i P(X_i)[/tex]

And replacing we got:

[tex] E(M) = 14*0.3 + 10*0.4 + 19*0.3 = 13.9 \%[/tex]

Part 2

[tex]E(J)= 22*0.3 + 4*0.4 + 12*0.3 = 11.8 \%[/tex]

Part 3

We can calculate the second moment first with the following formula:

[tex] E(M^2) = 14^2*0.3 + 10^2*0.4 + 19^2*0.3 = 207.1 [/tex]

And the variance would be given by:

[tex]Var (M)= E(M^2) -[E(M)]^2 = 207.1 -(13.9^2)= 13.89[/tex]

And the deviation would be:

[tex] Sd(M) = \sqrt{13.89}= 3.73[/tex]

Part 4

We can calculate the second moment first with the following formula:

[tex] E(J^2) = 22^2*0.3 + 4^2*0.4 + 12^2*0.3 =194.8 [/tex]

And the variance would be given by:

[tex]Var (J)= E(J^2) -[E(J)]^2 = 194.8 -(11.8^2)= 55.56[/tex]

And the deviation would be:

[tex] Sd(M) = \sqrt{55.56}= 7.45[/tex]

Answer:

The null and alternative hypothesis for this problem are:

[tex]H_0:\mu=380\\\\H_a: \mu>380[/tex]

Step-by-step explanation:

The alternative hypothesis shows the claim of the researchers. In this case, that the new type of fertilizer significantly increase the actual yield with the old fertilizer:

[tex]H_a: \mu>380[/tex]

The null hypothesis is the hypothesis to be nullified, so it states that the claim is not true and the yield is the same (or, at least, not significantly higher) as with the old fertilizer:

[tex]H_0: \mu=380[/tex]

Answer:

Age difference between oldest the  youngest = 48 years

Step-by-step explanation:

Given: Ratio of ages of Kissi and Esinam is 3:5, ratios of ages of Esinam and Lariba is 3:5 and sum of the ages of all 3 is 147 years

To find: age difference between oldest the  youngest

Solution:

Let age of Lariba be x years

As ratios of ages of Esinam and Lariba is 3:5,

Age of Esinam = [tex]\frac{3}{5}x[/tex]  years

As ratio of ages of Kissi and Esinam is 3:5,

Age of Kissi = [tex](\frac{3}{5}) (\frac{3}{5}x)=\frac{9}{25}x[/tex] years

Sum of the ages of all 3 = 147 years

[tex]x+\frac{3}{5}x+\frac{9}{25}x=147\\ \frac{25x+15x+9x}{25}=147\\ x=\frac{147(25)}{49}=75[/tex]

Age of Lariba = x = 75 years

Age of Esinam = [tex]\frac{3}{5}(75)=45\,\,years[/tex]

Age of Kissi = [tex]\frac{9}{25}(75)=27\,\,years[/tex]

So,

Age difference between oldest the  youngest = 75 - 27 = 48 years

Answer:

4/13

Step-by-step explanation:

There are 13 diamonds in a deck and 3 fours that aren't diamond

13+3=16

16/52 = 4/13