Rewrite the Product in Exponential Form : a. a. a. b. b. b. b ​

Answer: 0.0051

Step-by-step explanation:

Given: Mean : [tex]\mu = 50\text{ inch}[/tex]

Standard deviation : [tex]\sigma =1.1\text{ inch}[/tex]

Sample size : [tex]n=8[/tex]

The formula to calculate z is given by :-

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

For x= 51

[tex]z=\dfrac{51-50}{\dfrac{1.1}{\sqrt{8}}}=2.57129738613\approx2.57[/tex]

The P Value =[tex]P(Z>51)=P(z>2.57)=1-P(z<2.57)=1-0.994915=0.005085\approx0.0051[/tex]

Hence, the probability that the sample mean hardness for a random sample of 8 pins is at least 51 =0.0051

Answer:

[tex]\large\boxed{15\div6\dfrac{2}{3}=2\dfrac{1}{4}}[/tex]

Step-by-step explanation:

[tex]15\div6\dfrac{2}{3}\\\\\text{convert the mixed number to the improper fraction:}\ 6\dfrac{2}{3}=\dfrac{6\cdot3+2}{3}=\dfrac{20}{3}\\\\15\div\dfrac{20}{3}=15\cdot\dfrac{3}{20}=15\!\!\!\!\!\diagup^3\cdot\dfrac{3}{20\!\!\!\!\!\diagup_4}=\dfrac{(3)(3)}{4}=\dfrac{9}{4}=2\dfrac{1}{4}[/tex]

For this case we must rewrite the mixed number as a fraction:

[tex]6 \frac {2} {3} = \frac {3 * 6 + 2} {3} = \frac {20} {3}[/tex]

Rewriting the expression we have:

[tex]\frac {\frac {15} {1}} {\frac {20} {3}} =[/tex]

Applying double C we have:

[tex]\frac {3 * 15} {20 * 1} =\\\frac {45} {20} =[/tex]

We simplify dividing by 5 the numerator and denominator:

[tex]\frac {9} {4}[/tex]

Converting to mixed number we have:

[tex]2 \frac {1} {4}[/tex]

Answer:

[tex]\frac {9} {4} = 2 \frac {1} {4}[/tex]

Answer:

B. The expected value of the sample mean is equal to the population mean.

Step-by-step explanation:

The expected value of the sample mean is equal to the population mean  is NOT a property of the sampling distribution of the sample.

This is about understanding properties of sampling distribution of sample mean.

Option A is not a Property of Sampling distribution of Sample mean.

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Answer: 0.07

Step-by-step explanation:

Given: Mean : [tex]\mu = 82[/tex]

Standard deviation : [tex]\sigma = 13[/tex]

The formula to calculate z is given by :-

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

For x= 80

[tex]z=\dfrac{80-82}{13}=−0.15384615384\approx-1.5[/tex]

The P Value =[tex]P(z<-1.5)=0.0668072\approx0.07[/tex]

Hence, the  probability that a randomly selected score was less than 80 =0.07

If a set [tex]A[/tex] contains [tex]n[/tex] elements, then the number of subsets of this set is [tex]|\mathcal{P}(A)|=2^n[/tex].

[tex]A=\{4,5,6\}\\|A|=3[/tex]

[tex]|\mathcal{P}(A)|=2^3=8[/tex]

Hello There!

[tex]\frac{5}{100}[/tex] written as a decimal is 0.05

Step #1     5/100 is the same thing as 5/5 over 100/5

Step #2 you have a quotient of 1/20

Step #3 divide 1 by 20 and you get a quotient of 0.05

In the given problem, 0.05 is the fraction [tex]\frac{5}{100}[/tex] written as a decimal.

A fraction is a mathematical expression that represents a part or a division of a whole. It is used to represent numbers that are not whole numbers or integers. A fraction consists of two components:

1. Numerator: The numerator is the number on the top of the fraction. It represents the quantity or part of the whole being considered.

2. Denominator: The denominator is the number at the bottom of the fraction. It represents the total number of equal parts into which the whole is divided.

To convert the fraction [tex]\frac{5}{100}[/tex] to a decimal, you can simply divide the numerator, 5 by the denominator, 100.

5 [tex]\div[/tex] 100 = 0.05.

Therefore, [tex]\frac{5}{100}[/tex] is equal to 0.05 as a decimal.

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Answer:

4/7 < 6/9. Hope this helps

The cost of toolset before the discount was applied is:

                    Rs.  521.5189

It is given that:

A tool set has been discounted down to a price of Rs 412.00.

The percent discount that is provided to us is: 21%

Let the actual price of toolset be: Rs. x

This means that:

[tex]x-21\%\ of x=412\\\\i.e.\\\\x-0.21x=412\\\\i.e.\\\\(1-0.21)x=412\\\\i.e.\\\\0.79x=412\\\\i.e.\\\\x=\dfrac{412}{0.79}\\\\x=521.5189[/tex]

   Hence, the actual price of toolset i.e. cost before discount is:

                        Rs.   521.5189

To find the original price of the toolset before the discount was applied, we can set up an equation and solve for the original price. The original price of the toolset was R520.89.

To find the original price of the toolbox, we need to first calculate the amount of the discount. The discount given is 21%. Let's say the original price of the toolbox is P. We can calculate the amount of the discount by multiplying the original price by the discount percentage:

Discount = P * 21% = P * 0.21

The discounted price is given as R412.00. So we can set up the equation:

Original price - Discount = Discounted price

P - P * 0.21 = R412.00

We can now solve for P:

P(1 - 0.21) = R412.00

0.79P = R412.00

P = R412.00 / 0.79

P = R520.89

Therefore, the original price of the toolset before the discount was applied was R520.89.

Answer: 4 units.

Step-by-step explanation:

Once each point is plotted, you get the rectangle attached.

You can observe in the figure that the base of the rectangle is its longer side.

 Since the length of the base of the rectangle goes from [tex]x=-1[/tex] to [tex]x=3[/tex], you can say that the lenght of the base is the difference between 3 and -1.

So, you need to subtract this two coordinates, getting that the lenght of the base of the rectangle attached is:

[tex]lenght_{(base)}=3-(-1)\\\\lenght_{(base)}=3+1\\\\lenght_{(base)}=4\ units[/tex]

Answer: 4 units

Step-by-step explanation:

Answer:

Max = 86; min = 36.54

Step-by-step explanation:

[tex]f(x) = x^{2} + \dfrac{85}{x}[/tex]

Step 1. Find the critical points.

(a) Take the derivative of the function.

[tex]f'(x) = 2x - \dfrac{85}{x^{2}}[/tex]

Set it to zero and solve.

[tex]\begin{array}{rcl}2x - \dfrac{85}{x^{2}} & = & 0\\\\2x^{3} - 85 & = & 0\\2x^{3} & = & 85\\\\x^{3} & = &\dfrac{85}{2}\\\\x & = & \sqrt [3]{\dfrac{85}{2}}\\\\& \approx & 3.490\\\end{array}\[/tex]

(b) Calculate ƒ(x) at the critical point.  

[tex]f(3.490) = 3.490^{2} + \dfrac{85}{3.490} = 12.18 + 24.36 = 36.54[/tex]

Step 2. Calculate ƒ(x) at the endpoints of the interval

[tex]f(1) = 1^{2} + \dfrac{85}{1} = 1 + 85 = 86\\\\f(5) = 5^{2} + \dfrac{85}{5} = 25 + 17 = 42[/tex]

Step 3.Identify the maxima and minima.

ƒ(x) achieves its absolute maximum of 86 at x = 1 and its absolute minimum of 36.54 at x = 3.490

The figure below shows the graph of ƒ(x) from x = 1 to x = 5.

The maximum and minimum values of the mathematical function f(x) = x^2 + 85/x on the interval [1, 5] occur at the endpoints with the maximum being 86 at x=1 and minimum being 37 at x=5.

To find the maximum and minimum values of the function f(x) = x2 + 85/x over the interval [1, 5], we first find the critical points in that interval. The critical points occur where the derivative of the function is zero or undefined. The derivative of the function f(x) is 2x - 85/x2 and it is undefined at x = 0 and becomes 0 at x = sqrt (42.5).

Since x = 0 is not in our interval, we disregard it. The value x = sqrt (42.5) is also outside our interval [1, 5], so we disregard this too.

Therefore, the maximum and minimum values of the function on the interval [1, 5] occur at the endpoints. We substitute these endpoint values into the function:

Therefore, the maximum value is 86 and the minimum value is 37, at x equals 1 and 5, respectively.

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Answer:

The last option is correct

Step-by-step explanation:

Hope this helps!

Answer:

[tex]\text{1) }0.1141814[/tex]

[tex]\text{2) }0.6193473[/tex]

[tex]\text{3) }0.2003702[/tex]

Step-by-step explanation:

[tex]\text{1) }P(-0.3203\leq Z \leq-0.0287)=P(Z\leq -0.0287)-P(Z\leq-0.3203)\\\\=0.4885519-0.3743705\\\\=0.1141814[/tex]

[tex]\text{2) }P( -0.5156 \leq Z \leq1.4215)=P(Z\leq 1.4215)-P(Z\leq -0.5156 )\\\\=0.9224142-0.3030669\\\\=0.6193473[/tex]

[tex]\text{3) }P(0.1269\leq Z \leq0.6772)=P(Z\leq 0.6772)-P(Z\leq-0.1269)\\\\=0.7508604- 0.5504902\\\\=0.2003702[/tex]

[tex]6\cdot7\cdot5=210[/tex]

210 days

Answer: A.

Step-by-step explanation:

Equation: V=lwh

5 × 10 × 15 = 750 cubic cm

The probability that both firms offer Peter a job is 6%.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

let X be the probability that Peter would receive offer from the accounting firm.

and, Y be the probability that Peter would receive offer from the consulting firm.

We have P(X) = 30% and P(Y) = 20%.

Now we want to find  P(X∪Y)  = ?

We know that

P(A∩B) = P(A) × P(B

             = 30% x 20%

             = 0.30 x 0.20

             = 0.06

             = 6%

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To find the probability that both an accounting firm and a consulting firm offer Peter a job, we multiply the individual probabilities of him receiving an offer from each firm. This results in a 6% chance that Peter will receive job offers from both firms.

The question asks about calculating the probability that Peter receives job offers from both an accounting firm and a consulting firm. Since the events are independent, the probability that both events occur is the product of their individual probabilities.

To compute the probability that both firms offer him a job, we multiply the probability of receiving an offer from the accounting firm (30%) by the probability of receiving an offer from the consulting firm (20%):

Probability(Both offers) = Probability(Accounting offer)  times Probability(Consulting offer)

Probability(Both offers) = 0.30  times 0.20

Probability(Both offers) = 0.06 or 6%

Therefore, the probability that both firms offer Peter a job is 6%.

The scale factor of this dilation is 2/3.

It is required to find  scale factor of this dilation.

Scale Factor is defined as the ratio of the size of the new image to the size of the old image.

In the figure showing 6 to 9 is 2/3 dilation and 10 to 15 is also a 2/3 dilation.

So, the scale factor of this dilation is 2/3.

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Option b is correct. The scale factor is [tex]1 \frac{1}{2}[/tex].

To determine the scale factor of the dilation from Triangle ABC to Triangle A'B'C', we need to compare the lengths of corresponding sides.

The side lengths of Triangle ABC are:

The side lengths of Triangle A'B'C' are:

The scale factor is calculated by dividing the lengths of the corresponding sides of the triangles. Let's use AB and A'B' for our calculation:

Scale Factor = A'B'/AB = 9/6 = 3/2 = 1 whole 1/2

Thus, the scale factor is [tex]1 \frac{1}{2}[/tex], which corresponds to option b.

Complete question:

What is the scale factor of this dilation? Triangle ABC to A'B'C'.

Triangle ABC with AB = 6, BC = 10, CA = 6

Triangle A'B'C' with A'B'= 9, B'C'= 15, C'A' =9

a. 2/3

b. [tex]1 \frac{1}{2}[/tex]

c. 3

d. 5

Answer:

[tex]y=x^2+2x-8[/tex]

Step-by-step explanation:

When you graph those points on a piece of graph paper it appears that the points are in the form of a positive x^2 parabola, which has the standard form

[tex]y=ax^2+bx+c[/tex]

We just need to solve for a, b, and c.  Easy.  We have 3 points from the table.  We will use all three of them to find the values of a, b, and c.

Use the points (0, -8), (2, 0), and (4, 16).  You can use any points, but I chose the one with an x value of 0 for a good reason, and chose the other 2 because I don't like too many negatives!

Use the first point in those above to solve for c:

[tex]-8=a(0)^2+b(0)+c[/tex]

From this you solve for c:  c = -8

Now use the next point along with the value of c to find another equation:

[tex]0=a(2)^2+b(2)-8[/tex] and

[tex]0=4a+2b-8[/tex] so

8 = 4a + 2b

That equation will be used again in a minute.

Use the last point to solve for yet another equation (stay with me...we are almost there!):

[tex]16=a(4)^2+b(4)-8[/tex] and

24 = 16a + 4b

Now we will use the method of elimination to solve for b:

8  =  4a  +  2b

24 = 16a + 4b

Multiply the first equation by -4 to eliminate the a terms:

-32 = -16a - 8b

24 = 16a + 4b

leaves you with

-4b = -8 and b = 2.  Now plug that back in to solve for a:

If 8 = 4a + 2b, then 8 = 4a + 2(2) and 8 = 4a + 4

4a = 4 and a = 1

Again, your equation is

[tex]y=x^2+2x-8[/tex]

Answer:

D. 1/2

Step-by-step explanation:

Coin tosses are independent.  Past results don't affect future probabilities.  So the probability of getting heads on the fourth toss is still 1/2.

Answer:

D. 1/2

Step-by-step explanation:

Flipping coin is an INDEPENDENT event, meaning that if you flip a coin before, it is NOT going to affect the outcome of the next coin flipping

Since a coin has 2 sides, so the probability is 1/2

Answer:

165 combinations possible

Step-by-step explanation:

This is a combination problem as opposed to a permutation, because the order in which we fill these positions is not important.  We are merely looking for how many ways each of these 11 people can be rearranged and matched up with different candidates, each in a different position each time.  The formula can be filled in as follows:

₁₁C₃ = [tex]\frac{11!}{3!(11-3)!}[/tex]

which simplifies to

₁₁C₃ = [tex]\frac{11*10*9*8!}{3*2*1(8!)}[/tex]

The factorial of 8 will cancel out in the numerator and the denominator, leaving you with

₁₁C₃ = [tex]\frac{990}{6}[/tex]

which is 165

Answer with explanation:

Let me answer this question by taking two decimals less than 1.

A= 0.50

B= 0.25

→A × B

= 0.50 × 0.25

=0.125

It is less than both A and B.

→→A=0.99

B= 0.1

→C=A × B

= 0.99 × 0.1

=0.099

It is less than both A and B.

So, We can say with surety, that if take two decimals ,both less than 1, the product of these two decimals will be  less than each of the original decimals.

General Rule

→A =0. p ,

→ B=0. 0 q,

Product of , A × B, gives a number in which  there will be three digits after decimal which will be always less than both A and B as in A, there is one digit after decimal, and in B there are two digits after decimal.

Answer:

{P|P < -3 or P > 3}

Step-by-step explanation:

When we remove the absolute value bars, we take the positive value, and then flip the inequality and take the negative.  Since the original equation is a greater than, we use the or

p > 3   or    p < -3

Answer:

[tex]\large\boxed{\{P\ |\ P<-3\ or\ P>3\}}[/tex]

Step-by-step explanation:

[tex]\text{The absolute value:}\\\\|a|=\left\{\begin{array}{ccc}a&for&a\geq0\\-a&for&a<0\end{array}\right[/tex]

[tex]|P|>3\iff P>3\ or\ P<-3[/tex]

Answer:

  1.94%

Step-by-step explanation:

The desired percentage can be found using an appropriate calculator or spreadsheet. A nice on-line calculator is shown in the attachment.

Answer:

[tex](x-4)^2+(y-3)^2+(x-5)^2=6[/tex]

Step-by-step explanation:

The the center of the sphere is given as (a,b,c) and the radius is r, then the equation of the sphere would be:

[tex](x-a)^2+(y-b)^2+(x-c)^2=r^2[/tex]

From the info, we can say:

a = 4

b = 3

c = 5

r = [tex]\sqrt{6}[/tex]

Plugging into formula we get the equation:

[tex](x-a)^2+(y-b)^2+(x-c)^2=r^2\\(x-4)^2+(y-3)^2+(x-5)^2=(\sqrt{6} )^{2} \\(x-4)^2+(y-3)^2+(x-5)^2=6[/tex]

Remember to use

Answer:

378.5 or just 378

Step-by-step explanation:

This is a linear model with x representing the number of generations that's gone by, y is the number of butterflies after x number of generations has gone by, and the 350 represents the number of butterflies initially (before any time has gone by.  When x = 0, y = 350 so that's the y-intercept of our equation.)

The form for a linear equation is y = mx + b, where m is the rate of change and b is the y-intercept, the initial amount when x = 0.

Our rate of change is 1.5 and the initial amount of butterflies is 350, so filling in the equation we get a model of y = 1.5x + 350.

If we want y when x = 19, plug 19 in for x and solve for y:

y = 1.5(19) + 350

y = 378.5

Since we can't have .5 of a butterfly we will round down to 378

Answer:

Assumption: [tex]f(x)[/tex] is defined for all [tex]x\in \mathbb{R}[/tex] (all real values of [tex]x[/tex].)

Step-by-step explanation:

Evaluating [tex]f(x)[/tex] for a root of this function shall give zero.

Equate [tex]f(x)[/tex] and zero [tex]0[/tex] to find the root(s) of [tex]f(x)[/tex].

[tex]f(x) =0[/tex].

[tex](x - 6) \cdot 2 \cdot (x + 2) \cdot 2 = 0[/tex].

Multiply both sides by 1/4:

[tex]\displaystyle (x - 6) \cdot (x + 2) = 0\times\frac{1}{4} = 0[/tex].

[tex]\displaystyle (x - 6) \cdot (x + 2) = 0[/tex].

This polynomial has two factors:

Apply the factor theorem:

Answer:

X=6 , X = -2

Step-by-step explanation:

For any polynomial given in factorised form , the roots are determined as explained below:

Suppose we have a polynomial

(x-m)(x-n)(x+p)(x-q)

The roots of above polynomial will be m,n,-p, and q

Also if we have same factors more than once , there will be duplicate roots.

Example

(x-m)^2(x-n)(x+p)^2

For above polynomial

There will be total 5 roots . Out of which 2(m and -p) of them will be repeated. x=m , x=n , x =-p

Hence in our problem

The roots of f(x)= (x-6)^2(x+2)^2 are

x=6 And x=-2

Answer:

y=131°

x=53°

Step-by-step explanation:

∠ ABD and ∠ BDC are supplementary.

The sum of the supplementary angles =180 °

thus y-4+x=180...........i

x and 37° are complementary, that  is, they add up to 90°

Thus, x=90-37=53°

Using this value in equation 1 we obtain:

y-4°+53° =180°

y= 180°-53°+4°

y=131°

Answer:

x  = 53°

y = 131°

Step-by-step explanation:

From the figure we can see a right angled triangle.

AB∥CD

To find the value of x and y

Consider the large triangle, by using angle sum property we can write,

90 + 37 + x = 180

127 + x = 180

x = 180 - 127

x  = 53°

Since AB∥CD and BD is a traversal on these parallel lines.

Therefore <ABD and < CDB are supplementary

we have x  = 53°,

x + (y - 4) = 180

53 + y - 4 = 180

y = 180 - 49 = 131°

y = 131°

Answer:  The mean and variance of the wavelength distribution for this radiation are 642.5 nm and 75 nm.

Step-by-step explanation:

The mean and variance of a continuous uniform distribution function with parameters m and n is given by :-

[tex]\text{Mean=}\dfrac{m+n}{2}\\\\\text{Variance}=\dfrac{(n-m)^2}{12}[/tex]

Given : [tex]m=625\ \ \ n=655[/tex]

[tex]\text{Then, Mean=}\dfrac{625+655}{2}=642.5\\\\\text{Variance}=\dfrac{(655-625)^2}{12}=75[/tex]

Hence, the mean and variance of the wavelength distribution for this radiation are 642.5 nm and 75 nm.

Answer:

x is less than three-fourths

x is less than 0.75

Step-by-step explanation:

First distribute the 3 on the right side of the equation.

-2x + 3 > 3(2x-1)

-2x + 3 > 6x -3

Then you transpose and combine like terms

-2x -6x > -3 - 3

-8x > -6

Divide both sides by -8, but if you will do this, you need to remember if you divide both sides by a negative number, you need to swap the inequality.

x < 3/4

x < 0.75

Answer:

x is less than three-fourths

x is less than 0.75

Step-by-step explanation:

Answer:

The probability of E and F is 0.367236 ≅ 0.367

Step-by-step explanation:

* Lets study the meaning independent probability  

- Two events are independent if the result of the second event is not

  affected by the result of the first event

- If A and B are independent events, the probability of both events  

 is the product of the probabilities of the both events

- P (A and B) = P(A) · P(B)

* Lets solve the question  

- There are two events E and F

- E and F are independent

- P(E) = 0.404

- P(F) = 0.909

∵ Events E and F are independent

- To find P(E and F) find the product of P(E) and P(F)

∴ P (E and F) = P(E) · P(F)

∵ P(E) = 0.404

∵ P(F) = 0.909

∴ P(E and F) = (0.404) · (0.909) = 0.367236 ≅ 0.367

* The probability of E and F is 0.367236 ≅ 0.367

the probability that both event E and event F occur is 0.36.

When dealing with independent events, the probability of both events E and F occurring, denoted as P(E and F), is determined by multiplying the probability of event E by the probability of event F. In this case, since P(E)=0.4 and P(F)=0.9 and the events are independent, you calculate P(E and F) as follows:

P(E and F) = P(E)  × P(F) = 0.4 × 0.9 = 0.36.

Therefore, the probability that both event E and event F occur is 0.36.