Two previously undeformed cylindrical specimens of an alloy are to be strain hardened by reducing their cross-sectional areas (while maintaining their circular cross sections). For one specimen, the initial and deformed radii are 15 and 12 mm, respectively. The second specimen, with an initial radius of 11 mm, must have the same deformed hardness as the first specimen; compute the second specimen’s radius after deformation.

Answer:

252 candies

Step-by-step explanation:

Let A = 8x

Let B = 5x

Let C = 10x

10x = 8x + 24         Subtract 8x from both sides

10x - 8x = 24          Do the subtraction

2x = 24                   Divide by 2

2x/2 = 24/2            Do the division

x = 12

So Adrian has 8*12 = 96 candies.

Ben has 5 * 12 =         60 candies

Charlie has 10*12 =    120 candies

Total                      =  276 candies

The total number of sweets shared by Adrian, Ben, and Charlie is 276,

To solve how many sweets were shared by Adrian, Ben, and Charlie, with the given ratio of 8:5:10 and knowing Charlie got 24 more sweets than Adrian, we can set up a ratio problem. Let the ratio part be 'x', so Adrian has 8x sweets, Ben has 5x sweets, and Charlie has 10x sweets. As Charlie got 24 more sweets than Adrian, we can write the equation 10x = 8x + 24. Solving this equation for 'x' gives us x = 12. Thus, Adrian has 96 sweets (8 x 12), Ben has 60 sweets (5 x 12), and Charlie has 120 sweets (10 x 12). Adding these together gives us a total of 276 sweets.

The point estimates for the mean and standard deviation of the given data set is respectively; 68 and 17.6.

What is a point Estimate?

A) In order to find the point estimate of the mean, we will add up the data and divide it by the number of values.

Here,

∑x = 57 + 61 + 86 + 74 + 72 + 73 + 20 + 57 + 80 + 79 + 83 + 74

    = 816

n = 12 numbers

Thus;

Mean = ∑x/n

         = 816/12

Mean = 68

B) In order to find the estimate of the standard deviation, we have the formula;

s = √[(n*(∑x²) - (∑x)²)/n(n - 1)]

∑x² = 57² + 61² + 86² + ... + 74²

     = 59,010

s = √[ (12*(59,010) - (816)²)/(12)(11)]

s = 17.6

Hence, The point estimates for the mean and standard deviation of the given data set is respectively; 68 and 17.6.

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If both Bob and Fred make $20 less a week than twice John's weekly salary, then

[tex]B+F+20 = 2*J[/tex],

where B, F, and J are Bob's, Fred's, and John's salaries, respectively.

We want to find F, Fred's salary. Plugging in Bob's and John's salaries, we obtain

[tex]140+F+20 = 2*110[/tex]

[tex]F+160 = 220[/tex]

[tex]F = 60[/tex]

So Fred makes $60 a week.

Answer:

Fred makes $60/week.

Step-by-step explanation:

Fred makes f dollars per week, john j dollars and bob b dollars.

Then b = $140/week; j = $110/week; and b + f = 2j - 20.

Substitute $140/week for b in this equation; also substitute $110/week for j.  Then:  

    $140/week + f = 2($110) - $20.  There's only one variable here, f, so we're ready to solve for f:

    $140/week + f = $220/week - $20/week,   or:

     $140/week + f = $200/week

Subtract $140 from both sides, obtaining:

f = $60

Fred makes $60/week.

To find the distance between two points on a coordinate system, we can use the distance formula, which is derived from the Pythagorean theorem.

To find the distance between two points on a coordinate system, we can use the distance formula. The distance formula is derived from the Pythagorean theorem and is given by:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Using the given points (-3,4) and (8,-7), we can plug in the coordinates into the formula:

d = sqrt((8 - (-3))^2 + (-7 - 4)^2)

Simplifying the equation, we get:

d = sqrt(11^2 + (-11)^2)

Finally, calculating the square root, we find that the distance between the two points is sqrt(242), which is approximately 15.56 units.

Thus, the distance on the coordinate system from the point (-3,4)to the point (8,-7) is fond to be 15.56 units.

Answer:

20 ft out from the wall by 40 ft parallel to the wall

Step-by-step explanation:

Let x represent the length of fence in the direction parallel to the wall. Then the other dimension of the rectangular pen is (80 -x)/2. The area is the product of these dimensions:

area = x(80 -x)/2

This function describes a downward-opening parabola with zeros at x=0 and x=80. The vertex (maximum) is halfway between the zeros, at x=40.

The dimensions are 40 ft parallel to the wall and 20 ft out from the wall.

Length l=40 and Breadth b=20 will maximize the area of the pen.

let us take 'l' as the length of the rectangular pen.

'b' as the width of the rectangular pen.

let us assume that the barn will be built opposite to length.

so, according to the given condition

l +b+b=80

l+2b=80......(1)

area of the rectangular pen = lb= (80-2b)b

f(b)= (80-2b)b.......(2)

to get local maxima, differentiate the function and equate to zero, get the point say it 'x'

again check double derivative if its value is negative the point 'x' will give the maximum value of the function.

to maximize the area

let us derivate the f(b)= (80-2b)b

f'(b)= 80-4b=0

b=20

f"(b)= -4(-ve)

means we will have local maxima at b=20

it means at b=20, we will get maximum area.

l = 80-2b=80-2*20=40

therefore, l=40 and b=20 will maximize the area of the pen.

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The probability of rolling either a 3 or a 5 on a six-sided die is 1/3, or about 0.3333, as there are two favorable outcomes (3 or 5) and six possible outcomes in total.

The question asks to find the probability of rolling either a 3 or a 5 when a fair six-sided die is rolled. The sample space for a six-sided die is {1, 2, 3, 4, 5, 6}. To calculate the probability of rolling either a 3 or a 5, we need to count the favorable outcomes, which are 2 (rolling a 3 and rolling a 5), and divide this by the total number of possible outcomes, which is 6.

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability (rolling a 3 or 5) = 2 / 6 = 1 / 3.

Therefore, the probability of rolling either a 3 or a 5 on a six-sided die is 1/3, or approximately 0.3333.

Answer:

c. {(4, -12)}

Step-by-step explanation:

It is convenient to rearrange the equation to standard form:

5x +y = 8

Then check the offered points.

(6, -11): 5·6 -11 = 19 ≠ 8

(4, -12): 5·4 -12 = 8 . . . . . . this is in the solution set

(5, -9): 5·5 -9 = 16 ≠ 8

(3, -14): 5·3 -14 = 1 ≠ 8

To find the solution set, substitute the x and y values into the equation and check if it is true.

To find the solution set for the equation, we need to check which coordinates from the replacement set satisfy the equation y = -5x + 8.

The solution set for the equation, given the replacement set, is {(3, -14)}.

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Answer:

  3.5 years

Step-by-step explanation:

Each year, Louis earned

  $1500×0.035 = $52.50

in interest.

The amount of interest that had been credited to his account at the time of withdrawal was ...

  $1683.75 -1500.00 = $183.75

Then the length of time the money had been in the account was ...

  $183.75/($52.50/yr) = 3.5 yr

_____

Comment on the problem

We have assumed the account earned simple interest. Given the neatness of the answer, we believe that to be a correct assumption.

Answer:

  $58.75

Step-by-step explanation:

The monthly interest rate is 8.4%/12 = 0.7%, so the first month's interest is ...

  $95,000×0.007 = $665

The amount of the first payment that goes to note reduction is the part that does not go for paying interest. That difference is ...

  $723.75 - 665.00 = $58.75

Answer:$58.75

Step-by-step explanation:

The p-value is 0.0768. Since the p-value is less than the significance level of 0.05, we reject the null hypothesis.

- Decision regarding H0: Reject H0

- p-value: 0.0768.

The null hypothesis (H0) states that the mean waiting time is 3 minutes or more, while the alternate hypothesis (H1) states that the mean waiting time is less than 3 minutes.

- Null hypothesis (H0): μ ≥ 3

- Alternate hypothesis (H1): μ < 3

The decision rule is to reject H0 if the test statistic (z-score) is less than -1.645.

To compute the test statistic (z-score), we use the formula:

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

Where:

- [tex]\(\bar{x}\)[/tex] is the sample mean waiting time (2.75 minutes)

- [tex]\(\mu\)[/tex] is the population mean waiting time (3 minutes)

- [tex]\(\sigma\)[/tex] is the population standard deviation (1 minute)

- [tex]\(n\)[/tex] is the sample size (50)

Substituting the given values:

[tex]\[ z = \frac{{2.75 - 3}}{{\frac{1}{\sqrt{50}}}} \][/tex]

[tex]\[ z = \frac{{-0.25}}{{0.1414}} \][/tex]

[tex]\[ z ≈ -1.768 \][/tex]

Since -1.768 is less than -1.645, we reject the null hypothesis.

To find the p-value, we look up the z-score (-1.768) in the standard normal distribution table. The corresponding area to the left of -1.768 is approximately 0.0384. Since this is a one-tailed test, we multiply by 2 to get the total probability of both tails:

[tex]\[ p-value ≈ 2 \times 0.0384 = 0.0768 \][/tex]

Thus, the p-value is 0.0768. Since the p-value is less than the significance level of 0.05, we reject the null hypothesis.

Complete questions:

The waiting time for customers at MacBurger Restaurants follows a normal distribution with a population standard deviation of 1 minute. At the Warren Road MacBurger, the quality-assurance department sampled 50 customers and found that the mean waiting time was 2.75 minutes. At the 0.05 significance level, can we conclude that the mean waiting time is less than 3 minutes? State the null hypothesis and the alternate hypothesis. State whether the decision rule is true or false: Reject H0 if z < −1.645. True False Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) What is your decision regarding H0? Reject H0 Do not reject H0 What is the p-value? (Round your answer to 4 decimal places.)

Answer:

Already in standard form

Step-by-step explanation:

-4y=10

-4y= by

10= c

And in this case ax=0x, so it will not show up in the equation

0x-4y=10, which is already in standward form

-4y=10 divide both sides by -2, so 2y=5 subtract 5 from both sides,

2y-5=0

let's say "x" is the whole lot and thus the 100%.

we know 12 is 60%, how much is "x" or 100%?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 12&60 \end{array}\implies \cfrac{x}{12}=\cfrac{100}{60}\implies \cfrac{x}{12}=\cfrac{5}{3} \\\\\\ 3x=60\implies x=\cfrac{60}{3}\implies x=20[/tex]

Answer:

(B) is the homogeneous mixture

Step 4

The numerator of this fraction is right because there are 5 shaded sections, but the denominator is incorrect because there are 6 total boxes, not 5.

Hope this helps!!

Answer:

the answer is C step 3

Step-by-step explanation:

because out side the box said 1/2 when its 3/6 and the question sais

In which step did her first error occur? so thats the firt the second one

its 1/3 when its 2/6. Hope it helps :)

Answer:

-9⃣ = t

Step-by-step explanation:

You know that 6 - ? = -12, so just simply deduct six from both sides, leaving you with -18 = 2t; -9⃣ = t.

Answer:

  y = 2.5(x +4)(x -1.5) = 2.5x^2 +6.25x -15

Step-by-step explanation:

Each given zero corresponds to a factor that is zero at that point. Those factors are (x +4) and (x -1.5).

The y-intercept tells us the scale factor, the multiplier that is needed to make the function value be -15 at x=0.

  y = a(x +4)(x -1.5) = a(0 +4)(0-1.5) = -6a

  -15 = -6a

  -15/-6 = a = 2.5

So, the quadratic is ...

  y = 2.5(x +4)(x -1.5) = 2.5x^2 +6.25x -15

___

"The equation" can be written in many different forms. The simplest, given the information here, is the factored form (also called "intercept form"). We have also shown "standard form" (US version). The "standard form" (UK version) is also known as vertex form:

  y = 2.5(x +1.25)^2 -18.90625

Answer:

  x ∈ {-26, 22}

Step-by-step explanation:

A graph shows that the points (-26, -27) and (22, -27) lie on a circle of radius 40 centered at (-2, 5). That is, if Q is either one of these points, the vector PQ will have a length of 40:

You can call it -40 if you like, but you have to define what negative length means when you do that.

Explanation:

Multiply it out, collect terms, and look for a factor of 7:

  n(n +2) -(n -7)(n -5) = n² +2n -(n² -12n +35)

  = 14n -35

  = 7(2n -5)

The expression has a factor of 7, so is divisible by 7 with a resulting quotient of 2n-5.

Answer:

  AB = (2 +2√3)r

Step-by-step explanation:

Let X be the point of tangency of circle O3 and AB. Then length XO3 is r. The triangle BXO3 is a 30°-60°-90° right triangle. You know this because BO3 bisects the 60° angle at B of the equilateral triangle ABC.

A 30°-60°-90° triangle has side lengths in the ratios 1 : √3 : 2. That means side XB of triangle BXO3 has length r√3. The distance from A to the point of tangency of AB with circle O1 has the same measure.

Of course the distance between those points of tangency is the same measure as the distance between centers O3 and O1: 2r. So, the total length of AB is ...

  AB = r√3 + 2r + r√3

  AB = (2 +2√3)r

For this case we have the following inequality:[tex]d> 11[/tex]

Assuming that "d" is the variable that represents the number of hours worked by Mo during this week, we have that the hours were greater than 11, according to the inequality sign.

So, the correct option is:

Mo worked more than 11 hours this week.

Answer:

Option A

Answer: a

Step-by-step explanation:

Area of rectangles = Length x width.

Area of triangles = 1/2 x base x height.

1 face is 12 x 10 = 120 square units

1 face is 12 x 8 = 96 square units

1 face is 12 x 6 = 72 square units

And 2 faces are 1/2 x 8 x 6  = 24 square units

Answers are 24 , 72 and 96 square units.

Answer:

A.24 Square units

C.72 Square units

D.96 Square units

Step-by-step explanation:

I got it right edge 2020.

Answer:

• g(1) = 25

• g(n) = g(n-1) -49

Step-by-step explanation:

You can get a clue by filling in n=2 in the explicit formula:

g(2) = 25 -49(2-1) = 25 -49 = g(1) -49

The explicit formula is of the form for an arithmetic sequence:

g(n) = g(1) +d(n-1) . . . . where g(1) is the first term and d is the common difference

Of course, this translates to the recursive formula ...

• g(1) = g(1)

• g(n) = g(n-1) +d

Here you have g(1) = 25, and d = -49. Filling these into the recursive form, you get ...

• g(1) = 25

• g(n) = g(n-1) -49

Answer:

• g(1) = 25

• g(n) = g(n-1) -49

Step-by-step explanation:

You can get a clue by filling in n=2 in the explicit formula:

g(2) = 25 -49(2-1) = 25 -49 = g(1) -49

The explicit formula is of the form for an arithmetic sequence:

g(n) = g(1) +d(n-1) . . . . where g(1) is the first term and d is the common difference

Of course, this translates to the recursive formula ...

• g(1) = g(1)

• g(n) = g(n-1) +d

Here you have g(1) = 25, and d = -49. Filling these into the recursive form, you get ...

• g(1) = 25

• g(n) = g(n-1) -49

Answer:

If what you are doing here is trying to get the value of x then:

Those two lines passing through the circle are secants.

Now, a formula I was taught in class is:

(outside)(whole) = (outside)(whole)

**1 SEGMENT'S VALUES PER SIDE** **DO NOT MIX**

"Outside" represents the value of the segment which is found outside of the circle.

The "whole" would be the outside segment plus the inside segment.

Thus, the formula would be:

(4)(9+4) = (x)(x + 12)

Next, you would simplify by adding, multiplying, and doing the distributive property:

(4)(13) = (x)(x + 12)

52 = x² + 12x

In this case, you would have to use the quadratic formula, while at other times, you could simply move around the terms and get the square root of a number.

Set the equation to zero:

x² + 12x - 52 = 0

Next plug-in the values

(-b (+ or -)√b² - 4 (a)(c) )/ (2)(a)

(-(12) (+ or - )√12² - 4(1)(-52)) / (2)(1)

(-12 (+ or -) √144 + 208) / 2

(-12 (+ or -) √352) / 2

Now, the square root of 352 would be approximate, since 352 is not a perfect square.

352 is approximately 18.7616630393 or, when rounded to the nearest hundredth, 18.76.

So.....

(-12 (+ or -) 18.76) / 2

Solve for both the + and the -

(-12 + 18.76) /2 = (approximately) 3.38 = x

(-12 - 18.76)/2 = (approximately) -15.38 = x

Therefore, x would be equal to 3.

Answer:

x2+3

Step-by-step explanation:

The selected value is 3 units up from g (x), the correct option is C.

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

Linear function is a function whose graph is a straight line

We are given that;

g(x) = x2 + 3.

f(x) = g(x+2)

Now,

Using these rules, we can fill in the blanks as follows:

The function g(x)+3. The function f(x) = g(x+2),

The function /(x) is shifted horizontally

Select a Value

2 units left from g (x).

The function /(x)is shifted vertically

Select a Value

3 units up from g (x).

Therefore, the answer of the function will be 3 units up from g (x).

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Answer:

no solutions

Step-by-step explanation:

-2x+3y=8

 2x-3y=10

We can use elimination to solve for x and y

Add the two equations together

-2x+3y=8

 2x-3y=10

---------------------

0 = 18

Since this is never true, there are no solutions to this system of equations

Answer:

f(x) = 9(x -1/3)^2 -3

Step-by-step explanation:

In vertex form the equation of a quadratic with vertical scale factor "a" and vertex (h, k) is ...

y = a(x -h)^2 +k

To make the equation have (1, 1) as a solution, we need to find the value of "a". We can put the point coordinates in the equation and solve for "a":

1 = a(1 -1/3)^2 -3 . . . . . for (h, k) = (1/3, -3) as given

1 = (4/9)a -3 . . . . simplify

4 = (4/9)a . . . . . . add 3

9 = a . . . . . . . . . . multiply by 9/4

The quadratic function you desire is ...

f(x) = 9(x -1/3)^2 -3

Answer:

A. 5,2

Step-by-step explanation:

Coefficients are numbers with a variable next to it (ex. 5 in 5x^2).

For this case we have the following equation:

[tex]x ^ 3 = 375[/tex]

We must find the value of "x":

We apply cube root on both sides of the equation to eliminate the exponent:

[tex]x = \sqrt [3] {375}[/tex]

We can write 375 as [tex]5 ^ 3 * 3[/tex]

So:

[tex]x = \sqrt [3] {5 ^ 3 * 3}\\x = 5 \sqrt [3] {3}[/tex]

Then, the correct options are:

[tex]x = \sqrt [3] {375}\\x = 5 \sqrt [3] {3}[/tex]

Answer:

Option A and B

Answer:

9

Step-by-step explanation:

If n is the number of tablets, the maximum value it can have is given by ...

0.25n = 2.25

Dividing by the coefficient of n gives ...

n = 2.25/0.25 = 9

The patient can take a total of 9 tablets through the day.

Answer:

The answer is 2:9

Step-by-step explanation:

On plato

Find the ratio of the bases: 15 in / 5 in = 3

The triangle on the right side is 3 times larger.

X = 8 * 3

x = 24 inches.