The fracture toughness (in ) of a particular steel alloy is known to be normally distributed with a mean of 28.3 and a standard deviation of 0.77. We select one sample of this alloy at random and measure its fracture toughness. Given that the fracture toughness is at least 27, what is the probability that the fracture toughness will be between 29 and 40.3? is it just P(X <= 40.3) - P(X <= 29)? How do I use the 27?

Answers

Answer 1

This is a conditional probability question.

The conditional probability is given as follows: The probability of an event A given B is given by

[tex]P(A|B)= \frac{P(A\cap B)}{P(B)} [/tex]

Thus, given that the fracture toughness of a particular steel alloy is known to be normally distributed with a mean of 28.3 and a standard deviation of 0.77.

The probability that the fracture toughness will be between 29 and 40.3 given that the fracture toughness is at least 27 is given by

[tex]P(29 \leq X \leq 40.3 \, | \, X \geq 27)= \frac{P(29 \leq X \leq 40.3)\cap P(X \geq 27)}{P(X \geq 27)} \\ \\ =\frac{P(29 \leq X \leq 40.3)}{P(X \geq 27)}[/tex]

[tex]P(29 \leq X \leq 40.3)=P\left(z \ \textless \ \frac{40.3-28.3}{0.77}\right)- P\left(z \ \textless \ \frac{29-28.3}{0.77}\right) \\ \\ =P(z\ \textless \ 15.58)-P(z\ \textless \ 0.91)=1-0.81835=0.18165[/tex]

[tex]P(X \geq 27)=1-P(x\ \textless \ 27) \\ \\ =1-P\left(z\ \textless \ \frac{27-28.3}{0.77}\right)=1-P(z\ \textless \ -1.688) \\ \\ =1-0.04568=0.95432[/tex]

Thus, the probability that the fracture toughness will be between 29 and 40.3 given that the fracture toughness is at least 27 is given by

[tex]\frac{P(29 \leq X \leq 40.3)}{P(X \geq 27)}= \frac{0.18165}{0.95432} =\bold{0.1903}[/tex]

Related Questions

Use compatible numbers to estimate the quotient 5821/71?

Answers

Divide 5821 by 71

Round the number to the nearest hundred

5821 ÷ 71 → 5800 ÷ 70

Calculate mentally.

58 ÷ 7=8.2

Estimated quotient = 8

HELP WILL GIVE HIGHEST RATING!!!
36 POINTS TO CORRECT ANSWER Cindy has 26 nickels. She is getting rolls of nickels from the bank. She has enough money to get up to 10 rolls of nickels and each roll contains 40 nickels. The bank will not give partial rolls. The function that models the number of nickels Cindy will have after leaving the bank is f(r)=40r+26, where r is the number of rolls of nickels she gets. What is the practical domain of the function?

Answers

the practical domain would be the number of rolls she can get which is between 0 and 10

Answer:

The answer is all integers from 1 to 10, inclusive

Bye~~

Jessica's lab is 12 times as long as her hamster. Her hamster is 4.16 inches long. How long is her lab?

Answers

This is easy! You just have to multiply 12 by 4.16. And 12*4.16= 49.92. Which means Jessica's lab is 49.92 inches long.

Key words - times

all you have to do is multiply 4.16 by 12, which is
49.92

Jessica's lab is 49.92 inches long

i hope this helps!!

Chad bought a box of raisins. he gave 1/6 of it to one brother, 1/4 to another brother, and he kept the rest for himself. what fraction did he keep?

Answers

Greetings!

This can be solved by creating a simple equation.
[tex]1/4+1/6+x=1[/tex]

Solve for x.
[tex]1/4+1/6+x=1[/tex]
Find the LCM.
[tex]3/12+2/12+x=1[/tex]
[tex]5/12+x=1[/tex]
Add -5/12 to both sides.
[tex](5/12+x)+(-5/12)=(1)+(-5/12)[/tex]
Simplify.
[tex]x=1/1-5/12[/tex]
Find the LCM.
[tex]x=12/12-5/12[/tex]
[tex]x=7/12[/tex]

He kept 7/12 of the raisins for himself.

Hope this helps.
-Benjamin

Find the probability that the person is frequently or occasionally involved in charity work.

Answers

Given the table below which shows the result of a survey that asked 2,881 people whether they are involved in any type of charity work.

[tex]\begin{tabular} {|c|c|c|c|c|c|} &Frequently&Occassionally&Not at all&Total\\[1ex] Male&227&454&798&1,479\\ Female &205&450&747&1,402\\ Total&432&904&1,545&2,881 \end{tabular}[/tex]

Part A:

If a person is chosen at random, the probability that the person is frequently or occassinally involved in charity work is given by

[tex]P(being \ frequently \ involved \ or \ being \ occassionally \ involved)\\ \\= \frac{432}{2881} + \frac{904}{2881} = \frac{1336}{2881}=\bold{0.464}[/tex]

Part B:

If a person is chosen at random, the probability that the person is female or not involved in charity work at all is given by

[tex]P(being \ female \ or \ not \ being \ involved)\\ \\= \frac{1402}{2881} + \frac{1545}{2881}-\frac{747}{2881} = \frac{2200}{2881}=\bold{0.764}[/tex]

Part C:

If a person is chosen at random, the probability that the person is male or frequently involved in charity work is given by

[tex]P(being \ male \ or \ being \ frequently \ involved)\\ \\= \frac{1479}{2881} + \frac{432}{2881}-\frac{227}{2881} = \frac{1684}{2881}=\bold{0.585}[/tex]

Part D:

If a person is chosen at random, the probability that the person is female or not frequently involved in charity work is given by

[tex]P(being \ female \ or \ not \ being \ frequently \ involved)\\ \\= \frac{1402}{2881} + \frac{904}{2881} + \frac{1545}{2881}-\frac{450}{2881}-\frac{747}{2881} = \frac{2654}{2881}=\bold{0.921}[/tex]

Part E:

The events "being female" and "being frequently involved in charity work" are not mutually exclusive because being a female does not prevent a person from being frequently involved in charity work.

Indeed from the table, there are 205 females who are frequently involved in charity work.

Therefore, the answer to the question is "No, because 205 females are frequently involved charity work".

(a) The probability is [tex]\[\boxed{0.464}\][/tex]. (b) The probability is [tex]\[\boxed{0.763}\][/tex]. (c) The probability is [tex]\[\boxed{0.585}\][/tex]. (d) The probability is [tex]\[\boxed{0.921}\][/tex]. (e) No, because 205 females are frequently involved in charity work. The option (A) is correct.

To address the given questions based on the provided table, let's go through each question step-by-step:

(a) Find the probability that the person is frequently or occasionally involved in charity work.

First, we need the total number of people who are frequently or occasionally involved in charity work. This is the sum of people in the "Frequently" and "Occasionally" columns.

[tex]\[\text{Total frequently or occasionally involved} = 432 + 904 = 1336\][/tex]

Now, we divide this by the total number of people surveyed:

[tex]\[P(\text{frequently or occasionally involved}) = \frac{1336}{2881} \approx 0.464\][/tex]

So, the probability is [tex]\[\boxed{0.464}\][/tex].

(b) Find the probability that the person is female or not involved in charity work at all.

To solve this, we need to find the number of females and those not involved in charity work at all.

[tex]\[\text{Total females} = 1402\][/tex]

[tex]\[\text{Total not involved at all} = 1545\][/tex]

We need to subtract the overlap (females not involved in charity work) to avoid double-counting. From the table, the number of females not involved at all is 747.

[tex]P(\text{female or not involved at all}) = \frac{\text{Total females} + \text{Total not involved at all} - \text{Females not involved}}{\text{Total}}[/tex]

[tex]= \frac{1402 + 1545 - 747}{2881} = \frac{2200}{2881} \approx 0.763[/tex]

So, the probability is [tex]\[\boxed{0.763}\][/tex].

[tex]\[\text{Total males} = 1479\][/tex]

[tex]\[\text{Total frequently involved} = 432\][/tex]

We need to subtract the overlap (males frequently involved) to avoid double-counting. From the table, the number of males frequently involved is 227.

[tex]P(\text{male or frequently involved}) = \frac{\text{Total males} + \text{Total frequently involved} - \text{Males frequently involved}}{\text{Total}}[/tex]

[tex]= \frac{1479 + 432 - 227}{2881} = \frac{1684}{2881} \approx 0.585[/tex]

So, the probability is [tex]\[\boxed{0.585}\][/tex].

(d) Find the probability that the person is female or not frequently involved in charity work.

[tex]\[\text{Total females} = 1402\][/tex]

[tex]\[\text{Total not frequently involved} = 2881 - 432 = 2449\][/tex]

We need to subtract the overlap (females not frequently involved) to avoid double-counting. From the table, the number of females not frequently involved is 1197 (450 + 747).

[tex]P(\text{female or not frequently involved})=\frac{1402 + 2449 - 1197}{2881} = \frac{2654}{2881} \approx 0.921[/tex]

So, the probability is [tex]\[\boxed{0.921}\][/tex].

(e) Are the events "being female" and "being frequently involved in charity work" mutually exclusive?

Two events are mutually exclusive if they cannot occur at the same time.

From the table, 205 females are frequently involved in charity work.

Since there are females who are frequently involved in charity work, the events "being female" and "being frequently involved in charity work" are not mutually exclusive.

So, the answer is A. No, because 205 females are frequently involved in charity work.

The complete question is:

The table below shows the results of a survey that asked 2881 people whether they are involved in any type of charity work. A per selected at random from the sample. Complete parts (a) through (e).

(a) Find the probability that the person is frequently or occasionally involved in charity work.

P(being frequently involved or being occasionally involved) - (Round to the nearest thousandth as needed.)

(b) Find the probability that the person is female or not involved in charity work at all.

P(being female or not being involved) (Round to the nearest thousandth as needed.)

P(being male or being frequently involved) (Round to the nearest thousandth as needed.)

P(being male or being frequently involved) - (Round to the nearest thousandth as needed.)

(d) Find the probability that the person is female or not frequently involved in charity work.

P(being female or not being frequently involved) = (Round to the nearest thousandth as needed.)

(e) Are the events "being female" and "being frequently involved in charity work" mutually exclusive? Explain.

A. No, because 205 females are frequently involved in charity work.

B. Yes, because no females are frequently involved in charity work.

C. Yes, because 205 females are frequently involved in charity work.

D. No, because no females are frequently involved in charity work.

Solve for x.

x−1/4=38

Enter your simplified answer in the box.

Answers

Simplified answer is 5/8. This is how it has been solved:

1. x - 1/4 = 3/8;
2. x = 1/4 + 3/8;
3. x = 2/8 + 3/8;
4. x = 5/8;

Hope everything is clear.

a cylinder has a volume of 83 in3 and is 10 in. tall what is the radius of the cylinder in inches use 3.14 and round to the nearest 10th

Answers

check the picture below.

Which coin have a diameter with a 5 in a hundredths place

Answers

in inches it would be a quarter and a penny

Althea traveled 280 miles at a speed of 70 miles/hour. How much time did she take to cover this distance?

Answers

D = rt; r = t/d; t = d/r

t = d/r
t = 280/70
t = 4 hours

brian irons 2/9 of his shirt in 3 3/5 minutes. how much of his shirt does he iron each minute

Answers

[tex]\bf \begin{array}{ccll} shirt&minutes\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ \frac{2}{9}&3\frac{3}{5}\\\\ s&1 \end{array}\implies \cfrac{\frac{2}{9}}{s}=\cfrac{3\frac{3}{5}}{1}\implies \cfrac{\frac{2}{9}}{\frac{s}{1}}=\cfrac{\frac{3\cdot 5+3}{5}}{\frac{1}{1}}\implies \cfrac{2}{9}\cdot \cfrac{1}{s}=\cfrac{\frac{18}{5}}{\frac{1}{1}} \\\\\\ \cfrac{2}{9s}=\cfrac{18}{5}\implies 10=162s\implies \cfrac{10}{162}=s\implies \cfrac{5}{81}=s[/tex]

Consider the solid s described below. the base of s is the region enclosed by the parabola y = 5 - 5x2 and the x-axis. cross-sections perpendicular to the x-axis are isosceles triangles with height equal to the base. find the volume v of this solid.

Answers

Final answer:

To find the volume of the solid described, we can use the formula for the volume of a cylinder and integrate the cross-sectional area. The cross-sectional area is the base of the solid, and in this case, it is given by (25 - 50x^2 + 25x^4).

Explanation:

The solid described in the question has a base in the shape of the region enclosed by the parabola y = 5 - 5x^2 and the x-axis. The cross-sections perpendicular to the x-axis are isosceles triangles with a height equal to the base.

To find the volume of the solid, we can use the formula for the volume of a cylinder. The cross-sectional area of each triangle is the base times the height, and the height of the triangle is also the base. So, the cross-sectional area is A = (5 - 5x^2)(5 - 5x^2) = (25 - 50x^2 + 25x^4).

The volume of the solid is then given by integrating the cross-sectional area from the x-values that define the base of the solid. So, V = ∫(25 - 50x^2 + 25x^4)dx.

0.00000002 in scientific notation

Answers

Your answer is: 2⋅10^−8

Please mark Brainliest!

2*10^-8

I'm pretty sure that's right

The sum of three consecutive integers is 267. What is the largest integer?

Answers

middle number = 267 / 3 = 89

88 + 89 +90 = 267

largest number = 90

Find then selling price per liter of a mixture made from 70 L of cranberry juice which cost $1.20 per liter and 130 L of apple juice which cost $0.80 per liter

Answers

[tex]\bf \begin{array}{lccclll} &\stackrel{liters}{amount}&\stackrel{\$/liter}{price}&\stackrel{total}{cost}\\ &------&------&------\\ Cranberry&70&1.20&84\\ Apple&130&0.80&104\\ ------&------&------&------\\ mixture&200&&188 \end{array}\\\\ -------------------------------\\\\ \cfrac{\stackrel{\$}{188}}{\stackrel{liters}{200}}\implies \cfrac{47}{50}\approx 0.94\frac{\$}{liter}[/tex]

a cell phone company charges a monthly fee of $0.25 for each text. message the monthly fee is $30.00 and you owe $59.50. how many text messages did you have

Answers

now, the cell company charges a monthly usually for network access and routing to the device, this company charges 30 bucks monthly for it.

after that, you pay for the txt messages you use, the more you use, the more you pay, in this case is 25 cents for each.

so if you use say hmm 100 txt messages, then you owe for a month 30 + 0.25(100)

and if you use "x" txt messages, then you owe 30 + 0.25x.

[tex]\bf \stackrel{cost}{y}=\stackrel{monthly~fee}{30}+\stackrel{txt~charges}{0.25x}\implies 59.50=30+0.25x \\\\\\ 29.5=0.25x\implies \cfrac{29.5}{0.25}=x\implies 118=x[/tex]

WILL GIVE BRAINEST
which description matches the function that represents by the values in this table?

Answers

D. exponential growth

Hiya :)

d. exponential growth

Have a great day!!!

Hope this helped!!

:)))))

4- T = 3 (T-1)-5

A. 3
B. 6
C. No solution
D. Identity

If you can explain this to me I would really love that.

Answers

First lets expand it
next we subtract 3T - 3 - 5 so it can be 3T - 8
next we add T to both sides
next we subtract 3T - 8 + T so it can be 4T - 8
next we add 8 to both sides
next we add 4 + 8 so it can be 12
then we divide both sides by 4
and lastly we reduce the fraction 12/4 and we have our answer.

Answer: A) T = 3

Hi there!

To solve this equation, you need to first use the Distributive Property on the right side.

4 - t = 3t - 3 - 5

Now, add like terms.

4 - t = 3t - 8

Then, move terms to their own sides.

(4 - 4) - t = 3t + (-8 - 4)

(-t - 3t) = (3t - 3t) - 12

-4t = -12

Now, divide both sides by -4.

-4t / -4 = -12 / -4

t = 3

The answer is A. 3.

Hope this helps.

Write each expression as the product of two factors 2x1+(1+7)+(7x2)

Answers

The expression as the product of two factors is (1 + 7)(2 + 1).

What is termed as the product of the factors?A factor is a number which divides another number by itself and leaves no remainder. In other words, so unless multiplying two whole numbers yields a product, the numbers being multiplied are factors of a product because the product is divisible by them.Factors can be found using two methods: multiplication and division. Furthermore, rules of divisibility could be applied.

For the given question, the expression is;

= 2x1 + (1+7) + (7x2)

First, search for numbers that share a factor.

Consider the factors (2 x 1) and (7 x 2); this same common factor is two, so we factor.

= (2 x 1) + (7 x 2) + (1 +7)

Taking 2 common from first two numbers.

= 2 (1 + 7 ) + (1 + 7)

Now, take (1+7) common from both.

= (1 + 7)(2 + 1)

Thus, the expression as the product of two factors is (1 + 7)(2 + 1).

To know more about the product of the factors, here

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HELP ME Look at pics

Answers

9x^2 - 12y^2 - 11x, the last answer, number 4

combine all the like terms

8x^2 + x^2 = 9x^2

-9y^2 - 3y^2 = -12y^2

-4x-7x = -11x

so you have 9x^2 -12y^2-11x

Answer id the last one

The type of a parameter whose type is omitted in a function definition is

Answers

The answer is forgetting to return a value from a function that is supposed to return a value is a compilation error.

A sample of 12 measurements has a mean of 8.5 and a sample of 20 measurements has a mean of 7.5. Find the mean of all 32 measurements.

Answers

multiply 8.5 by 12, multiply 7.5 by 20, add them together to get 252, then divide that by 32 to get 7.875. 7.875 is the mean of all 32 measurements

Deon is riding his bicycle. He rides for 7 hours at a speed of 22.4 kilometers per hour. For how many kilometers does he ride

Answers

By hypothesis, Deon is riding at a speed of 22.4 kilometers per hour. So each hour, he completes 22.4 km.

If he rides for 7 hours, he completes 22.4 * 7 = 156.8 km

So in 7 hours, he rides 156.8 kilometers.

Hope this helps! :)

The Leukemia and Lymphoma Society sponsors a 5k race to raise money. It receives $55 per race entry and $10,000 in donations, but it must spend $15 per race entry to cover the cost of the race.

Write and solve an inequality to determine the number of race entries the charity needs to raise at least $55,000.

Answers

p=people subtract 10,000 already raised from 55,000 profit/p = 40 40p=45000 p=1125 1125 entries

The distance of planet Mercury from the Sun is approximately 5.8 ⋅ 107 kilometers, and the distance of planet Venus from the Sun is 1.1 ⋅ 108 kilometers. About how many more kilometers is the distance of Venus from the Sun than the distance of Mercury from the Sun? (1 point)
Select one:
a. 5.2 ⋅ 107 kilometers
b. 4.7 ⋅ 108 kilometers
c. 5.2 ⋅ 108 kilometers
d. 5.7 ⋅ 109 kilometers

Answers

a 5.2.107 kilometers

Answer:

a) 5.2 *10^7 km

Step-by-step explanation:

If we could describe our Solar System, in order of appearance nearer the Sun, it would be like this:

Sun --- Mercury --- Venus --- Earth

Sun --------------------- Venus

1.1 * 10^8 km

Sun -------Mercury

5.8 * 10^7 Km

To find out how many more kilometers is the distance of Venus from the Sun than the distance of Mercury from the Sun, all we have to do is simply subtract the distance Sun ---Venus minus Sun ---Mercury

So,

1.1 * 10^8 - 5.8 * 10^7 =

Adjusting the first distance to the same power

110*10^7- 5.8*10^7 =

Subtracting the factors

5.2 * 10^7

Can someone walk me through the steps in solving this question

Answers

so, we know that, in 1oz of baked potato, there are 48.3 calories, ok..how many calories in 3 and 1/3 oz then?

now, bear in mind, we first convert the mixed fraction to "improper", and then use that,

[tex]\bf \begin{array}{ccll} \stackrel{\stackrel{baked}{potato}}{oz}&calories\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 1&48.3\\ 3\frac{1}{3}&p \end{array}\implies \cfrac{1}{3\frac{1}{3}}=\cfrac{48.3}{p}\implies \cfrac{\frac{1}{1}}{\frac{3\cdot 3+1}{3}}=\cfrac{48.3}{p}[/tex]

[tex]\bf \cfrac{\frac{1}{1}}{\frac{10}{3}}=\cfrac{48.3}{p}\implies \cfrac{1}{1}\cdot \cfrac{3}{10}=\cfrac{48.3}{p}\implies \cfrac{3}{10}=\cfrac{48.3}{p} \\\\\\ 3p=483\implies p=\cfrac{483}{3}\implies \boxed{p=\stackrel{calories}{161}}[/tex]

now, we know that in 1oz of chicken gas 24.6 calories, so, how many calories then in 5 and 1/4 oz?

[tex]\bf \begin{array}{ccll} \stackrel{chicken}{oz}&calories\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 1&24.6\\ 5\frac{1}{4}&c \end{array}\implies \cfrac{1}{5\frac{1}{4}}=\cfrac{24.6}{c}\implies \cfrac{\frac{1}{1}}{\frac{5\cdot 4+1}{4}}=\cfrac{24.6}{c}[/tex]

[tex]\bf \cfrac{\frac{1}{1}}{\frac{21}{4}}=\cfrac{24.6}{c}\implies \cfrac{1}{1}\cdot \cfrac{4}{21}=\cfrac{24.6}{c}\implies \cfrac{4}{21}=\cfrac{24.6}{c} \\\\\\ 4c=516.6\implies c=\cfrac{516.6}{4}\implies \boxed{c=\stackrel{calories}{129.15}}[/tex]

so, how many calories in that meal? well, p + c.

what are the coordinates of a p;point on the unit circle if the angle formed by the positive x axis and the radius is 60 degrees

Answers

The diagram attached shows the graph described. Remember that the radius of the Unit Circle is 1. The In the corner of the diagram, we have the special right triangle 30-60-90 degrees, and its unit length ratios.

Using the ratios, we know that the side opposite the 30° angle (the x-axis) will be 1/2 the hypotenuse 1, which is 1/2. This means our x-coordinate is 1/2.

We also see that the side opposite the 60° angle will be the other leg, times √2. This means it will be (1/2) * √2 = √(2)/2. This is the y-coordinate.

Therefore, the coordinates of the point on the unit circle are (1/2, √(2)/2).

the line joining A(a, 3) to B(2 -3) is perpendicular to the line joining C(10,1) to B. The value of a is?

Answers

well, first off, let's find what is the slope of BC

[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) B&({{ 2}}\quad ,&{{ -3}})\quad % (c,d) C&({{ 10}}\quad ,&{{ 1}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{1-(-3)}{10-2}\implies \cfrac{1+3}{10-2} \\\\\\ \cfrac{4}{8}\implies \cfrac{1}{2}[/tex]

now, a line perpendicular to that one, will have a negative reciprocal slope, thus

[tex]\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad \cfrac{1}{2}\\\\ slope=\cfrac{1}{{{ 2}}}\qquad negative\implies -\cfrac{1}{{{ 2}}}\qquad reciprocal\implies - \cfrac{{{ 2}}}{1}\implies \boxed{-2}[/tex]

now, we know the slope "m" of AB is -2 then, thus

[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) A&({{ a}}\quad ,&{{ 3}})\quad % (c,d) B&({{ 2}}\quad ,&{{ -3}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-3-3}{2-a}=\boxed{-2} \\\\\\ \cfrac{-6}{2-a}=-2\implies -6=-4+2a\implies -2=2a\implies \cfrac{-2}{2}=a \\\\\\ -1=a[/tex]

The value of a is -1

What do perpendicular lines have a slope of?

Perpendicular lines have slopes that are negative reciprocals of each other. The given line's slope is 5, which means that the slope of the opposite line must be its negative reciprocal.

Conclusion: The slopes of two perpendicular lines are negative reciprocals of each other. This means that if a line is perpendicular to a line that is the slope of the line is -1/m.

let the slope of line AB is m1 and the slope of line BC be m2

m1= 3+3/a-2 = 6/a-2

m2=1+2/10-2 = 1/2

m1 * m2 = -1

6/a-2 * 1/2 = -1

3 = -a+2

a = -1

Learn more about reciprocal here

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Use the slope formula to find the slope of the line passing through the given points. (–4, 7) and (0, 8)

Answers

the first picture is for (-4, 7) and the second picture is for (0, 8)

Hi there!

Step-by-step explanation:

[tex]Slope=\frac{Y_2-Y_1}{X_2-X_1}=\frac{RISE}{RUN}[/tex]

[tex]\frac{8-7}{0-(-4)}=\frac{1}{4}[/tex]

Final answer is 1/4.

Slope is 1/4.

Hope this helps!

Thanks!

-Charlie

Have a nice day! :)

A cyclist rides his bike at a rate of 21 miles per hour. What is this rate in miles per minute? How many miles will the cyclist travel in 2 minutes? Do not round your answers.

Answers

5 days ago, hope this still helps though!

Alright 21 miles per hour. We know that there are 60 minutes in an hour. So this is basically saying 21 miles per 60 minutes. To find the rate for miles per minute, you divide 21 by 60 which is 0.35.

In one minute the cyclist rides 0.35 miles
In two minutes the cyclist rides 0.7 miles

What is the minimum number of degrees that a hexagram can be rotated so that it is carried onto itself?

Answers

The minimum number of degrees that a hexagram can be rotated so that it is carried onto itself is 60 degrees.

60 degresss is the answer

Other Questions

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