What does a straight angle look like

Answer:

y=5x-2

Step-by-step explanation:

Let x be the unknown number

Answer: 4/27 or 0.148148

First you solve for any grouping symbols ( absolute value, parentheses, brackets, etc.) Since there aren’t any you move on to exponents, 4^3 is the same as 4*4*4 which equals 64. Next you do multiplication 6*2 is 12 so our problem is currently

64-60 over 15+12. Next you simplify, which make the problem 4/27. You can divide which makes your problem 0.148148 but most of the times you keep it as a fraction.

Answer:

A score of 4.2 on a test with a mean of 2.5 and a standard deviation of 1.2 has the highest relative position.

Step-by-step explanation:

Which score has the highest relative position: a score of 38 on a test with a mean of 30 and a standard deviation of 10, a score of 4.2 on a test with a mean of 2.5 and a standard deviation of 1.2 or a score of 432 on a test with a mean of 396 and a standard deviation of 40.

In order to find the solution, we need to calculate the z score value for each test.

The z score formula: \(z = \dfrac{\bar{x} -\mu}{s}\) where \(\bar{x}\)  is the score, μ is the mean and s is the standard deviation.

Now for test 1:

Put \(\bar{x}=38, \mu=30 \text{ and } s=10\) in the above formula.

\(z = \dfrac{38 -30}{10}\)

\(z = 0.8\)

For test 2:

Put \(\bar{x}=4.2, \mu=2.5 \text{ and } s=1.2\) in the above formula.

\(z = \dfrac{4.2 -2.5}{1.2}\)

\(z \approx 1.417\)

For test 3:

Put \(\bar{x}=432, \mu=396 \text{ and } s=40\) in the above formula.

\(z = \dfrac{432 -396}{40}\)

\(z =0.9\)

Since the z score value of test 2 is greater so a score of 4.2 on a test with a mean of 2.5 and a standard deviation of 1.2 has a highest relative position.

Answer:

125^-4

125=5²

125^-4=5^-12

Answer:

Step-by-step explanation:

Assuming that the given dimensions of 13, 13, 13 refer to the base of the rectangular pyramid, we can calculate the surface area of the pyramid as follows:

First, we need to calculate the area of the rectangular base, which is simply length x width:

Area of rectangular base = 13 x 13 = 169 square units

Next, we need to calculate the area of each triangular face of the pyramid. Since the rectangular base has two sets of parallel sides, there are two types of triangular faces: the isosceles triangles on the sides and the right triangles on the front and back.

To calculate the area of the isosceles triangles, we need to first find the length of the slant height, which can be found using the Pythagorean theorem:

a² + b² = c²

where a and b are the base and height of the triangle (both equal to 13 in this case), and c is the slant height.

13² + 13² = c²

338 = c²

c ≈ 18.38

Now that we have the slant height, we can calculate the area of each isosceles triangle using the formula:

Area of isosceles triangle = (1/2) x base x height

Area of isosceles triangle = (1/2) x 13 x 18.38

Area of isosceles triangle ≈ 119.14 square units

To calculate the area of each right triangle, we need to use the same slant height of 18.38, along with the height of the pyramid, which is also 13. Then we can use the formula:

Area of right triangle = (1/2) x base x height

Area of right triangle = (1/2) x 13 x 18.38

Area of right triangle ≈ 119.14 square units

Since there are two of each type of triangular face, the total surface area of the pyramid is:

Surface area = area of rectangular base + 2 x area of isosceles triangle + 2 x area of right triangle

Surface area = 169 + 2 x 119.14 + 2 x 119.14

Surface area = 546.28 square units

Therefore, the surface area of the rectangular pyramid with base dimensions of 13 x 13 and height of 13 is approximately 546.28 square units.

Answer:

3

Step-by-step explanation:

x^2 + y^2 = 9

The equation of a circle is

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

( h,k) is the center and r is the radius

x^2 + y^2 = 3^2

The radius is 3

The value of Arc cosine (negative Start Fraction Start Root 3 End Root Over 2 End Fraction), which is also written as Arc cosine ( -√(3) / 2 ) is 150 degrees

The arc cosine is same as cos inverse, Arc cosine represents the angle for which the cosine in degree the angle is found.

Given data

Arc cosine (negative Start Fraction Start Root 3 End Root Over 2 End Fraction)

rewriting the equation gives:

Arc cosine ( -√(3) / 2 )

then solving as follows

= Arc cosine ( -√(3) / 2 )

= Arc cosine ( - 0.8860 )

using a calculator to press the value gives:

= 150 degrees

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Answer:

5pi/6

Step-by-step explanation:

edge

Gulf Coast Electronics should order 13,000 capacitors from Boston Components, 50,000 capacitors from Able Controls, and 14,000 capacitors from Lyshenko Industries to obtain 77,000 acceptable-quality reservoir capacitors at a minimum cost of $204,425.

To minimize the total cost of obtaining 75,000 acceptable-quality reservoir capacitors, we can formulate the following linear program:

Objective function:

Minimize: 2.35B + 2.6A + 2.85L

Subject to:

B + A + L = 77000 (total number of capacitors required)

B ≥ 0.1A (at least 10% of the volume given to Able Controls should be awarded to Boston Components)

L ≥ 29500 (at least 29,500 capacitors should be ordered from Lyshenko)

B ≤ 32500 (maximum of 32,500 capacitors should be ordered from Boston Components)

A ≤ 50000 (maximum of 50,000 capacitors should be ordered from Able Controls)

L ≤ 48500 (maximum of 48,500 capacitors should be ordered from Lyshenko)

0 ≤ B, A, L (non-negativity constraints)

Solving this linear program using a linear programming software, we get:

B = 13000

A = 50000

L = 14000

Correct Question :

Gulf Coast Electronics is ready to award contracts to suppliers for providing reservoir capacitors for use in its electronic devices. For the past several years, Gulf Coast Electronics has relied on two suppliers for its reservoir capacitors: Able Controls and Lyshenko Industries. A new firm, Boston Components, has inquired into the possibility of providing a portion of the reservoir capacitors needed by Gulf Coast. The quality of products provided by Lyshenko Industries has been extremely high; in fact, only 0.4% of capacitors provided by Lyshenko had to be discarded because of quality problems. Able Controls has also had a high quality level historically, producing an average of only 1% unacceptable capacitors. Because Gulf Coast Electronics has had no experience with Boston Components, it estimated Boston Components’ defective rate to be 12%. Gulf Coast would like to determine how many reservoir capacitors should be ordered from each firm to obtain 77000 acceptable-quality capacitors to use in its electronic devices. To ensure that Boston Components will receive some of the contract, management specified that the volume of reservoir capacitors awarded to Boston Components must be at least 10% of the volume given to Able Controls. In addition, the total volume assigned to Boston Components, Able Controls, and Lyshenko Industries should not exceed 32500, 50000, and 48500 capacitors, respectively. Because of Gulf Coast’s long-term relationship with Lyshenko Industries, management also specified that at least 29500 reports should be ordered from Lyshenko. The cost per capacitor is $2.35 for Boston Components, $2.6 for Able Controls, and $2.85 for Lyshenko Industries.

Formulate and solve a linear program for determining how many reservoir capacitors should be ordered from each supplier to minimize the total cost of obtaining 75,000 acceptable-quality reservoir capacitors. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. Enter "0" if your answer is zero. If the constant is "1" it must be entered in the box.

Let B = number of capacitors ordered from Boston Components

Let A = number of capacitors ordered from Able Controls

Let L = number of capacitors ordered from Lyshenko Industries

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Answer:

0.5625

Step-by-step explanation:

You do the parenthasis first and get 18 and then you divide 18/32 and get 0.5625

PEMDAS if need help understanding the order

(Parenthesis, Exponent, Multiply, Divide, Add, Subtract)

(21-3)÷32 (do parenthesis first)

18÷32 (divide)

answer is about 0.5625

The length of side AB in right angled triangle ABC  will be 48 cm.

Every triangle with one 90° angle is said to have a right angle. The triangle with a right angle is known as a right triangle because a right angle is 90 degrees.The longest side of a right angle is known as the hypotenuse, and it is opposite the right angle.

Given,

∠B= 90°, AC = 96 cm, ∠C = 30°

Now, we know, Trignometric ratio sin θ in triangle can be given by-:

sin θ = \(\frac{perpendicular}{hypotenuse}\)

From given figure,

Perpendicular= AB= ?

and Hypotenuse= AC = 96

and θ= 30°

Hence,

sin 30° =\(\frac{perpendicular}{hypotenuse}\)= \(\frac{AB}{96}\)

\(\frac{1}{2} = \frac{AB}{96}\)                                      (∵ sin 30°= 1/2)

\(AB=\frac{96}{2}\)

\(AB= 48 cm\)

Thus, AB= 48 cm

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Correct Question:ABC is a right angled triangle. if B = 90°, AC = 96 cm, C = 30°. Find AB = ?

Hello there. To solve this question, we'll have to remember some properties about convergence of series.

Starting by the fact that for a given series:

We always take the limit to see whether or not:

But in this case, we have to use the ratio test. Given two elements of the sequence we're adding the terms:

We say that for the following limit:

If L > 1, the series diverges by the ratio test.

If L = 1, the test is inconclusive.

If L < 1, the series converges by the ratio test.

In this case, the series is:

In which we can suppose that the general term is:

Hence we know that

Now plugging in these terms in the ratio test, we have:

Knowing that:

We have:

In which we can simplify the fraction by a factor 3^n

Answer:7 x 10 ^1 is the right answer

Step-by-step explanation:

Hope this helps :)

There is the bacterial cell 7 × 10¹ times smaller than the amoeba cell which is the correct answer would be an option (B).

Scientific Notation is a way of writing down in the easy form of very large or very small numbers.

We have been given that a bacterial cell is around 5 × 10⁻⁶ m long, while an amoeba cell is about 3.5 × 10⁻⁴ m long.

To determine the number of times smaller is the bacterial cell than the amoeba cell.

⇒ amoeba cell / bacterial cell

⇒ 3.5 × 10⁻⁴ m / 5 × 10⁻⁶ m

Apply the division operation, and we get

⇒ 0.7 × 10⁻⁴ × 10⁶

Adding the exponents of the above terms

⇒ 0.7 × 10⁻⁴⁺⁶

⇒ 0.7 × 10²

⇒ 7 × 10¹

Hence, there is the bacterial cell 7 × 10¹ times smaller than the amoeba cell.

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Answer:b

Step-by-step explanation:

The area of circle S will be 50.24 mm². Then the correct option is A.

Let r be the radius of the circle. Then the area of the circle will be

A = πr² square units

The radius of circle S is half the radius of circle L.

Let 'r₁' be the radius of circle S and 'r₂' be the radius of circle L. Then the equation is given as

r₁ = r₂ / 2

The radius of circle L is 8 millimeters. Then the radius of the circle S is calculated as,

r₁ = 8 / 2

r₁ = 4 mm

The area of the circle S is calculated as,

A = πr₁²

A = 3.14 x (4)²

A = 50.24 mm²

The range of the circle S is 4 mm. Then the region of the circle S will be 50.24 mm². Then the right choice is A.

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Answer:

-12

Step-by-step explanation:

3/5 * (1 + sqrt(16))^2 - (5 - 2)^3 =

= 3/5 * (1 + 4)^2 - (3)^3

= 3/5 * (5)^2 - 27

= 3/5 * 25 - 27

= 15 - 27

= -12

Answer:

29

Step-by-step explanation:

The problem is 5x + 6 = 150

I subtract 6 from each sides except the one with the variable.

6 - 6 = 0 and 150 - 6 = 144.

Then I bring 5x down.

Then I divided 5x with 5 and 144 with 5.

I got 28.8 for x, which means the friends had 28.8 action figures each.

And I don't think it would be possible for them to have 28.8 action figures, so you round to a whole number which would give you the answer 29.

I think I that makes sense.

The requried, 20 youths use both iPhone and Samsung, and 200 youths use neither iPhone nor Samsung.

Let A be the set of youths using only iPhones, B be the set of youths using only Samsung, and C be the set of youths using both. Then, we have:

|A| = 150

|B| = 770

|A ∪ B| = 900

We want to find |C| and |A ∩ B| (which is the number of youths using both).

Using the inclusion-exclusion principle, we have:

|A ∪ B| = |A| + |B| - |A ∩ B|

900 = 150 + 770 - |A ∩ B|

|A ∩ B| = 20

So, 20 youths use both iPhone and Samsung.

To find the number of youths who use neither, we can use the fact that:

|A ∪ B ∪ C| = 1100

|A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C|

Plugging in the values we know, we get:

1100 = 150 + 770 + |C| - 20 - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C|

|C| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C| = 200

Since the number of youths using both is 20, we have:

|A ∩ C| = |B ∩ C| = |A ∩ B ∩ C| = 0

So, we can simplify the equation to:

|C| = 200

Therefore, 200 youths use neither iPhone nor Samsung.

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Answer:

\(1216 = 64 \times 19\)

64 is 4 cubed, and 19 is a prime number between 10 and 20.

Step-by-step explanation:

The true statement is "the line that can be drawn through points D and E is contained in plane Y".

option B is the correct answer

The points x and y and points C,D,E and f are shown in the figure, the true statement is determined as follows;

We know that, if two points lie in a plane, then the line drawn through the points will contained in the same plane.

The points C lies outside the plane Y and the point D lies on the plane Y, so the line drawn through the points C and D will not contained in plane Y.

So, option (A) is NOT correct.

The points D and E, both lie in the plane Y, so the line drawn through the points D and E will also contained in plane Y.

So, option (B) is CORRECT.

Since the plane X contain infinitely many points, so F is not the only point that can lie in plane X.

So, option (C) is NOT correct.

Similarly, there are infinitely many points in the plane Y, so the points D and E are not the only points that can lie in plane Y.

So, option (D) is NOT correct.  

Thus, the correct option is;

The line that can be drawn through points D and E is contained in plane Y.

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The complete question is below:

Points x and y and points C,D,E and f are shown what is true about points

(A) The line that can be drawn through points C and D is contained in plane Y.

(B) The line that can be drawn through points D and E is contained in plane Y.

(C) The only point that can lie in plane X is point F.

(D) The only points that can lie in plane Y are points D and E

Answer:

simple look at y intercept then look at slope or you can solve two points by using the formula y2-y1/x2-x1

but your formula is

y =1/2 +5 so b would be your answer

The Slope of a Line

Suppose we have a couple of points with coordinates (x1,y1) and (x2,y2). If we draw a line that passes through them, the slope of that line can be calculated as follows:

Basically, we subtract the y-coordinates, we subtract the x-coordinates (in the same order) and then we divide both results.

We are given the points (-4,0) and (2,6). Substituting into the formula:

Operating:

The slope of the line is m=1

9514 1404 383

Answer:

  no

Step-by-step explanation:

The angle of the ramp as designed by the planning department is ...

  tan(angle) = (3 ft)/(25 ft)

  angle = arctan(3/25) ≈ 6.84°

This angle exceeds the required 4.75°, so does not meet code.

(a) The conditional PMF P X∣B (x) of X given the event B={X<4} can be calculated using the formula

P(X=x|B) = P(X=x and B)/P(B).

Since the event B={X<4} includes the events X=1, X=2, and X=3, we can calculate P(B) as the sum of the probabilities of these events:

P(B) = P(X=1) + P(X=2) + P(X=3) = (1/4) + (3/4)(1/4) + (3/4)^2(1/4) = 13/16.

Therefore, the conditional PMF P X∣B (x) is given by:

P(X=1|B) = P(X=1 and B)/P(B) = (1/4)/(13/16) = 4/13
P(X=2|B) = P(X=2 and B)/P(B) = (3/4)(1/4)/(13/16) = 3/13
P(X=3|B) = P(X=3 and B)/P(B) = (3/4)^2(1/4)/(13/16) = 6/13

(b) The probability that your favourite character is eliminated in one of the first two episodes given the spoiler is P(X=1|B) + P(X=2|B) = 4/13 + 3/13 = 7/13.

(c) The expected value of X conditioned on the event B can be calculated using the formula E[X|B] = sum(x*P(X=x|B)) for all x in the support of X. Therefore, E[X|B] = 1*(4/13) + 2*(3/13) + 3*(6/13) = 20/13.

(d) The conditional PMF P X∣C (x) of X given the event C={X>2} can be calculated using the formula P(X=x|C) = P(X=x and C)/P(C). Since the event C={X>2} includes the events X=3, X=4, ..., we can calculate P(C) as the sum of the probabilities of these events: P(C) = P(X=3) + P(X=4) + ... = (3/4)^2(1/4) + (3/4)^3(1/4) + ... = (3/4)^2/(1-(3/4)) = 12/16. Therefore, the conditional PMF P X∣C (x) is given by:

P(X=3|C) = P(X=3 and C)/P(C) = (3/4)^2(1/4)/(12/16) = 1/3
P(X=4|C) = P(X=4 and C)/P(C) = (3/4)^3(1/4)/(12/16) = 1/4
...

(e) The conditional PMF P Y∣C (y) of Y given the event C={X>2} can be obtained by shifting the conditional PMF P X∣C (x) of X given the event C={X>2} by 2 units to the left. Therefore, P Y∣C (y) = P X∣C (y+2) for all y in support of Y. This conditional PMF belongs to the family of geometric random variables with parameter 1/4.

(f) The conditional mean E[X|C] can be calculated using the formula E[X|C] = sum(x*P(X=x|C)) for all x in the support of X. Since the conditional PMF P X∣C (x) is a geometric distribution with parameter 1/4 shifted by 2 units to the right, we can use the formula E[X|C] = 2 + 1/(1/4) = 6.

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6 tables are required. Each prime number attender should serve 3 customers each.

The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

All the numbers other than prime numbers are composite numbers.

The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.

Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables

Therefore, 6 tables are required.

Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.

Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.

Thus, each prime number attender should serve 3 customers each.

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The probability, if Greg gets dressed in the dark, that he winds up wearing the white shirt and tan pants is 0.125 or 12.5%.

To find the probability that Greg winds up wearing the white shirt and tan pants while getting dressed in the dark, we need to find out all the possible outfit options. According to the question given, first we nned to find out number of outfit combinations possible.

Total number of Outfit Combinations:

There are 4 shirts: a white one, a black one, a red one, and a blue one and also two pairs of pants, one blue and one tan. So, total number of possible outfit combinations would be 4 * 2 = 8.

No of favourable options:

As given in the question, Greg wears white shirt and tan pants. There is only one white shirt and one tan pant. So, number of favourable options would be only 1 .

Probability = Number of favourable outcomes/Total no. of combinations

Probability = 1/8

Probability = 0.125 or 12.5%

Therefore, the probability, if Greg gets dressed in the dark, that he winds up wearing the white shirt and tan pants is 0.125 or 12.5%.

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Answer:

what is the expressio

Step-by-step explanation:

Answer:

7/4

Step-by-step explanation:

in PEMDAS

multiplication and division come before addition and subtraction.

otherwise we just read left to right.

could be written

2 + (7/4) + (1 x 12) - (4 / 2)

2 + 1.75 + 12 - 2

13.75

Answer:

8.6

Step-by-step explanation:

radius = diameter/2 = 10/2 cm = 5 cm

V = (1/3)πr²h

225 cm³ = (1/3)π(5 cm)²h

h = 27/π cm

h = 8.6 cm

Answer:

Your answer is 22.5 or 22

Step-by-step explanation:

divide 10 by 225 to get your height.

We can estimate that the percent change in the number of club members from last year to this year is approximately 94.1%. This represents an almost doubling of the club membership.

What is the percent change?

Percentage change is a way to describe the difference between an old value and a new value, expressed as a ratio and then multiplied by 100.

To estimate the percent change in the number of club members, we can use the percent change formula:

percent change = (new value - old value) / old value x 100%

where the "old value" is the number of club members last year and the "new value" is the number of club members this year.

Plugging in the numbers we have:

percent change = (33 - 17) / 17 x 100%

percent change = 16 / 17 x 100%

percent change ≈ 94.1%

Therefore, we can estimate that the percent change in the number of club members from last year to this year is approximately 94.1%. This represents an almost doubling of the club membership.

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