Josh wanted to buy a new shirt for a school dance. At the store, he couldn't decide between a purple plaid shirt and a scarlet striped shirt. Since the shirts were on sale for $19.95 each, Josh decided to buy them both. He saved a total of $9.10. If he saved the same amount on each shirt, what was the original price of each one?

Answer:

Option D. m<A = 43, m<B = 55, a = 20

Step-by-step explanation:

1. Determination of angle B.

Angle C = 82

Opposite C (c) = 29

Opposite B (b) = 24

Angle B =?

Using Sine rule, we can obtain the value of angle B as follow:

b/Sine B= c/Sine C

24/Sine B = 29/Sine 82

Cross multiply

29 × Sine B = 24 × Sine 82

Divide both side by 29

Sine B = (24 × Sine 82) /29

Sine B = 0.8195

Take the inverse of Sine.

B = Sine¯¹ (0.8195)

B = 55

2. Determination of angle A.

Angle C = 82

Angle B = 55

Angle A =?

The value of angle A can be obtained as follow:

A + B + C = 180 (sum of angle in a triangle)

A + 55 + 82 = 180

A + 137 = 180

Collect like terms

A = 180 – 137

A = 43

3. Determination of side a (Opposite A)

Angle C = 82

Opposite C (c) = 29

Angle A = 43

Opposite A (a) =?

The value 'a' can be obtained as by using sine rule as illustrated below:

a/Sine A = c/Sine C

a/Sine 43 = 29/Sine 82

Cross multiply

a × Sine 82 = 29 × Sine 43

Divide both side by Sine 82

a = (29 × Sine 43) /Sine 82

a = 20

Therefore,

m<A = 43, m<B = 55, a = 20

the mean of Y is 5 cm. the standard deviation of Y is 45 cm.

X is a random variable with mean μ = 75 cm and standard deviation σ = 9 cm. Let Y = -5 X + 140.

Mean of Y:

Y = -5X + 140 Mean = E(Y) = E(-5X + 140) = -5E(X) + 140 = -5(75) + 140 = 5 cm Hence, the mean of Y is 5 cm.

Standard deviation of Y:

σY=|-5|×σX=5×9=45 cm Therefore, the standard deviation of Y is 45 cm.

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There is a 0.0876 percent probability that six or more pages will include mistakes. There is a 1.64 x 10⁻⁶ chance that more than 10 pages may include mistakes.

Information about possibility of occurrence is provided by probability. For instance, weather patterns are used by meteorologists to predict the possibility of rain. In order to understand the relationship between exposures and the risk of health outcomes, epidemiology uses probability theory.

a) Chance that six or more pages may have mistakes:

To get this probability, we can utilise the binomial probability formula:

P(X>=6) = 1-P(X<6)

where X is the number of pages with errors.

P(X<6) = P(X=0)+P(X=1)+P(X=2) +P(X=3)+P(X=4)+P(X=5)

For each term, using the binomial probability formula, we obtain:

P(X < 6) = 0.9124

Therefore, P(X >= 6) = 1 - P(X < 6) = 1 - 0.9124 = 0.0876

Hence, there is a 0.0876 percent chance that six or more pages will include errors.

b) Chance that there are errors on more than 10 pages:

Using the same method, we can discover:

P(X > 10) = P(X = 11) + P(X = 12) + ... + P(X = 200)

To find the likelihood, we can use a calculator or software because performing the math by hand can be very time-consuming. Using a calculator for the binomial distribution, we obtain:

P(X > 10) = 1.64 x 10⁻⁶ (rounded to 3 decimal places)

Hence, there is a roughly 10% chance that there will be errors on more than 10 pages. 1.64 x 10⁻⁶.

c) Probability that none of the pages contain errors:

P(X = 0) can be calculated using the binomial probability formula:

P(X = 0) = (200 choose 0) * (0.009)⁰ * (1 - 0.009)²⁰⁰

= 0.8196

As a result, 0.8196 percent of the pages are likely to be error-free.

d) Probability that fewer than five pages contain errors:

P(X<5)=P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)

Again, using the binomial probability formula for each term, we get:

P(X < 5) = 0.8151

Hence, the likelihood that fewer than five pages are mistake-free is 0.8151.

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We can Long Division method to solve quotients step by step

What is long division method and its steps ?

When splitting huge numbers, the task is divided into several sequential parts using the long division approach. The dividend is divided by the divisor, just as in conventional division problems, and the result is known as the quotient; occasionally, it also produces a remainder.

We need to comprehend a few stages in order to divide. A vinculum or right parenthesis separates the dividend from the quotient, while a vertical bar separates the divisor from the dividend. Let's now go through the long division stages listed below to comprehend the procedure.

1. Take the dividend's first digit starting from the left . Verify if this digit exceeds or is equal to the divisor.

2. Next, divide it by the divisor, and write the result as the quotient on top.

3. Subtract the outcome from the digit, and then put the difference below.

Step 4: Decrease the dividend's subsequent digit (if present).

Step 5: Carry out Step 4 again.

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the probability that all 36 problems in the homework will be completed in less than 180 minutes

P(∑\(\left \{ {{i=36} \atop {i=1}} \right.\) \(X_{i}\) < 180) = P(X<5) = P(Z<-1) = ∅(-1)

given that

there are 36 independent problems

mean(μ) = 6minutes

standard deviation(σ) = 3 minutes

sample standard deviation = σ/\(\sqrt{n}\)

 = 3/\(\sqrt{36}\)

 =3/6

 =0.5

the sample mean x of 36 questions answering time approximately follows a normal distribution with mean 6 minutes and sample standard deviation is 0.5 minutes

now we need to find the probability that all 36 problems in the homework will be completed in less than 180 minutes

P(∑\(\left \{ {{i=36} \atop {i=1}} \right.\) \(X_{i}\) < 180) = P(X<5) = P(Z<-1) = ∅(-1)

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The equation to describe this will be y = 8x. It is assumed that Pass holders pay $8 each movie for the first five films. After five films, up to fifteen films, additional films are free. This will be represented by the function y = 40.

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Answer:

where are the problem?

Step-by-step explanation:

sorry no problem

16.

8 inch diameter -> 4 inch radius -> 50.2 in^2 area of the pizza.

the ratio of cost to size of first pizza is 0.199 $ per square inch of pizza.

14 inch diameter -> 7 inch radius -> 153.9 in^2 area of the pizza.

the ratio of cost to size of first pizza is 0.103 $ per square inch of pizza.

Since the 14 inch diameter pizza has a lower cost (0.103 $) than the 8 inch diameter pizza (0.199 $), the 14 inch diameter pizza is the "better buy".

17.

the circumference will double, and the area will multiply by 4!

16. You want to buy the one with more pizza (meaning larger area) for its cost. The first pizza has area π(8/2)² = 16π and costs $10. (Notice I did 8/2 because 8 is the diameter and you want to square the radius.) The second pizza has area π(14/2)² = 49π and costs $16.

The better pizza has a higher "area-to-cost" ratio (high area, low cost). The first pizza has a ratio of 16π/10 = 5.027, and the second pizza has a ratio of 49π/16 = 9.621. The second pizza's ratio is higher, so it is the better buy.

17. I answered this in the other post

Answer:

Step-by-step explanation:

y=mx+b   is the standard form

m= slope

If the slopes are the same they are parallel

If the slopes are Opposite signed and reciprocals, then they are perpendicular

both of the slopes are 5, so the lines are parallel

Answer:

Check out ironic p a n d u h on you tube

Step-by-step explanation:

the awnser is nowhere

Answer:

6000

Step-by-step explanation:

solved

Answer:

Hence the positive numbers are 246, and 41

(246, 41)

Step-by-step explanation:

From the question,

Let the first positve number be \(x\)

and the other number be \(y\)

Hence,

\(x = 6y\) ....... (1)

Also,

That is,

\(x - y =205\) ........(2).

To solve for the two unknowns, substitute the value of \(x\) in equation (1) into equation (2).

Since,

\(x = 6y\)

Then

\(x - y =205\) becomes

\((6y) - y =205\\\)

Then,

\(6y - y = 205\\5y = 205\\\)

Divide both sides by 5

\(\frac{5y}{5} = \frac{205}{5} \\ y = 41\\\)

∴ the value of \(y\) is 41

Now, substitute the value of y into equation (1) to find \(x\)

Then,

\(x = 6y\) becomes

\(x = 6(41)\\x = 246\\\)

∴ the value of \(x\) is 246

Hence the positive numbers are 246, and 41

(246, 41)

Question: In a sale, the price of a book is reduced by 25%. The price of the book in the sale is £12. Work out the original price of the book

Answer: £16

Step-by-step explanation:

To determine the original price of the book, we can use the fact that the sale price is 75% (100% - 25%) of the original price. Let's denote the original price as x.

75% of x = £12

To solve for x, we can set up the equation:

0.75x = £12

To isolate x, we divide both sides of the equation by 0.75:

x = £12 / 0.75

x = £16

Therefore, the original price of the book was £16.

The lengths of the legs of a right triangle, where one acute angle measures 65 degrees and the hypotenuse measures 12, are approximately 10.88 and 5.07.

To find the lengths of the legs of a right triangle, we can use the trigonometric functions sine and cosine. Since we know one acute angle and the hypotenuse, we can use the following formulas:

sin(65) = opposite/hypotenuse

cos(65) = adjacent/hypotenuse

Plugging in the known values and solving for the unknowns, we get:

sin (65) = opposite/12

opposite = 12sin (65) ≈ 10.88

cos (65) = adjacent/12

adjacent = 12cos (65) ≈ 5.07

Therefore, the lengths of the legs of the right triangle are approximately 10.88 and 5.07.

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The probability of rolling a six, and then getting heads upon tossing the coin is 1/12.

The probability of rolling a six on a die is one-sixth, while the likelihood of landing on heads on a coin flip is one-half. To find the probability of both events happening together, we need to multiply the probabilities.

P(rolling a six and getting heads) = P(rolling a six) × P(getting heads)

P(rolling a six and getting heads) = 1/6 × 1/2

P(rolling a six and getting heads) = 1/12

Therefore, the probability of rolling a six and getting heads upon tossing the coin is 1/12.

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Answer:

FED ~ MLF

Step-by-step explanation:

∠L = ∠E

∠F = ∠F

Since both angles are congruent, that would mean all angles are congruent.

If all angles are congruent, then the triangles are always similar no matter the length of the sides.

The complete statement is \(\triangle FED\sim \triangle FLM\).

Similar triangles are the triangles that have the same shape, but their sizes may vary.

If any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other.

When two lines intersect each other, then the opposite angles are formed due to intersection are called vertical angles or vertically opposite angles.

According to the given question.

We have two triangles LMF and EDF

In triangles LMF and EFD we have

∠MLF = ∠DEF   (given)

Also, ∠MFL = ∠DFE   (vertically opposite angles)

Since, we know that " if any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other".

Therefore, by AA similarity criteria triangle FED is similar to FLM.

Hence, the complete statement is \(\triangle FED\sim \triangle FLM\).

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Answer:

163

Step-by-step explanation:

What's great about these problems is that when there is a line that is divided by another line, causing 2 angles, the 2 angles must equal 180 degrees.  That means the 163-degree angle + either the x or the z angle would equal 180 degrees.  The second best part about this is that if it is separated how yours is, with 2 lines, opposite angles are equal.  That means that angle x and angle z are equal, as well as the 163 angle is equal to the y angle.  Hope this helps with more than just this problem!

Answer:

5,386,830

Step-by-step explanation:

The ways in which companies can attract and retain employees are given below.

The term human resources (HR) refers to the department responsible for managing employee-related resources.

It's an essential partner in an organization's success.

Given is that to answer some ways in which companies can attract and retain employees.

The ways in which companies can attract and retain employees are -

Therefore, the ways in which companies can attract and retain employees are given above.

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Answer:

Chord

Step-by-step explanation:

Notice that the highlighted part is the line segment that joins the points J and E on the circle, which is known as a chord.

Answer:

The determinant of this matrix is

2(5) - (-7)(-2) = 10 - 14 = -4.

This matrix has an inverse, but there are some square matrices whose determinant is zero and therefore do not have an inverse. Abid's friend is correct. So a + b + c + d = 2 + (-7) + (-2) + 5 = -2.

Answer:  see proof below

Step-by-step explanation:

Given: A + B + C = π                     →  A = π - (B + C)

                                                     → B + C = π - A

Use the Pythagorean Identity: cos² A + sin² A = 1   →  sin² A = 1 - cos² A

Use Double Angle Identities: cos 2A = 2 cos² A - 1 → cos² A = (cos 2A + 1)/2

                                             → cos A = 1 - 2 sin² (A/2)    

Use Sum to Product Identity: cos A + cos B = 2 cos [(A + B)/2] · cos [(A - B)/2]

Use Cofunction Identities:  cos (π/2 - A) = sin (A)

                                             sin (π/2 - A) = cos A

                                             cos (-A) = cos (A)

Proof LHS → RHS:

\(\text{LHS:}\qquad \qquad \sin^2\bigg(\dfrac{B}{2}\bigg)+\sin^2 \bigg(\dfrac{C}{2}\bigg)-\sin^2\bigg(\dfrac{A}{2}\bigg)\)

\(\text{Pythagorean:}\qquad 1-\cos^2 \bigg(\dfrac{B}{2}\bigg)+1-\cos^2 \bigg(\dfrac{C}{2}\bigg)-\bigg[1-\cos^2 \bigg(\dfrac{A}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =1-\cos^2 \bigg(\dfrac{B}{2}\bigg)-\cos^2 \bigg(\dfrac{C}{2}\bigg)+\cos^2 \bigg(\dfrac{A}{2}\bigg)\)

\(\text{Double Angle:}\quad 1-\bigg(\dfrac{\cos(2\cdot \frac{B}{2})+1}{2}\bigg)-\bigg(\dfrac{\cos (2\cdot \frac{C}{2})+1}{2}\bigg)+\bigg(\dfrac{\cos (2\cdot \frac{A}{2})+1}{2}\bigg)\\\\\\.\qquad \qquad \qquad =1-\dfrac{\cos B}{2}-\dfrac{1}{2}-\dfrac{\cos C}{2}-\dfrac{1}{2}+\dfrac{\cos A}{2}+\dfrac{1}{2}\\\\\\.\qquad \qquad \qquad =\dfrac{1}{2}[1-(\cos B+\cos C)+\cos A]\)

\(\text{Sum to Product:}\qquad \dfrac{1}{2}\bigg(1-\bigg[2\cos \bigg(\dfrac{B+C}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)\bigg]+\cos A\bigg)\)

\(\text{Given:}\qquad \dfrac{1}{2}\bigg(1-\bigg[2\cos \bigg(\dfrac{\pi -A}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)\bigg]+\cos A\bigg)\)

\(\text{Cofunction:}\qquad \dfrac{1}{2}\bigg(1-\bigg[2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)\bigg]+\cos A\bigg)\)    

\(\text{Double Angle:}\qquad \dfrac{1}{2}\bigg[1-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)+1-2\sin^2 \bigg(\dfrac{A}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =\dfrac{1}{2}\bigg[2-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)-2\sin^2 \bigg(\dfrac{A}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =1-\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)-\sin^2 \bigg(\dfrac{A}{2}\bigg)\)

\(\text{Factor:}\qquad \qquad 1-\sin \bigg(\dfrac{A}{2}\bigg)\bigg[ \cos \bigg(\dfrac{B-C}{2}\bigg)-\sin \bigg(\dfrac{A}{2}\bigg)\bigg]\)

\(\text{Given:}\qquad \qquad 1-\sin \bigg(\dfrac{A}{2}\bigg)\bigg[ \cos \bigg(\dfrac{B-C}{2}\bigg)-\sin \bigg(\dfrac{\pi -(B+C)}{2}\bigg)\bigg]\)

\(\text{Cofunction:}\qquad 1-\sin \bigg(\dfrac{A}{2}\bigg)\bigg[ \cos \bigg(\dfrac{B-C}{2}\bigg)+\cos \bigg(\dfrac{B+C}{2}\bigg)\bigg]\)

\(\text{Sum to Product:}\ 1-\sin \bigg(\dfrac{A}{2}\bigg)\cdot 2 \cos \bigg(\dfrac{(B-C)+(B-C)}{2\cdot 2}\bigg)\cdot \cos \bigg(\dfrac{(B-C)-(B+C)}{2\cdot 2}\bigg)\\\\\\.\qquad \qquad \qquad =1-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \cos \bigg(-\dfrac{C}{2}\bigg)\)\(\text{Cofunction:}\qquad =1-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \cos \bigg(\dfrac{C}{2}\bigg)\)

\(\text{LHS = RHS:}\quad \checkmark\\\\\quad 1-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \cos \bigg(\dfrac{C}{2}\bigg)=1-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \cos \bigg(\dfrac{C}{2}\bigg)\quad\)

The probability of getting a heart on the fourth card but not before that is 0.2278

The probability of getting a heart on the fourth card can be calculated by multiplying the probability of not getting a heart in the first three cards by the probability of getting a heart on the fourth card.

The probability of not getting a heart in the first three cards can be calculated as follows:

(39/52) * (38/51) * (37/50) = 0.862

where 39/52 is the probability of not getting a heart on the first card, 38/51 is the probability of not getting a heart on the second card (given that no heart was drawn in the first card), and 37/50 is the probability of not getting a heart on the third card (given that no heart was drawn in the first two cards).

The probability of getting a heart on the fourth card can be calculated as follows:

13/49 = 0.265

where 13/49 is the probability of getting a heart on the fourth card (given that no heart was drawn in the first three cards).

So, the probability of getting a heart on the fourth card, but not before, can be calculated as:

0.862 * 0.265 = 0.2278

So, the chance of getting a heart on the fourth card, but not before, is approximately 22.78%.

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The total area of the figure in this problem is given as follows:

41.3 ft².

The area of the composite figure is given by the sum of the areas of all the parts that compose the figure.

The figure in this problem is composed as follows:

Then the area of the triangle is given as follows:

At = 0.5 x 6 x 3 = 9 ft².

The area of the semicircle is given as follows:

Ac = π x 3² = 28.3 ft².

The area of the square is given as follows:

As = 2² = 4 ft².

Then the total area of the figure is given as follows:

9 + 28.3 + 4 = 41.3 ft².

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A circle can be defined as a geometric shape consisting of all points in a plane that are equidistant from a given point, which is known as the center. The distance between the center of the circle and any point on the circle is referred to as the radius.

In order to find the center and radius of a circle, we need to have three points on the circle's circumference, and then we can use algebraic formulas to solve for the center and radius. Let's look at the given problem to find the center and radius of the circle that passes through the points (-1,5), (5,-3), and (6,4).

Center of the circle can be determined using the formula:

(x,y)=(−x1−x2−x3/3,−y1−y2−y3/3)(x,y)=(−x1−x2−x3/3,−y1−y2−y3/3)

Let's plug in the values of the given points and simplify:

(x,y)=(−(−1)−5−6/3,−5+3+4/3)=(2,2/3)

Next, we need to find the radius of the circle. We can use the distance formula to find the distance between any of the three given points and the center of the circle:

Distance between (-1,5) and (2,2/3) =√(x2−x1)2+(y2−y1)2=(2+1)2+(2/3−5)2=√10.111

Distance between (5,-3) and (2,2/3) =√(x2−x1)2+(y2−y1)2=(5−2)2+(−3−2/3)2=√42.222

Distance between (6,4) and (2,2/3) =√(x2−x1)2+(y2−y1)2=(6−2)2+(4−2/3)2=√33.361

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The probability of getting one defective component per customer is very low, less than 1/14,254. The probability of getting five defective components to a single customer is also low, 1/14,254. And the probability of getting two defective components to two different customers and the rest of the customers getting none is 10/14,254.

(a) The probability that each customer will receive one defective component is the probability that the five defective components will be drawn in a specific order, divided by the total number of ways the 50 components can be drawn. There are 5049484746 ways that the 50 components can be drawn, and 5! (5 factorial) ways that the defective components can be drawn in a specific order. So the probability is (5!)/(5049484746) = 1/14,254.

(b) The probability that one customer will have drawn five defective components is the probability that all five defective components will be drawn in a row, divided by the total number of ways the 50 components can be drawn. There are 5049484746 ways that the 50 components can be drawn, and 5! (5 factorial) ways that the defective components can be drawn in a row. So the probability is (1!)/(5049484746) = 1/14,254,

(c) The probability that two customers will receive two defective components each, two none, and the other one, is the probability that the five defective components will be drawn in a specific order and then divided among the five customers in a specific way, divided by the total number of ways the 50 components can be drawn. The number of ways to divide the defective components among the customers is 5!/(2!2!1!) = 10. There are 5049484746 ways that the 50 components can be drawn, and 5! (5 factorial) ways that the defective components can be drawn in a specific order, so the probability is (105!)/(50494847*46) = 10/14,254.

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Answer:

1. 16

2. 125

3. 5

4. 10,000

5. 27

6. 0

7. 2.25

8. 243

The temperature of City A and City B on that day was 4°C and 3°C respectively.

Let x represent the temperature of city A and y represent the temperature of city B.

Four times the temperature of City A was 7° C more than three times the temperature of City B, hence:

4x = 3y + 7

4x - 3y = 7       (1)

The temperature of City A minus three times the temperature of City B was −5° C, hence:

x - 3y = -5        (2)

From both equations, solving simultaneously:

x = 4, y = 3.

The temperature of City A and City B on that day was 4°C and 3°C respectively.

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