A company can produce as many as 50 mountain bikes and as many as...

Answers

C = 58.84

B = 97.16°

Explanation

The sine rule states:

SinA/a = sinB/b

∴ sin24 / 77 = sinC / 162

 sinC = (162 × sin24)/77

         = 65.89/77

         = 0.85573

C = 58.84°

Angles in a triangle add up to 180°

∴ B + 24 + 58.84 = 180

  B = 180 - 24 - 58.84

      = 180 - 82.84

      = 97.16°

      =

Using the Law of Sines, which states that the ratio of a side length to the sine of its opposite angle is the same for all sides, you can solve for the missing angle. Rearrange the formula to sinC = c * sinA / a, then take the inverse sine of both sides to find the measure of the missing angle.

To find the missing angle m∠C using the Law of Sines, you first need to know the lengths of the sides of the triangle and one of the angles. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is the same for all three sides of the triangle. In other words, if a, b, and c represent the lengths of the sides and A, B, and C represent the measures of the opposite angles, we have: sinA/a = sinB/b = sinC/c.

To solve for m∠C, you rearrange the Law of Sines to: sinC = c * sinA / a. After that you take the inverse sine (or arcsin) of both sides to find m∠C = arcsin(c * sinA / a). Notice that you are assuming that the sine of the missing angle is positive, which is valid for angles less than 180 degrees.

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40hrs*60mins/1hr=2400mins

2400mins*60secs/min=144,000secs

First we can calculate how many seconds there are in an hour:​

​Since 1 hour has 60 minutes and each minute has 60 seconds.

​Then 1 hour = 60 minutes * 60 seconds/1minute = 3,600 seconds.

​Now we have to multiply x 40 to calculate how many seconds there are in 40 hours.

​In a 40-hour work week = 40 hours * 3,600 seconds/1hour = 144,000 seconds

​Answer : 144,000 seconds there are in a 40-hour work week

​Hope this helps!​​​​

​[tex]\textit{\textbf{Spymore}}[/tex]​​​​​​​

The fencing that is needed to enclose the garden is 36 meters.

Let the width be represented by x.

Let the length be represented by x+2.

The area is given as 80m².

Therefore, the length and width will be calculated thus;

x(x + 2) = 80

x² + 2x - 80 = 0

x² + 10x - 8x - 80 = 0

x(x + 10) - 8(x + 10) = 0

x - 8 = 0

x = 8

The width is 8 meters and the length is 10m.

The perimeter will be:

= 2(8m + 10m)

= 2 × 18m

= 36m

In conclusion, the correct option is 36 meters.

Read related link on:

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Answer:

Option B. 0.75 gallons is the right answer.

Step-by-step explanation:

Let the load of dishwasher used in house A = x gallons

Let the load of dishwasher used in house B is = y gallons

and similarly we assume for house C = z gallons

Now from the given question

On Friday amount of water used in all three houses = 17.5 gallons

From the table we will make the equation

x + 2y + 2z = 17.5-----(1)

For Saturday

2x + 3y + 4z = 31.5 ----(2)

For Sunday

2x + 2y + 3z = 24.75 -----(3)

By subtracting equation 3 from 2

y + z = 31.5 - 24.75 = 6.75 ------(4)

Equation (1) multiplied by 2 - equation (2)

2×(x + 2y + 2z) - (2x + 3y + 4z) = 17.5×2 - 31.5

y = 35 - 31.5 = 3.5

By putting y = 3.5 in the equation (4)

z = 6.75 - 3.5 = 3.25

By putting y = 3.5 and z = 3.25 in the equation (1)

x + 7 + 6.5 = 17.5

x = 17.5 - 13.5 = 4

Now the difference between load of dishwasher that uses least water and the most.

x - z = 4 - 3.25 = 0.75 gallons

Option B is the right answer.

Answer:

Option B. 0.75 gallons is the right answer.

Step-by-step explanation:

Edge 2020

Answer:

option 2=11/20  is the answer.

Step-by-step explanation:

given that there are 20 cards numbers 1,2... 20.

A card is randomly drawn.

We have to find the probability of drawing either 1 or even card.

P(drawing even card) = no of even cards/total cards = 10/20= 0.5

P(drawing one) = no of 1's/total cards = 1/20 = 0.05

P(drawing both one and even card) = 0 (since impossible)

Hence P(drawing even or one) =0.5+0.05-0

=0.55

= 11/20

Hence option 2 is the answer.

Answer : 11/20

There are 20 cards labeled from 1 to 20 in a bag. A card is randomly selected from the bag.

Total number of outcomes = 20

outcomes of an even number ={2,4,6,8,10,12,14,16,18,20}

So number of outcomes of even number = 10

outcomes of a 1 ={1}

So number of outcomes of a 1 = 1

Number of outcomes of even number and a 1 = 10+1 = 11

Probability ( any event) =number of favorable outcomes divide by total  number of outcomes

Probability (getting an even number or a 1) = [tex]\frac{11}{20}[/tex]

If 12*24=288 then your answer for 1.2*2.4=2.88

If it's wrong let me know and I'll help again.

Answer: It would be 2.88

Step-by-step explanation:

1) The probability of getting a queen is 187/10000 which is 0.0187 = 1.87%

2) The probability is 449 / 479 which is 0.937 = 93.7%

You may need to round the answers. It doesn't say if they need to be rounded or not.

Hi ShadowHawk,

1) If you conduct an experiment and randomly pull a card from a deck of cards 10,000 times, getting a Queen of Hearts 187 times, what is the experimental probability of drawing a Queen of Hearts the next time?

187/10,000 = 1.87% = 1.9%

2) If a kicker has kicked a ball 479 times for the extra point and scored the point 449 times, what is the experimental probability of the kicker making the next field?

449/479 = 93.7% = 94%

Answer:

  6

Step-by-step explanation:

The greatest common factor (GCF) of 18, 24, and 30 is 6.

Victor can make at most 6 bags with equal numbers of each type of cookie.

_____

18 = 6×3

24 = 6×4

30 = 6×5

One way to look for the GCF is to consider the differences between the numbers. The smallest difference between any pair is 6, which also divides all of the numbers evenly. Hence 6 is the GCF.

By finding the greatest common divisor (GCD) of the counts of each type of cookie (30, 18, 24), it is determined that Victor can make 6 identical bags for the bake sale.

To determine the greatest number of bags Victor can make, we need to find the greatest common divisor (GCD) of the counts of each type of cookie: 30 chocolate chip cookies, 18 peanut butter cookies and 24 sugar cookies. The GCD is the largest number that exactly divides all these counts.

First, list the divisors of each number:

Find the highest number that appears in each list. The highest common factor of 30, 18, and 24 is 6, so Victor can make a total of 6 equal bags with each type of cookie.

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Answer:12/4

Step-by-step explanation:

Solution:

The given complex expression is,

→(5+3 i) - (5+3 i)(5-5 i)

Keep in mind, i=√-1, i²= -1

=(5 + 3 i)[1- (5-5 i)]

=(5 + 3 i)[1-5+ 5 i]

= (5 + 3 i)[-4 + 5 i]

=5 × (-4 + 5 i) + 3 i×(-4 + 5 i)→→Used the identity, (a+b)×(c+d)=a×(c+d)+b×(c+d), Also Used distributive property of multiplication over addition and subtraction.

= -20 + 25 i-12 i +15 i²

= - 20 + 13 i-15

= -35 + 13 i

Aiden spent $22.20 on 60 candles. His sister spent $54.40 on 170 candles, $32.20 more than Aiden.

Let's break this down step by step:

a. To find out how much Aiden spent on candles, we multiply the number of candles he bought (60) by the price per candle ($0.37):

Total cost for Aiden = 60 × $0.37 = $22.20

So, Aiden spent $22.20 on candles.

b. Aiden's sister bought 170 candles and paid $0.05 less per candle than Aiden did. This means she paid $0.37 - $0.05 = $0.32 per candle.

To find out how much Aiden's sister spent on candles, we multiply the number of candles she bought (170) by the price per candle ($0.32):

Total cost for Aiden's sister = 170 × $0.32 = $54.40

So, Aiden's sister spent $54.40 on candles.

c. To compare who spent more on candles, we simply compare the total costs. Aiden spent $22.20 and his sister spent $54.40.

Aiden's sister spent more. To find out how much more she spent, we subtract Aiden's total from his sister's:

$54.40 - $22.20 = $32.20

So, Aiden's sister spent $32.20 more on candles than Aiden did.

The complete question is here:

To prepare for a wedding, Aiden bought 60 candles. He paid $0.37 for each candle. His sister bought 170 candles at a sale where she paid $0.05 less for each candle than Aiden did.

a. How much did Aiden spend on candles?

b. How much did Aiden's sister spend on candles?

c. Who spent more on candles? How much more?

Hey there!!

Equation Given : x + 3x - 36

In order to solve this, we will need to combine the like terms.

What are like terms?

Like terms are terms which have the same variable, in the equation given, the variable mentioned is x and hence, the like terms are x and 3x.

Now, we will need to combine x and 3x.

Let's take x as 1x and 3x as 3x.

Now, we will need to add both these like terms.

1x + 3x

x will be common, we will need to add 1 and 3

1 + 3 is 4 and hence, 1x + 3x = 4x

Hence, the final equation would be :

4x - 36

Hence, the answer is option ( c )

Hope my answer helps!

Answer:

4x-36 C

Step-by-step explanation:

Answer:

Jerry does [tex]2.11[/tex] cases per hour (Rounded to 2 decimal places). As we cannot do 0.11 cases. We can say Jerry does 2 cases per hour.

Step-by-step explanation:

to find the number of cases per hour, we have to divide the number of cases by number of hours taken for those cases,

Number of cases per hour = [tex]\frac{5cases}{2\frac{3}{8} hours}[/tex]

                                             =[tex]\frac{5}{\frac{19}{8} } \\[/tex] cases per hour

                                             =[tex]\frac{5*8}{19}[/tex] cases per hour

                                             =[tex]\frac{40}{19}[/tex] cases per hour

                                              =[tex]2.11[/tex] cases per hour (Rounded to 2 decimal places)

As we cannot do 0.11 cases. We can say Jerry does 2 cases per hour.

Answer:

1. Option B.

2. Option D.

3. Option C.

Step-by-step explanation:

(1)

The given function is

[tex]g(y)=2y+7[/tex]

Substitute y=8 to find the value of g(8).

[tex]g(8)=2(8)+7=16+7=23[/tex]

The value of g(8) is 23. Therefore, the correct option is B.

(2)

Area of a rectangle is

[tex]Area=length\times width[/tex]

From the given figure it is clear that the length of the seating area is 700 ft and width of the seating area is 525 ft.

The total seating area is

[tex]Area=700\times 525[/tex]

[tex]Area=367500[/tex]

The seating are is 367500 ft².

According to the “rule of thumb,” circulation Area comprises roughly 25 to 40% of the total Usable Area.

40 % of total area is

[tex]367500\times \frac{40}{100}=147000[/tex]

Using a standard rule of thumb the attendance is 147,000 People.

Therefore, the correct option is D.

(3)

Each person takes up 2 square feet. Then the total number of persons is

[tex]People=\frac{367500}{2}[/tex]

[tex]People=183750[/tex]

Therefore, correct option is C.

Answer:

The commutative property lets you group like terms together:

... 5x +3x +9x +20 +7

Step-by-step explanation:

If we divide the expression into 4 groups:

...[5x] +(20) +(3x +9x) +[7]

according to the commutative property of addition, we can swap the groups in curved parentheses.

... [5x] +(3x +9x) +(20) +[7]

_____

The distributive property lets you combine x terms:

... (5 +3 +9)x +27

... 17x +27 . . . . . . the simplified form of the expression

Answer:

B. (x-8)(x-5).

Step-by-step explanation:

Given  : Equations .

To find : Which of the given expressions results in 0 when evaluated at x = 5.

Solution : We have given equations

We need the result zero.

We can see from the given equation (x-8) (x-5)

If we plug x = 5.

(5 -8 )( 5 -5).

-3 (0).

0. (  multiply with zero to any number it will always be zero )

Therefore, B. (x-8)(x-5).

Solution is given in attachment below.

Final answer:

The percent drop in temperature from 80°F to 70°F is calculated as (10°F / 80°F) × 100%, which equals 12.5%.

Explanation:

To find the percent drop in temperature from 80°F to 70°F, we need to calculate the decrease in temperature and then express that decrease as a percentage of the original temperature. The decrease in temperature is 80°F - 70°F = 10°F. To find the percent drop, we use the formula for percentage change, which is (Change/Original) × 100%.

Therefore, the percent drop = (10°F / 80°F) × 100% = 12.5%. So, the temperature dropped by 12.5% from 80°F to 70°F.

Final answer:

To find the percent drop in temperature from 80°F to 70°F, calculate the difference between the temperatures and divide by the original temperature, then multiply by 100%. The result is a 12.5% decrease in temperature.

Explanation:

The question asks to find the percent drop in temperature when it drops from 80°F to 70°F. To calculate this, we use the formula for percent decrease, which is (original value - new value) / original value × 100%. Applying this formula, the original temperature is 80°F, and the new temperature is 70°F.

(80°F - 70°F) / 80°F × 100% = 10°F / 80°F × 100% = 0.125 × 100% = 12.5%.

Therefore, the temperature dropped by 12.5% when it fell from 80°F to 70°F.

Using proportion concepts, it is found that the equivalent statement is:

(F) The price now is 66 2/3 % of what it was before

The statement is:

"price decreased by 1/3"

It decreases by 1/3, thus it is [tex]\frac{2}{3} = 0.6667 = 66\frac{2}{3}\%[/tex] of what was before, which means that the equivalent statement is given by option F.

As for the other statements, they do not have the correct percentage or ratio, which we found above.

A similar problem is given at https://brainly.com/question/10491646

Two factors of x²-12x+36 are

(x-6) and (x-6)

Solution;

x²-12x +36

x²-6x -6x +36  ( split -12x in two parts such that if add them we will get-12x and if multiply will get 36x²)

Taking x common from first two terms and 6 from next two terms

x(x-6) -6(x -6)

taking (x-6) common

(x-6)(x-6)

Answer:

[tex]x^2 - 12x + 36 = (x-6)(x-6) = (x-6)^2[/tex]

Step-by-step explanation:

We are given the following expression:

[tex]x^2 - 12x + 36[/tex]

We need to factor the given expression.

We will do this with the help of technique of splitting the middle term.

Factorization can be done as:

[tex]x^2-12x + 36\\=x^2 - 6x-6x+36\\=x(x-6)-6(x-6)\\=(x-6)(x-6)\\=(x-6)^2[/tex]

Thus, the factored form of given expression is:

[tex]x^2 - 12x + 36 = (x-6)(x-6) = (x-6)^2[/tex]

Answer:

The answer is A. Substitution

Step-by-step explanation:

Looking at the previous proofs, you can see that:

∠Y≅∠4

∠Z≅∠6

∠X + ∠4 + ∠6 = 180°

Statement 5 then replaces ∠4 and ∠6 with ∠Y and ∠Z, respectively. Replacing it means that it was substituted with the GIVEN values by the previous statements.

The best answer is the Substitution.  

Answer:

My other answer was deleted, but yes, it should be A, substitution.