What value of x will make the triangles similar by the SSS similarity theorem?
15.9
59
77
96.8

To solve −3.64⋅|−5.3|−1.53, calculate the absolute value of −5.3, which is 5.3, then multiply by −3.64 to get −19.292, and finally, subtract 1.53 to result in −20.822.

You have presented a mathematical expression involving absolute value and multiplication: −3.64⋅|−5.3|−1.53. Let's solve this step by step:

Now performing the operations:

Therefore, the result of the given expression −3.64⋅|−5.3|−1.53 is −20.822.

To determine the probability of a patron waiting less than 18 minutes or more than 25 minutes at a restaurant, we calculate the Z-scores for each time, look up the corresponding probabilities in a standard normal distribution table, and add the probabilities together.

To find the probability that a patron will wait less than 18 minutes or more than 25 minutes at a restaurant with an average waiting time of 23.5 minutes and a standard deviation of 3.6 minutes, assuming a normal distribution, we need to calculate two separate probabilities and then add them together.

First, we calculate the Z-score for 18 minutes, which is (18 - 23.5) / 3.6. Then, we find the corresponding probability from the standard normal distribution table. This gives us the probability of waiting less than 18 minutes.

Secondly, we calculate the Z-score for 25 minutes, which is (25 - 23.5) / 3.6. The corresponding probability gives us the probability of waiting more than 25 minutes. However, we want the probability of waiting longer, so we subtract this probability from 1 to find the probability of waiting more than 25 minutes.

Adding both probabilities gives us the total probability of a patron waiting either less than 18 minutes or more than 25 minutes.

Answer:

add the parallel sides and divide by 2

then multiply it by the perpendicular side so  

Step-by-step explanation:

A=side one+side two x2

                2

Mia used [tex]3\frac{19}{36}[/tex] lb of flour to bake the chocolate cake.

Given:

Total flour [tex]10\frac{1}{9}[/tex] lbs

She used:

[tex]2\frac{3}{4}[/tex] for banana cake

x lbs for chocolate cake

Flour left [tex]3\frac{5}{6}[/tex] lbs

How much flour did she use to bake the chocolate cake?

so the flour that Mia use for banana cake is total flour subtract the flour that she used plus the left over.

x =Total flour - flour for banana cake - left over

[tex]\boxed {= 10\frac{1}{9} - 2\frac{3}{4} - 3\frac{5}{6} } \\[/tex]

I am going to put this into improper fraction

[tex]\boxed { = \frac{91}{9} - \frac{11}{4} - \frac{23}{6} }[/tex]

because the denominator is different, we are going to find the common denominator for 9, 4 and 6 which is 36

[tex]\boxed {= \frac{364-99-138}{36} }\\ \boxed {= \frac{127}{36} }\\\boxed {= 3\frac{19}{36} }[/tex]

So the flour that she use to bake the chocolate cake is [tex]3\frac{19}{36}[/tex] lbs

Part to whole relationship https://brainly.com/question/11677654

Math word problem brainly.com/question/997374

Mixed fraction brainly.com/question/745462

Keyword: mixed fraction, subtraction, improper fraction, part to whole relationship

Final answer:

The prediction method for the number of broken light bulbs in an order is based on a proportional relationship. Using the ratio from a smaller sample, it's calculated that an order of 125 light bulbs would result in 20 broken bulbs, assuming the breakage rate stays constant.

Explanation:

Given that 4 out of 25 light bulbs are broken in the initial order, we can predict the number of broken light bulbs in a larger order of 125 bulbs. The ratio of broken bulbs to total bulbs in the initial order is 4 broken bulbs for every 25 bulbs.

To find the predicted number of broken bulbs in a larger order, you multiply the total number of bulbs in the larger order by the ratio of broken bulbs in the smaller order. The calculation for the larger order of 125 bulbs would be:

(4 broken bulbs / 25 total bulbs) × 125 total bulbs in the larger order = 20 broken bulbs

Therefore, if 25 light bulbs yield 4 broken ones, an order of 125 light bulbs is predicted to have 20 broken bulbs, assuming the rate of breakage remains consistent.

In the 2005 regular season, the Chicago White Sox won 99 games and the Detroit Tigers won 71 games.

In the 2005 regular season, let's denote the number of games won by the Chicago White Sox as 'x' and the number of games won by the Detroit Tigers as 'y'. We know that the Chicago White Sox won 28 more games than the Detroit Tigers, so we can write x = y + 28.

Together, they won a total of 170 games, so we can write x + y = 170.

Now we can solve the system of equations:

Therefore, the Chicago White Sox won 99 games and the Detroit Tigers won 71 games.

The Chicago White Sox won 99 games and the Detroit Tigers won 71 games in the 2005 regular season.

To find out how many games each team won, we need to set up a system of equations using the given information. Let x represent the number of games won by the Chicago White Sox and y represent the number of games won by the Detroit Tigers.

We are given two pieces of information:

1. The White Sox won 28 more games than the Tigers, so we have the equation x = y + 28.

2. Together, both teams won a total of 170 games, so we have the equation x + y = 170.

We can use these equations to solve for the values of x and y. Substituting the first equation into the second equation, we get (y + 28) + y = 170. Combining like terms, we have 2y + 28 = 170. Subtracting 28 from both sides, we get 2y = 142. Dividing both sides by 2, we find that y = 71.

Now we can substitute the value of y back into the first equation to find x. x = 71 + 28, so x = 99. Therefore, the Chicago White Sox won 99 games and the Detroit Tigers won 71 games.

Answer:

19038

Step-by-step explanation:

Given : A culture started with 6000 bacteria after 3 hours to grew to 7200 bacteria

To Find: Predict how many bacteria will be present after 19 hours

Solution:

General Form of exponential function: [tex]y=ab^x[/tex]

where y is the amount after x hours

x is the time

a is the initial amount

b is the growth factor

Bacteria initial amount= a = 6000

Time = x = 3 hours

Amount of bacteria after 3 hours = 7200

Substitute the values in the general form

[tex]7200=6000(b)^3[/tex]

[tex]\frac{7200}{6000}=(b)^3[/tex]

[tex]\sqrt[3]{\frac{7200}{6000}}=b[/tex]

[tex]1.06265856918=b[/tex]

Now we are supposed to find how many bacteria will be present after 19 hours

So, Bacteria initial amount= a = 6000

Time = x = 19 hours

Amount of bacteria after 19 hours = y

Substitute the values in the formula:

[tex]y=6000(1.06265856918)^{19}[/tex]

[tex]y=19038.488[/tex]

Hence there will be approximately 19038 bacteria present after 19 hours

Answer:

So the answer is D

Step-by-step explanation:

1.) 9(4) + 8(5)

36 + 40 = 74

2.) 2(3) + 8(3)

6 + 24 = 30

3.) 4(5) + 7(5)

20 + 35 = 55

4.) 10(4) + 18(5)

40 + 90 = 130

5.) 2 + 8(1/4)

2 + 2 = 4

6.) 9(1/3) + 8(1/4)

3 + 2 = 5

7.) 3(8) + 7(4)

24 + 28 = 52

8.) 12(1/4) + 16(5)

4 + 80 = 84

Final answer:

To calculate the percentage discount of a book, subtract the sale price from the original price, divide by the original price, and multiply by 100. The detailed calculation shows that the book had a 30% discount during the sale.

Explanation:

The question asks how to calculate the percentage discount of a book that has been reduced from its normal price to a sale price. To find the percentage discount, we subtract the sale price from the original price, and then divide this difference by the original price. Finally, we multiply by 100 to get the percentage.

Step-by-Step Solution:

The percentage discount offered on the book during the sale was 30%.

The height of the cylinder is 14 centimetres.

To find the height of the cylinder, we use the formula for the volume of a cylinder, which is given by [tex]\( V = \pi r^2 h \),[/tex] where V is the volume, r is the radius, and h is the height.

Given that the volume V is [tex]224\pi[/tex] cubic centimetres and the radius r is 4 centimetres, we can substitute these values into the formula to solve for the height h:

[tex]\[ 224\pi = \pi (4)^2 h \][/tex]

Simplifying the equation by dividing both sides  [tex]\( \pi \) and \( (4)^2 \),[/tex]we get:

[tex]\[ \frac{224\pi}{\pi \cdot 16} = h \][/tex]

[tex]\[ \frac{224}{16} = h \][/tex]

[tex]\[ 14 = h \][/tex]

Therefore, the height h of the cylinder is 14 centimetres.

People will need to go through more than one obstacle at locations 1, 2, and 3 on the course.

let's break it down:

Tires: Appear every sixth of the course.

Cones: Appear every third of the course.

Hurdles: Appear every half of the course.

To find where people need to go through more than one obstacle, we need to find the common multiples of these fractions.

Tires (1/6 of the course):

Locations of tires: 1/6, 2/6, 3/6, 4/6, 5/6, 6/6 (which is the end)

Locations: 1, 2, 3, 4, 5, 6

Cones (1/3 of the course):

Locations of cones: 1/3, 2/3, 3/3 (which is the end)

Locations: 1, 2, 3

Hurdles (1/2 of the course):

Locations of hurdles: 1/2, 2/2 (which is the end)

Locations: 1, 2

Now, let's find where there are overlaps:

Location 1: There's a tire, a cone, and a hurdle.

Location 2: There's a tire and a cone.

Location 3: There's a tire and a cone.

Location 4: There's a tire.

Location 5: There's a tire.

Location 6: There's a tire.

So, people need to go through more than one obstacle at locations 1, 2, and 3.