Given G is the midpoint of EH, FG= GI, Prove triangle EFG= triangle HIG

We can fit 33 books on a 42-inch shelf if each book is 1 1/4 inches wide.

Using a unitary method, we can easily solve problems that involve proportional relationships between different units. In this problem, we used the unitary method to determine how many books can fit on a shelf based on its length and the width of one book.

To find out how many books can fit on a 42-inch shelf, we need to divide the length of the shelf by the width of one book. In this case, each book is 1 1/4 inches wide. However, it's important to convert this fraction to a decimal so we can do the math more easily. To do this, we can divide 1 by 4 and add it to 1 1/4:

1/4 = 0.25

1 1/4 = 1 + 0.25 = 1.25

Now that we know each book is 1.25 inches wide, we can use the unitary method to find how many books can fit on the shelf:

1 book = 1.25 inches

x books = 42 inches

To solve for x, we can cross-multiply:

1 book * 42 inches = 1.25 inches * x books

42 = 1.25x

Finally, we can divide both sides by 1.25 to isolate x:

42 / 1.25 = x

33.6 = x

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The expected value of the policy for the insurance company: $359.38

Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.

Probability of Event = Favorable Outcomes/Total Outcomes = X/n

The expected value of the policy for the insurance company can be calculated as follows:

Expected value = (Probability of survival) x (Annual payment)

= 0.999057 x $360

= $359.38

So, the expected value of the policy for the insurance company is $359.38.

It's important to note that this is just an estimate based on statistical probabilities and does not guarantee the outcome. The actual value could be higher or lower than this estimate, depending on the actual lifespan of the policyholder.

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Ari will likely think that the amount of caramel in Freeze Zone milkshakes is too high, since the ratio of ice cream to caramel is much higher than her ideal ratio.

Ari's ideal ratio of ice cream to caramel for a milkshake is 5 scoops of ice cream for every 3 spoonfuls of caramel. Freeze Zone's milkshakes, however, have a ratio of 10 scoops of ice cream for every 7 spoonfuls of caramel, which is significantly higher than Ari's ideal ratio. Therefore, Ari will likely think that the amount of caramel in Freeze Zone milkshakes is too high. The higher ratio of ice cream to caramel means that the milkshake will be sweeter, and may not have the desired balance of flavors that Ari prefers. Ari may also think the milkshake is too heavy or overly sweet, since the extra caramel creates a consistency that is different from what she is used to. Ultimately, Ari will likely think that the amount of caramel in Freeze Zone's milkshakes is too high for her liking.

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Using petid as a primary key in the pet relation is generally a good way to uniquely identify each data record in the relation. However, in some cases, it may be necessary to include personid as part of the primary key of the pet relation.

This is because each pet should have a unique identifier, and petid is specifically designed to serve this purpose. This would be the case if a person can have more than one pet in the database, and if the same petid value is used for more than one pet (which would violate the uniqueness requirement of a primary key).

By including personid as part of the primary key of the pet relation, we ensure that each pet in the database has a unique identifier (i.e., a unique combination of petid and personid). This allows us to avoid any confusion that might arise if two or more pets in the database had the same petid value. It also allows us to link each pet to its owner via the personid attribute, which can be useful for querying and reporting on the data.

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Answer:

So Andrea and Casey each make $52 after working for 3 hours.

Step-by-step explanation:

Let's call the number of hours that Andrea and Casey work "x".

The amount of money that Andrea makes in a given hour can be represented as 25 + 9x.

The amount of money that Casey makes in a given hour can be represented as 10 + 14x.

We want to find the number of hours it takes for Andrea and Casey to make the same amount of money, which we can represent as:

25 + 9x = 10 + 14x

To solve for x, we can isolate x by subtracting 10 from both sides of the equation:

15 + 9x = 14x

Next, we can isolate 9x by subtracting 14x from both sides of the equation:

15 = -5x

Finally, we can divide both sides of the equation by -5 to solve for x:

-3 = x

So it takes 3 hours for Andrea and Casey to make the same amount of money. To find the amount of money, we can plug in x = 3 back into either of the equations:

Andrea's equation: 25 + 9x = 25 + 9 * 3 = 25 + 27 = 52

So Andrea and Casey each make $52 after working for 3 hours.

Answer: 22

Step-by-step explanation:

f(x) is basically the y of the function and we sent x=3. go back to the function and plug in 3 in the x. then solve 3^2=9  2x9=18 18+4=22 BOOOM  MATHH

Answer:

160 pounds of algae

Step-by-step explanation:

10 times 2 is 20   ( first 5 hours )

20 times 2 is 40  (10 hours)

40 times 2 is 80 (15 hours)

80 times 2 is 160 ( 20 hours)

there would be 160 pounds of algae

130 estimated to the nearest integer is 130 itself as 130 itself is an integer.

Integers are numbers which includes the set of natural numbers, 0 and the negatives of all those natural numbers.

Set of integers are usually denoted as Z.

A number is normally rounded to the nearest integer when it is decimal.

First we have to look at the tenths place.

When the digit in the tenths place is 5 or numbers greater than 5, then increase digit in the ones place by 1.

If the digit in tenths place is less than 5, then leave the ones place as such.

Suppose that the number is 1.30.

Then the digit in tenths place is 3, less than 5. So leave the digit in one place which is 1, as such.

So 1.30 rounded to the nearest integer is 1.

Here 130 itself is an integer.

Hence 130 rounded to nearest integer is 130.

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Hi there, here's your answer:

Given, a basketball team averaged 68 points per game in the last season and averaged 77 points per game in the present season.

To find:

The approximate percentage of increase.
Solution:

If 68 points was the average last season, and 77 points was the increase this season, then the number of increase in points is 9.

Also we have that % increase = [tex]\frac{Difference}{Original}[/tex] × 100

Which is [tex]\frac{9}{68}[/tex] × 100 = 0.1323 × 100 = 13.23%

Therefore, the approximate percent increase is 13%.

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Bearing is measured from reference line clockwise or counter-clockwise - FALSE.

A bearing is an angle that is calculated clockwise from the north.

The vertical angle between an object's direction and either north or another object is known as a bearing or azimuth in navigation. You can specify the angle value in a number of different angular units, including degrees, mils, and grad.

Angles are measured in comportments clockwise from north.

The direction of north must be identified before taking a bearing measurement.

The math exam question will typically include this north direction. The required angle is then measured in a clockwise fashion. Since all bearings must be reported in three figures, we must begin the three-figure bearing with zero if the angle measured is less than 100 degrees.

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a) "What is your age?" is a quantitative data.

b) "Are you male or female?" is a categorical data.

c) "When did you first start reading the wsj?" is a categorical data.

d) "How long have you been in your present job or position?" is a quantitative data.

e) "What type of vehicle are you considering for your next purchase?" is a categorical data.

(a) "What is your age?" - This question provides quantitative data because age is a numerical value that can be measured and ordered in a meaningful way. Respondents could give an answer such as "25", "45", or "70", for example, which can be used to calculate statistics such as the mean or median age of the survey population.

(b) "Are you male or female?" - This question provides categorical data because the responses fall into discrete, non-numeric categories (in this case, "male" or "female"). It's not possible to order the responses in a meaningful way, since there is no inherent numerical value associated with being male or female.

(c) "When did you first start reading the WSJ?" - This question provides categorical data because the possible responses fall into discrete, non-numeric categories (high school, college, early career, mid career, late career, or retirement). While it's possible to order the categories in a logical sequence, they don't represent numerical values.

(d) "How long have you been in your present job or position?" - This question provides quantitative data because the responses can be measured as numerical values (for example, "3 years", "10 years", or "25 years"). The data can be used to calculate statistics such as the average length of time that respondents have been in their current position.

(e) "What type of vehicle are you considering for your next purchase?" - This question provides categorical data because the possible responses fall into discrete, non-numeric categories (sedan, sports car, SUV, minivan, etc.). While it's possible to order the categories in a logical sequence based on size, price, or other factors.

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Answer:

Step-by-step explanation:

To build a sequence, you have to create a rule. For example, if the rule is +2, then you add 2 to 10 to get 12, and then you add 2 to 12 to get 14, and so on. Your sequence would then be 10, 12, 14, 16, 18.

Based on the information, it can be inferred that Mr. Incredible did more work than Dash moving the train car.

To calculate the work that Mr. Incredible and Dash did moving the train car, we must apply the following mathematical formula:

According to the above, we only have to replace the values according to each case.

According to the above, it can be inferred that Mr. Incredible made more effort than Dash because they did 500,000 J and 500 J of work respectively.

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The graph of the function f(x) = x(x + 5)(x - 2) have x intercepts at x = 0, -5 and 2

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the equation:

f(x) = x(x + 5)(x - 2)

x(x + 5)(x - 2) = 0

x = 0, x + 5 = 0, x - 2 = 0

x = 0, -5 and 2

The graph of the function f(x) = x(x + 5)(x - 2) have x intercepts at x = 0, -5 and 2

Hence, the graph of the function f(x) = x(x + 5)(x - 2) have x intercepts at x = 0, -5 and 2

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Answer:

Step-by-step explanation:

To determine how long it will take for Louise to reach her goal of $30,000, we can use the formula for compound interest:

A = P * (1 + r/n)^(nt)

where:

A is the amount of money Louise will have after "t" years,

P is the initial investment of $20,000,

r is the annual interest rate of 4.28%,

n is the number of times the interest is compounded per year (12 times per year), and

t is the number of years.

We can rearrange this formula to solve for t:

t = (log(A/P)) / (log(1 + r/n))

Plugging in the values:

t = (log(30000/20000)) / (log(1 + (0.0428/12)))

t = 5.97 years

Rounding to the nearest tenth of a year, Louise will need to wait 6.0 years in order to reach her goal of $30,000.

The length x of the right triangle is 8.66 units.

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, the side of the right triangle can be found using trigonometric ratios as follows:

Hence,

tan 60° = opposite / adjacent

where

opposite side = x

adjacent side = 5

Therefore,

tan 60° =  x  / 5

cross multiply

x = 5 tan 60°

x = 5 × 1.73205080757

x = 8.66025403784

x = 8.66 units

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The order of processes that support the central dogma are:1.DNA replication: the process by which DNA makes a copy of itself.

2.Transcription: the process by which RNA is synthesized from a DNA template.

3.Translation: the process by which proteins are synthesized from RNA templates.

The central dogma of molecular biology describes the flow of genetic information within a biological system. The method by which DNA instructions are translated into useful products is known as the "Central Dogma." Francis Crick, who discovered the structure of DNA, first put up the idea in 1958.

The order of processes that support the central dogma are:

1.DNA replication: the process by which DNA makes a copy of itself.

2.Transcription: the process by which RNA is synthesized from a DNA template.

3.Translation: the process by which proteins are synthesized from RNA templates.

In summary, the central dogma can be described as follows: DNA is replicated to make more DNA, DNA is transcribed into RNA, and RNA is translated into proteins.

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Answer:

Step-by-step explanation:

so 1in is 2.5ft.

6.4 times 2.5 is 16.

4.8 times 2.5 is 12.

16+16+12+12

is 24+32.

which is 56.

answer: B

Given the angle bisector, the statements and reasons for the proof are explained.

A bisector splits a given line or angle into two equal parts. A straight line is said to be an angle bisector if it divides a given angle into two equal measures. Such that on comparison, the sum of the angles formed is equal to the measure of the bisected angle.

The statements and reasons for the proof are given below;

      STATEMENT                                                    REASONS

1. MK bisects <HKO and <HMO                           Given

2. m<HMK = m<OMK and m<HKM = m<OKM    Definition of angle bisector

3. HK ≅ KO, and HM ≅ OM                                 Congruent side property

4. ΔHMK ≅ ΔOMK                                               Angle-Angle-Side theorem

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Answer:

$1350.68 to nearest cent.

Step-by-step explanation:

At the beginning $500 is deposited and this accumulates interest for 3 years At the end of first year it increases to 500( 1 + r) dollars

Then at the end of the 2 years its value is

500(1+ r)(1 + r)(

and at the end of 3 years value =

500(1 + r)(1 + r)(1 + r)

= 500(1 + r)^3 dollars

and as 1 + r = x we have:

500x^3 dollars

In the same way 200 for 2 years = 200x^2

and 600 for 1 year = 600x dollars.

Total = 500x^3 + 200x^2 + 600x.

b.

So, if the interest r = 2 % (= 0.02)

and x = 1.02

Total value after 3 years

= 500(1.02)^3 + 200(1.02)^2 + 600(1.02)

= 530.604 + 208.08 + 612

= $1350.684

his selling rate is: 750 balloons / 15 days = 50 balloons per day . To calculate Jack's selling rate in balloons per day, we need to divide the total number of balloons he sold by the number of days he worked.

This means that Jack sold an average of 50 balloons per day over the last 15 days. This information is useful for several reasons. For example, the party supply store might use this information to evaluate Jack's performance and determine whether he is meeting their expectations. It might also be useful for forecasting future sales, since if Jack continues to sell balloons at a rate of 50 per day, we can estimate how many balloons he will sell in a future period of time by multiplying the number of days by 50. In this case,

Jack sold 750 balloons in 15 days, so his selling rate is: 750 balloons / 15 days = 50 balloons per day

It's important to note that the selling rate of 50 balloons per day is an average, and it's possible that Jack's sales varied from day to day. For example, he might have sold more balloons on some days and fewer on others. However, by calculating the average selling rate, we get a general sense of how many balloons Jack sold per day over the course of the last 15 days.

In conclusion, Jack's selling rate in balloons per day over the last 15 days was 50 balloons. This information provides insight into Jack's performance and can be used to make informed decisions about future sales.

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Answer:no

Step-by-step explanation:

Answer:

20% reduction in price

Step-by-step explanation:

Let the original price of each box be P and original quantity be Q. The unit rate is P/Q

Jack's approach

increase quantity by 25% = 0.25Q

New quantity = Q + 0.25Q = Q(1  +0.25) = 1.25Q

Unit rate = P/1.25Q

Sadia's approach

Reduce price and keep quantity same

Let price reduction be d% = d/100

Let us denote d/100 as r. This will be a decimal value. For example, a reduction of 10% means that the price is reduced by 0.10

Price reduction = P x r = Pr

New price = P - Pr = P(1-r)

Unit rate by this method =P(1-r) /Q

Both unit rates have to be the same if both values are the same

So
[tex]\dfrac{P}{1.25Q} = \dfrac{P(1-r)}{Q}\\\\\dfrac{P}{Q} \cdot \dfrac{1}{1.25} = \dfrac{P}{Q} \cdot (1-r)\\\\[/tex]

Eliminate [tex]\displaystyle {\dfrac{P}{Q}}[/tex]   common factor from both sides to get

[tex]\dfrac{1}{1.25} = 1- r[/tex]

[tex]\dfrac{1}{1.25} = 0.8\\\\[/tex]

So we get
[tex]1 - r = 0.8\\\\\implies r = 1 - 0.8 = 0.2\\\\[/tex]

0.2 works out to 0.2 x 100 = 20%

So for Sadia's idea to have the same value as Jack's idea, the price should be reduced by 20%

Answer:

C. 77.3% decrease

Step-by-step explanation:

To calculate the percent change, we can use the formula:

percent change = (new value - old value) / old value * 100

Plugging in the values, we get:

percent change = (20 - 88) / 88 * 100 = -68 / 88 * 100 = -0.772727 * 100 = -77.3

Since the new value is lower than the old value, this is a decrease, and the answer is -77.3, or 77.3% decrease.

Answer: -18x² + 3x +14y - 6

10y - 14x² + 3x - 4x² + 4y - 6

- 14x²- 4x² + 3x + 10y + 4y -6

-18x² + 3x +14y - 6

Greta feeds Lizzy 56 crickets when she feeds Draco 77.

Proportion, in general is referred to as a part, share or number considered in comparative relation to a whole.

According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.

The ratio is a way of comparing two quantities of the same kind by using division. The ratio formula for two numbers a and b is given by a: b or a/b

Given:

For every 11 crickets Greta feeds Draco, she always feeds Lizzy 8 crickets.

Let solve it by an equality

[tex]\frac{11}{8} = \frac{77}{x}[/tex]

We want to solve for x.

We can do so by finding how much larger the second fraction is than the first.

In this case, 77 is 7 times larger than 11.(77/11 = 7)

So, we know that x must be 7 times larger then 8( because the fractions are proportinal)

Since x is 7 times larger than 8, we can use 7 times 8 to find the value.

7 times 8 i s56

56 crickets for Lizzy.

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x is 7 times larger than 8, we can use 7 times 8 to find the value, 7 times 8 is 56. Greta feeds Lizzy 56 crickets while she feeds Draco 77.

What is the Proportion?

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole.

According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.

The ratio is a way of comparing two quantities of the same kind by using division. The ratio formula for two numbers a and b is given by a: b or a/b

Given:

For every 11 crickets Greta feeds Draco, she always feeds Lizzy 8 crickets.

Let solve it with an equality

11/8 = 77/x

We want to solve for x.

We can do so by finding how much larger the second fraction is than the first.

In this case, 77 is 7 times larger than 11.(77/11 = 7)

So, we know that x must be 7 times larger than 8( because the fractions are proportional)

Hence, x is 7 times larger than 8, we can use 7 times 8 to find the value.

7 times 8 is 56.

56 crickets for Lizzy.

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According to the model, around 521 people will be infected in three days.

A unitary method is a mathematical technique where we use ratios and proportions to find the value of an unknown quantity.

Let's start by breaking down the problem. We know that there are currently 392 people infected and the virus is spreading at a rate of 11% each day. This means that for every 100 people, 11 people are getting infected. To calculate how many people will be infected in three days, we need to use a unitary method.

To do this, we need to calculate the total increase in the number of infected people over three days. Since the virus is spreading at a rate of 11% each day, the total increase over three days will be 33% (11% x 3). We can then use this percentage increase to calculate the total number of people infected in three days.

To find the total number of people infected in three days, we can use the following formula:

Total infected = current infected + (current infected x percentage increase)

Plugging in the values from the problem, we get:

Total infected = 392 + (392 x 0.33)

Total infected = 392 + 129.36

Total infected ≈ 521

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Answer:

Step-by-step explanation:

2, there are 4, making it the most.