7. The expression below is evaluated as shown. In which step does the first
mistake appear?

the interest earned on 250000 at a 7.5% interest rate for half a year is 4687.50. This means that after half a year, the total amount that you would have is the sum of the principal and the interest, which is 254687.50.

To calculate the interest on 250000 at a 7.5% interest rate for half a year, we first need to determine the annual interest rate, as most interest rates are quoted on an annual basis. To do this, we can divide the annual interest rate of 7.5% by 2 to get the half-yearly interest rate, which is 3.75%.

Next, we can use the formula for simple interest to calculate the interest earned over half a year. Simple interest is calculated by multiplying the principal amount (in this case, 250000) by the interest rate (3.75%) and the time period (0.5 years).

So, the interest earned would be:

Interest = Principal x Rate x Time

= 250000 x 0.0375 x 0.5

= 4687.50

Therefore, the interest earned on 250000 at a 7.5% interest rate for half a year is 4687.50. This means that after half a year, the total amount that you would have is the sum of the principal and the interest, which is 254687.50.

It's worth noting that this calculation assumes that the interest is simple interest, which means that the interest earned is not reinvested. If the interest is compounded (i.e., the interest earned is reinvested), then the interest earned would be higher.

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Answer:

Rewrite the expression using the negative exponent rule b−n=1bn b - n = 1 b n . 1y98 1 y 9 8.

Step-by-step explanation:

If the number of people arriving for treatment at an emergency room is modeled by a Poisson process with a mean of 5 people per hour, we can use this information to estimate the expected number of people who will arrive during a 45-minute period.

The Poisson distribution describes the probability of a certain number of events occurring in a fixed interval of time, given the average rate at which the events occur. In this case, the Poisson distribution can be used to estimate the number of people who will arrive during a 45-minute period, given that the mean arrival rate is 5 people per hour.

To calculate the expected number of arrivals, we first need to convert the 45-minute time period into hours. There are 60 minutes in an hour, so 45 minutes is equivalent to 0.75 hours.

Next, we can use the Poisson distribution formula, which is:

P(X = k) = (e^(-λ) * λ^k) / k!

where λ is the mean arrival rate (in this case, 5 people per hour), k is the number of arrivals we are interested in, and e is Euler's number (approximately 2.71828).

Expected number of arrivals = λ * t = 5 * 0.75 = 3.75

Therefore, we can expect approximately 3.75 people to arrive for treatment during a 45-minute period, assuming that the number of arrivals follows a Poisson distribution with a mean of 5 people per hour.

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The phrase that reflects the amount of recordings, in thousands, owned by the collector 4 years later if it continues to expand at this rate is:   [tex]O 12 • (1.02)^48[/tex] Thus, option C is correct.

o calculate the number of records that will increase by a factor, you first need to know the initial number of records. Let's call this number "N".

To increase the number of records by a factor of "F", you can simply multiply the initial number of records by the factor:

New number of records = N x F

For example, if you have 100 records and you want to increase the number of records by a factor of 3, the new number of records would be:

New number of records  [tex]= 100 x 3 = 300[/tex]

So, the new number of records would be 300.

The growth rate is 2% per month, which means that the number of records will increase by a factor of 1.02 each month. After 4 years (48 months), the number of records owned by the collector can be calculated using the formula:

[tex]12,000 x (1.02)^48[/tex]

Simplifying this expression, we get:

[tex]12,00x0 1.02^48[/tex]

Therefore, the expression that represents the number of records, in thousands, owned by the collector 4 years later if it continues to grow at this rate is: O 12 • (1.02)^48

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The percentage of 65 out of 140 will be 46.428%.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

[tex]\text{Percentage (P) = [Final value - Initial value] / Initial value x 100}[/tex]

The whole numbers are 65 and 140.

Then the percentage is written as,

[tex]P = (65 \div 140) \times 100[/tex]

[tex]P=0.46428 \times 100[/tex]

[tex]P=46.428\%[/tex]

The percentage of 65 out of 140 will be 46.428%.

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can we see a picture or equation

According to a histogram that displays the percentage of replies over time, an April Gallup poll indicated that 55% of Americans think autonomous cars would be widely used in the next ten years.

Whether completely automated "driverless automobiles" would be widely deployed in the United States was the subject of a Gallup Poll conducted in April, which polled Americans ages 18 and older.

How soon, in your opinion, do you believe autonomous cars will be widely used in the US? According to the survey, 55% of Americans think autonomous cars will become commonplace over the next ten years.

The survey's results were displayed as a histogram, displaying the proportion of replies at various time intervals. This indicates how many respondents indicated that driverless cars will be widely utilised within a particular time period (e.g., within 5 years, within 10 years, etc.).

This survey reveals how people feel about autonomous cars in the future and how soon they believe they will be a common sight on the roads.

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The question is -

A Gallup Poll utilizing a random sample of adults ages or older was conducted in April. The survey indicated a majority of Americans () say driverless cars will be common in the next years (). The question asked was: Thinking about fully automated, "driverless cars," cars that use technology to drive and do not need a human driver, based on what you have heard or read, how soon do you think driverless cars will be commonly used in the [United States]? The figure below shows a summary of the results of the survey in a histogram indicating the percentage of the total responses in different time intervals.

There are 1960 different ways to distribute 8 identical pieces of candy to the five children, where the twins get an equal amount of candy.

First, distribute the candy to the twins.

Split the 8 pieces of candy into two equal parts for the twins using combinations:

C(8, 4)

This means selecting 4 pieces of candy from the 8 identical pieces for one twin, and the remaining 4 pieces will automatically go to the other twin.

C(8, 4) is calculated as:

[tex]^8C_4 = \dfrac{8!}{4!(8-4)!}[/tex]

     = 8! / (4! * 4!)

     = (8 * 7 * 6 * 5) / (4 * 3 * 2 * 1)

     = 70

Now, you have distributed 4 pieces of candy to each of the twins. Y

In this case, you have 6 pieces of candy to distribute among 3 children, and you can use two dividers (bars) to separate the candy for each child.

This can be represented as:

OO|OO|OO

The two bars split the 6 pieces of candy into three sections for the three children.

So, you have C(6 + 2, 2) ways to distribute the remaining candy:

[tex]^{6+2}C_2 = \dfrac{8!}{2!(8-2)!}[/tex]

         = 8! / (2!(8 - 2)!)

         = 8! / (2! * 6!)

         = (8 * 7) / (2 * 1)

         = 28

Now, the total number of ways to distribute the candy

Total ways = C(8, 4) * C(8, 2) = 70 * 28 = 1960

So, there are 1960 different ways to distribute.

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To enlarge Shape A by a scale factor of 1.5 with the center of enlargement (0, 0), we have to multiply every length by 1.5.

Enlargement of Shape A

Enlargement of a shape is when it is either stretched or shrunk in one or both directions. The original shape is called the pre-image, while the new shape is called the image. What is the centre of enlargement?

The center of an enlargement is the point about which all of the points of the pre-image are scaled to obtain the image. When the scale factor is greater than 1, the image of the pre-image is an enlargement. When the scale factor is between 0 and 1, the image of the pre-image is a reduction.In an enlargement, each point on the pre-image is mapped onto a corresponding point on the image along a straight line which goes through the centre of enlargement.

The new shape has a larger size than the original shape. To expand shape A by a scale factor of 1.5, you need to multiply each length by 1.5. You have to create new points. It's easy to use a scale ruler to make sure each length is multiplied by 1.5.

A Centre of enlargement is a point in the coordinate plane that enlarges or shrinks a figure by some scale factor. In the problem, the center of enlargement is (0, 0).

Thus, we have to extend every length of Shape A by 1.5, and our scale factor is 1.5. We get Shape B by doing so. Now, we can conclude that to enlarge Shape A by a scale factor of 1.5 with the center of enlargement (0, 0), we have to multiply every length by 1.5.

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The statement "Cleanups may be carried out by the Environmental Protection Agency or private parties" is true of the Comprehensive Environmental Response, Compensation, and Liability Act (CERCLA), also known as Superfund.

What is the Comprehensive Environmental Response, Compensation, and Liability Act (CERCLA)?

The Comprehensive Environmental Response, Compensation, and Liability Act (CERCLA), commonly known as Superfund, is a United States federal law aimed at cleaning up sites contaminated with hazardous substances as well as preventing future hazardous waste site contamination.

CERCLA was passed by the United States Congress in December 1980 as a means of counteracting the increasing risk of hazardous waste sites in the United States.

What does CERCLA cover?

CERCLA was enacted to offer a federal "Superfund" to clean up uncontrolled or abandoned hazardous waste sites, as well as responding to oil spills, chemical disasters, and other emergencies that present a threat to the public health and the environment.

Cleanups may be carried out by the Environmental Protection Agency or private parties.

When it comes to financing these cleanups, the law mandates that those responsible for the contamination pay for the cleanup or those who do not take responsibility for the pollution.

The legislation was enacted to provide for the cleanup of the country's most hazardous waste sites and to ensure that businesses that generate hazardous waste are held responsible for their toxic contributions to the environment.

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● < P=R " angles opp =sides"

●PQ =QR " Angles opposite = sides"

therefore PQR is an isosceles " 2 opp angles and sides are equal "

  LN/RT = NM/TS is the correct option in congruent triangle .

What in mathematics is congruent?

If two shapes are similar in size and shape, they are said to be congruent. The mirror image of one shape is the same as the other if two shapes are congruent.

                          Congruent refers to objects that are precisely the same size and shape. Even after the forms have been flipped, turned, or rotated, the shape and size ought to remain constant.

  In ΔLMN ≅ ΔRST

 In triangle are congruent .

    LN/RT = NM/TS

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The equation representing the situation is 4x = y - 1, where x is the number of households with one pet and y is the total number of households. This can be answered by the concept of Simple equation.

Let's assume that there are x households with a single pet. The number of households with no pets is given as one-fourth of the number of households with multiple pets, which means there are 4 times as many households with multiple pets as there are households with no pets. Let's represent the total number of households as y.

Therefore, we can say that the number of households with no pets is (y - x)/4, and the number of households with multiple pets is 3(y - x)/4 since there are 4 times as many households with multiple pets as there are households with no pets.

Now, we can use the given information that the number of households with no pets is one-fourth of the number of households with multiple pets to write the equation:

(y - x)/4 = x/3

Solving for y, we get:

y = 4x + 3x/4 = 16x/4 + 3x/4 = 19x/4

But we are given that the total number of households y includes the households with one pet, so we can write:

y = x + (y - x)/4 + 3(y - x)/4 = x + y/4

Substituting the value of y from the previous equation, we get:

19x/4 = x + 19x/16

Solving for x, we get:

x = 16/3

Therefore, the equation representing the situation is 4x = y - 1, where x = 16/3 and y = 19x/4, which simplifies to:

4(16/3) = y - 1

y = 21

Therefore, there are 16 households with one pet and 5 households without any pets.

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Answer: the answer would be 122

Step-by-step explanation:

To find the surface area you need to find the area of each face and add them together

2 (W L+H L+H W) = surface area  

2·(4·7+3·7+3·4)=122

Answer:

Step-by-step explanation:

Given dimensions of the rectangular prism ,

4"×3"×7"

We know, Total surface area of a cuboid= 2(lb+bh+hl)

where, l=length of the cuboid

 b= breadth " " "

 h= height " " "

Since, a rectangular prism holds the shape of a cuboid, therefore it's surface area should also be 2(lb+bh+hl)

Now, surface area of the rectangular prism = 2(4×3+3×7+7×4)

 =2(12+21+28)

 =2×61

 =122 square inches.

ANSWERS:
A ) x^2 + 5/6x + 25/144 = (x + 5/12)^2

B ) x^2 - 11x + 121/4 = (x - 11/2)^2

EXPLANATION:

a. To complete the square for the equation x^2 + 5/6x + ___,

first divide the coefficient of the linear term (5/6) by 2,

which gives you 5/12.

Then, square the result:

(5/12)^2 = 25/144.

So, the equation becomes:
x^2 + 5/6x + 25/144 = (x + 5/12)^2

b. To complete the square for the equation x^2 - 11x + ___,

first divide the coefficient of the linear term (-11) by 2,

which gives you -11/2.

Then, square the result:

(-11/2)^2 = 121/4.

So, the equation becomes:

x^2 - 11x + 121/4 = (x - 11/2)^2

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There are 4 different weekly plans that meet the condition

If Tycho wants to go for a run on the same weekdays every week, there are 7 choices for the first day of the week, 6 choices for the second day of the week, and 5 choices for the third day of the week (since he can't run on two consecutive days).

However, we have to be careful not to overcount the number of plans that meet the conditions. For example, if Tycho chooses Monday and Tuesday as his running days, that's the same as choosing Tuesday and Monday.

To avoid overcounting, let's first count the total number of possible plans, regardless of whether they meet the conditions or not. We can choose any two days of the week for Tycho to run, which can be done in 7 choose 2 ways (or C(7,2) ways), since order doesn't matter.

C(7,2) = 7!/(2!(7-2)!) = 21

So there are 21 possible plans, regardless of whether they meet the conditions or not.

Now let's count the number of plans that meet the conditions. Since Tycho wants to run on two days a week and not on consecutive days, there are only two possible patterns: (1) run on Monday and Thursday, or (2) run on Tuesday and Friday.

Each pattern can be done in 2 ways: either run on Monday and Thursday, or run on Thursday and Monday. Similarly, either run on Tuesday and Friday, or run on Friday and Tuesday.

So there are 4 plans that meet the conditions: (Monday, Thursday), (Thursday, Monday), (Tuesday, Friday), and (Friday, Tuesday).

Therefore, there are 4 different weekly plans that meet the condition

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The probability that a bat does not consume any mosquitoes in a 30-second interval is 0.0067379 or 0.67%.

In this case, the average rate of mosquitoes consumed by a bat is 10 per minute.

To find the rate for a 30-second interval, calculate the rate for 1 minute and then adjust it for the 30-second interval:

Average rate for 1 minute = 10 mosquitoes

Rate for 30 seconds = [tex]\dfrac{10 \,mosquitoes}{1 \,minute} \times \dfrac{1}{2}[/tex]

                                  = 5 mosquitoes

The Poisson distribution probability mass function is given by:

[tex]\[ P(X = k) = \dfrac{e^{-\lambda} \cdot \lambda^k}{k!} \][/tex]

Where:

[tex]\(\lambda\)[/tex] is the average rate of events.

In this case, to find the probability that k = 0.

So, let's plug in the values:

[tex]\(\lambda = 5\)[/tex]

[tex]\(k = 0\)[/tex], back to the formula as

[tex]\[ P(X = 0) = \dfrac{e^{-5} \cdot 5^0}{0!} \][/tex]

Calculating the probability as

[tex]\[ P(X = 0) = e^{-5}[/tex]

                [tex]= 0.0067379[/tex]

Therefore, the probability is 0.0067379 or 0.67%.

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Answer: y-98

Step-by-step explanation:

Since the linear model y = 11x + 41 can be used to represent the data when x≥0, the two statement which best describe the value 41 include the following:

B. initial number of students in attendance when x = 0.

E. y-intercept.

In Mathematics, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;

y = mx + c

Where:

Based on the information, an equation that models the line is given by this mathematical expression;

y = mx + c

y = 11x + 41

By comparison, we have the following:

mx = 11x

Slope, m = 11.

Initial number or y-intercept, c = 41.

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6. f(x)g(x)+h(x) = 20x3-4x. This answer is arrived at by using the rules of algebra and the values of the given functions.

7. f(x)g(x) = -15x2 - 18x - 15

Polynomials are algebraic expressions consisting of variables and coefficients that are combined through addition, subtraction, multiplication and division operations. For example, the polynomial 4x² + 3x - 5 can be written as the sum of 4x², 3x and -5.

6. In order to calculate f(x) g(x)+h(x), it is necessary to first multiply f(x) and g(x). Since f(x)=4x and g(x) = 5x2-4, it follows that f(x)g(x)=20x3-4x. Next, it is necessary to add h(x) to this product. Since h(x) = 9x, it follows that f(x)g(x)+h(x) = 20x3-4x+9x = 20x3-4x. Since each coefficient is correctly represented in the answer, it follows that the correct answer is 20x3-4x.

Multiplying f(x) and g(x) gives the product of 20x3-4x, and adding h(x) to this product gives the sum of 20x3-4x. As each coefficient is correctly represented in the answer, the correct answer is 20x3-4x.

7. The product of two polynomials is found by multiplying each term of one polynomial by each term of the other polynomial. This is known as the FOIL method (First, Outer, Inner, Last).

The first term is the product of the first terms of each polynomial, which is 3x x 4x = 12x2.

The second term is the product of the outer terms, which is 3x x -5x = -15x2.

The third term is the product of the inner terms, which is 5 x -5x = -25x.

Finally, the fourth term is the product of the last terms of each polynomial, which is 5 x -3 = -15.

We can now combine the terms to get the product of the two polynomials, which is:

f(x)g(x) = -15x2 - 18x - 15.

Therefore, the correct coefficient for each term is -15x2 for the first term, -18x for the second term, and -15 for the third term.

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By permutation and combination, Maximum 171 number of different  2 - person teams are possible.

Provide an example of permutation and combination?

An arrangement of things in a specific order is referred to as a permutation. In this arrangement, the components or components of sets are organized in a linear or sequential order.

                       As an illustration, set A=1,6 has the permutation 2, which is 1,6,1. Permutations include the arrangement of individuals, digits, numbers, alphabets, letters, and colors. Combinations include things like choosing a menu, cuisine, clothing, a subject, and a team.

Total number of ways to choose different 2 person out of 19 person.

                     = ¹⁹C₂

              = 19!/2! (19 - 2)!

              =  19!/2!   17!

             = 19 * 18 * 17!/2 * 1 * 17!

            = 19 * 7

              = 171

Hence, maximum 171 number of different  2 - person teams are possible.

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Answer:

Step-by-step explanation:

You want to know the side lengths of the triangles shown if DE = 8.

Side DE is marked as x+6. If its length is 8, then we have ...

  x +6 = 8

  x = 2 . . . . . subtract 6

The unknown side lengths are then ...

  PQ = x+1 = 3

  QR = x+3 = 5

  EF = x+8 = 10

__

Additional comment

These are both 3:4:5 right triangles. The larger is twice the size of the smaller. You can guess this because a 3:4:5 right triangle is the only one with a side length of 4 and integer lengths for the other sides.

Answer:

The number cube has 6 equally likely outcomes, so the probability of rolling a 1 or a 6 on any given roll is 2/6 = 1/3.

If Kenya rolls the number cube 90 times, we can use the expected value formula to find the expected number of times that a 1 or a 6 will land face up:

Expected number of 1's or 6's = (number of rolls) x (probability of rolling a 1 or a 6)

Expected number of 1's or 6's = 90 x (1/3)

Expected number of 1's or 6's = 30

Therefore, a reasonable prediction for the number of times that a 1 or a 6 will land face up is 30.

The probability that the socks will not be blue would be =11/14.

Probability can be defined as the expression that shows the possibility of the occurrence of an event.

The formula that is used to calculate probability = the chosen events/total number of outcomes.

The total number of black socks = 8

The total number of blue socks = 6

The total number of white socks = 14

The total number of socks (outcomes) = 8+6+14 = 28

The socks that are not blue = 8+14 = 2

Therefore the probability that they socks won't be blue = 22/28 = 11/14.

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Answer: B

Step-by-step explanation:

because I did it and it was right lol

The larger number if the difference of the numbers is 52 is 65.

A number is five times a smaller number. Let's find the larger number when their difference is 52.

Therefore,

let

x = smaller number

larger number = 5x

There difference is 52. Hence,

5x - x = 52

4x = 52

divide both sides of the equation by 4

x = 52 / 4

x = 13

Therefore,

larger number = 5(13) = 65

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8 Cans of mandarin oranges are needed to serve a part of 200 people if each person is to receive a 3-ounce serving and each can weights 5 pounds 10 oz (9 ounces of that as liquid which you will discard).

Given that each can of mandarin oranges weighs 5 pounds 10 oz (9 ounces of that as liquid which you will discard).We are to find out how many cans of mandarin oranges are needed to serve a part of 200 people if each person is to receive a 3-ounce serving.

Convert 3 ounces into pounds and ounces

3 ounces = 3/16 pound (1 pound = 16 ounces)

Amount of mandarin oranges required by one person = 3/16 pound

Amount of mandarin oranges required by 200 people = 200 * (3/16) pound

Amount of mandarin oranges required by 200 people = 37.5 pound

Convert the amount of mandarin oranges required into cans

Weight of one can of mandarin oranges = 5 pounds 10 oz = (5*16 + 10) ounce = 90 ounce

Weight of mandarin oranges only in one can = 90 ounce - 9 ounce = 81 ounce (9 ounce is liquid which you will discard)

Number of cans required = (total weight required) / (weight of one can)Number of cans required = (37.5 * 16) / 81 Number of cans required = 7.4 cans

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Answer:

y=2.05x

Step-by-step explanation:

Figure out what the total cost is for 1 of them then you put that in as your M value, then X stands for number of sheets so 2.05 multiplied by the number of sheets sold you get your Y which is the total cost in dollars for x sheets.

Consequently, in this rhombus-shaped skating rink, the longest distance that may be covered without changing directions is 40 metres.

The total distance encircling a two-dimensional shape's perimeter is known as its perimeter. It represents the total length of the shape's sides. The perimeter of a rectangle, for instance, can be determined by combining the lengths of its four sides: A rectangle's perimeter equals 2 x (length + width). Other shapes, such triangles, circles, and polygons, can have their perimeters determined using the appropriate formulas.

given

The formula for the perimeter of a rhombus, which is the sum of the lengths of its four sides, can be used to determine the greatest distance that can be covered in a rhombus-shaped skating rink without changing direction.

Given that the sides are each 26 metres long, the rhombus's perimeter would be:

Perimeter: (4 x 26) = 104 metres

But, we must consider that the smaller diagonal of the skating rink measures 40 metres in order to determine the most distance that may be traversed without changing directions. This means that the skater is limited to a 40-meter radius before having to change directions.

Consequently, in this rhombus-shaped skating rink, the longest distance that may be covered without changing directions is 40 metres.

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The complete question is:- 3.- What is the maximum distance that can be traveled without changing direction in a rhombus-shaped skating rink, if each side measures 26 meters and the smaller diagonal is 40 meters?

Answer: B $2,251.80

Step-by-step explanation:

:)