An environmentalist is studying a certain microorganism in a sample of city lake water. The function h(x) = 146(1.16)ˣ gives the number of the microorganisms present in the water sample at the end of x weeks. Which statement is the best interpretation of one of the values of the function?
F. After 1 week, there will be 146 microorganisms in the water sample.
G. The initial number of microorganisms in the water sample was 16.
H. The number of microorganisms decreases by 84% each week.
J. The number of microorganisms increases by 16% each week.

Answers

Answer 1

The best interpretation of one of the values of the function is  The number of microorganisms increases by 16% each week.

The given function of the number of the microorganisms present in the water sample at the end of x weeks is

h(x) = 146(1.16)ˣ

To find the number of microorganisms present in the water sample after one week, we substitute x = 1 in the above equation

h(1) = 146(1.16)¹

h(1) = 169.36

Therefore, after one week, there will be approximately 169 microorganisms in the water sample.

Thus, the correct interpretation of one of the values of the function is F.

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Related Questions

Find the seventh, twenty fifth and seventy ninth percentile from the following data: 15, 19, 26, 25, 11, 21, 22, 34, 41, 43, 45, 55, 58, 60, 50, 22, 19, 34, 62, 48, 49, 13​

Answers

Answer:

Step-by-step explanation:

The data set in order is: 11, 13, 15, 19, 19, 21, 22, 22, 25, 26, 34, 34, 41, 43, 45, 48, 49, 50, 55, 58, 60, 62.

The seventh percentile is 15.

The twenty fifth percentile is 22.

The seventy ninth percentile is 58.

Assume there are 0. 9 U. S. Dollars in a Canadian dollar. If gasoline costs 1. 50 Canadian dollars per liter, how many U. S. Dollars does it cost to buy a gallon of gas in Canada? (1 gallon = 3. 8 liters)


a. $3. 28


b. $5. 13


c. $2. 95


d. $5. 68

Answers

5.13 U. S. Dollars will it cost to buy a gallon of gas in Canada. The correct answer to the question is A

Given in the question,

Cost of 1 liter gasoline = 1.50 Canadian dollars

1 gallon = 3.8 liters

Thus, to calculate the price of 1 gallon we multiply the cost of 1 liter by 3.8

Cost of 3.8 liters of gasoline = 1.5 * 3.8

= 5.70 Canadian dollars

1 Canadian dollar = 0.9 U. S. dollars

5.70 Canadian dollars = 5.70 * 0.9

= 5.13 U. S. dollars

That is the cost of 1 gallon of gas in Canada is 5 U S dollars and 13 cents.

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) On January 2, 2019, Helmkamp Company purchased a $30,000 machine. It had an estimated useful life of 5 years and a residual value of $3,000. What is the amount of depreciation expense for 2020, the second year of the asset's life, using the double declining-balance method? (Round intermediary calculations to two decimal places and your final answer to the nearest dollar. )

Answers

The required answer is the double declining-balance method is $9,840.

To calculate the depreciation expense for 2020 using the double declining-balance method, we first need to determine the asset's straight-line depreciation rate. This is calculated by subtracting the residual value from the cost of the asset and dividing by the asset's useful life:

Depreciation base = $30,000 - $3,000 = $27,000
Annual depreciation expense (straight-line) = Depreciation base / Useful life = $27,000 / 5 = $5,400

Next, we need to determine the double declining-balance rate, which is twice the straight-line rate. Therefore:
Double declining-balance rate = 2 x (1 / Useful life) = 2 x (1 / 5) = 0.40 or 40%
Now we can calculate the depreciation expense for 2020:
Depreciation expense (2020) = Book value (beginning of year) x Double declining-balance rate

The book value at the beginning of 2020 would be the cost of the asset minus accumulated depreciation for the first year:
Book value (beginning of 2020) = $30,000 - ($5,400 x 1) = $24,600
As a result, depreciation increases during the initial year of possession and decreases thereafter.


Therefore:

Depreciation expense (2020) = $24,600 x 0.40 = $9,840

So the amount of depreciation expense for 2020, the second year of the asset's life,

using the double declining-balance method is $9,840.

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Mia crosses a river when she drives from her house to the beach. The function d(t)=40|t-1. 25| shows Mia's distance from the river, d, in miles after t hours. The domain of the function is 0

Answers

The domain of the function is given as 0<t<3, which means that the time elapsed is between 0 and 3 hours. Mia's distance from the river after 2 hours of driving is 30 miles.

The given function is:

d(t) = 40|t-1.25|

Here, t represents the time elapsed in hours and d represents the distance from the river in miles.

To find Mia's distance from the river, we need to plug in values of t into the function.

For example, if t=2, then:

d(2) = 40|2-1.25|

d(2) = 40|0.75|

d(2) = 30

So Mia's distance from the river after 2 hours of driving is 30 miles.

Similarly, we can find Mia's distance from the river at other points in time.

To graph the function, we can plot points by choosing different values of t and finding the corresponding values of d. We can then connect these points to get a graph of the function.

Graph of the function d(t) = 40|t-1.25|

The graph shows that Mia starts at a distance of 40 miles from the river and then approaches it until she reaches the other side of the river, where her distance from the river is again 40 miles. The graph is symmetric about t=1.25, which means that Mia spends the same amount of time on either side of the river.

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Explain why one-twelfth interest every month on an initial one pound will give you (1 + (1/12))¹² pounds at the end of the year

Answers

One-twelfth interest every month on an initial one pound will give (1 + (1/12))¹² pounds at the end of the year due to the compounding effect of interest.

How to find the formula for compound interest?

The interest rate of investment of one-twelfth per month means that for every pound invested, one-twelfth of that amount will be added as interest at the end of the month. Therefore, at the end of the first month, the initial investment of one pound will earn an additional interest of (1/12) pound, making the total amount of money to be 1+(1/12) pounds.

At the end of the second month, the new amount of money will earn another one-twelfth of interest, which will be added to the previous total. Therefore, the new total amount of money will be (1+(1/12))+(1/12) = (1+(2/12)) pounds, which can be simplified to (1+(1/6)) pounds.

By the end of the twelfth month, the initial one pound investment will have earned twelve one-twelfth interests, which can be calculated as (1+(1/12)[tex])^12[/tex] pounds, using the formula for compound interest. This simplifies to (1+1/12[tex])^12[/tex] pounds or (1.0833[tex])^12[/tex] pounds, which is approximately equal to 2.613 pounds.

Therefore, an initial investment of one pound with a one-twelfth interest rate per month will earn a total of (1+(1/12)[tex])^12[/tex] pounds or approximately 2.613 pounds by the end of the year.

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Calculate the costs of these home improvement and maintenance costs.

Annual real estate taxes on a property are $2046. Insurance premiums total $1236. Required flood insurance protection premiums are $380 annually. The county assesses an annual special assessment landfill fee of $125. Trash collection costs $65 quarterly. Annual homeowner's association is $720 for common area maintenance of the subdivision. The pool company charges $45 quarterly to maintain the pool. Ongoing termite and pest protection costs $39 monthly. How much should a buyer save each month to cover these fees?

Answers

Answer: To calculate the total amount a buyer should save each month to cover these fees, we need to add up all the costs and divide by 12 (the number of months in a year).

Annual real estate taxes = $2046

Insurance premiums = $1236

Flood insurance premiums = $380

Annual special assessment landfill fee = $125

Quarterly trash collection costs = $65 x 4 = $260

Annual homeowner's association fee = $720

Quarterly pool maintenance costs = $45 x 4 = $180

Monthly termite and pest protection costs = $39 x 12 = $468

Total annual costs = $2046 + $1236 + $380 + $125 + $260 + $720 + $180 + $468 = $5405

Total monthly costs = $5405 / 12 = $450.42

Therefore, a buyer should save $450.42 each month to cover these fees.

Step-by-step explanation:

Rewrite the expression using a single, positive exponent: 14^-3·14^12

Answers

Answer:

It's 14⁹.

Add the powers in the process of multiplying.

Which is -3 + 12 answer is 9.

Hope this helped!

Explain me that excersice step by step please3x((2x3)^-1x1/2^3)^-1x(3x2^2)^-2

Answers

Answer:

Begin by simplifying the phrases within the brackets, beginning with the innermost brackets:

(2 x 3)^-1 = 1/6 (because 2 x 3 = 6, and the negative exponent flips the fraction)

1/2^3 = 1/8 (because 2^3 = 8)

So, (2x3)^-1x1/2^3 = 1/6 x 1/8 = 1/48

Next, simplify the expression outside the parentheses:

(3x2^2)^-2 = 1/(3x2^2)^2 = 1/(3^2 x 2^4) = 1/36 x 1/16 = 1/576

Now, substitute the simplified terms back into the original expression and simplify:

3x(1/48)x(1/576) = 1/768

So the final answer is 1/768.

In 2015, Connecticut had a population of about 3,600,000 million, New York had a population of about


1. 947


×


1


0


7


1. 947×10


7


, and Rhode Island had a population of about


1. 056


×


1


0


6


1. 056×10


6
. What is the total population of all three states combined? Write the total population in scientific notation

Answers

The total population of all three states combined is 24,126,000 or 2.4126 × 10⁷ in scientific notation.

To find the total population of all three states combined, we simply need to add up the population of each state. In this case, we are given the populations of Connecticut, New York, and Rhode Island, so we can simply add those numbers together to get the total population.

When working with numbers that are very large or very small, scientific notation can be a helpful way to express them. In scientific notation, a number is expressed as a coefficient multiplied by a power of 10. The coefficient is a number greater than or equal to 1 and less than 10, and the power of 10 indicates how many places the decimal point has been moved to create the coefficient.

In this problem, we are given the populations of the three states in scientific notation. Connecticut's population is given as 3.6 × 10⁶, which means that the coefficient is 3.6 and the power of 10 is 6. To convert this number to standard notation, we simply move the decimal point 6 places to the right to get 3,600,000. Similarly, New York's population is given as 1.947 × 10⁷, which means that the coefficient is 1.947 and the power of 10 is 7, and Rhode Island's population is given as 1.056 × 10⁶, which means that the coefficient is 1.056 and the power of 10 is 6.

To find the total population, we add the populations of the three states together:

Total population = Connecticut population + New York population + Rhode Island population

Total population = 3.6 × 10⁶ + 1.947 × 10⁷ + 1.056 × 10⁶

Total population = (3.6 + 19.47 + 1.056) × 10⁶

Total population = 24.126 × 10⁶

We can simplify this expression by multiplying the coefficient by 10⁶:

Total population = 24.126 × 10⁶ = 2.4126 × 10⁷

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Find the derivative of the function f by using the rules of differentiation. f(x)=x^{0,9} f'(x) =

Answers

The derivative of the function f(x) = [tex]x^{0,9}[/tex] is f'(x) = [tex]0.9x^{-0.1}[/tex].

To find the derivative of f(x), we use the power rule of differentiation, which states that if f(x) = [tex]x^n[/tex], then f'(x) = [tex]nx^{(n-1)}[/tex].

In this case, we have f(x) = [tex]x^{0,9}[/tex]. Applying the power rule, we get:

f'(x) = [tex]0.9x^{0.9-1} = 0.9x^{-0.1}[/tex]

Note that [tex]x^{-0.1}[/tex] can be rewritten as [tex]1/x^{0.1}[/tex]. So we have:

f'(x) =[tex]0.9/x^{0.1}[/tex]

This expression tells us the slope of the tangent line to the curve of f(x) at any given point. For example, at x = 1, we have:

f'(1) = [tex]0.9/1^{0.1} = 0.9[/tex]

This means that the slope of the tangent line to the curve of f(x) at x = 1 is 0.9. As x increases or decreases from 1, the slope of the tangent line changes accordingly.

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You are shopping for a King & Queen size mattress, each of which are shaped like a rectangle. The Queen is 16 inches longer than it is wide. The King is 20 inches wider than the Queen, but has the same length. The area of the King-sized mattress is 1,600 in² larger than the Queen. Find the Area of both mattresses

Answers

The area of the King-sized mattress is 4,800 square inches and the area of the Queen-sized mattress is 3,200 square inches.

To find the dimensions of the Queen-sized mattress, let x be the width. Then, the length of the mattress is x + 16. The area of the Queen-sized mattress is x(x + 16) = x² + 16x.

Since the King-sized mattress has the same length as the Queen-sized mattress, its length is x + 16. Also, its width is 20 inches wider than the Queen-sized mattress, so its width is x + 16 + 20 = x + 36. Therefore, the area of the King-sized mattress is (x + 16)(x + 36) = x² + 52x + 576.

The area of the King-sized mattress is 1,600 square inches larger than the area of the Queen-sized mattress. So, we can set up the following equation:

x² + 52x + 576 - (x² + 16x) = 1600

Simplifying this equation, we get:

36x + 576 = 1600

36x = 1024

x = 28

Therefore, the width of the Queen-sized mattress is 28 inches and the length is 44 inches. So, its area is 3,200 square inches.

The width of the King-sized mattress is 28 + 36 = 64 inches and the length is 44 inches. So, its area is 4,800 square inches.

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Find the measure of angle D.

Answers

The measure of angle D is 25°

What is exterior angle theorem?

Exterior angle theorem states that the measure of an exterior angle of a triangle is greater than either of the measures of the opposite interior angles.

Angle D and angle C are the two opposite angles.

Therefore;

40+9x-2 = 20x +5

38+9x = 20x +5

38-5 = 20-9x

11x = 33

divide both sides by 11

x = 33/11

x = 3

Therefore since angle D = 9x-2

substitute 3 for x

D = 9(3) - 2

D = 27 -2

D = 25°

Therefore the measure of angle D is 25°

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A t test for a mean uses a sample of 24 observations. Find the t test statistic value that has a​ P-value of 0. 10 when the alternative hypothesis is​ (a) Ha Subscript a Ha​: μ ≠​0, ​(b) Ha: μ greater than >​0, ​(c) Ha​: mu μ<0. Find the t test statistic value when Ha​: μ≠0

Answers

The t-test statistic value that has a P-value of 0.10 when the alternative hypothesis is

(a) Ha: μ ≠ 0 is ±1.711.

(b) Ha: μ > 0 is 1.319.

(c) Ha: μ < 0 is -1.319.

(d) Ha: μ ≠ 0 is ±1.711.

To find the t-test statistic value for a given P-value and alternative hypothesis, we need to use a t-distribution table or a statistical software program. Here, we will use a t-distribution table to find the t-test statistic value for a sample of 24 observations and a P-value of 0.10 for each alternative hypothesis.

(a) Ha: μ ≠ 0 (two-tailed test)

The critical t-value for a two-tailed test with a P-value of 0.10 and degrees of freedom (df) of 23 (sample size - 1) is:

t = ±1.711

Therefore, the t-test statistic value that has a P-value of 0.10 when the alternative hypothesis is Ha: μ ≠ 0 is ±1.711.

(b) Ha: μ > 0 (one-tailed test)

The critical t-value for a one-tailed test with a P-value of 0.10 and df of 23 is:

t = 1.319

Therefore, the t-test statistic value that has a P-value of 0.10 when the alternative hypothesis is Ha: μ > 0 is 1.319.

(c) Ha: μ < 0 (one-tailed test)

The critical t-value for a one-tailed test with a P-value of 0.10 and df of 23 is:

t = -1.319

Therefore, the t-test statistic value that has a P-value of 0.10 when the alternative hypothesis is Ha: μ < 0 is -1.319.

(d) Ha: μ ≠ 0 (two-tailed test)

To find the t-test statistic value when Ha: μ ≠ 0, we can use the inverse t-distribution function in a statistical software program or a calculator. The t-test statistic value that corresponds to a P-value of 0.10 with 23 degrees of freedom is:

t = ±1.711

Therefore, the t-test statistic value that has a P-value of 0.10 when the alternative hypothesis is Ha: μ ≠ 0 is ±1.711.

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topic 3 providing lines are parallel
21

Answers

21. in the figure, provided line n and line m are parallel the values of x and y are

x = 7

y = 24

How to find x and y

21. When line m and line n are parallel then using corresponding angle theorem we have that:

7y - 23 + 8x - 21 = 180

7y - 8x = 180 + 23 - 21

7x - 8x = 182

Also

8x - 21 + 23x - 16 = 180

8x + 23x = 180 + 21 + 16

31x = 217

x = 217 / 31

x = 7

using vertical angle theorem we have:

7y - 23 = 23x - 16

plugging in the value of x

7y - 23 = 23 * 7 - 16

7y - 23 = 145

7y = 145 + 23

7y = 168

y = 24

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[ ( -28 )-( +42)]-(+3) CUAL ES EL RESULTADO

ME DICEN

POR FIS AYUDA

ES PARA HOY

Answers

First, solve the expression inside the parentheses: (-28) - (+42) = -70

Next, subtract 3 from -70: -70 - (+3) = -73

What is the result of: [(-28) - (+42)] - (+3)?

The given expression can be simplified as follows:

[( -28 )-( +42)]-(+3) = -28 - 42 - 3 = -73

So, the answer to the given expression is -73.

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Find angle C

SinC/4=sin104/8

Answers

Answer:

C = 52

Step-by-step explanation:

sin(c/4) = sin(104/8)

sin(c/4) = 0.22495

c/4 = 13

c = 52

Mr. ream mixes 12 cups of paint in a large bowl. he used the paint to fill 40 small dishes with 2 fluid ounces of paint each. how many cups of paint does mr. ream have left in the bowl

Answers

Mr. Ream has 7 cups of paint left in the bowl.

There are 12 cups of paint, which is equivalent to 192 fluid ounces of paint (1 cup = 16 fluid ounces). Mr. Ream filled 40 small dishes with 2 fluid ounces of paint each, for a total of 80 fluid ounces of paint used (40 x 2 = 80).

Therefore, Mr. Ream has 192 - 80 = 112 fluid ounces of paint left in the bowl.

To convert this to cups, we divide by 16 (1 cup = 16 fluid ounces):

112/16 = 7 cups

Therefore, Mr. Ream has 7 cups of paint left in the bowl.

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A bike wheel is 26 inches in diameter. What is the bike wheel's diameter in millimeters (1 inch = 25.4 millimeters)?







He concludes that she is not running fast enough to exceed her fastest time.

What errors did the coach make? Check all that apply.

He used an incorrect time ratio converting hours to minutes.
His units do not cancel.
He used an incorrect distance ratio converting miles to feet.
He incorrectly concluded that she is not running fast enough.
He cannot determine her average rate in miles per hour after only 15 minutes.

Answers

In a case whereby A bike wheel is 26 inches in diameter  the bike wheel's diameter in millimeters (1 inch = 25.4 millimeters) the  the diameter is  660.4mm

How can the diameter be calculated?

Note; the bike man do not make any calculation, so we can not know mat be he make any mistake.

Since the bike wheel is 26 inches in diameter then we can calculate the diameter of the bike wheel  through the multiplication of the two numbers.

Diameter in milimeters = ( 26.0 x 25.4)

Diameter in milimeters =  660.4 mm.

Hence diameter of the bike wheel in millimeters will be 660.4.

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A bead is formed by drilling a cylindrical hole, with a 2 mm diameter, through a sphere
with an 8 mm diameter. estimate the surface area of the bead. leave the answer in
terms of pi

Answers

The estimated surface area of the bead is 52π square millimeters.

To estimate the  face area of the blob, we need to find the  face area of the sphere and abate the  face area of the spherical hole.   The  face area of a sphere is given by the formula   A =  4πr2   where r is the compass of the sphere.

 The radius of the sphere is: r = 8 mm / 2 = 4 mm.

The surface area of the sphere is: S_sphere = 4π[tex]r^{2}[/tex] = [tex]4π(4 mm)^{2}[/tex] =64 [tex]mm^{2}[/tex]

The radius of the cylinder is: r = 2 mm / 2 = 1 mm.

The height of the cylinder is: h = 8 mm - 2 mm = 6 mm.

The surface area of the cylinder is: S_cylinder = 2πrh = 2π(1 mm)(6 mm) = 12π [tex]mm^{2}[/tex]

The estimated surface area of the bead is: S_bead = S_sphere - S_cylinder = 64π [tex]mm^{2}[/tex] - 12π [tex]mm^{2}[/tex] = 52π [tex]mm^{2}[/tex]

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Anna ate 58of an orange and gave the other 38 to her brother. which equation can be used to find the difference between the amount anna ate and the amount she gave her brother?

Answers

The result of this equation will give us the numerical value representing the difference between the amounts Anna ate and the amount she gave to her brother. In this case, the difference would be 20.

To find the difference between the amount of orange Anna ate and the amount she gave to her brother, we can use the equation: 58 - 38 = x
Here, x represents the difference between the two amounts. We can solve for x by subtracting 38 from 58.
58 - 38 = 20

Therefore, the difference between the amount of orange Anna ate and the amount she gave her brother is 20. Anna ate 58 of an orange and gave 38 to her brother, so the remaining 20 must be the difference between the two amounts.

In summary, the equation that can be used to find the difference between the amount Anna ate and the amount she gave her brother is 58 - 38 = x, where x represents the difference. The answer is 20.

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the scale is 1 inch=50 miles. 5 inches is what

Answers

Answer:

Step-by-step explanation:

you multiply 5 by 50 and that would equal 250

5 x 50 = 250

Lana plotted 3 vertices of a square on a coordinate plane. Which are the coordinates of the missing vertex of Lana's square?

Answers

These values (x4, y4) represent the coordinates of the missing vertex of Lana's square.

Find out the coordinates of the missing vertex?

To determine the missing vertex of Lana's square, we need to know the location of the three given vertices. Let's assume that Lana plotted the vertices in a clockwise direction, starting from the top left.

If we denote the coordinates of the first vertex as (x1, y1), the second vertex as (x2, y2), and the third vertex as (x3, y3), then the coordinates of the missing vertex can be found as follows:

1. Calculate the distance between the first and second vertices:

d1 = sqrt((x2 - x1)^2 + (y2 - y1)^2)

2. Calculate the distance between the second and third vertices:

d2 = sqrt((x3 - x2)^2 + (y3 - y2)^2)

If the square is regular (i.e., all sides are of equal length), then d1 = d2. Otherwise, the shape is not a square.

3. Calculate the midpoint between the first and second vertices:

xm = (x1 + x2) / 2

ym = (y1 + y2) / 2

4. Calculate the vector that goes from the midpoint to the third vertex:

vx = x3 - xm

vy = y3 - ym

5. Calculate the coordinates of the missing vertex by adding the vector to the midpoint:

x4 = xm + vx

y4 = ym + vy

Hence concluded.

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Ryan went shopping and purchased two shirts for $16 each, and a pair of sneakers that cost 2 1/2 times as much as a shirt. How much money did Ryan spend?

Answers

Answer:

Ryan spent $72 on his shopping trip.

Step-by-step explanation:

To find out how much money Ryan spent, we need to add up the cost of the shirts and the sneakers.

First, we know that Ryan purchased two shirts for $16 each. So we can find the total cost of the shirts by multiplying the cost per shirt by the number of shirts:

$16 per shirt x 2 shirts = $32

So the total cost of the shirts is $32.

Next, we know that Ryan purchased a pair of sneakers that cost 2 1/2 times as much as a shirt. We can use this information to find the cost of the sneakers.

If the cost of a shirt is $16, then we can find the cost of the sneakers by multiplying $16 by 2 1/2:

$16 x 2 1/2 = $16 x 2.5 = $40

So the cost of the sneakers is $40.

Finally, we can find the total cost of Ryan's shopping trip by adding up the cost of the shirts and the sneakers:

$32 + $40 = $72

Therefore, Ryan spent $72 on his shopping trip.

HELP MARKING BRAINLEIST IF RIGHT ASAP

Answers

Answer:

{51

Step-by-step explanation:

10^2 - 7^2= 51

You can’t square 51 because no two same whole numbers multiplied creates 51

B= 51

Check answer

7^2 + 51= 100

{100 = 10^2

A tired frog is jumping across a pond. Her first jump will be her longest. She travels 300 cm. Her second jump carries her another 270 cm. How far will the frog travel before she cannot jump anymore?



S= 1560cm


S= 570cm


S= 2700cm


S= 3000cm

Answers

The frog will travel a total distance of 1650 cm before she cannot jump anymore. None of the options given are correct.

To find the total distance the frog will travel, we need to add up the distances of all her jumps. Given that her first jump is her longest at 300 cm and her second jump is 270 cm, we can assume that each subsequent jump is shorter than the one before it.

The difference between the first jump and the second jump is 30 cm. So let's assume that the common difference between each jump is 30 cm. So the frog takes a total of 10 jumps before she cannot jump anymore.

The total distance the frog will travel is:

300 + 270 + (240 + 210 + 180 + 150 + 120 + 90 + 60 + 30) = 1650 cm

So here none of the options are correct.

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Write the standard form of the equation of the circle with the given characteristics. Endpoints of a diameter: (0, 0), (8, 6)

Answers

The standard form of the equation of the circle with the given characteristics is[tex] {(x - 4)}^{2} + {(y - 3)}^{2} = 25[/tex]

To get the equation of the circle using the endpoints of a diameter, we have to use the standard form :

[tex](x - h) ^{2} + (y - k)^{2} = {r}^{2} [/tex]

In which (h, k) represents the middle point of the circle and r as the radius. so, we need to find the midpoint of the diameter using the endpoints (0, 0) and (8, 6).

Midpoint = ((0+8)/2, (0+6)/2) = (4, 3)

Next, we need to calculate the radius by using the distance formula to calculate the distance between the center and one of the diameter endpoints.

[tex] {r}^{2} = {(8 - 4)}^{2} + {(6 - 3)}^{2} = {4}^{2} + {3}^{2} = 16 + 9 = 25[/tex]

Now, substituting the values of (h, k) and

[tex] {r}^{2} [/tex] into the standard form equation to get the equation:

[tex] {(x - 4)}^{2} + {(y - 3)}^{2} = 25[/tex]

Therefore, the standard form equation of the circle with the given characteristics is

[tex] {(x - 4)}^{2} + {(y - 3)}^{2} = 25[/tex]

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The standard form of the given question is (x - 4)² + (y - 3)² = 25, under the condition endpoints of a diameter: (0, 0), (8, 6).

In order To write the standard form of the equation of a circle with endpoints of a diameter (0, 0), (8, 6), we first need to find the center and radius of the circle.

The diameter comprises the midpoints of  the center of the circle. The midpoint of (0, 0) and (8, 6) is ((0+8)/2, (0+6)/2) = (4,3). Center point of the circle is (4,3).

Diameter = 2× radius
. The distance between (0, 0) and (8, 6) is √((8-0)² + (6-0)²)
= √(64+36)
= √100
= 10.
Then, the radius of the circle is 10/2 = 5.

Then,

(x - h)² + (y - k)² = r²
here
(h,k) = center of the circle
r = radius.

Staging in this equation
h=4,
k=3
r=5

(x - 4)²+ (y - 3)² = 25


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A surveyor at an intersection noticed that over the past 24 hours, 318 cars turned left, 557 turned right, and 390 went straight. Based on the activity of the past 24 hours, what fraction is closest to the probability that the next car will turn left?

Answers

probability that the next car will turn left, we need to divide the number of cars that turned left by the total number of cars that passed through the intersection in the past 24 hours. This will give us a fraction that represents the likelihood of a car turning left.

Using the numbers provided, the total number of cars that passed through the intersection in the past 24 hours is:
318 (cars turned left) + 557 (cars turned right) + 390 (cars went straight) = 1265
So, the probability of the next car turning left is:

318 (cars turned left) ÷ 1265 (total number of cars) = 0.251 (rounded to three decimal places)

This means that there is a 25.1% chance that the next car will turn left at the intersection.
As a surveyor, it is important to be able to analyze data and calculate probabilities to make informed decisions. Understanding the probability of different outcomes can help to plan for future events and anticipate potential issues.

In this case, knowing the probability of a car turning left can help to inform traffic flow and reduce congestion at the intersection.

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A store sells four ears of sweetcorn for one dollar how much will nine ears cost

Answers

Nine ears of sweetcorn will cost $2.25 at this store.

To determine the cost of nine ears of sweetcorn, given that four ears cost one dollar, you can follow these steps:

1. Determine the cost of one ear of sweetcorn: Since four ears cost one dollar, we can calculate the cost per ear by dividing the total cost by the number of ears: $1 / 4 ears = $0.25 per ear.

2. Calculate the cost of nine ears: Multiply the cost of one ear by the number of ears desired: $0.25 per ear × 9 ears = $2.25.

So, nine ears of sweetcorn will cost $2.25 at this store.

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I need questions 3,4,5 with answers and explanations/work

Answers

The family with 8 pets cannot be used to represent the whole because it is an outlier

Bar chartCircle graph

Explaining why the family with 8 pets cannot be used to represent the whole

Given that we have

A dot plot that represents the display

On the dot plot, we have

Outlier = 8

This data value is considered an outlier because it is relatively far from other values

As a general rule, outliers cannot be used to represent the whole

The display that could be used to show trend

Here, we have

Dot plotBar chartCircle graph

Of the three displays, the bar chart is used to represent data such that users may readily recognize patterns or trends.

So, the bar chart is to be used

The display that could be used not to show trend

Here, we have

Dot plotBar chartCircle graph

Of the three displays, the circle graph does not show that users  patterns or trends.

So, the circle graph is to be used

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Given that f is continuous on [1, 5] and differentiable on the interval (1,5), with f'(x) ≤ 23, for all x, and f(1) = 4. Find the largest possible value for f(5).

Answers

We are given that f is continuous on [1, 5], differentiable on (1, 5), and f'(x) ≤ 23 for all x. We want to find the largest possible value for f(5). the largest possible value for f(5) is found to be 96.


We can apply the Mean Value Theorem (MVT) here, which states that if a function is continuous on [a, b] and differentiable on (a, b), there exists a number c in the interval (a, b) such that f'(c) = (f(b) - f(a))/(b - a). In this case, a = 1, b = 5, and f(1) = 4.


Since f'(x) ≤ 23 for all x, we know that f'(c) ≤ 23. Plugging into the MVT equation, we have:
[tex]f'(c) = (f(5) - f(1))/(5 - 1) ≤ 23, f'(c) = (f(5) - 4)/4 ≤ 23[/tex]



To find the largest possible value for f(5), we assume f'(c) is equal to its maximum, 23: 23 = (f(5) - 4)/4. Solving for f(5), we get: f(5) = 4 + 4 * 23 = 4 + 92 = 96. So, the largest possible value for f(5) is 96.

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