Find the missing dimensions of each figure. Round your answer to the nearest tenth. PLEASE HELP

It will take about 225.25 years of time for 15 grams to be present.

The half-life of a radioactive substance is the time it takes for half of the substance to decay.

For this substance with a half-life of 170 years, we can use the following formula to find the value of k:

[tex]0.5 = e^(^-^1^7^0^k^)[/tex]

Taking the natural logarithm of both sides, we get:

ln(0.5) = -170k

Solving for k, we get:

k = ln(0.5) / (-170)

= 0.004085

Now, we can use the model [tex]y = y_0e^(^-^k^t^)[/tex] to find the time t required for the substance to decay from 40 grams to 15 grams.

We have:

[tex]15 = 40e^(^-^0^.^0^0^4^0^8^5^t^)[/tex]

Dividing both sides by 40 and taking the natural logarithm of both sides, we get:

ln(15/40) = -0.004085t

Solving for t, we get:

t = ln(15/40) / (-0.004085)

= 225.25 years

Therefore, it will take about 225.25 years for 15 grams to be present.

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To the nearest mile, the distance that Marcus ran is 6 miles.

To calculate the total distance that Marcus ran in the morning, we will sum up the distance for all the routes that he ran.

From the map, the distances that Marcus ran are as follows:

1 inches + 3 inches + 2 inches + 3 inches

= 8.3 inches

The scale then shows that 4 inches equal 3 miles. Now, we convert 8.3 inches to miles and this gives us:

8.3 inches × 3 miles/4 inches

= 6.225

To the nearest miles, this is 6 miles.

Complete Question:

Marcus looked up the path that he had taken on his run this morning on the map shown below.

To the nearest mile, what is the total distance that he ran?

6 miles

8 miles

11 miles

25 miles

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Answer:

2, area=42.39 arc length=14.13

3, area=604.9 arc length=71.1

The type of pay modeled in the given image is c. Commission pay.

Commission pay is a form of variable pay where the employee is paid based on the percentage of sales that they make. In this case, the y-axis represents the pay earned and the x-axis represents the sales made.

The straight line represents the commission rate, which is constant at 15%. The more sales the employee makes, the more pay they will earn.

Therefore the correct option is C.

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Using the ratios, 1 yd/3 feet, 1 mi/5,280 feet, and 200 yards/1 feet, the number of flags required to mark the racecourse with a flag every 200 yards is 22.

Ratios are relative sizes of one quantity or value compared to another.

Ratios are depicted as fractional values using decimals, percentages, or fractions, including the standard ratio form (:).

The total distance of the racecourse = 2.5 miles

The common distance between each flag = 200 yards

1 mile = 1,760 yards

2.5 miles = 4,400 yards

1 yard = 3 feel

The number of flags required to cover the distance = 22 (4,400 ÷ 200)

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Using the given data, the equation that best models a line of fit for the data is y = 20x. The slope of the line of fit indicates that for each additional hour that Sally works, she earns an additional $20, on average. So, the correct option is D).

For finding the equation of the line of best fit and the slope

Firstly, Find the mean of x and y.

Mean of x = (2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) / 8 = 5.5

Mean of y = (40 + 70 + 110 + 120 + 150 + 140 + 180 + 190) / 8 = 127.5

Calculate the deviations from the mean for x and y.

Deviation from mean of x = x - mean of x

= [2 - 5.5, 3 - 5.5, 4 - 5.5, 5 - 5.5, 6 - 5.5, 7 - 5.5, 8 - 5.5, 9 - 5.5]

= [-3.5, -2.5, -1.5, -0.5, 0.5, 1.5, 2.5, 3.5]

Deviation from mean of y = y - mean of y

= [40 - 127.5, 70 - 127.5, 110 - 127.5, 120 - 127.5, 150 - 127.5, 140 - 127.5, 180 - 127.5, 190 - 127.5]

= [-87.5, -57.5, -17.5, -7.5, 22.5, 12.5, 52.5, 62.5]

Calculate the product of the deviations for each data point.

Product of deviations = deviation from mean of x * deviation from mean of y

[(2-5.5) * (40-127.5)] + [(3-5.5) * (70-127.5)] + [(4-5.5) * (110-127.5)] + [(5-5.5) * (120-127.5)] + [(6-5.5) * (150-127.5)] + [(7-5.5) * (140-127.5)] + [(8-5.5) * (180-127.5)] + [(9-5.5) * (190-127.5)]

= [-135.625, -51.875, 32.625, 28.125, 17.8125, 26.25, 137.8125, 229.0625]

Calculate the sum of the deviations of x squared.

Sum of deviations of x squared = (deviation from mean of x)²

= (-3.5)² + (-2.5)² + (-1.5)² + (-0.5)² + 0.5² + 1.5² + 2.5² + 3.5²

= 70

Calculate the slope of the line of best fit.

slope = sum of products of deviations / sum of deviations of x squared

= (−135.625 + (−51.875) + 32.625 + 28.125 + 17.8125 + 26.25 + 137.8125 + 229.0625) / 70

= 20

Calculate the y-intercept of the line of best fit.

y-intercept = mean of y - slope * mean of x

= 127.5 - 20 * 5.5

= 10

The equation of the line of best fit in slope-intercept form.

y = slope * x + y-intercept

= 20x + 10

Therefore, the equation that best models a line of fit for the data is D) y = 20x, and the slope is 20. So, the correct answer is D).

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Answer:

3 yards

Step-by-step explanation:

Answer:

B

D

E

( all of the answers (E, D, B) have no real solutions)

The largest number of people for whom she can buy tickets, is 4 people.

:: Available money = $6000

:: Cost per person = $1300

So,

No. of maximum tickets = 6000/1300 = 4.6

That is,

Only 4.6 persons can have the tickets, and since, number of persons can only be a positive integer, so we have to only take the integer part of the number and eliminate the decimal part.

Therefore, the largest number of people for whom she can buy tickets, is 4 people.

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Bob needs to make at least 9 two-point baskets in the second half to break the school record of scoring 30 points in his basketball game.

To break the school record of scoring 30 points, Bob needs to score more than 30 points in his basketball game. Since he scored 13 points in the first half, he needs to score at least 17 points in the second half to break the record.

Let's assume that Bob makes x two-point baskets in the second half. Since each two-point basket contributes 2 points to his score, his total score from two-point baskets would be 2x.

Therefore, to break the school record, we need to solve the following inequality:

2x + 13 > 30

Subtracting 13 from both sides, we get:

2x > 17

Dividing both sides by 2, we get:

x > 8.5

Since Bob cannot make a fractional number of baskets, he needs to make at least 9 two-point baskets in the second half to break the school record.

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The sample space describing all possible outcomes is {1. 2. 3. 4. 5. 6}

From the question, we have the following parameters that can be used in our computation:

A number cube with faces labeled from 1 to 6 will be rolled once.

This means that

Sample space = {1. 2. 3. 4. 5. 6}

Using the above as a guide, we have the following:

The outcomes for the event of rolling the number 1 ,3 , or 4. is

Outcome = {1, 3, 4} where we have

P(1) = 1/6

P(3) = 1/6

P(4) = 1/6

Altogether, we have

P(1, 3, or 4) = 1/6 + 1/6 + 1/6

P(1, 3, or 4) = 3/6

P(1, 3, or 4) = 1/2

Hence, the probability is 1/2

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Complete question

A number cube with faces labeled from 1 to 6 will be rolled once. The number rolled will be recorded as the outcome.

Give the sample space describing all possible outcomes.

Then give all of the outcomes for the event of rolling the number 1 ,3 , or 4.

If there is more than one element in the set, separate them with commas.

There are 960 bikes in the repair department and  1.98% of the bikes need two repairs.

The number of bikes with flat tires only is 0.25x, where x is the total number of bikes

The number of bikes with bent handlebars only is 0.05x

The number of bikes with ripped seats only is 0.1x

The number of bikes that need two repairs is 0.01Tx, where T is the percentage of bikes that need two repairs (expressed as a decimal)

The number of bikes that need all three repairs is 0.0833...x

So we have the equation:

0.25x + 0.05x + 0.1x + 0.01Tx + 0.0833...x = 101

Simplifying and solving for x, we get:

x = 960

So there are 960 bikes in the repair department.

To find the number of bikes that need two repairs, we can use the equation:

0.25x + 0.05x + 0.1x + 0.01Tx = 101 - 0.0833...x

Substituting x = 960, we get:

0.25(960) + 0.05(960) + 0.1(960) + 0.01T(960) = 101 - 0.0833...(960)

240 + 48 + 96 + 9.6T = 101 - 80

9.6T = 19

T = 1.98

About 1.98% of the bikes need two repairs.

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Answer:

(x - 8)^2 + (y + 10)^2 = 169

Step-by-step explanation:

you need to do completing the square

x^2 + y^2 -16x + 20y - 5 = 0

(x)^2 - 2(8)(x) + (y)^2 + 2(10)(y) - 5 = 0

(x)^2 + 2(-8)(x) + (-8)^2 - (-8)^2 + (y)^2 + 2(10)(y) + (10)^2 - (10)^2 - 5 = 0

[(x)^2 + 2(-8)(x) + (-8)^2] + [(y)^2 + 2(10)(y) + (10)^2] - (10)^2 - (-8)^2 - 5 = 0

### (a)^2 + 2(a)(b) + (b)^2 = (a + b)^2 ###

(x - 8)^2 + (y + 10)^2 -100 - 64 - 5 = 0

(x - 8)^2 + (y + 10)^2 -169 = 0

(x - 8)^2 + (y + 10)^2 = 169

The probability that the first roll is a total of at least 5 and the second roll is a total of at least 4  is 0.764 or 76.4%.

The probability is the chance that an expected event occurs out of many possible events.

For two independent events happening, we use the rule of multiplication of independent events based on dice probabilities.

The event that the first roll is a total of at least 5 = A

In the event that the second roll is a total of at least 4 = B

The number of faces on each die, n = 6

The probability of event A = ³⁰/₆ = ⁵/₆

The probability of event B = ³³/₃₆ = ¹¹/₁₂

Multiplying the two probabilities, P(A) and P(B) = ⁵/₆ ​× ¹¹/₁₂

= ⁵⁵/₇₂ = 0.764

Thus, there is a ⁵⁵/₇₂ or 0.764 chance that the first roll is at least 5 and the second roll is at least 4.

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The area of the shaded region is 117.8 m².

Given is a semicircle and a triangle in it, we need to find the area that is shaded,

So, we know that a triangle in a semicircle is always a right triangle whose hypotenuse is the diameter of the semicircle,

So, let us find the hypotenuse of the triangle (diameter of the semicircle) using the Pythagorean theorem,

diameter / hypotenuse = √21.6²+9²

= 23.4m

So the radius = 23.4/2 = 11.7 m

To find the area of the shaded region we will subtract the area of triangle from the semicircle,

So,

Area of the shaded region = π×r²/2 - 1/2×base×height

= 3.14×11.×7²/2 - 1/2×21.6×9

= 215 - 97.2

= 117.8 m²

Hence the area of the shaded region is 117.8 m².

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For the given question the values,

Given value of the function when the condition for x is less than '0' is =

f(x) = x²   for x < 0

The value of the function when the condition x is equals to '0' is =

f(x) = 0     for x = 0

The value of the function when the condition x is greater than '0' is =

f(x) = 3x + 4    for x > 0

From the above information,

To find f(-1) we have to use the x value as x². So, f(-1) = (-1)² = 1

To find f(0) we have to use x value as 0. So, f(0) = 0

To find f(3) we have to use the x value as 3x + 4. So, f(3) = 3(3) + 4 = 13.

From the above analysis, we find the values of f(-1), f(0), and f(3).

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The rule used to obtain the transformed function is given as follows:

g(x) = -0.5f(x).

Examples of transformations are given as follows:

The parent function in this problem is given as follows:

f(x).

The parent function is reflected across the x-axis, hence:

g(x) = -f(x).

The parent function is also compressed by a factor 0.5, hence:

g(x) = -0.5f(x).

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The statement that analyzes difference between an irrational number and a rational number is: the expression √25 - √21 can be rewritten as 5 - √21. since the exact value of √21 cannot be found, the difference is irrational, The Option D is correct.

A rational number refers to number that can be expressed as the ratio of two integers where the denominator is not zero. For example 1/2, 3/4, and -5/7  all rational numbers.

Irrational number refers to one that cannot be expressed as a ratio of two integers. Examples include pi (π) and the square root of 2 (√2).

The difference is that one is expressed as a ratio of two integers or a decimal that either terminates or repeats other cannot be expressed as a ratio of two integers and have a decimal representation that does not terminate or repeat.

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Answer:

53 es el pr espero que te ayude

Answer:

B) 48

Step-by-step explanation:

3, 13, 22, 30, 37, 43…

3 to 13 is +10

13 to 22 is +9

22 to 30 is +8

We are adding one less each time

3, 13  , 22,   30,   37,    43   …

 +10  +9   +8    +7    +6    +5

Add 5 to 43

43+5 = 48

(A) The down payment of the toaster = $ 11.5

(B)  The total installment price of the toaster = $151.02

(A) The down payment of the toaster made by Kelly is 10 % of $ 115

Down payment = 115 × 10/100

Down payment = 1150/100

Down payment = 11.5

The down payment of the toaster = $ 11.5

(B) Total installment price of the toaster for 9 months with payment of $ 16.78

Total installment price of toaster = 9 × 16.78

Total installment price of toaster = $ 151.02

The total installment price of the toaster = is $ 151.02

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Answer: 8

Step-by-step explanation:

pemdas its not that deep

Answer:

Vertex= (-5, 2)

Step-by-step explanation:

The vertex shifts 5 to the right (x-axis), and 2 up (y-axis) from the point of origin. Then plug in the x values to find other y values.

The expression of the function which is represented by the given graph is given by,

xy = -8

The given figure is a rectangular hyperbola.

So the equation of the given graphed curve be, xy = c, where c is a constant.

We can clearly see that the curve passes through the point with coordinates (-2, 4). So it must satisfy the equation of the curve.

Substituting the point (-2, 4) in the equation of the curve xy = c we get,

(-2)*4 = c

c = -8

Hence the expression for the graph the function represents is given by,

xy = -8.

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Answer:

a. 14:8

b. 6:14

Step-by-step explanation:

all books on the shelf = 6+8=14

a. 14:8

b. 6:14

A graph is a visual representation of data that shows the relationship between two or more variables. It is also known as a chart or plot.Difference in S-P (sec):

The S-P difference is the interval of time between the arrival of the S wave and the P wave at a seismic station.We can observe from the accompanying diagram that the S wave begins to arrive at roughly 16 seconds, and the P wave begins to arrive at roughly 8 seconds. The S-P differential is therefore 16 – 8 = 8 seconds.(mm) Amplitude:

The amplitude of a seismic wave exhibits the greatest departure from the equilibrium position. We can observe from the provided diagram that the wave's maximum displacement is roughly 70 mm. Therefore, the wave's amplitude 70mm.

(km) Distance:

The S-P time difference and a journey time graph can be used to calculate how far the earthquake was from the seismic station.

Using the equation:

Distance is calculated as ((S-P time difference)*(km/sec))

where the travel time graph provides the km/sec value, we obtain:

distance = 56 km (8 * 7).

As a result, the quake's distance from the seismic station is 56 kilometres.

Magnitude (M):

An earthquake's magnitude is a logarithmic scale representation of the energy released by the earthquake. By measuring the greatest wave's amplitude (in mm) and applying the method below, we can determine the magnitude from the provided seismogram:

M = log(A) + 1.5 * log(S-P) - 3.2

where S-P is the S-P time difference in seconds, and A is the amplitude in millimetres. Inputting the numbers provided yields:

M = log(70) + 1.5 * log(8) - 3.2

M ≈ 4.1

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The volume of the new object is approximately 439.3 cubic inches

To find the volume of the new object, we need to first know the volume of the prism before the cylinder is removed hence we do this:

The volume of a cylinder: = πr²h

where:

r = radius

h  = height

Note that the volume of a rectangular prism is :  = lwh

l = length

w = width

h = height

Assumption: In the above case, we will  assume that the dimensions of the rectangular prism because the cylinder can be cut out from the center of one of the faces.

Hence the length and width of the prism will be taken to be twice the radius of the cylinder, that is 16 inches, and the height will be taken to be same as the radius of the cylinder, that ia 8 inches.

So  V_prism = lwh

 = 16 × 16 × 8

= 2048 cubic inches

V_cylinder = πr²h

= π × 8² × 8

= 512 π cubic inches

Hence To get  the volume of the new object, we need to subtract the volume of the cylinder from the volume of the prism:

V_new = V_prism - V_cylinder

= 2048 - 512π

= 2048  - 1608.70

= 439.3 cubic inches

Hence, the volume of the new object is about 439.3 cubic inches

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I: TRUE - A limit is a value that a function, pattern, or sum of a series approaches as the number of terms or input value increases.

II: TRUE - A limit can also be a value that a function approximates for a specific input value, especially when dealing with continuity or differentiability.

III: FALSE - Although a limit might seem like a value that is never quite achieved, it can be reached or even exceeded, depending on the function and its behavior.

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Answer:0,2,4,6,8,10

Step-by-step explanation:

take it, spread it, find the bars.