see picture of problem

We can use Newton's law of cooling to solve this problem:

T(t) = T_a + (T_0 - T_a) * e^(-kt)

where T(t) is the temperature of the object at time t, T_a is the ambient temperature, T_0 is the initial temperature of the object, and k is a constant. We can solve for k by using the information that the object cools from 200 degrees to 131 degrees in 5 minutes:

131 = 20 + (200 - 20) * e^(-5k)

Simplifying this equation, we get:

e^(-5k) = 0.625

Taking the natural logarithm of both sides, we get:

-5k = ln(0.625)

k = -ln(0.625) / 5

k ≈ 0.1078

Now we can use this value of k to find the temperature of the object after 9 minutes:

T(9) = 20 + (200 - 20) * e^(-0.1078 * 9)

T(9) ≈ 94.9 degrees Celsius

Therefore, the temperature of the object at the end of 9 minutes will be approximately 94.9 degrees Celsius.

The measure of angle θ is 45 degrees.

The measure of angle θ is calculated by applying trigonometry ratio as follows;

SOH CAH TOA

SOH = sin θ = opposite /hypothenuse side

TOA = tan θ = opposite side / adjacent side

CAH = cos θ = adjacent side / hypothenuse side

The height and the adjacent side is given, so the value of θ is calculated as follows;

tan θ = (206 - 7 ) / (199)

tan θ = 1

θ = arc tan (1)

θ = 45⁰

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3

Sydney has enough ribbon to make 3 bows

Answer:

3

Step-by-step explanation:

I multiplied 1 1/5 x 2/5 because each bow is made from a piece of ribbon that is 2/5 yards long. 1 1/5 x 2/5 = 12/25 I simplified to get the product of 3.

There are 190 pennies and 110 nickels.

Let's begin by giving the unknown quantities variables. y is the quantity, in cents.

Let x represent the quantity of nickels and y represent the quantity of pennies.

The issue reveals that the combined worth of the coins is $7.40. The following equation can be written since a nickel is worth $0.05 and a penny is worth $0.01:

0.05x + 0.01y = 7.40.

The fact that there are 80 more pennies than nickels is also known. You can write this as

y = x + 80.

Now we can use substitution to solve for x:

0.05x + 0.01(x + 80) = 7.40

0.05x + 0.01x + 0.80 = 7.40

0.06x = 6.60

x = 110

There are 110 nickels in total. The second equation can be used to calculate the amount of pennies:

y = x + 80 = 110 + 80 = 190

Therefore, there are 190 pennies and 110 nickels.

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The calculated area of the figure is 59/2 square units

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

A (1, 2) B (1, 7) C (9, 7) D (9, 3) E (6, 5)

The area is then calculated as

Area = 1/2 * | (x1y2 + x2y3 + ... + xny1) - (y1x2 + y2x3 + ... + ynx1) |

So, we have

Area = 1/2 * | (1 * 7 + 1 * 7 + 9 * 3 + 9 * 5 + 6 * 1) - (2 * 1 + 7 * 9 + 7 * 9 + 3 * 6 + 5 * 1) |

Evaluate

Area = 1/2 * 59

So, we have

Area = 59/2

Hence, the area is 59/2 square units

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Step-by-step explanation:

45 minutes is 3/4 of an hour.

how often does 3/4 fit into 3 ?

3 / 3/4 = 3/1 / 3/4 = (3×4)/(1×3) = 4

so, it will be rung 4 times.

Answer: 4 times.

Step-by-step explanation:

We can divide 3 hours by 45 minutes, to get the number of times the bell will ring in 3 hours:

3 hours ÷ 45 minutes = 4

Therefore, the bell will be rung 4 times in 3 hours.

We can also think of it like this: 3 hours is 180 minutes, and the bell rings every 45 minutes.

So, we can divide 180 by 45 to get the number of times the bell will ring:

180 minutes ÷ 45 minutes = 4

Therefore, the bell will be rung 4 times in 3 hours.

The statements about the attached daily temperature data that are true include the following:

A. the average temperature was below 90°F on less than 75% of the days.

C. the average temperature was below 75°F on less than 25% of the days.

In Mathematics and Statistics, a box plot is sometimes referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the information provided about the given box-and-whisker plot for the daily temperature data, the five-number summary for the given data set include the following:

Minimum (Min) = 65.

First quartile (Q₁) = 70.

Median (Med) = 75.

Third quartile (Q₃) = 85.

Maximum (Max) = 90.

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Answer:

-5.44

Step-by-step explanation:

Y/3.4+4.1 =2.5

Y+(3. 4)(4.1)/(3.4)=2.5

Y+13.94/3.4 =2.5 cross multiply (3.4)(2.5)to get

Y+13.94=8.5

Y=8.5-13.94

= (-5.44)

Answer: To find A and B such that g(x) = f(x) is bijective, we need to ensure that g(x) satisfies the conditions for a bijective function, namely, that it is both injective and surjective.

To show that g(x) is injective, we need to show that for any distinct x1, x2 in A, g(x1) ≠ g(x2). We can do this by assuming that g(x1) = g(x2) and then showing that it leads to a contradiction.

So, let's assume that g(x1) = g(x2). Then, we have:

f(x1) = f(x2)

x1(x1-1) = x2(x2-1)

x1^2 - x1 = x2^2 - x2

x1^2 - x2^2 - x1 + x2 = 0

(x1 - x2)(x1 + x2 - 1) = 0

Since x1 and x2 are distinct, we must have x1 + x2 = 1.

But this is impossible, since x1 and x2 are both real numbers, and the sum of two real numbers cannot equal 1 unless one of them is complex. Therefore, our assumption that g(x1) = g(x2) must be false, and g(x) is injective.

To show that g(x) is surjective, we need to show that for any y in B, there exists at least one x in A such that g(x) = y. In other words, we need to find an expression for x in terms of y.

So, let's solve the equation f(x) = y for x:

x(x-1) = y

x^2 - x - y = 0

Using the quadratic formula, we get:

x = (1 ± √(1 + 4y))/2

Since we want to define g(x) on R, we need to ensure that the expression under the square root is non-negative. This means that 1 + 4y ≥ 0, or y ≥ -1/4.

Therefore, we can define A = [-1/4, ∞) and B = [0, ∞), and g(x) = f(x) is a bijective function from A to B.

Answer:

x=-7

Step-by-step explanation:

Solve for x by simplifying both sides of the equation, then isolating the variable.

The value of the given summation is:

[tex]\sum (29a_i - 13b_i) ]= -30[/tex]

Here we know that the sums are:

[tex]\sum a_i = -10\\\\\sum b_i = -20[/tex]

And we want to find the value of the sum:

[tex]\sum (29a_i - 13b_i)[/tex]

First we can distribute the sum to get:

[tex]\sum 29a_i + \sum - 13b_i[/tex]

And take the coefficients out of the sum:

[tex]29\sum a_i -13\sum b_i[/tex]

Now replace the known values:

[tex]29\sum a_i -13\sum b_i = 29*-10 - 13*-20 = -290 + 260 = -30[/tex]

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The system of linear equations with infinite solutions is:

2y = x - 8 and y = (1/2)*x - 4

A system of linear equations  :

y = ax + b

y = cx + d

Has infinite solutions if and only if both equations represent the same line (then the lines intercept at infinite points)

The equations given are:

y = 2x + 7

2x + y = -7

y = (1/2)x - 4

y = -2x + 7

2y - x = -8

If we take the last one:

2y - x = -8

We can rewrite this as:

2y = x - 8

y = (1/2)*x - (1/2)*8

y = (1/2)*x - 4

That is other of the equations no the list, so the system with infinite solutions is:

2y = x - 8 and y = (1/2)*x - 4

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After 200 years, there will be 47.43 pounds left of the material.

We know that we start with 68 pounds, and after 40 years there are 63.3 pounds left, so we have an exponential decay:

63.3 = 68*(b)^40

Where b defines how it decays, we can solve that equation for b to get:

(63.3/68)^(1/40) = b

0.9982 = b

Then the decay is:

f(x) = 68*(0.9982)^x

The amount left after 200 years will be:

f(200) = 68*(0.9982)^200 = 47.43

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The inverse of the function f(x) = 15x - 45 is g(x) = x + 45 / 15

An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by f-1 or F-1.

In this problem, f(x) = 15x - 45, we can find the inverse as;

To determine the inverse function, switch x and y and solve the resulting equation for x

If the initial function is not one-to-one, then there will be more than one inverse.

y = 15x - 45

x = 15y - 45

Let's solve for y

15y = x + 45

y = x + 45 / 15

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a) The mean number of paintings owned by these five people is 40. b) No, the mean is not a good average to use to describe the number of paintings that these people own

a) To find the mean number of paintings owned, we add up all the values and divide by the total number of people:

Mean = (1+0+2+196+1)/5 = 40

Therefore, the mean number of paintings owned by these five people is 40.

b) No, The mean is not necessarily a good average to use to describe the number of paintings that these people own.

This is because the data is skewed by the one outlier value of 196, which is much larger than the other values.

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Answer:

To solve for k, we first need to isolate k on one side of the equation by subtracting 61.1 from both sides:

K/7.8 + 61.1 - 61.1 = 17.8 - 61.1

K/7.8 = -43.3

Next, we multiply both sides by 7.8 to isolate k.

K = -43.3 * 7.8

K = -338.34

Therefore, k is approximately equal to -338.34.

Because the angles add up to 180°, we conclude that the shelves are parallel.

Two adjacent angles always should add up to 180°. The top shelve and middle shelve will be parallel only if:

∠1 = ∠5

∠2 = ∠6

And we know that:

∠1 + ∠2 = 180°

Then we could rewrite this as:

∠5 + ∠2 = 180°

Replacing the measures we will get:

60° + 120° = 180°

180° = 180°

That equation is true, this, the shelves are parallel.

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For all the questions the correct option is 3 units² because nor the translation not the reflection change the size.

Remember that for any shape, the transformations that change the area of the shape are dilations and contractions.

Here we start with a triangle of base B = 3 and height H = 2, then its area is:

A = 3*2/2 = 3 square units.

Now, any translation will result in a triangle of the same area.

Any reflection will result in a triangle of the same area.

Then for all the given questions, the correct option is 3 units²

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Answer:

The distribution for the number of weeks pregnancy lasts for a mother is typically a unimodal distribution, with a single peak. The majority of pregnancies last around 38-42 weeks, with fewer pregnancies lasting shorter or longer than this period. This creates a bell-shaped curve, with the peak at the most common duration and a gradual decrease in frequency as the duration becomes shorter or longer than the mode.

However, it's worth noting that there can be some variations in this distribution based on different factors, such as the age of the mother, health status, and other demographic characteristics. For example, teenage pregnancies and pregnancies in older women may have slightly different distributions with different peaks due to biological and social factors. Nonetheless, a unimodal distribution is the most commonly observed distribution for the number of weeks pregnancy lasts for a mother.

In the initial value problem the value of f(π/5) ≅ -5.26

Given the initial value problem f"(x) = -25sin(5x) and f'(0) = 3 and f(0) = -2, we desire to find f(π/5). We proceed as follows

f"(x) = -25sin(5x)

Integrating both sides of the equation, we have that

∫f"(x) = ∫-25sin(5x)

f'(x) = -25∫sin(5x)

f'(x) = -25∫sin(5x)

f'(x) = -25(-cos(5x))/5 + C

f'(x) = 5cos(5x) + C

Given that f'(0) = 3, substituting the values of the variables into the equation, we have that

f'(x) = 5cos(5x) + C

f'(0) = 5cos(5(0)) + C

3 = 5cos(0) + C

3 = 5(1) + C

3 = 5 + C

C = 3 - 5

C = -2

So, we have that f'(x) = 5cos(5x) - 2

To find f(x), we integrate f'(x). So, we have that

f'(x) = 5cos(5x) - 2

∫f'(x) = ∫(5cos(5x) - 2)dx

f(x) = ∫5cos(5x)dx - ∫2dx

= 5sin(5x)/5 - 2x + C'

f(x) = sin(5x) - 2x + C'

Since f(0) = -2, we have that

f(0) = sin(5(0)) - 2(0) + C'

-2 = sin0 - 0 + C'

- 2 = 0 - 0 + C'

- 2 = 0 + C'

C' = -2

So, substituting C' into the equation, we have that

f(x) = sin(5x) - 2x + C'

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

So, to find f(π/5), substituting this into the equation, we have that

f(π/5) = sin(5π/5) - 2(π/5) - 2

f(π/5) = sin(π) - 2π/5 - 2

f(π/5) = 0 - 2π/5 - 2

f(π/5) = - 2π/5 - 2

f(π/5) = (- 2π - 10)/10

f(π/5) = - 2(π + 10)/10

f(π/5) = - 2(π + 10)/5

f(π/5) = - 2(π + 10)/5

f(π/5) = - 2(3.142 + 10)/5

f(π/5) = - 2(13.142)/5

f(π/5) = - 26.284/5

f(π/5) = -5.2568

f(π/5) ≅ -5.26

So, f(π/5) ≅ -5.26

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Answer:

The final price of the stapler is 11.97 dollars and they would get 4.49 dollars in revenue.

After 8 years, Savings Account B will have more money because it is modeled by the equation A = 975 * (1 + 52.65 * t), where the investment grows at a much faster rate

Account A shows an end balance of approximately $1,622.40 after eight years based on a model of continual compounding with an annual percentage rate of 5.4%.

In contrast, account B's future balance prediction is roughly $411,641.00 at the end of an eight-year period, which utilizes a simple interest model and grows at breakneck speeds due to a growth percentage of 5265%.

After 8 years, Savings Account B will have more money because it is modeled by the equation A = 975 * (1 + 52.65 * t), where the investment grows at a much faster rate

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Each of two savings accounts begins with $975 as an initial deposit and 5.4% annual interest rate; however, the interest is accrued distinctly for each account. As demonstrated below in Table I:

- Savings Account A: A = 975 * (1 + 0.054 / 12) ^ (12 * t);

- Savings Account B: A = 975 * (1 + 52.65 * t).

Thus, after eight years, which account will yield a higher balance and why remains to be determined?

The amount is $4,000 invested in the 3% account.

Let x be the amount invested in the 3% account. Then, the amount invested in the 5% account is $6,000 - x.

The interest earned from the 3% account is 0.03x, and the interest earned from the 5% account is 0.05($6,000 - x) = $300 - 0.05x.

The total interest earned is given as $220, so we can write the equation:

0.03x + 300 - 0.05x = 220

Simplifying the equation, we get:

-0.02x + 300 = 220

-0.02x = -80

x = 4,000

Therefore, $4,000 was invested in the 3% account.

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1. radius = 13cm

2. Diameter = 27.2cm

3. Diameter = 24m

4.  Radius = 24. 5m

The formula used for determining the area and also the circumference of a circle is given thus;

For the  area of a circle, we have;

A = πr²

Given that the parameters are;

For the circumference of a circle, we have;

C = 2πr

To calculate the  diameter of a circle, we have the formula;

Diameter = 2Radius

Now, substitute the values for each

1. radius = diameter/2 = 26/2

radius = 13cm

2. When the radius = 13.6m

diameter = 2(13.6) = 27.2m

3. When the radius = 12m

diameter = 2(12) =  24m

4. When the diameter  = 49m

Then, radius 49/2 = 24. 5m

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If the Federal Reserve sells $60,000 in Treasury bonds to a bank at 8% interest, the immediate effect on the money supply is B. It is decreased by $60,000.

One of the monetary factors that decreases the money supply in the economic is when the Federal Reserve raises the banks' reserve requirements.

Another factor that can decrease the money supply is the sale of treasury bonds to banks.

Raising the interest rates also decreases the money supply.

Thus, by selling $60,000 in Treasury bonds to a bank at 8% interest, it decreases the money supply.

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The equation (x - 3)² + (y - 7)² = 36 in general form will be x² + y² - 6x - 14y + 22 = 0

Given that:

(x - 3)²+(y - 7)² = 36

Expanding the square in the given equation, we get:

(x - 3)² + (y - 7)² = 36

(x - 3)(x - 3) + (y - 7)(y - 7) = 36

x² - 6x + 9 + y² - 14y + 49 = 36

x² + y² - 6x - 14y + 22 = 0

Therefore, the equation of the circle (x - 3)² + (y - 7)² = 36 in general form will be x² + y² - 6x - 14y + 22 = 0

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84 adult tickets were consequently sold on that day.

Let's fix this issue using a set of equations. Let x represent how many adult tickets were sold, and y represent how many kid tickets were sold.

We learn the following from the issue:

Total number of tickets sold = x + y

Total sales equal 9.9x + 5.5y = 1216.6.

To find y, we can utilize the first equation:

y = 146 - x

We obtain the following by substituting this into the second equation: 9.9x + 5.5(146 - x) = 1216.6

The result of simplifying and finding x is: 4.4x = 369.6 x = 84

Therefore, 84 adult tickets were consequently sold on that day.

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The probability that her Internet service is not broken for five days in a row is given by P ( A ) = 0.0102

Given data ,

Let the probability that the internet connection is lost = 60 %

Now , We may utilize the probability of independent occurrences occurring sequentially to determine the likelihood that her Internet service won't be down for five days in a row. We may add the probability for five days as the occurrences of her Internet service being down or up on each day are independent.

The likelihood of her Internet service remaining operational for one day is 0.40.

Her chances of having uninterrupted Internet access for five days are equal to (0.40)⁵

P ( A ) =  (0.40)⁶ is about equivalent to 0.0102

Hence , the probability of Ashley's Internet service remaining up for five consecutive days is around 0.0102 or 1.02%

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