Find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results.
f(t) = 3 −7/4t, (1/3,-9/4)
f(1/3)

The base of the ladder must be placed 3 ft from the base of the building. The total length of the ladder is 15 ft.

1. The ladder must reach 12 ft up the wall, so we need to calculate the distance from the base of the building to 12 ft.

2. The total length of the ladder is 15 ft.

3. Subtract the length of the ladder (15 ft) fromthe desired height (12 ft) to get the distance from the base of the building.

4. 12 ft - 15 ft = -3 ft

5. Since the distance cannot be negative, the base of the ladder must be placed 3 ft away from the base of the building.

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Answer:

........................

Answer:

\(144ft^{2}\) (144ft^2)

Step-by-step explanation:

Since the living room is 6 inches by 6 inches, the formula of the living room can be seen as: \(6in^{2}\). And since each inch is equal to 2 feet, (6*2=12) we can turn the equation into: \(12ft^{2}\). 12 times 12 is 144, so the answer is \(144ft^{2}\)

Answer:

C. 3 × 100 + 4 × 10 + 7 × 1 + 8 × (1/10) + 5 × (1/100)

Step-by-step explanation:

3: hundreds

4: tens

7: ones

8: tenths

5: hundreths

Answer:

76

Step-by-step explanation:

The given data is 64, 72, 85, 80, 72, 89.

First we arrange it in ascending order.

64,72,72,80,85,89

The middle two terms are 72 and 80.

There are 6 no of observations.

The median when n is even is given by :

\(M=\dfrac{72+80}{2}\\\\=76\)

So, the median of given data is 76.

The polynomial 6x³ + x² - 2x + 15 divided by 2x + 3 will give a quotient of 3x² - 4x + 5 and a remainder of zero, which makes option a correct.

The long division method will require us to; divide, multiply, subtract, bring down the next number and repeat the process to end at zero or arrive at a remainder

We shall divide the polynomial 6x³ + x² - 2x + 15 by 2x + 3 as follows;

x³ divided by 2x equals 3x²

2x + 3 multiplied by 3x² equals 6x³ + 9x²

subtract 6x³ + 9x² from 6x³ + x² - 2x + 15 will result to -8x² - 2x + 15

-8x² divided by 2x equals -4x

2x + 3 multiplied by -4x equals -8x² - 12x

subtract -8x² - 12x from -8x² - 2x + 15 will result to 10x + 15

10x divided by 2x equals 5

2x + 3 multiplied by 5 equals 10x + 15

subtract 10x + 15 from 10x + 15 will result to a remainder of 0

Therefore by the long division method, 6x³ + x² - 2x + 15 divided by 2x + 3 gives a quotient 3x² - 4x + 5 and a remainder of 0.

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Evaluating p(4) using Horner's algorithm:

1. To use Horner's algorithm, we write the polynomial in nested form as follows:

p(z) = ((3z - 7)z - 5)z^2 + (z - 8)z + 2

Now, we can evaluate p(4) by starting from the inside and working our way out:

p(4) = ((3(4) - 7)4 - 5)4^2 + (4 - 8)4 + 2

= (5)4^2 - 4 + 2

= 78

Therefore, p(4) = 78.

2. Finding the Taylor series expansion of p(z) about z0 = 4:

To find the Taylor series expansion of p(z) about z0 = 4, we need to compute the derivatives of p(z) at z0 = 4. First, we compute p'(z) = 6z^2 - 28z^3 - 10z^2 + 2z - 8, then p''(z) = 12z - 84z^2 - 20z + 2, p'''(z) = 12 - 168z - 20, and so on.

Using these derivatives, we can write the Taylor series expansion of p(z) about z0 = 4 as follows:

p(z) = p(4) + p'(4)(z - 4) + p''(4)(z - 4)^2/2! + p'''(4)(z - 4)^3/3! + ...

Substituting in the values we computed, we get:

p(z) = 78 + 10(z - 4) - 41(z - 4)^2/2! - 14(z - 4)^3/3! + ...

Therefore, the Taylor series expansion of p(z) about z0 = 4 is:

p(z) = 78 + 10(z - 4) - 20.5(z - 4)^2 - 2.333(z - 4)^3 + ...

3. Using Newton's method to find a root of p(z):

To use Newton's method to find a root of p(z), we start with an initial guess z0 = 4 and iterate the formula z1 = z0 - p(z0)/p'(z0) until we reach a desired level of accuracy.

4. We already computed p'(z) in part 2, so we can use the formula to compute z1 as follows:

z1 = z0 - p(z0)/p'(z0)

= 4 - (78 + 10(4) - 20.5(4 - 4)^2 - 2.333(4 - 4)^3)/[6(4)^2 - 28(4)^3 - 10(4)^2 + 2(4) - 8]

= 3.9167

We can continue to iterate using this formula to get better approximations for the root of p(z).

Horner's algorithm is a fast and efficient way to evaluate a polynomial at a particular point. It involves using the distributive property of multiplication to rewrite a polynomial in a nested form, then evaluating the polynomial from the inside out.

In this problem, we will use Horner's algorithm to evaluate p(4) for a given polynomial, find its Taylor series expansion about the point z0 = 4, and then use Newton's method to find an approximation for a root of the polynomial.

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Answer:

1862.25

Step-by-step explanation:

Answer:

Add the lengths:

5x - 16 + 2x - 4 = 7x - 20

Step-by-step explanation:

find the points of intersection of the parabola 4y squared + 8 y - 16 x equal to 12 in the line x equals to 3

Answer:

44

Step-by-step explanation:

10 x 3 = 30

8 + 6 =14

30 + 14 = 44

Answer:

110ft²

Step-by-step explanation:

Area of figure=(10×8)+(1/2×6×8)

=80+24

=112 ft²

=110 ft² (to nearest tenth)

Answer:

The LCM of 315 and 450 is 3150. Hope this helps :)

Step-by-step explanation:

Let

x -----> number of orange balls

y -----> number of green balls

we have that

x+y=123 -----> x=123-y ------> equation A

y=5x+9 -----> equation B

Solve the system of equations

substitute equation A in equation B

y=5(123-y)+9

solve for y

y=615-5y+9

y+5y=615+9

6y=624

y=104

Find out the value of x

x=123-104

x=19

therefore

Answer:

The answer to 2+3(4.3 x 00.009) is 2.1161.

Step-by-step explanation:

Hope this helps!

Answer:

2.1161

Step-by-step explanation:

Answer:

O D. Luis had 6 pencils. He placed them in 4 groups. How many were in each group?

Step-by-step explanation:

this makes more sense, since he had 6 pencils and put them in 4 different groups. so, 6 *4 = 24 c:

Answer:

\(\{0, 1, 2, 3\}\) is a partition of Z

Step-by-step explanation:

Given

\($$A _ { 0 } = \{n \in \mathbf { Z } | n = 4 k$$,\) for some integer k\(\}\)

\($$A _ { 1 } = \{ n \in \mathbf { Z } | n = 4 k + 1$$,\) for some integer k},

\($$A _ { 2 } = { n \in \mathbf { Z } | n = 4 k + 2$$,\) for some integer k},

and

\($$A _ { 3 } = { n \in \mathbf { Z } | n = 4 k + 3$$,\)for some integer k}.

Required

Is \(\{0, 1, 2, 3\}\) a partition of Z

Let

\(k = 0\)

So:

\($$A _ { 0 } = 4 k\)

\($$A _ { 0 } = 4 k \to $$A _ { 0 } = 4 * 0 = 0\)

\($$A _ { 1 } = 4 k + 1$$,\)

\(A _ { 1 } = 4 *0 + 1$$ \to A_1 = 1\)

\(A _ { 2 } = 4 k + 2\)

\(A _ { 2} = 4 *0 + 2$$ \to A_2 = 2\)

\(A _ { 3 } = 4 k + 3\)

\(A _ { 3 } = 4 *0 + 3$$ \to A_3 = 3\)

So, we have:

\(\{A_0,A_1,A_2,A_3\} = \{0,1,2,3\}\)

Hence:

\(\{0, 1, 2, 3\}\) is a partition of Z

Answer:

c. Smaller than the fraction

Step-by-step explanation:

have a great night :)

Answer:

0.07 (7/100) is closer to 0.

1.150 (1150/1000) is closer to 1.

0.391 (391/1000) is closer to 1/2.

0.0999 (999/10,000) is closer to 0.

0.99 (99/100) is closer to 1.

0.599 (599/1000) is closer to 1/2.

Put everything as a fraction. The first spot after the decimal means you put the number over 10, the second place means you put it over 100, the third 1,000, fourth 10,000 and so on. Hope I helped! ^^Step-by-step explanation:

The closeness of the given function is found to be by writing it in the simplest form as 1.

A fraction is a number written in the form a / b, where a and b are integers and b ≠ 0.

The number a is called as the numerator and b is the denominator.

The given fraction is 15/20.

It can be simplified as below,

Divide numerator and denominator by the common factor 5 as,

(15 ÷ 5)/(20 ÷ 5)

⇒ 3/4

The given fraction 3/4 is greater than zero and closest to 1.

Hence, the given fraction is closest to integer 1.

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Answer:

narato???????

Step-by-step explanation:

its from men dadd

Answer:

Beyblaes lol my brother used to love them. :)

Step-by-step explanation:

Answer:

x=5, y=41

Step-by-step explanation:

Because both equations are equal to Y, you can set them equal to each other like this:

8x+1=3x+26

From here, solve for x:

1. 5x+1=26

2. 5x=25

3. x=5

Once you have x, plug it back in to one of the original equations:

y=8(5)+1

y=41 and then you have your answer

If this answer was particularly helpful, please feel free to give it brainliest!! I would greatly appreciate it.

Answer:

(x, y) = (5, 41)

Step-by-step explanation:

y = 8x + 1

y = 3x + 26

Substituting the value of y (first equation) into the second equation, we get:

8x + 1 = 3x + 26

5x = 25

x = 5.

So, to get y, all we have to do is to substitute the value of x into the second equation.

y = 3 * 5 + 26

y = 15 + 26

y = 41

Answer:

I would say a bar graph because it is used best for data that needs groups.

In order to get samples from each age group, you would need to use stratified sampling. This involves dividing the population into subgroups, or strata, based on a particular characteristic - in this case, age.

Once the population has been stratified, a random sample can be taken from each subgroup in proportion to its size.

For example, if the population consists of 1000 people, with 300 aged 20-40, 400 aged 40-60, and 300 aged 60-80, you would need to take a sample of 60 people (20% of the population) in order to get 20 people from each age group. This could be done by randomly selecting 18 people from the 20-40 age group, 24 people from the 40-60 age group, and 18 people from the 60-80 age group.

Stratified sampling is often used when there are important subgroups within a population that need to be represented in the sample. It can help to ensure that the sample is representative of the population as a whole, and can improve the accuracy of the survey results. However, it can also be more time-consuming and expensive than other sampling methods.

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Answer:

Isosoles triangleddndnndnendndne

The sequence of transformations used to show the congruence of polygons JKLMN and PQRST is to reflect PQRST across the y-axis and then translate the result down 10 units.

We are given two polygons. Both the polygons are congruent, and to prove it, we can use the concept of transformations. The first transformation we need to perform is to reflect the polygon PQRST across the y-axis. The next transformation that needs to be performed is to translate the result down by 10 units. We find that the polygon PQRST now coincides with the polygon JKLMN. Hence, it is proved that the polygons are congruent to each other.

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Answer:

5x + 6y

Hope it helps!

Average Auction Price is 0.9925the noncompetitive bidders will receive $750 million at a price of $0.9925 per $1 of par value.

To determine who will receive T-bills, what quantity, and at what price, we need to rank the bidders based on the bid prices and allocate the T-bills in descending order of bid prices until the entire $2.5 billion par value has been allocated. The bid prices listed are quoted as a percentage of par value, so we need to calculate the dollar amount bid for each bidder as follows:

Bid Amount = Bid Price × Par Value

For Bidder A:

Bid Amount = 0.9940 × 500 million

Bid Amount = $497 million

For Bidder B:

Bid Amount = 0.9901 × 750 million

Bid Amount = $742.6 million

For Bidder C:

Bid Amount = 0.9925 × 1.5 billion

Bid Amount = $1.48875 billion

For Bidder D:

Bid Amount = 0.9936 × 1 billion

Bid Amount = $993.6 million

For Bidder E:

Bid Amount = 0.9939 × 600 million

Bid Amount = $596.34 million

Total Bid Amount = $3.31874 billion

Since the total bid amount exceeds the $2.5 billion par value of the T-bills being auctioned, we need to allocate the T-bills to the highest bidders until the entire $2.5 billion has been allocated.

Ranking the bidders in descending order of bid prices, we have:

Bidder B with a bid price of $0.9901

Bidder C with a bid price of $0.9925

Bidder D with a bid price of $0.9936

Bidder E with a bid price of $0.9939

Bidder A with a bid price of $0.9940

Allocating T-bills to the highest bidders until the entire $2.5 billion par value has been allocated, we have:

Bidder B will receive $750 million at a price of $0.9901 per $1 of par value.

Bidder C will receive $750 million at a price of $0.9925 per $1 of par value.

Bidder D will receive $500 million at a price of $0.9936 per $1 of par value.

Bidder E will receive $250 million at a price of $0.9939 per $1 of par value.

The noncompetitive bids of $750 million will be allocated at the average auction price, which is calculated as the simple average of the four highest accepted bid prices:

Average Auction Price = (0.9901 + 0.9925 + 0.9936 + 0.9939) / 4

Average Auction Price = 0.9925

Therefore, the noncompetitive bidders will receive $750 million at a price of $0.9925 per $1 of par value.

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Step 1

Find the distance between the sun and the star using SohCahToa.

For this problem we use Toa.

where;

Step 2

Substitute and find the value of d

Answer: $684

Step-by-step explanation: Add 300 to 75 and you have 375, next subtract the total payment she wants to have per week (which is 1059) so, subtract 1059 to 375 then you have $684. To check your answer, add 684 to 375 and you come up with 1059.

We have found the two ordered pairs that satisfy the given inequality in each case. In this question, we need to choose two ordered pairs that will satisfy each case's given inequality. Let's evaluate each inequality using each of the given ordered pairs to find the solution.

1. y < x + 3

Using the given ordered pairs, we have:

(2, 5): 5 < 2 + 3, which is true.

(5, 2): 2 < 5 + 3, which is false.

(-5, -5): -5 < -5 + 3, which is false.

(4, 0): 0 < 4 + 3, which is true.

The two ordered pairs that satisfy the given inequality are (2, 5) and (4, 0).

2. 3x + y > 10

Using the given ordered pairs, we have:

(-1, 2): 3(-1) + 2 > 10, which is false.

(1, 10): 3(1) + 10 > 10, which is true.

(3, 1): 3(3) + 1 > 10, which is true.

(3, 3): 3(3) + 3 > 10, which is true.

The two ordered pairs that satisfy the given inequality are (1, 10), (3, 1), and (3, 3).

3. 2y + x ≥ 5

Using the given ordered pairs, we have:

(1, 2): 2(1) + 2 ≥ 5, which is true.

(0, 4): 2(4) + 0 ≥ 5, which is true.

(2, 2): 2(2) + 2 ≥ 5, which is false.

(-1, -5): 2(-5) - 1 ≥ 5, which is false.

The two ordered pairs that satisfy the given inequality are (1, 2) and (0, 4).

4. 3x - 2y ≤ 10 Using the given ordered pairs, we have:

(5, 1): 3(5) - 2(1) ≤ 10, which is true.

(0, -5): 3(0) - 2(-5) ≤ 10, which is true.

(-1, -6): 3(-1) - 2(-6) ≤ 10, which is false.

(10, 2): 3(10) - 2(2) ≤ 10, which is false.

The two ordered pairs that satisfy the given inequality are (5, 1) and (0, -5).

5. 5x + 3y > 15

Using the given ordered pairs, we have:

(2, 1): 5(2) + 3(1) > 15, which is false.

(-3, 1): 5(-3) + 3(1) > 15, which is false.

(0, 6): 5(0) + 3(6) > 15, which is true.

(2, 2): 5(2) + 3(2) > 15, which is false.

The only ordered pair that satisfies the given inequality is (0, 6). Thus, we have found the two ordered pairs that satisfy the given inequality in each case.

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An old campfire is uncovered during an archaeological dig. Its charcoal is found to contain less than 1/1000 the normal amount of 14C. Estimate the minimum age of the charcoal (in years), noting that 210

To estimate the minimum age of the charcoal, we can use the concept of half-life. The half-life of 14C is approximately 5730 years.

Since the charcoal is found to contain less than 1/1000 the normal amount of 14C, it means that more than 99.9% of the 14C has decayed.

To find the number of half-lives that have passed, we can use the equation:

(1/2)^n = 1/1000

Solving for n, we get:

n = log(1/1000) / log(1/2)

n ≈ 9.966

Since each half-life is approximately 5730 years, we can estimate the minimum age of the charcoal by multiplying the number of half-lives by the half-life time:

9.966 * 5730 ≈ 57,254 years

Therefore, the minimum age of the charcoal is approximately 57,254 years.

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