How can you tell if a partitioning problem is giving you "part to part" or "part to whole"?

An equation for this line in the point-slope form will be y-7 = -2(x + 4).

What is the Point-slope form?

The equation of the straight line has its slope and given point. If we have a non-vertical line that passes through any point(x1, y1) and has a gradient m. then general point (x, y) must satisfy the equation. Point-slope is a specific form of linear equations in two variables:

y - y₁ = m(x - x₁)

Which is the required equation of a line in a point-slope form.

We need to find the equation of the line that passes through (-4, 7) and whose slope is -2.

Well, we will simply plug m = -2, x₁= -4, and y₁  = 7 into point-slope form.

y-y₁ = m(x-x₁)

Now substitute;

y-7 = -2(x - (-4))

y-7 = -2(x + 4)

Therefore, an equation for this line in the point-slope form will be y-7 = -2(x + 4).

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The cumulative total in Vietnam j(n) is 23(n-1),cumulative takes into account all data up to the present. In month four, j(n) will be worth more than v(n).

The distinction between total and cumulative is that total refers to the entirety of something, whereas cumulative takes into account all data up to the present.

When a new number is added to a series of numbers, the running total is updated by adding the new number's value to the previous running total. Partially sum is another name for it. Running totals serve two distinct objectives.

We take it for granted that you mean that vehicles delivered to Vietnam should be modeled by v(n) = 5 + 11 and those sent to Japan by j(n) = 23(n-1).

In month four, j(n) will be worth more than v(n).      

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Answer:

4/6, 8/12, 16/24, etc. are examples of equivalent fractions, but there are none with the denominator of 10.

Step-by-step explanation:

Hope this helps, and have a great day! :D

As W is spanned by n linearly independent vectors in ℝ^n, it means that the dimension of W is also n. This implies that W has the same dimension as ℝ^n, and therefore, W is equal to ℝ^n.

If w is a subspace of rnspanned by n non zero orthogonal vectors, then w is at most n-dimensional because there are only n vectors that can be used to span w. Any vector outside of the span of these n vectors will not be in w. Therefore, the dimension of w is less than or equal to n. Since w is a subspace of rn, which is n-dimensional, w must be a subset of Rn with a dimension less than or equal to n. Therefore, w d Rn. Suppose W is a subspace of ℝ^n spanned by n nonzero orthogonal vectors. This means that W is a vector space that is a subset of ℝ^n, and it can be generated by taking linear combinations of the n nonzero orthogonal vectors. Since the vectors are orthogonal, they are linearly independent, and their linear combinations form a basis for the subspace W.

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Answer: 9/2, 2.63, -2.47, -5sqrt(3), -18

Step-by-step explanation:

To show that each function is O(x^2) using the Definitional proof, we need to find a constant c and a positive number k such that |f(x)| ≤ c|x^2| for all values of x greater than some value k.

(a) For function f(x) = x:

We need to find a constant c and k such that |x| ≤ c|x^2| for all x > k.

Let's choose c = 1 and k = 1.

|f(x)| = |x| ≤ 1 * |x^2| for all x > 1.

Therefore, f(x) = x is O(x^2).

(b) For function f(x) = 9x + 5:

We need to find a constant c and k such that |9x + 5| ≤ c|x^2| for all x > k.

Let's choose c = 14 and k = 1.

|f(x)| = |9x + 5| ≤ 14 * |x^2| for all x > 1.

Therefore, f(x) = 9x + 5 is O(x^2).

(c) For function f(x) = 2x^2 + x + 5:

We need to find a constant c and k such that |2x^2 + x + 5| ≤ c|x^2| for all x > k.

Let's choose c = 8 and k = 1.

|f(x)| = |2x^2 + x + 5| ≤ 8 * |x^2| for all x > 1.

Therefore, f(x) = 2x^2 + x + 5 is O(x^2).

(d) For function f(x) = 10x^2 + log(x):

We need to find a constant c and k such that |10x^2 + log(x)| ≤ c|x^2| for all x > k.

Let's choose c = 11 and k = 1.

|f(x)| = |10x^2 + log(x)| ≤ 11 * |x^2| for all x > 1.

Therefore, f(x) = 10x^2 + log(x) is O(x^2).

In each case, we have found a constant c and a value k such that the inequality |f(x)| ≤ c|x^2| holds for all x greater than k. This satisfies the definition of f(x) being O(x^2).

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The probability is given by:

Therefore:

- The probability of spinning blue is:

Favorable outcomes = 1 (blue color)

Total outcomes = 3 (red, blue, and yellow)

- The probability of flipping heads is:

Favorable outcomes = 1 (head)

Total outcomes = 2 (head and tail)

- The probability of spinning a one is:

Favorable outcomes = 1 (number 1)

Total outcomes = 3 (numbers 1, 2 and 3)

Next, the probability of the compound event:

Answer: the probability of the compound event is 1/18

Answer:

7,250.

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Answer:

4.

Step-by-step explanation:

You could list all the factors and find the highest number, use a factor tree or the table.

Hope this helps and hope you're having a splendiferous day or night.

Answer:

The answer is 13 hope it helps!<3

Step-by-step explanation:

==========================================================

Work Shown:

x = first number

x+1 = second number

x+2 = third number

x+3 = fourth number

x+4 = fifth number

Note how the numbers are one after another. Consecutive numbers follow this pattern. For example: 6,7,8,9,10 are consecutive numbers. One number follows right after the other.

---------------

Add up those five expressions. Set the sum equal to 70 and solve for x

(x)+(x+1)+(x+2)+(x+3)+(x+4) = 70

(x+x+x+x+x)+(1+2+3+4) = 70

5x+10 = 70

5x = 70-10

5x = 60

x = 60/5

x = 12 is the first number and the smallest number

x+1 = 12+1 = 13 is the second number

x+2 = 12+2 = 14 is the third number

x+3 = 12+3 = 15 is the fourth number

x+4 = 12+4 = 16 is the fifth number

Check:

12+13+14+15+16 = 70

which confirms our answer

-----------------

You could use a guess and check method, but the algebraic approach is much more efficient.

Answer:

this should be the answer 4x^3 & 2x^2

Answer:

Step-by-step explanation:

Suppose an upward force of 15 N is added to the box. What will be the net vertical force on the box?

THIS IS THE COMPLETE QUESTION BELOW;

1. Explain how you calculate the net force in any direction on the box.

2. Suppose an upward force of 15 N is added to the box. What will be the net vertical force on the box?

3. What force could be applied to the box to make the net force in the horizontal direction zero? Explain.

4. Suppose a force of 25 N to the right is added to the box. What will be the net force to the right?

CHECK THE ATTACHMENT FOR THE FIQURE.

1)since the given horizontal forces are acting on the box at opposite direction then

NET FORCE= (100- 50)N

= 50N( this is because the 100N and 50N acting Horizontally will cancel each other, then the remaining force is 50N.

✓Since, the  two vertical forces also acted on the box in opposite direction, then

NET FORCE= (25 25)N

= 0N

Note: horizontal forces are one acting from right to left and vice versa, while vertical forces are ones acting from up to down and vice versa.

HENCE, NET FORCE = 50N + 0N= 50N

2) since the net vertical force was 0N, if

15N force is added then we still have NET FORCE OF 15N

3) if  force of 50N is applied to horizontal forces moving from left to right then NET HORIZONTAL FORCES= 0N

4) since, the net force for the box is 50N, if  Horizontal force of 25N is added  moving left to right then NET FORCE = 25N for whole box.

You would need to deposit approximately $78,425.99 today in order to withdraw $14,000 a year for the next 7 years and receive an additional $28,000 in the last year, assuming an interest rate of 11%.

To calculate the present value of the complex cash flows, we need to find the present value of the annuity payments for the next 7 years and the present value of the additional amount in the last year. Let's calculate each part separately: Present Value of the Annuity Payments: The annuity payments are $14,000 per year for 7 years. We can calculate the present value using the formula for the present value of an ordinary annuity: PV = CF * [(1 - (1 + r)^(-n)) / r]. Where PV is the present value, CF is the cash flow per period, r is the interest rate, and n is the number of periods. Using an interest rate of 11% and 7 periods, we have: PV_annuity = $14,000 * [(1 - (1 + 0.11)^(-7)) / 0.11]

Present Value of the Additional Amount: The additional amount in the last year is $28,000. Since it is a single cash flow in the future, we can calculate its present value using the formula for the present value of a single amount: PV_single = CF / (1 + r)^n. Where PV_single is the present value, CF is the cash flow, r is the interest rate, and n is the number of periods. Using an interest rate of 11% and 6 periods (since it occurs in the 17th year), we have: PV_single = $28,000 / (1 + 0.11)^6. Total Present Value: The total present value is the sum of the present value of the annuity payments and the present value of the additional amount:

Total PV = PV_annuity + PV_single

Now let's calculate the values: PV_annuity = $14,000 * [(1 - (1 + 0.11)^(-7)) / 0.11] ≈ $66,698.92, PV_single = $28,000 / (1 + 0.11)^6 ≈ $11,727.07, Total PV = $66,698.92 + $11,727.07 ≈ $78,425.99. Therefore, you would need to deposit approximately $78,425.99 today in order to withdraw $14,000 a year for the next 7 years and receive an additional $28,000 in the last year, assuming an interest rate of 11%.

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The estimated probability of finding at most 50 acceptable circuits in a batch of 60 is approximately 0.6591.

To estimate the probability of finding at most 50 acceptable circuits in a batch of 60 from a certain factory, where the probability of passing the quality test is (p = 0.8) and the outcomes of the tests are mutually independent, we can use the Central Limit Theorem (CLT).

The CLT states that for a large enough sample size, the distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution.

Let's denote (X) as the number of acceptable circuits in a batch of 60. Since each circuit passes the test with a probability of 0.8, we can model (X) as a binomial random variable with parameters (n = 60) and (p = 0.8).

To estimate the probability of finding at most 50 acceptable circuits, we can calculate the cumulative probability using the normal approximation to the binomial distribution.

Since the sample size is large \((\(n = 60\))\), we can approximate the distribution of (X) as a normal distribution with mean \(\(\mu = np = 60 \times 0.8 = 48\)\) and standard deviation \(\(\sigma = \sqrt{np(1-p)}\) = \(\sqrt{60 \times 0.8 \times 0.2} \approx 4.90\).\)

Now, we want to find the probability of\(\(P(X \leq 50)\)\). We can standardize the value using the z-score:

\(\[P(X \leq 50) = P\left(\frac{X - \mu}{\sigma} \leq \frac{50 - 48}{4.90}\right) = P(Z \leq 0.41)\]\)

Using the standard normal distribution table or calculator, we can find that \(\(P(Z \leq 0.41) \approx 0.6591\).\)

Therefore, the estimated probability of finding at most 50 acceptable circuits in a batch of 60 is approximately 0.6591.

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The value of the principal investment is given as follows:

$5,725.90.

The amount of money earned, in compound interest, after t years, is given by:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

In which:

The parameters for this problem are given as follows:

t = 15, A(t) = 12065.51, r = 0.05, n = 4.

Hence the principal can be obtained as follows:

P(1 + 0.05/4)^(4 x 15) = 12065.51

2.1072P = 12065.51

P = 12065.51/2.1072

P = $5,725.90

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The central angle (in radians ) is 0.8 radians.
What is a cricle ?

A circle is a basic 2D shape measured by its radius. A circle divides the plane into two areas: interior and exterior. Similar to line type. Imagine a line segment bending until the ends connect. Arrange the loops so that they form a perfect circle.

we know that,

arc length = radius *  central angle (in radians)

and central angle (in radians) = arc length / radius

by substituting the given values

arc length = 7.2

radius=9

we get,

central angle (in radians) = 7.2 / 9

=0.8 radians

Hence , the central angle = 0.8 radians

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The value of expression is,

⇒ 0.335

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that;

The expression is,

⇒ 0.581 - 0.246

Now,

Since, The expression is,

⇒ 0.581 - 0.246

After subtraction we get;

⇒ 0.581 - 0.246

⇒ 0.335

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Answer:

(

i

4

)

11

(

i

2

⋅

i

)

(i4)11(i2⋅i)

thats the answer

Answer:

B.) The interquartile range of the data is 2

Step-by-step explanation:

Replacing the values in the equation, we have:

D(t) = (200 ft/s)*t + 0.5*(100 ft/s2)*t^2

D(t) = (200 ft/s)*t + (50 ft/s2)*t^2 (Multiplying)

The answer is:

D(t) = (200)*t + (50)*t^2 (Distance in ft)

a) The data in ascending Order; -83/4 < -67/4 < -62/4 < -1/4.

b) Sea Grass is the furthest the Surface of water.

Numbers can be arranged in ascending order, from least value to highest value. The arrangement is left to right. Increasing order is another name for ascending order.

Given that -20 3/4, -15 1/2, -14 3/4, -1/4

Now, the above fraction into Normal fraction;

-83/4, -31/2, -67/4, -1/4.

Now, Arranging the data in ascending Order;

-83/4 < -67/4 < -62/4 < -1/4.

b) Since Sea Grass is the furthest below the Surface of water.

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Answer:

16,384

Step-by-step explanation:

Answer:

1.132d

Step-by-step explanation:

Cost of the dinner=$d

Coupon=10% after

Tax=8%

Tax=0.08d

Tax + cost of dinner= d + 0.08d

Coupon for 10% discount after tax

10% coupon discount means she will pay 100% - 10%( coupon)

=90%

Price=90%(d + 0.08d)

=0.9(1.08d)

She added 16% tip to the total cost before any price or discount was applied

16% of d

=0.16*d

=0.16d

New price= 0.09(1.08d) + 0.16d

=0.972d + 0.16d

=1.132d

Answer:

45 feet

Step-by-step explanation:

Set up Ratios

1/2 in/5 ft = 4 1/2 in/x

Solve for x by cross-multiplying:

\(\frac{1/2}{5}\) times \(\frac{4 1/2}{x}\)

4 1/2 times 5 = 22 1/2

1/2 times x = 1/2x

22 1/2 = 1/2x

45 = X

Therefore the actual length of the bus is 45 feet.

Hope it helps :)

the answer is the same

The value of x is (2w - t)/5.

The value of w is (5x + t)/2.

The value of t is  2w - 5x.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

5x - 2w + t = 0

Solve for x.

5x - 2w + t = 0

5x = 2w - t

x = (2w - t)/5

Solve for w.

5x - 2w + t = 0

5x + t = 2w

w = (5x + t)/2

Solve for t.

5x - 2w + t = 0

t = 2w - 5x

Thus,

The value of x, w, and t is given above.

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the population in 1915 and 1940 is 24264.5

the population reach 50,000 is 77 years

In 1891 the population would be 6250 x  ( 1+ 0.0275)

In 1832 the population would be [ 6250 x ( 1+0.0275 ) ] x (1+0.0275)

in 1893 the population would be [6250 x ( 1+0.0275) ] x ( 1+0.0275) x (1+0.0275)

p= 6250(1.0275)^t

where t= number of years till 1890

t=25

p= 6250(1.0275) ²⁵

= 6250 x 1.9704

= 12314.8

t=50

p= 6250(1.0275) ⁵⁰

= 6250 x 3.8823

=24264.5

To reach 50,000

50000= 6250(1.0275)^t

(1.0275)^t = 50000 /6250

(1.0275)^t =8

Take log on both sides

log (1.0275)^t = log 8

t= log8/ log (1.0275)

t=76.6%

Hence

the population in 1915 and 1940 is 24264.5

the population reach 50,000 is 77 years

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Answer:

5.38 inches

Step-by-step explanation:

The formula for Area of an Heptagon

= A=7/4a²cot(180°/7)

Area = 105in²

Side a = ?

The formula for Side a

= √4A ×tan (180°/7)/7

= √4 × 105 × tan (180°/7) /7

= 5.37536 inches

Approximately = 5.38 inches.