if i get this wrong im gonna fail plsfkdsjsdkl

The side length of each square represent for the rectangle to correctly represent (0, 3) · (0, 5) is 1 units.

A rectangle represented by (0, 3) · (0, 5) has length 3 units and breadth 5 units. To represent that rectangles with minimum number of squares of same size, we calculate the highest common factor.

Highest Common Factor is a mathematical concept used to find the greatest number that divides two or more numbers without leaving a remainder. It is also known as the greatest common divisor (GCD) or the greatest common factor (GCF).

Highest common factor of 3 and 5 is 1 as both are prime numbers. So squares with side length 1 unit best represent the rectangle to correctly represent (0, 3) · (0, 5).

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The marginal benefit from studying one extra hour is 5 percent.

Now,

Given:

To find: Marginal benefit on studying one hour extra.

Finding:

Now, marks scored on studying 4 hours is 80 percent and 5 hours is 85 percent.

Thus, the extra percentage that is scored is because of the 1 hour of extra studying.

The extra percentage = marginal benefit of studying extra = 85 - 80 = 5 percent.

Hence, the marginal benefit from studying one extra hour is 5 percent.

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Answer:

A general line can be written as:

y = a*x + b

Where a is the slope, and b is the y-intercept.

if we know that the line passes through the points (x1, y1) and (x2, y2), the slope will be:

a = (y2 - y1)/(x2 - x1)

In this case, we can see that the line passes through the points (0,0) and (4,2) then the slope will be:

a = (2 - 0)/(4 - 0) = 2

Then the equation is:

y = 2*x + b

And because we have the point (0, 0), we know that the y-intercept is equal to zero, then the equation is:

y = 2*x

This means that Pablo does 2 revolutions per feet, and we already found that the slope of the equation is 2.

Therefore, 5x - y = 5(4) - (-2) = 22.

The answer of Linear Equation is (e) 22.

An equation is a mathematical statement that asserts the equality of two expressions. It consists of two sides, a left-hand side (LHS) and a right-hand side (RHS), separated by an equals sign (=). The LHS and RHS may contain variables, constants, and operators such as addition, subtraction, multiplication, and division.

To find the value of 5x - y, we need to first solve the system of equations given:

\(3x + 5y = 2 ...(1)\\2x - 6y = 20 ...(2)\)

We can solve this system of equations by either substitution or elimination. Here, we will use the elimination method:

Multiplying equation (1) by 2 and equation (2) by 3, we get:

\(6x + 10y = 4 ...(3)\\6x - 18y = 60 ...(4)\)

Subtracting equation (4) from equation (3), we get:

28y = -56

Dividing both sides by 28, we get:

y = -2

Now substituting this value of y in either equation (1) or (2), we can solve for x. Let's use equation (1):

\(3x + 5(-2) = 23x - 10 = 2\)

3x = 12

x = 4

Therefore, \(5x - y = 5(4) - (-2) = 22.\)

Hence, the answer is (e) 22.

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This question requires estimating the probability of various occurrences related to the roll of two dice, one red, and one blue. The occurrences A, B, and C occur when the sum of the two dice is even, when the sum is at least 10, and when the red die comes up 5, respectively. Calculating the likelihood of each individual event, as well as conditional probabilities, and distinguishing independent pairs of occurrences are all part of the process.

(a) Probability of each individual event is as follows:

P(A) = probability of an even sum = (number of favorable outcomes)/(number of possible outcomes)= 18/36 = 1/2

P(B) = probability of a sum at least 10= (number of favorable outcomes)/(number of possible outcomes) = 3/36= 1/12

P(C) = probability of red die shows 5 = (number of favorable outcomes)/(number of possible outcomes) = 1/6

(b) P(A|C) = probability of getting an even sum on the dice given that the red die shows 5= (number of favorable outcomes)/(number of possible outcomes)

Since we know that the red die shows 5, there are three favorable outcomes to getting an even sum: (4, 1), (4, 3), and (6, 5). The probability of one of these outcomes occurring is P(A|C) = 3/3 = 1

(c) P(B|C) = probability of getting a sum of 10 or more on the dice given that the red die shows 5= (number of favorable outcomes)/(number of possible outcomes). Since we know that the red die shows 5, there are no possible outcomes that will result in a sum of 10 or more. Thus, P(B|C) = 0

(d) P(A|B) = probability of getting an even sum on the dice given that the sum is at least 10 = (number of favorable outcomes)/(number of possible outcomes)We know that the only way to obtain a sum of 10 or more is to get a 5 and a 5 or a 6 and a 4. Out of these two possible outcomes, only one of them has an even sum: (6, 4). Therefore, the probability of getting an even sum given that the sum is at least 10 is: P(A|B) = 1/2

(e) To determine which pairs of events among a, b, and c are independent, we have to determine whether P(A) = P(A|C), P(B) = P(B|C) and P(A)P(B) = P(A∩B).- P(A) = 1/2, P(A|C) = 1, P(A) ≠ P(A|C), so events A and C are not independent.- P(B) = 1/12, P(B|C) = 0, P(B) ≠ P(B|C), so events B and C are not independent.- P(A)P(B) = (1/2)(1/12) = 1/24, P(A∩B) = 1/36 = P((6, 4)), P(A)P(B) ≠ P(A∩B), so events A and B are not independent.

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Answer:

Hello!

YOUR ANSWER IS 315 DEGREES MORE

Step-by-step explanation:

To get it to the start position is the same as TURNING IT 360 DEGREES!

So from 45 degrees to reach 360 degrees...another 315 degrees will be needed!

HOPE THIS HELPS!!

Answer:

Area = 6x² - 20x + 16

Step-by-step explanation:

The area of a rectangle is length x width.

Plug the values into that equation:

\(A = (2x-4)(3x-4)\)

Now you use the FOIL method to find the answer:

First: 2x × 3x = 6x²

Outer: 2x × (-4) = - 8x

Inner: (-4) × 3x = - 12x

Last: (-4) × (-4) = 16

Area = 6x² + (-8x) + (-12x) + 16

Area = 6x² - 20x + 16

Celine has already knitted 0.8 meters. Her final result should be 1.2 meters.

To calculate how many meters Celine has to knit we should subtract the already knitted length of scarf from the entire length. This give the equation:

\(x=1.2m-0.8m\)

x is the unknown

x = 0.4 meters

Answer:

15x-3y

Step-by-step explanation:

Ok, this question might seem hard but its not! theres only 2 varibles here, x and y. In this problem we add the 2 numbers that are x which gives us 15x and then the -3y gets added to the rephrasment.

Answer:

(i) 2197

Step-by-step explanation:

(i) 13^3

=  (10+3)^3

=  10^3 + 3^3 + 3(10)(3) (10+3)

=  1000 + 27 + 90(13)

=  1027 + 1170

= 2197

Answer:

Step-by-step explanation:

You want to know the down payment, amount financed, monthly payment, and total paid for a home costing $340,000 with a 12% down payment and a 30 year loan at 5.8%.

The down payment is 12% of the purchase price:

  $340,000 × 0.12 = $40,800

Julie paid $40,800 as a down payment.

The amount financed is the remaining amount of the house value after the down payment is made:

  $340,000 -40,800 = $299,200

The amount financed is $299,200.

The monthly payment is found using the amortization formula:

  A = P(r/12)/(1 -(1 +r/12)^(-12·t))

where P = principal financed, r = annual interest rate, t = number of years

  A = $299,200(0.058/12)/(1 -(1 +0.058/12)^(-12·30)) ≈ $1,755.57

Julie's monthly payment is $1755.57.

If Julie makes 360 payments of $1755.57, together with her down payment, her total cost is ...

  360 × $1755.57 + 40,800 = $672,805.20

Julie will spend $672,805.20 on this home.

Every time the same instrument is used for a measurement, it produces consistent results, which denotes: -reliability.

The degree to which a measurement tool produces consistent, repeatable estimates of what is believed to be a true score at the core.

The same set of people receives the same instrument again. The correlation between the results on the two instruments is what defines dependability. The scores ought to be comparable if the outcomes remain constant over time. How long to wait between the two administrations is the key to test-retest reliability.

Reliability is defined as the probability that a given item will perform its intended function with no failures for a given period of time under a given set of conditions.

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True. A p-value is indeed a probability.

In statistical hypothesis testing, the p-value represents the probability of obtaining results as extreme as, or more extreme than, the observed data, assuming the null hypothesis is true. It measures the strength of evidence against the null hypothesis. The p-value ranges between 0 and 1, where a smaller p-value indicates stronger evidence against the null hypothesis.

The p-value is calculated based on the test statistic and the assumed distribution under the null hypothesis. It is commonly used in hypothesis testing to make decisions about rejecting or failing to reject the null hypothesis. If the p-value is smaller than a predetermined significance level (usually 0.05 or 0.01), it is considered statistically significant, and the null hypothesis is rejected in favor of an alternative hypothesis.

In summary, a p-value represents a probability and is a crucial component in hypothesis testing, providing a quantitative measure of the evidence against the null hypothesis.

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We can use the concept of similar triangles. Since the building and the statue are casting shadows simultaneously, the angle of elevation of the sun is the same for both. Therefore, the triangles formed by the building, its shadow, and the ground and the statue, its shadow, and the ground are similar triangles.

Let's use the given information:
- Building height = 51 feet
- Building shadow length = 48 feet
- Statue shadow length = 16 feet
- Statue height = x (this is what we need to find)

Now, set up a proportion using the ratios of the corresponding sides of the similar triangles:

(Building height / Building shadow length) = (Statue height / Statue shadow length)

(51 / 48) = (x / 16)

To find the statue height (x), cross-multiply and solve for x:

51 * 16 = 48 * x

816 = 48x

Now, divide by 48 to find the value of x:

x = 816 / 48
x = 17

So, the statue is 17 feet tall.

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Answer:

-12

Step-by-step explanation:

The solution to the absolute value of the inequality is given as 1 ≤ t ≤ 4

To represent the number of hours this student spent studying every day, we can use the variable t. Given that the average study time is 2.5 hours a day, we can write the absolute value inequality as:

|t - 2.5| ≤ 1.5

To solve this inequality, we consider two cases:

Case 1: t - 2.5 ≥ 0 (t ≥ 2.5)

In this case, the absolute value inequality simplifies to:

t - 2.5 ≤ 1.5

Solving for t:

t ≤ 4

Case 2: t - 2.5 < 0 (t < 2.5)

In this case, the absolute value inequality becomes:

-t + 2.5 ≤ 1.5

Solving for t:

t ≥ 1

Therefore, the solution to the absolute value inequality is 1 ≤ t ≤ 4.

Interpretation in context:

The inequality 1 ≤ t ≤ 4 implies that the student spent between 1 and 4 hours studying each day. This satisfies the condition that the student always studied within 1.5 hours of the daily average of 2.5 hours.

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Equation shows that Tom's indirect utility function V(p, w) is convex in p, as desired.

V(λ\(p1\) + (1-λ)\(p2\), w) ≤ λV(\(p1\), w) + (1-λ)V(\(p2\), w)

To prove that Tom's indirect utility function V(p, w) is convex in p, where p is the price vector and w is the wealth, we need to show that for any two price vectors p1 and p2, and for any λ ∈ [0,1], the following inequality holds:

V(λ\(p1\) + (1-λ)\(p2\), w) ≤ λV(\(p1\), w) + (1-λ)V(\(p2\), w)

To prove this, we can use the concept of homothetic preferences.

Homothetic preferences imply that the utility function is homogeneous of degree zero, meaning that multiplying prices and income by the same positive constant does not affect the consumer's preferences.

Let's assume Tom's utility function is U(x), where x represents the consumption bundle.

Tom's indirect utility function can be defined as:

V(p, w) = max { U(x) | px ≤ w }

Now, consider two price vectors p1 and p2, and let x1 and x2 be the optimal consumption bundles for p1 and p2, respectively.

Since U(x) is homogeneous of degree zero, we have:

U(λ\(x1\)+ (1-λ)\(x2\)) = U(x1 + λ(x2 - x1)) = U(x1) [using homogeneity]

From the definition of the indirect utility function, we know that V(p, w) = U(x), where x is the consumption bundle that maximizes U(x) subject to the budget constraint.

Therefore, we have:

V(λp1 + (1-λ)p2, w) = U(x1) [since λx1 + (1-λ)x2 is the optimal consumption bundle for λp1 + (1-λ)p2]

Now, let's consider the right-hand side of the inequality:

λV(p1, w) + (1-λ)V(p2, w) = λU(x1) + (1-λ)U(x2) [using the definition of the indirect utility function]

Since U(x1) = U(x2) (as shown above), we can simplify the right-hand side:

λV(p1, w) + (1-λ)V(p2, w) = U(x1)

Therefore, we have:

V(λp1 + (1-λ)p2, w) ≤ λV(p1, w) + (1-λ)V(p2, w)

This shows that Tom's indirect utility function V(p, w) is convex in p, as desired.

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\( \huge \boxed{\mathfrak{Question} \downarrow}\)

\( \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}\)

\( \frac{1}{5} (4 - 3x) = \frac{1}{7} (3x - 4) \\ \)

Use the distributive property to multiply 1/5 by 4-3x.

\(\frac{1}{5}\times 4+\frac{1}{5}\left(-3\right)x=\frac{1}{7}\left(3x-4\right) \\ \)

Multiply 1/5 and 4 to get 4/5.

\(\frac{4}{5}+\frac{1}{5}\left(-3\right)x=\frac{1}{7}\left(3x-4\right) \\ \)

Multiply 1/5 and -3 to get -3/5.

\(\frac{4}{5}+\frac{-3}{5}x=\frac{1}{7}\left(3x-4\right) \\ \)

Use the distributive property to multiply 1/7 by 3x-4.

\(\frac{4}{5}-\frac{3}{5}x=\frac{1}{7}\times 3x+\frac{1}{7}\left(-4\right) \\ \)

Multiply 1/7 and 3 to get 3/7 & 1/7 × -4 to get -4/7.

\(\frac{4}{5}-\frac{3}{5}x=\frac{3}{7}x-\frac{4}{7} \\ \)

Subtract \(\frac{3}{7}x\\\) from both sides.

\(\frac{4}{5}-\frac{3}{5}x-\frac{3}{7}x=-\frac{4}{7} \\ \)

Combine \(-\frac{3}{5}x\\\) and \(-\frac{3}{7}x\\\) to get \(-\frac{36}{35}x\\\).

\(\frac{4}{5}-\frac{36}{35}x=-\frac{4}{7} \\ \)

Subtract 4/5 from both sides.

\(-\frac{36}{35}x=-\frac{4}{7}-\frac{4}{5} \\ \)

The least common multiple of 7 and 5 is 35. Convert -4/7 and 4/5 to fractions with denominator 35.

\(-\frac{36}{35}x=-\frac{20}{35}-\frac{28}{35} \\ \)

Because \(-\frac{20}{35} \\\) and \(\frac{28}{35}\\\) have the same denominator, subtract them by subtracting their numerators.

\(-\frac{36}{35}x=\frac{-20-28}{35} \\ \)

Subtract 28 from -20 to get -48.

\(-\frac{36}{35}x=-\frac{48}{35} \\ \)

Multiply both sides by \(-\frac{35}{36}\\\), the reciprocal of \(-\frac{36}{35}\\\).

\(x=-\frac{48}{35}\left(-\frac{35}{36}\right) \\ \)

Multiply \(-\frac{48}{35}\\\) by \(-\frac{35}{36}\\\) by multiplying the numerator by the numerator and the denominator by the denominator.

\(x=\frac{-48\left(-35\right)}{35\times 36} \\ \)

Carry out the multiplications in the fraction \(\frac{-48\left(-35\right)}{35\times 36}\\\).

\(x=\frac{1680}{1260} \\ \)

Reduce the fraction 1680/1260 to its lowest terms by extracting and cancelling out 420.

\( \huge \boxed{ \boxed{ \bf \: x=\frac{4}{3} \approx \: 1.33}}\)

Answer:

c.) y=2x+3

Step-by-step explanation:

the slope is 2 and the y-intercept is 3

The simplified form of the expression 4hk/20h²k is 1/5h.

Given the expression in the question;

4hk / 20h²k

To simplify, first cancel out the common factor of 4 and 20.

4hk / 20h²k

4(hk) / 4(5h²k)

hk / 5h²k

Next, cancel out the common factor of h and h²

h(k) / h(5hk)

k / 5hk

Now, cancel out the common factor of k

k(1) / k(5h)

1/5h

Therefore, the simplified form is 1/5h.

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Answer:

The phrasing of the question is a bit weird maybe, I think, but it's one of the lobes in your brain, I suppose.

Answer:

bottom middle portion of the brain

Step-by-step explanation:

The temporal lobe sits at the bottom middle portion of the brain, just behind the temples within the skull, which is also where it gets its name. It also sits above the brain stem and cerebellum. The frontal and parietal lobes are above the temporal lobe. The occipital lobe sits just behind it.

x1 and x2 are orthogonal if and only if t^2 - st = 0 for all s and t. This is equivalent to t(t-s) = 0 for all s and t. Since t is nonzero, it follows that s = t, which means that x1 and x2 are not orthogonal.

To show that any two eigenvectors of the symmetric matrix A corresponding to distinct eigenvalues are orthogonal, let v and w be two eigenvectors corresponding to distinct eigenvalues λ1 and λ2 respectively. Then we have:

Av = λ1v     ...(1)

Aw = λ2w     ...(2)

Taking the dot product of both sides of equations (1) and (2) with v and w respectively, we get:

v^T Av = v^T (λ1v) = λ1(v^T v) = λ1 ||v||^2    ...(3)

w^T Aw = w^T (λ2w) = λ2(w^T w) = λ2 ||w||^2   ...(4)

Since A is a symmetric matrix, we have:

v^T Aw = w^T Av

Multiplying both sides by λ1 and λ2, respectively, we get:

λ1(v^T Aw) = λ1λ2(w^T Av)

Substituting equations (1) and (2) into the above equation, we obtain:

λ1λ2(v^T w) = λ1λ2(w^T v)

Simplifying, we get:

(v^T w)(λ1 - λ2) = 0

Since λ1 and λ2 are distinct, it follows that (λ1 - λ2) ≠ 0. Therefore, we must have v^T w = 0, which means that v and w are orthogonal.

For the matrix A=[44​44​], the characteristic polynomial is given by:

|λI - A| = |(λ-4)  -4 |

|-4       (λ-4)|

Expanding along the first row, we get:

|λ-4  -4| - (-4)(-4) = (λ-4)^2 - 16

Setting the characteristic polynomial equal to zero, we obtain:

(λ-4)^2 - 16 = 0

Solving for λ, we get:

λ1 = 0 and λ2 = 8

To find the eigenvectors corresponding to λ1 = 0, we solve the homogeneous system of linear equations:

(A - λ1I)x = 0

which gives:

|0-4   -4| |x1|   |-4x1|

| -4   0-4| |x2| = |-4x2|

Simplifying, we get:

-4x1 - 4x2 = 0

Dividing by -4, we get:

x1 + x2 = 0

Taking x2 = s as the parameter, we have:

x1 = -s

Therefore, the general form for every eigenvector corresponding to λ1 = 0 is given by:

x1 = -s and x2 = s where s is any non-zero constant.

To find the eigenvectors corresponding to λ2 = 8, we solve the homogeneous system of linear equations:

(A - λ2I)x = 0

which gives:

|-4  -4| |x1|   |-8x1|

| -4  -4| |x2| = |-8x2|

Simplifying, we get:

-4x1 - 4x2 = -8x1

-4x1 - 4x2 = -8x2

Dividing by -4, we get:

x1 + x2 = 2x1

x1 + x2 = 2x2

Subtracting the second equation from the first, we get:

x1 - x2 = 0

Taking x2 = t as the parameter, we have:

x1 = t

Therefore, the general form for every eigenvector corresponding to λ2 = 8 is given by:

x1 = t and x2 = t where t is any non-zero constant.

To find whether x1 and x2 are orthogonal, we compute their dot product:

x1^T x2 = (-s)(t) + (t)(t) = t^2 - st

Since s and t are arbitrary constants, x1 and x2 are orthogonal if and only if t^2 - st = 0 for all s and t. This is equivalent to t(t-s) = 0 for all s and t. Since t is nonzero, it follows that s = t, which means that x1 and x2 are not orthogonal.

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Answer:

10th term is the answer

Step-by-step explanation:

33-8= 25

25-8= 17

17-8= 9

9-8= 1

1-8= -7

-7-8= -15

-15-8= -23

-23-8= -31

-31-8 = -39

Answer:

\(f'(x)= \frac{13}{(2x+3)^2}\\\)

Step-by-step explanation:

\(f(x)= \frac{3x-2}{2x+3} \\\)

\(f'(x)=\frac{dy}{dx} = \frac{d}{dx}(\frac{3x-2}{2x+3})\\ f'(x)= \frac{(2x+3)\frac{d}{dx}(3x-2)-(3x-2)\frac{d}{dx}(2x+3) }{(2x+3)^{2} } \\f'(x)= \frac{(2x+3)(3)-(3x-2)(2)}{(2x+3)^{2} } \\\)

\(f'(x)= \frac{6x+9-6x+4}{(2x+3)^{2} }\\ f'(x)= \frac{13}{(2x+3)^2}\\\)

The drink will be F + 7.5 degrees Fahrenheit warm if left out for 30 minutes.

Let us first find the rate at which the drink is warming up.

We can use the formula,

T = T0 + k.t

where T is the temperature of the drink after time t,

T0 is the initial temperature, `

k is the rate of warming and t is the time.

Since the drink goes from F to F in 4 minutes,

we have F = F + 4k or k = 1/4.

Therefore, after 30 minutes, we have T = F + (1/4) * 30 = F + 7.5`.

Hence, the drink will be F + 7.5 degrees Fahrenheit warm if left out for 30 minutes.

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Answer:

Step-by-step explanation:

B

Answer:

1-24

2-15 books for 9 pupils

3-Worker 1

3x = 3(1,750)

    = 5,250

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

Worker 2

4x = 4(1,750)

    = 7,000

4-368

5-22 days and a half (22.5 days)

Step-by-step explanation:

hope this helps if u need the calclations tell me!

Answer:

z=kx/y

zy=kx

zy/x=kx/x ( divided both side by x. to find k)

k=zy/x

k=6×4/3(z=6,y=4,x=3)

k=24/3

k=8

so z=kx/y

z=8×5/2(replace the numbers in the place of variables,k=8,x=5,y=2)

z=40/2

z=20

Answer:

(-4,5) is located on the 2nd quadrant

Answer:

(-4, 5)

Step-by-step explanation:

Quadrant II is at the top left. So, point (-4, 5) is located in Quadrant II.