18/11 = 5/n N= _____ ? Plz

Answer:

A is 3 b is 2 C is 8 D is 9 hope it helps

Step-by-step explanation:

The correct answer is A. a-c+b-d=0. This is because when two sets of numbers are both negative, the result of subtracting the larger number from the smaller number will always be negative.

Subtraction involves taking one number or value away from another. It is one of the four basic operations in mathematics, along with addition, multiplication, and division.

When subtracting a from c and b from d, the result of either subtraction will always be a negative number. When the two negative numbers are added together, the result will always be 0.

The other options are not always true. In option B, ac > bd, this is not always true because when a, b, c, and d are all negative, it is possible for the result of ac to be less than the result of bd. In option C, a+c>b+d, this is not always true because when both sets of numbers are negative, it is possible for the result of a+c to be less than b+d. Finally, in option D, a/d < b/c, this is not always true because when both sets of numbers are negative, it is possible for the result of a/d to be greater than b/c.

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The correct answer is A. a-c+b-d=0 because the expression is always true when a, b, c and d are all less than zero.

Expression is a combination of symbols and operators that evaluate to a single value. It could be a mathematical equation, an arithmetic expression, a logical expression, or a combination of these.

This is because the expression is equivalent to (a-c)+(b-d)=0, which is always true when a, b, c and d are all less than zero.

This can be proven through a simple calculation.

Let us assume that the values of a, b, c and d are -1, -3, 8 and -4 respectively.

Substituting these values into the expression gives us

(-1-3)+(8-4)=0, which is clearly true.

Therefore, A. a-c+b-d=0 is the correct answer as the expression is always true when a, b, c and d are all less than zero.

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The expansion of Cos(A-B) is:

We are provided with the following:

We will have to obtain the values of Cos B and Sin A. Thus, we have:

To be obtain Sin A, we have to get the value of the third side, which is the opposite side, by applying the pythagoras theorem. Thus, we have:

To be obtain Cos B, we have to get the value of the third side, which is the adjacent side, by applying the pythagoras theorem. Thus, we have:

Now that we have obtained the values of Cos B and Sin A, we can then go on to solve the original problem.

In the given triangle, the length of g, to the nearest 10th of a centimeter is  134.3 cm

From the question, we are to determine the length of side g in the given triangle.

From the given information,

We have triangle FGH

From the law of sines, we can write that

g/sinG = h/sinH

From the given information,

h = 40 cm

∠H = 17°

and ∠F = 84°

Therefore,

∠H + ∠G + ∠F = 180° (Sum of angles in a triangle)

17° + ∠G + 84° = 180°

∠G + 101° = 180°

∠G = 180° - 101°

∠G = 79°

Thus,

g/sinG = h/sinH

g/sin79° = 40/sin17°

g = (40×sin79°)/sin17°

g = 134.3 cm

Hence, the length is 134.3 cm

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Answer:

9

Step-by-step explanation:

because the 9 is the highest point

Answer:

steps below

Step-by-step explanation:

x -7√x + 10 = 0

(√x)² - 7√x + 10 = 0

(√x - 2)(√x - 5) = 0

√x - 2 = 0      or      √x - 5 = 0

√x = 2      or      √x = 5  

(√x)² = x = 4        or     (√ x)² = x = 25  ...

Answer:

c. 5

Step-by-step explanation:

Try each choice on the right side of the inequality, and see which one makes the inequality true.

a. 0

x(9 - x) = 0 * (9 - 0) = 0 * 9 = 0

10 < x(9 - x)

10 < 0

10 is not less than 0, so a. is out.

b. 1

x(9 - x) = 1 * (9 - 1) = 1 * 8 = 8

10 < x(9 - x)

10 < 8

10 is not less than 8, so b. is out.

c. 5

x(9 - x) = 5 * (9 - 5) = 5 * 4 = 20

10 < x(9 - x)

10 < 20

10 is less than 20, so c. works.

d. 10

x(9 - x) = 10 * (9 - 10) = 10 * (-1) = -10

10 < x(9 - x)

10 < -10

10 is not less than -10, so d. is out.

The only number that works is

c. 5

The correct option that indicates how Christa sliced the rectangular pyramid is the second option.

Christa sliced the pyramid perpendicular to its base through two edges.

A rectangular pyramid is a pyramid with a rectangular base and four triangular faces.

The height of the cross section indicates that the location where Christa sliced the shape is lower than the apex of the pyramid.

The trapezoid shape of the cross section of the pyramid indicates that the top and base of the cross section are parallel, indicating that Christa sliced the pyramid parallel to a side of the base of the pyramid, such that it intersects two of the edges of the pyramid

The correct option is therefore the second option;

Christa sliced the pyramid perpendicular to its base through two edges

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The finite population correction factor is used in computing the standard error of the sample mean when the sample size is smaller than 5% of the population size.

The finite population correction factor is a adjustment made to the standard error of the sample mean when the sample is taken from a finite population, rather than an infinite population.

It accounts for the fact that sampling without replacement affects the variability of the sample mean.

When the sample size is relatively large compared to the population size (more than half), the effect of sampling without replacement becomes negligible, and the finite population correction factor is not necessary.

In this case, the standard error of the sample mean can be estimated using the formula for sampling with replacement.

On the other hand, when the sample size is small relative to the population size (less than 5%), the effect of sampling without replacement becomes more pronounced, and the finite population correction factor should be applied.

This correction adjusts the standard error to account for the finite population size and provides a more accurate estimate of the variability of the sample mean.

Therefore, the correct answer is option 2: the finite population correction factor is used when the sample size is smaller than 5% of the population size.

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Answer:

(a) There is $1740.88 in Mary's account after 2 years

(b) The interest earned on Mary's investment after 2 years is $40.88

Step-by-step explanation:

Let us revise the rule of the compound interest

→  \(A=P(1+\frac{r}{n})^{nt}\) , where

∵ She invested $1700

∴ P = 1700

∵ The rate is 1.19%

∴ r = 1.19/100 = 0.0119

∵ It is compounded quarterly

∴ n = 4

∵ She decided to invest her money for 2 years

∴ t = 2

Let us substitute these values in the rule above to find her new amount of money in her account

→  \(A=1700(1+\frac{0.0119}{4})^{4(2)}\)

→ \(A=1700(1.002975)^{8}\)

→ \(A=1740.883806\) dollars

Round it to the nearest cent → means 2 decimal places

→ A = $1740.88

(a) There is $1740.88 in Mary's account after 2 years

The interest amount is the difference between the new amount and the initial amount

\(I=A-P\)

∵ P = 1700

∵ A = 1740.88

∴ \(I=1740.88-1700\)

∴ I = $40.88

(b) The interest earned on Mary's investment after 2 years is $40.88

Answer:

The interest earned on Mary's investment after 2 years is $40.88

Answer:

3x+5y=20

Step-by-step explanation:

Answer:

3x + 5y = 20

Step-by-step explanation:

The given y = -3x/5 + 4 is in slope-intercept form.  We are to put it into standard form, which would be Ax + By = C.

Start by eliminating the fraction representing the slope (-3/5); to do this, multiply all three terms by 5:

5y = -3x + 20

Next, rearrange the terms to resemble Ax + By = C:

3x + 5y = 20

Answer:

Step-by-step explanation:

The dimensions of the garden will be 4m by 3m. To determine the dimensions of the garden, we need to use the formula A = l x w, where A is the area of the garden (12m), l is the length of the garden and w is the width of the garden.

We can then rearrange the formula to solve for either l or w. We can rearrange the formula to solve for l by dividing both sides of the equation by w: A/w = l.

We know that the area is 12m, so we can substitute 12m for A in the equation. We need to find the dimensions that use the least amount of fencing, so let's set w equal to 3m. We can then substitute 3m for w in the equation and solve for l: 12m/3m = 4m.

Therefore, the dimensions of the garden are 4m by 3m.

The solutions are given in the ordered pairs.

An equation is a statement that asserts the equality of two expressions, the expressions are written one on each side of an '=' equal to sign.

We have to choose a value for x to find the corresponding y value to make the equation true.

1)6x=7y

To find x:

divide both sides by 6.

We get, \(\frac{6x}{6} =\frac{7y}{6}\)⇒\(x=\frac{7y}{6}\)

To find y:

divide both sides by 7.

We get, \(\frac{6x}{7} =\frac{7y}{7}\) ⇒ \(y=\frac{6x}{7}\)

Therefore solution for the given equation is \((\frac{7y}{6} ,\frac{6x}{7})\)

2) 5x+3y=9

To find x:

subtract 3y from both sides,

⇒ 5x=9-3y then divide 5 on both sides,

⇒ \(\frac{5x}{5}=\frac{9-3y}{5}\)⇒ \(x= \frac{9-3y}{5}\)

To find y:

subtract 5x from both sides.

⇒3y=9-5x, then divide by 3 on both sides we get,

\(\frac{3y}{3}=\frac{9-5x}{3}\)⇒\(y=\frac{-5x}{3}+3\)

The solution for this equation is \((\frac{9-3y}{5},\frac{-5x}{3}+3)\)

3) y+5-(1/3)x =7

To find x:

subtract y-5 from both sides we get,

\(-\frac{1}{3}x=2-y\) then multiply both sides by -3,

\(\frac{\frac{-1}{3}x }{\frac{-1}{3}}=\frac{2-y}{\frac{-1}{3}}\)⇒x=3y-6

To find y:

Subtract 5 from both sides.\(y-\frac{1}{3}x = 7-5\) and add \(\frac{1}{3} x\)

we get, \(y=2+\frac{1}{3}x\)

The solution for this equation is (\((3y-6, 2+\frac{1}{3})\)

Hence, the solutions are given in the ordered pairs.

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Answer:

QP = 2

QR = 2√3

Step-by-step explanation:

This is a special right triangle with angle measures as follows:

30° - 60° - 90°

And side lengths represented with:

x - x√3 - 2x respectively to angle measures.

The side length that sees angle measure 90, hypotenuse, is given as 4 so the legs would be:

2 and 2√3

Answer: 3g - 5 = 19 ; 8 pounds

Step-by-step explanation:

Given that :

Difference between weight of 3 gallons of a liquid and a brick that weighs 5 pounds = 19 pounds.

Mathematically,

Let one gallon of the liquid = g

Hence,

(3 × g) - 5pounds = 19 pounds

3g - 5 = 19

The weight of one gallon(g) of the liquid equals :

From the expression above :

3g - 5 = 19

3g = 19 + 5

3g = 24

Divide both sides by 3

3g/3 = 24 /3

g = 8 pounds

Hence, weight of 1 gallon of the liquid is 8 pounds.

The correct answer is $15

Explanation:

The first step is to determine the total of oil that was used for the 5 batches. To find this, you just need to multiply the amount of oil used for one batch by the total batches.

1 cup of oil per batch x 5 batches = 5 cups of oil

This means, in the 5 batches the oil Dinesh used was 5 cups of oil. Additionally, you know the total of cups in the bottle of oil is 12 cups, and these 12 cups or total costs $36. Now to find what is the cost of the 5 cups use the rule of three and cross multiplication.

12 cups of oil = $36   1. Write the values

5 cups of oil  = x      

12 x = 180           2.  Cross multiply this means 36x 5 and 12 multipy by x

x = 180 ÷ 12        3. Solve the equation

x=  15 - Cost for 5 cups used in the batches

As given by the question,

There are given that the equation:

Now,

First, suppose any number, for which the given equation has satisfied.

So, the number is, x = 2 and y = 6

Then,

Put both values into the given equation

Then,

Put the same value of x and y into the given option and check whether it is satisfied:

So,

From option 3:

Hence, the correct option is 3.

To construct a square with vertex A inscribed in a given circle, follow these steps: (1) Draw the circle with the given center and radius. (2) Choose point A on the circumference. (3) Draw the radius from the center to A. (4) Construct a perpendicular bisector of the radius to intersect the circle at points B and C. (5) Connect B to C and C to A to complete the square.

1)Start by drawing a circle with the given center and radius.

2)Choose a point A on the circumference of the circle to serve as one of the vertices of the square.

3)Draw a line segment from the center of the circle to point A. This line segment will be the radius of the circle and also one side of the square.

4)Construct a perpendicular bisector of the line segment drawn in step 3. This will intersect the circumference of the circle at two points.

5)Label the points of intersection as B and C. These points will be the other two vertices of the square.

6)Finally, draw line segments from B to C and from C to A to complete the square.

By following these steps, we can construct a square with vertex A inscribed in the given circle.

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Answer:

6x + 2y

Step-by-step explanation:

6x + 4y - 2y =

6x + 2y

Hope that helps!

The candidate solution T(n) = (n+1)/n satisfies the given recurrence relation T(n) = T(n-1) + n(n+1)/2, for n > 1, with the initial condition T(1) = 2/1.

To verify the candidate solution T(n) = (n+1)/n for the given recurrence relation T(n) = T(n-1) + n(n+1)/2, we will use mathematical induction.

First, we establish the base case: T(1) = (1+1)/1 = 2/1 = 2, which matches the given initial condition T(1) = 2/1.

Next, we assume that the candidate solution holds for some arbitrary positive integer k, i.e., T(k) = (k+1)/k. We will use this assumption to prove that the solution also holds for k+1.

Using the assumption, we substitute T(k) = (k+1)/k into the recurrence relation:

T(k+1) = T(k) + (k+1)(k+2)/2

       = (k+1)/k + (k+1)(k+2)/2

       = (2(k+1) + (k+1)(k+2))/2k

       = ((k+1)(k+3))/2k

       = (k+2)(k+3)/(2k+2)

       = (k+2+1)/(k+1)

       = (k+2+1)/(k+1)

We observe that the expression for T(k+1) matches the candidate solution (k+2)/(k+1), confirming that the candidate solution holds for k+1.

Therefore, by the principle of mathematical induction, we can conclude that the candidate solution T(n) = (n+1)/n satisfies the given recurrence relation T(n) = T(n-1) + n(n+1)/2, for n > 1, with the initial condition T(1) = 2/1.

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Answer: 340

Step-by-step explanation:

100 - 74 = 26%

26% = .26

x * .26 = 88.4

  /.26    /.26

x = 340

check

340 * .74 = 251.6

340 - 251.6 = 88.4

Answer:

Solution given:

Cos -θ:\(\frac{\sqrt{3}}{4}\)

since cos -θ=Cos θ

Cos θ :\( \frac{\sqrt{3}}{4} \)

\(\frac{\sqrt{b}}{h} \)=:\( \frac{\sqrt{3}}{4} \)

b=\(\sqrt{3} \)

h=4

p=\( \sqrt{4²-(\sqrt{3})²} \)=\( \sqrt{13}\)

So

Sin θ=\(\frac{p}{h} \)=\(\frac{\sqrt{13}}{4} \)

So third one is a required answer.

Answer:

y=-3x+10

Step-by-step explanation:

The Pearson correlation coefficient between the scores on the first and final exams is approximately -0.165. This indicates a weak negative correlation between the two variables.

What is correlation coefficient?

To find the Pearson correlation coefficient between the scores on the first and final exams, we need to use the formula:

r = ΣZxZy / √(ΣZx² * ΣZy²)

Using the given data, we can calculate the values of Zx and Zy (standardized scores for first and final exam scores, respectively) and then calculate r as follows:

ΣZxZy = (0.481)(-0.345) + (-0.102)(0.366) + (1.720)(-0.548) + (-0.904)(-0.548) + (0.189)(-0.041) + (-0.612)(-0.650) + (0.991)(0.670) + (1.280)(1.280) + (-1.767)(-0.410) = -0.023

ΣZx² = 0.723 + 0.011 + 2.958 + 0.818 + 0.036 + 0.374 + 0.982 + 1.638 + 3.127 = 10.667

ΣZy² = 0.119 + 0.135 + 0.302 + 0.302 + 0.002 + 0.423 + 0.449 + 1.638 + 3.125 = 6.695

r = -0.023 / √(10.667 * 6.695) = -0.165

Therefore, the Pearson correlation coefficient between the scores on the first and final exams is approximately -0.165. This indicates a weak negative correlation between the two variables.

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Answer:

x = y(w-z)

Step-by-step explanation:

x/y + z = w

subtract 'z' from each side to get:

x/y = w-z

multiply each side by 'y' to get:

x = y(w-z)

Answer:

1. X < 75

2. X < 7.5

3. X > 10,000

4. X < 25

Step-by-step explanation:

Inequality expression or signs which represents the scenarios given can be expressed thus ;

1.)

Klint has to spend a minimum of $75 on other to use his coupon ;

2.)

Molly went shopping and her bank account got below $7.50.

3.)

Sharon’s organization hopes to raise more than $10,000 at their annual 5k race.

4.)

Mrs. Johnson informed her students that their exam will have at most 25 questions.

Hence, the inequality expression.

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a). The system of equations will give us the values of p and q.

b). f(x) is fully factorized as (x - 1)(x + 1)(x + 3).

c). We can solve 5x² - 13x - 6 = 0 using factoring, completing the square, or the quadratic formula.

(a) Finding the values of p and q:

We are given that f(x) is exactly divisible by (x - 1) and leaves a remainder of 3 when divided by (x + 2).

When f(x) is divided by (x - 1), it should leave no remainder. So we can substitute x = 1 into f(x) and set it equal to zero:

f(1) = 1³ + p(1)² + q(1) - 3 = 0

1 + p + q - 3 = 0

p + q - 2 = 0

When f(x) is divided by (x + 2), it should leave a remainder of 3. So we can substitute x = -2 into f(x) and set it equal to the remainder:

f(-2) = (-2)³ + p(-2)² + q(-2) - 3 = 3

-8 + 4p - 2q - 3 = 3

4p - 2q = 14

Now we have a system of equations:

p + q - 2 = 0

4p - 2q = 14

Solving this system of equations will give us the values of p and q.

(b) Factorizing f(x) fully:

Now that we have the values of p and q, we can substitute them back into f(x) and factorize it completely.

From equation (a), we have p + q - 2 = 0, so q = 2 - p.

Substituting this into equation (b), we get:

4p - 2(2 - p) = 14

4p - 4 + 2p = 14

6p = 18

p = 3

Substituting p = 3 into q = 2 - p, we get:

q = 2 - 3

q = -1

Now we can substitute p = 3 and q = -1 into f(x) and factorize it:

f(x) = x³ + px² + qx - 3

= x³ + 3x² - x - 3

= (x - 1)(x + 1)(x + 3)

Therefore, f(x) is fully factorized as (x - 1)(x + 1)(x + 3).

(c) Solving 5x³ - 3x² - 32x - 12 = 0:

To solve 5x³ - 3x² - 32x - 12 = 0, we can factorize the equation using the factor theorem or synthetic division.

By synthetic division or using a calculator, we find that x = -2 is a root of the equation. Performing synthetic division by dividing 5x³ - 3x² - 32x - 12 by (x + 2), we get:

(x + 2) | 5 -3 -32 -12

| -10 26 -4

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

5 -13 -6 -16

The quotient is 5x² - 13x - 6 with a remainder of -16.

Now, the equation can be written as:

(5x² - 13x - 6)(x + 2) = 0

To find the roots further, we can solve 5x² - 13x - 6 = 0 using factoring, completing the square, or the quadratic formula.

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Answer:

D

Step-by-step explanation:

1. Find which of these 4 (four) has a y-intercept of positive 4, in this case, B and D. Recall, that the y-intercept means when X is 0 (zero) what is the value of Y?

2. Find the slope of B and D
The formula to find slope is change in y/change in x (Y/X)

B:

X: 0 - 4 = -4
Y: 4 - 0 = 4

4/-4 = -1

D:

X: 0 - -4 = 4

Y: 4 - 0 = 4

4/4 = 1