Which expression is equivalent to 30c - 24d?

Answer:

Value of n:

Since the first three terms in the binomial expansion are 1 + kx - x^2, we can compare this with the general binomial expansion formula:

(1 + bx)^n = 1 + n(bx) + (n(n-1)/2)(bx)^2 + ...

Comparing the terms, we see that n(bx) = kx, which means n = k.

Value of k:

From the given expression, we have 1 + kx - x^2. Since the coefficient of x is k, we can conclude that k = 1.

Therefore, the value of n is 1 and the value of k is 1.

Step-by-step explanation:

hope this helps :)

Answer:

the answer would be 43 degrees.

Step-by-step explanation:

Answer: Therefore, the y value rounded to the nearest tenth is 47.9.

Step-by-step explanation:

To find the value of y, you can use the trigonometric function tangent (tan). First, find the angle between the y-side and the hypotenuse by subtracting the given grades from 180°:

180° - 42° - 85° = 53°

Then, use this angle and the opposite side (31) to solve for y:

tan(53°) = y/31

y = 31 * tan(53°)

y ≈ 47.9

Therefore, the value of y rounded to the nearest tenth is 47.9.

Answer:

62 + 6x + 10y

Step-by-step explanation:

1. add the x's together

3x+3x = 6x

2. add the constants together

66-6-6+4+4 = 62

3. add the y's together

5y + 5y = 10y

Step-by-step explanation:

Assuming the speed of car B to be x and the speed of car A to be x+20

156 = 208

x. x+20

156(x+20)= 208x

156x+3120=208x

3120=208x-156x

3120=52x

x=60

The speed of car A is (x)= 60

The speed of car B is(x+20)= 80

Answer:

\(\huge\colorbox{red}{Car\: A=80}\colorbox{blue}{Car B=60}\)

Step-by-step explanation:

let the speed of car A be A

let the speed of car B be B

according to the first condition:

\(\quad A=B+20\)

according to the second condition:

\(\quad 156(A)=208B\)

therefore

\(\text{the speed of car A is 60+20=80}\)

average =65%

average = (60+70)/(100+100)*100

= 130/200*100

= 65%

The eigenvalues of matrix A are 5 and 0, while the singular values are √5 and 0.

The eigenvalues of matrix A are 5 and 0, while the singular values are √5 and 0.

The eigenvectors of a matrix are not necessarily orthogonal, but the eigenvectors of AᵀA are guaranteed to be orthogonal. This can be proven by observing that AᵀA is a symmetric matrix, and symmetric matrices have orthogonal eigenvectors corresponding to distinct eigenvalues. In this case, the eigenvalues of AᵀA are 25 and 0, and since they are distinct, the eigenvectors must be orthogonal.

Learn more about Eigenvalues

brainly.com/question/29861415

#SPJ11

Answer:

Krystal=$9 , Zoe=$28

Step-by-step explanation:

Zoe = x+19

Krystal = x

Equation - x+x+19=37

Simplify -   2x+19=37

                  2x=18

                   x=9

Using the slope formula, the required equation is y = -4x + 1.

The slope or gradient of a line in mathematics is a numerical representation of the steepness and direction of the line.

The slope of a line can be used to gauge how steep it is.

The slope is theoretically determined as "rise over run" (change in y divided by change in x).

So, slope formula: m = y2 - y1/x2 - x2

Now we have: y = - 1/4 x + 6 and points (2, 9)

Now, substitute as follows:

(y-9) = -4(x+2)

In order to convert this equation into the slope-internet form, we can additionally solve it for y:

(y-9) = (-4*x+(4*2)

(y-9) = -4x - 8

y - 9 + 9 = -4x - 8 + 9

y - 0 = -4x + 1

y = -4x + 1

Therefore, using the slope formula, the required equation is y = -4x + 1.

Know more about the slope here:

https://brainly.com/question/29280886

#SPJ1

Answer:

The correct option is;

CGB

Whereby, we have;

Triangle RKB ~ Triangle CGB

Step-by-step explanation:

The given triangles have the following congruent angles;

Angle ∠RKB on triangle ΔRKB is congruent to angle ∠CGB on triangle ΔCGB

We are given angle ∠KBR on triangle ΔRKB is congruent to angle ∠GBC on triangle ΔCGB

Therefore,  ΔRKB is similar to ΔCGB by the Angle-Angle (AA) rule for similarity.

The equation of the line perpendicular to the tangent to the curve y=x^3-4x+1 at the point (2,1) is y = (-1/8)x + 9/8.

To find the equation of the line perpendicular to the tangent to the curve at (2,1), we need to first find the slope of the tangent line at that point.

The derivative of y=x^3-4x+1 is y'=3x^2-4, so the slope of the tangent line at (2,1) is y'(2) = 3(2)^2-4 = 8.

Since we want the line perpendicular to the tangent, we know that its slope will be the negative reciprocal of the tangent's slope. Therefore, the slope of the line we're looking for is -1/8.

Next, we use the point-slope form of the equation of a line to write the equation of the line with the slope we found and passing through the point (2,1):

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

Simplifying and putting the equation in slope-intercept form:

y = (-1/8)x + 9/8

Therefore, the equation of the line perpendicular to the tangent to the curve y=x^3-4x+1 at the point (2,1) is y = (-1/8)x + 9/8.

Learn more about perpendicular here:

https://brainly.com/question/11707949

#SPJ11

Answer: 6 guides

Step-by-step explanation:

Question wants to know the number of Guides present on Sunday.

On Saturday there were 120 tourists and 18 guides. The ratio was therefore:

120 : 18

On Sunday, the ratio must be the same and there are 40 tourists. You can solve this using direct proportion and multiplying:

120 : 18

40   :  x

120x = 18 * 40

x = 720/120

x = 6 guides

The point of diminishing returns is (20.98, 21247.3).

The point of diminishing returns occurs when the marginal cost of producing an extra unit of output exceeds the marginal revenue generated from selling that unit. Mathematically, it is the point at which the derivative of the production function equals zero and the second derivative is negative.

Given the polynomial function N(x) of degree 3, we can find the point of diminishing returns by finding the critical points where the first derivative equals zero and evaluating the second derivative at those points.

The derivative of N(x) is N'(x) = -18x² + 360x + 2250. To find the critical points, we set N'(x) = 0:

0 = -18x² + 360x + 2250

Dividing by -18 simplifies the equation:

0 = x² - 20x - 125

Using the quadratic formula, we find the solutions to the equation:

x₁,₂ = (20 ± √(20² - 4(1)(-125))) / 2(1)

x₁,₂ = 10 ± 5√5

Thus, the two critical points of N(x) are at x = 10 - 5√5 and x = 10 + 5√5.

To determine the point of diminishing returns, we evaluate the second derivative N''(x) = -36x + 360 at these critical points:

N''(10 - 5√5) = -36(10 - 5√5) + 360 ≈ -264.8

N''(10 + 5√5) = -36(10 + 5√5) + 360 ≈ 144.8

From the evaluations, we find that N''(10 + 5√5) is negative while N''(10 - 5√5) is positive. Therefore, the point of diminishing returns corresponds to x = 10 + 5√5.

To find the corresponding y-coordinate (N(10 + 5√5)), we can substitute the value of x into the original function N(x).

Hence, the point of diminishing returns is approximately (20.98, 21247.3).

Learn more about diminishing returns

https://brainly.com/question/30766008

#SPJ11

Answer:

Interest = Rs. 1297.26

Step-by-step explanation:

To calculate the final amount, we can use the following formula:

\(\boxed{A = P(1 + \frac{r}{100})^n}\),

where:

A = final amount

P = principal (initial) amount

r = rate

n = time in years,

and then we can subtract the initial amount from the final amount to find the interest.

We have been told in the question that the principal, P = Rs. 10,000; and the time is \(2\frac{1}{2}\) years, therefore n = 2.5. The rate is 5%, therefore r = 5.

Using this information, and the formula above, we can calculate the final amount:

\(A = 10000(1 + \frac{5}{100})^{2.5}\)

⇒ \(A = 10000(1.05)^{2.5}\)

⇒ \(A = \bf 11297.26\)

Now that we know what the final amount was, we can calculate the interest by subtracting the initial amount from it:

Interest = 11297.26 - 10000

             = 1297.26

Therefore the interest was Rs. 1297.26.

Answer:

2

Step-by-step explanation:

just see the slope of FG

from F to G is 5 to the right and 1 goes up.

then, see the F'G' slope

its 10 to the right and 2 goes up

it TWICE

Step-by-step explanation:

the sum of all angles in any triangle is always 180°.

therefore here

180 = 31 + 90 + angle

angle = 180 - 31 - 90 = 59°

Answer:

Step-by-step explanation:

if x = y, and y = z, you can write that as x = y = z, which means that x = z

Answer:

0 < x ≤ 11

Step-by-step explanation:

perimeter = (x - 6) + (x - 6) + x + x

⇒ perimeter = 4x - 12

If the perimeter is "at most 32" then

4x - 12 ≤ 32

⇒ 4x ≤ 44

⇒ x ≤ 11

Therefore,  0 < x ≤ 11

The total volume of the snow cone including the half scoop on top is approximately 122.66 cubic inches.

To calculate the volume of the snow cone, we can use the formula for the volume of a cone:

where r is the radius of the base of the cone and h is the height of the cone. In this case, the cone cup has a diameter of 4 inches, so the radius of the base is 2 inches and the height is 5 inches. Therefore, the volume of the cone cup is:

To calculate the volume of the half scoop on top of the cone, we can use the formula for the volume of a sphere:

where r is the radius of the sphere. In this case, the snow cone scoop has a radius of 3.5 inches, so the volume of the half scoop is:

Therefore, the total volume of the snow cone including the half scoop on top is:

\(V_{total\) = \(V_{cone\) cup + \(V_{half\) scoop

= 20.94 cubic inches + 40.72 cubic inches

= 61.66 cubic inches + 61 cubic inches/2

= 122.66 cubic inches (approx.)

Learn more about the volume of a cone

https://brainly.com/question/1082469

#SPJ4

Incomplete question. I inferred you want to know the properties of parallel and perpendicular lines. Which I provided below.

Explanation:

In geometry, parallel lines are two lines that are always drawn at the same distance apart and never touch each other. Parallel lines are usually denoted by the symbol ∥.

Here are some of their properties;

When a transversal intersects two parallel lines:

Perpendicular lines are two lines that meet at a right angle (90 degrees) to each other.

Properties: two lines that meet, implies all four angles are right angles.

The correct response is d) All the above. The arithmetic mean is equal to the median, the median is equal to the mode, and the mode is equal to the arithmetic mean.

If the data are graphed symmetrically, the distribution demonstrates 0% skewness regardless of how long or fat the tails are. When the median of a data set is utilized, 50% of the data points in the collection have values lower than or equal to the median, and 50% of them have values greater than or equal to the median. The middle score in the set is known as the median. The first step in calculating the median is to order the data points from smallest to greatest. The median in an odd-numbered set will be the value that falls exactly in the middle of the list. You must determine the average of the two middle numbers in a set of even numbers. The average is determined by summing up each value individually and dividing that sum by the total number of observations.

To know more about median here

brainly.com/question/26940257

#SPJ4

explain:

Estimating Differences of Fractions and Mixed Numbers

Estimating Differences of Fractions and Mixed NumbersRecall that estimation is a method for finding an approximate solution to a problem. Even when you are asked to find an exact ko, estimation is a useful way to get an idea of a reasonable solution to a problem. Once you have found an exact answer, you can check your answer against the estimate.

, estimation is a useful way to get an idea of a reasonable solution to a problem. Once you have found an exact answer, you can check your answer against the estimate.When working with fractions and mixed numbers, you can use the fraction benchmarks of 0,

, estimation is a useful way to get an idea of a reasonable solution to a problem. Once you have found an exact answer, you can check your answer against the estimate.When working with fractions and mixed numbers, you can use the fraction benchmarks of 0, 12

, estimation is a useful way to get an idea of a reasonable solution to a problem. Once you have found an exact answer, you can check your answer against the estimate.When working with fractions and mixed numbers, you can use the fraction benchmarks of 0, 12, and 1 to help you to estimate differences.

, estimation is a useful way to get an idea of a reasonable solution to a problem. Once you have found an exact answer, you can check your answer against the estimate.When working with fractions and mixed numbers, you can use the fraction benchmarks of 0, 12, and 1 to help you to estimate differences.Here are the steps for estimating the differences of fractions and mixed numbers using benchmarks.

Among the given options, the only variable that is a discrete random variable is a) the number of patients in a hospital.

a. the number of patients in a hospital

A discrete random variable is a variable that can only take on a finite or countably infinite set of distinct values. In this case, the number of patients in a hospital can only be whole numbers (e.g., 0, 1, 2, 3, etc.), which is a countable set of values. Therefore, it is a discrete random variable.

b. the average amount of electricity consumed

The average amount of electricity consumed is not a discrete random variable but a continuous random variable. It can take on any real number value within a certain range, and it is not restricted to specific distinct values.

c. the amount of paint used in repainting a building

The amount of paint used in repainting a building can be measured in continuous quantities (e.g., liters or gallons). It is not restricted to specific distinct values, and therefore, it is not a discrete random variable.

d. the average weight of female athletes

Similar to the average amount of electricity consumed, the average weight of female athletes is not a discrete random variable but a continuous random variable. It can take on any real number value within a certain range and is not restricted to specific distinct values.

Among the given options, the only variable that is a discrete random variable is a) the number of patients in a hospital.

To know more about variable follow the link:

https://brainly.com/question/28248724

#SPJ11

answer:

R -> R' (2,1)

T -> T' (0,2)

I -> I' (4,4)

reflection across the x axis

The probability that the system is idle in a single-server waiting line system can be calculated using the formula for the probability of zero arrivals during a given time period. In this case, the arrival pattern is characterized by a Poisson distribution with a rate of 3 customers per hour.

The arrival rate (λ) is equal to the average number of arrivals per unit of time. In this case, λ = 3 customers per hour. The average service time (μ) is given as 12 minutes, which can be converted to hours by dividing by 60 (12/60 = 0.2 hours).
The formula to calculate the probability that the system is idle is:
P(0 arrivals in a given time period) = e^(-λμ)
Substituting the values, we have:
P(0 arrivals in an hour) = e^(-3 * 0.2)
Calculating the exponent:
P(0 arrivals in an hour) = e^(-0.6)
Using a calculator, we find that e^(-0.6) is approximately 0.5488.
Therefore, the probability that the system is idle is approximately 0.5488.

To know more about probability visit:

https://brainly.com/question/31828911

#SPJ11

Hello! I'm happy to help you with your question. Here's the notation for each sequence:

(a) 2 + 4 + 6 + 8 + ... + 2n can be rewritten as:
∑(2i) where i goes from 1 to n.

(b) 1 + 5 + 9 + 13 + ... + 425 can be rewritten as:
∑(4j-3) where j goes from 1 to 106. (Note: 425 is the 106th term in this sequence)

(c) 1 + 12 + 13 + 14 + ... + 150 can be rewritten as:
1 + ∑(k) ,where k goes from 12 to 150

Know more  about summation notation

https://brainly.com/question/31366683

#SPJ11

Answer:

Step-by-step explanation:

y = a * x(x - 3)(x + 1)^2

2,12 is used to find the value of a

y = a (2)(2 - 3)(2 + 1)^2

12 = a (2)(-1)(3)^2

12 = a (2) (-1) (9)

12 = - 18*a

12/-18 = a

a = - 2/3

y = (-2/3)*x*(x - 3)(x + 1)^2

Answer:

Angles are 174 and 6

Step-by-step explanation: