How can i solve this using a flow chart?

a. f'(x) = 40x³

To find the derivative of f(x) = 10x⁴, we apply the power rule.

The power rule states that if f(x) = axⁿ, then f'(x) = naxⁿ⁻¹. Applying this rule, we get f'(x) = 4 * 10x³ = 40x³.

b. : f'(x) = 20 + 90x²

To find the derivative of f(x) = 20x + 30x³, we differentiate each term separately. The derivative of 20x is 20, and the derivative of 30x³ is 90x² (applying the power rule). Adding these derivatives, we get f'(x) = 20 + 90x².

r: f'(x) = (20x - 4x²)(5x - x²) + (10 + 2x²)(-2x + 5)

To find the derivative of f(x) = (10 + 2x²)(5x - x²), we apply the product rule. The product rule states that if f(x) = g(x) * h(x), then f'(x) = g'(x) * h(x) + g(x) * h'(x). Differentiating each term, we get f'(x) = (20x - 4x²)(5x - x²) + (10 + 2x²)(-2x + 5).

d.: f'(x) = 40x

To find the derivative of f(x) = 20x / (x²), we use the quotient rule. The quotient rule states that if f(x) = g(x) / h(x), then f'(x) = (g'(x) * h(x) - g(x) * h'(x)) / (h(x)²). In this case, g(x) = 20x and h(x) = x². After differentiating and simplifying, we obtain f'(x) = 40x.

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Answer:

the answer is × = -1, -4 is the answer

Answer:

$85.60

Step-by-step explanation:

Price + tax = total

80 + (80(7/100)) = 85.6

The completely factored form of 2x^2 + 4x - 2 is 2(x - 1)(x + 1).

To factor the expression 2x^2 + 4x - 2 completely, we can use the method of factoring by grouping.

Here are the steps:

1. Multiply the coefficient of the quadratic term (2) with the constant term (-2) to get -4.

2. Find two numbers that multiply to give -4 and add up to the coefficient of the linear term (4). In this case, the numbers are -2 and 2.

3. Rewrite the expression by splitting the middle term using the numbers found in step 2:

2x^2 + 2x - 2x - 2

4. Now, factor by grouping. Take out the common factors from the first two terms and the last two terms separately:

2x(x + 1) - 2(x + 1)

5. Notice that (x + 1) is a common factor in both terms. Factor it out:

(2x - 2)(x + 1)

6. Simplify further if possible. In this case, we can divide each term by 2:

2(x - 1)(x + 1)

Therefore, the completely factored form of 2x^2 + 4x - 2 is 2(x - 1)(x + 1).

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Answer:

74,812.50

Step-by-step explanation:

To show that v is an eigenvector of matrix A and find the corresponding eigenvalue, we need to check if Av = λv, where A is the given matrix, v is the proposed eigenvector, and λ is the eigenvalue.

Matrix A:
[1 2]
[2 1]

Vector v:
[ 8]
[-8]

Let's compute Av: [1 2]   [ 8]   [ 8 + (-16)]   [-8]
[2 1] x [-8] = [16 +  8  ] = [ 8], Now, we can see that Av = [-8, 8]. To find the eigenvalue, we need to find a scalar λ such that Av = λv. Let's compare Av with λv: Av = [-8], [ 8], λv = [λ *  8], [λ * -8]
Comparing the two, we can see that λ = -1, since -1 * 8 = -8 and -1 * -8 = 8. Therefore, v is an eigenvector of matrix A, and the corresponding eigenvalue is λ = -1.

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Answer:

$1.56

Step-by-step explanation:

hope this helps!

Answer:

B

Step-by-step explanation:

Therefore, none of the answer choices (4, 5, 6, or 7) are correct. The value of b, to the nearest hundredth, is approximately 27.97.

An angle is made up of two half-lines that have a common terminal. The rays, on the other hand, are alternately referred to as the angle's arms and legs, the latter of which serves as the angle's vertex.

Given that sine of x° equals four-fifths, we can use the definition of sine to set up the ratio:

sin(x) = opposite/hypotenuse

We can let the opposite side be 4 units and the hypotenuse be 5 units, since the sine of x is equal to 4/5. Then, using the Pythagorean theorem, we can solve for the adjacent side:

a² + 4² = 5²

a² + 16 = 25

a² = 9

a = 3

Now, we can use the given information about triangle LMN to set up another ratio using the sine function:

sin(x) = opposite/hypotenuse = NM/ML

NM/ML = 4/5

We can substitute in the given values for NM and solve for ML:

22.5/ML = 4/5

ML = 22.5 / (4/5)

ML = 22.5 x 5/4

ML = 28.125

Finally, we can use the Pythagorean theorem again to solve for b:

a²+ b² = ML²

3² + b² = 28.125²

b² = 28.125² - 3²

b² = 782.015625

b ≈ 27.97

Therefore, none of the answer choices (4, 5, 6, or 7) are correct. The value of b, to the nearest hundredth, is approximately 27.97.

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To verify that ab=ac, we need to calculate the matrix products and compare the results.

ab = (−2 3 4 −6) (7 1 7 10) = (−2(7)+3(1)+4(7)−6(10)) = (−14+3+28−60) = −43 − which is a 1x1 matrix.

ac = (−2 3 4 −6) (−2 −8 1 4) = (−2(−2)+3(−8)+4(1)−6(4)) (−2(7)+3(1)+4(7)−6(10)) = (4−24+4−24) (−14+3+28−60) = −40 −43 = −83 - which is a 1x1 matrix.

Therefore, ab=ac.

However, b and c are not equal matrices as they have different elements. For example, b has a 10 in the fourth position while c has a 4 in the fourth position. Therefore, b≠c.

First, let's define the given vectors:

Let a = [-2, 3, 4, -6], b = [7, 1, 7, 10], and c = [-2, -8, 1, 4].

Now, let's calculate the dot product of a and b (ab), and a and c (ac):

ab = a·b = (-2 * 7) + (3 * 1) + (4 * 7) + (-6 * 10) = -14 + 3 + 28 - 60 = -43

ac = a·c = (-2 * -2) + (3 * -8) + (4 * 1) + (-6 * 4) = 4 - 24 + 4 - 24 = -40

Since ab = -43 and ac = -40, it is clear that ab ≠ ac.

Now, let's verify if b ≠ c:

Comparing the components of b and c:

b = [7, 1, 7, 10]
c = [-2, -8, 1, 4]

We can see that the components of b and c are different, so b ≠ c.

To summarize:
- ab ≠ ac (-43 ≠ -40)
- b ≠ c ([7, 1, 7, 10] ≠ [-2, -8, 1, 4])

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Answer:

coordinates of H = (1, 0)

Coordinates of G = ( - 3.6, -2) or (5.6, -2)

Step-by-step explanation:

E(5,3) and F (2,-1) are two vertices of a square EFGH and H is in the x-axis.

Let the coordinates of H is (x, 0) and G is (a, b).

The length of side EF is

\(EF = \sqrt{(5 -2)^2 + (3 +1)^2} = 5\)

So,

\(EH = \sqrt{(5 -x)^2 + (3 -0)^2} = 5\\\\(5 -x)^2+ 9 = 25\\\\5 - x = 4\\\\x = 1\)

And

\(GH = \sqrt{(a -x)^2+ b^2} = 5\\\\(a -1)^2+ b^2 = 25\\\\a^2 + b^2 + 1 - 2 a = 25\\\\a^2 + b^2 - 2a = 24 .... (1)\)

Now

\(FG = \sqrt{(a -2)^2+ (b +1)^2} = 5\\\\(a -2)^2+ (b+1)^2 = 25\\\\a^2 + b^2 + 2b - 2 a = 20\\ ..... (2)\)

Solving (1) and (2)

b = - 2 ,

\(a = \frac{2 \pm\sqrt{4 + 80}}{2}\\\\a = \frac{2 \pm 9.2}{2}\\\\a = - 3.6, 5.6\)

Answer:

Step-by-step explanation:

given data

mean = 1.9 hours

standard deviation = 0.3 hours

solution

we get here first  random movie between 1.8 and 2.0 hours

so here

P(1.8 < z < 2 )

z = (1.8 - 1.9) ÷ 0.3

z = -0.33

and

z = (2.0 - 1.9) ÷ 0.3

z = 0.33

z = 0.6293

so

P(-0.333 < z < 0.333 )

=  0.26

so random movie is between 1.8 and 2.0 hours long is 0.26

and

A movie is longer than 2.3 hours.

P(x > 2.3)

P( \(\frac{x-\mu }{\sigma}\)  > \(\frac{2.3-\mu }{\sigma}\) )

P (z  > \(\frac{2.3-1.9 }{0.3}\)  )

P (z  > 1.333  )

= 0.091

so chance a movie is longer than 2.3 hours is 0.091

and

length of movie that is shorter than 94% of the movies is

P(x > a ) = 0.94

P(x <  a ) = 0.06

so

P( \(\frac{x-\mu }{\sigma }\) <  \(\frac{a-\mu }{\sigma }\) )

\(\frac{a-1.9 }{0.3 } = -1.55\)

a = 1.43

so length of the movie that is shorter than 94% of the movies about 1.4 hours.

Answer:

Answer is A

Step-by-step explanation:

(14x^4y^6)/(7x^8y^2)

because everything is one term, you can split into three terms

14/7, x^4 / x^8 , and y^6/y^2

multiplying these three terms will get us the starting term

14/7 = 2

x^4 / x^8

with division of exponents, you subtract the smaller exponent (4), from the big exponent (8), and leave it on the same side (bottom) as the big exponent

1/x^4

same thing with our y's

y^6/y^2

this time, the term stays on the top

y^4

take the simplified terms and multiply them together

(2) * (1/x^4) * (y^4) =

A: (2y^4) / (x^4)

Answer:

1. 9/10 x 3 = 93/10

2. 9/8

Espero que esto ayude a tener un buen día!

Answer:

AB = 10

Step-by-step explanation:

Use the distance formula: √(12 - 18)^2 + (1 - 9)^2

√36 + 64

10

Answer:

10 units

Step-by-step explanation:

Use the distance formula. Substitute the values, (1-9)²+(12-18)²=100. The square root of 100 is 10.

a. The median number of calls = 55

b. The first and third quartiles, Q1 = 48 and Q3 = 66

c. The first decile and the ninth decile, D1 = 45 and D9 = 71.

d. The 33rd percentile = 52.5

To answer the questions, let's first organize the data in ascending order:

38 40 41 45 48 48 50 50 51 51 52 52 53 54 55 55 55 56 56 57 59 59 59 62 62 62 63 64 65 66 66 67 67 69 69 71 77 78 79 79

(a) The median is the middle value of a dataset when arranged in ascending order.

Since we have 40 observations, the median is the value at the 20th position.

In this case, the median is the 55th visit.

(b) The quartiles divide the data into four equal parts.

To find the first quartile (Q1), we need to locate the position of the 25th percentile, which is 40 * (25/100) = 10.

The first quartile is the value at the 10th position, which is 48.

To find the third quartile (Q3), we need to locate the position of the 75th percentile, which is 40 * (75/100) = 30.

The third quartile is the value at the 30th position, which is 66.

Therefore, Q1 = 48 and Q3 = 66.

(c) The deciles divide the data into ten equal parts.

To find the first decile (D1), we need to locate the position of the 10th percentile, which is 40 * (10/100) = 4.

The first decile is the value at the 4th position, which is 45.

To find the ninth decile (D9), we need to locate the position of the 90th percentile, which is 40 * (90/100) = 36.

The ninth decile is the value at the 36th position, which is 71.

Therefore, D1 = 45 and D9 = 71.

(d) To find the 33rd percentile, we need to locate the position of the 33rd percentile, which is 40 * (33/100) = 13.2 (rounded to 13). The 33rd percentile is the value at the 13th position.

Since the value at the 13th position is between 52 and 53, we can calculate the percentile using interpolation:

Lower value: 52

Upper value: 53

Position: 13

Percentage: (13 - 12) / (13 - 12 + 1) = 1 / 2 = 0.5

33rd percentile = Lower value + (Percentage * (Upper value - Lower value))

                = 52 + (0.5 * (53 - 52))

                = 52.5

Therefore, the 33rd percentile is 52.5.

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Answer:

x+8z-9y-ty

2x+5z-9y + x-8z+9y+ty

=3x+ty-3z

Answer:

b=2.5

Step-by-step explanation:

We know that,

Area of a rectangle= Length X Breadth

Perimeter of a rectangle= 2( Length + Breadth)

From the provided information we get that,

Area= Perimeter

lb=2(l+b)

Substituting l=10,

10b=2(10+b)

10b=20+2b

10b-2b=20

8b=20

b=20/8

b=2.5

To calculate the center line of a control chart, you compute the average of the mean for every period.

A control chart is a graphical representation of a process's performance over time. It is utilized to determine whether a process is in control (i.e., consistent and predictable) or out of control (i.e., unstable and unpredictable).

The center line is used to represent the procedure average on a control chart. When the procedure is in control, the center line is the process's average. When the process is out of control, it can be utilized to assist in identifying where the out-of-control signal began.

The control chart is a valuable quality control tool because it helps detect process variability, identify the source of variability, and determine if process modifications have improved process quality. Additionally, the chart can serve as a visual guide, alerting employees to process variations and assisting them in responding appropriately.

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To decrease the type II error in a hypothesis test while maintaining the type I error at its current level, we need to increase the sample size.

Type I error shows when we reject a null hypothesis which is actually true. Type II error shows when we fail to reject a null hypothesis which is actually false.

Increasing the sample size can decrease the probability of making a Type II error, as it increases the power of the hypothesis test. Probability of correctly rejecting a false null hypothesis is called power.

By increasing the sample size, we can increase the power of the test while maintaining the significance level (and thus the type I error) at its current level.

This means that we will be less likely to miss a true effect (i.e., lower the probability of making a Type II error) while still controlling the probability of false positives (i.e., Type I error) at the desired level.

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The expression that represents the discounted price of the T-shirt is the one with the 30% discount, which is given by `x - 0.3x`. Therefore, the answer is B. `0.7x`.

Explanation:

When a store offers a discount on an item, the discounted price is calculated as follows:

Discounted price = Regular price - (Discount rate × Regular price)

where Discount rate = Discount ÷ 100

So, if the discount offered is 30%, then the discount rate is 30 ÷ 100 = 0.3.

Substituting this in the above equation,

Discounted price = Regular price - (0.3 × Regular price)

Simplifying the above expression, we get

Discounted price = (1 - 0.3) × Regular price

Discounted price = 0.7 × Regular price

Therefore, the expression that represents the discounted price of the T-shirt is given by `x - 0.3x = 0.7x`.

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Answer: valu of a

Step-by-step explanation: I Did the test

Answer:

The value of A affects the answer.

The correct answer is OD. Although the word "then" appears in the statement, it is not used as a logical connective. So the statement is not compound.

The statement "If Laura sells her quota, then Marie will be happy" is a single declarative sentence. It consists of a conditional clause ("If Laura sells her quota") and a consequent clause ("then Marie will be happy"). However, these two clauses are not independent statements that can stand alone. Instead, they are connected in a cause-and-effect relationship. The word "then" in this context is not functioning as a logical connective, but rather as an indicator of the consequent clause.

A compound statement is formed by combining two or more independent statements using logical connectives such as "and," "or," or "if...then." In the given statement, there is no logical connective joining two independent statements.

Therefore, the statement is not compound.

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\(y > 2x + 1 \\ 3 > 2(1) + 1 \\ 3 > 3 \\ false\)

\(y < - 3x \\ 3 < - 3(1) \\3 < - 3 \\ also \: false\)

A complete list of the numbers in the pattern: 3, 6, 10, 14, 18, etc.

The number pattern you described is as follows:

3,

(2*5)-4 = 6,

(2*7)-4 = 10,

(2*9)-4 = 14,

(2*11)-4 = 18,

The first number is 3, and then each subsequent number is found by multiplying the previous odd number by 2 and then subtracting 4.

For example, the second number is found by multiplying the first number by 2 and then subtracting 4, which gives us 6. The third number is found by multiplying the second number by 2 and then subtracting 4, which gives us 10.

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Answer:

Top Right

Step-by-step explanation:

The greater than or equal to sign makes the line solid, and the greater than 2 makes the shading go to the right

Answer:

31.5 cm

Step-by-step explanation:

scale of an architecture is ratio of size of drawing to size of actual object.

Given size of football field is 160 feet by 360 feet

Given that on map shortest side is 14

since value of shortest side is 160 feet

then

scale defined for this football filed will be

scale = size of shortest side on model/size of shortest side of actual football field

scale = 14/160

Given that scale will remain same for longer side as

14/160= size of longer side on model/size of longer side of actual

14/160 =  size of longer side on model/360

thus,

size of longer side on model = (14/160) * 360

size of longer side on model = 14*360/160 = 31.5

Thus, the other side of model that is longer side is 31.5 cm

Answer:

x = 15

m∠B = 108°

Step-by-step explanation:

From the picture attached,

There are two parallel lines and another line (transversal line) is intersecting the given lines making angle A and angle B.

Since, ∠A and ∠B are the exterior alternate angles,

measure of both the angles will be same.

m∠A = m∠B

(6x + 18)° = (x + 93)°

6x - x = 93 - 18

5x = 75

x = 15

m∠A = (6x + 18) = 90 + 18

                         = 108°

m∠A = m∠B = 108°

Answer: A random variable.

Step-by-step explanation:

a numerical description of the outcome of an experiment is called a random variable.