does the function satisfy the hypotheses of the mean value theorem on the given interval? f(x) = 5x2 − 2x 3, [0, 2]

Answer:

Larger angle: 104 degrees

Smaller angle: 76 degrees

Step-by-step explanation:

(9x+5) + (6x+10) = 180

x = 11

Answer: C Omar did not make a mistake.

Answer:

OPTION C : omar didn't make a mistake

Step-by-step explanation

\(\frac{3x}{3}\) = \(\frac{4.5}{3}\)  is equal to 1.5

so x = 1.5

For any price of h and k = -12, the system x + 3y = h and -4x + ky = -9 will haven't any answer.

To determine the values of h and okay for which the device of equations has no answer, we want to locate the situations underneath which the equations are inconsistent or parallel.

The given system of equations is:

Equation 1: x + 3y = h

Equation 2: -4x + ky = -9

For the gadget to haven't any answer, the lines represented with the aid of these equations should be parallel and in no way intersect. In different phrases, the slopes of the traces need to be equal, but the y-intercepts should be specific.

Let's first discover the slopes of the traces. The slope-intercept form of Equation 1 is y = (-1/3)x + (h/3), wherein the slope is -1/3. The slope-intercept shape of Equation 2 is y = (4/k)x - (9/k), wherein the slope is 4/k.

For the strains to be parallel, the slopes should be equal. Therefore, we have the condition: -1/3 = 4/k.

To locate the values of h and okay for which the gadget has no answer, we need to locate the values of h that satisfy the situation -1/3 = 4/k.

Solving this equation for ok, we've got:

-1/3 = 4/k

-1 = 12/k

k = -12

Substituting k = -12 returned into the equation -1/3 = 4/k, we've:

-1/3 = 4/(-12)

-1/3 = -1/3

Since the equation holds real for any value of h, there aren't any restrictions at the price of h.

Therefore, for any price of h and k = -12, the system x + 3y = h and -4x + ky = -9 will haven't any answer.

To know more about equations,

https://brainly.com/question/29797709

#SPJ4

The system of equations has no solution when k is equal to 12. The value of h can be any real number.

To determine the values of h and f for which the system has no solution, we need to analyze the coefficients of the variables and the constants in the equations.

The given system of equations is:

x + 3y = h

-4x + ky = -9

We can rewrite the second equation as:

-4x + ky = -9

Dividing both sides of the equation by -4, we get:

x - (k/4)y = 9/4

Comparing the coefficients of x and y in the two equations, we can see that the slopes of the lines represented by the equations are different when k is not equal to 12.

Therefore, for the system to have no solution, k must be equal to 12.

As for the value of h, it can be any real number since it does not affect the slopes of the lines.

About system of equations here:

https://brainly.com/question/21620502

#SPJ11

Answer:

2x/4y = x/2y = x : 2y

Step-by-step explanation:

The question only gave us the cost of each white tiles and blue tiles respectively . The cost of each white tiles is £2  while the cost of each blue tiles is £4. The total cost of the blue tiles and the white tiles can only be calculated if we know the number of blue and white tiles available.

Let us assume

the number of white tiles = x

the number of blue tiles = y

total cost of white tiles = 2 × x = 2x

total cost of blue tiles =  4 × y = 4y

Therefore, the ratio of the total cost of white tiles to the total cost of the blue tiles can be expressed as follows

2x/4y = x/2y = x : 2y

If the number of white and blue tiles is known it can be replaced in the ratio to find the ratio of the total cost of the white tiles to the total cost of the blue cost.

The cost of direct labor per unit is $5.628 per apple.

To calculate the cost of direct labor per unit, we need to determine the total labor hours required to produce one unit of output and then multiply it by the wage rate.

Let's denote the labor hours required for the first resource as "L₁" and the labor hours required for the second resource as "L₂".

The first resource has a capacity of 2.1 apples per hour, and the demand is 1.6 apples per hour. Therefore, the labor hours required for the first resource per unit of output are:

L₁ = 1 apple / (2.1 apples/hour) = 0.4762 hours/apple (rounded to 4 decimal places)

The second resource has a capacity of 4.4 apples per hour, and the demand is 1.6 apples per hour. Therefore, the labor hours required for the second resource per unit of output are:

L₂ = 1 apple / (4.4 apples/hour) = 0.2273 hours/apple (rounded to 4 decimal places)

Now, let's calculate the total labor hours required per unit:

Total labor hours per unit = L₁ (first resource) + L₂ (second resource)

= 0.4762 hours/apple + 0.2273 hours/apple

= 0.7035 hours/apple (rounded to 4 decimal places)

Finally, to calculate the cost of direct labor per unit, we multiply the total labor hours per unit by the wage rate:

Cost of direct labor per unit = Total labor hours per unit * Wage rate

= 0.7035 hours/apple * $8/hour

= $5.628 per apple (rounded to 3 decimal places)

To know more about direct labor:

https://brainly.com/question/13126873

#SPJ4

Answer:

Step-by-step explanation:

The two have a total of 5+2 = 7 "ratio units" so have a total of 140 cars.

can you mark me as brainliest?

Answer: i think C sorry if i get it wrong :)

Step-by-step explanation:

Answer:the  median lies  between $112 and $132 since median is middle no. but as for this question the median is 122

Step-by-step explanation:

Margo borrows $700 (P), the interest rate is 8% (0.08 as a decimal), and the time is 7 months, which is equivalent to 7/12 of a year (approximately 0.583 years).

Margo borrowed $700 and agreed to pay it back with 8% annual interest after 7 months. In order to calculate the amount of interest she will pay, we need to use the following formula: Interest = Principal x Rate x Time. Here, the principal is $700, the rate is 8%, and the time is 7/12 (as 7 months is equivalent to 7/12 of a year). So, we can plug in these values to get: Interest = $700 x 0.08 x (7/12)
Interest = $28
Therefore, Margo will pay $28 in interest.

Margo borrowed $700 and agreed to pay it back with 8% annual interest after 7 months. To calculate the amount of interest she will pay, we use the formula Interest = Principal x Rate x Time. Plugging in the values, we get Interest = $700 x 0.08 x (7/12), which equals $28. In summary, Margo will pay $28 in interest on her $700 loan.

To know more about decimal visit :-

https://brainly.com/question/31708708

#SPJ11

Answer:

17

Step-by-step explanation:

20 divided by 5 + 19 - 6

20 divided by 5 = 4

4 + 19 = 23

23 - 6 = 17

Answer:

0.54

Step-by-step explanation:

Answer:

0.54

Step-by-step explanation:

calculator. easy.

Answer:

34

Step-by-step explanation:

Substitute the values.

s = 3 and t = -2

8s-5t

8 (3) - 5(-2)

( 8 x 3 ) - ( 5 x -2 )

24 + 10 [ - x - = + ]

= 34

Answer:

-300

Step-by-step explanation:

Answer:

Which ordered pairs are solutions to the inequality 2x + y > - 4?

Select each correct answer.

(-1, -1), (4, -12), (5, -12), (0, 1), (-3, 0)

The correct answer is:

(4, -12)

Answer:

X=3 Y=10

Step-by-step explanation:

Answer:

x=6 and y=-4

Step-by-step explanation:

4x+y=20

x-y=10

5x=30

x=30/5

x=6

4x+y=20

4(6)+y=20

24+y=20

y=20-24

y=-4

Yes, there will be a collision between Speedy Sue's car and the slow-moving van in the tunnel. The collision will occur at a distance of approximately 146.5 meters into the tunnel, and the time of the collision will be around 7.72 seconds.

To determine whether there will be a collision, we need to calculate the time it takes for Speedy Sue to reach the van and compare it with the time it takes for the van to exit the tunnel.

First, we calculate the time it takes for Sue to reach the van. The relative velocity between Sue and the van is (33.0 m/s - 5.40 m/s) = 27.6 m/s. Using the formula time = distance / velocity, the time it takes for Sue to reach the van is approximately 175 m / 27.6 m/s ≈ 6.34 seconds.

Next, we calculate the time it takes for the van to exit the tunnel. The distance the van needs to travel to exit the tunnel is the sum of the distance from its initial position to the end of the tunnel and the distance Sue needs to travel to reach the end of the tunnel. The total distance is 175 m + 175 m = 350 m. The velocity of the van is 5.40 m/s. Using the formula time = distance / velocity, the time it takes for the van to exit the tunnel is approximately 350 m / 5.40 m/s ≈ 64.81 seconds.

Since 6.34 seconds is less than 64.81 seconds, Sue will collide with the van before it exits the tunnel. To determine the distance into the tunnel where the collision occurs, we subtract the distance Sue travels in 6.34 seconds from the initial distance between Sue and the van. The distance Sue travels is (33.0 m/s - 1.90 m/s^2 * 6.34 s^2 / 2) * 6.34 s ≈ 146.5 meters.

Therefore, the collision between Sue's car and the van will occur at a distance of approximately 146.5 meters into the tunnel, and the time of the collision will be around 7.72 seconds.

Learn more about meters here:

https://brainly.com/question/29367164

#SPJ11

Answer/Step-by-step explanation:

a. Since both cones, as shown in the figure attached below, are similar, 11/8 = l/4

Cross multiply to find l

4*11 = 8*l

44 = 8l

l = 44/8

l = 5.5cm

b. Given the slant height and diameter of cone, volume of cone can be calculated using the formula ⅓πr²*√(l² - r²)

Where, r = diameter ÷ 2 = 4/2 = 2cm

l = 5.5cm

Volume of smaller cone = ⅓*3.142*2²*√(5.5² - 2²)

= ⅓*3.142*4*√30.25 - 4)

= ⅓*12.568*√26.25

= ⅓*12.568*5.124

= 64.40/3

Volume of small cone ≈ 21.5 cm³

There will be a pivot position in each row. If a row did not have a pivot position then the equation Ax = b would be inconsistent. The correct answer is C.

A matrix is a collection of numbers, encompassed by brackets.

The numbers are known as matrix elements or entries. The components are organized in rows (horizontal) or columns (vertical), which determine the matrix's size (dimension or order).

This statement C is true because, in the reduced echelon form of a matrix, the pivot position in each row indicates the non-zero leading term in that row, which corresponds to a unique unknown variable. If a row did not have a pivot position, then the corresponding equation would be equivalent to 0 = b, which is inconsistent.

Therefore, in order for Ax = b to have a unique solution, it is necessary that each row in the reduced echelon form of A has a pivot position.

To learn more about the matrix click here:

https://brainly.com/question/28180105

#SPJ1

The sum of angle in a triangle is 180°

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC.

The sum of angle A, B and C is 180 i.e A+B +C = 180°

Also a triangle is a 3 sided polygon. The sum of of angle in a polygon is( n-2)180

How do we prove that the sum of angle in a triangle is 180°?

Since triangle is 3 sided, n= 3, because n denote the number if sides

therefore the sum of angle = (n-2) 180 = (3-2)×180

= 180°

therefore the sum of angle In a triangle is 180°

learn more about sum of angle In a triangle from

https://brainly.com/question/25215131

#SPJ1

Answer:

option D. 10

Step-by-step explanation:

\(\frac{34}{85} = \frac{4}{x}\\\\34 \times x = 4 \times 85\\\\x = \frac{340}{34} = 10\)

Answer:

x = 10

Step-by-step explanation:

\( \dfrac{34}{85} = \dfrac{4}{x} \)

Cross multiply.

34x = 4 × 85

34x = 340

Divide both sides by 34.

x = 10

The mean of all exam scores in the class is 72.67 ~ 73 . Mean is ratio of sum of score in all exam to the total numbers of all exams.

The exam scores are normally distributed , normally distributed is an arrangement in which most of values in middle and rest are symmetrically distributed at the ends 80th percentile of scores earned 85 it implies that 80% of students score is 85 or less and 30th percentile of scores earned 65 means 30% of students score is 65 or less .

Z-score value for 80th percentile is 0.841

Z-score value for 30th percentile is – 0.524

Formula for normally distributed,

Z =( X – μ) / σ

where μ is mean of scores , σ is standard deviations of scores ,X is sample mean

For 80th percentile , X= 85 , Z= 0.841

0.841=( 85- μ) /σ ----(1)

-0.524= (65-μ) / σ ----(2)

Solving equations (1) and (2)

- (841/524)= (85-μ )/( 65-μ) => 841μ – 841(65) = -524μ +85(524)

⇒ 1365μ= 99,205 => μ= 72.67

So, the value of mean of scores obtained by students in a class is 72.67 ~ 73

To learn more about normal distribution, refer:

https://brainly.com/question/27241794

#SPJ4

Answer:

B. <

Step-by-step explanation:

Each number in the sequence is greater than the previous number so the correct answer is b. <

Answer: 13/20

Step-by-step explanation: First to find the first part, we need to find a common denominator. So we must ask ourselves, which number is a multiple that both 5 and 4 have in common? The answer then would be 20. So, it would look like this:

\(\frac{1}{4} = \frac{?}{20}\)

\(\frac{2}{5} = \frac{?}{20}\)

So to find what "?" equals for both fractions, we must use this formula:

Amount =  Right denominator / Left denominator (1st part)

So, now we do 20 / 5 and 20 / 4

20 / 5 = 4

20 / 4 = 5

So, the 2nd part is taking the quotient from that and multiplying it by the left numerators. This would look like this:

5 * 1 = 5

4 * 2 = 8

So your "?" should look like this:

\(\frac{1}{4} = \frac{5}{20}\)

\(\frac{2}{5} = \frac{8}{20}\)

Then, you'd just add! So, 8 + 5 = 13 and 20 + 20 would stay that same ; 20. So your result is \(\frac{13}{20}\)

I hope this helped!

The probabilities are given as follows:

a) Square: 1/6.

b) Not the triangle: 43/48.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The total area of the figure is given as follows:

12 x 8 = 96 units². (rectangle).

The area of the square is given as follows:

4² = 16 units² (square of the side lengths).

Hence the probability of the square is given as follows:

p = 16/96

p = 1/6.

The area of the triangle is given as follows:

A = 0.5 x 4 x 5 = 10 units². (half the multiplication of the side lengths).

Hence the complement of the area of the triangle is of:

96 - 10 = 86 units².

And the probability of the complement is of:

86/96 = 43/48.

More can be learned about probability at https://brainly.com/question/24756209

#SPJ1

The volume of the second parallelepiped will be 1 cm³. According to the given conditions, α is 50% of a, β is 20% of b and γ is 10% of c.

The term “volume” refers to the amount of three-dimensional space taken up by an item or a closed surface. It is denoted by V and its SI unit is in cubic cm.

Given condition;

α is 50% of a, β is 20% of b and γ is 10% of c

α =  a/2

β = b/5

γ = c/10

The volume of the first parallelepiped:

V = abc

100cm³=abc

The volume of the second parallelepiped:

\(\rm V'= \alpha \times \beta \times \gamma \\\\ \rm V'= \frac{a}{2} \times \frac{b}{5} \times \frac{c}{10} \\\\ V' = \frac{abc}{100} \\\\ V'=\frac{100}{100} \\\\ V' = 1 cm^3\)

Hence, the volume of the second parallelepiped willl be 1 cubic meter.

To learn more about the volume, refer to https://brainly.com/question/1578538

#SPJ1

To use the integral test, we need to evaluate the following integral: ∫[infinity]1 6/5x dx Using integration by substitution with u = 6/5x, we get: ∫[infinity]1 6/5x dx = (5/6)∫[infinity]6/5 1 du.

Evaluating this integral gives us: (5/6)∫[infinity]6/5 1 du = (5/6)(1/u)|[infinity]6/5 = (5/6)(0 - 5/6) = -25/36 Since the integral evaluates to a finite value, and the series has the same general term as the function being integrated, we can conclude that the series is convergent by the integral test.

The new limits for the integral will be 5 (lower) and infinity (upper). ∫(5 to infinity) 6/u * (1/5) du. Thus, the integral is divergent. Since the integral is divergent, the original series Σ (n = 1 to infinity) 6/(5n) is also divergent.

To know more about function click here

brainly.com/question/28193995

#SPJ11

In the experiment, the independent variable is the amount of sunlight received by the clover plants.

The amount of sunlight the clover plants receive throughout the experiment serves as the independent variable, as it is being manipulated by the experimenters to determine its effect on the size of the clover leaves.

The dependent variable is the size of the clover leaves, which is being measured as a result of the change in the independent variable (amount of sunlight). The water is a controlled variable, as it is kept constant across both conditions to eliminate its effect on the outcome.

To learn more about variable here:

https://brainly.com/question/29521826

#SPJ4

Answer:

B po? I'm not sure ehh hehehe

Answer:

18

Step-by-step explanation:

2y+3y+5y=180

10y/10=180/10

Y=18