What is the value of 6(2b-4) when b =5

Answer:

Step-by-step explanation:

length. To find the missing horizontal length, we will look at the values of the other horizontal lengths. Looking at the composite shape, the side that is 12 cm long is the same as both the missing side plus the side that is 4 cm long. We can therefore find the missing length by subtracting 6 cm from 9 cm.

Answer:

To find the missing horizontal length, we will look at the values of the other horizontal lengths. Looking at the composite shape, the side that is 12 cm long is the same as both the missing side plus the side that is 4 cm long. We can therefore find the missing length by subtracting 6 cm from 9 cm

Step-by-step explanation:

Answer:

can u include a picture of the cylinder pls luv

Step-by-step explanation:

First find height using Pythagorean theorem.

\(h^2+4^2=13^2\implies h=\sqrt{153}\approx12.37\).

Then use cone surface area formula and compute the result:

\(A=\pi r(r+\sqrt{h^2+r^2})\approx\boxed{68\pi}\mathrm{units^2}\).

Hope this helps.

total number of students = 8

each student = 18 chocolate

so, total number of chocolates = 18×8 = 144 chocolate s

Answer:

45%

Step-by-step explanation:

In Tanvi's simulation, landing on a white section represents a chocolate with a caramel filling. Tanvi records 20 trials, and the spinner lands on at least 1 white section in 9 of them. So, the probability that at least 1 of the chocolates has a caramel filling is

9

20

Convert

9

20

to a percent. Write an equivalent fraction with 100 as the denominator.

9

20

=

95

205

=

45

100

Based on Tanvi's results, the probability that at least 1 of the chocolates has a caramel filling is 45%.

It take 22.22 minutes for the two math students to finish the assignment together.

To determine how long it would take for the two math students to finish the assignment together, we can use the concept of "work done per unit of time."

Let's assume that the amount of work required to complete the assignment is represented by 1 unit.

If the first math student can complete the assignment in 50 minutes, then their work rate is 1/50 units per minute. Similarly, the second math student's work rate is 1/40 units per minute.

When they work together, their work rates are additive. So, the combined work rate of both students is (1/50 + 1/40) units per minute.

To find out how long it would take for them to finish the assignment together, we can calculate the reciprocal of the combined work rate:

1 / (1/50 + 1/40) = 1 / (0.02 + 0.025) = 1 / 0.045 = 22.22 minutes (approximately)

Therefore, it would take approximately 22.22 minutes for the two math students to finish the assignment together.

Learn more about work at https://brainly.com/question/13956476

#SPJ11

The polynomial function is f(x) = (x - 3)((x - 2)² + 9)

From the question, we have the following parameters that can be used in our computation:

Zeros: x=3, 2 +-3i

The polynomial can be repesented as

f(x) = product of (x - zeros)

using the above as a guide, we have the following:

f(x) = (x - 3)(x - (2 - 3i))(x - (2 + 3i))

This can be expressed as

f(x) = (x - 3)((x - 2)² + 9)

hence, the polynomial is f(x) = (x - 3)((x - 2)² + 9)

Read more about polynomial at

brainly.com/question/7693326

#SPJ1

The correct value of the product of a and b is 224

Taking the prime factorization of 161 reveals that it is equal to 23*7. Therefore, the only ways to represent 161 as a product of two positive integers are 161*1 and 23*7. Because neither 161 nor 1 is a two-digit number, the only two-digit factor of 161 is 23, we know that a and b are 23 and 7. Because 23 is a two-digit number, we know that a, with its two digits reversed, gives 23.

Therefore, a = 32 and b = 7. Multiplying our two correct values of a and b yields.

The correct product must have been

a*b =32*7

=224

Learn more about multiplying positive integers  here: https://brainly.com/question/11453536

#SPJ4

It takes Sally 4 hours, working alone, to paint one room.

Let's use the variable "x" to represent the number of hours it takes Sally to paint one room. According to the problem, it takes Henry 8 hours longer, or "x + 8" hours, to paint one room.

When they work together, they can paint one room in 3 hours. This means that their combined rate of painting is 1/3 of a room per hour. We can use this information to set up an equation:

1/x + 1/(x+8) = 1/3

To solve for x, we first need to simplify the equation by finding a common denominator:

(3(x+8) + 3x) / x(x+8) = 1

(6x + 24) / x(x+8) = 1

6x + 24 = x^2 + 8x

0 = x^2 + 2x - 24

Using the quadratic formula, we get:

x = (-2 ± sqrt(2^2 - 4(1)(-24))) / (2(1))

x = (-2 ± sqrt(100)) / 2

We can ignore the negative solution since it doesn't make sense in the context of the problem:

x = (-2 + 10) / 2

x = 4

To know more about quadratic formula refer here:

https://brainly.com/question/29077328#

#SPJ11

Answer:

  (3, 6)

Step-by-step explanation:

You want the coordinates of the orthocenter of triangle WXY with vertices W(2,7), X(3, 4), and Y(6, 7).

The orthocenter is the point where the altitudes of the triangle meet. An altitude is the line through a vertex that is perpendicular to the opposite side.

This is an acute triangle, so the orthocenter is within the boundaries of the triangle.

We note that side WY of the triangle is a horizontal line, so the orthocenter will lie on the vertical line through point X. The x-coordinate of point X is 3, so that vertical line has equation x=3.

Side XY can be seen on the graph to have a slope of 1. Or, you can compute it from the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (7 -4)/(6 -3) = 3/3 = 1

Then the point-slope equation of the altitude to that line will have the opposite reciprocal slope, and will go through point W(2, 7):

  y -7 = -1(x -2)

The y-value of the point of intersection of the altitude through W with the altitude through X will be the solution to ...

Substituting for x in the second equation, we have ...

  y -7 = -3 +2

  y = 6 . . . . . . . . . . add 7

The orthocenter is (x, y) = (3, 6).

__

Additional comment

The orthocenter of a right triangle is the vertex where the right angle is located. The orthocenter of an obtuse triangle is outside the triangle.

Answer:

y = 0.35x + 18.99

Answer:

21

Step-by-step explanation:

Answer:

The angles are supplementary.

x = 31

Step-by-step explanation:

The way the two angles lay together and make a straight line shows that they are supplementary. Supplementary means that they add up to 180°

Use this idea to write an equation.

2x + 3x + 25 = 180

combine like terms

5x + 25 = 180

subtract 25

5x = 155

divide by 5

x = 31

Answer:

x = 31

Step-by-step explanation:

(3x + 25) and 2x are a linear pair and are supplementary, that is

3x + 25 + 2x = 180

5x + 25 = 180 ( subtract 25 from both sides )

5x = 155 ( divide both sides by 5 )

x = 31

(a) As this limit is finite and positive, the series is said to converge.

(b) As this limit is finite and positive, the series is said to converge.

(c) The numerator tends to infinity faster than the denominator, so we can say that the series diverges.

(d) As this limit is finite and positive, the series is said to converge.

(a) Use the limit comparison test to determine whether the following series converge or diverge:

$$\sum_{n=3}^\infty \frac{5n}{7+n^2}$$We have that:$$\lim_{n \to \infty} \frac{\frac{5n}{7+n^2}}{\frac{1}{n}} = \lim_{n \to \infty} \frac{5n^2}{7+n^2} = 5$$

As this limit is finite and positive, the series is said to converge.

(b) Use the limit comparison test to determine whether the following series converge or diverge:

$$\sum_{n=1}^\infty \frac{\ln^2 n}{n^2}$$We have that:$$\lim_{n \to \infty} \frac{\frac{\ln^2 n}{n^2}}{\frac{1}{n}} = \lim_{n \to \infty} \frac{\ln^2 n}{n} = 0$$

As this limit is finite and positive, the series is said to converge.

(c) Use the limit comparison test to determine whether the following series converge or diverge:

$$\sum_{n=1}^\infty \frac{2^n}{4^{n-n^2}}$$We have that:$$\lim_{n \to \infty} \frac{\frac{2^n}{4^{n-n^2}}}{\frac{1}{n}} = \lim_{n \to \infty} \frac{n2^n}{4^{n-n^2}}$$

The numerator tends to infinity faster than the denominator, so we can say that the series diverges.

(d) Use the limit comparison test to determine whether the following series converge or diverge:

$$\sum_{n=1}^\infty \frac{\sin(1/n)}{n}$$We have that:$$\lim_{n \to \infty} \frac{\frac{\sin(1/n)}{n}}{\frac{1}{n}} = \lim_{n \to \infty} \sin\left(\frac{1}{n}\right) = 0$$

As this limit is finite and positive, the series is said to converge.

Visit here to learn more about limit comparison test brainly.com/question/30401939

#SPJ11

Answer:

47 cupcakes

Step-by-step explanation:

Assuming there aren’t any rules about what type of cupcakes he should buy.

\(101 - 21 - 33 = 47\)

Since he's already bought 21 + 33 he just have to buy

101 - (21 + 33) which is 47

Happy to help ^^

The z-score for Hugo's typing speed of 72 words per minute is 3.16, indicating that it is 3.16 standard deviations to the right of the mean.

Given that Hugo's words per minute on a typing test are normally distributed with a mean of 42 and a standard deviation of 9.5, we can calculate the z-score for the typing speed of 72 words per minute using the formula:

\(z = (x - μ) / σ\)

where x is the observed value, μ is the population mean, and σ is the population standard deviation.

Plugging in the values, we get:

z = (72 - 42) / 9.5

z = 3.16

This means that the typing speed of 72 words per minute is 3.16 standard deviations to the right of the mean.

The z-score also tells us the probability of observing a value as extreme as 72 words per minute or more, assuming a normal distribution. We can use a standard normal distribution table or a calculator to find this probability, which turns out to be approximately 0.001.

In summary, the z-score for Hugo's typing speed of 72 words per minute is 3.16, indicating that it is 3.16 standard deviations to the right of the mean. This also means that the probability of observing a value as extreme as 72 words per minute or more is very low, at around 0.001.

Learn more about minute here:

https://brainly.com/question/15600126

#SPJ11

The limits of integration of ∬R(8x+5y)2dA = ∫BA∫DC(8x+5y)2dxdy ∬R(8x+5y)2dA = ∫AB∫CD(8x+5y)2dxdy are A = (-1, 0), B = (1, 0), C = (-1, 1), D = (0, 1). The integral in part (a) is 5832/5.

(a) The vertices of the triangle R are (-1, 0), (0, 1), and (1, 0). We can find the limits of integration by considering the bounds of x and y in the region.

The line segment connecting (-1, 0) and (0, 1) has equation y = x + 1, so y ranges from 0 to x + 1. The line segment connecting (0, 1) and (1, 0) has equation y = -x + 1, so y ranges from 0 to -x + 1. The x-values of the left and right sides of the triangle are -1 and 1, respectively, so x ranges from -1 to 1.

Therefore, the limits of integration are:

A = (-1, 0)

B = (1, 0)

C = (-1, 1)

D = (0, 1)

(b) We have:

∬R(8x+5y)2dA=∫AB∫CD(8x+5y)2dxdy

= ∫_{-1}¹ ∫_0^{x+1} (8x+5y)² dy dx + ∫_{-1}⁰ ∫_0^{-x+1} (8x+5y)² dy dx

To evaluate the inner integral with respect to y, we can use the substitution u = 8x + 5y, du/dy = 5, and y = (u - 8x)/5. When y = 0, u = 8x, and when y = x+1 or -x+1, u = 8x + 5(x+1) = 13x+5 or 8x - 5(-x+1) = 13x + 5, respectively. Therefore, we have:

∫_0^{x+1} (8x+5y)² dy = ∫_{8x}^{13x+5} u² (1/5) du = (1/15)(u³)|_{8x}^{13x+5} = (1/15)(2197x³ + 7025)

∫_0^{-x+1} (8x+5y)² dy = ∫_{8x}^{13x+5} u² (1/5) du = (1/15)(2197x³ + 7025)

Substituting these integrals and limits of integration into the original expression, we get:

∬R(8x+5y)2dA = ∫_{-1}^1 [(1/15)(2197x³ + 7025) + (1/15)(2197x³ + 7025)] dx

= (2/15) ∫_{-1}¹ (4394x³ + 14050) dx

= (2/15) [(1098x⁴)/4 + 14050x]_{-1}^1

= (2/15) [(1098/4) + 14050 - (-1098/4) - 14050]

= 5832/5

Therefore, the integral is 5832/5.

Know more about integration here:

https://brainly.com/question/18125359

#SPJ11

The value of the expression given as√9x^3/25y^2 is 3x^3/25y^2

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

√9x^3/25y^2

Evaluate the square root of 9

So, we have the following equation

√9x^3/25y^2 = 3x^3/25y^2

The above expression cannot be further simplified

Hence, the solution to the expression is 3x^3/25y^2

Read more about expressions at

https://brainly.com/question/723406

#SPJ1

If you want the probability of randomly drawing a red marble to be 3/5, you need to add 13 red marbles.

The probability of drawing a red marble is equal to the quotient between the number of red marbles and the total number of marbles in the bag.

Initially, there are 12 red marbles and 32 in total, so if we add another x red marbles, we will have:

Then the probability will be:

p = (12 + x)/(32 + x)

And we want this to be 3/5, then we need to solve:

(12 + x)/(32 + x) = 3/5

(12 + x)*5 = 3*(32 + x)

60 + 5x = 96 + 3x

5x - 3x = 96 - 60

2x = 36

x = 36/2 = 13

x = 13

You need to add 13 red marbles.

Learn more about probability.

https://brainly.com/question/25870256

#SPJ1

Rounding to two decimal places, the confidence interval of the mean length of stay for patients who have had abdominal surgery is (5.03, 6.37).

To find the 95% confidence interval for the mean length of stay for patients with abdominal surgery, we can use the formula:

CI = \(\bar{X}\) ± Z * (σ / √n)

where:

CI = Confidence Interval

\(\bar{X}\) = Sample mean

Z = Z-score corresponding to the desired confidence level (95% confidence level corresponds to a Z-score of 1.96)

σ = Population standard deviation (since we don't have the population standard deviation, we'll use the sample standard deviation as an estimate)

n = Sample size

Given the information:

Sample mean (\(\bar{X}\)) = 5.7 days

Sample standard deviation (σ) = 1.6 days

Sample size (n) = 22

When the values are entered into the formula, we obtain:

CI = 5.7 ± 1.96 * (1.6 / √22)

Calculating this, we find:

CI = 5.7 ± 1.96 * (1.6 / 4.69)

CI = 5.7 ± 1.96 * 0.341

CI = 5.7 ± 0.668

Rounding to two decimal places, the confidence interval of the mean length of stay for patients who have had abdominal surgery is (5.03, 6.37).

Learn more about confidence interval here

https://brainly.com/question/32546207

#SPJ4

The required expression for the fenced region is lw = 650.

Given that,
A homeowner wants to fence in a rectangular space in her yard along one side of her house for her dogs. the total area she can fence in is 650 square feet.

The rectangle is 4 sided geometric shape whose opposites are equal in length and all angles are about 90°.

Here,
Let the length of the area be l and the width of the area be w,
The total area she can fence in is 650 square feet.
lw = 650

Thus, the required expression for the fenced region is lw = 650.

learn more about rectangles here:

brainly.com/question/15019502

#SPJ1

Answer:

almonds needed= 20z

raisins needed=6/10 oz

cashews needed= 1  4/10 oz

Step-by-step explanation:

Answer:

music off

Step-by-step explanation:

its doesn't equals right

The approximate speed at which the trolley should travel to achieve minimum cost is about 4 km/h.

To find the speed at which the trolley should travel to achieve minimum cost, we need to analyze the given cost function, c(x) = -2.1x² - 12.7x + 1674. This function represents the cost, in dollars per hour, of running the trolley at different speeds (x) in kilometers per hour.

To determine the speed that minimizes the cost, we look for the vertex of the parabolic function. The vertex of a quadratic function is the point where it reaches its minimum or maximum value. In this case, since the coefficient of the x² term is negative, the parabola opens downwards, indicating a minimum value.

To find the x-coordinate of the vertex, we can use the formula x = -b / (2a), where a and b are the coefficients of the quadratic function. From the given cost function, we have a = -2.1 and b = -12.7. Plugging these values into the formula, we get x = -(-12.7) / (2 * -2.1) ≈ 4.

Therefore, the trolley should travel at an approximate speed of 4 km/h to achieve the minimum cost.

Learn more about quadratic function

brainly.com/question/18958913

#SPJ11

Answer:

Step-by-step explanation:

alternate interior angles

More formally:

If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel (Since ∠1 = ∠4)

Answer: Alternate Interior Angles Converse

Step-by-step explanation:

If two lines are cut by a transversal so the alternate interior angles are congruent, then the lines are parallel.

Answer:

A

Step-by-step explanation:

Answer:

The answer is C - conjugation

Hope this helps!

Furthermore, we can use mathematical induction to prove statements about any well-ordered set, not just the natural numbers

Mathematical induction is a valid proof technique because it allows us to prove a statement for an infinite number of cases by proving it for just two cases: a base case and an induction step.

Suppose: We suppose the statement is true for some particular case, usually the base case.

To show: We then show that the statement is also true for the next case, usually the induction step.

Then the: We can then conclude that the statement is true for all cases.

We know that: We know that the base case is true because we have verified it directly. We also know that the induction step is true because we have assumed that the statement is true for some particular case and then shown that it must also be true for the next case.

Furthermore: Furthermore, we can use mathematical induction to prove statements about any well-ordered set, not just the natural numbers.

To learn more about induction visit:

https://brainly.com/question/18575018

#SPJ11

Therefore, Pump B will have a longer average cycle time compared to Pump A.

To determine which pump will have a longer average cycle time, we need to calculate the cycle time for each pump based on the given information and compare the results. The cycle time for a single-server system can be calculated using Little's Law: Cycle Time = (1 / Arrival Rate) * (1 / (1 - Utilization))

Given:

Arrival Rate = 0.2 car per minute

Squared-Coefficient of Variation (CV^2) for Arrival Rate = 1

Utilization can be calculated as the product of the mean effective process time and the arrival rate:

Utilization = Mean Effective Process Time * Arrival Rate

For Pump A:

Mean Effective Process Time (A) = 4 minutes

Squared-Coefficient of Variation for Pump A = 0.5

Utilization (A) = 4 * 0.2 = 0.8

For Pump B:

Mean Effective Process Time (B) = 3 minutes

Squared-Coefficient of Variation for Pump B = 5

Utilization (B) = 3 * 0.2 = 0.6

Now, let's calculate the cycle time for each pump:

Cycle Time (A) = (1 / 0.2) * (1 / (1 - 0.8))

= 5 minutes

Cycle Time (B) = (1 / 0.2) * (1 / (1 - 0.6))

= 2.5 minutes

To know more about Pump,

https://brainly.com/question/32143195

#SPJ11