solve for b in the trapezoid.

The ratio of cost to the number of cans = 5: 2  

A ratio is a mathematical concept that represents the relationship between two or more values.

In the given problem, the ratio represents the relationship between the cost of the soup and the number of cans purchased.

Ratios are commonly used in mathematics, finance, and other fields to express comparisons and relationships between different quantities.

Here we have

$10 for 4 cans of soup  

The required ratio can be formed as follows

=> 10: 4

=> 10/2: 4/2   [ Divided by 2 ]

=>  5: 2

Therefore,

The ratio of cost to the number of cans = 5: 2    

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Statistics report that the average successful quitter is able to stop smoking after multiple attempts, usually between 8 to 10 times.  everyone's journey to quitting smoking is unique and may take more or fewer attempts to achieve success.

According to statistics, the average successful quitter is able to stop smoking after attempting to quit 6 to 30 times. This number varies due to individual factors and the methods used for quitting. Remember, persistence is key, and it is never too late to quit smoking for a healthier lifestyle.

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Answer:

V = Bh = πr2h

Step-by-step explanation:

Answer:

A. 8 feet

Step-by-step explanation:

96 = 12 (x)

96/12 = x

8 = x

Answer:

13 hours

Step-by-step explanation:

155 + 92 = 247

247 / 19 = 13

Answer:

Approximately 0.1894 or 18.94% of the population is less than 10.0.

Step-by-step explanation:

On use the z-score formula and the standard normal distribution.

a. To compute the z-value associated with 14.3, we use the formula:z = (x - μ) / σWhere:

x = 14.3 (the value)

μ = 12.2 (mean)

σ = 2.5 (standard deviation)

Substituting the values:

z = (14.3 - 12.2) / 2.5

z = 2.1 / 2.5

z ≈ 0.84

Therefore, the z-value associated with 14.3 is approximately 0.84.

b. To obtain the proportion of the population between 12.2 and 14.3, we need to get the area under the standard normal distribution curve between the corresponding z-scores.

Using a standard normal distribution table or a calculator, we can find the area associated with each z-score.The z-value for 12.2 can be calculated using the same formula as in part a:

z1 = (12.2 - 12.2) / 2.5

z1 = 0 / 2.5

z1 = 0

The z-value for 14.3 is already known from part a: z2 ≈ 0.84.

Now, we obtain the proportion by subtracting the area associated with z1 from the area associated with z2:

Proportion = Area(z1 < z < z2)

Using a standard normal distribution table or a calculator, we obtain:

Area(z < 0) ≈ 0.5000 (from the table)

Area(z < 0.84) ≈ 0.7995 (from the table)

Proportion = 0.7995 - 0.5000

Proportion ≈ 0.2995

Therefore, approximately 0.2995 or 29.95% of the population is between 12.2 and 14.3.

c. To obtain the proportion of the population less than 10.0, we need to get the area under the standard normal distribution curve to the left of the corresponding z-score.Using the z-score formula:z = (x - μ) / σ

Where:

x = 10.0 (the value)

μ = 12.2 (mean)

σ = 2.5 (standard deviation)

Substituting the values:

z = (10.0 - 12.2) / 2.5

z = -2.2 / 2.5

z ≈ -0.88

Now, we obtain the proportion by looking up the area associated with z ≈ -0.88 using a standard normal distribution table or a calculator:

Area(z < -0.88) ≈ 0.1894 (from the table)

Therefore, approximately 0.1894 or 18.94% of the population is less than 10.0.

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The inequality that is different is C. X is no less than 12

Inequalities are created through the connection of two expressions. It should be noted that the expressions in inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥  <  >   ≤.

An inequality is created when two or more algebraic expressions are compared using the symbols. They represent mathematical expressions where neither side is equal.

p ≠ q means that p is not equal to q

p < q means that p is less than q

p > q means that p is greater than q

p ≤ q means that p is less than or equal to q

p ≥ q means that p is greater than or equal to q

It should be noted that x is no less than 12 isless than the other inequalities that are given. Therefore, the correct option is C.

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Answer:

y = \(\frac{3x -6}{5}\)

Step-by-step explanation:

3x - 5y = 6 ( subtract 3x from both sides )

- 5y = - 3x + 6 ( multiply through by - 1 )

5y = 3x - 6 ( divide both sides by 5 )

y = \(\frac{3x-6}{5}\)

Therefore, Peterson's solution is not a valid solution to the critical section problem on modern multi-core system  so it is false.

A multicore processors is an electronic component that has two or more processor cores attached for higher performance and lower power consumption. These processors also enable more efficient execution of numerous activities, such as with parallelization and multithreading.

Here,

It is because of the following disadvantages:

Although Peterson's technique is effective for two processes, it is the best plan for the important part in user mode.

Additionally, this solution involves busy waiting, wasting CPU time. So that “SPIN LOCK” problem can emerge. And any busy waiting solution may encounter this issue.

Therefore, Peterson's solution is not a valid solution to the critical section problem on modern multi-core system  so it is false.

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Answer:

8+6x=30+4x+2 The answer is 12

Step-by-step explanation:

Reason - The sum of opposite interior of a triangle is equal to opposite exterior angle .

Step-by-step explanation:

The scalar projection of a vector b onto a vector a is given by the dot product of b and the unit vector of a:

p = (b · u) * u

where u is the unit vector of a, and can be found by dividing a by its magnitude:

u = a / ||a||

The vector projection of b onto a is simply the scalar projection scaled by the unit vector:

p = p * u

For the given vectors a = ⟨-5,12⟩ and b = ⟨4,6⟩, we first find the unit vector u:

u = a / ||a|| = ⟨-5,12⟩ / ||⟨-5,12⟩|| = ⟨-5/13,12/13⟩

Next, we find the dot product of b and u:

p = (b · u) = ⟨4,6⟩ · ⟨-5/13,12/13⟩ = (4 * -5/13) + (6 * 12/13) = -20/13 + 72/13 = 52/13

So the scalar projection of b onto a is p = 52/13.

Finally, we find the vector projection by scaling the unit vector u by the scalar projection:

p = p * u = (52/13) * ⟨-5/13,12/13⟩ = ⟨-52/169,104/169⟩

So the vector projection of b onto a is p = ⟨-52/169,104/169⟩.

Answer:

I believe the answer is function

Step-by-step explanation:

The probability that Marshall wins a prize on his second spin =  0.1875

Consider an event X = the number of spins until Marshall wins a prize.

Given that a prize wheel with 4 segments of equal size, one of which is labeled winner.

So, the sample space n = 4

For given event x, the possible outcomes = 1

Using the formula of probability,

p = x/n

p = 1/4

p = 0.25

So, the probability of success p = 0.25

q = 1 - p

q = 1 - 0.25

q = 0.75

To find the probability that Marshall wins a prize on his 2nd spin.

Using formula, \(P(X = k) = (1 - p)^{k-1}p\)

For  k = 2,

\(P(X = 2) = (1 - 0.25)^{2-1}\times 0.25\)

P(X = 2) = 0.75 × 0.25

P(X = 2) = 0.1875

Thus, the required probability is  0.1875

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To analyze the variances in April, we need to compare the actual costs with the standard costs for materials, labor, and manufacturing overhead.

By calculating the price and quantity variances for materials, rate and efficiency variances for labor, and spending and efficiency variances for variable manufacturing overhead, we can assess the deviations from the standard costs. Additionally, the fixed manufacturing overhead budget and volume variances can be determined by comparing the actual fixed overhead costs with the budgeted amount.

1. Materials Price and Quantity Variances:
The materials price variance measures the difference between the actual cost of materials and the standard cost based on the quantity purchased. It can be calculated as (Actual Price - Standard Price) x Actual Quantity. In this case, the materials price variance is ($18.00 - $18.20) x 6,000 meters.

The materials quantity variance assesses the difference between the actual quantity used and the standard quantity allowed. It can be calculated as (Actual Quantity - Standard Quantity) x Standard Price. Here, the materials quantity variance is (6,000 meters - (2,000 robes x 2.8 meters per robe)) x $18.20.

2. Labour Rate and Efficiency Variances:
The labor rate variance measures the difference between the actual hourly rate and the standard hourly rate, multiplied by the actual hours worked. It can be calculated as (Actual Rate - Standard Rate) x Actual Hours. In this case, the labor rate variance is ($3.80 - $3.60) x 760 hours.

The labor efficiency variance assesses the difference between the actual hours worked and the standard hours allowed, multiplied by the standard rate. It can be calculated as (Actual Hours - Standard Hours) x Standard Rate. Here, the labor efficiency variance is (760 hours - (2,000 robes x 1.5 hours per robe)) x $3.60.

3. Variable Manufacturing Overhead Spending and Efficiency Variances:
The variable manufacturing overhead spending variance measures the difference between the actual variable overhead costs and the standard variable overhead costs. It can be calculated as Actual Variable Overhead - (Standard Variable Rate x Actual Hours). In this case, the variable overhead spending variance is $3,800 - ($1.20 x 760 hours).

The variable manufacturing overhead efficiency variance assesses the difference between the actual hours worked and the standard hours allowed, multiplied by the standard variable overhead rate. It can be calculated as (Actual Hours - Standard Hours) x Standard Variable Rate. Here, the variable overhead efficiency variance is (760 hours - (2,000 robes x 1.5 hours per robe)) x $1.20.

4. Fixed Manufacturing Overhead Budget and Volume Variances:
The fixed manufacturing overhead budget variance measures the difference between the actual fixed overhead costs and the budgeted fixed overhead costs. It can be calculated as Actual Fixed Overhead - Budgeted Fixed Overhead. In this case, the fixed overhead budget variance is $4,600 - $4,680.

The fixed manufacturing overhead volume variance assesses the difference between the standard hours allowed and the budgeted fixed overhead rate, multiplied by the standard fixed overhead rate. It can be calculated as (Standard Hours - Budgeted Hours) x Standard Fixed Overhead Rate. Here, the fixed overhead volume variance is ((2,000 robes x 1.5 hours per robe) - 780 hours) x $2.40.

By calculating these variances, we can analyze the deviations from the standard costs and identify areas where the actual costs differ from the expected costs.

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It would take approximately 71.5 hours for the activity of the sample of cesium-129 to fall to 18.0 percent of its original value.

To calculate the time required for the activity of a sample of cesium-129 to fall to 18.0 percent of its original value, we can use the formula for half-life:

N = \(N_{0} \frac{1}{2}^{\frac{t}{T} } }\)

Where N is the remaining activity, N0 is the initial activity, t is the time passed, and T is the half-life.

We know that T = 32.0 hours, and we want to find t when N/N0 = 0.18. So we can rearrange the formula as:

0.18 = \(\frac{1}{2}^{\frac{t}{32} } }\)

Taking the logarithm of both sides, we get:

log(0.18) = (t/32)log(1/2)

Solving for t, we get:

t = -32(log(0.18))/log(1/2) = 71.5 hours

Therefore, it would take approximately 71.5 hours for the activity of the sample of cesium-129 to fall to 18.0 percent of its original value.

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Answer:

C) The problem has two operations

Step-by-step explanation:

a) Population of city in 2015 = 640000

b) Population of city in 2019 = 777924

Population-growth happens when an initial population increases by the same percentage or factor over equal time increments or generations.

Given,

Population of city in 2017 (P) = 705600

Rate per annum r = 5% = 0.05

a) Population of city in 2015 (p) = ?

Time difference 2015 and 2017 = 2 years

Population of city in 2017

P = p(1 + r)ⁿ

705600 = p(1 + 0.05)²

p = 705600/1.05²

p = 705600/1.1025

p = 640000

b) Population of city in 2019 = ?

Time difference 2017 and 2019 n = 2 years

Population of city in 2019

= P(1 + r)ⁿ

= 705600(1+0.05)²

=  705600(1.05)²

= 705600 × 1.1025

= 777924

Hence, 640000 is population of city in 2015.

777924 is population of city in 2019

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Answer:

400 miles

Step-by-step explanation:

Distance = rate * time

Distance = 50 miles per hour * 8 hours

Distance = 400 miles

Answer:

400 miles

Step-by-step explanation:

Distance =rate×time

50miles×8hrs=400

The double integral is 1270.5.

To set up a double integral that represents the area of the surface given by z = f(x, y) above the region R, where \(f(x, y) = x^2 - 4xy - y^2\) and R = {(x, y): 0 ≤ x ≤ 9, 0 ≤ y ≤ x}.

We can express the area as the double integral of the function f(x, y) over the region R.

The double integral can be written as:

A = ∬R f(x, y) dA

where dA represents the infinitesimal area element.

Since the region R is defined by 0 ≤ x ≤ 9 and 0 ≤ y ≤ x, we can express the limits of integration for x and y accordingly. The integral becomes:

A = ∫₀⁹ ∫₀ˣ (x² - 4xy - y²) dy dx

Here, the outer integral goes from x = 0 to x = 9, and the inner integral goes from y = 0 to y = x.

The double integral to calculate the area above the region R is given by:

A = ∫₀⁹ ∫₀ˣ (x² - 4xy - y²) dy dx

Integrating the inner integral with respect to y first, we get:

A = ∫₀⁹ [x²y - 2xy² - y³/3]₀ˣ dx

Simplifying this expression, we have:

A = ∫₀⁹ (x³ - 2x²y - y³/3) dx

Now, integrating with respect to x, we get:

A = [x⁴/4 - 2x³y/3 - y³x/3]₀⁹

Substituting the limits of integration, we have:

A = (9⁴/4 - 2(9)³(9)/3 - (9)³(9)/3) - (0⁴/4 - 2(0)³(0)/3 - (0)³(0)/3)

Simplifying further, we get:

A = (6561/4 - 2(729)/3 - (729)/3) - (0)

A = 6561/4 - 1458 - 243

A = 5082/4

A = 1270.5

Therefore, the desired result is 1270.5.

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SOLUTION

The angles at points L and O make up a straight line.

These angles are

Angles on a straight line = 180 degrees. So

Therefore, angle LOQ = 29 degrees

Angle OPQ at point P is opposite to the angle at point L.

The angle at point L = 65 + 35 = 100 degree

Opposite angle of a parallelogram are equal.

Therefore, angle OPQ = 100 degrees

Angle OPL is alternate to angle PLQ. And angle PLQ = 65 degrees

Alternate angles are always equal.

Therefore, angle OPL = 65 degrees

Before we find LQP, let's find LOP.

Recall that LOQ = 29 degrees. So, LOP = 29 + 51 = 80 degrees

LQP is opposite to LOP. Since opposite angles of a parallelogram are equal,

Therefore, LQP = 80 dgrees.

Angle LPQ is alternate to angle OLP. OLP = 35 degrees

Since alternate angles are equal,

Angle LPQ = 35 degrees

The area inside the ellipse is 8π. The area of the interior of the curve is 3π.

a) Using Green's theorem, we can compute the area inside the ellipse using the line integral around the boundary of the ellipse. Let C be the boundary of the ellipse. Then, by Green's theorem, the area inside the ellipse is given by A = (1/2) ∫(x dy - y dx) over C. Parameterizing the ellipse as x = 2 cos(t), y = 4 sin(t), where t varies from 0 to 2π, we have dx/dt = -2 sin(t) and dy/dt = 4 cos(t). Substituting these into the formula for the line integral and simplifying, we get A = 8π, so the area inside the ellipse is 8π.

b) To find a parametrization of the curve x^(2/3) + y^(2/3) = 4^(2/3), we can use x = 4 cos^3(t) and y = 4 sin^3(t), where t varies from 0 to 2π. Differentiating these expressions with respect to t, we get dx/dt = -12 sin^2(t) cos(t) and dy/dt = 12 sin(t) cos^2(t). Substituting these into the formula for the line integral, we get A = (3/2) ∫(sin^2(t) + cos^2(t)) dt = (3/2) ∫ dt = (3/2) * 2π = 3π, so the area of the interior of the curve is 3π.

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Answer:

h(5) = 20

Step-by-step explanation:

Assume that '2' is an exponent.

So the question for you should be:-

\( \displaystyle \large{h(x) = {x}^{2} - x}\)

We want to find h(5); we substitute x = 5 in.

\( \displaystyle \large{h(x) = {5}^{2} - 5}\)

5^2 is 5•5 = 25.

\( \displaystyle \large{h(x) = 25 - 5} \\ \displaystyle \large{h(x) = 20}\)

Therefore, h(5) is 20.

Answer:

B) It represents the product of two irrational numbers and is equivalent to an irrational number.

Step-by-step explanation:

Hi there!

The square root of 3 and the square root of 2 are both irrational numbers, because they do not simplify to a rational number.

Now, let's multiply them together:

\(\sqrt{3} *\sqrt{2}\\=\sqrt{3*2}\\=\sqrt{6}\)

Again, 6 is not a perfect square, so they multiply to another irrational number.

I hope this helps!

It is true that the sample mean and the sample standard deviation remain unaffected.

Mean is the average of the given data.

According to the given question when each entry is multiplied by a constant k each term will k times of the previous term.

Suppose we have 3 terms x, y, z.We know that their mean will the middle term as there are odd number of terms which is y.

Now if we multiply each term by a constant k the terms will be kx, ky, kz and the middle term is ky.

As each term is multiplied by k we have divide by k which is

= ky/k

= y.

So from both the results we can observe that the mean and the standard deviation remains same.

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Answer:

5 : 7

Step-by-step explanation:

groom's side: 40

bride's side: 56

ratio groom to bride = 40/56 = 20/28 = 10/14 = 5/7

Answer: 5 : 7

Option (a) is correct. There'll be No Solution to the given system of linear equations.

According to the solutions of linear equations, we know the following things,
1. If two intersecting lines are at one common point, the system has only one solution.
2. If two coincidental lines mean both equations give the same line, that means the system has infinitely many solutions.
3. If the lines are parallel to each other, the system will have no solution.

We can see lines are parallel but we can also find whether the given lines are parallel or not by simply finding their slope m.

For Line 1, we have the following data
\($\left(\mathrm{x}_1, \mathrm{y}_1\right)=(0,2)$\)

\($\left(\mathrm{x}_2, \mathrm{y}_2\right)=(3,1)$\)

For slope m of the line 1,
slope m₁ = \(\frac{y_2-y_1}{x_2-x_1}=\frac{1-2}{3-0}=-\frac{1}{3}\)

For Line 2, we have the following data

\($\left(\mathrm{x}_1, \mathrm{y}_1\right)=(0,-1)$\)

\(- $\left(x_2, y_2\right)=(3,-2)$\)

For slope m of line 2,
slope m₂\($=\frac{y_2-y_1}{x_2-x_1}=\frac{-2-(-1)}{3-0-x_1}=-\frac{1}{3}$\)

As the slope of both lines is equal, so lines are parallel to each other, and hence, if lines are parallel so there'll be no solution to the system.
Hence, option (a) is correct.

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Your question was incomplete, the most probably question you asked was:

How many solutions does the system of linear equations represented in the graph have? Coordinate plane with one line that passes through the points (0, 2) and (3, 1) and another line that passes through the points (0, -1) and (3, -2).
(a) No solution
(b) One solution at (−1, 0)
(c) One solution at (0, −1)
(d) Infinitely many solutions

Answer:

137 servings.

Step-by-step explanation:

What you need to do is make the denominators the same, then multiply out the numerators to match. After that, just divide it by two.

Using the given conditions that sin(20) = cos(2u) = tan(24) = 3, we can find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas. By substituting the known values into the formulas, we can determine the exact values of these trigonometric functions.

Given sin(20) = 3, we can use the double-angle formula for sine to find sin(2u).

The double-angle formula for sine is sin(2u) = 2sin(u)cos(u). We know that sin(u) = -3/5, so we can substitute this value into the formula to calculate sin(2u).

Therefore, sin(2u) = 2(-3/5)(cos(u)).

Given cos(2u) = 3, we can use the double-angle formula for cosine to find cos(2u).

The double-angle formula for cosine is cos(2u) = cos^2(u) - sin^2(u). Since we already know sin(u) = -3/5 and cos(u) can be calculated using the Pythagorean identity (cos^2(u) = 1 - sin^2(u)), we can substitute these values into the formula to determine cos(2u).

Finally, given tan(24) = 3, we can use the double-angle formula for tangent to find tan(2u).

The double-angle formula for tangent is tan(2u) = (2tan(u))/(1 - tan^2(u)). By substituting the known value of tan(24) = 3 into the formula, we can calculate the exact value of tan(2u).

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To determine if there has been a change in the distribution of motivations for using a credit card among college students, a survey of 425 students was conducted.

The alternate hypothesis states that the distribution of motivations differs from the old survey. The critical value and rejection region need to be determined to test this hypothesis.

To test if there has been a change in the distribution of motivations, the null hypothesis assumes that the distribution remains the same as in the old survey, while the alternate hypothesis suggests a difference. In this case, the alternate hypothesis is that the distribution of motivations differs from the old survey.

To determine the critical value and rejection region, the significance level (α) needs to be specified. In this case, α is given as -0.005. However, it seems there may be some confusion in the provided information, as a negative significance level is not possible. The significance level should typically be a positive value between 0 and 1.

Without a valid significance level, it is not possible to determine the critical value and rejection region for hypothesis testing. The critical value is typically obtained from a statistical table or calculated based on the significance level and the degrees of freedom.

In conclusion, without a valid significance level, it is not possible to determine the critical value and rejection region to test the hypothesis regarding the change in the distribution of motivations for credit card usage among college students.

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