assume that a varies directly as b. when the value of a is 5 the value of b is 18. when the value of a is 22 what is the value of b?

Answer:

x = 2, y = -3 and z = 1.

Step-by-step explanation:

3x+4y-z=-7  ............. A

X-5y+2z=19 ..............B

5x+y-2z=5  ...............C

Adding equations B and C to eliminate z:

6x - 4y + 0 =  24

6x - 4y = 24.............D

Now we multiply Equation A by 2:-

6x + 8y - 2z = -14

Now adding this to equation B, ( again to eliminate z) we get equation E:

7x + 3y = 5 -----------E

Bring down equation D:

6x - 4y = 24.............D

Multiplying  E by 4 and D by 3:

28x + 12y = 20

18x - 12y = 72

Adding:

46x = 92

x = 2.

and substituting in equation D

6(2)- 4y = 24

-4y = 12

y = -3.

Finally we find z by substituting in equation A:

3(2) + 4(-3) - z = -7

-z = -7 - 6 + 12

-z = -1

z = 1.

Answer:

2.5 is the dividend and 0.5 is the divisor.

Step-by-step explanation:

Happy to help

The probability that all 4 players have an ace is approximately 0.00000369 or about 0.00037%.

To find the probability that all 4 players have an ace, we can use the principle of multiplication, which states that the probability of two independent events occurring together is the product of their individual probabilities.

There are 4 aces in the deck of 52 cards. The probability that the first player gets an ace is 4/52. After the first ace has been dealt, there are 51 cards remaining, including 3 aces. Therefore, the probability that the second player gets an ace is 3/51. Similarly, the probability that the third player gets an ace is 2/50, and the probability that the fourth player gets an ace is 1/49.

Using the principle of multiplication, we can multiply these probabilities to find the probability that all four players get an ace:

P(all 4 players have an ace) = (4/52) x (3/51) x (2/50) x (1/49) = 0.00000369

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Answer:

1

Step-by-step explanation:

X power y would be written as 2^0, and any number to the power of 0 is equal to 1.

1

I didn't know this was possible so I looked it up :)

Have an amazing day/afternoon/night! <3

The answers to the respective questions are as follows-a) The current monthly cost is $1267.b) The marginal cost when x = 30 is $24.6 per chair. c) The estimated monthly cost of increasing production to 32 chairs is $49.2.d) The additional monthly cost of increasing production to 32 chairs is $50.22.

a) To find the current monthly cost, we need to evaluate C(30):

C(30) = 0.002*\(30^{3}\) + 0.07(30)*30 + 15(30) + 700

C(30) = 54 + 63 + 450 + 700

C(30) = 1267

Therefore, the current monthly cost is $1267.

b) The marginal cost is the derivative of the cost function with respect to x. So, we need to find C'(x) and evaluate it at x = 30:

C'(x) = 0.006\(x^{2}\) + 0.14x + 15

C'(30) = 0.006*\(30^{2}\) + 0.14(30) + 15

C'(30) = 5.4 + 4.2 + 15

C'(30) = 24.6

Therefore, the marginal cost when x = 30 is $24.6 per chair.

c) The marginal cost represents the additional cost of producing one more unit. So, to estimate the cost of increasing production to 32 chairs, we can multiply the marginal cost by the increase in production:

Cost of increasing production to 32 chairs = 24.6 x 2 = 49.2

Therefore, the estimated monthly cost of increasing production to 32 chairs is $49.2.

d) To find the actual additional monthly cost of increasing production to 32 chairs, we need to find the difference between the cost of producing 32 chairs and the cost of producing 30 chairs:

C(32) = 0.002*\(32^{3}\) + 0.07*\(32^{2}\) + 15(32) + 700

C(32) = 65.536 + 71.68 + 480 + 700

C(32) = 1317.216

Actual additional monthly cost of increasing production to 32 chairs = C(32) - C(30) = 1317.216 - 1267 = 50.216

Therefore, the actual additional monthly cost of increasing production to 32 chairs is $50.22.

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Answer:

10

Step-by-step explanation:

How many times less is 50 than 500?

500/50 = 10

The correct simplification of the expression is c12 (option c).

The expression (c^4)^3 can be simplified using the exponent rules for powers of a power, which states that when a power is raised to another power, we can multiply the exponents.

Thus, we have:

(c^4)^3 = c^(43) [Using the rule (a^m)^n = a^(mn)]

Simplifying the exponent 4*3, we get:

c^(4*3) = c^12

Therefore, the correct simplification of the expression is c^12.

Option (c) is the correct answer as it correctly represents the simplified form of the given expression. Option (a) c^-1, option (b) c^7, and option (d) c^64 are not correct because they do not follow the exponent rules used to simplify the expression.

In summary, the expression (c^4)^3 simplifies to c^12, which is option (c) in the given options.

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Using proportions, the amounts needed of brown and green material for 52 gallons of compost are given as follows:

Brown material: 36 gallons.

Green material: 12 gallons.

A proportion is a fraction of a total amount, and in problems involving it, basic arithmetic operations such as multiplication or division are used along with the unit rates to find the equivalent measures.

On the first column of the table, the total amount is:

⇒ 12.75 + 4.25 = 17 gallons.

So, The fractions of each material are given as follows:

Brown material: 12.75/17 = 0.75

Green material: 4.25/17 = 0.22.

Hence the amount of brown material needed with 48 gallons is:

⇒ 0.75 x 48 = 36 gallons.

And, The amount of green material needed with 48 gallons is:

⇒ 0.25 x 48 = 12 gallons.

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Answer:

3 pairs of shoes cost 189

Step-by-step explanation:

Oh yes it's quite simple but sort of difficult to explain, I'll try the best I can though!

in "C(x)" what ever is in the ( ) is the x value, so where they give you "C(3)" that means x=3. And since in this x represents number of shoes, that means the cost of three shoes is $189.

Hope this helps! If you have any questions about my answer feel free to ask. Stay safe!

Answer: A. Translate 10 units to the right and 8 units up.

Step-by-step explanation:

A ship sails from port a, on a bearing of 050, to port b which is 80km to the east of a. it then sails on a bearing of 062 for 72km until it reaches pot c. West is 270 degrees. Hence Answer would be 80 km.

Answer:

163.75

Step-by-step explanation:

a scale factor applies normally to lengths (one-dimensional sizes).

and the perimeter is calculated just by lengths (the side lengths).

so, we can apply the scaling factor directly to the perimeter.

perimeter of DEF = 5/2 × perimeter of ABC = 5/2 × 65.5 =

= 163.75 ft

what was step 1 ? we did not need it ?

Using a system of equations, it is found that a value of h = 4 will result in an infinite number of solutions.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

If two equations are equal, the system has infinite solutions.

In this problem, the equations are:

4x - 16 = h(x - 4).

Then:

4(x - 4) = h(x - 4).

h = 4.

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The minimum value of the function f(x) =0. 9x2+3. 4x-2. 4 is -3.77 and its parabolic curve is upward because of its minimum value.

Let's consider the equation of a function.

f(x) = \(0.9x^{2} + 3.4x -2.4\)

Now, divide each and every element and assume that a, b, and c are coefficients of the function given.

a: 0.9

b: 3.4

c: -2.4

The sign of the coefficient of a determines the exposure of the parabola. Since a >  0, the parabola is open upwards and has a minimum value.

We can find the "x" of the vertex using the following expression.

x(v) = -b/2a = -3.4/(0.9)

x(v) = -3.77

We can find the "y" of the vertex by replacing this x in the equation

y(v) = 0.9(-3.77)² + 3.4(-3.77) -2.4

y(v)  = -2.42

The minimum value of the function is -3.77

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Answer:

8.5 glasses

Step-by-step explanation:

6.8L / 0.8L = 8.5 glasses

Answer:

8 glasses

Step-by-step explanation:

You divide \(6.8/0.8\)

This gives you 8.5 glasses

since 9 glasses is too much, at 7.2 liters. The maximum glasses possible is 8 assuming you're not filling a half of the glass which would be 8.5 glasses.

Answer:

\(Domain = (-\infty, \infty)\)

\(Range = (-\infty, 4]\)

Increasing interval is: \((-\infty, 0)\)

Decreasing interval is: \((0, \infty)\)

Constant at no interval

Step-by-step explanation:

Given

See attachment for graph

Solving (a): The domain

From, the attached graph, we have:

\(y = -x^2 + 4\)

The degree of the polynomial (i.e 2) is even.

Hence, the domain is the set of all real numbers, i.e.

\(Domain = (-\infty, \infty)\)

Solving (b): The range

The curve of \(y = -x^2 + 4\) opens downward, and the maximum is:

\(y_{max} = 4\)

This means that the minimum is:

\(y_{mi n} = -\infty\)

Hence, the range of the set is:

\(Range = (-\infty, 4]\)

Solving (c): Interval where the function increases/decreases/constant

In (a), we have:

\(Domain = (-\infty, \infty)\)

Split to 2 (at vertex x = 0)

\((-\infty, 0)\) and \((0, \infty)\)

So:

The increasing interval is: \((-\infty, 0)\)

The decreasing interval is: \((0, \infty)\)

The function has a tangent at \(x = 0\) but at no interval, was the function constant

We have

tennis racket price $54

Firs we need to obtain the 30 %

54*.30=16.2

then in order to know the sale price we need to substract the 30% of the original price

54-16.2=37.8

the sale price is $37.8

A difference of 336.49 SAT points is predicted to lead to a colgpa difference of 50.

A coefficient is a numerical value that represents the degree of association or effect of one variable on another.

(i) It makes sense for the coefficient on hsperc to be negative because as hsperc increases, there is a smaller percentage of students who perform better than the individual. Therefore, higher hsperc is associated with lower colgpa.

(ii) When hsperc = 20 and sat = 1,050, the predicted college GPA can be calculated by plugging in the values into the equation:

colgpa = 1.392 - .0135(20) + .00148(1,050) = 1.120

(iii) Holding hsperc constant, the predicted difference in college GPA for two students with SAT scores that differ by 140 points is:

∆colgpa = .00148(140) = .2072

Therefore, the predicted difference in college GPA is about .21 grade points, which can be considered a moderate difference.

(iv) To find the difference in SAT scores that leads to a predicted colgpa difference of .50, we can set up the equation as follows:

.50 = .00148(x)

where x is the difference in SAT scores. Solving for x, we get:

x = 336.49

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The required proportion of cupcakes that have no creme filling with 98% confidence interval is equal to (0.012, 0.058).

Total number of cupcakes = 346

Number of defective cup cakes = 12

Confidence interval = 98%

To construct a confidence interval for the proportion of all cupcakes that have no creme filling,

Use the following formula,

CI = p ± z√((p(1-p))/n)

where,

p = proportion of defective cupcakes

n = sample size

z = z-value for the desired confidence level (98% in this case)

Plug in the values we have,

p = 12/346

  = 0.0347

n = 346

z = 2.33 (from a standard normal distribution table for a 98% confidence level)

CI = 0.0347 ± 2.33√((0.0347(1-0.0347))/346)

   = 0.0347 ± 0.023

So the 98% confidence interval for the proportion of all cupcakes that have no creme filling is (0.012, 0.058).

Therefore, 98% confidence interval that have true proportion of all cupcakes with no creme filling is between 0.012 and 0.058.

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Answer:

y=20.25

Step-by-step explanation:

Answer:

The equation of the line that passes through the point (-6, -7) and has a slope of 1/3 is:

x - 3y + 15 = 0

Step-by-step explanation:

The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis).

To find the equation of the line that passes through the point (-6, -7) and has a slope of 1/3, we can use the point-slope form of a line:

y - y1 = m(x - x1)

Where (x1, y1) is a point on the line and m is the slope of the line.

Plugging in the given values, we have:

y - (-7) = (1/3)(x - (-6))

Which simplifies to:

y + 7 = (1/3)x + 2

Multiplying both sides by 3, we have:

3y + 21 = x + 6

Subtracting 21 and 6 from both sides, we have:

3y - x - 15 = 0

Therefore, the equation of the line that passes through the point (-6, -7) and has a slope of 1/3 is:

x - 3y + 15 = 0

The classification of the polynomials are as follows;

4b) -5·p⁴;

5b) -4 + 7·z is a;

6b) -9·b² - 15 - n;

A polynomial consists of variables and coefficients, joined by mathematical operations such as multiplication, subtraction and addition

4b) A quartic polynomial is a polynomial of the degree 4, and a polynomial with only one term is a monomial, therefore, the polynomial -5·p⁴ is a quartic monomial. The correct option is therefore;

5b) A binomial is a polynomial that has only two terms, while a linear polynomial is a polynomial that has a degree of 1, therefore, the polynomial -4 + 7·z is a linear binomial. The correct option is therefore;

6b) A polynomial with three terms is a known as a trinomial, while a polynomial of degree 2 is a quadratic polynomial, therefore, the polynomial, -9·m² - 15 - m is a quadratic trinomial.

The correct option is therefore;

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Answer:

47:3

Step-by-step explanation:

Answer:

47:3

Step-by-step explanation:

Hope this helps,

Have a good day!!!!

Answer:

\(5\)

Step-by-step explanation:

Let \(x =\) number of smoothies Jackson drank last week.

\(200\% x = 10\)

\(x=10\div 200\%\)

\(=10\div 2\)

\(=5\)

∴ Jackson drank 5 smoothies last week, 10 is 200% of 5.

Hope this helps :)

a) To determine if the sequence bn converges or diverges, we need more information about the sequence bn. The given information only provides the initial term b₁, but we don't have a general formula for the terms of bn. Therefore, we cannot determine the convergence or divergence of the sequence bn.

b) Without additional information about the sequence bn, we cannot directly compare the values of an and bn or make any conclusive statements about their relative magnitudes.

c) The series Σ(2n² + n) diverges. To see why, note that the terms of the series do not approach zero as n goes to infinity. As n increases, the dominant term becomes 2n², which grows without bound. Therefore, the series diverges.

3. a) To determine the convergence or divergence of the series Σ(6n/(5n^2 + 1)), we can use the Comparison Test.

Consider the series Σ(6n/(5n^2 + 1)). We can compare it to the series Σ(6n/(5n^2)), which is a simplified version of the original series by neglecting the "+1" term.

By comparing the two series, we see that 6n/(5n^2) is a fraction that simplifies to 6/(5n). As n goes to infinity, 6/(5n) approaches zero.

Since the series Σ(6/(5n)) is a convergent p-series with p = 1, and the terms of the original series Σ(6n/(5n^2 + 1)) are always less than or equal to the terms of Σ(6/(5n)), we can conclude that Σ(6n/(5n^2 + 1)) converges by the Comparison Test.

c) To determine the convergence or divergence of the series Σ(2n/(3√(n^4 + 1))), we can use the Comparison Test.

Consider the series Σ(2n/(3√(n^4 + 1))). We can compare it to the series Σ(2n/n^2), which is a simplified version of the original series by neglecting the "+1" term and considering the leading terms of the denominator.

By comparing the two series, we see that 2n/n^2 simplifies to 2/n. As n goes to infinity, 2/n approaches zero.

Since the series Σ(2/n) is a convergent harmonic series, and the terms of the original series Σ(2n/(3√(n^4 + 1))) are always less than or equal to the terms of Σ(2/n), we can conclude that Σ(2n/(3√(n^4 + 1))) converges by the Comparison Test.

4. a) To determine the convergence or divergence of the series Σ(2n/(3n - 2)), we can use the Limit Comparison Test.

Let's consider the series Σ(2n/(3n - 2)) and compare it to the series Σ(2n/3n), which is a simplified version of the original series by neglecting the "-2" term and considering the leading terms.

Taking the limit as n approaches infinity of the ratio of the terms:

lim(n->∞) (2n/(3n - 2)) / (2n/3n)

= lim(n->∞) ((2n)/(3n - 2)) * (3n/2n)

= lim(n->∞) (3n^2)/(2n(3n - 2))

= lim

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a) The series bn converges or diverges depending on the value of b₁.

b) The value of an is greater than the value of b for all n ≥ 1.

c) The series Σ(2n² + n)/(n³ - 2cos²n) diverges.

In the second paragraph, we can explain the reasoning and provide justifications for each answer.

a) To determine the convergence or divergence of the series bn, we need to examine the behavior of b₁. Since no specific information is given about the value of b₁, we cannot make a definitive conclusion about the convergence or divergence of bn.

b) Comparing the values of an and b for all n ≥ 1, we can observe that an is always greater than b. This can be justified by analyzing the formulas for an = 2n + n and bn = (, which show that an has a larger summand than b for any given n.

c) For the series Σ(2n² + n)/(n³ - 2cos²n), we can apply the Comparison Test. By comparing it with the divergent p-series Σ1/n, we can see that the terms of the given series do not decrease in magnitude as quickly as the terms of the harmonic series. Therefore, the given series also diverges.

In conclusion, the convergence or divergence of the series bn is undetermined, the value of an is greater than the value of b, and the series diverges.

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Answer:

hbhjb

Step-by-step explanation:

Answer:

2x=3

Step-by-step explanation:

\(x + x = 1 + 1 + 1 \\ 2x + = 3\)

Answer:

We are given x represent the number of pencils purchased, and let y represent the total cost.

We also given 18 pencils for $4.50.

Therefore, cost of each pencil = 4.50/18 = $0.25

Total cost (y) = cost of each pencil × number of pencils.

Therefore, equation would be

y = 0.25x.

In order to graph it, let us find some points for graph using table.

Plugging x=4, we get

y = 0.25(4) = 1.

Plugging x=8, we get

y = 0.25(8) = 2.

We got two coordinates, (4,1) and (8,2).

Plotting those points on the graph and joining the points.

We can see that graph represents the proportional relationship.

Step-by-step explanation:

Answer:

\(13-6x=2\left(8+3x\right)\)

\(13-6x=16+6x\)

\(13-6x-13=16+6x-13\)

\(-6x=6x+3\)

\(-6x-6x=6x+3-6x\)

\(-12x=3\)

\(\frac{-12x}{-12}=\frac{3}{-12}\)

\(x=-\frac{1}{4}\)

or

\(x=-0.25\)

Answer:

-1/4 = x

Step-by-step explanation:

first, we distribute the 2 into the parenthesis

13 - 6x = 2(8 + 3x)

13 - 6x = 16 + 6x

then, we add 6x to both sides to move all of the x terms onto one side

13 - 6x = 16 + 6x

13 = 16 + 12x

next, we subtract 16 on both sides

13 = 16 + 12x

-3 = 12x

next, we divide both sides by 12 to isolate x

-3 = 12x

-3/12 = x

finally, we simplify the fraction

-3/12 = x

-1/4 = x

Answer:

There are 200 base balls

Step-by-step explanation:

240 divided by 6 is 40, times 40 by the 5 and you get 200

Answer:

f is 14 And 8 is E

Step-by-step explanation:

so you have to solve the first step of 14 and 8 it is 90 dress angle