To solve a system of equations, you can use elimination method. This means you will __________ or __________ the two equations to eliminate one variable

Answer:

Surface Area varies by object/shape.

Ask your teacher/learning helper for those formulas of surface area

Step-by-step explanation:

Surface area is the sum of all faces (or surfaces) on a 3D shape. A cuboid has 6 rectangular faces. To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area.

Answer:

You can buy 8.18 gallons of milk.

Step-by-step explanation:

12.79/4.89 = 2.62

21.44/2.62 = 8.18

The statistic that the value 24.7 represents in this context is the median of the gas mileages for the cars tested.

Popular magazine that tests cars and trucks for mileage on the road and around the city. They report that 50% of the cars tested had mileages below 24.7 mpg on the road, and the other 50% had mileages above 24.7 mpg. The 24.7 mpg statistic represents the median of the gas mileages for the cars tested. This is because the median is the middle value when the data is arranged in ascending order, and in this case, it separates the lower 50% from the upper 50% of the mileages.

The median is the value that separates the data set into two halves. In this case, the magazine reports that 50% of the cars tested had mileages below 24.7 mpg on the road and the other 50% of the cars tested had mileages above 24.7 mpg. This means that 24.7 mpg is the exact middle value of the distribution of the gas mileages for the cars tested.

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Answer:

Step-by-step explanation:

For all Plato users

The amount of concrete needed after doubling the diameter of the circle will be multiplied by 4 by the initial amount. Hence, the correct option is (B).

Direct proportions are the proportions where a variable changes with another variable by direct mean so the coefficient of constant will be direct.

For example y ∝ x² here y varies with respect to x square.

y = Kx² where k will be the coefficient of constant.

Given that amount is Amount ∝ d²

Amount = k d²

By doubling the diameter

Amount = k (2d)²

Amount = 4 kd²

Amount = 4 × initial amount hence, the amount will be multiplied by 4.

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Answer:

Step-by-step explanation:

1,3        2,6        4,8

I hope it helps, thank you!

Answer:

John will run out of toner cartridges first

Step-by-step explanation:

First, find how many sheets he can print with the 3 toner cartridges:

3(2000)

= 6000 sheets of paper

Find how many sheets of paper he has:

15(500)

= 7500 sheets of paper

Since 6000 is less than 7500, John will run out of toner cartridges first.

Answer: The values of x are 9 and 1

Step-by-step explanation:

Answer:

X  =  3  √ 2  ( 3 x + 8 )

Step-by-step explanation:

The probability that it will take at least four launches before a second missile fails is 0.784.

Given that,

A specific kind of missile has a 0.30 failure probability. Launches of missiles happen separately.

We have to determine the probability that it will take at least four launches before a second missile fails.

Take k as 2 and p as 0.3.

Using negative binomial distribution,

Required probability is

P(X≥4)= 1-P(X>4)

Using negative binomial distribution,

=1-[P(X=2)+P(X=3)]

=1- [(1  1)(0.3)²(0.7)°+(2  1)(0.3)²(0.7)]

=1-[0.09+0.126]

=0.784.

Therefore, The probability that it will take at least four launches before a second missile fails is 0.784.

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Answer:

3600

Step-by-step explanation:

3000 + 3000(0.20) = 3000 + 600 = 3600

hope this helped!

Answer:

£3600

Step-by-step explanation:

20% of £3000

= \(\frac{1}{5}*3000\)

= (£) 600

So he should sell the car for

3000 + 600

= (£) 3600

Using an exponential function, it is found that:

a) \(N(t) = 75(0.5)^{\frac{t}{3.8}}\)

b) 37.5 grams of the gas remains after 3.8 days.

c) The amount remaining will be of 10 grams after approximately 11 days.

A decaying exponential function is modeled by:

\(A(t) = A(0)(1 - r)^t\)

In which:

Item a:

We start with 75 grams, and then work with a half-life of 3.8 days, hence the amount after t daus is given by:

\(N(t) = 75(0.5)^{\frac{t}{3.8}}\)

Item b:

This is N when t = 3.8, hence:

\(N(t) = 75(0.5)^{\frac{3.8}{3.8}} = 37.5\)

37.5 grams of the gas remains after 3.8 days.

Item c:

This is t for which N(t) = 10, hence:

\(N(t) = 75(0.5)^{\frac{t}{3.8}}\)

\(10 = 75(0.5)^{\frac{t}{3.8}}\)

\((0.5)^{\frac{t}{3.8}} = \frac{10}{75}\)

\(\log{(0.5)^{\frac{t}{3.8}}} = \log{\frac{10}{75}}\)

\(\frac{t}{3.8}\log{0.5} = \log{\frac{10}{75}}\)

\(t = 3.8\frac{\log{\frac{10}{75}}}{\log{0.5}}\)

\(t \approx 11\)

The amount remaining will be of 10 grams after approximately 11 days.

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(a) By plugging in different values for x1, we can plot the indifference curves passing through the given points (2, 2), (1, 2), and (4, 2).

(b) The shape of the indifference curves shows convexity.

(c) The property used to determine this is the non-satiation property of preferences.

(d) The Walrasian demand may not always be single-valued.

(e) Receiving the voucher makes the consumer better-off .

(f) The cash payment allows the consumer to maximize utility by making trade-offs

For 4x1 + x2 = x1 + 2x2, rearranging the equation gives x2 = 3x1, representing the linear part of the indifference curves.

For x1 + 2x2 = 4x1 + x2, rearranging the equation gives x2 = 3x1, representing the kink in the indifference curves.

By substituting different values for x1, we can plot the indifference curves. They will be upward sloping straight lines with a kink at x2 = 3x1.

(b) Properties of the preferences deduced from the shape of indifference curves and utility function:

Diminishing Marginal Rate of Substitution (MRS): Indifference curves are convex, indicating diminishing MRS. The consumer is willing to give up less of one good as they consume more of it, holding the other good constant.

Non-Satiation: Indifference curves slope upwards, showing that the consumer prefers more of both goods. They always prefer bundles with higher quantities.

Convex Preferences: The kink in the indifference curves indicates convexity, implying risk aversion. The consumer is willing to trade goods at different rates depending on the initial allocation.

(c) UMP does not have a solution when Pk = 0 and X -> R2+. This violates the assumption of finite resources and prices required for utility maximization. The property used is non-satiation, as a consumer will always choose an infinite quantity of goods when they are available at zero price.

(d) Walrasian demand depends on relative prices:

If p1 = p2 > 4, the maximizing bundle lies on the linear portion of indifference curves, where x2 = 3x1.

If 4 < p1 = p2 < 1/2, the maximizing bundle lies on the linear portion of indifference curves but at lower x1 and x2.

If p1 = p2 < 1/2, the maximizing bundle lies at the kink point where x1 = x2.

Walrasian demand may not be single-valued due to the shape of indifference curves and the kink point, allowing for multiple optimal solutions based on relative prices.

(e) Given p1 = p2 = 1 and w = $60, the initial budget set is x1 + x2 = 60. With a $10 voucher for good 1, the new budget set becomes x1 + x2 = 70. Since p1 = 1, the consumer spends the voucher on good 1, resulting in x1 = 20 and x2 = 40. Receiving the voucher improves the consumer's welfare by allowing more consumption of good 1 without reducing good 2.

(f) If given the choice between a $10 cash payment and a $10 voucher for good 1 only, the consumer would choose the cash payment. It provides flexibility to allocate the funds based on individual preferences. The answer remains the same even if the assistance were $30, as the cash payment still allows optimal allocation based on preferences. Cash payment offers greater utility-maximizing options compared to the voucher, which restricts choices.

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Answer:

100

Step-by-step explanation:

Givens

WX = 4 + 3 = 7

ZY = 7 + 6 = 13

Height = 4 + 6 = 10

Formula

Area = (WX + ZY ) * height /2

Solution

Area = (7 +13)*10 / 2

Area = 20*10/2

Area = 200/2

Area = 100

Answer:

25.13

Step-by-step explanation:

2(3.14)(4)

4 is the radius 8 would be the diameter

The derivative of t^4*r1(t) is (6t^5, 9t^6, t^4 + 4t^3).

To evaluate the derivative of r1(t).r2(t) using the Product Rule, we first need to find the derivatives of r1(t) and r2(t) separately. The derivative of r1(t) is (2t, 3t^2, 1) and the derivative of r2(t) is (0, 0, e^t). Now we can apply the Product Rule, which states that the derivative of two functions multiplied together is the first function times the derivative of the second function plus the second function times the derivative of the first function. So the derivative of r1(t).r2(t) is:

d/dt (r1(t).r2(t)) = r1(t) * (0, 0, e^t) + r2(t) * (2t, 3t^2, 1)

= (0, 0, t^2*e^t) + (2t*e^3, 2t*e^2, 2t*e^t)

= (2t*e^3, 2t*e^2, t^2*e^t + 2t*e^t)

20. Similarly, to evaluate the derivative of t^4*r1(t) using the Product Rule, we first need to find the derivatives of t^4 and r1(t) separately. The derivative of t^4 is 4t^3 and the derivative of r1(t) is (2t, 3t^2, 1). Now we can apply the Product Rule:

d/dt (t^4*r1(t)) = t^4 * (2t, 3t^2, 1) + r1(t) * 4t^3

= (2t^5, 3t^6, t^4) + (4t^5, 6t^5, 4t^3)

= (6t^5, 9t^6, t^4 + 4t^3)

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since r is so widely used, it is appropriate to calculate r for nonlinear data: False.

The calculation of r (Pearson's correlation coefficient) is based on the assumption that the relationship between the two variables is linear. Therefore, it is not appropriate to calculate r for nonlinear data as it may give misleading results.

In summary, it is not appropriate to calculate r for nonlinear data as it assumes a linear relationship between the variables. Other methods such as Spearman's rank correlation or Kendall's tau may be used for nonlinear data.


n: The correlation coefficient 'r' is specifically designed to measure the strength and direction of a linear relationship between two variables. While it is widely used, calculating 'r' for nonlinear data is not appropriate, as it will not accurately capture the true nature of the relationship between the variables.

When dealing with nonlinear data, it is better to use other statistical methods designed for such data, rather than relying on the correlation coefficient 'r'.

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Answer:

4.5826

Step-by-step explanation:

Your total bill is approximately $7.13.

To calculate the total bill, we need to multiply the weight of each item by its respective price per pound and then sum up the individual costs.

Given the following prices:

Oranges: $1.09 per pound

Grapes: $1.19 per pound

Apples: We'll assume a price of $0.99 per pound for apples.

Let's calculate the total cost:

Cost of oranges = 3.18 pounds * $1.09 per pound = $3.4662 (rounded to two decimal places)

Cost of grapes = 1.15 pounds * $1.19 per pound = $1.3685 (rounded to two decimal places)

Cost of apples = 2.32 pounds * $0.99 per pound = $2.2968 (rounded to two decimal places)

Total bill = Cost of oranges + Cost of grapes + Cost of apples          

= $3.4662 + $1.3685 + $2.2968          

= $7.1315 (rounded to two decimal places)

Therefore, your total bill is approximately $7.13.

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Answer:

Below

Step-by-step explanation:

h = .4 p     <====== given     divide both sides of the equation by .4

h/.4 = p

2.5 h = p       p is 250 % of h    ( 2.5 is decimal for 250%)

If you make annual payments of $1400 for 8 years at a 6% interest rate compounded annually, the total amount accumulated over the 8-year period would be approximately $12,350.

To explain further, when you make annual payments of $1400 for 8 years, you are essentially depositing $1400 into an account each year. The interest rate of 6% compounded annually means that the interest is added to the account balance once a year.

To calculate the total amount accumulated, you can use the formula for the future value of an ordinary annuity:

FV = P * ((1 + r)^n - 1) / r

where FV is the future value, P is the payment amount, r is the interest rate per compounding period (in this case, 6% or 0.06), and n is the number of compounding periods (in this case, 8 years).

Plugging in the values, we have:

FV = $1400 * ((1 + 0.06)^8 - 1) / 0.06

≈ $12,350

Therefore, the total amount accumulated over the 8-year period would be approximately $12,350.

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Answer:

As it is a linear function, not restricted, both the domain and the range are R (set of real numbers), so from minus infinite to plus infinite.

The domain and range of the given function both are the real numbers.

Considering working in real numbers, domain is \(\mathbb{R}\) and range is \(\mathbb{R}\) too.

Domain can be complex numbers too, but for the sake of daily life cases, we consider working in real numbers.

Thinking of it as equation of straight line can help.

The given function is monotonically increasing and continuous.

Thus Range can be calculated as  interval ( f(min value of domain), f(max value of domain) ) which gives us \(\mathbb{R}\) as range.

Below is the plot of f(x) = 3x + 5 in real number plane.

In fact, any linear equation of the form

\(y = mx + c ; \: \: c \in R \: and \: m \in {R-\{0\}}\)

has  both domain and range as real numbers.

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The required white effective interest rate is 0.71% more than his nominal interest rate.

Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.

Here,

White Effective interest R,
\(R=(1+i/m)^m)-1\\R=(1+0.1362/4)^4)-1\\R =0.1433*100=\)
R = 14.33 percent

So

Difference in interest = 14.33%-13.62%
                                    =0.71%

Thus, the required white effective interest rate is 0.71% more than his nominal interest rate.

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It is a function that describes a certain aspect of a sequence based on the relationship between the elements that make up that sequence.

The explicit form of the recurrence relation is:T(n)

= T(n-1) + log2 n; T(0)

= 0Let us find a formula to compute T(n) for any n value. In general, the recurrence relation can be written as: \[T(n)

=T(n-1)+\log _{2} n ; \quad T(0)

=0\]We are given that \[n ! \approx \sqrt{2 \pi n}\left(\frac{n}{e}\right)^{n}\]Let us determine the value of T(n) in terms of the formula of n! by using mathematical induction:Base case: For n=0, T(0) = 0 which satisfies the initial condition.Inductive step:Assume that T(k) has the formula given by the recurrence

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a) The estimated profit for selling 45 beef burgers and 30 veggie

burgers is 546.

b) The food truck would need to sell approximately 643 veggie burgers

to compensate for the decrease in beef burger sales and maintain a

profit of 5240. Rounded up to the nearest whole number, the answer is

644 veggie burgers.

(a) To estimate the food truck's profit when they sell 30 veggie burgers

and only 45 beef burgers, we can use the profit function P(b,v) and

substitute b=45 and v=30:

P(45,30) = 240Pb(45,30) + Pv(45,30)

= 240(2.7) + (-3.4)(30)

= 648 - 102

= 546

(b) To maintain a profit of 5240 when they only sell 45 beef burgers, we

need to find the number of veggie burgers they need to sell.

Let's call this number x.

We can set up an equation using the profit function P(b,v) and the given

information:

P(45,x) = 5240

240Pb(45,x) + Pv(45,x) = 5240

240(2.7)(45) + (-3.4)x = 5240

3060 - 3.4x = 5240

-3.4x = 2180

x ≈ 643

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Answer: 38

Step-by-step explanation:

Subtract 1/8 from 1/2

12 - 18 is 38.

Steps for subtracting fractions

Find the least common denominator or LCM of the two denominators:

LCM of 2 and 8 is 8

Next, find the equivalent fraction of both fractional numbers with denominator 8

For the 1st fraction, since 2 × 4 = 8,

12 = 1 × 42 × 4 = 48

Likewise, for the 2nd fraction, since 8 × 1 = 8,

18 = 1 × 18 × 1 = 18

Subtract the two like fractions:

48 - 18 = 4 - 18 = 38

Answer:

x^2 + y^ = 36

Step-by-step explanation:

See attached worksheet.

Answer:

PLEASE GIVE BRAINLIEST AND THANKS

700mg

Step-by-step explanation:

560 divided by 80= 7

7 x 100=700mg

Answer:

116

Step-by-step explanation: