11) Carlos wants to mix granola and cranberries together to make trail mix. Granola costs $3 per pound and cranberries cost $5.50 per pound. Carlos is willing to spend $29 and wants to make 8 pounds of trail mix. Which system of equations could Carlos use to figure out how many pounds of granola (g) and cranberries (c) she should buy?

Paying off the lowest outstanding balance credit card first can be beneficial for motivation and momentum, even if it's not the most mathematically efficient approach.

When paying off credit card debt, it can be beneficial to start by paying off the credit card with the lowest outstanding balance. This approach is called the Snowball Method and is popularized by financial expert Dave Ramsey. The Snowball Method focuses on tackling the smallest debt first, regardless of the interest rate, as it provides a psychological boost and motivates individuals to continue paying off their debts.

By paying off the smallest debt first, you can quickly eliminate one of your credit card balances. This can give you a sense of accomplishment and momentum to continue paying off your other debts. It's important to note that while the Snowball Method may not be the most mathematically efficient approach in terms of saving on interest payments, it can be effective in helping individuals stay motivated and committed to paying off their debts.

The surface area of a soap bubble with a volume of 5 cm³, given the relationship V = 0.094 [tex]A^{3/2[/tex], can be calculated by rearranging and solving the formula, resulting in an approximate surface area of 36.3 cm².

To find the surface area of a soap bubble with a volume of 5 cm³, using the given relationship V = 0.094 [tex]A^{3/2[/tex], we need to rearrange the formula to solve for A (the surface area). We will take the following steps to find A:

First, divide both sides of the equation by 0.094 to isolate [tex]A^{3/2[/tex] on one side:

[tex]A^{3/2[/tex] = V / 0.094

Next, substitute V = 5 cm³ into the equation:

[tex]A^{3/2[/tex] = 5 / 0.094

Calculate the right-hand side:

[tex]A^{3/2[/tex] ≈ 53.19

Finally, raise both sides of the equation to the power of 2/3 to solve for A:

A = [tex](53.19)^{2/3[/tex]

Calculating the right-hand side gives us the surface area A. After performing these calculations, we find that the surface area of a bubble with a volume of 5 cm³ is approximately 36.3 cm².

Answer:

The correct answer is, mRs = 121°

Step-by-step explanation:

From figure we get ,

mAR=55° mRB=66° AB=8 m RS=8 m

To find mRS

Using given information we can write,

mAB = mAR + mRB = 55 + 66 = 121°

Since AB=8 m RS=8 m,

AB = RS

⇒ mAB = mRS

mAB = 121°

Therefore mRS = 121°

The correct answer is given by,

mRS = 121°

Answer: [tex]81^{\circ}\ \text{ and }\ 9^{\circ}[/tex]

Step-by-step explanation:

We know that the sum of two complementary angles is [tex]90^{\circ}[/tex].

Given : An angle measures 72° less than the measure of a complementary angle.

Let x be the angle , then the measure of other angle will be x-72.

Since they area complementary , then we have

[tex]x+x-72=90\\\\\Rightarrow\ 2x=90+72\\\\\Rightarrow\ 2x=162\\\\\Rightarrow\ x=\dfrac{162}{2}=81[/tex]

Therefore, the measure of angles are :

[tex]81^{\circ}\ \text{ and }\ (81-72)^{\circ}=9^{\circ}[/tex]

Answer:

decay

just answered this question.

Step-by-step explanation:

Answer:

decaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecay

Step-by-step explanation:

The solution of  x  is √(S/6).

The formula to find the surface area of a cube with side lengths x is:

S = 6x2

To solve for x:

Divide both sides by 6: S/6 = x2

Take the square root of both sides to isolate x: x = √(S/6)

Answer:

37.5 miles is the answer.

Step-by-step explanation:

Since car is travelling with a speed = 50 mph

Angle between the highway and the track on which the car is travelling = 30°

Now we know sin∅ = distance between highway and the car/Distance traveled by the car on the new track

Distance traveled by the car in 1.5 hours = speed × time

                                                                   = 50 × 1.5 = 75 mi.

Therefore sin 30° = x/75

x = 75×sin30° = 75 × 1/2 = 37.5 mi.

Therefore the answer is 37.5 mi away.

Variance is not expressed in the same units as the original data.

Variance is measured by:

Because variance is squared, it is no longer the same units as the rest of the data set. For instance, if the data set is in centimeters, the variance will be in centimeters².

In conclusion, the variance of a data set is not measured in the same unit as the data set.

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Final answer:

The measure of dispersion which is not measured in the same units as the original data is the variance.

Explanation:

The measure of dispersion which is not measured in the same units as the original data is the variance. The variance is a squared measure and does not have the same units as the data. On the other hand, the standard deviation is derived from the variance and it measures the spread in the same units as the data.

Then again, the standard deviation, which is the square foundation of the fluctuation, is estimated in similar units as the first information. It gives a proportion of the spread of the information that is all the more effectively interpretable. The middle is a proportion of focal inclination and doesn't give data about the scattering or spread of the information.

The coefficient of assurance, otherwise called R-squared, is a proportion of how well the relapse line fits the information and isn't straightforwardly connected with scattering.

No, at least one segment length is not preserved, making this a nonrigid transformation. Option B is correct.

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

It is given that, all side lengths of ΔJKL equal 2 units. A transformation maps ΔJKL to ΔJ'K'L'. The length of side J'K' is 5 units.

A transformation that leaves a geometric figure's size or shapes unchanged is known as a rigid transformation. It is a unique type of metamorphosis in which a figure's size or shape is left unchanged.

From the definition, it is obtained that there is no rigid transformation because at least one segment length is not preserved.

Thus, no at least one segment length is not preserved, making this a nonrigid transformation. Option B is correct.

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Answer:

Option B 61.10

Step-by-step explanation:

Given is a chart giving the premium to be paid for 10 year term insurance for different age groups for an amount of 1000 policy.

We have to calculate the premium for a 35 year old man for 10 year term insurance for 10000 policy.

From the chart we find that for a 35 year old man premium = 6.11

This premium is for 1000 dollars.

Since here sum assured is 10000 dollars, we get the premium

=6.11(10) = 61.10 dollars

Option B is correct

Premium = 61.10 dollars

Final answer:

To solve this problem, we set up equations based on the total number of eyes and legs. By solving the system, we find that the group consists of 5 horses.

Explanation:

The question asks us to solve a problem involving a group of kids and horses by using the given information about the total number of eyes and legs. Since humans have two eyes and two legs, and horses have two eyes and four legs, we can set up a system of equations to find the solution.

Let's denote the number of kids as 'k' and the number of horses as 'h'. Since each human and horse has two eyes, the total number of eyes is given by the equation: 2k + 2h = 20. Similarly, the total number of legs is given by the equation: 2k + 4h = 30. Solving these equations will give us the number of kids and horses in the group.

Solving for 'k' from the first equation gives us k = 10 - h. Substituting this into the second equation gives us 2(10 - h) + 4h = 30. Simplifying this equation results in 20 - 2h + 4h = 30, which further simplifies to 2h = 10, and thus h = 5. Therefore, there are 5 horses in the group.

Answer:

$3.40

Step-by-step explanation:

To find out the amount each person paid, let's find the total cost of the pretzels first.

6 pretzels ----- $5.10

1 pretzel ----- $5.10 ÷6= $0.85

8 pretzels ----- 8($0.85)= $6.80

The total cost of 8 pretzels is thus $6.80.

Since the total cost was shared equally amongst two people, each person paid half of the total cost.

Amount each person paid

= $6.80 ÷2

= $3.40

By taking a quotient between the total cost and the number of people, we can see that each one pays $3.40

We know that the price of 6 pretzels is $5.10, then the price for each pretzel is given by the quotient:

$5.10/6 = $0.85

We know that Simon and Sofia bought 8 pretzels, so they pay:

P = 8*$0.85 = $6.80

And they divide that evenly between the two, so we can take the quotient:

p = $6.80/2 = $3.40

That is the amount that each person pays.

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