K
If your car gets 30 miles per gallon, how much does it cost to drive 320 miles when gasoline costs $2.80 per gallon?
The cost is $
(Simplify your answer. Round to the nearest cent as needed.)

Answer:

General admission: 895

Reserved seats: 291

Step-by-step explanation:

x = general admission

y = reserved seats

a) 2.50x + 3.50y = 3256

b) x + y = 1186

b) x = 1186 - y

Substitution:

a) 2.50 * (1186-y) + 3.50y = 3256

2965 - 2.50y + 3.50y = 3256

y = 3256 - 2965

y = 291

Substitution:

b) x + 291 = 1186

x = 1186 - 291

x = 895

The length of the hypotenuse is 12.52 yards.

Given that a right triangle, we need to find the value of the hypotenuse x,

Trigonometric ratios can be calculated by taking the ratio of any two sides of the right-angled triangle.

We can evaluate the third side using the Pythagoras theorem, given the measure of the other two sides. We can use the abbreviated form of trigonometric ratios to compare the length of any two sides with the angle in the base.

Let us consider a right-angled triangle with one of its acute angles to be x. Then the cosine formula is, cos x = (adjacent side) / (hypotenuse), where "adjacent side" is the side adjacent to the angle x, and "hypotenuse" is the longest side (the side opposite to the right angle) of the triangle.

We know that, the cosine of the angle is the ratio of the base to the hypotenuse,

So,

Cos 37° = 10 / x

x = 10 / Cos 37°

x = 12.52

Hence the length of the hypotenuse is 12.52 yards.

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Answer: The is down there

Step-by-step explanation: Glad to help but hope it helps you.

Answer:

no. 2/8 is equivalent to 1/4 and not equal to 1/6

The correct answer is option C: \(\(k + 4 = 16\).\) This linear equation represents the relationship between Tina and Kai's volunteer times.

To represent the given situation, the equation that correctly represents the relationship between Tina's volunteer times (Tina = 16) and Kai's volunteer times (Kai = k) is:

\(\[Tina = Kai + 4\]\)

In this equation, Tina's volunteer times are represented by "Tina," and Kai's volunteer times are represented by "Kai." Since Tina has volunteered 4 more times than Kai, we add 4 to Kai's volunteer times to get the total number of times Tina has volunteered.

Substituting the given values, we have:

\(\[16 = k + 4\]\)

This equation represents the fact that Tina has volunteered \(16\) times, which is equal to Kai's volunteer times (k) plus the additional 4 times that Tina volunteered.

Simplifying the equation:

\(\[k + 4 = 16\]\)

This equation is equivalent to the original equation and represents the relationship between Tina and Kai's volunteer times. Hence, the correct answer is option C: \(\(k + 4 = 16\).\)

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The total weight of Rice that Mark buys is given as follows:

2.5 pounds.

The total weight of Rice that Mark buys is obtained applying the proportions in the context of the problem.

The weight of each bag is given as follows:

5/8 pounds = 0.625 pounds.

The number of bags is given as follows:

4 bags.

Hence the total weight of Rice that Mark buys is given as follows:

4 x 0.625 = 2.5 pounds.

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Answer:

I think it is since i already passed that i think that is correct , well good job !!

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

anything that is divided by 0 makes 0

have a good day!

Answer:

D Undefinited

Step-by-step explanation:

(-6 * 3)/0=

-18 * 0 =

-0

Answer:

c, i just got it right on edge

Step-by-step explanation:

Answer:

f(x)=100x

Step-by-step explanation:

Answer:

Step-by-step explanation:

15

The function that can represent the profit P(s) of the sneaker company is D. P(s) = – s2 + 60s – 1,500.

Mathematically, a function shows a set of inputs that produce one output.

Functions have the domain (independent variable) and the codomain or range (dependent variable).

The domain is always the set of input values, while the range is the output value of the function.

Revenue function R(s) = 90s – s2

Fixed cost = $1,500

Variable cost per unit = $30

Profit = Revenue - Variable and Fixed Costs

Profit function P(s) = 90s – s2 - 30s - 1,500

= 60s - s2 - 1,500

or -s2 + 60s - 1,500

Thus, the correct profit function is Option D.

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Cliff pays a total interest of approximately $679.90 on his $5,000 loan.

To calculate the total interest paid on the loan, we need to use the formula for compound interest:

\(A = P(1 + r/n)^{(nt)}\)

Where:

A is the final amount (loan amount + interest)

P is the principal (loan amount)

r is the annual interest rate (in decimal form)

n is the number of times interest is compounded per year

t is the number of years

Given that Cliff takes out a $5,000 loan with a fixed annual interest rate of 7% compounded monthly, we can substitute the values into the formula:

P = $5,000

r = 7% = 0.07

n = 12 (monthly compounding)

t = 2 years

\(A = 5000(1 + 0.07/12)^{(12 \times 2)\)

Calculating this expression:

A ≈ 5000\((1.00583)^{(24)\)

A ≈ 5000(1.13598)

A ≈ 5679.90

The final amount (A) is the loan amount plus the total interest paid. Therefore, to find the total interest paid, we subtract the principal (P) from the final amount (A):

Total Interest = A - P

Total Interest = 5679.90 - 5000

Total Interest ≈ $679.90

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The domain and the range of the piecewise function in this problem are given as follows:

The function in this problem is defined for all values of x between -6 and 2, except x = 0, and assumes all values of y between 0 and 6, except y = 1, hence the domain and range are given as follows:

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Answer:

  about -4.7622

Step-by-step explanation:

You want the cube root of -108.

Your calculator will tell you the cube root of -108 is about -4.7622.

__

Additional comment

Some calculators compute roots using logarithms. Since the logs of negative number are not real, they will give you an error if you try to do this directly. You have to know that the odd index root of a negative number is the opposite of the same root of its absolute value.

The prime factoring of 108 is 2²·3³. Factoring out the perfect cube gives the simplified form ...

  ∛-108 = -3∛4

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Answer:

The 90% confidence interval for the difference between means is (4.189, 8.011).

The point estimate is the difference between sample means and has a value of Md=6.1.

Step-by-step explanation:

We have to calculate a 90% confidence interval for the difference between means.

The sample 1 (American students), of size n1=12 has a mean of 69.4 and a standard deviation of 2.79.

The sample 2 (non-American students), of size n2=17 has a mean of 63.3 and a standard deviation of 3.22.

The difference between sample means is Md=6.1.

\(M_d=M_1-M_2=69.4-63.3=6.1\)

The estimated standard error of the difference between means is computed using the formula:

\(s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{2.79^2}{12}+\dfrac{3.22^2}{17}}\\\\\\s_{M_d}=\sqrt{0.649+0.61}=\sqrt{1.259}=1.12\)

The critical t-value for a 90% confidence interval is t=1.703.

The margin of error (MOE) can be calculated as:

\(MOE=t\cdot s_{M_d}=1.703 \cdot 1.12=1.911\)

Then, the lower and upper bounds of the confidence interval are:

\(LL=M_d-t \cdot s_{M_d} = 6.1-1.911=4.189\\\\UL=M_d+t \cdot s_{M_d} = 6.1+1.911=8.011\)

The 90% confidence interval for the difference between means is (4.189, 8.011).

x = number of small boxes

y = number of large boxes

x + y = 125

20x + 55y = 4425

Let's solve the system.

Isolate y in the first equation:

x + y = 125

y = 125 - x

Now plug that information in the second equation:

20x + 55y = 4425

20x + 55.(125 - x) = 4425

20x + 6875 - 55x = 4425

Now solve for x:

20x - 55x = 4425 - 6875

-35x = -2450

Multiply by -1 both sides:

35x = 2450

x = 2450 / 35

x = 70

So there are 70 small boxes in the delivery truck.

Now let's find the ammount of large boxes. Go back the first equation and plug the value of x:

x + y = 125

70 + y = 125

y = 125 - 70

y = 55

So there are 55 large boxes in the truck.

Answer: there are 70 small boxes and 55 large boxes in the delivery truck.

Melinda practice tennis for 50 minutes.

Given,

Number of balls Melinda hits in a minute = 32

Number of balls Melinda hits before practice = 45

Total number of balls Melinda hit = 1645

We have to find the total time Melinda taken for practice:

Number of balls Melinda hits at practice:

= Total number of balls Melinda hit - Number of balls Melinda hits before practice

= 1645 - 45 = 1600

Now,

The total time Melinda taken for practice:

= Number of balls Melinda hits at practice / Number of balls Melinda hits in a minute

= 1600 / 32

= 50

That is, Melinda practice tennis for 50 minutes.

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Answer:

189 is the next number bacause we multiply 3+3+3=9 now, 9+9+3=21, again ,21+21+3=45 ,again 45+45+3, therefore we observed that this number add itself and its last add 3 so, 93+93+3=189

The next term will be of the sequence is 189.

A sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members. The number of elements is called the length of the sequence.

According to the question

The sequence:       3,    9,    21,    45,    93,

Next term be x

The sequence:       3,    9,    21,    45,    93,    x

Difference :                 6    12      24     48    

as we can see that

every difference is difference of previous terms *2

i.e

6*2 = 12

12*2 = 24

24*2 = 48

48*2 = 96

Therefore ,

The sequence:       3,    9,    21,    45,    93,    x

Difference :                 6    12      24     48    96

i.e

x = 96 + 93

x = 189

Hence , the next term will be of the sequence is 189.

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Hello!

The distance, d, is less than 200 miles.

B. d > 200

The value of x in the triangles are 9.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

The triangles are congruent.

That means, their corresponding angles are also congruent.

In ΔJKL,

the sum of all the angles of the triangle is 180°.

So,

x²-2x + x + 29 + 3x + 52 = 180

x² + 2x - 99 = 0

Solving the quadratic equation,

x² +11x - 9x - 99 = 0.

x (x + 11) -9 (x + 11) = 0

x = 9 and x = -11

Here, we take x = 9.

Therefore, the value of x is 9.

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Answer:

fifty-two. Explanation: g(h(−1 ))=g(x). x=h(−1)=4(−1)−3=−4−3=−7. g(x)= g(−7)=72+3=49+3=52.

Answer:

a) .38 × 2,450 = 931 people buy the local newspaper.

b) 2,450 - 931 = 1,519 people do not buy the local newspaper.

Answer:

0.00085

Hope this helps

Answer:

0.00085

Step-by-step explanation:

2/2348= 0.00085

Answer: C

Step-by-step explanation: A P E X

Answer:

Here the pic

Step-by-step explanation:

According to the information, the missing number from the box is number 40.

To find the missing number of the table we must take into account different elements. In particular we must look at the totals and the columns and rows in which the empty space is. Once we identify the totals we can subtract the other values from the total and find the missing number in the table.

According to the above we can infer that the missing number is 40.

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Answer:

C. 44.805

Step-by-step explanation:

41,390,000 milligrams is 41.39 in kilograms and then 3,415 grams in kilograms is 3.415 so add those up 41.39+ 3.415= 44.805kg

The total weight in kilograms is C. 44.805 kg

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Convert mg to kg;

Caroline weighs 41,390,000 mg

1 mg = 0.000001 kg

41,390,000 mg = x

x = 41,390,000 mg × 0.000001 kg

= 41.39 kg

Now, Converting her baby sister's weight to kg

1000g = 1 kg

3415 g = x

Cross Multiply;

1000x = 3415g × 1 kg

x = 3415g × 1 kg/1000

x = 3.415 kg

Therefore, the total weight in kilograms is;

41.39 kg + 3.415 kg

= 44.805 kg

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