On a recent trip to the convenience store, you picked up 3 gallons of milk, 4 bottles of water, and 7 snack-size bags of
chips. Your total bill (before tax) was $23.40. If a bottle of water costs twice as much as a bag of chips, and a gallon of
milk costs $2.20 more than a bottle of water, how much does each item cost?

The given exponential function is increasing so it will be growth and the percentage increase is 97%.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.

As per the given function,

y = 7000(1.97)^x

As x increase the 1.97^x will be increased thus, y will be increased so it will be growth.

Suppose x = 0

y = 7000

Suppose x = 1

y = 1.97 x 7000

% increase = (1.97 x 7000 - 7000)/7000

% increase = 97 %

Hence "The given exponential function is increasing so it will be growth and the percentage increase is 97%".

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The unit price for brand A is $0.0517 and the unit price for brand B is $0.0828. Based on the unit price Brand A is better to buy.

Given that, Brand A has a box of 42 forks for $2.17. Brand B has a box of 48 forks for $3.97.

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

Here,

The cost of each fork of brand A

= 2.17/42

= $0.0517

The cost of each fork of brand B

= 3.97/48

= $0.0828

Therefore, the unit price for brand A is $0.0517 and the unit price for brand B is $0.0828. Based on the unit price Brand A is better to buy.

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The statement that if a is an m × n matrix and b is in r m, the general least-squares problem is  is; TRUE

The way that we compute a least-squares solution of Ax = b is;

By definition, the least squares problem is to find xˆ such that |Axˆ − b| ≤ |Ax − b| for all x in IRⁿ

This means that we are to find a vector x that makes Ax (which is in

the Col(A)) as close to b as possible.

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The amount of principal for the given situation is $87,894.37

What is compound interest?

The interest that is paid on both the initial principal and the accumulated past interest is known as compound interest.

The principal, interest rate, and time period are used to calculate compound interest.

Given, compound amount (A) = $225,300

time period (t) = 12 years

interest rate (r) = 8% = 0.08

compounded semiannually (n) = 2

principal amount (P) =?

Then. the compound amount is given by

[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]

or, [tex]225300 = P(1 + \frac{0.08}{2} )^{2*12}[/tex]

or, [tex]P= 225300/(1+0.04)^{24}[/tex]

or, P = 87,894.37

Hence, the amount of investment today is $87,894.37

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Answer: D

Step-by-step explanation:

Answer:

to be real i don´t think you can do anything because they´re not like terms. you can´t combine them (add) because they don´t have anything in common

Step-by-step explanation:

The quadratic function of the given graph is y = (x + 3)² + 8.

Quadratic function:

Basically, the standard form of the quadratic function is written as,

f(x) = a(x - h)² + k,

And a not equal to zero.

Here if a is positive, the graph opens upward, and if a is negative, then it opens downward. And the line of symmetry is the vertical line x = h, and the vertex is the point (h,k).

Given,

Here we have the graph and we have to find the quadratic function of the graph.

While we looking in to the given graph,

We have identified then the graph is opening the upward direction, So, the value of a is positive.

Now, we have to find the value of a which is 1.

And the vertex of the graph is (-3, 8).

So, the standard form of the quadratic function of the graph is written as,

=> y = (x + 3)² + 8.

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a) The original claim expressed in symbolic form is; p > 0.032

b) The hypotheses are defined as;

Null hypothesis; H₀: p ≤ 0.032

Alternative hypothesis; Hₐ: p > 0.032

A hypothesis is defined as an educated guess while using reasonable thinking, about the answer to a scientific question.

a) We are told that the claim is that more than 3.2% (0.032) of homes have only a landline telephone and no wireless phone. Thus, the original claim in symbolic form is; p > 0.032

b) From the sample survey that we see, it is clear that among 15800 homes, 5.81% had landline phones without wireless phones. This would be the sample proportion.

This means that we can define the alternative hypothesis as;

Hₐ: p > 0.032

Null hypothesis is;

H₀: p ≤ 0.032

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Answer: 1/5

Step-by-step explanation:

Answer: 5/10

Step-by-step explanation:5/10 is the smallest answer here you et get to 0 concluding your answer to 5/10

Answer:

f(3)=13

Step-by-step explanation:

f(x)=5x-2

f(3)=5(3)-2

 =15-2

 =13

The given inequalities have real or infinite solutions and the graph of the given inequalities is given below.

In the given question we have to solve for x and graph the solution on the number line below. If possible, resolve your answer to a single inequality. In case of no solution (∅), leave the number line blank.

The give inequalities are

−3x+4≤−23...............(1)

−29≥−3x+4

We can write it as

−3x+4≤−29.......................(2)

Subtract equation 1 and 2

−3x+4−(−3x+4)≤ −23−(−29)

Simplifying

−3x+4+3x−4≤ −23+29

0≤ 6

The statement is true. 6 is greater than the 0. So inequality have real or infinite solutions.

The graph of the given inequalities is given below;

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The graph of g(x) = f(x - 5) has a slope of 1 and the y-intercept is -5

A graph is a pictorial representation of data and the graph presented represents g(x) = f(x - 5) is attached

The graph shows a linear function written in the slope intercept form  form as

y = mx + c

where

m = slope

c = intercept

x = input variables

y = output variables

Comparing the equation with the above we can see that

m = 1

y intercept, c

this is a point where the graph cuts the y axis

c = -5

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Answer: 0.06 sq km

Step-by-step explanation:

We first convert each dimension from meters to kilometers. 300 meters is equal to 0.3 kilometers. 200 meters is 0.2 kilometers. We now compute the area: 0.3 km * 0.2 km = 0.06 sq km.

The nth term of the series is 0.8 < 1 so, the series converges. Therefore, option C is the correct answer.

Given that, the nth term of a series represented by [tex]a_n=\frac{4^n}{5^{n+1}.n}[/tex].

A convergent series is a series whose partial sums tend to a specific number, also called a limit. A divergent series is a series whose partial sums, by contrast, don't approach a limit. Divergent series typically go to ∞, go to −∞, or don't approach one specific number.

Next term in the series is [tex]a_{n+1}=\frac{4^{n+1}}{5^{n+2}.(n+1)}[/tex]

Now, the ratio is [tex]|\frac{a_{n+1}}{a_n}| =|\frac{\frac{4^{n+1}}{5^{n+2}.(n+1)}}{\frac{4^n}{5^{n+1}.n}}}|[/tex]

⇒ [tex]\lim_{n \to \infty}| \frac{a_{n+1}}{a_n} |= \lim_{n \to \infty} | \frac{\frac{4^{n+1}}{5^{n+2}.(n+1)}}{\frac{4^n}{5^{n+1}.n}}}|[/tex]

⇒ [tex]\lim_{n \to \infty}| \frac{a_{n+1}}{a_n} |= \lim_{n \to \infty} |\frac{4^{n+1}}{4^n}.\frac{5^{n+2}}{5^{n+1}} .\frac{(n+1)}{n} |[/tex]

⇒ [tex]\lim_{n \to \infty}| \frac{a_{n+1}}{a_n} |= \lim_{n \to \infty} |4.\frac{1}{5}} .\frac{(n+1)}{n} |[/tex]

⇒ [tex]\lim_{n \to \infty}| \frac{a_{n+1}}{a_n} |= \frac{4}{5} \lim_{n \to \infty} |\frac{(n+1)}{n} |[/tex]

⇒ [tex]\lim_{n \to \infty}| \frac{a_{n+1}}{a_n} |= \frac{4}{5} \lim_{n \to \infty} |1+\frac{1}{n} |[/tex]

⇒ [tex]\lim_{n \to \infty}| \frac{a_{n+1}}{a_n} |= \frac{4}{5} \lim_{n \to \infty} |1+0|[/tex]

⇒ [tex]\lim_{n \to \infty}| \frac{a_{n+1}}{a_n} |= 0.8[/tex]

Since 0.8 < 1 so the series converges.

The nth term of the series is 0.8 < 1 so, the series converges. Therefore, option C is the correct answer.

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Answer:

From the ratio test, r = 0.8. The series converges.

Step-by-step explanation:

TTT

a) The claim is given as follows:

[tex]\mu < 122[/tex]

b) The null and the alternative hypothesis are given as follows:

The claim in this problem is given as follows:

The mean systolic blood pressure of all healthy adults is less than 122 mm Hg.

Symbolically, the claim is given as follows:

[tex]\mu < 122[/tex].

As:

At the null hypothesis, it is tested if there is not enough evidence to conclude that the claim is true, that is, not enough evidence to conclude that the mean systolic blood pressure of all healthy adults is less than 122 mm Hg, hence:

[tex]H_0: \mu \geq 122[/tex].

At the alternative hypothesis, it is tested if there is enough evidence to conclude that the claim is true, that is, enough evidence to conclude that the mean systolic blood pressure of all healthy adults is less than 122 mm Hg, hence:

[tex]H_1: \mu < 122[/tex].

The questions are given by the image at the end of the answer.

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The test statistics that reject the null hypothesis are given as follows:

t such that |t| > 1.6766.

The null hypothesis is rejected when the test statistic is out of the accept done, defined by the critical value.

The critical value is obtained considering these three features are follows:

These parameters in this problem are given as follows:

Using a t-distribution calculator, the critical value is given as follows:

t = 1.6766.

Hence, as we have a two-tailed test, test statistics with absolute value greater than the critical value reject the null hypothesis.

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The two column proof showing that p ║r is as shown below concluding that p ║r due to The Converse of the Alternate Exterior Angles Theorem

The two column proof will be made up of statements and reasons to prove that p ║r. Thus;

Statement 1; g║ h

Reason 1; Given

Statement 2; ∠1 ≅ ∠2

Reason 2; Given

Statement 3; ∠1 ≅ ∠3

Reason 3; Corresponding angles theorem

Statement 4;  ∠2 ≅ ∠3

Reason 4; Transitive property

Statement 5; p ║r

Reason 5; The Converse of the Alternate Exterior Angles Theorem

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The balance of the account at the end of 21 years, given the deposit amount and the interest rate is $10, 351. 41

The balance on the account at the end of 21 years is the future value of the amount in the account today. This means that this balance can be found by the formula:
= Amount deposited x ( 1 + rate) ^ number of years

The balance on the Credit union client's account after 21 years is therefore:
= 2, 500 x ( 1 + 7%) ²¹

= $10, 351. 41

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Answer:

It is "The y-intercept is one space higher."

Step-by-step explanation:

Assuming your original equation is 6(9)^X, the + 1 at the end is moving the entire function up since all y values that are the output are 1 higher. This means the point on the y-axis will be one higher, leading us to the answer.

Answer: D

Step-by-step explanation:

We can rewrite the equation of the line as [tex]5x-y+12=0[/tex].

Using the perpendicular distance formula, the distance is [tex]\frac{|(5)(5)+(-1)(12)+12|}{\sqrt{5^2 +(-1)^2}} \approx 4.90[/tex]

The solutions to the trigonometric equation sin(2x) = sin(x) on the first quadrant is given as follows:

The trigonometric equation in this problem is defined as follows:

sin(2x) = sin(x).

To verify the solutions, we replace each possible solution into each side of the equation, and verify if they are equal, as follows:

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The value of the given limits [tex]\lim_{x \to \infty} 1/x^2[/tex] is 0,[tex]\lim_{x \to \22} \frac{(x^2-4)}_(x-2)}[/tex] is 4  ,[tex]\lim_{x \to \pi} sinx\\[/tex] is 0 and [tex]\lim_{x \to \55} e[/tex] is e.

Limit, a nearness in mathematical notion, is largely used to give values to some functions at locations that were usually not given or defined, in a manner consistent with neighboring values.

Because the value of that function at that point doesn't define.

a)

[tex]\lim_{x \to \infty} 1/x^2[/tex] by substitute limit 1/∞² = 0

b)

[tex]\lim_{x \to \22} \frac{(x^2-4)}_(x-2)}[/tex] here (x² - 4)/(x - 2) = (x - 2)(x + 2)/(x - 2) = (x + 2)

Putting x = 2 will give the limit as 2 + 2 = 4.

c)

[tex]\lim_{x \to \pi} sinx\\[/tex] herer put x to π so sinπ = 0.

c)

[tex]\lim_{x \to \55} e[/tex] here no variable thus e will be the answer.

Hence "The value of [tex]\lim_{x \to \infty} 1/x^2[/tex] is 0,[tex]\lim_{x \to \22} \frac{(x^2-4)}_(x-2)}[/tex] is 4  ,[tex]\lim_{x \to \pi} sinx\\[/tex] is 0 and [tex]\lim_{x \to \55} e[/tex] is e".

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Answer:

  True

Step-by-step explanation:

You want to know if My-Lien has enough room in a truck with a capacity of 3.385 tons to move 3 5/16 tons of gravel.

The empty space can be found by subtracting the load from the capacity of the truck. The attached calculator output shows there is room for an addition 0.0725 tons.

My-Lien will have enough room to move the gravel.

__

Alternate solution

You can convert 3 5/16 to a decimal: 3.3125. Clearly, this amount is less than 3.3850.

The points that must be on the graph for the quantities to be proportional to each other are (2, 44), (3, 66) and (4, 88)

From the question, we have the following parameters that can be used in our computation:

Championship T-shirts sell for $22 each.

The above parameter means that

The unit rate of a T-shirt = $22

This can be represented as

Unit rate = 22

The interpretation of the above rate is that:

The number of n T-shirts is the unit rate multiplied by n

So, we have the following equation

Cost of n shirts = Unit Rate * n

When the number of shirts is 2, we have

Cost of 2 shirts = 22 * 2

Cost of 2 shirts = 44

When the number of shirts is 3, we have

Cost of 3 shirts = 22 * 3

Cost of 3 shirts = 66

When the number of shirts is 4, we have

Cost of 8 shirts = 22 * 4

Cost of 4 shirts = 88

So, the points are (2, 44), (3, 66) and (4, 88)

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13 is slope of parallel line and -1/13 is slope of perpendicular line.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The given points are  ​(7​, 3​) and ​(6​, −10​)

m=-10-3/6-7

m=-13/-1=13

So slope of line is 13

The equation of line is y=13x+b

Now let us find b.

3=13(7)+b

3=91+b

-88=b

y=13x-88

Now we have to find slope of line parallel to y=13x-88.

The slope of parallel line is 13 because in parallel lines slopes will remain same.

-1/13 is the slope of perpendicular line.

Hence , 13 is slope of parallel line and -1/13 is slope of perpendicular line.

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Answer:

b. 45 ft

Step-by-step explanation:

The scale is 1 in : 3 ft.

1 inch in the model equals 3 feet real.

To go from the model size to the real size, multiply the model inch measurement by 3 and change to feet.

15 inch model size = 15 × 3 ft real size

Answer: 45 ft

Answer:

A and C = 13 and D and E = 24

Step-by-step explanation:

Answer:

0

-7+7 = 0  0/82=0   0x8-3=0

The first guitar lesson will cost (E $80

The cost of the first lesson is solved by comparing the costs

Since the cost of the first lesson is twice the cost of each additional lessons, double counting the first lesson makes the total number of lesson to be 9

if 9 lessons costs $360 then 1 lesson will cost

9 = 360

1 = ?

cross multiplying

8 * ? = 360 * 1

? = 360 / 9

? = 40

The unit cost is 40 taking the double counts makes the first lesson to be 2 * 40 = $80 then other lessons are 40

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