3. At the start of summer, Ben has $250 . He takes a summer
job and saves $ 150 per week. Tim has $ 1,650 at the start of
summer , he travels and spends $ 200 per week. At the end of
which week do Ben and Tim have the same amount of money ?

Answer:

X * 12 = 9

Step-by-step explanation:

The required model of the given situation is given as y = 9 (x + 12).

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
the product of 9 and the sum of the number x and 12 is given as
Let the product is equal to y
y = 9 (x + 12)

Thus, the required model of the given situation is given as y = 9 (x + 12).

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Answer:

[tex]\displaystyle \int \sec\left(\frac{x}{2}\right)\tan^5\left(\frac{x}{2}\right)dx=\frac{2\sec^5\left(\dfrac{x}{2}\right)}{5}-\frac{4\sec^3\left(\dfrac{x}{2}\right)}{3}+2\sec\left(\frac{x}{2}\right)+C[/tex]

Step-by-step explanation:

We want to find the integral:

[tex]\displaystyle \int \sec\left(\frac{x}{2}\right)\tan^5\left({\frac{x}{2}\right)dx[/tex]

First, perform the substitution y = x / 2. This yields:

[tex]\displaystyle dy = \frac{1}{2} \, dx \Rightarrow dx = 2\, dy[/tex]

Hence, the integral becomes;

[tex]\displaystyle =2\int \sec y\tan^5 y \, dy[/tex]

Next, as you had done, let's expand the tangent term but to the fourth:

[tex]\displaystyle =2\int \sec y\tan^4 y\tan y\, dy[/tex]

Recall that:

[tex]\tan^2(y)=\sec^2(y)-1[/tex]

Hence:

[tex]\displaystyle =2\int \sec y(\sec^2 y-1)^2\tan y\, dy[/tex]

We can use substitution once more. This time, let u = sec(y). Hence:

[tex]\displaystyle du = \sec y \tan y \, dy[/tex]

Rewrite:

[tex]\displaystyle =2\int \left((\sec^2y-1)^2\right)\left(\sec y \tan y\right)dy[/tex]

Therefore:

[tex]\displaystyle = 2\int (u^2 - 1)^2\, du[/tex]

Expand:

[tex]\displaystyle =2\int u^4-2u^2+1\, du[/tex]

Reverse Power Rule:

[tex]\displaystyle = 2\left(\frac{u^5}{5} - \frac{2u^3}{3} + u\right) + C[/tex]

Simplify:

[tex]\displaystyle = \frac{2u^5}{5} - \frac{4u^3}{3} + 2u + C[/tex]

Back-substitute:

[tex]\displaystyle = \frac{2\sec^5 y }{5}-\frac{4\sec^3 y}{3}+2\sec y+C[/tex]

Back-substitute:

[tex]\displaystyle =\frac{2\sec^5\left(\dfrac{x}{2}\right)}{5}-\frac{4\sec^3\left(\dfrac{x}{2}\right)}{3}+2\sec \left(\frac{x}{2}\right)+C[/tex]

Therefore:

[tex]\displaystyle \int \sec\left(\frac{x}{2}\right)\tan^5\left(\frac{x}{2}\right)dx=\frac{2\sec^5\left(\dfrac{x}{2}\right)}{5}-\frac{4\sec^3\left(\dfrac{x}{2}\right)}{3}+2\sec\left(\frac{x}{2}\right)+C[/tex]

Answer:

= 2 (sec (x/2) - 2sec³(x/2) +  sec⁵(x/2) ) + C

                              3                     5

Step-by-step explanation:

∫sec(x/2) tan⁵(x/2) dx

apply u substitute u = x/2

= ∫sec(u) tan⁵(u) * 2du

= 2 *  ∫sec(u) tan⁴(u) tan(u) du

= 2 *  ∫sec(u) (tan²(u))² tan(u) du

= 2 *  ∫sec(u) (-1 + sec²(u))² tan(u) du

apply u substitute v = sec(u)

= 2 * ∫(-1 + v²)² dv

expand

= 2 * ∫1 - 2v² + v⁴ dv

sum

= 2 (v - 2v³ + v⁵ )

             3      5

substitute it back

= 2 (sec (x/2) - 2sec³(x/2) +  sec⁵(x/2) )

                              3                     5

add constant to the solution.

= 2 (sec (x/2) - 2sec³(x/2) +  sec⁵(x/2) ) + C

                              3                     5

Answer:

20

Step-by-step explanation:

The total gains of Jack if, In the first play, he gained 12 yards, in the second play lost 15 yards, in the third play gained 25 yards, and in the fourth play lost 2 yards is 20 yards.

The action of subtracting a matrix, vector, or other quantity from another according to predetermined rules in order to find the difference.

In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the total refers to the outcome of the operation.

Given:

In the first play, he gained 12 yards, in the second play lost 15 yards, in the third play gained 25 yards, and in the fourth play lost 2 yards.

Assume the gains can be denoted by positive and loss by negative,

Gains = 12 yards, 25 yards.

Total gain = 12 + 25 = 37 yards

Loss = -15 yards, -2 yards

Total loss = -15 + (-2) = -17 yards

Calculate the total gain as shown below,

Total gain = total gain + total loss

Total gain = 37 + (-17)

Total gain = 20 yards.

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Answer:

3550

Step-by-step explanation:

I hope this helps!

Answer:

3550

Step-by-step explanation:

Round each number: 709 ⇒ 700, 645 ⇒ 650, 798 ⇒ 800, 704 ⇒ 700, 658 ⇒ 700

Add the rounded numbers: 700 + 650 + 800 + 700 + 700

Start slow: 700 + 650 = 1350

1350 + 800 = 2150

2150 + 700 = 2850

2850 + 700 = 3550

Answer:

4 pints

Step-by-step explanation:

16 oz in a pint

Answer:

31xy

Step-by-step explanation:

28xy + 3xy = 31xy

Answer:

Step-by-step explanation:

Step-by-step explanation:

A good example that comes to find is the fuel gauge found on a car, this gauge allows the driver to monitor the percentage of fuel left in the car.

Let's assume the car fuel tank has a capacity of 100 liters. if the indicator is showing half-filled, to illustrate this in percentage it is written as 50% while decimal it will be 0.5.

Answer:

You spent $1349

Step-by-step explanation:

sweaters s = $29

t-shirts t = $16

pants p = $25

Cost = C

28s + 7t + 17p = C

28 ($29) + 7 ($16) + 17 ($25) = C

$812 + $112 + $425 = C

$1349 = C

Answer:

21

Step-by-step explanation:

The answer is negitive 21 becuase it you sub and

After conducting some mathematical operations, we can conclude that Florida is warmer than Texas by 21°F.

So, Florida is warmer than Texas by:

Now, calculate as follows:

Therefore, after conducting some mathematical operations, we can conclude that Florida is warmer than Texas by 21°F.

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Answer:

$4.44

Step-by-step explanation:

Cost per yard = $10/2.25

= $4.44 (nearest cent)

the answer $ 4.44

explanation :

so first of all you need to divide 10 by 2 1/4

when you divide both number you'll get 4 4/9

4 4/9 can also be written as 4.44444444444

which is also 4.4 recurring

now we can round this off

when you round it off, you should round it off to two decimal points cause the answer should be in dollars

you should get 4.44 as an answer

so the answer will be $ 4.44

really hope that helped :)

Answer:4782984

Step-by-step explanation:

Answer:4782984

Step-by-step explanation:

Answer:

$50 is profit because every $50 it intersects.

X would be the $50 so 10x50=500-150=which would be $350.

I think this is right hope this helps!

Answer:

Step-by-step explanation:

y -6 = -3(x + 1)

y - 6 = -3x - 3

y = -3x + 3

Answer:

The numbers are 25 and 26.

Step-by-step explanation:

When you multiply 25 with 26 you get their product, 650. And when you add them you get the answer 51.

Answer:

1.00-.35=.65

.65×140.00=$91.00

Answer:

4/5*3/4&6/7*2/5

Step-by-step explanation:

4/5*3/4=12/20

6/7*2/5=12/35

Answer:

[tex]n=26[/tex]

Step-by-step explanation:

So we have the equation:

[tex]-413.4=-15.9n[/tex]

To figure out the value of n, divide both sides by -15.9. The right will cancel. Thus:

[tex]n=(-413.4)/(-15.9)[/tex]

Use a calculator:

[tex]n=26[/tex]

So, the answer is 26.

So, yes, you are very correct!

Answer:

n=26

Step-by-step explanation:

We are given the equation:

[tex]-413.4=-15.9n[/tex]

We want to solve for the unknown variable, which is n. Therefore, we must isolate n on one side of the equation.

n is being multiplied by -15.9. The inverse of multiplication is division. Divide both sides of the equation by -15.9

[tex]\frac{-413.4}{-15.9} =\frac{-15.9n}{-15.9}[/tex]

[tex]\frac{-413.4}{-15.9}=n[/tex]

[tex]26=n[/tex]

Let's check our solution. Plug 26 in for n and solve.

[tex]-413.4=-15.9n[/tex]

[tex]-413.4=-15.9(26)[/tex]

Multiply -15.9 and 26.

[tex]-413.4=-413.4[/tex]

This checks out, so we know our solution is correct.

The solution to this equation is n=26 and you are correct!

Answer:

false or not true

Step-by-step explanation:

5x + 8x < 4x + -7

combine like terms

13x<4x+-7

4x divided by 4  -7 divided by 4

x= -7/4

13x<-7/4

Answer:

92%

Step-by-step explanation:

Answer:

0.00000014 x

Step-by-step explanation:

Answer: 3 seconds

Step-by-step explanation: the pump fills 1 tire per second

The answer to your question is 4.8 kilometers. Brainliest?

Answer:

1.86

Step-by-step explanation:

Answer:

there are 4 quarts in a gallon so therefore the glasses are half a quart

Step-by-step explanation:

yes

Answer:

4096

Step-by-step explanation:

Answer:

4096

Step-by-step explanation:

4 to the third power is 64 and 64 to the 2nd power is 4096 so that should be your answer

Answer:

(a) Shown below

(b) Positively Skewed

(c) No Outlier

(d) 15%

Step-by-step explanation:

Arrange the data set in ascending order as follows:

S = {5.7 , 6.2 , 6.3 , 6.5 , 6.8 , 6.8 , 7 .0, 7 .0, 7.2 , 7.3 , 7.4 , 7.6 , 7.7 , 7.7 , 7.8 , 7.8 , 7.9 , 8.1 , 8.2 , 8.7 , 9 .0, 9.7 , 9.7 , 10.6 , 11.5 , 11.6 , 11.8}

(a)

Construct a stem-and-leaf display of the data as follows:

5 | 7

6 | 2  3  5  8  8

7 | 0  0  2  3  4  6  7  7  8  8  9

8 | 1  2  7

9 | 0  7  7

10 | 6

11 | 5  6  8

The representative strength value is the mid-value.

The mid-value is: 7.7

Thus, the representative strength value is 7.7.

(b)

No, the data does not appear to be highly concentrated about the representative value or rather spread out.

As we take the stem-and-leaf plot into consideration we observe that most of the observations are concentrated towards the right of the graph.

So, the data is right or positively skewed.

(c)

No, there doesn't appear to be any outlying strength values.

This is because all the values are closer to each other and none of the observations are too extreme.

(d)

The number of observations more than 10 MPa is, 4.

Total number of observations, 27.

Compute the proportion of strength observations that exceed 10 MPa as follows:

[tex]P(>10\ \text{MPa})=\frac{4}{27}=0.14815\approx 0.15[/tex]

Thus, the proportion of strength observations that exceed 10 MPa is 15%.