A car is travelling at a constant speed until the car’s brakes are applied. The car’s speed changes at a rate given by -0.08t ms^{-2} after the brakes are applied, where t s is the time since the brakes were applied. 3 seconds after the brakes are applied, the speed of the car is 5 ms^{-1} . How far will the car travel with the brakes applied before it stops?

Answer:

Step-by-step explanation:

Do you want to know how to write the decimal number 12.95 as a fraction?

Here we will show you step-by-step how to convert 12.95 so you can write it as a fraction.

You can take any number, such as 12.95, and write a 1 as the denominator to make it a fraction and keep the same value, like this:

12.95 / 1

To get rid of the decimal point in the numerator, we count the numbers after the decimal in 12.95, and multiply the numerator and denominator by 10 if it is 1 number, 100 if it is 2 numbers, 1000 if it is 3 numbers, and so on.

Therefore, in this case we multiply the numerator and denominator by 100 to get the following fraction:

1295 / 100

Then, we need to divide the numerator and denominator by the greatest common divisor (GCD) to simplify the fraction.

The GCD of 1295 and 100 is 5. When we divide the numerator and denominator by 5, we get the following:

259 / 20

Therefore, 12.95 as a fraction is as follows:

259 / 20

Answer:

if you meant (b+3)+(2^b-2), the answer is b+1+2^b

Step-by-step explanation:

but if you meant (b+3)+(2b-2), the aanswer is 3b+1

Answer:

3b+1

Step-by-step explanation:

(b+3)+(2b-2)

b+3+2b-2

3-2

b+1+2b

b+2b

3b+1

Answer:

b.$120

Step-by-step explanation:

Party Favors rounded= 40

Dollars rounded= 3

40x3= 120

926+729299277=5289+83783

Answer: 168

Step-by-step explanation:

Times the two numbers together to get the combinations.

24x7=168

Possible number of committees formed is equals to 3.

" Number is defined as the arithmetic value which represents the count of any given quantity."

According to the question,

Total number of candidates for positions = 24

Number of candidate selected  for 1 committee = 7

Total possible number of committees = [tex]\frac{24}{7}[/tex]

                                                               = 3.428

                                                               ≈ 3 committees (approximate)

As one committee is formed by 7 candidates , it can not be in decimals or fractions.

Hence, possible number of committees formed is equals to 3.

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Answer:

$49.28 is the sale cost.

Step-by-step explanation:

0.35 x 75.82 = 26.537

75.82 - 26.537

= 49.283 and round

The selling cost of the book will be equal to $49.28.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Judy is looking to buy a textbook. The book normally costs $75.82, but it is on sale for 35% below the regular cost.

The selling cost of the book will be calculated as,

Selling Cost = 0.35 x 75.82 = 26.537

Selling Cost  = 75.82 - 26.537

Selling Cost  = 49.283

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Answer: the answer is A. The x-intercept shows that he can download 53 songs before running out of storage on his phone

Step-by-step explanation:

Chris got a new cell phone and wanted to download some music. The graph shows the storage on his cell phone as a function of

-intercept in terms of this problem.

A. The x-intercept shows that he can download 53 songs before running out of storage on his phone

B. The x-intercept shows that he started with 16 songs downloaded before adding more.

C. The x-intercept shows that he has 53 GB of storage on his phone.

D. The x-intercept shows that he can download 16 songs before running out of storage on his phone.

Answer:

(-2,2)

Step-by-step explanation:

Answer:

x^2-1

Step-by-step explanation:

you must use the distributive property

first you do x•x=x^2,

then you do x•1 and x•-1 to get x and -x and those cancel out,

the you do 1•-1=-1, then you put it together to get x^2-1

Step-by-step explanation:

It's a factored form of the quadratic equation

[tex] {x}^{2} - 1[/tex]

in the form of [tex] {ax}^{2} + bx + c[/tex]

in which a = 1, b = 0, c = 1.

Answer:

cost of renting from company A

C = 15 + 2.30x

cost of renting from company B

C = 22 + 1.90x

equate both the equations

15 + 2.30x = 22 + 1.90x

2.30x - 1.90x = 22-15

0.4x = 7

x = 7/0.4 = 17.5

At 17.5 miles, cost will be equal.

Answer: 17.5 miles

Answer:

<2 = 28°

Step-by-step explanation:

3y+ 53 = 7y -55 (Corresponding angles)

collect like terms

-4y= -108

y= 27°

3y-53 = 28

<2 =28° (Alternating angles ; 2 parallel lines)

Answer:

Step-by-step explanation:

No . B'  (reflection of B) and C' (reflection of C) are in the right position,  but D' should be at  (4, 1) and A' should be at (-2,-4).

Answer:

p ≥ 1,000,000,000

Step-by-step explanation:

since it says "at-least" that is implying that, that is the estimate and there is most likely more people and it is not exactly 1,000,000,000 so we need to use ≥ to show that it could be greater than or equal to 1,000,000,000.

Using probability of complementary events, it is found that there is a 0.41 probability that such a person moves to one of the higher income classes fifteen years later.

When two events are complementary, the sum of their probabilities are 1.

In this problem, either a person moves to a higher income class or they do not, hence, the events are complementary.

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Answer:

30

Step-by-step explanation:

Answer:

95 minutes

Step-by-step explanation:

Deduct the flat rate from the total to see how much was spent on minutes

9.56 - 1.01 = 8.55

to get minutes divide that by the cost per minute

8.55/0.09 = 95

95 minutes

In the experiment, the response variable is the dependent variable, or the measured variable.

Reasons:

The study Leonard conducts is a study to determine if the number of

hawks located in the park affects the number of squirrels in the park.

The response variable is the variable of the experimental result, which is

the dependent or output variable obtained by manipulating the input

variable.

In the experiment conducted by Leonard, the variable that is being

manipulated, which is the input variable is the number of hawks in the park

The variable that is being measured, which is the output variable or the

response variable, is; B. the number squirrels in the park.

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Answer:

15:8=15/8

Step-by-step explanation:

45:24=45/24

15/8=15:8

Answer: 12

I am not sure what you need help with exactly but

3 ÷ 1/4 = 12

Reason: 3 ×4/1 = 12 3×4= 12/1 take off the 1 and the answer is 12

why 4/1 you would find the reciprocal of 1/4 and the reciprocal of 1/4 is 4/1 or just 4 you dont need the 1 but if you cant handle your math problem without the 1 you can use it but always remember to take out the 1 in your final answer.

I really hopes this helps you.

Answer:

If they both sell half then Kyle would have 1.5:1 and Yasmine would have 18 pennants.

Step-by-step explanation:

It will change because if they both sell half, they would have to multiply by .05  or divide by 2 because that is half of something.

3/2 or 3*0.5 = 1.5

2/2 or 2*0.5 = 1

36/2 or 36*0.5 = 18

So Kyle would have 1.5:1 pennants left and Yasmine would have 18 pennants left.

Answer:

[tex] \frac{13}{50} to \: \frac{12}{25} [/tex]

Answer:

31/18

Step-by-step explanation:

Answer:

The underline one is 40.

Missing numbers. 35, 40 45, 50, 55, 60, 65, 70.

Step-by-step explanation:

Add 5 rule

Answer:

5. The tens place.

6. 35, 40, 45, 50, 55, 60, 65.... (And so on)

Step-by-step explanation:

Hoped this helped.

Just because 2 things are related doesn't mean they will both be changed when one thing happens. For example steak and candy, just because they are both food doesn't mean they taste the same or interact with each other.

Step-by-step explanation:

=> 2x-1/4 + x/3 = 2

=> 3(2x-1) +4x / 12 = 2

=> 6x -3 + 4x = 24

=> 10x = 27

=> x = 2.7

Answer:

x = 27/28

Step-by-step explanation:

Solve 2x-1/4 + x/3 = 2

2x - 1/4 + x/3 = 2

2x + (-1/4) + 1/3x = 2

(2x + 1/3x) + (-1/4) = 2

7/3x + (-1/4) = 2

7/3x = 9/4

3/7 * 7/3x = 3/4 * 9/4

x = 27/28

---------------------

check

2 * 27/28 - 1/4 + 27/28 *1/3 = 2

2 = 2

the answer is good

Answer:

Step-by-step explanation:

Hope this helps!

Answer:

Below

Step-by-step explanation:

The following are true:

B. F is the incenter.

D. F is the point of concurrency of the angle bisectors of the angles of the

F.    F is equidistant from the three sides of the triangle.

The following statements are true:

B. F is the incenter.

D. F is the point of concurrency of the angle bisectors of the angles of the

F. F is equidistant from the three sides of the triangle.

Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles. It is one of the fundamental shapes in geometry and is represented by the symbol Δ. It has three connected vertices.

The circumcenter of a triangle is measured from the point at which the perpendicular bisectors of its sides cross.

The incenter of a triangle is the point at which the triangle's three internal angle bisectors meet.

Thus, the following statements are true:

B. F is the incenter.

D. F is the point of concurrency of the angle bisectors of the angles of the

F. F is equidistant from the three sides of the triangle.

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Let [tex]x = \arcsin(y)[/tex], so that

[tex]\sin(x) = y[/tex]

[tex]\tan(x)=\dfrac y{\sqrt{1-y^2}}[/tex]

[tex]dx = \dfrac{dy}{\sqrt{1-y^2}}[/tex]

Then the integral transforms to

[tex]\displaystyle \int_{x=0}^{x=\frac\pi2} \tan(x) \ln(\sin(x)) \, dx = \int_{y=\sin(0)}^{y=\sin\left(\frac\pi2\right)} \frac{y}{\sqrt{1-y^2}} \ln(y) \frac{dy}{\sqrt{1-y^2}}[/tex]

[tex]\displaystyle \int_{x=0}^{x=\frac\pi2} \tan(x) \ln(\sin(x)) \, dx = \int_0^1 \frac{y}{1-y^2} \ln(y) \, dy[/tex]

Integrate by parts, taking

[tex]u = \ln(y) \implies du = \dfrac{dy}y[/tex]

[tex]dv = \dfrac{y}{1-y^2} \, dy \implies v = -\dfrac12 \ln|1-y^2|[/tex]

For 0 < y < 1, we have |1 - y²| = 1 - y², so

[tex]\displaystyle \int_0^1 \frac{y}{1-y^2} \ln(y) \, dy = uv \bigg|_{y\to0^+}^{y\to1^-} + \frac12 \int_0^1 \frac{\ln(1-y^2)}{y} \, dy[/tex]

It's easy to show that uv approaches 0 as y approaches either 0 or 1, so we just have

[tex]\displaystyle \int_0^1 \frac{y}{1-y^2} \ln(y) \, dy = \frac12 \int_0^1 \frac{\ln(1-y^2)}{y} \, dy[/tex]

Recall the Taylor series for ln(1 + y),

[tex]\displaystyle \ln(1+y) = \sum_{n=1}^\infty \frac{(-1)^{n+1}}n y^n[/tex]

Replacing y with -y² gives the Taylor series

[tex]\displaystyle \ln(1-y^2) = \sum_{n=1}^\infty \frac{(-1)^{n+1}}n (-y^2)^n = - \sum_{n=1}^\infty \frac1n y^{2n}[/tex]

and replacing ln(1 - y²) in the integral with its series representation gives

[tex]\displaystyle -\frac12 \int_0^1 \frac1y \sum_{n=1}^\infty \frac{y^{2n}}n \, dy = -\frac12 \int_0^1 \sum_{n=1}^\infty \frac{y^{2n-1}}n \, dy[/tex]

Interchanging the integral and sum (see Fubini's theorem) gives

[tex]\displaystyle -\frac12 \sum_{n=1}^\infty \frac1n \int_0^1 y^{2n-1} \, dy[/tex]

Compute the integral:

[tex]\displaystyle -\frac12 \sum_{n=1}^\infty \frac1n \int_0^1 y^{2n-1} \, dy = -\frac12 \sum_{n=1}^\infty \frac{y^{2n}}{2n^2} \bigg|_0^1 = -\frac14 \sum_{n=1}^\infty \frac1{n^2}[/tex]

and we recognize the famous sum (see Basel's problem),

[tex]\displaystyle \sum_{n=1}^\infty \frac1{n^2} = \frac{\pi^2}6[/tex]

So, the value of our integral is

[tex]\displaystyle \int_0^{\frac\pi2} \tan(x) \ln(\sin(x)) \, dx = \boxed{-\frac{\pi^2}{24}}[/tex]

[tex]\displaystyle \int \limits_{0}^{ \frac{ \pi}{2} } \tt\tan (x) \ln ( \sin (x))\\ \\\displaystyle \sf{ \implies \: I = \int^{ \frac{\pi}{2} }_{0} \: \ln \left( sin \left( \dfrac{\pi}{2} - x \right) \right) \: dx } \\ \\\displaystyle \sf{ \implies \: I = \int^{ \frac{\pi}{2} }_{0} \: \ln \left( cos(x) \right) \: dx } \\ \\\displaystyle \sf{ \implies \:2I =\int^{ \frac{\pi}{2} }_{0} \:\ln \left( sin(x) \right) \: dx + \int^{ \frac{\pi}{2} }_{0} \: \ln \left( cos(x) \right) \: dx } \\ \\\displaystyle \sf{ \implies \: 2I =\int^{ \frac{\pi}{2} }_{0} \: \ln \left( sin(x) \right) +\ln\left( cos(x) \right) \: dx }[/tex]

[tex]\displaystyle \sf{ \implies \: 2I =\int^{ \frac{\pi}{2} }_{0} \: \ln \left( sin(x) \: cos(x) \right) \: dx } \\ \\\displaystyle\sf{ \implies \: 2I =\int^{ \frac{\pi}{2} }_{0} \: \ln \left( \dfrac{sin(2x)}{2}\right) \: dx } \\ \\\displaystyle \sf{ \implies \: 2I =\int^{ \frac{\pi}{2} }_{0} \:\ln \left( sin(2x) \right)\:dx-\ln(2) \int^{ \frac{\pi}{2} }_{0} \: dx}[/tex]

[tex]\displaystyle\sf{ \implies \: 2I = \dfrac{1}{2} \int^{ \pi}_{0} \: \ln \left( sin(t) \right) \:dt - \ln(2) \int^{ \frac{\pi}{2} }_{0} \: dx} \\ \\\displaystyle\tt{ \implies \: 2I = \dfrac{1}{2} \cdot2 \int^{ \frac{\pi}{2}}_{0} \: \ln \left( sin(t) \right) \: dt - \ln(2) \int^{ \frac{\pi}{2} }_{0} \: dx}[/tex]

[tex]\displaystyle \tt{ \implies \: 2I =\int^{ \frac{\pi}{2}}_{0} \: \ln \left( sin(t) \right) \: dt - \ln(2)\int^{ \frac{\pi}{2} }_{0} \: dx} \\ \\ \displaystyle \tt{ \implies \: 2I = I - \ln(2) \left[x \right] ^{ \frac{\pi}{2} }_{0} } \\ \\ \displaystyle \tt{ \implies \: I = -\ln(2)\left[ \dfrac{\pi}{2} - 0 \right] }[/tex]

[tex]\displaystyle \sf{ \implies \: I = - \dfrac{\pi}{2} \ln(2) }[/tex]

☞︎︎︎Apologies,if incorrect.