The length of a rectangle is 4 inches longer than it is wide. If the perimeter is 52 inches, what are the
dimensions of the rectangle?

Answer:

[tex]\displaystyle \displaystyle \int {sin(3x)} \, dx = \frac{-cos(3x)}{3} + C[/tex]

General Formulas and Concepts:

Calculus

Antiderivatives - Integrals

Integration Constant C

Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Trig Integration: [tex]\displaystyle \int{sin(x)} \, dx = -cos(x) + C[/tex]

U-Substitution

Step-by-step explanation:

Step 1: Define

[tex]\displaystyle \int {sin(3x)} \, dx[/tex]

Step 2: Identify Substitution Variables

u = 3x

du = 3dx

Step 3: Integrate

Answer:

big

Step-by-step explanation:

pp

Answer:

4536

Step-by-step explanation:

Hesap makinesi kulan

Answer:

the answer is 8/5

Step-by-step explanation:

LCM = 10

(14+2)/10 = 16/10

= 8/5

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Answer:

a)

For Section 1 -

Mode : 45 , 98

Median - 78

Mean - 73.8

Range - 65

Variance - 537.03

Standard Deviation - 23.17

For Section 2 -

Mode : 67 , 77 , 87 , 88 , 98

Median - 77

Mean - 76.4

Range - 55

Variance - 333.11

Standard Deviation - 18.25

b)

Section 2 did better overall on the exam

Step-by-step explanation:

As given,

Section 1: 89, 56, 45, 78, 98, 45, 55, 77, 88, 99, 98, 97, 54, 34, 94

Section 2: 77, 88, 87, 67, 98, 87, 55, 77, 45, 44, 88, 99, 69, 67, 98

a)  

For Section 1 -

Mode : 45 , 98

Median - 78

Mean - 73.8

Range - 65

Variance - 537.03

Standard Deviation - 23.17

For Section 2 -

Mode : 67 , 77 , 87 , 88 , 98

Median - 77

Mean - 76.4

Range - 55

Variance - 333.11

Standard Deviation - 18.25

b)

As,

Standard deviation of section 2 < Standard deviation of section 1

⇒ Students of Section 2 are more consistent.

Also,

mean of Section 2 > mean of Section 1,

⇒average score of Section 2 student > Average score of  Section 1 student.

∴ we get

Section 2 did better overall on the exam.

Answer:

A. 3

Step-by-step explanation:

The formula for slope is (y2-y1)/(x2-x1), for two points (x1,y1) and (x2,y2) on the line.

Our points are (-1,-1) and (1,5):

(5-(-1))/(1-(-1))

6/2

3

The slope of the line shown below is 3.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

We have,

Points from the graph (1, 5) and (-1,-1).

So, the slope of line

= (-1 - 5)/ (-1 - 1)

= -6 / (-2)

= 3

Thus, the slope of line is 3.

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Answer:

 5 8 as decimal is: 0.625

Step-by-step explanation:

What is 5/8 as a decimal?

To write 5/8 as a decimal you have to divide numerator by the denominator of the fraction.

We divide now 5 by 8 what we write down as 5/8 and we get 0.625

And finally we have:

5/8 as a decimal equals 0.625

Answer:

we get 180 minutes; this is equivalent to 3 hours

Step-by-step explanation:

Solving this problem is easier if we convert 2 hr 30 min to min:  150 min.

In the ratio 6:5, the 5 represents the 150 min and we need to determine how long the time interval will be if increased in this ratio.

We write and solve an equation of ratios:

6        x

--- = ------                          This becomes 5x = 900 through cross multiplication.

5     150

solving this for x, we get 180 minutes; this is equivalent to 3 hours.

The time taken should be 180 minutes or 3 hours.

Since there is an increase of 2 hours 30 minutes by the ratio of 6:5​

So here we convert 2 hr 30 min so it comes 150 min.

Now the time taken should be

5x = 900

x = 150 minutes

hence, The time taken should be 180 minutes or 3 hours.

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Answer:

5x-2=3

5x=3+2

5x=5

x=5÷5

x=1

Answer:

option B

Step-by-step explanation:

I did it.

Lamont's total earnings this week come to be $480.

Lamont spends $120 on groceries and this is 25% of the money he earns this week.

This means, $120 = 25% of the total earnings of Lamont

Suppose total earnings =x

The percentage is the value per hundred.

25% of x= [tex]\frac{25*x}{100}=\frac{x}{4}[/tex]

Given [tex]\frac{x}{4} =120[/tex]

So, [tex]x=480[/tex]

So, his total earnings is $480.

Thus, Lamont's total earnings come to be $480.

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Step-by-step explanation:

g*f(x)=g(x+4)=(x+4)³

g*f(-3)=(-3+4)³

= 1³=1

Answer:

follow PEMDAS (parentheses exponents multiplication division add subtract)

Option C is correct, the value of y is 8 square root of 2.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We need to find the value of y.
The given triangle is right angle triangle with opposite side of 8 inches.

Hypotenuse is y and adjacent side is x.

Now let us solve for sinB

sin45 =8/y

1/√2=8/y

Apply cross multiplication

y=8√2

8 square root of 2

Hence, option C is correct, the value of y is 8 square root of 2.

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Answer:

$5809.17

$6149.01

$2211.72

Step-by-step explanation:

Continous interest formula:

(pv)e^(rt)

we have

5000e^(5*.03)= 5809.17

Same equation from before

2500e^(.09*10)= 6149.01

2000e^(.0575*(21/12))

(we write 21/12 because that's how many years has passed)

= 2211.72

sin(45degrees) or BC/AB is 1/sqrt2(that's the value of sin45 degrees I recommend you to memorize this.)

x/12=1/sqrt2

x*sqrt2=12

x=12/sqrt2

Now rationalize this fraction to make the answer more formal.

x=12sqrt2/2(I multiplied both top and bottom by sqrt2)

Now simplify

x=6sqrt2

Question done! answer is C 6 square root of 2

Hope this helped any questions just put them in the comments.

Answer:

6 square root 2

Step-by-step explanation:

Answer:

We have,

3+4(w+5)

=31 Or, 3+20+4w

=31 or, 4w

=31−23

w=8/4

Thus, w comes out to be 2 .

Step-by-step explanation:

Hope it is helpful....

Answer:

w=2

Step-by-step explanation:

3 + 4(w + 5) = 31

distribute 4(w + 5)

4 x w = 4w

4 x 5 = 20

rewrite your equation

3 + 4w + 20 = 31

add like terms

3 + 20 = 23

rewrite equation

4w + 23 = 31

subract 23 on both sides

4w + 23 = 31

-23 -23

4w = 8

divide by 4 on both sides to get w by itself

4w = 8

4      4

w = 2

Answer:

8ile 6 yı çarp sonucu 800 ile topla 48+800= 848

Answer:

72

Step-by-step explanation:

step 1: 10(4+14/7)+12

step 2: 10(4+2)+12

step 3: 10(6)+12

step 4: 60+12=72

Answer:

how are we gonna answer the question if there is no picture of it

Step-by-step explanation:

Answer:

a = 28

Step-by-step explanation:

[tex] a_n = a + (n-1) d[/tex]

[tex] 4 = a + (7-1) (-4)[/tex]

[tex] 4 = a + 6 (-4)[/tex]

[tex] 4 = a - 24[/tex]

[tex] 4 +24= a [/tex]

[tex] a = 28[/tex]

Answer:

y=3/2x-17

Step-by-step explanation:

y-y1=m(x-x1)

y-(-5)=3/2(x-8)

y+5=3/2(x-8)

y=3/2x-24/2-5

y=3/2x-12-5

y=3/2x-17

Answer:

Step-by-step explanation:

15

Answer: 1/2

Step-by-step explanation:4

4

×  

1

2

=  

1

2

Result in decimals: 0.5

Calculation steps:

4

4

×  

1

2

=  

4 × 1

4 × 2

=  

4

8

=  

4 ÷ 4

8 ÷ 4

=  

1

2

Further explanation

For the problem:

4

4

×  

1

2

= ?

Multiply all of the numerators by each other. Do the same with the denominators and form a new fraction with these values:

4 × 1

4 × 2

=  

4

8

The Greatest Common Factor (GCF) of 4 and 8 is 4. The result can be simplified by dividing both the numerator and denominator by 4.

4

8

=  

4 ÷ 4

8 ÷ 4

=  

1

2

The result is:

4

4

×  

1

2

=  

1

2

Answer:

1/2

Step-by-step explanation:

any expression divided by itself is 1

1×1/2

any expression multiplied by 1 remains the same

1/2

60 percentage of the tickets were sold to fans of the home team.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

To find the percentage of tickets sold to fans of the home team,

we need to divide the number of tickets sold to home team fans by the total number of tickets sold, and then multiply by 100 to convert the fraction to a percentage:

Percentage of tickets sold to home team fans = (Number of tickets sold to home team fans / Total number of tickets sold) x 100%

Number of tickets sold to home team fans = 90

Total number of tickets sold = 150

Percentage of tickets sold to home team fans = (90 / 150) x 100%

Percentage of tickets sold to home team fans = 0.6 x 100%

Percentage of tickets sold to home team fans = 60%

Therefore, 60% of the tickets were sold to fans of the home team.

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Answer:

Step-by-step explanation:

boy count is 1476

Explanation:

There is an important difference between the way counts are viewed in ratio to that in fractions.

The ratio of boys : girls

→

4

:

5

so you have 4 boys and 5 girls making the whole count

4

+

5

=

9

in its simplest form.

So to change the ratio proportion into fraction proportion we have:

boys

→

4

9

of the whole.

girls

→

5

9

of the whole.

It is given that the whole is 3321 therefore the count of boys is:

4

9

×

3321

=

1476

Answer:

P value = 0.407

Hence, as P-value (0.407) is greater than 0.1

Fail to reject Null hypothesis

Step-by-step explanation:

Given the data in the question;

sample size n = 13

sample mean x" = 415

standard deviation s = 30

level of significance = 0.1

so;

Null hypothesis H₀ : μ = 417

Alternative hypothesis Hₐ : μ < 417

degree of freedom DF = n - 1 = 13 -1 = 12

Rejection Region { level of significance = 0.1, df = 12 }

critical value of t is - 1.356 as { left tailed test }

Test Statistics;

t = (x" - μ) / [tex]\frac{s}{\sqrt{n} }[/tex]

we substitute

t =  (415 - 417) / [tex]\frac{30}{\sqrt{13} }[/tex]

t = -2 / [tex]\frac{30}{\sqrt{13} }[/tex]

t = -0.24

so, from table;

P value = 0.407

Hence, as P-value (0.407) is greater than 0.1

Fail to reject Null hypothesis