Write an equation of the line with a slope of -3 and y -intercept of 0 .

y=

Answer: 3/4 hour

Step-by-step explanation: Add them all to get 3 3/4. subtract that from 4 1/2.

Answer:

Q13)A man is four times as old as his son. After 20 years, he will be twice as old as his son at that time. Find their present ages. Present age of the father is = 4 x = 4 × 10 = 40 4x=4\times10=40 4x=4×10=40 years.

Answer:

Length=14.4

Width=3.6

Step-by-step explanation:

l=4w

2l+2w=36

2(4w)+2w=36

8w+2w=36

10w=36

w=3.6

l=4w

4(3.6)

l=14.4

*check by plugging in answers into 2l+2w=36*

Answer:

[tex]L=\frac{72}{5}[/tex]      or 14.4

[tex]W=\frac{18}{5}[/tex]     or 3.6

Step-by-step explanation:

Please take note this probably not the easiest way to do the problem.

Formula for the Perimeter of Rectangle

[tex]P=2L+2W[/tex]

We are given the perimter.

[tex]36=2L+2W[/tex]

[tex]L=4*W[/tex]

To solve I would use the Gauss-Jordan method. (it is advanced, but it makes sense to me)

[tex]36=2L+2W[/tex]

[tex]L=4*W[/tex]

Write the coefficients of each eqaution as rows in the matrix.

[tex]\left[\begin{array}{ccc}2&2&36\\1&-4&0\\\end{array}\right][/tex]

Divide the first row by 2.

[tex]\left[\begin{array}{ccc}1&1&18\\1&-4&0\\\end{array}\right][/tex]

Multiply row 1 by -1 and add it to row 2.

[tex]\left[\begin{array}{ccc}1&1&18\\0&-5&-18\\\end{array}\right][/tex]

Divide the second row by -5.

[tex]\left[\begin{array}{ccc}1&1&18\\0&1&\frac{18}{5} \\\end{array}\right][/tex]

Multiply row 2 by -1 and add it to row 1.

[tex]\left[\begin{array}{ccc}1&0&\frac{72}{5} \\0&1&\frac{18}{5} \\\end{array}\right][/tex]

We now have an augmented matrix.

[tex]L=\frac{72}{5}[/tex]

[tex]W=\frac{18}{5}[/tex]

Answer:

$3,623.84 Exact answer without rounding | $3,623.85 ~ (Approximent Answer with rounding.)

Step-by-step explanation:

Compound Interest Has a Specific Formula:

This case is Exponential Growth.

Formula: y= ab^x

You need to set up the equation.

First we need to define the rate of growth meaning what do you have to do for the 6.5%.

You need to do 100% + 6.5% = 106.5%

You need to convert the percent to a decimal which will be 1.065

Now we need to start plugging things into our formula to solve.

Your initial Starting amount was $3000

So you need to have y=3000(b)^x

We now know that the rate of growth is 1.065 so the b would be 1.065

y=3000(1.065)^x

Our power to x is our 3.5 years.

Our Equation now:

y=3000(1.065)^3

Now you need to use a calculator to do this due to the amount of decimals and digits.

Remember pemdas when doing this!!!

The answer should result to $3,623.84 but if rounded then: $3,623.85

The value of cos (a+b) when cos a= 3/5 with 0<a< π/2 and Sin b = - 8/17 with 3π / 2 <b < 2 π​, is 0.906.

According to the triangle angle sum theorem, the sum of all the angle(interior) of a triangle is equal to the 180 degrees. The formula for cos compound angle using angle sum theorem can be given as,

[tex]\cos (a+b)=\cos (a)\cos (b)-\sin (a)\sin (b)[/tex]

The exact value of cos (a+b)  has to be find out. It is given that,

[tex]\cos a= \dfrac{3}{5}[/tex]

The value of a is lies between 0<a< π/2. The value of other side of the triangle using the Pythagoras theorem,

[tex]5^2={x^2+3^2}\\x^2=25-9\\x=\sqrt{16}\\x=4[/tex]

Thus, the value of sin a is 4/5 from the trigonometry ratio. the value of sine b is,

[tex]\sin b = -\dfrac{8}{17}[/tex]

The value of b is lies between  3π / 2 <b < 2 π​. The value of the other side of the triangle using the Pythagoras theorem,

[tex]17^2={(-8)^2+y^2}\\y^2=289-64\\y=\sqrt{225}\\y=15[/tex]

Thus, the value of cos b is, 15/17. Put the values in above formula,

[tex]\cos (a+b)=\cos (a)\cos (b)-\sin (a)\sin (b)\\\cos (a+b)=\dfrac{3}{5}\times\dfrac{15}{17}-\dfrac{4}{5}\times\dfrac{-8}{17}\\\cos (a+b)=\dfrac{9}{17}+\dfrac{32}{85}\\\cos (a+b)=0.906[/tex]

Thus, the value of cos (a+b) when cos a= 3/5 with 0<a< π/2 and Sin b = - 8/17 with 3π / 2 <b < 2 π​, is 0.906.

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The volume of the bag of nuts is the amount of nuts it can contain

The volume of the bag of nuts is 84.78 cubic inches

From the figure, we have the following parameters:

The volume of a cone is calculated using:

V = 1/3 πr^2h

Substitute the known values

V = 1/3  * 3.14 * 3^2 * 9

Evaluate the product

V = 84.78

Hence, the volume of the bag of nuts is 84.78 cubic inches

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Answer:

57

Step-by-step explanation:

There are 30 English

There are 28 German

There is one that speaks all 3

30 + 28 - 1 = 57

Answer:

Daughter is now 10 The mother is 30

Step-by-step explanation:d

d=daugter

5d=mother

5d = 2d +5 +10

3d =15

d=5

5 years ago    d=5  m=25

now                  d=10 m=30

in10 years        d=20 m=40

Answer:

option A

Step-by-step explanation:

Answer os option a

Answer:

180

Step-by-step explanation:

because there are 60 minutes in an hour and you need 3 you need to add 60 + 60 + 60 or your can do 60 x 3 which equals 180

Answer:

180 minutes

Step-by-step explanation:

1 hour - 60 minutes

2 hours - 120 minutes

3 hours - 180 minutes

Because there is 60 minutes in an hour, you can do 60 x 3 = 180. This will directly tell us how many minutes are in 3 hours. Or, you can add 60 minutes 3 times for 3 hours.

So, 60 x 3 = 180. There are 180 minutes in 3 hours.

Answer:

There are 1.07 non winners in group A for every 1 non winner in group B

Or: 1.07:1

Or: 7% more non winners in group A

Step-by-step explanation:

Group A:

765*3/5 = 459 non winners

Group B:

716*3/5 = 429 non winners

Final Calculation:

459/429 = 1.07

Answer:

put x=1/2, you will get, r(1/2)=20*1/2-89

=10-89= -70.

hope it will help.

Check the picture below, so the circle looks more or less like so, with a radius of 9.

[tex]\textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=9 \end{cases}\implies C=2\pi (9)\implies C\approx 57[/tex]

Answer:

See below ↓↓

Step-by-step explanation:

A to B

C to D

Answer:

3/10

Step-by-step explanation:

Taking the decimal values (upto the thousandths place)

Clearly,

3/10 is the smallest number among the given options.

Given that are numbers we need to check which is the smallest from this,

To determine which of the given numbers is the smallest, we can compare them by finding a common denominator and then comparing the numerators.

The common denominator for 1/3, 3/10, 2/5, and 3/8 is 120 (the least common multiple of 3, 10, 5, and 8).

Now, let's convert each fraction to have a denominator of 120:

1/3 = 40/120

3/10 = 36/120

2/5 = 48/120

3/8 = 45/120

Comparing the numerators, we can see that 36/120 (3/10) is the smallest.

Therefore, 3/10 is the smallest number among the given options.

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The elevation of the plane is 3600 ft

Let

From the triangle, we have the trigonometric ratio

tanФ = h/D

Making h subject of the formula, we have

h = DtanФ

substituting the values of the variables into the equation, we have

h = DtanФ

h = 3600 ft × tan45°

h = 3600 ft × 1

h = 3600 ft

So, the elevation of the plane is 3600 ft

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Answer:

1/36

Step-by-step explanation:

The chance of you rolling a 5 is 1/6

While the chance of you rolling a 3 is a 1/6

If you want both a 5 then a 3 then you multiply the fractions

1/6 * 1/6 = 1/36

Answer:

3/4

Step-by-step explanation:

⇒ P(T) = 1/2

⇒ P(Q) > P(T)

⇒ P(Q) > 2

A possible probability is :

Answer:

8840

Step-by-step explanation:

Answer:

8,840

Step-by-step explanation:

Answer:

Yes and yes

Step-by-step explanation:

Answer:

(x−1)43x3−8x2+10 can be resolved into partial fraction as x−1A+(x−1)2B+(x−1)3C+(x−1)4D

So , 3x3−8x2+10=A(x−1)3+B(x−1)2+C(x−1)+D

Put x=1 , we get 3−8+10=D

D=5

Comparing the coefficient of x3 on both sides we get , A=3 .

So equation reduces to 3x3−8x2+10=3(x−1)3+B(x−1)2+C(x−1)+5

Now compare the constant on both sides , 10=−3+B−C+5

=>8=B−C - (1)

Comparing the coefficent of x2 we get −8=−9+B

=>B=1

So , put B=1 in (1) , we get C=−7

Therefore , (x−1)43x3−8x2+10=x−13+(x−1)21−(x−1)37+(x−1)45

Step-by-step explanation:

hope it helps

Answer:

Step-by-step explanation:

-5i+6j=x(1i+2j)+y(3i+4j)

-5=x+3y(multiply by 2)

6=2x+4y

-10=2x+6y

subtract

16=-2y

y=-8

-5=x+3(-8)

x=-5+24=19

-5i+6j=19(i+2j)-8(3i+4j)

so we can write (-5,6) as a linear combination of (1,2) and (3,4)

Answer:

90°

Step-by-step explanation:

Angle subtended by diameter from circumference is a right angle(Circle Theorem)

The marginal product of labour is -6+K a and the marginal product of capital is 2K + 4 + L.

From the information given, the production process is Q = K² + 4K + 12 - 6L + KL.

The marginal product of labour will be the first derivative which will be:

= -6 + K.

The marginal product of capital will be the first derivative which will be:

= 2K + 4 + L

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Step-by-step explanation:

[tex]0.07 \times x = 441[/tex]

[tex]x = \frac{441}{0.07} [/tex]

[tex]x = 6300[/tex]

Answer:

  0.34

Step-by-step explanation:

You know from the empirical rule that 68% of the area of the normal distribution lies in the range z=-1 to z=1. The distribution is symmetrical, so half that area lies in the range z = -1 to z = 0.

  area = 68%/2 = 34% = 0.34

__

Your calculator can tell you the same thing.

Answer:

-1

Step-by-step explanation:

Given function:  [tex]f(x)=-x^2+4x-3[/tex]

[tex]\implies f(-2)=-(-2)^2+4(-2)-3=-15[/tex]

[tex]\implies f(7)=-(7)^2+4(7)-3=-24[/tex]

[tex]\textsf{Average rate of change}=\dfrac{f(b)-f(a)}{b-a}\quad\textsf{for}\:a\leq x\leq b[/tex]

Therefore, average rate of change over the interval -2 ≤ x ≤ 7

[tex]\implies \textsf{Average rate of change}=\dfrac{f(7)-f(-2)}{7-(-2)}=\dfrac{-24-(-15)}{9}=-1[/tex]

Answer:

Step-by-step explanation:

No solution; 3x+y-1 =/ 0