If two opposite sides of a square are increased by 8 meters and the other sides are decreased by 5 meters, the area of the rectangle that is formed is 68 square meters. Find the area of the original square.

Answer:

1.5 per hour.

Step-by-step explanation:

By proportion that is 5.4 / 3.6

= 1.5 per hour.

Answer:

12 miles

Step-by-step explanation:

60 min in 1 hr and 10 min = 1 mile..... so 6, 10 min intervals..... and so 6 time 2 is 12

3xcubed y to the fifth over 2

Answer: C

Step-by-step explanation:

For this problem, we need to graph y=2x-5. We can eliminate A and D because the graph is not y=2x-5. The main difference between B and C is the shading and line. Since we see the inequality is less than, but NOT equal to, we know that the line will be dashed. The solid line tells us that the graph reaches the line, meaning it is equal to. Therefore, we can eliminate B. C is the correct answer. We also know that the shading would be under the dashed line because it is LESS THAN.

Answer:

A) 14

Step-by-step explanation:

x - 6 > 10

Add 6 to both sides.

x > 16

The solution is all numbers greater than 16.

In the choices, only 14 is less than 16.

Answer: A) 14

Answer:

a

Step-by-step explanation:

x-6 [tex]>[/tex] 10

14-6 [tex]>[/tex]10

8 is less than 10

Answer:

37,  ABD = CBD = 44 degrees, and ABC = 88 degrees

38.  ABD = CBD = 24 degrees, and ABC = 48 degrees

39.  ABD = CBD = 65 degrees, and ABC = 130 degrees

40.  ABD = CBD =67 degrees, and ABC = 134 degrees

Step-by-step explanation:

Recall that when a segment bisects an angle, the angle is divided in equal parts then we have:

37.  

6 x + 14 = 3 x + 29

3 x = 19 - 14 = 15

x = 15/3

x = 5

then ABD = 6 (5) + 14 = 30 + 14 = 44 degrees

CBD must equal ABD , so CBD = 44 degrees

And the total angle ABC = 88 degrees

38.

3 x + 6 = 7 x - 18

24 = 4 x

x = 24/4 = 6

Then ABD = 3 (6) + 6 = 24 degrees. Also CBD = 24 degrees and ABC = 48 degrees

39.

- 4 x + 33 = 2 x + 81

- 6 x = 81 - 33

-6 x = 48

x = - 48/6

x = -8

Then ABD = -4 (-8) + 33 = 32 + 33 = 65 degrees

The also CBD = 65 degrees, and ABC = 130 degrees

40.

8 x + 35 = 11 x + 23

35 - 23 = 11 x - 8 x

12 = 3 x

x = 12/3

x = 4 degrees

Therefore:

ABD = 8 (4) + 35 = 32 + 35 = 67 degrees.

Then also CBD = 67 degrees, and ABC = 134 degrees

Answer:

3239.95

Step-by-step explanation:

Answer:

The method of moment (MOM) estimator as:  [tex]\mathbf{\hat {\theta} =(\dfrac{\overline X}{1-\overline X})^2}[/tex]

[tex]\overline X = \dfrac{4}{9}[/tex]

[tex]\mathbf{\hat {\theta} =\dfrac{16}{25} }[/tex]

Step-by-step explanation:

From the question, the correct format for the probability density function is:

[tex]fx(x ; \theta) = \left \{ {{\sqrt{\theta x}^{\sqrt{\theta}-1}}\ \ 0 \leq x \leq 1 \atop {0} \ \ \ \ \ \ \ otherwise } \right.[/tex]

where θ > 0 is an unknown parameter.

(a) The MOM estimator can be calculated as follows:

[tex]E(X) = \int ^1_0x. \sqrt{\theta} \ x^{\sqrt{\theta}-1} \ dx[/tex]

[tex]E(X) = \int ^1_0 \sqrt{\theta} \ x^{\sqrt{\theta}} \ dx[/tex]

[tex]E(X) = \dfrac{\sqrt{\theta} }{\sqrt{\theta} +1 } ( x ^{\sqrt{\theta}+1})^1_0[/tex]

[tex]E(X) = \dfrac{\sqrt{\theta} }{\sqrt{\theta} +1 }[/tex]

suppose E(X) = [tex]\overline X[/tex]

Then;

[tex]\overline X = \dfrac{\sqrt{\theta} }{\sqrt{\theta} +1 }[/tex]

[tex]\dfrac{1}{\overline X} = \dfrac{\sqrt{\theta} +1 }{\sqrt{\theta}}[/tex]

[tex]\dfrac{1}{\overline X} =1 + \dfrac{1}{\sqrt{\theta}}[/tex]

making [tex]\dfrac{1}{\sqrt{\theta}}[/tex] the subject of the formula, we have:

[tex]\dfrac{1}{\sqrt{\theta}} =\dfrac{1}{\overline X} - 1[/tex]

[tex]\dfrac{1}{\sqrt{\theta}} =\dfrac{1-\overline X}{\overline X}[/tex]

[tex]\sqrt{\theta} =\dfrac{\overline X}{1-\overline X}[/tex]

squaring both sides, we have:

The method of moment (MOM) estimator as:  [tex]\mathbf{\hat {\theta} =(\dfrac{\overline X}{1-\overline X})^2}[/tex]

b) If the observations are [tex]\dfrac{1}{2}, \dfrac{1}{3}, \dfrac{1}{2}[/tex]

Then,

[tex]\overline X = \dfrac{\dfrac{1}{2}+ \dfrac{1}{3}+\dfrac{1}{2}}{3}[/tex]

[tex]\overline X = \dfrac{\dfrac{3+2+3}{6}}{3}[/tex]

[tex]\overline X = \dfrac{\dfrac{8}{6}}{3}[/tex]

[tex]\overline X = \dfrac{8}{6} \times \dfrac{1}{3}[/tex]

[tex]\overline X = \dfrac{8}{18}[/tex]

[tex]\overline X = \dfrac{4}{9}[/tex]

Finally, the point estimate of the estimator [tex]\theta[/tex] is

[tex]\mathbf{\hat {\theta} =\begin {pmatrix} \dfrac{\dfrac{4}{9}}{1-\dfrac{4}{9}} \end {pmatrix}^2}[/tex]

[tex]\mathbf{\hat {\theta} =\begin {pmatrix} \dfrac{\dfrac{4}{9}}{\dfrac{5}{9}} \end {pmatrix}^2}[/tex]

[tex]\mathbf{\hat {\theta} =\begin {pmatrix} \dfrac{4}{5} \end {pmatrix}^2}[/tex]

[tex]\mathbf{\hat {\theta} =\dfrac{16}{25} }[/tex]

Answer:

-2

Step-by-step explanation:

-15+7y=-25+2y

7y-2y=-25+15

5y= -10

5y/5= -10/5

y= -2

Answer:

y= -17/5 or -3.4

Step-by-step explanation:

-8+7y= -25+2y

5y= -17

y= -17/5 or -3.4

Answer:

10

Step-by-step explanation:

Remember that the formula for the sum of an arithmetic series is:

[tex]S=\frac{k}{2}(a+x_k)[/tex]

Where k is the number of terms, a is the initial term, and x_k is the last term of the series.

We essentially want to find k, the number of terms, given that the sum S is equal to 105. So, substitute 105 into our equation:

[tex]105=\frac{k}{2}(a+x_k)[/tex]

To do so, we need to final term x_k. We don't know what it is yet, but that doesn't matter. All we need to do is to write it in terms of k. First, remember that the standard form for the explicit formula of an arithmetic sequence is:

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

Where a is the first term, d is the common difference, and n is the nth term.

From our sequence, we can see that the first term is -3.

Also, we can determine that our common difference is +3, since each subsequent term is 3 more than the previous one. -3+3 is 0, 0+3 is 3, 3+3 is 6, and so on.

Therefore, our explicit formula is:

[tex]x_n=-3+3(n-1)[/tex]

Therefore, our final term, x_k, will be if we substitute k for n. So, we can acquire the equation:

[tex]x_k=-3+3(k-1)[/tex]

Now that we know what x_k is, we can substitute that into our original equation:

[tex]105=\frac{k}{2}(a+x_k)[/tex]

Substitute the equation into x_k. Also, let's substitute -3 (our first term) for a. So:

[tex]105=\frac{k}{2}(-3+(-3+3(k-1)))[/tex]

And now, all we have to do is to solve for k.

First, distribute the 3:

[tex]105=\frac{k}{2}(-3+(-3+3k-3))[/tex]

Add within the parentheses:

[tex]105=\frac{k}{2}(3k-9)[/tex]

Multiply both sides by 2. This removes the fraction on the right:

[tex]210=k(3k-9)[/tex]

Distribute. We will get a quadratic:

[tex]210=3k^2-9k[/tex]

So, let's solve for k. Let's divide everything by 3:

[tex]70=k^2-3k[/tex]

Subtract 70 from both sides:

[tex]0=k^2-3k-70[/tex]

Factor. We can use -10 and 7. So:

[tex]0=(k-10)(k+7)[/tex]

Zero Product Property:

[tex]k-10=0\text{ or } k+7=0[/tex]

Solve for k for each equation:

[tex]k=10\text{ or } k=-7[/tex]

-7 doesn't make sense (we can't have -7 terms). Remove that solution. So, we are left with:

[tex]k=10[/tex]

Therefore, the number of terms we have in our series for our sum to be 105 is 10.

And we're done!

Answer:

35:60 times

Step-by-step explanation:

The proportion of time in which the coin land on Heads is 0.58

A proportion is an equation in which two ratios are set equal to each other.

Now it is given that,

Number of times coins tossed = 60

Number of times coin landed on Heads = 35

Therefore, the proportion of time in which the coin land on Heads is given as,

Proportion of time the coin land on Heads = Number of times coin landed on Heads/Number of times coins tossed

⇒ Proportion of time the coin land on Heads = 35/60

⇒ Proportion of time the coin land on Heads = 7/12 = 0.58

Thus, the proportion of time in which the coin land on Heads is 0.58

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Answer:

8%

Step-by-step explanation:

I=Pr

104=2600*r/2

r/2=104/2600

r=(104/2600)(2)

r=0.08=8%

Eliana must invest at a rate of 0.33% of simple interest to earn $104.

Given,

Eliana has $2600 to invest for 6 months.

If she needs the money to earn $104 in that time.

We need to find at what rate of simple interest must Eliana invest.

It is given as:

SI = PRT / 100

P = principal amount

R = rate

T = time in years.

Find the rate of interest.

We have,

Simple interest = PRT / 100

SI = $104

T = 6 months

Convert it into years.

12 months = 1 year

6 months = 6/12 years

T = 1/2 years

$104 = ($2600 x R x 1/2) / 100

104 = (2600 x R x 1/2) / 100

100 x 104 = 2600 x R x 12

R = (100 x 104 ) / (2600 x 12)

R = 104 / 312

R = 0.33 %

Thus the rate of simple interest is 0.33%

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Answer: [tex]tan(\frac{13\pi }{4})-cos(\frac{\pi }{3})=\frac{1}{2}[/tex]

Step-by-step explanation:

To find [tex]tan(\frac{13\pi }{4})-cos(\frac{\pi }{3})[/tex], we first need to understand the unit circle. Let's find the value of tan and cos before we subtract them.

[tex]tan(\frac{13\pi }{4} )[/tex] is the same as [tex]tan(\frac{5\pi }{4} )[/tex]. The point for [tex]\frac{5\pi }{4}[/tex] is (-0.5,-0.5). Tangent is [tex]\frac{sin}{cos}[/tex]. Since sin and cos are both -0.5, we can divide them.

[tex]\frac{-0.5}{-0.5} =1[/tex]

Now, we know that [tex]tan(\frac{13\pi }{4} )=1[/tex]. All we have to do is find [tex]cos(\frac{\pi }{3})[/tex].

[tex]cos(\frac{\pi }{3})=\frac{1}{2}[/tex]

Now that we know the values of both, we can directly subtract them.

1-0.5=0.5

Therefore, [tex]tan(\frac{13\pi }{4})-cos(\frac{\pi }{3})=\frac{1}{2}[/tex].

Step-by-step explanation:

yf.bfz

vcg ,kgu nkkgfgvvxvh

Answer:

3/8

Step-by-step explanation:

if u simplify you get half then add them the bigger dinominator is the bottom so only add the tops

Answer:

C. the number of non-guppies

Step-by-step explanation:

The number of non-guppies is the only variable the other two options have defined values.

Answer:

C, The number of non- guppies is the most important variable.

Step-by-step explanation:

The answer is the unknown variable that you're trying to find and the entire problem is to help you find the unknown.

When something varies directly as something else, their ratio of change always stays the same.

56 / 7 = 8

Therefore,

8 * 3 = 24

If x = 3 then y = 24

Complete Question

Find a particular solution to [tex]ty''-(1+t)y'+y=t^2e^t , t > 0[/tex]  

[tex]y_1 = 1 + t , \ y_2 = e^t[/tex]

Answer:

The solution is    [tex]y_p = -e^{2t} + t + \frac{3t^2}{2} + \frac{t^3}{2}[/tex]

Step-by-step explanation:

  Now the given equation is [tex]ty''-(1+t)y'+y=t^2e^t , t > 0[/tex]

             dividing through by  t

       We have  

         [tex]y'' - \frac{1 + t }{t}y' + \frac{1}{t} y = te^t \\\\ let's\ call\ it \ g(t)[/tex]

Now for the given initial value we can generate our Wronskian as follows

        [tex]W(y_1 ,y_2) = | \left y_1} \atop {y_1'}} \right. \left y_2} \atop {y_2'}} \right | = | \left {(1 + t)} \atop {1}} \right. \left e^t} \atop {e^t}} \right | = (1 + t )e^t - e^t = te^t[/tex]

Now applying  method of variation of parameters to obtain the particular solution

So here we assume that

          [tex]y_p = v_1 y_1 + v_2 y_2[/tex]

So

       [tex]v_1 = - \int\limits {\frac{y_2 (t) g(t)}{W(t)} } \, dt = - \int\limits {\frac{e^t te^t}{te^t} } = - \int\limits { e^t} } = -e^t[/tex]

And

    [tex]v_2 = - \int\limits {\frac{y_1 (t) g(t)}{W(t)} } \, dt = - \int\limits {\frac{(1 + t) te^t}{te^t} } = - \int\limits (1 + t) = t + \frac{t^2}{2}[/tex]

So

     [tex]y_p = -e^t * e^t + t + \frac{t^2}{2} * 1 + t[/tex]

     [tex]y_p  =  -e^{2t}   +  t +   \frac{3t^2}{2} + \frac{t^3}{2}[/tex]

Answer:

The price of the ticket before tax - P

The amount of tax Jennifer pays- 0.08P

Jennifer's total amount for the ticket- P + 0.08P

Step-by-step explanation:

The price of the plane ticket is P dollars, before airport security tax. Here P is an independent variable.

An airport security tax of 8% is applied to the price of a plane ticket. So, the amount of airport security tax that Jennifer pays is 8% of the cost of her plane ticket, or 0.08P.

To find Jennifer's total amount for the plane ticket, add the price of the ticket before airport security tax and the amount of airport security tax Jennifer pays. So, the total amount of the plane ticket is P + 0.08P.

The table below shows the expressions matched to their meanings.

An expression is defined as a set of numbers, variables, and mathematical operations. Jennifer's total amount for the ticket is P+0.08P.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

Given that Jennifer is buying a plane ticket to travel abroad. The price of the plane ticket is P dollars, and she has to pay the additional 8% airport security tax. Therefore, we can write the expressions as,

The price of the ticket before tax → P

The amount of tax Jennifer pays → 8% of P = 0.08p

Jennifer's total amount for the ticket → Price of ticket + Tax = P + 0.08P

Hence, Jennifer's total amount for the ticket is P+0.08P.

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Answer:

Center: (0, 0)

Radius: 4

Step-by-step explanation:

Circle Standard Equation: (x - h)² + (y - k)² = r²

(h, k) is center

r is radius

We see that our h and our k are both 0.

∴ Our center is (0, 0), origin.

We see that our r² = 16

√r² = √16

∴ Our radius is equal to 4

Answer:

[tex]x^{20}[/tex]

Step-by-step explanation:

[tex](x^{2} )^{5}[/tex]·[tex](x^{5})^{2}[/tex]

[tex](x^{10} )[/tex] · [tex](x^{10})[/tex]

[tex]x^{20}[/tex]

Answer: D

Step-by-step explanation: if you write it out it will be the exact same thing as D so it will be d

Divide 30 by 25% to find the full amount:

30/0.25 = 120

Now multiply the full amount by 40%:

120 x 0.40 = 30

Answer:

Sound travels 2258 feet in 2 seconds while travelling through air.

Step-by-step explanation: