1. Find the focus of the parabola that has vertex (-7, 2), opens vertically, and passes through the point (-5,0).

The value of the principal investment would be = $12,500.75

A principal investment is defined as the capital amount of money that is being deposited into an account with the purpose of receiving interest for a particular period of time.

The years of investment (t) = 9 years

The annual interest rate (r) = 3.9% = 3.9/100= 0.039

The total worth of the investment (A) = $17,757.16

Then, solve the equation for P

P = A / ert

P = 17,757.16 / e(0.039*9)

P = $12,500.75

Therefore, the principal amount that is needed which can be compounded continuously to get the total amount given = $12,500.75

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Answer:

The equation of the line is: [tex]y = 0.6x + 0.6[/tex]

Step-by-step explanation:

Equation of a line:

The equation of a line has the following format:

[tex]y = mx + b[/tex]

In which m is the slope and b is the y-intercept.

Two points:

We have these following two points in this exercise:

x = -6, y = -3, so (-6,-3)

x = 4, y = 3, so (4,3)

Finding the slope:

Given two points, the slope is given by the change in y divided by the change in x.

Change in y: 3 - (-3) = 3 + 3 = 6

Change in x: 4 - (-6) = 4 + 6 = 10

So

[tex]m = \frac{6}{10} = 0.6[/tex]

Then

[tex]y = 0.6x + b[/tex]

Finding b:

We replace one of the points in the equation to find b. I will use (4,3).

[tex]y = 0.6x + b[/tex]

[tex]3 = 0.6*4 + b[/tex]

[tex]2.4 + b = 3[/tex]

[tex]b = 0.6[/tex]

The equation of the line is: [tex]y = 0.6x + 0.6[/tex]

Answer:

1. 29. Solve for the variable and graph the solution on a number line: –2x < –10 30. Solve for the variable and graph the solution on a number line: 9 + c > –2 31. Solve for the variable and graph the solution

2.  v – 4 ≥ 3 (6 + 2v

3. The last term, "the constant", is -5 Step-1 : Multiply the coefficient of the first term by the constant 4 • -5 = -20 Step-2 : Find two factors of -20 whose sum equals the coefficient of the middle term, which is -8

4.The first term is, 4p 2 its coefficient is 4 . The middle term is, -8p its coefficient is -8 . The last term, "the constant", is -5 Step-1 : Multiply the coefficient of the first term by the constant 4 • -5 = -20

Step-by-step explanation:

the rest is up to you, and u better say thanks and give me brainliest this took ages to explain

answer:

h

Step-by-step explanation:

if there is more blues and green cards than purple there is a lower chance of getting purple

Answer:

[tex]K)~\frac{3}{16+x}[/tex]

Step-by-step explanation:

[tex]green~ cards=4[/tex]

[tex]blue ~cards=9[/tex]

[tex]purple~ cards=3[/tex]

[tex]pink ~cards=x[/tex]

[tex]total:-[/tex] 4×9×3×x

→ [tex]16+x[/tex]

[tex]p(x)=\frac{3}{16+x}[/tex]

[tex]Answer:K[/tex]

[tex]------------[/tex]

hope it helps...

have a great day!!

Answer:

D) ASA

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

768 can be broken down to:

2×2×2×2×2×2×2×2×3

The part made up of twos is already a perfect square. The 3 needs a partner for it to be a perfect square also.

768 × 3 is 2304.

Sqrt2304 is 48.

Multiply 768 by 3 to make it a perfect square.

Refer To The Given Image

Using the Algebraic tile method we get x=2 solution for equation model

The algebra tile method is a method of solving equations by using visual models, such as tiles with different values on them, to represent the unknowns and constants in the equation. It is often used to help students understand the process of solving equations and to see how the operations of addition and subtraction correspond to the process of combining or separating algebraic expressions.

In the question, we have 3 kinds of tile

Equation will be :

⇒ 3x - 1 - 1 = 1 + 1 + 1 + 1

⇒ 3x - 2 = 4

⇒ 3x = 6

⇒ x = 2

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Answer:

Step-by-step explanation:

8.4

Answer:

$8.4

Step-by-step explanation:

[tex]3.36*2.5[/tex]

Answer:

40 Balcony/15 floor

Step-by-step explanation:

A and C are out instantly cause the amount of tickets sold doesnt equal 55 and B is out cause 50x5=250 and 5x10=50 which totals to 300 not 350

Answer:

Rounding to tenths

E: 56.8 %

F: 48.8 %

G: 44.9 %

H: 50.4 %

Step-by-step explanation:

Hope this helps!

Answer:

50.4 percent is f

Step-by-step explanation:

and the steps is calculate it

Answer: -3√3

Step-by-step explanation: Factor out the square roots from each term

2√54 -> 6√6

√27 -> 3√3

3√24 -> 6√6

The equation becomes 6√6 - 3√3 - 6√6

By combining like terms we can eliminate 6√6

This leaves us with -3√3 as the simplified solution

Answer:

-3√3

Step-by-step explanation:

do the hcf method to get all the values outside

hcf of 54= 2, 3, 3, 3

hcf of 27 = 3, 3, 3

hcf of 24 = 2,2,3,3

2✓2×3×3×3 - √3,3,3 - 3√2,2,3,3

take out the common factor and multiply it with the value we have outside leave it if it doesnt have a number

2×3√2×3 - 3✓3 -3×2×3

6√6 - 3√3 - 3×2×3

6×3 - 3√3 - 3×2×3

18-18 - 3✓3

-3√3

Answer:

the average no of customers in the system is 0.9

Step-by-step explanation:

Given that

The average number of arrivals is 6 per minute

And, the average service rate of a single server is 10 minutes

We need to find out the average no of customers in the system

So,

Lq = rho^2 / 1 ÷ rho

= (6 ÷ 10)^2 ÷ (1 - 6 ÷ 10)

= 36 ÷ 100  ×  10 ÷ 4

= 0.9

Hence, the average no of customers in the system is 0.9

Solution :

Along the edge [tex]$C_1$[/tex]

The parametric equation for [tex]$C_1$[/tex] is given :

[tex]$x_1(t) = 9t , y_2(t) = 0 \ \ for \ \ 0 \leq t \leq 1$[/tex]

Along edge [tex]$C_2$[/tex]

The curve here is a quarter circle with the radius 9. Therefore, the parametric equation with the domain [tex]$0 \leq t \leq 1 $[/tex] is then given by :

[tex]$x_2(t) = 9 \cos \left(\frac{\pi }{2}t\right)$[/tex]

[tex]$y_2(t) = 9 \sin \left(\frac{\pi }{2}t\right)$[/tex]

Along edge [tex]$C_3$[/tex]

The parametric equation for [tex]$C_3$[/tex] is :

[tex]$x_1(t) = 0, \ \ \ y_2(t) = 9t \ \ \ for \ 0 \leq t \leq 1$[/tex]

Now,

x = 9t, ⇒ dx = 9 dt

y = 0, ⇒ dy = 0

[tex]$\int_{C_{1}}y^2 x dx + x^2 y dy = \int_0^1 (0)(0)+(0)(0) = 0$[/tex]

And

[tex]$x(t) = 9 \cos \left(\frac{\pi}{2}t\right) \Rightarrow dx = -\frac{7 \pi}{2} \sin \left(\frac{\pi}{2}t\right)$[/tex]

[tex]$y(t) = 9 \sin \left(\frac{\pi}{2}t\right) \Rightarrow dy = -\frac{7 \pi}{2} \cos \left(\frac{\pi}{2}t\right)$[/tex]

Then :

[tex]$\int_{C_1} y^2 x dx + x^2 y dy$[/tex]

[tex]$=\int_0^1 \left[\left( 9 \sin \frac{\pi}{2}t\right)^2\left(9 \cos \frac{\pi}{2}t\right)\left(-\frac{7 \pi}{2} \sin \frac{\pi}{2}t dt\right) + \left( 9 \cos \frac{\pi}{2}t\right)^2\left(9 \sin \frac{\pi}{2}t\right)\left(\frac{7 \pi}{2} \cos \frac{\pi}{2}t dt\right) \right]$[/tex]

[tex]$=\left[-9^4\ \frac{\cos^4\left(\frac{\pi}{2}t\right)}{\frac{\pi}{2}} -9^4\ \frac{\sin^4\left(\frac{\pi}{2}t\right)}{\frac{\pi}{2}} \right]_0^1$[/tex]

= 0

And

x = 0,  ⇒ dx = 0

y = 9 t,  ⇒ dy = 9 dt

[tex]$\int_{C_3} y^2 x dx + x^2 y dy = \int_0^1 (0)(0)+(0)(0) = 0$[/tex]

Therefore,

[tex]$ \oint y^2xdx +x^2ydy = \int_{C_1} y^2 x dx + x^2 x dx+ \int_{C_2} y^2 x dx + x^2 x dx+ \int_{C_3} y^2 x dx + x^2 x dx $[/tex]

                        = 0 + 0 + 0

Applying the Green's theorem

[tex]$x^2 +y^2 = 81 \Rightarrow x \pm \sqrt{81-y^2}$[/tex]

[tex]$\int_C P dx + Q dy = \int \int_R\left(\frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y}\right) dx dy $[/tex]

Here,

[tex]$P(x,y) = y^2x \Rightarrow \frac{\partial P}{\partial y} = 2xy$[/tex]

[tex]$Q(x,y) = x^2y \Rightarrow \frac{\partial Q}{\partial x} = 2xy$[/tex]

[tex]$\left(\frac{\partial Q}{\partial x}-\frac{\partial P}{\partial y} \right) = 2xy - 2xy = 0$[/tex]

Therefore,

[tex]$\oint_Cy^2xdx+x^2ydy = \int_0^9 \int_0^{\sqrt{81-y^2}}0 \ dx dy$[/tex]

                            [tex]$= \int_0^9 0\ dy = 0$[/tex]

The vector field F is = [tex]$y^2 x \hat i+x^2 y \hat j$[/tex]  is conservative.

Answer:

2.25 cups

Step-by-step explanation:

There are 5 eights in 40.

1.25 × 5 = 6.25

1.5 × 5 = 7.5

1 × 5 = 5

1 quart = 4 cups

6.25 cups - 4 cups = 2.25 cups

Answer:

2/3

Step-by-step explanation:

4/9 divided by 2/3 = 4/9 times 3/2

= 2/3

Answer:

m = 2

Step-by-step explanation:

[tex]\frac{13-5}{6-2}=\frac{8}{4} =\boxed{2}[/tex]

Hope this helps.

Answer:

-85º

Step-by-step explanation:

275 - 360 = -85

Answer:

Step-by-step explanation:

Let's solve for x.

2x+3y=9

Step 1: Add -3y to both sides.

2x+3y+−3y=9+−3y

2x=−3y+9

Step 2: Divide both sides by 2.

2x/ 2 = −3y+9/ 2

x= −3/ 2 y+ 9/ 2

Answer:

x= −3/ 2 y+ 9/ 2

Answer:

189 sq mm

Step-by-step explanation:

area = (21×18)/2 = 189 sq mm

Answer:

78

Step-by-step explanation:

a + 8b = 6 + 8 x 9 = 6 + 72 = 78

Answer: 78

Step-by-step explanation:

value of a=6

value of b=9

a+8b= 6+8*9

as the 8 will be multiplied by 9

6+8*9= 6+72

6+72 = 78

Answer:

1) Yes

2) No

Step-by-step explanation:

In the first test  t distribution is  appropriate to use because  in the dot plot the  16 data points can be seen other the the data points clustered round the mean.

Here degrees of freedom = n-1= 74

S. E= s/√n

S.E= 10.1/ √74= 1.17

For t - distribution it is assumed that the sample is approximately normal which is  visible in the dot plot in the first test.

In the second case z test should be applied.

Z test is used when the population standard deviation is not known .

In the second test  t distribution is   not appropriate to use because  in the dot plot only 2 data points can be seen other the the data points clustered round the mean.

For t - distribution it is assumed that the sample is approximately normal which is not visible in the dot plot.

Answer:

1

Step-by-step explanation:

9 - 3  ÷ 1/3 + 1

first do division

3 ÷ 1/3 = 9

9 - 9 + 1 = 1

Answer:

0.2

Step-by-step explanation:

1/10 = 0.1

10/100 = 0.1

0.1+0.1 = 0.2

Answer:

90

Step-by-step explanation:

A regular quadrilateral is a square.

The sum of the exterior angles of a polygon is always

360 degrees

Therefore a quadrilateral has four exterior angles making the individual exterior angles

360 over 4=90 degrees

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