Gabe is designing a flashlight that uses a parabolic reflecting mirror and a light source. The shape of the mirror can be modeled by a parabola that opens upward with a diameter of 4 in. and a depth of 1 in. The vertex of the parabola is at the the origin. Where should Gabe place the bulb to ensure a perfect beam of light?
(0,1)
(0,4)
(1,0)
(4,0)

Answer:

7.

4.7 * 10^14 , 9.99 * 10^14 , 2.9 * 10^15 , 4.5 * 10^15

8.

9.99 * 10^-8 , 4.8 * 10^-8 , 9.99 * 10^-4 , 6.5 * 10^-4

Answer:

the answer is -85 good luck on your test or honework :)

Using the t-distribution, it is found that the 95% confidence interval for the population mean is (1413.18, 1564.82).

The confidence interval is:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which:

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 65 - 1 = 64 df, is t = 1.9977.

The parameters of the interval are given as follows:

[tex]\overline{x} = 1489, s = 306, n = 65[/tex].

Hence, the bounds of the interval are given by:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 1489 - 1.9977\frac{306}{\sqrt{65}} = 1413.18[/tex]

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 1489 + 1.9977\frac{306}{\sqrt{65}} = 1564.82[/tex]

The 95% confidence interval for the population mean is (1413.18, 1564.82).

More can be learned about the t-distribution at https://brainly.com/question/16162795

Answer:

= 12 x^8

Step-by-step explanation:

Answer:

-1/2

Step-by-step explanation:

pemdas rules

1. 18 x 2 - 30 = 6

2. 3-6= -3

3. 36/-3 = -12

4. 96/-12 = -8

5.  (31-16+1) = 16

6. -8/16 = -1/2

Answer:

y<7

Step-by-step explanation:

3y-10 < 11     add 10 to both sides of the equation

3y < 21      divide by 3

y < 7

Answer:

f(3) = -37

Step-by-step explanation:

f (x) = -6x - 19

Let x = 3

f (3) = -6*3 - 19

      = -18-19

      = -37

Step-by-step explanation:

see this this will help you

#1

#2

#3

Not more factorable

Step-by-step explanation:

The centroid O cuts every median in the ratio 2:1. The distance between a vertex and the centroid is twice the distance between the centroid and the midpoint of the opposite side.

Therefore: |OD| = 2|OCI

3x-2=2(5x)

3x-2=10x

7x=-2

x=(-2/7)

Using the z-distribution, as we are working with a proportion, it is found that the p-value of the test is of 0.

At the null hypothesis, it is tested if the proportion is of 71%, that is:

[tex]H_0: p = 0.71[/tex]

At the alternative hypothesis, it is tested if the proportion has decreased, that is:

[tex]H_1: p < 0.71[/tex].

The test statistic is given by:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

In this problem, we have that the parameters are:

[tex]n = 300, \overline{p} = \frac{165}{300} = 0.55[/tex]

Hence, the value of the test statistic is found as follows:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.55 - 0.71}{\sqrt{\frac{0.71(0.29)}{300}}}[/tex]

z = -6.11

Using a z-distribution calculator, with a left-tailed test, as we are testing if the proportion is less than a value, and z = -6.11, it is found that the p-value is of 0.

More can be learned about the z-distribution at https://brainly.com/question/26454209

Answer:

7.1 cm^2

Step-by-step explanation:

Area  = pie * radius^2

Area = pie * 1.5^2

= 7.0685

Answer: 7.1 cm ^2

Step-by-step explanation:

Answer: it’s simply a

Step-by-step explanation: X =bsquare

Answer:

0

Step-by-step explanation:

tan(x + [tex]\frac{\pi }{2}[/tex] ) ← substitute x = [tex]\frac{\pi }{2}[/tex]

tan([tex]\frac{\pi }{2}[/tex] + [tex]\frac{\pi }{2}[/tex] )

= tanπ

= 0

Answer:

282.3 gallons

Step-by-step explanation:

if needed you can round to 282

Answer:

Step-by-step explanation:

We know that first 150 postive even Integers are 2,4,6,8,10... 300.

Here,

[tex]\\[/tex]

Substituting values in the formula:

[tex] \\ :\implies \sf \: \: S_{n} = \dfrac{n}{2} (a + a_{n}) \\ \\[/tex]

[tex] :\implies \sf \: \: S_{n} = \dfrac{150}{2} (2 + 300) \\ \\ [/tex]

[tex] :\implies \sf \: \: S_{n} = 75(302) \\ \\ [/tex]

[tex] :\implies \: \:{ \underline{ \boxed{ \pmb{ \pink { \rm{S_{n} = 22650 }}}}}} \\ \\[/tex]

Answer:

Formula for finding sum of nth terms =

n/2 × (a + an)

putting the known values ,

Sum = 150/2 × ( 2+300)

Sum = 75 × 302

Sum of first 150 positive even integers = 22650

Answer:

108m

Step-by-step explanation:

2 sides are 30m long and 2 sides are 24m long.

Add all 4 sides of the playground to find the perimeter.

30m + 24m + 30m + 24m = 108 m

Answer:

Step-by-step explanation:

C≈50.27

r Radius

Solution

C=2πr=2·π·8≈50.26548

Answer:

[D] 62°

Step-by-step explanation:

A right triangle = 90 degree angle

A triangle =  180 degrees

Therefore,

90 + 28 = 118

180 - 118 = 62

Hence, the measure of the other acute angle is 62

Thus, the answer is [D] 62 degree

Kavinsky

Answer:

D. 62

Step-by-step explanation:

Answer:

c po

because that is the answer in the bakc of my module hope its help

Answer:

5i√5

Step-by-step explanation:

Remark

125 factors

It is factored into 5*5*5

The rule for √5*5*5  is that two can be taken outside the square root sign. I is placed in front of the root sign like 5√ and the other 5 is thrown away.

The remaining 5 is left under the root sign

As usual

√-1 is i is taken outside the root sign

Solution

5i √5 is what you get.

Answer:

Step-by-step explanation:

In the question we have given volume of Sphere that is 562.5 π in³ and we have asked to find the radius of given sphere. We know that the volume of sphere ,

[tex] \blue{ \boxed{ \rm{Volume \: of \: Sphere = \frac{4}{3} \pi r {}^{3} }}}[/tex]

So equating it with given volume for finding the radius of sphere :

[tex] \longmapsto \: \frac{4}{3} \pi r{}^{3} = 562.5\pi[/tex]

Step 1 : Cancelling π as it was present in both side :

[tex]\longmapsto\:\frac{4}{3} \cancel{\pi }r{}^{3} = 562.5 \cancel{\pi}[/tex]

Step 2 : Transposing 4/3 to right hand side :

[tex]\longmapsto \: r {}^{3} = 562.5 \times \frac{3}{4} [/tex]

Step 3 : Multiplying 562.5 with 3 :

[tex]\longmapsto \:r {}^{3} = \frac{1687.5}{4} [/tex]

Step 4 : Dividing 1687.5 by 4 :

[tex]\longmapsto \:r {}^{3} = 421.875[/tex]

Step 5 : Finding cube root of 421.875

[tex]\longmapsto \:r = \sqrt[3]{421.875} [/tex]

Step 6 : We get :

[tex]\longmapsto \: \red{ \boxed{r = 7.5}}[/tex]

Answer:

If the interval is 1 < x < 3, then you are examining the points (1,4) and (3,16). From the first point, let a = 1, and f (a) = 4. From the second point, let b = 3 and f (b) = 16. The average rate of change is 6 over 1, or just 6.

Step-by-step explanation:

If the interval is 1 < x < 3, then you are examining the points (1,4) and (3,16). From the first point, let a = 1, and f (a) = 4. From the second point, let b = 3 and f (b) = 16. The average rate of change is 6 over 1, or just 6.

Answer:

Step-by-step explanation:

Use distributive property: a*(b+c) =a*b +a*c

1) 785 * 105 = 785 * (100 + 5)

                  = 785*100 + 785*5

                  = 78500 + 3925

                  = 82425

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

2) 1006 * 95 = (1000 + 6) *95

                     = 1000*95 + 6*95

                      = 95000 + 570

                     = 95570

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

3) 3096*91  = 3096 * (100 - 9)

                    = 3096*100 - 3096*9

                    = 309600 - 27864

                    = 281736

Answer:

x=1, y=3

Step-by-step explanation:

using sublimation method

y-3x=0 ....eqn(1)

2y+5x=11....eqn(2)

from eqn 1

y-3x=0

y=3x

substitute y=3x into eqn 2

2y+5x=11

2(3x)+5x=11

6x+5x=11

11x=11 (divide both sides by the coefficient of x)

x=1

since x=1 , substitute x=1 into eqn 1 to get y

y-3x=0

y-3(1)=0

y-3=0

y=3

Using elimination method

y-3x=0....eqn (1)

2y+5x=11....eqn (2)

multiply eqn 1 through by 2 and eqn 2 through by 1 to eliminate y

2y-6x=0.... eqn 3

2y+5x=11.... eqn 4

subtract eqn 4 from from eqn 3

-11x=-11 (divide both sides by the coefficient of x)

x=1

substitute x=1 into eqn 2 to get y

2y+5x=11

2y+ 5(1) =11

2y+5=11

2y=11-5

2y= 6 (divide both sides by the coefficient of y)

y=3

Answer:

180 units^2

Step-by-step explanation:

The formula to find the area of a sphere is:

A=4(pi)(r)^2

A sphere with radius 2r has an area = 4π(2r)² = 4π.4r² = 16πr²

The ratio of the larger sphere to the smaller = 16πr² : 4πr² = 4 : 1

If the area of the smaller sphere is 45 units then the area of the larger sphere is 45 x 4 = 180 units^2.

hope this helps :)