The top most point of a pyramid is at the center of a cube The height of a cube is 10 inches what is the volume of the square pyramid inside the cube?

Answer:

  5.7

Step-by-step explanation:

The altitude divides right triangle ABC into similar right triangles ADB and BDC. The ratios of short leg to long leg will be proportional in these similar triangles, so you have ...

  AD/BD = BD/CD

Cross multiplying gives ...

  AD·CD = BD²

  (x+3)(2x+3) = 5²

  2x² +9x = 16 . . . . . perform the multiplication, subtract 9

  2(x² +4.5x) = 16

  2(x² +4.5x +2.25²) = 16 +2(2.25²) . . . . . add 2(2.25²) to complete the square

  2(x +2.25)² = 26.125 . . . . . write as a square

  x +2.25 = √13.0625 . . . . . .divide by 2, take the positive square root

  x = -2.25 +√13.0625 . . . . subtract 2.25 to find x

We want the value of CD, so ...

  CD = 2x +3 = 2(-2.25 +√13.0625) +3

  CD = -1.5 +2√13.0625 ≈ 5.7284

The length of CD is about 5.7 units.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Here,

H_o: The way of reservation is independent of gender.

H_a: The way of reservation is not independent of gender.

We use a chi square test because we can calculate the expected frequencies for this chart.

Doing an Expected Value Chart,          

33.7625   9.7125   30.525  

39.2375   11.2875   35.475

Using chi^2 = Sum[(O - E)^2/E],          

chi^2 =    4.482385929

With df = (a - 1)(b - 1), where a and b are the number of categories of each variable,

a =    3      

b =    2

df =    2

Thus, the critical value is

significance level =    0.05

chi^2(critical) =    5.991464547

Also, the p value is

P =    0.106331579

Thus, comparing chi^2 and chi^2(critical) [or, p and significance level], we   FAIL TO REJECT THE NULL HYPOTHESIS.

Thus, there is no significant evidence that the way of reservation is dependent of gender. [CONCLUSION]

Answer:

63 cubic inches

Step-by-step explanation:

You have to first find the volume of each mold:

6 × 4 × 2= 48 cubic inches

3 × 5 × 1= 15 cubic inches

Add these two volumes together to find the overall volume of the whole sand castle.

48+15= 63 cubic inches

Answer:

The whole castle can hold 63 in² of sand.

Step-by-step explanation:

First, find the volume of the first mold.

V = whl          Substitute

V = (6)(2)(4)    Multiply

V = 48 in²

Now, find the volume of the second mold.

V = whl          Substitute

V = (5)(1)(3)    Multiply

V = 15 in²

Add together both volumes to find the volume of the whole castle.

48 + 15 = 63 in²

Answer:

13 2/3 cm

Step-by-step explanation:

To find the perimeter, add up all the sides

2 1/2 + 3 1/3+ 4 1/2 + 3 1/3

Add up the whole numbers

2+3+4+3 = 12

Add up the fractions

1/2+1/3+1/2+1/3

2/2 + 2/3

1 +2/3

Put them together

12+1+2/3

13 2/3

Answer: 13 2/3 cm

Step-by-step explanation:

1. Turn mixed fractions into improper fractions:

2 1/2 = 5/2

3 1/3 = 10/3

3 1/3 = 10/3

4 1/2 = 9/2

2. Formula for perimeter: left side + right side + upper base + lower base

3. Put your numbers in replace: 10/3 + 10/3 + 5/2 + 9/2

4. Solve: 41/3

5. Simplify into mixed fraction: 41/3 = 13 2/3

6. Don't forget to add the unit!

Answer:

raising a number to the 34th power

Step-by-step explanation:

Rotating the graph of [tex]Ax^2+Bxy+Cy^2+Dx+Ey+F=0[/tex] with [tex]B\ne0[/tex] counterclockwise by [tex]\theta[/tex] eliminates the [tex]xy[/tex] term, where [tex]\cot2\theta=\frac{A-C}{B}.[/tex] Plugging in, we have [tex]\cot2\theta=\frac{7}{24},[/tex] since [tex]C=0.[/tex] Solving, we have [tex]\theta=\frac{1}{2}\cot^{-1}(\frac{7}{24})\approx\boxed{36.9^\circ}.[/tex]

Answer:

1/2 hour

Step-by-step explanation:

I am assuming you meant "lives 5km"

The first km would take 1/4 an hour because she is going 4km/h for one hour. One hour she would go 4km but we only need 1 mile so it would be cut to a fraction.

The same fraction goes for the bus. 4 is 1/4 of 16 so you would have to add them together and have 1/2 and hour to get home.

Answer:

[tex] \frac{11}{24} [/tex]

Answer:

D. 11/24

Step-by-step explanation:

Total students' reading preferences = 240

Using electronic device = 110

Probability of having electronic device = 110/240

= 11/24

Answer:

  (13, 11)

Step-by-step explanation:

The vertex of g(x) = |x| is (0, 0).

When the function is transformed to ...

  f(x) = g(x -h) +k

the vertex is moved to (h, k).

Here, we have (h, k) = (13, 11), translating the function to ...

  f(x) = |x -13| +11

and moving the vertex to (13, 11).

Answer:

D. (13, 11)

Step-by-step explanation:

EDGE 2020 :)

Answer:

$5759.12

Step-by-step explanation:

$5759.12

At the end of the year, the compound interest on her loan is: $5000(1+0.1212)12=$5000(1.01)12≈$5634.12. To pay off the loan at the end of the year, she pays 5634.12+125=$5759.12.

Answer:

8

Step-by-step explanation:

(290-25)/30

265/30

8 and 5/6

so how many full 30 cm lengths?

8

Answer:

7

Step-by-step explanation:

3 × 25 = 75cm

He cuts 75cm of 290cm so the remaining length is 290 - 75 = 215 cm

→ He then cuts the rest of the wire into as many 30 cm lengths as possible.

215 ÷ 30 = 7.17

Answer:

number of box of pen = 16

number of box of ribbon bands = 8

Step-by-step explanation:

Let

number of boxes of pen = p

number of boxes of rubber bands = r

He ordered 24 boxes of both items. Therefore,

p + r = 24...............(i)

The total cost of what he ordered is $200 . Therefore,

10p + 5r = 200.......(ii)

combine the equations

p + r = 24...............(i)

10p + 5r = 200.......(ii)

from equation (i)

p = 24 - r

insert the value of p in equation (ii)

10(24 - r) + 5r = 200

240 - 10r + 5r = 200

240 - 200 = 5r

40 = 5r

divide both sides by 5

r = 40/5

r = 8

insert the value of r in equation(i)

p + 8 = 24

p = 24 - 8

p = 16

number of box of pen = 16

number of box of ribbon bands = 8

Answer:

56 out of 224 times

Step-by-step explanation:

8 out of 32 = 1 out of 4

56 out of 224 = 1/4

Answer:56

Step-by-step explanation:

Answer:

Step-by-step explanation:

We can complete the squares of the x- and y-terms by adding the square of half the linear term coefficient.

  (x^2 +4x) +(y^2 -10y) = 7

  (x^2 +4x +4) +(y^2 -10x +25) = 7 + 4 + 25

  (x +2)^2 +(y -5)^2 = 6^2

Compare to ...

  (x -h)^2 +(y -k)^2 = r^2 . . . . . standard form equation of a circle

We see that the center is ...

  (h, k) = (-2, 5)

and the radius is ...

  r = 6

Answer: answer is D

Step-by-step explanation:

Answer: The correct answer is 6,4,2

Step-by-step explanation: Doing a 100 point giveaway stay tuned!

Answer:

Error interval is [tex]35\leq x< 45[/tex]

Step-by-step explanation:

Given: A number x becomes 40 if it is rounded to 1 significant figure

To find: error interval for x

Solution:

In the given question, an error interval is the range of values that a number x can be equal to before it is rounded to 1 significant figure.

As a number x becomes 40 if it is rounded to 1 significant figure, error interval is [tex]35\leq x< 45[/tex].

A number x in this interval becomes equal to 40 if it is rounded to 1 significant figure.

Answer: 2sqrt(33)

Step-by-step explanation:

We want to find the length of the line y = 4 in the circle x^2+y^2=49.

Substitute y = 4 to get x^2 = 33, so x = sqrt(33) or -sqrt(33).

That means the total length is sqrt(33) * 2 = 2sqrt(33).

Hope that helped,

-sirswagger21

The approximate length of the portion of the line is 11.49.

Circle centered at (h,k) with radius r is  [tex](x-h)^{2} + (y-k)^{2}=r^{2}[/tex]

A circle of a radius 7 centered at the origin:

[tex]x^{2} +y^{2}=49[/tex]   ......... (i)

[tex]y=4[/tex]               ..........(ii)

We have a circle and a line.  We need to find the points of

intersection and find the distance between those two points.

Replace y with 4 in the 1st equation and solve for x.

[tex]x^{2} +4^{2} =49\\x^{2} =49-16\\x^{2} =33\\[/tex]

[tex]x=[/tex] ±[tex]\sqrt{33}[/tex]

We have the 2 values of x where the line intersects the circle.

Plug those into one of the original equations to find the associated

y values.

[tex]\sqrt{33} ^{2} +y^{2} =49\\y^{2}=49-33\\y=4[/tex]

Two points on the circle are [tex](\sqrt{33} , 4)[/tex] and [tex](-\sqrt{33} , 4)[/tex]

Using the distance formula:-

[tex]=\sqrt{(4-4)^{2}+(-\sqrt{33}-\sqrt{33)} ^{2} } \\=\sqrt{(2\sqrt{33}) ^{2} } \\=2\sqrt{33}\\[/tex]

≈ 11.49

Therefore, the length of the portion of the line is approximately 11.49.

For more information:

https://brainly.com/question/24214108

Answer:

x =42

Step-by-step explanation:

(3x+12)+x=180

Combine like terms

4x +12 = 180

Subtract 12 from each side

4x +12-12=180-12

4x = 168

Divide by 4

4x/4 =168/4

x =42

Answer:

x=42

Step-by-step explanation:

180-12=168

168 divided by 4 = 42

x=42

Answer:

the standard error of the proportion is 0.0272

Step-by-step explanation:

We have that if the sample size is greater than 5% of the entire population, a finite population correction factor (fpc) is multiplied with the standard error :

fpc = [tex]\sqrt{\frac{N -n}{N -1} }[/tex]

We know that N = 250 n = 91, replacing:

fpc = [tex]\sqrt{\frac{250 - 91}{250 -1} }[/tex]

fpc = 0.799

Now, the formula would then be:

SE  = [tex]\sqrt{\frac{p * (1 -p)}{n} }[/tex]*fpc

Now replacing, knowing that p = 0.12

SE= [tex]\sqrt{\frac{0.12 * (1 - 0.12)}{91} }[/tex]*0.799

SE = 0.0272

So the standard error of the proportion is 0.0272

Answer:

8 pieces

Step-by-step explanation:

Take 6 yds and divide by the length of each piece

6 ÷ 3/4

Copy dot flip

6 * 4/3

24/3

8

We can get 8 peices

Answer:

2500

Step-by-step explanation:

Monthly total cost, C(x) = 400 + 200x dollars

Monthly total revenue, R(x) = [tex]350x -\dfrac{1}{100}x^2[/tex] dollars

Profit = Revenue - Cost

[tex]=R(x)-C(x)\\=(350x -\dfrac{1}{100}x^2)-(400 + 200x)\\=350x -\dfrac{1}{100}x^2-400 - 200x\\P(x)=150x-\dfrac{1}{100}x^2-400[/tex]

To determine how many items, x, the firm should produce for maximum profit, we maximize P(x) by taking its derivative and solving for its critical points.

[tex]P(x)=150x-\dfrac{1}{100}x^2-400\\P'(x)=150-\dfrac{x}{50}\\\\$Set $ P'(x)=0\\150-\dfrac{x}{50}=0\\150=\dfrac{x}{50}\\$Cross multiply\\x=150*50\\x=7500[/tex]

Next, we check if the point x=7500 is a maxima or a minima.

To do this, we find the second derivative of P(x).

[tex]P''(x)=-\dfrac{1}{50} $ which is negative[/tex]

Hence, the point x=7500 is a point of maxima. However, since the firm can only produce 2500 units per month.

Therefore, the company needs to produce 2500 units to maximize profit.

Answer:

Step-by-step explanation:

remove parentheses by multiplying factors.

use exponent rules to remove parentheses in terms with exponents.

combine like terms by adding coefficients.

combine the constants.

Answer:

A. [tex]F(x) = (\frac{3}{4}x )^2-1[/tex]

Step-by-step explanation:

The correct answer is "A," because the function F(x), shifted downwards 1 unit. This means that the function has to have a -1 being subtracted. Note that when the number in front of x is less than one, the function widens. In this case, [tex]\frac{3}{4}[/tex] is less than one, making it grow bigger as shown on the graph above.

Answer:

Given:

Sample size, n = 350

Sample proportion, P' = 0.21

H0 : p = 0.16

Ha : p ≠ 0.16

a) A 90% confidence interval for P.

Significance level = 1 - confidence interval = 1 - 0.90 = 0.10

For Z critical, we have:

Z critical = [tex] Z_0_._1_/_2 = Z_0_._0_5 = 1.645 [/tex] (using z table)

Standard error, S.E = [tex] \sqrt{\frac{P'(1 - P')}{n}} = \sqrt{\frac{0.21(1 - 0.21)}{350}} = 0.02177 [/tex]

Margin of error, E = 1.645 * 0.02177 =0.03581

The 90% confidence interval =

0.21 ± 0.03581

The lower limit: 0.21 - 0.03581 = 0.17419

The upper limit: 0.21+0.03581 =0.24581

b) Based on the confidence interval at significance level = 0.10,

We reject null hypothesis, H0, since 0.16 is not cointained in the confidence interval. We conclude that p ≠ 0.16.

c) Standard error is based on sample proportion p^ while standard deviation is based on hypothesized proportion Po.

d) Standard error is used to compute the confidence interval.

Answer:

(5,2)

Step-by-step explanation:

From the graph attached below:

Since the temperature at 5 p.m. is halfway between the temperature at 2 p.m. and 8 p.m. , the coordinate of the temperature at 5 p.m. is the midpoint of (2,7)  and (8,-3).

For two coordinate points [tex]A(x_1,y_1)$ and B(x_2,y_2)[/tex]

[tex]\text{Midpoint of AB }=\dfrac{1}{2} \left( x_1+x_2,y_1+y_2 \right)[/tex]

Therefore, the coordinates for 5p.m.

[tex]=\dfrac{1}{2} \left( 2+8,7+(-3) \right) \\=\dfrac{1}{2} \left( 10,4 \right)\\\\=(5,2)[/tex]

Answer:

d=2

Step-by-step explanation:

Shape: Circle

Solved for diameter

Radius: 1

Formula: d=2r

Formula: Radius

Answer: 2

Hope this helps.

Answer:

1 and 4 are alternate interior angles.

m5 + m1 = 180

m5 = m3 + m2

Question:

The complete version of your question as found in other site is stated below:

In the diagram provided, line l is parallel to line m. Select which of the following statements could be used to prove that the interior angles of a triangle have a sum of 180°. You may choose more than one correct answer.

1 and 4 are alternate interior angles.

m4 + m5 + m6 = 180.

m5 + m1 = 180.

m5 = m3 + m2

Step-by-step explanation:

Given: line l is parallel to line m

We need prove that the interior angles of a triangle have a sum of 180°. In order to do that, the angles in the triangle = 180°

∠1 + ∠2  + ∠3  = 180°

Alternate angles:

∠1 = ∠4

∠6 = ∠2

∠5 = ∠3 + ∠6

Checking the options and inserting the values above in them:

a) 1 and 4 are alternate interior angles

∠1 = ∠4

This gives one of the side of the interior angles. The alternate angles enables us to find the sum of the interior angles. It is correct

b) m4 + m5 + m6 = 180

∠4 + ∠5 + ∠6 = 180°

∠1 + (∠3 + ∠6) + ∠2 = 180°

The above option wont give ∠1 + ∠2  + ∠3  = 180°. Hence it is wrong.

c) m5 + m1 = 180

(∠3 + ∠6) + ∠1 = 180°

∠5 = (∠3 + ∠6) = ∠3 + ∠2

∠3 + ∠2 + ∠1 = 180°

This option is correct

d) m5 = m3 + m2

∠5 = ∠3 + ∠2

From the diagram, ∠5 + ∠1 = 180° (angles on a straight line)

∠5 = ∠3 + ∠2

This option can be used to get sum of interior angles.

Answer:

54

Step-by-step explanation:15+15+9+9+3+3=54