A cone fits inside a square pyramid as shown. For every cross section, the ratio of the area of the circle to the area of the square is StartFraction pi r squared Over 4 r squared EndFraction or StartFraction pi Over 4 EndFraction. A cone is inside of a pyramid with a square base. The cone has a height of h and a radius of r. The pyramid has a base length of 2 r. Since the area of the circle is StartFraction pi Over 4 EndFraction the area of the square, the volume of the cone equals StartFraction pi Over 4 EndFraction the volume of the pyramid or StartFraction pi Over 4 EndFractionStartFraction pi Over 4 EndFraction (StartFraction (2 r) (h) Over 3 EndFraction) or One-sixthπrh. StartFraction pi Over 4 EndFraction the volume of the pyramid or StartFraction pi Over 4 EndFractionStartFraction pi Over 4 EndFraction (StartFraction (2 r) squared (h) Over 3 EndFraction) or One-thirdπr2h. StartFraction pi Over 2 EndFraction the volume of the pyramid or StartFraction pi Over 2 EndFraction or Two-thirdsπr2h. StartFraction pi Over 2 EndFraction the volume of the pyramid or StartFraction pi Over 4 EndFraction or One-thirdπr2h.

Answer:

3/8

Step-by-step explanation:

If 5/8 of the staff is male, then 8/8 is the total number of staff.

8/8 - 5/8 = 3/8

3/8 of the staff is female.

Hope this has helped. If the question has more to it, then please specify.

Answer:

(1,4)

Step-by-step explanation:

Which ordered pair is a solution of the equation? y = 7 x − 3

a. (1,4) b. (-1,-4) c. both d. neither

Solution

y=7x-3

Solve by trying each ordered pair

a. (1,4)

x=1, y=4

Substituting the value of x and y into the equation

y=7x-3

4=7(1)-3

4=7-3

4=4

This is a true statement

b. (-1,-4)

x=-1, y=-4

Substitute the value into the equation

y=7x-3

-4=7(-1)-3

-4= -7-3

-4= -11

This is not a true statement

This true statement is when x=1 and y=4

So, the ordered pair (1, 4) is the solution

Answer:

Step-by-step explanation:

given data

mean = 1.9 hours

standard deviation = 0.3 hours

solution

we get here first  random movie between 1.8 and 2.0 hours

so here

P(1.8 < z < 2 )

z = (1.8 - 1.9) ÷ 0.3

z = -0.33

and

z = (2.0 - 1.9) ÷ 0.3

z = 0.33

z = 0.6293

so

P(-0.333 < z < 0.333 )

=  0.26

so random movie is between 1.8 and 2.0 hours long is 0.26

and

A movie is longer than 2.3 hours.

P(x > 2.3)

P( [tex]\frac{x-\mu }{\sigma}[/tex]  > [tex]\frac{2.3-\mu }{\sigma}[/tex] )

P (z  > [tex]\frac{2.3-1.9 }{0.3}[/tex]  )

P (z  > 1.333  )

= 0.091

so chance a movie is longer than 2.3 hours is 0.091

and

length of movie that is shorter than 94% of the movies is

P(x > a ) = 0.94

P(x <  a ) = 0.06

so

P( [tex]\frac{x-\mu }{\sigma }[/tex] <  [tex]\frac{a-\mu }{\sigma }[/tex] )

[tex]\frac{a-1.9 }{0.3 } = -1.55[/tex]

a = 1.43

so length of the movie that is shorter than 94% of the movies about 1.4 hours.

Answer:

3

1/5

3/4

3/4

Step-by-step explanation:

Coefficient is a number that is always written in front of a term.

3xy^3=3

xy/5=1/5

3/4xy=3/4

3/4x^2y=3/4

Hope this helps ;) ❤❤❤

Answer:

g(x) = $16.49x + $10.50

$208.38

Step-by-step explanation:

Given the following:

Cost per bag = $16.49

Shipping and handling fee = $10.50

Number of bags ordered = x

If g(x) = total cost of bags

Bag cost = cost per bag × number of bags ordered

Bag Cost = $16.49 * x = $16.49x

Shipping and handling fee = $10.50

Total cost of bags = Bag cost + shipping and handling fee

g(x) = $16.49x + $10.50

Where x is the number of bags ordered.

Therefore, total cost of 12 bags equals ;

g(12) = $16.49(12) + $10.50

g(12) = $197.88 + $10.50

g(12) = $208.38

Answer:

g(x)=16.49x+10.50

$208.38

Step-by-step explanation:

let the cost of x bags = g(x)

cost of one bag = $16.49

cost of x bags = $16.49x

shipping and handling charges = $10.50

total cost of x bags = 16.49x + 10.50

g(x) = 16.49x + 10.50

To determine the cost of 12 bags, substitute x with 12 and simplify:

g(12) = 16.49(12) + 10.50

= 208.38

Answer:

your answer is incorrect.  The correct answer is  [tex]h=-13[/tex]  and [tex]k=13[/tex] .

Step-by-step explanation:

If a quadratic function is [tex]f(x)=ax^2+bx+c[/tex] and a>0, then minimum value of the function at point [tex]\left(-\dfrac{b}{2a},f(-\dfrac{b}{2a})\right)[/tex].

The given function is

[tex]f(x)=x^2+bx+182[/tex]

Here, a=1, b=b and c=182. So.

[tex]-\dfrac{b}{2a}=-\dfrac{b}{2(1)}=-\dfrac{b}{2}[/tex]

Put [tex]x=-\dfrac{b}{2}[/tex] in the given function to find the minimum value of the function.

[tex]f(-\dfrac{b}{2})=(-\dfrac{b}{2})^2+b(-\dfrac{b}{2})+182[/tex]

We know that minimum value is 13. So,

[tex]13=\dfrac{b^2}{4}-\dfrac{b^2}{2}+182[/tex]

[tex]13-182=-\dfrac{b^2}{4}[/tex]

[tex]-169=-\dfrac{b^2}{4}[/tex]

[tex]169\times 4=b^2[/tex]

Taking square root on both sides.

[tex]13\times 2=b[/tex]

[tex]b=26[/tex]

The value of b is 26.

So, the given function is  

[tex]f(x)=x^2+26x+182[/tex]

Now, add and subtract square of half of coefficient of x.

[tex]f(x)=x^2+26x+182+(13)^2-(13)^2[/tex]

[tex]f(x)=(x^2+2(13)x+(13)^2)+182-169[/tex]

[tex]f(x)=(x+13)^2+13[/tex]

On comparing with [tex]f(x)=(x-h)^2+k[/tex], we get

[tex]h=-13[/tex]

[tex]k=13[/tex]

Therefore, your answer is incorrect.

Answer: (upside down fancy u) q5

Step-by-step explanation:

Simply apply the law of conservative (upside down fancy u)

Answer:

Step-by-step explanation:

In order to convert a binary number into a decimal, it is expanded in the power of 2. Then, by simplifying the expanded form of the binary number, we obtain a decimal number.

Let's solve:

[tex]1000110[/tex]

[tex] = 1 \times {2}^{6} + 0 \times {2}^{5} + 0 \times {2}^{4} + 0 \times {2}^{3} + 1 \times {2}^{2} + 1 \times {2}^{1} + 0 \times {2}^{0} [/tex]

[tex] = 1 \times 64 + 0 \times 32 + 0 \times 16 + 0 \times 8 + 1 \times 4 + 1 \times 2 \times 0 \times 1[/tex]

[tex] = 64 + 0 + 0 + 0 + 4 + 2 + 0[/tex]

[tex] = 70[/tex]₁₀

Hope I helped!

Best regards!!

Answer:

the ansewr is b

Step-by-step explanation:

Answer:

9 and 23

Step-by-step explanation:

Let x be smaller length in inches.

x+3x-4=32

4x=36

x=9

9*3-4=23

So they're 9 and 23 inches long.

The lengths of the two parts of the pipe are 9 and 23 inches long.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Let x be the smaller length in inches.

x + 3x - 4 = 32

4x = 36

x  =9

Now substitute;

9*3 - 4 = 23

Hence, the lengths of the two parts of the pipe are 9 and 23 inches long.

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Answer:

The value of the exponent of the base 10 for this product is -2.

Step-by-step explanation:

[tex]5.86\,\,10^{-7}\,\,*\,\,3.1\,\,10^4=18.166\,\,10^{-7+4}=18.166\,\,10^{-3}[/tex]

Now, in order to represent this number in scientific notation, we need to reduce the coefficient 18.166 to a coefficient larger or equal to 1 and smaller strictly than 10, by using division or multiplications by powers of 10. In order to reduce it to 1.8166, we need to divide the original 18.166 by ten so we do the following in order not to change the given number (multiply and divide by ten at the same time):

[tex]\frac{18.166\,\,10}{10} \,10^{-3}=1.8166\,*\,10\,*\,10^{-3}=1.8166\,\,10^{-2}[/tex]

Answer:

-2

Step-by-step explanation:

1. Write the expression:       (5.86 × 10–7)(3.1 × 104)

2. Rearrange the expression:     (5.86 × 3.1)(10–7 ∙ 104)

3. Multiply the coefficients:      (18.166)(10–7 ∙ 104)

4. Apply the product of powers:    18.166 × 10-3

5. Write in scientific notation:     1.8166 × 10n

do all this get negitive two

Answer: B

Step-by-step explanation:

Answer:

a]2.3 hrs

b]3.6hrs

Step-by-step explanation:

4hrs = 12 miles

x       =  7miles

4 x 7=28/12=2.3

4 x 11=44/12=3.6hrs

Answer:

Below in bold.

Step-by-step explanation:

His rate of walking =  12/4 = 3 miles per hour.

So the times for 7 and  11 miles are

(a)  7/3 = 2 1/3 hours.

(b) 11/3 = 3 2/3 hours.

Answer: radius = 6.5millimeters; Area = 132.7m²

Step-by-step explanation:

The circumference of a circle = 2πr

The area of a circle = πr²

The circumference of a button is 40.8 millimeters. Then we can get the radius, thus will be:

Circumference = 2πr

40.8 = 2 × 3.14 × r

40.8 = 6.28r

r = 40.8/6.28

r = 6.5

Radius is 6.5 millimeters

Area = πr²

Area = 3.14 × 6.5 × 6.5

Area = 132.7m²

Answer:

12.5%

Step-by-step explanation:

The price for the ski = $2000

The payments made each = $250

percentage of the total cost that the payment is = ?

The percentage will be calculated as

the ratio of the payments made to the price of ski times 100%

250/2000 x 100%

==> 0.125 x 100% = 12.5%

Step-by-step explanation:

Given:

x = 26214.47

s = 5969.25

n = 15

t = 2.046

The confidence interval is:

CI = x ± t (s / √n)

CI = 26214.47 ± 2.046 (5969.25 / √15)

CI = (23061.06, 29367.88)

Answer:

Your correct answer is -b/2a

Step-by-step explanation:

What you need to do is  find the coordinates of the vertex from the equation itself, using this formula: x = -b/2a

Answer:

∆ABC=∆DBC

Step-by-step explanation:

The angle of ABC, which is 90° is the same as the angle DBC which is also 90°

Answer:

He deposited 16 $5 bills.

Step-by-step explanation:

State your variables

let x be the number of $1 bills

let y be the number of $5 bills

Create a system of equations

x + 5y = 200       (eq'n 1 -- for amount of money)

x + y = 136           (eq'n 2 -- for number of bills)

Solve the system for y

I will solve using substitution.  Rearrange eq'n 2 to isolate variable x.

x + y = 136

x = 136 - y           (eq'n 3)

Substitute eq'n 3 into eq'n 1.

x + 5y = 200

136 - y + 5y = 200

136 + 4y = 200

4y = 64

y = 16

Solve for x to check answer

Substitute y = 16 into eq'n 2.

x + y = 136

x + 16 = 136

x = 120

Substitute x = 120 into eq'n 1.

x + 5y = 200

120 + 5(16) = 200

120 + 80 = 200

200 = 200

LS = RS          Both sides are equal, so the solution is correct.

Therefore, Jack deposited 16 five dollar bills.

Answer:

[tex]\boxed{87.5\%}[/tex]

Step-by-step explanation:

Convert fraction to a decimal.

[tex]\frac{7}{8} =0.875[/tex]

Multiply the decimal by 100.

[tex]0.875 \times 100= 87.5[/tex]

Answer:

87.5%

Step-by-step explanation:

100 divided by 8 = 12.5

We know that one eighth of 100 is 12.5. Now we multiply an eighth by 7 to get seven-eighths (7/8)

12.5 * 7 = 87.5

So 7/8 as a percent is 87.5%

Have a good day :)

Answer:

[tex]\large \boxed{\sf \ \ 70\% \ \ }[/tex]

Step-by-step explanation:

Hello,

We assume that the year is 52 weeks, and we note r the interest rate we are looking for. The rate is expressed in percent and is annually, meaning that the investment is, after the first week :

   [tex]1000\cdot (1+\dfrac{r\%}{52})=1000\cdot (1+\dfrac{r}{5200})[/tex]

For the second week

   [tex]1000\cdot (1+\dfrac{r}{5200})^2[/tex]

After 52 weeks

   [tex]1000\cdot (1+\dfrac{r}{5200})^{52}[/tex]

and we want to be equal to 2000 so we need to solve:

[tex]1000\cdot (1+\dfrac{r}{5200})^{52}=2000\\\\\text{*** divide by 1000 both sides ***}\\\\(1+\dfrac{r}{5200})^{52}=\dfrac{2000}{1000}=2\\\\\text{*** take the ln **}\\\\52\cdot ln(1+\dfrac{r}{5200})=ln(2)\\\\\text{*** divide by 52 ***}\\\\ln(1+\dfrac{r}{5200})=\dfrac{ln(2)}{52}\\\\\text{*** take the exp ***}\\\\\displaystyle 1+\dfrac{r}{5200}=exp(\dfrac{ln(2)}{52})=2^{(\dfrac{1}{52})}=\sqrt[52]{2}\\\\r = 5200\cdot (\sqrt[52]{2}-1)=69.77875...[/tex]

Rounded to the nearest percent, the solution is 70%.

If you want to double your capital in one year with weekly compounding you need an interest rate of 70% !!

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

4%

Step-by-step explanation:

Answer:

6.09

Step-by-step explanation:

in ADB

[tex]a ^{2} + b^{2} = c ^{2} [/tex]

to get hypotenuse=8.96

this is height of ABC so use tan

[tex] tan(55.8)= 8.96 \x[/tex]

x=6.09

Answer:

D

Step-by-step explanation:

To find x, we first to to find the line between A&B.

Use the pythagoram theorem to do this A^2+B^2=C^2

4.9^2+7.5^2=C^2

80.26=C^2

square root each side

Side AtoB=8.958

We now know the side length of the opposite and adjacent for the angle C. So according to SohCahToa we need to use Tangent.

So Tan(55.8)=(8.958/x)

We you solve for x, the answer is 6.088

Answer:

k=4

Step-by-step explanation:

We can use the slope formula

m = (y2-y1)/(x2-x1)

-2 = (k-2)/(-4 - -3)

-2 = (k-2)/(-4+3)

-2 = (k-2)/ ( -1)

Multiply by -1

-2 * -1 =  (k-2)/ ( -1) * -1

2 = k-2

Add 2 to each side

2+2 = k-2+2

4 =k

Answer:

[tex]7\sqrt{2}[/tex]

Step-by-step explanation:

Use trigonometry.

sin 45 degrees = x/14

plug in values and you get x = [tex]7\sqrt{2}[/tex]

Answer:

72

Step-by-step explanation:

Answer:

125 : 729

Step-by-step explanation:

Given the ratio of the radii of 2 similar spheres = a : b , then

ratio of volumes = a³ : b³

Here the ratio of radii = 5 : 9 , thus

ratio of volumes = 5³ : 9³ = 125 : 729

Answer:

C. Rectangle ABCD was dilated with center (0, 0) and a scale factor of 1/2 followed by a translation right 3.5 units and down 8 units.

Step-by-step explanation:

See figure for intermediate steps.

The transformed rectangle ABCD was dilated with center (0, 0) and a scale factor of 1/2 followed by a translation right 3.5 units and down 8 units.

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units: y=f(x+c) (same output, but c units earlier)

Right shift by c units: y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the rectangle be represented as ABCD

Now , the coordinates of the rectangle are

A ( 1 , 9 ) , B ( 1 , 6 ) , C ( 7 , 6 ) and D ( 7 , 9 )

Now , the rectangle is dilated with scale factor of 1/2 , we get

A ( 0.5 , 4.5 ) , B ( 0.5 , 3 ) , C ( 3.5 , 3 ) and D ( 3.5 , 4.5 )

And , the rectangle is translated right 3.5 units and down 8 units.

So , the new coordinates of the rectangle is

E ( 4 , -3.5 ) , F ( 4 , -5 ) , G ( 7 , -5 ) and H ( 7 , -3.5 )

Hence , the transformed rectangle is E ( 4 , -3.5 ) , F ( 4 , -5 ) , G ( 7 , -5 ) and H ( 7 , -3.5 )

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Answer:

1,000

Step-by-step explanation:

1,000,000 x 1,000 = 1,000,000,000

1,000,000,000 has 4 more zeros than   1,000,000 and 1,000 has 4 zeros so there 1000 is  the answer.

Answer:

See below.

Step-by-step explanation:

To find the equation, we need to find the slope and the y-intercept. Afterwards, we can put the numbers into the slope-intercept form:

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

From the graph, we can see that the line crosses the y-intercept at y=-6. Thus, the y-intercept (b) is -6.

Now we need to find the slope. Pick any two points where the line crosses. I'm going to pick (0,-6) and (4,-7).

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-7-(-6)}{4-0}= -1/4[/tex]

Therefore, the equation of the line would be:

[tex]y=mx+b\\y=-1/4x-6[/tex]

Answer:

[tex]Volume = 1017.36\ in^3[/tex] -- Cone

[tex]Volume = 3052.08\ in^3[/tex] -- Cylinder

[tex]Volume = 3052.08\ in^3[/tex] -- Sphere

Best Buy: Sphere Clay

Step-by-step explanation:

Given

Solid Shapes: Cone, Cylinder, Sphere

Cost of Cone Clay = $12

Cost of Cylinder Clay = $30

Cost of Sphere Clay = $28

Required

Determine the volume of each shape

Which is the best buy

The volume of a cone is calculated as thus;

[tex]Volume = \frac{1}{3}\pi r^2h[/tex]

From the attached diagram

Radius, r = 9 inches; Height, h = 12 inches and [tex]\pi = 3.14[/tex]

Substitute these values in the above formula;

[tex]Volume = \frac{1}{3} * 3.14 * 9^2 * 12[/tex]

[tex]Volume = \frac{3052.08}{3}[/tex]

[tex]Volume = 1017.36\ in^3[/tex]

The unit cost of the cone is calculated as thus;

[tex]Volume:Price = \frac{Volume}{Total\ Cost}[/tex]

Where

[tex]Volume = 1017.36\ in^3[/tex]

[tex]Total\ Cost = \$12[/tex] (Given)

[tex]Volume:Price = \frac{1017.36\ in^3}{\$ 12}[/tex]

[tex]Volume:Price = 84.78 in^3/\$[/tex]

[tex]Volume:Price = 84.78 in^3:\$1[/tex]

The volume of a cylinder is calculated as thus;

[tex]Volume = \pi r^2h[/tex]

From the attached diagram

Radius, r = 9 inches; Height, h = 12 inches and [tex]\pi = 3.14[/tex]

Substitute these values in the above formula;

[tex]Volume = 3.14 * 9^2 * 12[/tex]

[tex]Volume = 3052.08\ in^3[/tex]

The unit cost of the cone is calculated as thus;

[tex]Volume:Price = \frac{Volume}{Total\ Cost}[/tex]

Where

[tex]Volume = 3052.08\ in^3[/tex]

[tex]Total\ Cost = \$30[/tex] (Given)

[tex]Volume:Price = \frac{3052.08\ in^3}{\$ 30}[/tex]

[tex]Volume:Price = 101.736\ in^3/\$[/tex]

[tex]Volume:Price = 101.736\ in^3:\$1[/tex]

The volume of a sphereis calculated as thus;

[tex]Volume = \frac{4}{3}\pi r^3[/tex]

From the attached diagram

Radius, r = 9 inches; and [tex]\pi = 3.14[/tex]

Substitute these values in the above formula;

[tex]Volume = \frac{4}{3} * 3.14 * 9^3[/tex]

[tex]Volume = \frac{9156.24}{3}[/tex]

[tex]Volume = 3052.08\ in^3[/tex]

The unit cost of the cone is calculated as thus;

[tex]Volume:Price = \frac{Volume}{Total\ Cost}[/tex]

Where

[tex]Volume = 3052.08\ in^3[/tex]

[tex]Total\ Cost = \$28[/tex] (Given)

[tex]Volume:Price = \frac{3052.08\ in^3}{\$ 28}[/tex]

[tex]Volume:Price = 109.003\ in^3/\$[/tex]

[tex]Volume:Price = 109.003\ in^3:\$1[/tex]

Comparing the Volume:Price ratio of the three clay;

The best buy is the sphere because it has the highest volume:price ratio.

Having the highest volume:price ratio means that with $1, one can get more clay from the sphere compared to other types of clay

Answer:

4x-2

Step-by-step explanation:

4x(3x+5)-2(3x+5)

(4x-2)(3x+5)

you can see that 4x-2 is a factor