A perfume company is coming out with a new perfume called "Nile" that has a bottle in the shape of a square pyramid the height of the bottle is 6 centimeters and each side is 8 centimeters long.What is the volume of the Perfume bottle in cubic cm?

Answer:

An expression for the area of the pathway is [tex]4x^2+42x[/tex]

Step-by-step explanation:

Length of garden = 9 feet

Breadth of garden = 12 feet

Area of garden = [tex]Length \times Breadth = 9 \times 12 =108 ft^2[/tex]

We are given that you want to buy a pathway around the garden that is x feet

Width of pathway = x feet

Outer length = 9+x+x=9+2x

Outer breadth = 12+x+x=12+2x

Area of path including garden =[tex]Length \times Breadth = (9+2x)(12+2x)[/tex]

Area of path = Area of path including garden - Area of garden

Area of path =[tex](9+2x)(12+2x)-108[/tex]

Area of path =[tex]108+18x+24x+4x^2-108[/tex]

Area of path =[tex]4x^2+42x[/tex]

Hence an expression for the area of the pathway is [tex]4x^2+42x[/tex]

Answer:

-

[tex] \frac{ - \sqrt{2} }{10} [/tex]

step by step:

[tex] \frac{ - 1}{5 \sqrt{2 } } \times \frac{ \sqrt{2} }{ \sqrt{2} } = \frac{ - \sqrt{2} }{5 \times 2} = \frac{ - \sqrt{2} }{10} [/tex]

multiply by the square root of 2 to get rid of the square root of 2 on the bottom, then simplify. hope this helped :)

[tex]\\ \sf{:}\longrightarrow \dfrac{-1}{5\sqrt{2}}[/tex]

[tex]\\ \sf{:}\longrightarrow \dfrac{-1(5√2)}{(5√2)^2}[/tex]

[tex]\\ \sf{:}\longrightarrow \dfrac{-5√2}{25(2)}[/tex]

[tex]\\ \sf{:}\longrightarrow \dfrac{-5√2}{50}[/tex]

[tex]\\ \sf{:}\longrightarrow \dfrac{-√2}{10}[/tex]

Answer: it will take the faster computer 15 minutes to do the job on its own.

Step-by-step explanation:

Let t represent the number of minutes it will take the faster computer to do the job on its own. It means that the rate at which it does the job per minute is 1/t

If it takes the slower computer 30 minutes to do the job on its own. It means that the rate at which it does the job on its own per minute is 1/30

By working together, they would work simultaneously and their individual rates are additive. Working together it takes two computers 10 minutes to send out a company's email. It means that the rate at which both computers work together per minute is 1/10 Therefore,

1/t + 1/30 = 1/10

Cross multiplying by 30x, it becomes

3x = x + 30

3x - x = 30

2x = 30

x = 30/2

x = 15 minutes

To find the distance between the ranger station and the fire, we can use trigonometry and the angle of depression.

To solve this problem, we can use trigonometry. Let's call the distance from the ranger station to the fire 'x'.

Using the angle of depression of 35°, we can set up the trigonometric equation:

tan(35°) = (height of the ranger station) / x

Plugging in the known values, we get:

tan(35°) = 100 / x

To find 'x', we can rearrange the equation:

x = 100 / tan(35°)

Using a calculator, we can find:

x ≈ 100 / 0.7002

x ≈ 142.811 feet

Therefore, the ranger station is approximately 142.811 feet away from the fire.

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Final Answer:

The ranger station is approximately 142.8 feet away from the fire horizontally.

Explanation:

To find how far the ranger station is from the fire, we can use trigonometry. The ranger is 100 feet above ground, and the angle of depression from the station to the fire is 35 degrees.

Here's how you solve the problem step by step:
1. Imagine a right triangle where the ranger station is at the top, the fire is at the right angle (on the ground), and the line of sight from the ranger makes the hypotenuse.

2. The angle of depression is measured from the horizontal down to the line of sight. However, because alternate interior angles formed by a transversal with two parallel lines are congruent, the angle of depression from the ranger's horizontal line of sight to the fire is equal to the angle of elevation from the ground up to the ranger's line of sight. Therefore, the angle at the bottom of the triangle (the fire's location) is also 35 degrees.

3. We are dealing with the opposite side (the height of the station, 100 feet) and the adjacent side (the distance from the base of the station to the fire, which we want to find). For such problems, we use the tangent function, which relates the opposite to the adjacent side in a right triangle:

  [tex]\(\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}\)[/tex]

4. Plug in the known values:

 [tex]\(\tan(35^\circ) = \frac{100 \text{ feet}}{\text{distance to fire}}\)[/tex]

5. We want to solve for the distance to the fire, so we rearrange the equation:

  [tex]\(\text{distance to fire} = \frac{100 \text{ feet}}{\tan(35^\circ)}\)[/tex]

6. To find the distance to the fire, calculate [tex]\(\frac{100 \text{ feet}}{\tan(35^\circ)}\)[/tex]. You need to ensure you're working in degrees if using a calculator.

Let's do the math using an approximation for [tex]\(\tan(35^\circ)\)[/tex] (which is roughly 0.7002):
 [tex]\(\text{distance to fire} = \frac{100 \text{ feet}}{0.7002}\\\\ \(\text{distance to fire} = 142.8 \text{ feet}\)[/tex]
Hence, the ranger station is approximately 142.8 feet away from the fire horizontally.

Step-by-step explanation:

X interprets (0,0), (-5, 0) all you must do is divide 5 by 2 so 5÷2=2.5 that is your answer

Answer:

16

Step-by-step explanation:

(-3r ^-4) ^-4

(-3) ^-4  * (r^-4) ^-4

We know a^-b = 1/a^b   and c^d^f = c^(d*f)

1/(-3)^4 * (r)^((-4*-4)

1/81 * r^16

The value of m is 16

Answer:

Purse A will contain 2400 (by magic) and Purse B will have 64 pennies

Step-by-step explanation:

how this happened is, by magic Purse A went up by 200 every day for 7 days a week. 7*200 would be 1400 so you add that to the money from today and get 2400. Purse B somehow got from 1 penny to 64 in 7 days. The rule on this is to multiply by 2 every day. 1,2,4,8,16,32 and 64. have fun with your magic :3

Answer: 314cm

Step-by-step explanation:

The area of a circle = πr^2

where π = 3.14

r = radius

From the question, we've been given the radius as 10cm. So, we plug the radius into the formula.

Area= πr^2

= 3.14 × (10 × 10)

= 3.14 × 100

= 314 cm

Answer:

Step-by-step explanation:

Given a composite figure,

A circle of radius r = 10cm

We want to find the area of the circle?

Area of a circle is calculated using

A = πr²

Where π is given to be 3.14

π = 3.14

And r is the radius of the circle

Then, area of the composite figure is

A = πr²

A = 3.14 × 10²

A = 3.14 × 100

A = 314 cm²

The last option is correct

Answer:

The length of line segment QP is 20 units ⇒ 4th answer

Step-by-step explanation:

If a secant and a tangent are drawn from a point outside the circle, then the product of the lengths of the secant and its external segment equals the square of the length of the tangent segment

Look to the attached figure

∵ PQ is a tangent to the circle

∵ PM is a secant intersects the circle at points N and M

- That means the product of the lengths of PM and PN is

   equal to the square of the length of PQ

∴ (PQ)² = (PN). (PM)

∵ The length of Q P is n units

∴ PQ = n

∵ The length of N P is 11.5 units

∴ NP 11.5

∵ The length of M N is 24 units

∴ MN = 24

- The length of the secant PM is the sum of the lengths of PN

   and MN

∵ PM = PN+ NM

∴ PM = 11.5 + 24 = 35.5

Substitute the values of PQ, PN, and PM in the formula above

∵ n² = 11.5 × 35.5

∴ n² = 408.25

- Take √  for both sides

∴ n = 20.205197

- Round it to the nearest unit

∴ n = 20

∵ n is the length of PQ

∴ The length of line segment QP is 20 units

Answer:

D. 20 units

Step-by-step explanation:

Answer:

[tex]\frac{32}{56}\ < \frac{35}{56}[/tex]

[tex]\frac{27}{72} \ < \frac{32}{72}[/tex]

[tex]\frac{20}{24}\ < \frac{21}{24}[/tex]

[tex]\frac{9}{30}\ >\frac{8}{30}[/tex]

Step-by-step explanation:

Given that,

First set of fraction is [tex]\frac{4}{7}\ and \ \frac{5}{8}[/tex].

Second set of fraction is [tex]\frac{3}{8}\ and \ \frac{4}{9}[/tex].

Third set of fraction is [tex]\frac{5}{6}\ and \ \frac{7}{8}[/tex].

Fourth set of fraction is [tex]\frac{3}{10}\ and \ \frac{4}{15}[/tex].

Now,

Considering the first set of fraction:

LCM of 7 and 8 is 56. Now, multiply by 8 to both numerator and denominator to [tex]\frac{4}{7}[/tex]. and multiply by 7 to both the numerator and denominator to [tex]\frac{5}{8}[/tex]. We get new set of fraction as [tex]\frac{32}{56}\ and\ \frac{35}{56}[/tex].

∴[tex]\frac{32}{56}\ < \frac{35}{56}[/tex]

Again considering the second set of fraction:

LCM of 8 and 9 is 72. Now, multiply by 9 to both the numerator and denominator to [tex]\frac{3}{8}[/tex]. and multiply by 8 to both the numerator and denominator to [tex]\frac{4}{9}[/tex]. We get new set of fraction as [tex]\frac{27}{72} \ and \ \frac{32}{72}[/tex].

∴[tex]\frac{27}{72} \ < \frac{32}{72}[/tex].

Again considering the third set of fraction:

LCM of 6 and 8 is 24. Now, multiply by 4 to both the numerator and denominator to [tex]\frac{5}{6}[/tex]. and multiply by 3 to both the numerator and denominator to [tex]\frac{7}{8}[/tex]. We get the new set of fraction as [tex]\frac{20}{24}\ and \ \frac{21}{24}[/tex].

∴[tex]\frac{20}{24}\ < \frac{21}{24}[/tex].

Again considering the fourth set of fraction:

LCM of 10 and 15 is 30.Now, multiply by 3 to both the numerator and denominator to [tex]\frac{3}{10}[/tex]. and multiply by 2 to both the numerator and denominator to [tex]\frac{4}{15}[/tex].We, get the new set of fraction as [tex]\frac{9}{30}\ and \ \frac{8}{30}[/tex].

∴ [tex]\frac{9}{30}\ >\frac{8}{30}[/tex]

Answer:

The angular velocity of the wheel in radians per minute is 96·π·rad/min

Where π = 22/7 then the angular velocity is [tex]301\frac{5}{7} \ rad/min[/tex]

Step-by-step explanation:

The number of revolutions completed per 3 seconds = 2.4 revolutions

∴ The number of revolutions completed per second = 2.4/3 = 0.8 = 4/5 revolutions

The angle per revolution = 2π radians

∴ Angular velocity per second = 0.8×2×π rad/sec

The angular velocity of the wheel in radian per second = 1.6·π·rad/sec

1 minute = 60 Seconds

∴The angular velocity of the wheel in radians per minute = 96·π·rad/minute

Where π = 22/7 then the angular velocity = [tex]301\frac{5}{7} \ rad/min[/tex].

Answer:96pi

Step-by-step explanation:

Answer:

x = -3

Step-by-step explanation:

simplify

3(x - 4) = -21

3x - 12 = -21

3x = = -9

x = -3

Final answer:

Using the recursive relationship f(n) = -5f(n-1) - n, we calculated the values step by step to find that f(4) is -914.

Explanation:

The question asks us to find the value of f(4) given that f(1) = 7 and the recursive relationship f(n) = -5f(n-1) - n.

To find f(4), we need to compute it in a step-by-step manner by first finding f(2) and f(3), and using those results to finally compute f(4).

Starting with f(1) = 7, we calculate f(2):

f(2) = -5f(1) - 2 = -5*7 - 2 = -35 - 2 = -37.

Next, calculate f(3):

f(3) = -5f(2) - 3 = -5*(-37) - 3 = 185 - 3 = 182.

Finally, calculate f(4):

f(4) = -5f(3) - 4 = -5*182 - 4 = -910 - 4 = -914.

Therefore, the value of f(4) is -914.

Final answer:

Using the recursive function given, by computing step by step from f(1) up to f(4), we find that f(4) equals -914.

Explanation:

To find the value of f(4), we must use the given recursive relation f(n) = -5f(n-1) - n, starting with the base case f(1) = 7.

Therefore, f(4) = -914.

Answer:

b

Step-by-step explanation:

Answer:The answer is B

Step-by-step explanation:

Answer:

The number of viewers Network A expects will watch their show is 1.4 million viewers.

Step-by-step explanation:

The expected value is calculated by multiplying the possible outcomes by the probability of their occurrence and adding the results

Therefore, we have the expected value given by the following expression;

Estimated network A viewers  where network B schedule top show = 1.1 million viewers

Estimated network A viewers where network B schedule a different show = 1.6 million viewers

Probability that Network B will air its top show = 0.4

Probability that Network B will air another show = 0.6

We therefore have;

Expected value, E of Network A viewers is therefore;

E = 1.1 × 0.4 + 1.6 × 0.6 =  0.44 + 0.96 = 1.4 million viewers.

Network A expects 1.4 million viewers will watch their show.

Answer:

160/3 got it on the ed thing

The volume of the cone is 167.5 cubic centimeters

The given parameters are:

Radius, r = 4 cm

Height, h = 10 cm

The volume is calculated using:

[tex]V = \frac 13 * \pi r^2h[/tex]

So, we have:

[tex]V = \frac 13 * 3.14 * 4^2 *10[/tex]

Evaluate

[tex]V = 167.5[/tex]

Hence, the volume of the cone is 167.5 cubic centimeters

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Answer:

0.395 kilometre

Step-by-step explanation:

Given:

On Martin's first stroke, his golf ball traveled 4/5 of the distance to the hole.

On his second stroke, the ball traveled 79 meters and went into the hole.

Question asked:

How many kilometres from the hole was Martin when he started?

Solution:

Let distance from Martin starting point to the hole in meters = [tex]x[/tex]

On Martin's first stroke, ball traveled = [tex]\frac{4}{5} \ of \ total \ distance\ to\ the\ hole[/tex]

                                                             [tex]=\frac{4}{5} \times x=\frac{4x}{5}[/tex]

On his second stroke, the ball traveled and went to the hole = 79 meters

Total distance from starting point to the hole = Ball traveled from first stroke + Ball traveled from second stroke

[tex]x=\frac{4x}{5} +79\\ \\ Subtracting\ both\ sides\ by \ \frac{4x}{5}\\ \\ x- \frac{4x}{5}= \frac{4x}{5}- \frac{4x}{5}+79\\ \\ \frac{5x-4x}{5} =79\\ \\ By \ cross\ multiplication\\ \\ x=79\times5\\ \\ x=395\ meters[/tex]

Now, convert it into kilometre:

1000 meter = 1 km

1 meter = [tex]\frac{1}{1000}[/tex]

395 meters = [tex]\frac{1}{1000}\times395=0.395\ kilometre[/tex]

Thus, there are 0.395 kilometre distance from Martin starting point to the hole.

Answer:

Is not a possible solution

Because the number of hours can not be negative

Step-by-step explanation:

Let

x------> the number of hours in the dog walking job

y----->  the number of hours in the sales job

we know that

-----> inequality A

------> inequality B

Remember that

If a ordered pair is a solution of the system of inequalities

then

the ordered pair must satisfy both inequalities

we have

------> Is not a possible solution

Because the number of hours can not be negative

Final answer:

Yes, (-3, 50) is a possible solution

Explanation:

The given system of inequalities is:

x + y < 60

7x + 12y > 450

To check if the solution (-3, 50) is possible, we substitute the values of x and y into the inequalities and check if the inequalities are true.

For the first inequality: (-3) + 50 < 60

47 < 60. This inequality is true.

For the second inequality: 7(-3) + 12(50) > 450

-21 + 600 > 450

579 > 450. This inequality is also true.

Since both inequalities are true when x = -3 and y = 50, we can conclude that (-3, 50) is a possible solution.

Final answer:

The actual distance between Madison and Franklin is 42 miles.

Explanation:

To find the actual distance between Madison and Franklin, we can use the given scale of 1 in: 7 mi. Since Madison and Franklin are 6 inches apart on the map, we can multiply the scale by the number of inches to find the distance in miles.

Distance in miles = Scale x Number of inches apart = 7 mi/in x 6 in = 42 miles

Therefore, the actual distance between Madison and Franklin is 42 miles.

Answer:

The answer is kite.

Step-by-step explanation:

Well, just looking at the definition of a kite, we can see that it lines up with Mr. Tesoro's description and drawing of the quadrilateral. A kite has one right angle that meets up witht two equal lines. The opposite pair of lines, that are much longer, don't meet up to be a right angle. The definitions line up, so there's your match; the anser is kite.

Answer:

4

Step-by-step explanation:

Answer:

Jess used 34 blocks

Step-by-step explanation:

the first stack =7

second stack =7+3=10

third stack =10+7=17

total: 7+10+17=34

Answer:

Increase by 8.75

Step-by-step explanation:

75+82+67+72=296

296/4= 74

74 = Original Mean

75+82+96+78=331

New mean 82.75

82.75-74=8.75

Answer:

The mean increased by 6.8

Step-by-step explanation:

Answer:

23

Step-by-step explanation:

3 times 4 equals 12

then do

35 minus 12

Answer:

a=4

35-3a=

35-3(4)=

35- 12=23

Step-by-step explanation:

Answer:

Statistic

Step-by-step explanation:

-In statistics, a statistic is a characteristic or an attribute of a sample used to estimate or calculate the true values/characteristics of an entire population.

-The value 9.6 is only representative of the small sample size of 104 children.

-If the sample size is sufficient enough it can be used to calculate the population's mean, standard deviation and other Central Limit Theorem measures.

The number 9.46 is referred to as a statistic in this context. A statistic is a characteristic that can be computed from the data in a sample, like the average sleep time of 104 children in this case.

The average number of hours of sleep per night was 9.46 hours for a sample of 104 five to seven year-old children. In this context, the number 9.46 is referred to as a statistic.

A statistic is a characteristic that can be computed from the data in a sample. For example, in this case, the data was collected from a group (or sample) of 104 children, and the average hours of sleep they got per night was calculated. The resultant number, 9.46 hours, serves as an estimation of the parameter we are interested in: the average sleep time of all 5 to 7 year-olds.

The term is frequently used in

statistics

, a branch of math that refers to the collection, analysis, interpretation, presentation, and organization of data.

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Answer:

[tex]y=27x+20[/tex]

8 people went to the game.

Step-by-step explanation:

Let x represent number of tickets.

We have been given that the family parked the car in a parking lot which charged ​$20. The cost per ticket was ​$27.

The cost of x tickets would be [tex]27x[/tex].

The total cost of going to baseball game would be equal to cost x tickets plus parking cost that is [tex]27x+20[/tex].

Therefore, the equation [tex]y=27x+20[/tex] represents the total cost (y) of going to the baseball​ game.

To find the number of people who went to game, we will equate total cost with 236 as:

[tex]236=27x+20[/tex]

[tex]236-20=27x+20-20[/tex]

[tex]216=27x[/tex]

[tex]\frac{216}{27}=\frac{27x}{27}[/tex]

[tex]8=x[/tex]

Therefore, 8 people went to the game.

Answer:

66,000

Step-by-step explanation:

Answer:

GH¢32,500

Step-by-step explanation:

Monthly salary of Mensah=GH¢10,000.00

Commission=15%

15/100×GH¢ 1,500,00.00=GH¢22,500

Total amount earned=

Monthly salary+ Commission

GH¢10,000+GH¢22,500=GH¢32,500

Answer:

GH¢32,500

Step-by-step explanation:

Monthly salary of Mensah=GH¢10,000.00

Commission=15%

15/100×GH¢ 1,500,00.00=GH¢22,500

Total amount earned=

Monthly salary+ Commission

GH¢10,000+GH¢22,500=GH¢32,500