Determine what would happen to the volume of a square based right pyramid if the original dimensions of the base of 10 feet by 10 feet reduced to one fifth. The height of the pyramid is 12 feet.

Answer:

143.2 L

Step-by-step explanation:

1 pm: 1870 L

Each hour, 14% is drained.

x - 14% of x = x - 0.14x = 0.86x

To decrease a number by 14%, multiply the number by 0.86

2 pm: 0.86 × 1870 L = 1608.2 L

3 pm: 0.86 × 1608.2 L = 1383.052 L

4 pm: 0.86 × 1383.052 L = 1189.4247 L

5 pm: 0.86 × 1189.4247 L = 1022.9052 L

6 pm: 0.86 × 1022.9052 L = 879.69847 L

From 5 pm to 6 pm, the volume decreased from 1022.9052 L to 879.69847 L:

1022.9052 L - 879.69847 L = 143.2068 L

Answer: 143.2 L

Answer:

6 1/2

Step-by-step explanation:

The difference between 13 9/20 and 6 7/8 can be found by converting both fractions to decimals and subtracting the two values.

13 9/20 can be expressed as a decimal as 13.45.

6 7/8 can be expressed as a decimal as 6.875.

So, the difference between 13 9/20 and 6 7/8 can be expressed as:

13.45 - 6.875 = 6.575

So the reasonable difference between 13 9/20 and 6 7/8 is 6.575.

By using the unitary method and dividing the time into equal intervals, the number of bacteria doubled every 3 hours, the final total of 32,000 bacteria after 14 hours.

Unitary method involves dividing the time interval into equal parts, and calculating the growth for each unit of time before adding them all up to get the total growth.

To start, let's divide the 14 hours into 3 hour intervals. We have

=> 14 hours / 3 hours = 4 intervals.

Next, we need to calculate the growth in each 3 hour interval. Since the number of bacteria doubles every 3 hours, we can find the growth by multiplying the initial number of bacteria by 2.

Starting with the first interval, we have 2000 bacteria * 2 = 4000 bacteria.

We can now repeat this calculation for each interval, multiplying the previous total by 2 each time.

For the second interval, we have 4000 bacteria * 2 = 8000 bacteria.

For the third interval, we have 8000 bacteria * 2 = 16,000 bacteria.

Finally, for the fourth interval, we have 16,000 bacteria * 2 = 32,000 bacteria.

So, at the end of 14 hours, there will be 32,000 bacteria in the culture.

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The distance between the two corners of the garden is approximately equal to 3 units.

Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using this formula:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represents the data points (coordinates) on a cartesian coordinate.

Substituting the given parameters into the distance formula, we have the following;

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance = √[(5 - 8)² + (-3 - (-2))²]

Distance = √[(-3)² + (-3 + 2)²]

Distance = √[(-3)² + (-1)²]

Distance = √(9 + 1)

Distance = √10

Distance = 3.1623 ≈ 3 units.

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Answer:

as 92 is 2 std deviaiton above mean ; th

Step-by-step expla

If you draw 2 cards, the probability of drawing 1 heart and 1 non-heart card are: 26/676.

It's crucial to keep in mind that your chances may change depending on the particular rules of the card game you're playing. B. The quantity of cards in the deck, the number of cards drawn, and whether or not the cards drawn after play were replaced.

A regular deck of 52 cards has a chance of producing exactly one heart depending on how many cards are drawn.

The likelihood of drawing a heart if you only draw one card is 13/52, or 1/4.

The probabilities of getting a card with a heart and a non-heart are:

(13/52) × (39/51) + (39/52) × (13/51) = 26/676

And if more cards are drawn, the odds of drawing exactly one heart are different.

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Answer:

16

Step-by-step explanation:

You need to find 25% of 64.

To find a percent of a number, multiply the percent by the number.

25% of 64 = 25% × 64

To multiply a percent by a number, change the percent to a decimal by dividing the percent by 100. Move the decimal point two places to the left.

25% × 64 = 0.25 × 64 = 16

The value of the standard deviation depends on the value of the mean.

As per the given data, we have to determine that the value of the standard deviation depends on the value of the mean

Yes, the value of the standard deviation depends on the value of the mean.

Because you have to know the mean to calculate the standard deviation.

The size of the standard deviation of a data set depends on what the mean is because the calculation of the mean is essential for calculating Standard Deviation.

The standard deviation determines how much the values deviate from the mean.

Besides, Standard deviation in simple terms means the deviation of data from the Mean.

The most popular way to assess dispersion is standard deviation, which is based on all values. As a result, even a small change in one value can modify the standard deviation's value.

Hence, Standard Deviation depends on the Mean.

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Answer:

.

Step-by-step explanation:.

Answer:

34/50 or 68% or 0.68

Step-by-step explanation:

S= {16, 12, 22}

16 + 12 + 22 = 50

50 - 16 = 34

34/50

or

68%

or

0.68

Answer:

14

Step-by-step explanation:

14 divided by -2 = -7

Answer: 324

Step-by-step explanation: Take 25% and enter it into a calculator with the percentage sign and times it by 480 and then subtract the number you get from 480, which is 360. Take 10% and enter it and times it by 360 and subtract that number from 360 and you should get 324. :)

The median daily electricity use is 1 kW-hr than the average (arithmetic mean) daily electricity use.

The median is the middle value of a set of data when the data is arranged in order. If there is an odd number of observations, the median is the middle value. If there is an even number of observations, the median is the average of the two middle values.

The data in ascending order is : 19 24 27 29 31

The median of the data is 27.

The mean, or average, is calculated by summing all the values in a set of data and dividing by the total number of observations.

Average of the data is

= ( 19 + 24 + 27 + 29 + 31)/ 5

= 26

The difference is therefore

= 27 - 26

= 1

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If the right triangle has side lengths of 12 feet and 5 feet then the length of hypotenuse is 13 feet.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given that a right triangle has side lengths of 12 feet and 5 feet

We need to find the length of the hypotenuse.

By using pythagoras theorem we find hypotenuse.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides

12²+5²=x²

144+25=x²

169=x²

Take square root on both sides

x=13

Hence, if the right triangle has side lengths of 12 feet and 5 feet then the length of hypotenuse is 13 feet.

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The probability of getting exactly two heads when three coins are tossed is 25%, and the probability of getting one heads and one tail when three coins are tossed is 37.5%.

The probability of getting exactly two heads when three coins are tossed is 1/4 or 25%. This can be calculated using the formula for probability of an event: P(E) = Number of favorable outcomes / Total number of outcomes. In this case, the favorable outcome is two heads, and the total number of outcomes is 8 (2^3) since each coin has two possible outcomes (head or tail). So P(E) = 1/8 = 0.125 = 25%.

The probability of getting one heads and one tail when three coins are tossed is 3/8 or 37.5%. This can be calculated using the same formula as above. In this case, the favorable outcome is one heads and one tail, and the total number of outcomes is 8 (2^3). So P(E) = 3/8 = 0.375 = 37.5%.

The probability of getting exactly two heads when three coins are tossed is 25%, and the probability of getting one heads and one tail when three coins are tossed is 37.5%.

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Answer:

Step-by-step explanation: what you have to do is 36 divided by 3 because he used 3 scoops = 12 now 12 x 4( amount of how many scoops he used)= 48

* you times 4 by 12 because that's the amount he makes with 1 scoop

The stated statement indicates that the item's new cost of goods sold is $37.7.

Exempt and non-exempt workers are the two basic categories into which employees fall. Your business may need to hire a variety of workers in order to function effectively and complete the task. This varies according to the type of organization.

A store manager gives his staff the order to mark up every item by 30%. The retailer paid $29 for the item, and 30% is shown in decimal form.

30/100 = 0.30

30% of the $29 = 0.30 × 29

                         = $8.7

Selling price of the item = Original price of item + 30% of the $29

                                       = $29 + $8.7

                                      = $ 37.7

Consequently, the item's new selling price is $37.7.

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The value of cos(a - B) is 63/65.

option C.

The value of cos(a - B) is calculated by applying the following formula as shown below.

sina = 3/5,

sinb = 5/13

The values of cos(a) and cos(b) is determined by applying Pythagoras tipple.

sin = opp/hypo

third side = adj

if sin (a) = 3/5, cos (a) = 4/5

if sin (b) = 5/13, cos (b) = 12/13

cos (a - b) = cos(a)cos(b) + sin(a)sin(b)

cos (a-b) = (4/5 x 12/13)  +  ( 3/5 x 5/13)

cos ( a -b ) = ( 48 / 65 )  +  ( 3/13 )

cos ( a - b ) = ( 63/65)

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Answer:

14

Step-by-step explanation:

8/9 = 0.888888888......

<5 round down

[tex]\geq[/tex]5 round up

8/9 = 0.888888888....

larger than 0.5

the answer is 14

11,160 cubes can be fit in the prism.

The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

Given:

Cube edge length = 1/2 cm

We have a rectangular prism that measures

= (7 + 1/2)cm by 12cm by (15 + 1/2) cm.

So, the volume is

V = (7 + 1/2)cm x 12cm x (15 + 1/2)cm

   = 1,395 cm³

Now, a cube with an edge length of 1/2 cm has a volume of:

V' = (1/2cm)³

   = 0.125 cm³

Now, the number of cubes fitted

V/V' = ( 1,395 cm³)/(0.125 cm³)

       = 11,160

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Answer:

see below

Step-by-step explanation:

Put first equation into second

18x+3*(-6x+7) =21

open up the bracket

18x -18x+21=21

21 = 21

so infinite many solutions

The expression is solved with x = 6 to 62

Algebraic expressions are simply described as expressions that are composed of variables, coefficients, terms, factors and constants.

They are also composed of mathematical operations

From the information given, we have that;

1/2 x + 7.5 (x) + 11.4 + 2.6

Now, expand the bracket

1/2x + 7.5x + 11.4 + 2.6

Substitute the value of x as 6 , we get;

1/2(6) + 7.5(6) + 11.4 + 2.6

Multiply the values

3 + 45 + 11.4 + 2.6

Add the values

62

Hence, the value is 62

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Step-by-step explanation:

[tex]3x - \frac{8}{2} = x - 6[/tex]

[tex] \frac{8}{2} = 4[/tex]

[tex]3x - 4 + 4 = x - 6 + 4[/tex]

[tex]3x = x - 6 + 4[/tex]

[tex]3x - x = - 6 + 4 - x[/tex]

[tex]3x - x = - 6 + 4[/tex]

[tex]2x = - 2[/tex]

[tex] \frac{2x}{2} = \frac{ - 2}{2} [/tex]

[tex]x = - 1[/tex]

The diameter in inches of the small tire on the toy tractor is; 6 inches

The diameter is defined as the length of the line through the center that touches two points on the edge of the circle.

The parameters are;

Diameter of large tire = 5 ft

Diameter of small tire = 3.75 ft

The sizes are proportional, and as a result we have;

Toy size / actual size = (8 in)/(5 ft) = x/(3.75 ft)

Multiply both sides by 3.75 ft to get;

x = (8 in)(3.75/5)

x = (8 in)(0.75)

x = 6 in

The small tire on the toy is 6 inches in diameter.

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Complete question is;

On tractor,the diameter of the large tire is 5 feet and the diameter of the small tire is 3.75 feet.

A toy tractor is made to scale from the actual tractor. On the toy tractor, the diameter of the large tire is 8 inches

What is the diameter in inches of the small tire on the toy tractor?

The value of x is  x€ {( x1=- 3/4+(√151)/4 i), (- 3/4  - (√151)/4 i)}

2X^2 + 3X + 20 = 0

Here we will use the Quadratic formula:

Once in standard form, identify a,b and c from the original equation and plug them into the quadratic formula.

2x∧2+ 3x +20=0

Give:

Here,

a= 2

b= 3

c= 20

x= (-3±√(3^2-4.2.20))/2a

x= (-3±√(3^2-4.2.20))/2.2

x= (-3±√(9-160))/(      2^(1+1) )

Now take x1 and x2 , as we have two signs + and -.

x1  = (-3+√(9-160))/(      2^2 )

x2   =   (-3-√(9-160))/(      2^2 )

x1  = (-3+√(-151))/(      2^2 )

x2  = (-3-√(-151))/(      2^2 )

x1   =   (-3+√(-151).  √(-1))/(      2^2 )  

x2   =   (-3-√(-151).  √(-1))/(      2^2 )

x1   =   (-3+√151.  i)/(      2^2 )  

x2   =   (-3-√151.  i)/(      2^2 )

x1   =   (-3+√151.  i)/(      4)  

x2   =  - (3+√151.  i)/(      4)

x1= - 3/4+(√151)/4 i

x2= - 3/4  - (√151)/4 i

x€ {( x1=- 3/4+(√151)/4 i), (- 3/4  - (√151)/4 i)}

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The value of an angle in radians that corresponds to a given trigonometric function value can be found using the inverse trigonometric functions.

In the field of mathematics known as trigonometry, correlations between angles and length ratios are studied.

In this case, since sinθ = 1/2, we can use the inverse sine function, denoted as sin^-1, to find the value of θ:

θ = sin^-1 (1/2)

Note that the inverse sine function returns an angle in the range of [−π/2, π/2].

The actual value of the angle may also lie in other ranges, depending on the context in which it is used.

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Answer:

Step-by-step explanation:

A cake recipe says to bake the cake until the center is 180°F, then let the cake cool to 120°F. The table shows

temperature readings for the cake.

a. Given a room temperature of 70°F, what is an

exponential model for this data set?

b. How long does it take the cake to cool to the desired

temperature?

Time (min)

a. The exponential model is y= 114.910(0.854) +70

(Type an expression using x as the variable. Use integers or decimals for any numbers in the expression. Round to three decimal places as needed.)

b. The cake takes about ____ min to cool to 120°F

(Use the answer from part a to find this answer. Round to one decimal place as needed.)

Mar 7, 2019 · Do you know how to solve this? A cake recipe says to bake the c

ata set? How long does it take the cake to cool to the desired temperature? Follow • 1

Mar 7, 2019 · Do you know how to solve this? A cake recipe says to bake the cake until the center is 180° F, then let the cake cool to 100°F. The table shows temperature readings for the cake. Given a room temperature of 69 ° F, what is an exponential model for this data set? How long does it take the cake to cool to the desired temperature? Follow • 1

The correct option for the true proportion is  AB/EF = CD/GH (option D)

Two figures are called similar if they have equal corresponding angles and their side are in same  ratios,

Given that, there are two similar polygons, ABCD and EFGH, we need to find the true proportion for the side of the polygons,

We know that, similar figure have equal ratios of the corresponding sides,

Therefore, we get,

AB/EF = CD/GH = BC/FG = AD/EH

From the options given, the true proportion is

AB/EF = CD/GH (option D)

Hence, the correct option for the true proportion is  AB/EF = CD/GH (option D)

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The total value of the loan in simple interest is $59,625, which is the lowest amount and hence is the best option.

Simple interest is defined as the interest obtained over the principal amount on a certain rate.

Compound interest is defined as the amount of interest which has been calculated on the principal amount and the amount accumulated over the previous period.

Principal amount, P = $50,000

Rate of interest, r = 5.25% = 0.0525

Time,t = 3 years 8 months = 3 + 0.6667 years = 3.6667 years

Part A :

For simple interest, total amount is,

A = P (1 + rt) = 50,000 ( 1 + (0.0525 × 3.6667 ))

                   = $59,625

Part B :

For compounded interest. total amount is,

A = P (1 + [tex]\frac{r}{n}[/tex])^(nt), where n is the number of times compounding is done in an year.

Here, n = 4, since compounding is quarterly

A = 50,000 [ 1 + [tex]\frac{0.0525}{4}[/tex]] ^(4 × 3.6667)

   = $60,537.9639 ≈ $60,537.96

Part C :

For continuously compounded interest, final amount is,

A = P [tex]e^r^t[/tex]

   = 50,000 [tex]e^{0.0525*3.6667[/tex]

   ≈ 60,613.83

Part D :

The option of simple interest is best for the small business owner since the total value of the loan is lowest for it.

Hence the value of the loan for simple interest is $59,625, value of the loan when compounded quarterly is $60,537.96 and the value of the loan when continuously compounded is 60,613.83. Simple interest is the best option since the value of the loan is lowest for it.

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Answer: One Half

Step-by-step explanation: 3 is half of 6 and  I took the test ;)