Triangle ABC
A
B
C
and triangle DEF
D
E
F
are similar. What is the measure of side DF
D
F
?

The surface area of each square pyramid, we used the formula Surface Area = Base Area + 4 x (1/2 x Base x Height of Face) is 1049.2mm², 1285.8mm² and 2100mm². The cost to cover each pyramid was $1.05, $1.29 and $2.10.

To calculate the surface area of each pyramid, we need to use the formula

Surface Area = Base x Height of face + 2 x ((Base/2) x Slant Height)

For the small pyramid, we have

Surface Area = 20 x 25 + 2 x ((20/2) x 26.46)

Surface Area = 500 + 2 x 10 x 26.46

Surface Area = 1049.2 mm²

Cost to cover the small pyramid

Cost = Surface Area x 0.001

Cost = 1049.2 x 0.001

Cost = $1.05

For the medium pyramid, we have

Surface Area = 20 x 40 + 2 x ((20/2) x 42.43)

Surface Area = 800 + 2 x 10 x 42.43

Surface Area = 1285.8 mm²

Cost to cover the medium pyramid

Cost = Surface Area x 0.001

Cost = 1285.8 x 0.001

Cost = $1.29

For the large pyramid, we have

Surface Area = 30 x 40 + 2 x ((30/2) x 50)

Surface Area = 1200 + 2 x 15 x 50

Surface Area = 2100 mm²

Cost to cover the large pyramid

Cost = Surface Area x 0.001

Cost = 2100 x 0.001

Cost = $2.10

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The area of a flower bed is 24 square feet and the equation to represent the equal area is 24+20x+4x²=24.

Given that, the dimensions of rectangular flower bed are length= 6 feet and  width = 4 feet.

Dimensions of large rectangle are Length = 6+2x and width = 4+2x

Now, area of large rectangle = (6+2x)×(4+2x)

= 24+8x+12x+4x²

Area of a rectangular flower bed = 6×4

= 24 square feet

Tulips and Daisy have same area to plant

So, the equation is 24+20x+4x²=24

4x²+20x=0

Therefore, the area of a flower bed is 24 square feet and the equation to represent the equal area is 24+20x+4x²=24.

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The calculated area of this triangle is 43.50 sq units

From the question, we have the following parameters that can be used in our computation:

The triangle

The area of the triangle is calculated as

Area = 1/2 * Product of adjacent legs * sin of middle angle

Substitute the known values in the above equation, so, we have the following representation

Area = 1/2 * 12 * 8 * sin(65)

Evaluate

Area = 43.50

Hence, the area is 43.50 sq units

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Answer: x < 5, see attached

Step-by-step explanation:

     To solve for x, we will isolate the given variable.

Given:

  [tex]\displaystyle 1 > \frac{x}{5}[/tex]

Multiply both sides of the equation by 5:

  [tex]\displaystyle5 > x[/tex]

Flip equation:

  [tex]\displaystyle x < 5[/tex]

     To graph, we will first plot a point on 5 with an open circle. Then, we will shade to the left since x is less than 5. See attached.

The value of row total of the column total's is 165.

The value of row total of field is 91

Column total of maple can be found by:

(46.32 /100) * y =44

Or y = (44 *100)/46.32

Or y = 94.991 =95 (approx)

Now we get value of field under maple by

Value of field under maple = (column total - value of pond under maple) = (95 - 44) = 51

Value of row total of the column total's = (column total of oak + column total of maple = (70 + 95) = 165 (total data)

Value of row total of field = ( value of field under oak + value of field under maple) = (40 + 51) = 91

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Answer:

y=mx + b

Step-by-step explanation:

y=3x-4

3 is the slope and -4 is the y intercept

Answer:

m/2 -6= m/4+2 can be solved as follows:

Multiply both sides of the equation by the least common multiple of the denominators, which is 4:

4(m/2 - 6) = 4(m/4 + 2)

2m - 24 = m + 8

Subtract m from both sides:

m - 24 = 8

Add 24 to both sides:

m = 32

Therefore, the value of m is C) 32.

k/12 = 25/100 can be solved as follows:

Multiply both sides of the equation by 12:

k = 12 * (25/100)

k = 3

Therefore, the value of k is A) 3.

9/5 = 3x/100 can be solved as follows:

Multiply both sides of the equation by 100:

100 * (9/5) = 3x

Simplify:

180/5 = 3x

36 = 3x

Divide both sides by 3:

x = 12

Therefore, the value of x is not one of the options provided.

Step-by-step explanation:

Answer:

[tex] \sf \longrightarrow \: \frac{m}{2} - 6 = \frac{m}{4} + 2 \\ [/tex]

[tex] \sf \longrightarrow \: \frac{m - 12}{2} = \frac{m + 8}{4}\\ [/tex]

[tex] \sf \longrightarrow \: 4(m - 12) =2(m + 8)\\ [/tex]

[tex] \sf \longrightarrow \: 4m \: - 48 =2m + 16\\ [/tex]

[tex] \sf \longrightarrow \: 4m \: - 2m = 16 + 48\\ [/tex]

[tex] \sf \longrightarrow \:2m = 64\\ [/tex]

[tex] \sf \longrightarrow \:m = \frac{64}{2} \: \\ [/tex]

[tex] \sf \longrightarrow \:m = 32 \: \\ [/tex]

[tex] \qquad{ \underline{\overline{ \boxed{ \sf{ \: \: C) \: \: \: 32 \: \: \: \: \: \checkmark }}}}} \: \: \bigstar[/tex]

__________________________________________

[tex] \sf \leadsto \: \frac{k}{12} = \frac{25}{100} \\ [/tex]

[tex] \sf \leadsto \: 100(k)= 12(25) \\ [/tex]

[tex] \sf \leadsto \: 100 \times k= 12 \times 25 \\ [/tex]

[tex] \sf \leadsto \: 100 k= 300 \\ [/tex]

[tex] \sf \leadsto \: k= \frac{300}{100} \\ [/tex]

[tex] \sf \leadsto \: k= 3 \\ [/tex]

[tex] \qquad{ \underline{\overline{ \boxed{ \sf{ \: \: a) \: \: \: 3 \: \: \: \: \: \checkmark }}}}} \: \: \bigstar[/tex]

__________________________________________

[tex] \sf \longrightarrow \: \frac{9}{5} = \frac{3x}{100} \\ [/tex]

[tex] \sf \longrightarrow \: 100(9)= 5(3x) \\ [/tex]

[tex] \sf \longrightarrow \: 100 \times 9= 5 \times 3x \\ [/tex]

[tex] \sf \longrightarrow \: 900= 15x \\ [/tex]

[tex] \sf \longrightarrow \: x= \frac{900}{15} \\ [/tex]

[tex] \sf \longrightarrow \: k= 60 \\ [/tex]

[tex]\qquad{\underline{\overline {\boxed{ \sf{ \: \: a) \: \: \: 60 \: \: \: \: \: \checkmark }}}}} \: \: \bigstar[/tex]

__________________________________________

When distributed directly proportionally among the people, using age, the result would be b) 3 years = 6,000, 7 years = 14,000, 10 years = 20,000.

First, find the total age of the people give :

= 10 + 7 + 3

= 20

To amount that would go to 10 as a directly proportional measure is:

= 10 / 20 x 40, 000

= 20, 000

The amount to 7 as a directly proportional value would be:

= 7 / 20 x 40, 000

= 14, 000

The amount to 3 would follow the same pattern :

= 3 / 20 x 40, 000

= 6, 000

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Answer:

Step-by-step explanation:

1. Get mileage per gallon by dividing miles traveled by gallons used

[tex]\frac{125}{5} = 25 mpg\\[/tex]

2. Divide miles you want to travel by the mileage per gallon you got on the first step

[tex]\frac{400}{25} = 16 gallons[/tex]

The simplified expression is:

8y + 4 - 3y + 12 = 5y + 16

Remember the distributive property:

A*(B + C) = A*B + A*C

Now let's look at our expression, it is:

8y + 4 - 3y + 12

We can reorder the terms to get:

8y - 3y +4 + 12

Now we can take y as a common factor:

(8 - 3)y + 4 + 12

Now simplify the two operations:

(8 - 3)y + 4 + 12 = 5y + 16

That is the expression simplified.

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The value of x and y are,

x = 8 and y = 4

We have to given that;

Tim has $20 to buy snacks for 12 people in an office.

And., Tim is buying bags of pretzels that cost $1.50 per bag and bags of crackers that cost $2.00 per bag.

Let x represent bags of pretzels.

And, y represent bags of crackers.

Hence, We can formulate;

x + y = 12  .., (i)

And, 1.5x + 2y = 20  .. (ii)

From (i);

x = 12 - y

Plug in (ii):

1.5 (12 - y) + 2y = 20

18 - 1.5y + 2y = 20

18 + 0.5y = 20

0.5y = 2

y = 2/0.5

y = 4

And, x = 12 - 4

x = 8

Thus, The value of x and y are,

x = 8 and y = 4

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Answer: 6.5

Step-by-step explanation:

26/4 = 6.5 hours

The original sample box had a volume of 343 cubic cm, which is half the volume of the new sample box.

Since the height of the new sample box is twice as long as the original box, its height will be 2×7=14 cm.

The length and width remain the same at 7 cm.

The volume of the new sample box is given by the formula:

V = lwh

Substituting the values, we get:

V = (7)(7)(14) = 686 cubic cm

Therefore, the volume of the new sample box is 686 cubic cm.

Comparing the volumes of the two boxes, we see that the new sample box has a larger volume than the original sample box.

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It will take approximately 8 days for the virus to grow from 180 to 260.

We can set up a proportion to solve this problem. Let "x" represent the number of days it will take for the virus to grow from 180 to 260.

The proportion can be set up as follows;

(Change in value) / (Time taken) = (Change in value) / (Time taken)

Using the given information, we have;

(260 - 180) / x = (230 - 180) / 5

Simplifying the fractions on both sides of the equation, we get:

80 / x = 50 / 5

Cross-multiplying, we have;

80 × 5 = 50 × x

400 = 50x

Dividing both sides of the equation by 50, we get;

x = 400 / 50

x = 8

Therefore, it will take 8 days.

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The total surface area of the composite figure is: 288.62 mm²

From the attached image, we can see that the composite figure is made up of 2 triangles and one rectangle. Thus:

Formula for area of rectangle is:

A = Length * Width

Formula for area of triangle is:

A = ¹/₂ * base * height

Using Pythagoras theorem, length of rectangle is:

L = √(10.4² + 15.3²)

L = 18.5 mm

Thus:

TSA = (18.5 * 7) + 2(¹/₂ * 15.3 * 10.4)

TSA = 129.5 + 159.12

TSA = 288.62 mm²

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Answer:

x= -18

Step-by-step explanation:

-2/3x + -21/4 = 27/4

-8x-63=81

-8x-63+63=81+63

-8x=144

-8x/-8 = 144/-8

x=-18

Answer:

0 ≤ < 2

Step-by-step explanation:

Answer:1.02 5.27 are correct

Step-by-step explanation:We can solve this quadratic equation in cos(θ) by using the substitution u = cos(θ):

3u^2 + 6u - 4 = 0

Now we can use the quadratic formula to solve for u:

u = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 3, b = 6, and c = -4. Substituting these values, we get:

u = (-6 ± sqrt(6^2 - 4(3)(-4))) / 2(3)

u = (-6 ± sqrt(84)) / 6

u = (-3 ± sqrt(21)) / 3

Therefore, either:

The expansion and simplification of the expression (x - 2)² is x² - 4x + 4.

An algebraic expression is a combination of variables with constants, numbers, and values using the mathematical operands addition, subtraction, multiplication, or division.

(x - 2)²

Expanding the square:

(x - 2)² = (x - 2)(x -2)

Distributing the square:

x(x - 2) - 2(x - 2)

x² - 2x - 2(x -2)

x² - 2x - 2x + 4

x² - 4x + 4

Thus, after expanding and simplifying the algebraic expression (x - 2)², the solution is x² - 4x + 4.

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Based on the standard deviation given and the sample size, the test statistic can be found to be 134.20.

The test statistic can be found by the formula:

= ((Sample size - 1) x Standard deviation of sample²) / Standard deviation of population

Solving gives:

= ((173 - 1) x 10.6²) / 12²

= 19,325.92 / 144

= 134.20

Hence, the test statistic is 134.20.

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Answer:

If 2:3 = x:12, then:

2/3 = x/12

Multiplying both sides by 12, we get:

x = 2/3 x 12 = 8

Therefore, the value of x is 8.

Krell's equity cost of capital, or expected total return, is 5.57%.

We have,

The dividend yield is the annual dividend divided by the current share price:

Dividend yield

= Annual dividend / Share price

= $0.98 / $22.08 = 0.0444 = 4.44%

The equity cost of capital is the expected total return on the stock, which includes both the dividend yield and the expected capital appreciation:

Equity cost of capital = Dividend yield + Capital Appreciation

= 4.44% + [(24.98 - 22.08) / 22.08]

= 4.44% + 0.1314

= 5.57%

Therefore,

Krell's equity cost of capital, or expected total return, is 5.57%.

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The required solution to the equation 1/5 + s = 32/40 is s = 3/5.

To solve the equation 1/5 + s = 32/40 for s, we can begin by subtracting 1/5 from both sides to isolate s:

1/5 + s = 32/40

s = 32/40 - 1/5

We need a common denominator to combine the fractions on the right side of the equation. The least common multiple of 5 and 40 is 40, so we can convert both fractions to have a denominator of 40:

s = (32/40) - (8/40)

s = 24/40

Simplifying the fraction 24/40 by dividing both the numerator and denominator by their greatest common factor, which is 8, we get:

s = 3/5

Therefore, the solution to the equation 1/5 + s = 32/40 is s = 3/5.

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Answer:

To calculate the minimal cost of logistics from a factory to a warehouse, you would need to consider various factors such as the distance between the factory and the warehouse, the mode of transportation, the weight and volume of the goods being transported, the number of trips required, and any applicable taxes or fees.

To formulate this as a mathematical problem, you could use linear programming, which is a method for optimizing a linear objective function subject to linear equality and inequality constraints.

Let's say we have a factory that produces goods and a warehouse that stores those goods. We want to transport the goods from the factory to the warehouse in a cost-effective way. Let's assume that there are three transportation options available: truck, train, and ship. Each option has a different cost per unit of distance traveled, and a different maximum weight and volume capacity.

Let x1, x2, and x3 be the number of units transported by truck, train, and ship, respectively. Then, the objective function we want to minimize would be:

C = 10x1 + 8x2 + 6x3

where C is the total cost of transportation.

Next, we would need to set up constraints based on the transportation options and the available resources. For example:

Truck capacity: 3x1 <= 15000 (maximum weight capacity of 15000 units for the truck)

Train capacity: 5x2 + 2x1 <= 40000 (maximum weight capacity of 40000 units for the train)

Ship capacity: 2x3 + 3x1 <= 30000 (maximum weight capacity of 30000 units for the ship)

Distance constraint: 2x1 + 3x2 + 5x3 <= 10000 (maximum distance of 10000 units for all transportation modes combined)

The above constraints limit the total weight transported, the capacity of each mode of transport, and the total distance that the goods are transported.

Finally, we would need to add non-negative constraints to ensure that all variables are greater than or equal to zero:

x1 >= 0, x2 >= 0, x3 >= 0

Once we have set up this linear programming problem, we can use optimization techniques to solve for the values of x1, x2, and x3 that minimize the cost of transportation while satisfying all of the constraints.

Step-by-step explanation:

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Answer:

The height of the kite is 63.40 feet.

Trigonometric ratio is used to show the relationship between the sides of a triangle and its angles.

Let h represent the height of the kite. Hence, using trigonometric ratios:

sin(30) = h / 95

h = 47.5 feet

Therefore the height of the kite is 63.40 feet.

The value of the identities are;

1. tan θ = 5/12

2. cot θ = √7/3

To determine the value of the identities, we need to take note of the different identities;

From the information given, we need to take note that;

tan θ = opposite/adjacent

cot θ = inverse of tangent identity

cot θ = adjacent/opposite

then,

1. tan θ =

Opposite = 5

Adjacent = 12

tan θ = 5/12

2. cot θ = 4√7/12 = √7/3

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The probability of at least 8 homes would prefer brand B compare to compare A is given by 0.672.

Sample size 'n'= 25

Proportion of people prefer brand A = 0.4

This implies ,

Proportion of people prefer brand B 'p' = 1 - 0.4

                                                                  = 0.6

Using the binomial distribution.

Let X be the number of homes that prefer brand B out of the 25 homes surveyed.

Then X follows a binomial distribution with parameters n = 25 and p = 0.6

Probability that at least 8 homes would state a preference for brand B. expressed as,

P(X ≥ 8) = 1 - P(X < 8)

Using the binomial distribution, compute P(X < 8) as follows,

P(X < 8) = Σ [²⁵Cₓ] × 0.6ˣ × 0.4²⁵⁻ˣ, for x = 0, 1, 2, ..., 7

where ²⁵Cₓ is the binomial coefficient which represents the number of ways to choose k homes out of 25.

Use a binomial calculator ,

⇒P(X < 8) = [²⁵C₀] × 0.6⁰× 0.4²⁵⁻⁰ + [²⁵C₁] × 0.6¹× 0.4²⁵⁻¹ + [²⁵C₂] × 0.6²× 0.4²⁵⁻² + .......+ [²⁵C₇] × 0.6⁷× 0.4²⁵⁻⁷  

⇒P(X < 8) ≈ 0.328

This implies,

P(X ≥ 8) = 1 - P(X < 8)

             ≈ 1 - 0.328

             = 0.672

Therefore,  the probability that at least 8 homes would state a preference for brand B is approximately 0.672.

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The above question is incomplete , the complete question is:

A manufacturer of floor wax has developed two new brands, A and B.  which she wishes to subject to homeowners' evaluation to determine which of the two is superior. Both waxes are applied to the floor surfaces in each of a sample of 25 homes. It is known that the proportion of people that prefer A is 0.4 while the rest prefer brand B.

Find the probability that at least 8 homes would state a preference for brand B.

The 30th percentile in the uniform distribution is 2.4 min.

The correct option is (b)

The probability formula is defined as the ratio of favorable outcomes to the ratio of total outcomes. For any event (E), :

P(E)= Number of favorable outcomes/ Number of total outcomes

[tex]\mu=\frac{a +b}{2}[/tex]

[tex]\sigma=\sqrt{\frac{(b-a)^2}{12} }[/tex]

P(x) = 1/ b - a if a < x < b

P(X < a) = 0

and

P(X > b) = 0

In this case, a = 0 and b = 8

The 30th percentile in the uniform distribution, this means that the probability is 0.30. Therefore:

0.3 = [tex]\frac{1}{8-0}.x[/tex]

0.3 (8 -0) = x

2.4 = x

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The given question is incomplete, complete question is :

The Sky Train from the terminal to the rental-car and long-term parking center is supposed to arrive every eight minutes. The waiting times for the train are known to follow a uniform distribution. Find the 30th percentile for the waiting times (in minutes).

a. 2

b. 2.4

c. 2.75

d. 3

Answer:

  499,237 ft²

Step-by-step explanation:

You want the lateral area of a square pyramid 580 feet on a side and 318 feet tall.

To find the area of each triangular face, we must know its slant height. That can be found from the base and height of the pyramid using the Pythagorean theorem. Once we know the slant height, we can use the formula for the area of a triangle:

  A = 1/2bh

There are 4 congruent triangular faces, so the lateral area of the pyramid will be 4 times the area of one face:

  4A = 4(1/2bh) = 2bh

The slant height of a face of the pyramid is the hypotenuse of a right triangle with one leg equal to the height of the pyramid, and the other leg equal to half the length of a base edge. (This is the distance from the midpoint of the bottom edge of a face to the center of the base, under the peak of the pyramid.)

  h = √((580/2)² + 318²) ≈ 430.3766 . . . . feet

  lateral area = 2(580 ft)(430.3766 ft) ≈ 499237 ft²

The surface area of the glass is about 499237 square feet.

The number of cans brought by Joes team is J = 299 cans

Given data ,

Let the number of cans brought by Joes team be J

Now , sage team brought 224 cans

And , sage team brought 3 times cans as asifs team

And , joes team brought 4 times as asifs team

On simplifying the equation , we get

Asif's team brought 224/3 = 74.67 (rounded to the nearest whole number) cans.

Joe's team brought 74.67 x 4 = 298.68

So , J = 299 cans

Hence , the equation is solved and J = 299 cans

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