Simplify the expression: 8y + 4 - 3y + 12

Answer: b=18.1 and c=14.3

Step-by-step explanation:o solve for the lengths of the sides b and c in triangle ABC, we can use the law of sines, which relates the lengths of the sides of a triangle to the sines of the angles opposite those sides. Specifically, the law of sines states that:

a/sin(A) = b/sin(B) = c/sin(C)

where A, B, and C are the angles of the triangle opposite sides a, b, and c, respectively.

Given that a = 17, B = 70°, and C = 48°, we can write:

b/sin(70°) = 17/sin(A)

c/sin(48°) = 17/sin(A)

To solve for b and c, we need to find sin(A). We can do this by using the fact that the angles of a triangle sum to 180°:

A + B + C = 180°

A = 180° - B - C

A = 180° - 70° - 48°

A = 62°

Now we can substitute sin(A) = sin(62°) into the equations above and solve for b and c:

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:

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:

if this helps, please mark my answer as brainliest

Answer:

  h(x) = 3·2^x

Step-by-step explanation:

You want the equation of the exponential curve h(x) = a·b^x when it goes through the points (0, 3) and (1, 6).

When x=0, the equation is ...

  h(0) = a·b^0 = a

We know that h(0) = 3, so a = 3.

When x=1, the equation is ...

  h(1) = 3·b^1 = 3b

We know that h(1) = 6, so 3b = 6, or b = 2.

The equation is h(x) = 3·2^x.

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The point after a dilation by a scale factor of 2 with the origin as the center of dilation, and a translation over the y-axis is (-16, 2).

Given is a point, (8, 1) we need to find the coordinates of a point which is dilated from the origin by the scale factor of 2 and translation over the y-axis,

So, the coordinates of after dilation by k scale factor =

(x, y) = (kx, ky)

So, (8, 1) = (16, 2)

Now, the translation over the y-axis gives,

(x, y) = (-x, y)

Therefore, (16, 2) = (-16, 2)

Hence, the point after a dilation by a scale factor of 2 with the origin as the center of dilation, and a translation over the y-axis is (-16, 2).

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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: 6.5

Step-by-step explanation:

26/4 = 6.5 hours

The value of sin A using trigonometric ratios is: 12/13

There are three main trigonometric ratios in right angle triangles and they are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

We want to find sin A and as such using trigonometric ratios on the attached right angle triangle, we have:

sin A = 12/13

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The value of the missing length of the enlarged triangle in the simplest form would be = 60mm.

To calculate the missing length, the formula for scale factor should be used such as follows;

Scale factor = Larger dimensions/smaller dimensions

length of ∆T = 10mm

length of ∆S = 3mm

scale factor = 10/3 = 3.33

If the width of ∆S = 18mm

width of ∆ T = 18×3.33

= 59.94 = 60mm

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Answer:

0.375

Step-by-step explanation:

The surface area of the polyhedron is calculated be equal to 224 square inches.

The polyhedron can be observed to have a large rectangle between two identical triangles by the sides

area of rectangle = length × width

The large rectangle have;

length = (12 + 10 + 10) in = 32 in

width = 4 in

area of large rectangle the = 32 in × 4 in = 128 in²

area of one identical triangles = 1/2 × 12 in × 8 in = 48 in²

area of 2 identical triangles = 2 × 48 in² = 96 in²

Surface area of the polyhedron = 128 in² + 96 in²

Surface area of the polyhedron = 224 in²

Therefore, the surface area of the polyhedron is calculated be equal to 224 square inches.

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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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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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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.

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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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.

Answer:

We can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where A is the ending amount, P is the principal (starting amount), r is the interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time in years.

We know P = $5700, A = $6100, n = 1 (since the interest is compounded annually), and t = 12. We can solve for r:

$6100 = $5700(1 + r/1)^(1*12)

$6100/$5700 = (1 + r)^12

1.0702 = (1 + r)^12

log(1.0702) = log[(1 + r)^12]

0.0291 = 12log(1 + r)

0.00243 = log(1 + r)

10^(0.00243) = 1 + r

r = 0.0059 or 0.59%

Therefore, the interest rate of the savings account is 0.59%.

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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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 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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Yes, of course!

Ricardo has made 4 out of the 12 recipes in his cookbook.

To find out what fraction of the recipes he has made, you can write it as a fraction:

4/12

To simplify this fraction, you can divide both the numerator and denominator by 4, which gives:

4/12 = 1/3

Therefore, Ricardo has made 1/3 of the recipes in his cookbook.

Answer:

approximately 183.4 square centimeters.

Step-by-step explanation:

We can use the formula for the circumference of a sphere, which is:

C = 2πr

where C is the circumference and r is the radius.

We know that the circumference of the pincushion is 24 cm. We can use this to find the radius:

C = 2πr

24 = 2πr

r = 24/(2π)

r ≈ 3.82 cm

Now that we know the radius, we can use the formula for the surface area of a sphere, which is:

A = 4πr^2

Substituting the value we found for the radius, we get:

A = 4π(3.82)^2

A ≈ 183.4 cm^2

Therefore, the surface area of the pincushion is approximately 183.4 square centimeters.

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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A function of the form y= A sin (Bx-C)+D that has period 8, phase shift -2, and the range -12 ≤y≤-4 is y = 4 sin (π/4 x + π/2) - 8

To write a function of the form y = A sin (Bx - C) + D that has a period of 8 and phase shift of -2, we can use the general formula:

y = A sin [(2π/P)(x - C)] + D

where P is the period, C is the phase shift, and D is the vertical shift. In this case, P = 8 and C = -2, so we have:

y = A sin [(2π/8)(x + 2)] + D

Simplifying the equation, we get:

y = A sin (π/4 x + π/2) + D

To find the amplitude A and vertical shift D that satisfy the range -12 ≤ y ≤ -4, we can use the fact that the sine function oscillates between -1 and 1. If we set A = 4, then the maximum value of y is 4 + D, and the minimum value of y is -4 + D. To ensure that the range is -12 ≤ y ≤ -4, we need to choose D such that:

4 + D ≤ -4 and -4 + D ≥ -12

Solving these inequalities, we get:

-8 ≤ D ≤ 0

Therefore, a function that satisfies the given conditions is:

y = 4 sin (π/4 x + π/2) - 8

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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

The quantity of pasta is served to Olivia is 60 in³.

Olivia's mother packed her lunch in a lunch box which is in the shape of rectangular prism, with dimension = length= 5 in, width= 4 in, height= 3 in,

We need to find the quantity of the lunched packed in the box,

So, we will find the volume of the box = length × width × height

= 5 × 4 × 3

= 60 in³

Hence the quantity of pasta is served to Olivia is 60 in³.

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Answer:

16.5 = 6

Step-by-step explanation:

The equation given is (+25)-5x5:2+2² = 27-5×5=2+2². When calculating, we first simplify the division to get (+25)-12.5+4 = 27-25+4. Then we add and subtract the values on either side to get 16.5 = 6. Finally, as the equation is incorrect, we can conclude that the initial assertion is false. It is important to carefully follow the order of operations and simplify expressions correctly to avoid errors in equations.

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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