Find the area of triangle ABC.
Give your answer correct to 1 decimal

Answer:

x=24

Step-by-step explanation:

Answer:

Step-by-step explanation:

x / -4 = -6

x = -6 (-4)

x = 24

Answer:

60%= 40

50%=not possible

Step-by-step explanation:

x=grade on final

(65*.8) + (x*.2)=60

52+.2x=60

.2x=8

x=40

(65*.8) + (x*.2)=50

52+.2x=50

.2x=-2

x=-10

not possible

Answer:

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Answer:

Each pizza needs 1/6 pound (lb) of cheese.

for one pizza = 1/6 pound (lb)

If A chef is making 14 pizzas.

so, 14 pizza = 14 . 1/6 pound (lb)

                   = 14/6 pound (lb)

                    = 7/3pound (lb)

Step-by-step explanation:

Answer:

h= -5.8

Step-by-step explanation:

Answer:

luxury=15

sports cars 25

Step-by-step explanation:

Step one:

let the luxury cars be x

and the sports cars be y

the objective function is

maximize

15000x+16000y=625000------1

the constraints are

1. Man-hours

1600x+1500y=61500-----------2

Step two:

the system of equation for the situation is

15000x+16000y=625000------1

1600x+1500y=61500-----------2

let us reduce both equation

divide equation 1 be 1000

and equation 2 by 100 we have

15x+16y=625--------1 x15

16x+15y=615--------2 x16

  225x+240y=9375

 -256x+240y=9840

=-31x+0=-465

31x=465

x=465/31

x=15

put x=15 in 15x+16y=625 we have

15(15)+16y=625

225+16y=625

16y=625-225

16y=400

y=400/16

y=25

The sampling method that is most likely to be appropriate for calculating confidence intervals is simple random sampling.

This method ensures that every member of the population has an equal chance of being selected for the sample. This reduces the risk of bias and ensures that the sample is representative of the population. Stratified sampling is also a useful method for calculating confidence intervals, especially when the population has subgroups that need to be represented in the sample. However, other sampling methods like convenience sampling or quota sampling are not appropriate for calculating confidence intervals as they can introduce bias into the sample and do not guarantee a representative sample. Therefore, it is important to use an appropriate sampling method when calculating confidence intervals to ensure that the results accurately reflect the population.

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Math SAT scores explain about 98.7% of the variation in the total SAT scores.

In statistics, correlation or dependence exists as any statistical relationship, whether causal or not, between two random variables or bivariate data.

A correlation exists as a statistical measure (expressed as a number) that defines the size and direction of a relationship between two or more variables. A correlation between variables, however, does not automatically mean that the change in one variable exists as the cause of the change in the values of the other variable.

Since r² exists = (0.9935)² = 0.9870, we interpret r² as 98.7% of the variation in the y variable exists explained by the x variable.

In context, math SAT score explains about 98.7% of the variation in total SAT score.

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Answer:

b = -2.7

Step-by-step explanation:

Isolate the variable, b

-5 = b - 2.3

add 2.3 to both sides (to isolate variable b)

-5 + 2.3 = b - 2.3 + 2.3

-2.7 = b + 0

-2.7 = b

Check work:

-5 = -2.7 - 2.3

-5 = -5

Correct

Displacement is the length of the straight line drawn from an object’s initial position to the object’s final position

The term "displacement" refers to a change in an object's position. It is a vector quantity with a magnitude and direction. The symbol for it is an arrow pointing from the initial position to the ending position. For instance, if an object shifts from position A to position B, its position changes.

If an object moves with respect to a reference frame, such as when a passenger moves to the back of an airplane or a professor moves to the right with respect to a whiteboard, the object's position changes. This change in location is described as displacement.

The displacement is the shortest distance between an object's initial and final positions. Displacement is a vector. It is visualized as an arrow that points from the initial position to the final position, indicating that it has both a direction and a magnitude.

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For the multisets {3 · a, 2 · b, 1 · c} and {2 · a, 3 · b, 4 · d} the solutions are  A ∪ B is {3 · a, 2 · b, 1 · c, 2 · a, 3 · b, 4 · d},A ∩ B is {2 · a, 2 · b},A − B is {1 · a, 0 · b, 1 · c} ,B − A is {0 · a, 1 · b, 4 · d} and A + B is {5 · a, 5 · b, 1 · c, 4 · d}.

We will use the given multisets A and B:

A = {3 · a, 2 · b, 1 · c}
B = {2 · a, 3 · b, 4 · d}

a) A ∪ B (union): This operation combines all elements of both multisets.
A ∪ B = {3 · a, 2 · b, 1 · c, 2 · a, 3 · b, 4 · d}

b) A ∩ B (intersection): This operation finds the common elements between both multisets.
A ∩ B = {2 · a, 2 · b} (as a and b are the common elements)

c) A − B (difference): This operation removes elements in B from A.
A − B = {1 · a, 0 · b, 1 · c}

d) B − A (difference): This operation removes elements in A from B.
B − A = {0 · a, 1 · b, 4 · d}

e) A + B (sum): This operation adds the counts of the elements in both multisets.
A + B = {5 · a, 5 · b, 1 · c, 4 · d}

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Answer:$2.40

Step-by-step explanation: divide the ounce with the cost

12 / 4.99 =2.40

I would say maybe 41 or 42 cents

Answer:

115

Step-by-step explanation:

Hi! Just took the star test! Its A.115. Hope this helped! Please give brainliest if so! Have an amazing day! :)

Answer:

1: +

2: +

3: -

4: +

5: -

6: -

Step-by-step explanation:

hope this helps!

Answer:

D) the bridge is about 381.16 ft. above the river, and the length of the bridge above the arch is 1,792.58 ft

Answer:

domain: (4, 1, 0, -1, 1)

range: (2, 3, 0, -1, -3)

Step-by-step explanation:

domain: x-values

range: y-values

Answer:

Domain: {-1, 0, 1, 4}       Range: {-3, -1, 0, 2, 3}

Step-by-step explanation:

Hi there,

To find the domain, list all of the x values and put them in numerical order. Don't repeat the same numbers.

Do the same thing for the y values when finding the range.

Hope this helps. Cheers.

Answer: $164

Step-by-step explanation:

25*7=175

175+12.5

226.50-187.50

5*25=125+39

Jones family payed $164

Answer:

1/2 or one half

Step-by-step explanation:

I did this question

The correct statement is (c) Only (3) is correct. There is no bijective function from set A to set B.


To determine which statements are correct, we need to consider the properties of surjective (onto), injective (one-to-one), and bijective (one-to-one correspondence) functions.

(1) For a function to be surjective, every element in the codomain (set B) must have a corresponding element in the domain (set A). However, in this case, set A has duplicate elements (⊕), making it impossible for a surjective function to exist. So, statement (1) is incorrect.

(2) An injective function requires that each element in the domain (set A) maps to a unique element in the codomain (set B). Since set B has more distinct elements than set A, it is impossible to have an injective function. Therefore, statement (2) is incorrect.

(3) A bijective function is both surjective and injective. As explained above, neither a surjective nor an injective function exists between sets A and B due to the mismatch of elements. Hence, statement (3) is correct.

Therefore, the correct answer is (c) Only (3) is correct.

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Question - Let A={⊕,⊕,1,2,3,4,5} and B={□,∇,x,y,z}. Consider the following statements: (1) There exists a surjective function from A to B; (2) There exists an injective function from A to B; (3) There exists no bijective functions from A to B. Which of the following is correct? (a) Only (1) is correct. (b) Only (2) is correct. (c) Only (3) is correct. (d) Only (1) and (3) are correct. (e) Only (2) and (3) are correct.

Answer:

b = 48 yards

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Geometry

Step-by-step explanation:

Step 1: Define

Leg a = x

Leg b = 64

Hypotenuse c = 80

Step 2: Solve for x

The Ordering them from least to greatest: -3.75, -3, 3.1, 3.5, 31/5

To evaluate the given expressions and order them from least to greatest in value:

|3.1|

= 3.1 (since the absolute value of a positive number is the number itself)

-3

-3.75

|-3 1/2| = 3.5

(since the absolute value of a negative number is the positive value of that number)

|-31/5| = 31/5

(since the absolute value of a fraction is the positive value of that fraction)

Ordering them from least to greatest:

-3.75, -3, 3.1, 3.5, 31/5

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Answer:

3

Step-by-step explanation:

The answer is 3 because first you add -2 + 1 which is -1 then you multiply -3 by -1 and you get 3

The relationship between the heights of two right circular cylinders with the same volume. The radius of the second cylinder increases, its height must decrease to maintain the same volume as the first cylinder.

In order to find the volume of a cylinder, we use the formula V = πr²h, where V represents the volume, r is the radius, and h is the height of the cylinder.

Given that both cylinders have the same volume, let's denote their volumes as V1 and V2, their radii as r1 and r2, and their heights as h1 and h2. The given information states that r2 > r1. We can now write the equations for the volumes of the two cylinders:

V1 = π(r1)²h1
V2 = π(r2)²h2

Since V1 = V2, we can set the two equations equal to each other:

π(r1)²h1 = π(r2)²h2

We can now solve for the relationship between the heights of the two cylinders:

h1/h2 = (r2/r1)²

This equation shows that the ratio of the heights of the two cylinders is equal to the square of the ratio of their radii. As the radius of the second cylinder is greater than the radius of the first (r2 > r1), the height of the second cylinder will be less than the height of the first (h2 < h1). In other words, as the radius of the second cylinder increases, its height must decrease to maintain the same volume as the first cylinder.

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1) The gravimetric moisture content of the soil at field capacity is approx 27.62%.

2) The dry bulk density of the sample is approximately 1.193 g/cm^3.

3) The porosity of the sample, as a percentage of the total volume, is approximately 54.96%.

1) The gravimetric moisture content of the soil at field capacity can be calculated using the following formula:

Gravimetric Moisture Content = ((Wet Weight - Dry Weight) / Dry Weight) * 100

Given:

Wet Weight = 274.1 g

Dry Weight = 214.7 g

Using the formula, we can substitute the values:

Gravimetric Moisture Content = ((274.1 - 214.7) / 214.7) * 100

Gravimetric Moisture Content = (59.4 / 214.7) * 100

Gravimetric Moisture Content ≈ 27.62%

The gravimetric moisture content of the soil at field capacity is approximately 27.62%.

The gravimetric moisture content represents the amount of water present in a given mass of soil. By subtracting the dry weight of the soil from the wet weight and dividing by the dry weight, we can determine the proportion of water in the sample. Multiplying by 100 gives the moisture content as a percentage.

1a. The dry bulk density of the sample can be calculated using the following formula:

Dry Bulk Density = Dry Weight / Sample Volume

Given:

Dry Weight = 214.7 g

Sample Volume = 180 cm^3

Substituting the values into the formula:

Dry Bulk Density = 214.7 g / 180 cm^3

Dry Bulk Density ≈ 1.193 g/cm^3

The dry bulk density of the sample is approximately 1.193 g/cm^3.

Dry bulk density refers to the mass of dry soil per unit volume. To calculate it, we divide the dry weight of the soil by the sample volume.

1b. The porosity of the sample can be calculated using the following formula:

Porosity = (1 - (Dry Bulk Density / Particle Density)) * 100

The particle density for soil is usually around 2.65 g/cm^3.

Given:

Dry Bulk Density = 1.193 g/cm^3

Particle Density = 2.65 g/cm^3

Substituting the values into the formula:

Porosity = (1 - (1.193 / 2.65)) * 100

Porosity ≈ 54.96%

The porosity of the sample, as a percentage of the total volume, is approximately 54.96%.

Porosity represents the void space within a soil sample. It is calculated by subtracting the ratio of the dry bulk density to the particle density from 1 and multiplying by 100 to get the percentage. In this case, the particle density of 2.65 g/cm^3 is a typical value for soil.

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Answer:

1) C

Step-by-step explanation:

Step 1)

First we have to plot ↓

2x ≥ y + 2

And that looks like Image 1

Step 2)

Second we have to plot ↓

2x - 5y ≤ 10

and that looks like Image 2

Answer:

Integers are 48, 49, 50

Step-by-step explanation:

x+(x+1)+(x+2) = 147

3x + 3 = 147

3x = 147-3

x = 144 / 3 = 48

The dimensions of the rectangle are 10 feet (length) and 8 feet (width).

To find the dimensions of the rectangle with an area of 80 square feet and a width that is 2 feet less than the length,

follow these steps:

1. Let the length of the rectangle be L feet and the width be W feet.

2. According to the given information, W = L - 2.

3. The area of a rectangle is calculated by multiplying its length and width: Area = L × W.

4. Substitute the given area and the relationship between L and W into the equation: 80 = L × (L - 2).

5. Solve the quadratic equation: 80 = L² - 2L.

6. Rearrange the equation: L² - 2L - 80 = 0.

7. Factor the equation: (L - 10)(L + 8) = 0.

8. Solve for L: L = 10 or L = -8 (since the length cannot be negative, L = 10).

9. Substitute L back into the equation for W: W = 10 - 2 = 8.

So, the dimensions of the rectangle are 10 feet (length) and 8 feet (width).

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Answer:

The number of cartons of concentrated orange juice she needs in 4.5 gallons of orange juice is 12 cartons of orange juice

Step-by-step explanation:

The given parameters are;

The volume of the concentrated orange juice = 12 fluid ounce cartons

The ratio of orange juice concentrate to water = 12 fluid ounces to 36 fluid ounces

The amount of orange juice James need = 4.5 gallons = 576 fluid ounces

Therefore;

The  ratio of orange juice concentrate to water is 12:36

Therefore;

Let 'x' represent the amount of concentrated orange juice in 4.5 gallons of orange juice, and let 'y' represent the amount of water in the 4.5 gallons of orange juice, we have;

x + y = 4.5 (gallons)...(1)

x:y = 12:36 = 1:3

∴ x/y = 1/3

3·x = y...(2)

From equation (1) and equation (2), we have;

x + y = 4.5

x + 3·x = 4.5

x = 4.5/4 = 1.125

x = 1.125

The amount of concentrated orange juice in 4.5 gallons of orange juice, x = 1.125 gallons

∴ y = 3 × x = 3 × 1.125 = 3.375

y = 3.375

The amount of water in the 4.5 gallons of orange juice, y = 3.375

Therefore, we have;

4.5 gallons = 576 fluid ounces

∴ 1.125 gallons = (576/4.5) × 1.125 = 144 fluid ounces

The amount of fluid ounces per carton = 12 fluidounces/carton

∴ The number of cartons in 144 fluid ounces = 144 fluidounces ÷ 12 fluidounces/carton = 12 cartons

The amount of concentrated orange juice she needs in 4.5 gallons of orange juice, x = 1.125 gallons = 144 fluidounces = 12 cartons

The amount of concentrated orange juice she needs in 4.5 gallons of orange juice, x = 12 cartons of orange juice

The amount (number of cartons) of concentrated orange juice she needs in 4.5 gallons of orange juice, x = 12 cartons of orange juice.

In the given situation, the required value of x for the given pair of adjacent angles is 30°.

When two angles have a similar vertex and side, they are referred to as neighboring angles.

The vertex of an angle is the point at which the rays that make up its sides come to an end.

When adjacent angles have the same vertex and side, they can be a complimentary angle or supplemental angle.

The definition of adjacent is next to or nearby.

Two next-door residences are an illustration of proximity.

Typically, we think of those who live on our street as neighbors.

So, we have:

x + x + 30 = 90

Now, solve for x as follows:

x + x + 30 = 90

2x + 30 = 90

2x = 90 - 30

2x = 60

x = 60/2

x = 30

Therefore, in the given situation, the required value of x for the given pair of adjacent angles is 30°.

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The directional derivative of f(x, y) in the direction of vector v at the point (-1, 2) is (-36/√13).

a. Find the gradient of f(x, y) at the point (x, y) = (-1, 2).Vf(-1, 2) = ∇f (-1, 2)

The gradient of f(x, y) = ∇f(x, y) = fx(x, y) = (d/dx) [x³y²] = 3x²y²fy(x, y) = (d/dy) [x³y²] = 2x³y∴ ∇f(x, y) = <3x²y², 2x³y>At the point (-1, 2), the gradient is:<3 (-1)² (2)², 2 (-1)³ (2)> = <12, -4>

b. Find the unit vector u in the direction of v = (-2, 3). The unit vector u in the direction of vector v is given as;

u = v/||v||where ||v|| = √(v1)² + (v2)²= √((-2)² + 3²)= √13∴ u = (-2/√13, 3/√13)

c. Find the directional derivative of f(x, y) in the direction of vector v at the point (-1, 2). Dif(-1, 2) = ∇f (-1, 2)·u= <12, -4> · (-2/√13, 3/√13)= (-24/√13) + (-12/√13)= (-36/√13)

Therefore, the directional derivative of f(x, y) in the direction of vector v at the point (-1, 2) is (-36/√13).

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Answer:

14800

Step-by-step explanation:

The formula for simple interest (I) in terms of principal (P), rate (R) and time (T) is given as follows;

I = P x R x T / 100         ------------- (i)

Given:

Principal (P) = Initial amount being put into the account = 10000

Rate (R) = The interest rate being offered by the account manager = 4%

Time (T) = Time taken = 12 years

Substitute these values into equation (i) as follows:

I = 10000 x 4 x 12 / 100

I = 4800

Therefore, the initial amount will yield an interest of 4800 for those 12 years.

The total amount the employee will thus have in 12 years will be the sum of the initial amount and the interest. i.e

Amount = P + I

Amount = 10000 + 4800

Amount = 14800