Which of the following are solutions to the equation 4cos^2x - 3 = 0? Check all that apply.

Answer: The altitude of the triangle is [tex]h = 7 \sqrt{3}.[/tex]

Step-by-step explanation:

Suppose that we separate the equilateral triangle with the altitude of the triangle, as shown in the diagram I attached.

Then the length of the altitude [tex]h[/tex] can be found through the Pythagorean theorem:

[tex]h = \sqrt{14^2-\left( \frac{14}{2} \right)^2} = \sqrt{147} = \boxed{7 \sqrt{3}}.[/tex]

Therefore, the altitude of the equilateral triangle is [tex]h = 7 \sqrt{3}.[/tex]

Answer:

124

Step-by-step explanation:

You'll need a calculator for this one

The surface area of the triangular prism with rectangular base is 736 cm².

Surface area refers to the total area that the surface of an object covers. It is a measure of how much exposed area there is on the outside of an object. The surface area of an object is usually expressed in square units, such as square meters, square centimeters, or square feet.

Here,

The formula for the surface area of a triangular prism with rectangular base is:

SA = 2lw + lh + wh

where l is the length of the rectangular base, w is the width of the rectangular base, h is the height of the triangular prism.

Given:

Side of triangle = 16 cm and 12 cm

Side of rectangle = 20 cm and 10 cm

Since we are not given the height of the triangular prism, we cannot calculate the exact surface area. However, we can give a general formula for the surface area in terms of the height h:

SA = 2(20)(10) + (16)(h) + (12)(h)

SA = 400 + 28h

So the surface area of the triangular prism with rectangular base is 400 + 28h, where h is the height of the triangular prism in cm.

h=12 cm

400+28h=400+28*12

=736 cm²

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The calculated area of the quadrilateral is 35.82 square units.

Given that

BAse = 6.5

Height = 5.51

To find the area of a quadrilateral, we need to multiply the base by the height.

Area of quadrilateral = base x height

Substituting the given values, we get:

Area = 6.5 x 5.51

Area = 35.815

Rounding to the nearest hundredth, the area of the quadrilateral is 35.82 square units.

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The relation that is a function is D: {(–3, 2), (–2, 3), (–1, 2), (0, 4), (1, 1)}.

A function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. In other words, for a relation to be a function, each input can only be related to one output.

In relation D, each input (x-value) has a unique output (y-value), meaning that each x-value is only paired with one y-value. In contrast, relations A, B, and C have repeated x-values with different y-values, which means that they are not functions.

In relation A, the input -1 is paired with two different outputs (2 and 3). In relation B, both inputs 0 and -1 are each paired with two different outputs. In relation C, both inputs 0 and -3 are each paired with two different outputs. Therefore, only relation D satisfies the definition of a function.

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The answers below provides the elements of the sets L1 ∪ L2, L1 ∩ L2, L1 concatenation L2, L1*, and L2* where L1 and L2 are languages over Σ = {a, b}.

a) L1 ∪ L2:

The union of two sets is the set of all elements that are in either set. Therefore,

L1 ∪ L2 = {a, b, ab, λ, bb}

b) L1 ∩ L2:

The intersection of two sets is the set of all elements that are in both sets. Therefore,

L1 ∩ L2 = {ab}

c) L1 concatenation L2:

The concatenation of two languages is the set of all possible combinations of elements where the first element comes from the first language and the second element comes from the second language. Therefore,

L1 concatenation L2 = {aλ, a bb, aab, bλ, bbb, bab, abλ, abb, abab}

d) L1*:

L1* is the Kleene star of L1, which is the set of all possible combinations of elements from L1, including the empty string λ. Therefore,

L1* = {λ, a, b, ab, aa, bb, aaa, aab, abb, bbb, aaaa, aaab, aabb, abbb, ...}

e) L2*:

Similarly,

L2* = {λ, bb, ab, bbbb, abb, aabb, abbb, aabbb, ...}

Note that the Kleene star of L2 includes only elements made up of b's and λ.

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The distance between city A and city B is approximately 442.3 km.

What is the law of cosine?

The Law of Cosines, also known as the Cosine Rule, is a mathematical formula that relates the lengths of the sides of a triangle to the cosine of one of its angles. Specifically, it states that:

c² = a² + b² - 2ab cos(C).

We can use the Law of Cosines to find the distance between City A and City B. Let's call this distance d.

From the information given, we know that:

The distance between the satellite and city A is 450 km.

The distance between the satellite and city B is 340 km.

The angle between city A, the satellite, and city B is 1.5 degrees.

Using the Law of Cosines, we have:

d² = 450² + 340² - 2(450)(340)cos(1.5)

d² = 202500 + 115600 - 2(450)(340)cos(1.5)

d² = 318100 - 122328.8

d² = 195771.2

d = √195771.2

d ≈ 442.3

Therefore, the distance between city A and city B is approximately 442.3 km (rounded to the nearest tenth).

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Answer:

8x+26

Step-by-step explanation:

distribute the 5 into the numbers in the parentheses. you get (5x+20) then do the same with 3(x+2) which wll be (3x+6) now add like terms, which are 5x+3x=8x and 20+6=26. boom 8x+26.

8x + 26

multiply the outside number by the inside numbers and add them. remember, if the variable is singular example x, then it equals 1 :) I hope this helps you understand, I'm currently doing algebraic expressions.

The value of Cscθ is 1/y.

What is a trigonometric function?

The right-angled triangle's angle and the ratio of its two side lengths are related by the trigonometric functions, which are actual functions. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.

Here, we have

Given: if p(x,y) is the point on the unit circle defined by the real number theta.

We have to find the value of the csc theta.

P(x,y) is the point on the unit circle  (the unit circle has a radius of 1 and center (0,0))

Now in a diagram, we can see that

OA= x

AP= y

radius OP =1

∠POA =θ

Now in ΔAOP

Cscθ = hypotenuse/opposite side

Cscθ = OP/AP

Cscθ = 1/y

Hence, the value of Cscθ is 1/y.

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Step-by-step explanation:

Setting 1   = 100   rpm

Setting 2  = 200 rpm

Setting  3 = 400 rpm  

400 rotations each minute   for 15 minutes =  400 * 15 = 6000 rotations

The height of the heater is approximately 6.6 feet.

According to Pythagoras's Theorem, the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides. Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides.

We can use the Pythagorean theorem to find the height of the pyramid. Let's call the height "h". Then, the slant height is the hypotenuse of a right triangle with base and height both equal to 10 feet, so we have:

h² + 10² = 12²

Simplifying and solving for h, we get:

h² + 100 = 144

h² = 44

h ≈ 6.6 feet

Therefore, the height of the heater is approximately 6.6 feet.

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Al needs to read 752 more pages to reach his goal of 2,000 pages.

The act of deleting items from a collection is represented by subtraction. Subtraction is denoted by the minus sign.

To find out how many more pages Al needs to read to reach his goal of 2,000 pages, we can subtract the number of pages he has already read from his goal:

Number of pages Al needs to read = Goal - Pages already read

Number of pages Al needs to read = 2,000 - 1,248

Number of pages Al needs to read = 752

Therefore, Al needs to read 752 more pages to reach his goal of 2,000 pages.

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Answer: 50 Dollars

Step-by-step explanation:

Minimum pay: $50 / week

Bonus: $7.5 or more / Potential Customer

The least amount of money you can earn after contacting eight businesses in 1 week is $50, since there is a possibility none of the eight businesses you contacted is a potential customer.

Feel free to correct me if I'm wrong :)

Answer:

0.222

Step-by-step explanation:

2 divided by 9 is:

0.222 (rounded to the nearest thousandth)

Answer:

oh

Step-by-step explanation:

idrk i just searched it up

The simplified radical expression is given as follows:

[tex]\sqrt{363} - 3\sqrt{27} = 2\sqrt{3}[/tex]

The radical expression for this problem is given as follows:

[tex]\sqrt{363} - 3\sqrt{27}[/tex]

The first step in simplifying the expression is obtaining the prime factors of 363 and of 27, hence:

Hence the radicals are simplified as follows:

Hence the simplified expression is:

[tex]\sqrt{363} - 3\sqrt{27} = 11\sqrt{3} - 3 \times 3\sqrt{3} = (11 - 9)\sqrt{3} = 2\sqrt{3}[/tex]

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The correct answer will be option D. Y intercept will be greater and X will be less.

A "coordinate system" is a mathematical framework that uses a set of coordinates to identify points in space or on a surface. It describes the location of a point in relation to a reference point or origin, often using numerical values. A coordinate system is made up of one or more axes, which are imaginary lines that cross at the origin, and units of measurement that run along each axis.

When the trucking firm starts paying a driver 0.25 cents per mile, it raises their operational expenditures, which has a direct influence on their profit (Y-axis). As a result, the Y-intercept (the point at which the profit crosses the Y-axis) will be larger since the company's costs will be bigger.

The X-axis, on the other side, displays the distance travelled by the vehicle. Because the corporation is now paying for a driver, it may decide to decrease the amount of kilometres the truck goes to save money. This indicates that the X-axis will be shorter, suggesting that the truck will drive fewer miles than previously.

As a result of the modification, the Y-intercept will be higher (showing higher costs) and the X-axis will be lower (meaning less kilometres travelled).

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Answer:

The answer is 0.777

Step-by-step explanation:

0.3÷3×7

0.3=1/3

=1/3×1/3×7

=7/9

=0.777

Answer:  33.51 cubic units.

Step-by-step explanation: The equation for the volume of a circle is:

V = (4/3)πr³

where r is the sweep of the circle.

Since the distance across of the circle is given as 4, we are able discover the span by partitioning the distance across by 2:

r = d/2 = 4/2 = 2

Presently we are able plug within the esteem of the sweep into the equation for the volume:

V = (4/3)π(2³) = (4/3)π(8) = 32/3π

Answer: 33.51

Step-by-step explanation:

The formula is 4/3 pi r^3. The radius is 2. If you do the equation, you get roughly 33.51.

Answer:

I believe it’s because they were adding by 5 with each number in the sequence.

Step-by-step explanation:

if you take 3+_= 8 what goes in the missing spot? 5 would, so we look at the next number and see if it’s a pattern. 13 so 8+_= 13 we know that’s 5 as well. So there’s a pattern of +5 hence why 7 is not part of the sequence.

The side length of the the rectangular garden are 20 feet by 5 feet.

Let

s = side length of the square garden

l = length of the rectangular garden

w = width of the rectangular garden

From the problem statement,

area of the square garden = area of the rectangular garden

Since the area of a square is just the side length squared, we can write:

s² = l * w

We also know that the length of the rectangular garden is 10 feet longer than the side of the square garden, and that the width of the rectangular garden is 5 feet shorter than the side of the square garden. We can express them as:

l = s + 10

w = s - 5

Now we can substitute these expressions for l and w into our first equation:

s² = (s + 10) * (s - 5)

Expanding the right-hand side, we get:

s² = s² + 5s - 50

0 = 5s - 50

5s = 50

Dividing both sides by 5, we get:

s = 10

Since the side length of the square garden is 10 feet.

We can use this to find the dimensions of the rectangular garden:

l = s + 10 = 10 + 10 = 20

w = s - 5 = 10 - 5 = 5

So the dimensions of the rectangular garden are 20 feet by 5 feet.

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The measurements for area of Jacobs yard are;

Part A = 6m x 3m = 18m

Part B = 4.5m x 3m = 13 m

Part C = 1/2 x 3m x 3m = 4.5 m²

Total area = 18m² + 13.5m² + 4.5m² = 36m²

To identify sections that would help in calculating area, you need to look for shapes or figures that can be divided into simpler geometric shapes, such as squares, rectangles, triangles, and circles.

Once you have identified the simpler shapes, you can use their formulas to calculate their areas and then add them together to find the total area of the larger shape or figure.

For example, a rectangle can be divided into two triangles or two smaller rectangles, and a circle can be divided into a sector or a ring. Breaking down a larger shape into smaller, simpler shapes can make it easier to calculate their areas accurately.

Jacob is putting tiles on the section of his yard labeled A, B, C. What is the area of the parts that need tiles?

Part A = .............. x ........... = ...........m

Part B = + .............. x ............. = ............ m

Part C = 1/2 x ................. x ............ = ............... m²

Total area = ................... + ..................... + .................. = ..............m

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Answer: y^3/5

Step-by-step explanation:

Answer:

We can factor out a y^3 term from the expression y^3 - y^5:

y^3 - y^5 = y^3(1 - y^2)

So, y^3 - y^5 can be written as the product y^3(1 - y^2).

a. The probability that the total number of brownies sold for a random sample of 56 days is less than 2070 is approximately 0.0107.

b. The probability that 2X₁ + X₂ + 3X₃ + X₄ is less than or equal to 17.6

Explain probability

Probability is the measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event will not occur, and 1 means the event will definitely occur. Probability is a fundamental concept in mathematics and is used in many fields, including statistics, science, and finance.

According to the given information

a. The total number of brownies sold for a random sample of 56 days, Y, is a normal random variable with mean µ_Y = 56µ_X = 5638 = 2128 and standard deviation σ_Y = √(56)*σ_X = √(56)*6 = 25.21.

We want to find P(Y < 2070). Standardizing Y, we get:

Z = (Y - µ_Y) / σ_Y = (2070 - 2128) / 25.21 = -2.31

Using a standard normal distribution table or calculator, we can find that P(Z < -2.31) is approximately 0.0107. Therefore, the probability that the total number of brownies sold for a random sample of 56 days is less than 2070 is approximately 0.0107.

b. 2X₁ + X₂ + 3X₃ + X₄ is also a normal random variable with mean 2µ₁ + µ₂ + 3µ₃ + µ₄ = 2(3.6) + 0.9 + 3(1.8) + 7.4 = 18.5 and variance 4o² + o² + 9o² + o² = 14o².

We want to find P(2X₁ + X₂ + 3X₃ + X₄ ≤ 17.6). Standardizing the variable, we get:

Z = (17.6 - 18.5) / √(14o²) = -0.5735 / √(o²)

To find P(Z ≤ -0.5735 / √(o²)), we need to know the value of o². If o² = 1, then P(Z ≤ -0.5735) = 0.2831. If o² is a different value, we would need to adjust accordingly.

Therefore, the probability that 2X₁ + X₂ + 3X₃ + X₄ is less than or equal to 17.6

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the employer's total FUTA and SUTA tax is: $2,928

What is tax rate?

The percentage of income that a person or corporation must pay or withhold as taxes is known as the effective tax rate.

$7,000 (for Zachary Fox) + $7,000 (for Calvin Bell) + $7,000 (for David Alexander) + $7,000 (for Michael Sierra) = $28,000

The FUTA tax for this amount is:

$28,000 × 6.0% = $1,680

Therefore, the total taxable earnings subject to SUTA tax is:

$26,000 (for each employee) × 4 (number of employees) = $104,000

The SUTA tax for this amount is:

$104,000 × 1.2% = $1,248

The year-to-date FUTA and SUTA taxes are not given explicitly, so we cannot calculate the current period FUTA and SUTA taxes.

Therefore, the employer's total FUTA and SUTA tax is:

$1,680 (FUTA tax) + $1,248 (SUTA tax) = $2,928

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The measures of the arcs on the circle are;

mPQ = 71°

mSR = 161°

mQRT = 119°

mPSR = 270°

mPS = 109°

An arc is a part of the circumference of a circle.

The vertical angles theorem indicates that we get;

m∠QUR = m∠TUS = 19°

∠PUQ and ∠QUR are complementary angles (Specified angle of ∠PUR)

∠PUQ + ∠QUR = 90°

m∠PUQ = 90° - m∠QUR

m∠PUQ = 90° - 19° = 71°

The measure of arcPQ = m∠PUQ = 71°

Therefore, mPQ = 71°

∠SUR and ∠QUR are supplementary angles (Definition of linear pair angles)

Therefore; m∠SUR + m∠QUR = 180°

m∠SUR  = 180° - 19° = 161°

mSR = m∠SUR = 161°

mQRT = m∠QUS + m∠TUS

m∠QUS = 180°, therefore;

mQRT = 180° + 19° = 199°

mQRT = 199°

mPSR = 360° - m∠PUR (Sum of angle at the the center of a circle)

mPSR = 360° - 90° = 270°

mPS = m∠TUS + m∠PUT

m∠PUT and m∠PUR are linear pair angles,m∠PUR = 90°, therefore;

m∠PUT = 90°

mPS = 19° + 90° = 109°

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The probability of spinning an even number, flipping tails, then spinning an odd number is:

1/9   (as fraction) or 11.11% (as percent)

To find the probability of spinning an even number, flipping tails, then spinning an odd number. We need to consider the individual probabilities. That is:

We have only one even number in the spinner, and that is 2. Thus,

P(even number) = 1/3

For a coin, the probability of head or tail is 1/2. Thus,

P(tail) = 1/2

We have two odd number in the spinner, and that is 1 and 3. Thus,

P(odd number) = 2/3

Therefore, the probability of spinning an even number, flipping tails, then spinning an odd number will be:

P(even, tail, odd) = 1/3 * 1/2 * 2/3

                            = 2/18

                            = 1/9   (as fraction)

In percent:

P(even, tail, odd) =  1/9 * 100

                            = 11.11%

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