A student stands 50 feet away from the front of a building and measures the angle of elevation to the top of the building. From the student's eye level 5 feet off the ground, the angle of elevation to the top of the building is 30^\circ. Approximately, what is the height of the building?

Answer:

Area Δ = 102.3 units² ⇒ The answer is (d)

Step-by-step explanation:

* Use the formula of the area:

∵ Area of the triangle = 1/2 (a)(b) sin(C)

∵ We have the length of the 3 sides

∴ Use cos Rule to find the angle C

∵ cos(C) = (a² + b² - c²)/2ab

∵ a = 25 , b = 13 , c = 17

∴ cos(C) = (25² + 13² - 17²)/2(25)(13) = 625 + 169 - 289/650 = 505/650

∴ m∠C = 39°

∴ Area Δ = (1/2)(25)(13)sin(39) = 102.3 units²

∴ The answer is (d)

Answer:

Area Δ = 102.3 units² ⇒ The answer is (d)

Step-by-step explanation:

Use the formula of the area:

∵ Area of the triangle = 1/2 (a)(b) sin(C)

∵ We have the length of the 3 sides

∴ Use cos Rule to find the angle C

∵ cos(C) = (a² + b² - c²)/2ab

∵ a = 25 , b = 13 , c = 17

∴ cos(C) = (25² + 13² - 17²)/2(25)(13) = 625 + 169 - 289/650 = 505/650

∴ m∠C = 39°

∴ Area Δ = (1/2)(25)(13)sin(39) = 102.3 units²

∴ The answer is (d)

Answer:

There are 470 students at the school.

Step-by-step explanation:

141 / x = 3 / 10 since 3/10 is equal to 30% you're looking for a denominator that corresponds equally to 141 and when simplified, 141 / x equals 3 / 10.

Use algebra to solve: 141 * 10 = 3x → 1410 = 3x → 470 = x.

Final answer:

There are 470 students at the school.

Explanation:

In the given question, we are dealing with a basic percentage problem. We are told that 141 students, which is 30% of all students at the school, are playing at least one sport. To find the total number of students in the school, we need to solve for the whole when a part and its percentage are known.

Let x represent the total number of students at the school. According to the question:

30% of x = 141 students

We can set up the equation:

0.30 * x = 141

To find x, we'll divide both sides of the equation by 0.30:

x = 141 / 0.30

Performing the division gives us:

x = 470

Therefore, there are 470 students at the school.

Which is the most appropriate to describe a quantity decreasing at a steady rate?

With a linear equation.

Answer:

no

got correct on algebra nation

Answer:

  v = 0, or v = 8

Step-by-step explanation:

The quadratic can be factored, then the zero product rule applied.

  v^2 -8v = 0

  v(v -8) = 0

A product will be zero when any of the factors is zero. So, the solutions are values of v that make the factors be zero.

  v = 0

  v -8 = 0 . . . ⇒ . . . v = 8

Answer:

Step-by-step explanation:

The angle where the chords cross is the average of the two intercepted arcs:

  ∠AEB = (∠AOB +∠COD)/2 = (76° +80°)/2 = 78°

___

Chord AD connects points A and D.

1. You do 180-88 because supplementary angles add up to 180°.

2. 180-88=92°. Angle 4 is 92°

Answer:

92 degrees

Step-by-step explanation:

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x^-2 matches 1/36

x^-1 matches -1/6

x^0 matches 1

x^1 matches -6

x^2 matches 36

When evaluating expressions with exponents for a specific value, we simply substitute that value for x and follow the order of operations (PEMDAS). Here's the breakdown for each expression:

x^-2: (-6)^-2 = 1/(-6)^2 = 1/36

x^-1: (-6)^-1 = 1/(-6) = -1/6

x^0: (-6)^0 = 1 (any non-zero number raised to the power 0 equals 1)

x^1: (-6)^1 = -6 (any non-zero number raised to the power 1 equals itself)

x^2: (-6)^2 = (-6) * (-6) = 36

Therefore, the matches are as listed above.

Answer:

[tex]\large\boxed{d.\ 6x^3+8x}[/tex]

Step-by-step explanation:

[tex]2x(3x^2+4)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\=(2x)(3x^2)+(2x)(4)\\\\=6x^3+8x[/tex]

Answer:

x = -3/2  or  -1.5

Step-by-step explanation:

You have to get X on one side by itself.

2x + 4 - 7x + 9x = -2

Subtract the 4

2x - 7x + 9x = -6

Combine like terms

-5x + 9x = -6

Combine like terms

4x = -6

Divide by 4

x = -6/4

Simplify

x = -3/2  or  -1.5

Answer:

30 add-on sales to make the goal

Step-by-step explanation:

multiply 35*85% (or 0.85)

  35*0.85 = 29.75

Since you can't make 0.75 of a goal, round up to the next highest number = 30

Answer:

Pham earns 6,500 per month.

Step-by-step explanation:

To get the monthly salary, divide the yearly salary by 12.

78,000/12 = 6,500

Answer:

78,000 / 12 = 6,500

Step-by-step explanation:

Pham's annual salary is $78,000

To find Pham's month salary

Divide 78,000 by 12

Thus 6,500

Answer:

Joey ran 39 yards

Step-by-step explanation:

a²+b²=c²

15²+36²=c²

225+1296=c²

1521=c²

√1521=√c²

39=c

Answer:

Your answer would be 1/4

Step-by-step explanation:

The probability that a randomly selected carton of yoghurt will be raspberry is 1/4. The correct option is b.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favourable outcomes / Number of sample

Given that a grocery store has 12 cartons of yoghurt for sale, of which 3 are raspberry.

The probability that a randomly selected carton of yogurt will be,

Probability = Number of favourable outcomes / Number of sample

Probability = 3 / 12

Probability = 1 / 4

Therefore, the probability that a randomly selected carton of yoghurt will be raspberry is 1/4. The correct option is b.

To know more about probability follow

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The answer is 12 questions per minute as you divide 36 by 3

Answer=12 questions per minute

Answer:

12

Step-by-step explanation:

we can simply put both fractions with the same denominator, and thus then we can just compare which numerator is larger.

we can do so by multiplying each fraction by the other's denominator, let's proceed.

[tex]\bf \stackrel{Laura}{\cfrac{3}{4}\cdot \cfrac{3}{3}}\implies \cfrac{9}{12}~\hfill \stackrel{Anna}{\cfrac{2}{3}\cdot \cfrac{4}{4}}\implies \cfrac{8}{12} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{Laura}{\cfrac{9}{12}}~>~\cfrac{8}{12}~\hfill[/tex]

Answer:

red marble out of the same jar, without replacing the first marble.

Step-by-step explanation:

Dependant events means one depends on the other.  If you don't replace the first marble then the chance of drawing any other marble is changed.  To better see it try giving them numbers, how many blue and red marbles start in the jar  and calculate probability before and after removing a blue marble.  

Dependent events are those in which the outcome of one affects others. Drawing a marble from a jar and then drawing another without replacing the first one is an example of dependent events. Independent events don't affect each other, as when drawing marbles from different jars or replacing a marble before drawing another from the same jar.

The question you've asked pertains to the concept of dependent and independent events in probability theory. Dependent events are events in which the outcome of one affects the outcome of the others.

If we draw a blue marble from the jar and then, without replacing the first marble, we draw another marble, these are dependent events because the second event is affected by the outcome of the first.

On the other hand, if we draw a blue marble from one jar and then draw a marble from another jar, these are independent events because they do not affect each other.

Similarly, if we draw a marble from a jar, replace it, and then draw another, these are also independent events because putting the first marble back makes the second draw unaffected by the first one.

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C is the correct answer. Appreciate it if you gave me brainliest!

Answer:

C

Step-by-step explanation:

and thank you for this it was funny and a good break from algebra 1! XD

Answer:

C. Both functions have a y-intercept of -2

Step-by-step explanation:

A. Function F in decreasing then increasing, therefore it's incorrect

B. Function F is symmetrical about the y-axis, but Function G is not

C. Both functions intercept the y-axis at (0,-2) so it's correct

D. Only function G shows a linear relationship.

To look at a picture of what Function G looks like. Press y= on your Ti-84 calculator (top left) put the function in, and then press graph (top right)

This is 100% correct. I took algebra 1 last year.

Answer: [tex]x=10.2[/tex]

Step-by-step explanation:

The triangle shown in the image attached is a right triangle.

Therefore, you can calculate the value of x as you can see below:

[tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex]

In this case, you have that:

adjacent=x

hypotenuse=11

[tex]\alpha=22\°[/tex]

Therefore, when you substitute values and solve for x, you obtain the following result:

[tex]cos(22\°)=\frac{x}{11}\\\\x=11*cos(22\°)\\x=10.2[/tex]

Answer:

The value of x = 10.2

Step-by-step explanation:

From the figure we can see a right angled triangle. One side and one angle are given.We have to find one side of triangle.

Points to remember

Cos θ = Adjacent side/Hypotenuse

To find the value of x

Here  θ = 22°, Hypotenuse = 11, Adjacent side =?

Cos 22 = Adjacent side/Hypotenuse = x/11

x = 11 * Cos 22 = 11 * 0.9271 = 10.2 units

Answer:

{π/4 +2πn, 3π/4 +2πn}

Step-by-step explanation:

csc = 1/sin, so when csc(θ) = √2, sin(θ) = 1/√2. Then θ = π/4 or 3π/4.

This means arccsc(√2) will be the set of angles shown above.

___

Once you recognize that π/4 is one of the angles, you can eliminate all but the correct answer choice.

Of course this is much easier if you have memorized the short list of trig function values:

sin(π/6) = cos(π/3) = 1/2

sin(π/4) = cos(π/4) = 1/√2 = (√2)/2

sin(π/3) = cos(π/6) = (√3)/2

tan = sin/cos

sec = 1/cos

csc = 1/sin

Answer:

the above answer is correct

There should be 4.5 oz of vinegar and 22.5 oz of oil

-5x+y=0

x+y=27

-6x=-27

Answer: 43 more times

2580÷60=43.

Step-by-step explanation: 43×60 =2580

This proves that 43 times is correct.

Answer:

c 43

Step-by-step explanation:

Answer:

Friction

Step-by-step explanation:

Because friction between the floor and the ball made the ball stopped from rolling.

Answer:

Friction

Step-by-step explanation:

The force that acts in opposite direction to the motion of the ball thereby causing it to stop is the force of friction.

This frictional force is a force of opposition that causes bodies moving in a particular direction to come to an halt. The force always acts in the opposite direction to the moving force acting on a body.

Answer:

[tex]d=0.75m[/tex]

Step-by-step explanation:

Let

d------> the distance in miles

m----> the time in minutes

we know that

The speed is equal to divide the distance by the time

so

[tex]speed=d/m[/tex]

we have

[tex]d=2\frac{5}{8}\ miles=\frac{2*8+5}{8}=\frac{21}{8}\ miles[/tex]

[tex]m=3\frac{1}{2}\ minutes=\frac{3*2+1}{2}=\frac{7}{2}\ minutes[/tex]

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

so

In this problem the speed is the constant of proportionality

[tex]d=km[/tex]

Find the value of k

[tex]k=\frac{(21/8)}{(7/2)} =0.75\frac{miles}{minute}[/tex]

[tex]d=0.75m[/tex] ----> linear equation that represent the distance, d, that the car travels in m minutes

Answer:

AAA (Angle Angle Angle) Proving that the angles are the same (Or of the same ratio if diluted), if this is true, the two figures are similar.

SSS (Side Side Side) Proving all the sides are the same size (Or again of the same ratio) also proves similarity.

SAS (Side Angle Side) If two sides and the angle in between are the same, then the triangles are similar.

Step-by-step explanation:

EX)

Triangle A has sides 10, 5, and 12

Triangle B has sides 20, 10, and 24

The relationship is the same between both triangles, just that the sides are multiplied by 2. This is SSS

If Triangle A has two sides 5 and 10 with an angle of 25 degrees, then Triangle B must have that same angle alongside those two sides, or at least a consistent ratio if diluted. Proof SAS

If Triangle A and B have the same angles, they are similar.

Answer:

1.) 0.9265

2.) 63%

3.) 1683

4.) 5.9

I hope this helped and give me brainiest please

Answer:

Step-by-step explanation:

1) From standard distribution table we find that

P(Z<1.45) = 0.5+0.4265

=0.9265 Option d

2) Given that X, The scores on a standardized test is N(500,60)

percent of students who scored below Jake

[tex]=100*P(X<520)\\=100*P(Z<\frac{20}{60} )\\=100(0.5+0.1293)\\=62.93%\\=63%[/tex]

3) X, lengths of new born girls is N(49.2, 1.8)

n = 2000

P(X<51) = P(Z<1) =0.84

No of girls =2000(0.84) =1683

4) P(Z<2.72) is the answer

5)X, ages of cars driven is N(8,3.2)

75% correspond to z=0.675

X = 8+0.675(3.2) =10.16=10.2

Final answer:

The value of sin A cannot be determined without knowing the value of angle A.

Explanation:

The question is asking for the value of sin A. In mathematics, sin A represents the sine of angle A. The sine function is a mathematical function that relates the ratio of the length of the side opposite the angle to the length of the hypotenuse of a right triangle.

The correct answer to the question is 3/5. To find this value, you need to know the value of angle A. Without that information, we cannot determine the exact value of sin A.

Final answer:

The correct value of SIN A from the given options cannot be determined without additional context. SIN A refers to the ratio of the side opposite to angle 'A' to the hypotenuse in a right triangle or the y-coordinate on the unit circle at angle 'A'. Possible values are within the range of -1 to 1.

Explanation:

The question 'What is SIN A?' is seeking the trigonometric value of the sine function at a particular angle denoted by 'A'. When presented with options like 3/4, 4/3, 3/5, and 4/5, we need additional information regarding angle 'A' or the context of a right triangle or unit circle to determine the correct value. Without this information, we cannot definitively answer which option is correct.

Generally, in a right triangle, SIN A would represent the ratio of the length of the side opposite to angle 'A' to the length of the hypotenuse. Therefore, it is a value between -1 and 1. The options 3/4 and 3/5 could potentially be correct since they are within this range, but 4/3 cannot be because it exceeds this range. In a unit circle context, sin A would represent the y-coordinate of a point on the circle's circumference at an angle 'A' from the x-axis.

Answer:

27 meters

Step-by-step explanation:

Think of it like a right triangle. One leg is 50m long (the distance you are from the balloon) and the goal is to find the other leg of the triangle. From the place you're standing, the angle is 28°. In relation to that angle, you're given the adjacent side (50m) and need to find the opposite side. Recall SOH-CAH-TOA. You have to use tangent to get the length. Tan = opposite/adjacent. The tan of 28 = x / 50. Use algebra to solve: tan28 (50) = x; aproximately 26.6m = x. So, the height of the hot air balloon is roughly 26.6m or 27m depending on how you round.

Answer:

The length of the arc is [tex]8\pi\ ft[/tex]  

Step-by-step explanation:

we know that

The measure of the arc shown in brown is equal to

[tex]180\°-60\°=120\°[/tex] -----> by central angle

Remember that

The length of the arc of the complete circle (360 degrees) is equal to the circumference

[tex]C=\pi D[/tex]

we have

[tex]D=24\ ft[/tex]

substitute

[tex]C=\pi (24)=24 \pi\ ft[/tex]

so

by proportion

Find the length of the arc for a measure of [tex]120\°[/tex]

[tex]\frac{24\pi }{360} \frac{ft}{degrees} =\frac{x }{120} \frac{ft}{degrees}\\ \\x=120*(24\pi )/360\\ \\ x= 8\pi\ ft[/tex]