in a 30-60-90 triangle, the length of the side opposite the 30 degree angle is 8. Find the length of the side opposite the 60 degree angle.

Answer:

20.7 and 500.200

Step-by-step explanation:

Answer:

20/7 = 2.8571

500/22000 = 0.0227

Step-by-step explanation:

Answer:

6n²  +85

Step-by-step explanation:

Changes made to your input should not affect the solution:

(1): "n2"   was replaced by   "n^2".  1 more similar replacement(s).

(85 +  7n²) -  n²

In a week, the parlor would make about $300 from milkshakes

The total amount the ice cream parlor makes in a week is dependent is the product of the number of days in a week , the number of milkshakes sold in a day and the price of a milkshake.

Total amount = number of milkshakes sold in a week x price of a milkshake

There are 7 days in a week, in a week the parlor would sell : 11 x 7 = 77 milkshakes

price of a milkshake = $3.99

77 x $3.99 = $307.23

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Don's null hypothesis is that there is no statistically significant difference between the mean debt of students who attended private college and the mean debt of students who attended public colleges, represented as H₀: μ₁ - μ₂ = 0

The null hypothesis (H0) is a statement of "no difference" or "no effect" and is typically represented as "there is no statistically significant difference between the mean debt of students who attended private college and the mean debt of students who attended public colleges." Therefore, in this case, Don's null hypothesis can be stated as

H₀: μ₁ - μ₂ = 0

where μ₁ represents the population mean debt for students who attended private college, and μ₂ represents the population mean debt for students who attended public colleges.

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Answer:

77 m (nearest metre)

Step-by-step explanation:

Angle of Elevation

If a person stands at a point and looks up at an object, the angle between their horizontal line of sight and the object is called the angle of elevation.

To find how tall the flagpole is, model as a right triangle and solve using the tan trigonometric ratio.

Tan trigonometric ratio

  \(\sf \\tan(\theta)=\dfrac{O}{A}\)

where:

Given information:

Therefore:

As the person is 1.6 m tall, we model the line of sight as 1.6 m above ground level.  Therefore, when calculating the height of the flagpole, we will need to add the height of the person to the value found using the trig ratio.

Substitute the given values into the formula and solve for O:

\(\implies \sf \tan(65^{\circ})=\dfrac{O}{35}\)

\(\implies \sf O=35\tan(65^{\circ})\)

Therefore the height of the flagpole is:

\(\implies \sf 35\tan(65^{\circ})+1.6=76.65774222...\)

\(\implies \sf Height\:of\:flagpole=77\:m\:(nearest\:metre)\)

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P(X = 2) is not equal to P(X = 3)

To show that P(X = 2) = P(X = 3) in a binomial distribution with n = 5 and p = 0.5, we need to use the formula for the probability mass function (PMF) of a binomial distribution.

The PMF of a binomial distribution is given by the formula:

P(X = k) = C(n, k) *\(p^k * (1-p)^{(n-k)}\)

where n is the number of trials, k is the number of successes, p is the probability of success, and C(n, k) represents the binomial coefficient.

In our case, n = 5 and p = 0.5. Let's calculate P(X = 2) and P(X = 3) using the formula:

P(X = 2) = \(C(5, 2) * (0.5)^2 * (1-0.5)^{(5-2)}\)

        = 10 * 0.25 * 0.125

        = 0.3125

P(X = 3) = C(5, 3) * \((0.5)^3 * (1-0.5)^{(5-3)}\)

        = 10 * 0.125 * 0.125

        = 0.125

As we can see, P(X = 2) = 0.3125 and P(X = 3) = 0.125.

Therefore, P(X = 2) is not equal to P(X = 3) in this specific case of a binomial distribution with n = 5 and p = 0.5.

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The expression to represent the total cost of ink supplies in two different ones is 7% × (12×2)

Total cost = $12 × 3

= $36

Amount of tax = 7% of $36

= 0.07 × 36

= $2.52

Amount paid = $2.52 + $36

= $38.52

Equation to represent total cost of 2 different ones = 7% × (12×2) + 24

= 0.07 × 24 + 24

= $1.68 + 24

= $25.68

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Answer:

m∠1 = 89°

Step-by-step explanation:

     Since m∠2 is a part of ∠GFH, he can do the following.

∠GFH - m∠2 = m∠1

133° - 44° = 89°

The length of the shorter piece of wire would be 22.

An electrician must divide a 49 m piece of wire into two sections, with the longer portion being 5 m longer than the shorter piece:

By using a simple Unitary Method We can solve this question

In order to calculate the required value using the unitary technique, multiply the value of one unit by the necessary number of units.

First wire - 27m

Second wire - 22m

27+22=49m

Also 27-22= 5

hence, s the length of the shorter piece of wire would be 22.

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Assume that m arc VUX = 228° and m ∠UVW = 121° in the circle below.

m∠VUX = 66° and m m∠UXW = 59° respectively.

1) The given information is;

The angle of arc m∠VUX = 228°, the measured angle of ∠UVW = 121°

Given that m∠VUX = 228°, therefore, arc ∠XWV = 360 - 228 = 132°

Therefore, the angle subtended by arc ∠XWV at the centre = 88°

The angle subtended by arc ∠XWV at the circumference = m∠VUX

∴ m∠VUX = 132°/2 = 66° (Angle subtended at the center = 2×angle subtended at the circumference)

m∠VUX = 66°

2) Similarly, m∠XWV is subtended by arc m∠VUX, therefore, m∠XWV = (arc m VUX)/2 = 228°/2 = 114°

A quadrilateral's angles add up to 360°.

Therefore;

m∠VUX + m∠XWV + m∠UVW + m∠UXW = 360° (The sum of angles in a quadrilateral XWVU)

m∠UXW = 360° - (m∠VUX + m∠XWV + m∠UVW)

m∠UXW = 360° - (66 + 114 + 121)

m∠UXW = 360° - 301

m∠UXW = 59°.

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Answer:

905789 x 9417 = 8529815013

Step-by-step explanation:

I hope this helps, friend :)

Answer:

5

Step-by-step explanation:

You will need the distance formula. \(d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}\\\)

(\(x_{1}\), \(y_{1}\)) (\(x_{2}\), \(y_{2}\))

Now plug in the two points into the distance formula.

d= \(\sqrt{(2-6)^{2}+(1-4)^{2} }\)

d= 5

Based on the information provided, the archaeological sample's estimated age is = 0.214136  years

Half life given is 5730

t₆.₅ = Ln2/k

k= ln 2/ 5730

The rate constant ,

k = 0.00012 year⁻¹

Given that 23 % of the 14C remains

then |A1|/|A2|  = 0.23

As we know ,

|A1|/|A2| = e ⁻₍kt₎

Hence, on solving the equation we get ,

ln(0.23)= -1.46967

t = -0.31471/ --1.46967

= 0.214136 years

The amount of time needed for a quantity (of substance) to decrease to half of its initial value is known as the half-life (symbol t12). In nuclear physics, the phrase is frequently used to indicate how rapidly unstable atoms decay radioactively or how long stable atoms last. The phrase is also used more broadly to describe any kind of exponential decay (or, very infrequently, nonexponential decay).

The biological half-life of medications and other compounds in the human body, for instance, is a term used in the medical sciences. Half-opposite life's in exponential growth is time's doubling.

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The total surface area that Lisa would need to cover is given as follows:

9800 mm².

The surface area of a rectangular prism of height h, width w and length l is given by:

S = 2(hw + lw + lh).

This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas.

The dimensions of the prisms in this problem are given as follows:

Hence the total surface area is obtained as follows:

S = 2 x (10 x 10 + 10 x 80 + 10 x 80) + 2 x (40 x 40 + 40 x 20 + 40 x 20)

S = 9800 mm².

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Answer:

Base area is 36 square meters

Step-by-step explanation:

The volume of a rectangular prism is V = (height)(length)(width).  We know all of these dimensions except for the area of the base, which is (length)(width).

Solving this equation for (length)(width), we get:

                                                       volume        72 m^3

(length)(width) = (area of base) = -------------- = -------------  = 36 m^2

                                                         height          2 m

To determine the coordinate of point P after the described rotations, let's go step by step.

First, the point P(3, 5) is rotated 180 degrees clockwise about the point A(3, 2). To perform this rotation, we need to find the vector between the center of rotation (A) and the point being rotated (P). We can then apply the rotation matrix to obtain the new position.

Let \(\vec{AP}\) be the vector from A to P. We can calculate it as follows:

\(\vec{AP} = \begin{bmatrix} 3 \\ 5 \end{bmatrix} - \begin{bmatrix} 3 \\ 2 \end{bmatrix} = \begin{bmatrix} 0 \\ 3 \end{bmatrix}\).

Now, we can apply the rotation matrix for a 180-degree clockwise rotation:

\(\begin{bmatrix} x' \\ y' \end{bmatrix} = \begin{bmatrix} \cos(\theta) & -\sin(\theta) \\ \sin(\theta) & \cos(\theta) \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix}\),

where \(\theta\) is the angle of rotation in radians. Since we want to rotate 180 degrees, we have \(\theta = \pi\).

Applying the rotation matrix, we get:

\(\begin{bmatrix} x' \\ y' \end{bmatrix} = \begin{bmatrix} \cos(\pi) & -\sin(\pi) \\ \sin(\pi) & \cos(\pi) \end{bmatrix} \begin{bmatrix} 0 \\ 3 \end{bmatrix} = \begin{bmatrix} -1 & 0 \\ 0 & -1 \end{bmatrix} \begin{bmatrix} 0 \\ 3 \end{bmatrix} = \begin{bmatrix} 0 \\ -3 \end{bmatrix}\).

The new position of P after the first rotation is P'(0, -3).

Next, we need to rotate P' (0, -3) 90 degrees counterclockwise about the point B(1, 1).

Again, we calculate the vector from B to P', denoted as \(\vec{BP'}\):

\(\vec{BP'} = \begin{bmatrix} 0 \\ -3 \end{bmatrix} - \begin{bmatrix} 1 \\ 1 \end{bmatrix} = \begin{bmatrix} -1 \\ -4 \end{bmatrix}\).

Using the rotation matrix, we rotate \(\vec{BP'}\) by 90 degrees counterclockwise:

\(\begin{bmatrix} x'' \\ y'' \end{bmatrix} = \begin{bmatrix} \cos(\theta) & -\sin(\theta) \\ \sin(\theta) & \cos(\theta) \end{bmatrix} \begin{bmatrix} x' \\ y' \end{bmatrix}\),

where \(\theta\) is the angle of rotation in radians. Since we want to rotate 90 degrees counterclockwise, we have \(\theta = \frac{\pi}{2}\).

Using the rotation matrix, we get:

\(\begin{bmatrix} x'' \\ y'' \end{bmatrix} = \begin{bmatrix} \cos \left(\frac{\pi}{2}\right) & -\sin\left(\frac{\pi}{2}\right) \\ \sin\left(\frac{\pi}{2}\right) & \cos\left(\frac{\pi}{2}\right) \end{bmatrix} \begin{bmatrix} -1 \\ -4 \end{bmatrix} = \begin{bmatrix} 0 & -1 \\ 1 & 0\end{bmatrix} \begin{bmatrix} -1 \\ -4 \end{bmatrix} = \begin{bmatrix} 4 \\ -1 \end{bmatrix}\).

The final position of P after both rotations is P''(4, -1).

Therefore, the coordinate of point P after the rotations is (4, -1).

Answer:

80%

Step-by-step explanation:

16/20 = 0.80

80%

Answer:

80 is the answer

Step-by-step explanation:

16×100÷20

Answer:

a) A'= (8,7)

B'=(10,-6)

C'=(2,-3)

b) A"=(-4,-5)

B"=(-6,8)

C"=(2,5)

Answer:

b = 9 cm

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = \(\frac{1}{2}\) bh ( b is the base and h the height )

here h = 2b , then

\(\frac{1}{2}\) × b × 2b = 81

\(\frac{1}{2}\) × 2b² = 81

b² = 81 ( take square root of both sides )

b = \(\sqrt{81}\) = 9 cm

Rewriting the given expression using partial fraction, we have 5/(x-3) + 6/(x+2)

First, factor out the denominator

Write the given fraction as the sum of two fractions whose denominators are the two factors of the denominator.

(11x-8) = A(x+2) + B(x-3)

choose values for x to eliminate one of the variables.

33-8 = A(3+2)

25 = 5A

A = 5

-22-8 = B(-2-3)

-30 = -5B

B = 6

Hence, we have 5/(x-3) + 6/(x+2) using partial fraction .

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Answer:

AC = 3.06

Step-by-step explanation:

Answer:

4. 33 = 33

5. 19 > 10

6. 1 = 1

7. 0.95 > 0.9

8. 39 > 38

9. 14 > 2

10. x = 4

11. m = 44

12. p = 3

13. \(z=\frac{15}{23}\)

Answer:

1436.8

Step-by-step explanation:

the second number after the decimal is 5 so we rounded the first number up

Answer:

17

Step-by-step explanation:

The image is not too clear. Let us assume we need the base AB

AB  = opposite

BC = hypotenuse

Sin theta = opp/hyp

Sin 37 = AB/BC

Sin 37 = AB/28

AB = 28sin37

AB = 28(0.6018)

AB = 16.85

AB ≈ 17

Hence the length of AB is 17

Answer:

A

Step-by-step explanation:

Just like in the last problem, we have a right triangle but in this case, x is a leg, 10 / 2 = 5 is the other leg, and 13 is the hypotenuse. Using the 5 - 12 - 13 Pythagorean Triple, we know that x = 12.

Answer:

392

Step-by-step explanation:

sequence is generalized as

\(a_n=6n-4\)

to find 66th term substitute n=66

\(a_n=6*66-4\\\)

Answer:

Shawna buys her rug at STORE B and she has $1.84 left over after purchasing her rug.

Step-by-step explanation:

Store a

Store a sells their rug for $45

Store a offers a discount of 10%

Discount = 10% × $45 = $4.5

Amount payable after discount = $45 - $4.5

= $41.5

There is a sales tax of 6%

The total amount payable

Amount of sales tax + Discounted price of rug

Amount of sales tax = 6 % × $41.5

= $2.472

= Discounted amount + Sales tax

= $41.5 + $2.472

=$43.972

Store b

Store a sells their rug for $46

There is a sales tax of 6%

The total amount payable

Store b offers a 10 dollar coupon off for the rug

= $46 - 10

Amount payable after = $36

Amount of sales tax + price of rug(After coupon is deducted)

Amount of sales tax = 6 % × $36

= $2.16

Amount payable by Shawna in Store a = $36 + Sales tax

= $36 + $2.16

=$38.16

Since Shawna has , only $40 to spend, she buys her rug at STORE B

The amount she has left = $40 - $38.16

= $1.84

Answer:

12

Step-by-step explanation:

1/2*12=6

6/2=3

11+2=13

13-3=10

10+2=12

P.E.M.D.A.S

Hope this helps!

Answer:

12

Step-by-step explanation:

Multiply 1/2 by 12 and get 6, divide 6 by 2 and get 3, 3-2 is 1, then add 1 and 11 to get the answer 12