What is 34.48 rounded to the
nearest whole number?

The measure of angle A is 30 degree, the value of tan A is 1/√3 and the area of triangle ABC is 280.6 squared inches.

When the three sides of a triangle is known, then to find any angle, the law of cosine is used.

It can be given as,

[tex]\angle A=\cos^{-1}\left(\dfrac{b^2+c^2-a^2}{2bc}\right) \\\angle B=\cos^{-1}\left(\dfrac{a^2+c^2-b^2}{2ac}\right) \\\angle C=\cos^{-1}\left(\dfrac{a^2+b^2-c^2}{2ab}\right)[/tex]

Here, a,b and c are the sides of the triangle and A,B and C are the angles of the triangle.

Triangle ΔABC has side lengths of a = 18, b=18√3  and c = 36 inches.

Put the value, in the cosine law, the measure of angle A.

[tex]\angle A=\cos^{-1}\left(\dfrac{b^2+c^2-a^2}{2bc}\right) \\\angle A=\cos^{-1}\left(\dfrac{(18\sqrt{3})^2+36^2-18^2}{2(18\sqrt{3})(36)}\right) \\\angle A=0.5236\rm\; rad\\\angle A=30^o\rm\; degree\\[/tex]

Using the chart of unit circle, the value of tangent A can be found out. The tangent A is,

[tex]\tan A=\tan 30^o\\\tan A=\dfrac{1}{\sqrt{3}}[/tex]

Use the following formula to find area of ΔABC.,

[tex]A=\dfrac{ab.\sin C}{2}\\A=\dfrac{18\times18\sqrt{3}.\sin C}{2}\\A=280.6\rm\; in^2[/tex]

Thus, the measure of angle A is 30 degree, the value of tan A is 1/√3 and the area of triangle ABC is 280.6 squared inches.

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Answer:

it's simple math honey, just look it up

Answer:

126 square units

Step-by-step explanation:

Area of section 1 is 8 square units which is triangle and,

Area of triangle is =  [tex]\frac{1}{2}\times b\times h[/tex]

b= 2 units and height =8 units

So,

Area of section 1  =  [tex]\frac{1}{2}\times 2\times 8=8 \quad\text{ square units}[/tex]

Same Area is of section 2 which is also a triangle and has same base and height.

So,

Area of Section 2 = [tex]\frac{1}{2}\times 2\times 8=8 \quad\text{ square units}[/tex]

Now the Area of section 3 which is square with side of 10 units

So,

Area of section 3 =  [tex]a^{2} =10\times10=100\quad \text{square units}[/tex]

Total Area of Trapezoid = [tex]8+8+100=126 \quad \text{square units}[/tex]

Answer:

4

Step-by-step explanation:

So, 5/15 shirts are gray.

This can be simplified to 1/3. (5÷5 = 1, 15÷5=3)

So taking this data into account, if we have 12 shirts, one third of them should be gray. So, 12/3 = 4.

Answer:

4

Step-by-step explanation:

Trust

Answer:

d

Step-by-step explanation:

Since it had the lowest mean absolute deviation, his scores were closest together in Math.

Hence, lower values of the mean absolute deviation means that the scores are closer, and thus his scores were closest together in Math.

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Find the volume of a cylinder with a radius of 4 meters and a height of 13 meters. Use * 3.14.

radius of the cylinder = 4 m

height of the cylinder = 13 m

To find: The volume of the cylinder (where pi = 3.14)

We know that volume of cylinder

[tex] \pi {r}^{2} h[/tex]

Now by using the formula = 3.14 × (4) × (4) × 13

= 3.14 × 208

= 653.12 m³

3n+19

Explanation:

(1/2)(6n + 38)

Answer:

√250 + 2 = 5√10 + 2

Step-by-step explanation:

1. refer to image attached

2. split the area into a rectangle and triangle (see red line)

3. find the area of the triangle

a. find the base (2)

b. find the height (2)

area = base * height / 2 = 2 * 2 / 2 = 2

4. find the area of the rectangle

a. find the width

the width can be found from the right triangle at the top right. the height is 2 and the bottom leg is 1, so using the pythagorean theorem, the hypotenuse, which is the width of the triangle, equals

√(2²+1²)  = √5 as our width

b. find the length

given the top right triangle, we have a height of 5 and another leg length of 5, so the length = √(5²+5²) = √50

the area of the rectangle is thus √50 * √5 = √250

4. the area is thus the two areas added up, or √250 + 2

For a rotation of 180° clockwise or counterclockwise, the x and y will always be the opposite. For instance, if coordinates (4, 7) are being 180° rotated, the new set of coordinates will be (-4, -7).

Remembering the rule, the final answer to your question is A, 180° clockwise rotation about the origin.

Answer:

A, g(x) = -f(x)+5

Step-by-step explanation:

Answer:

Length =5cm

Step-by-step explanation:

When there's a problem ask

Answer:

1) 108 A+    2) 98 B+

Step-by-step explanation:

Answer:

3,052.08

Step-by-step explanation:

Formula for sphere: (4/3)(pi)(r^3)

Filled in: (4/3)(3.14)(729)

Calculated: 3,052.08

Answer:

39 units

Since two side lengths and a right angle are given, we can use pythogoras theorem to determine the missing side (c) of the triangle. It should be noted that pythgoras theorem can only be used if the triangle is a right triangle.

Pythogoras theorem formula:

[tex](\text{Side}_{1} })^{2} + (\text{Side}_{2} )^{2} = (\text{Hyptenuse})^{2}[/tex]

Substitute the legs of the triangle and the hyptenuse

[tex]\implies (36)^{2} + (15 )^{2} = (c)^{2}[/tex]

Simplify both sides of the equation

[tex]\implies 1296 + 225 = (c)^{2}\\[/tex]

[tex]\implies 1521 = (c)^{2}\\[/tex]

Take square root both sides

[tex]\implies \sqrt[2]{1521 } = \sqrt[2]{c^{2} }[/tex]

Solve for "c" by simplifying the roots

[tex]\implies \sqrt[2]{39 \times 39 } = \sqrt[2]{c \times c }[/tex]

[tex]\implies \boxed{39 = c}[/tex]

Thus, the measure of the missing side length (c) is 39 units.

A curve asymptote is a line where the distance between the curve and the line approaches 0. The function is undefined for the value of x=(5/2). Thus, x=(5/2) is an asymptote.

A curve asymptote is a line where the distance between the curve and the line approaches 0 when one or both of the x or y coordinates approaches infinity.

The asymptotes are the values for which the function is not defined. The asymptotes of a fractional function are found by equating its denominator's factors against zero. Therefore, the value of the asymptotes is,

[tex](2x-5)=0\\\\2x=5\\\\x=\dfrac52[/tex]

[tex]x-5=0\\\\x=5[/tex]

Now, substitute the value of x as (5/2) and 5, to know if the function is defined or not.

[tex]f(x) = \dfrac{(7x-1)(x-5)}{(2x-5)(x-5)}\\\\\\f(5) = \dfrac{[7(5)-1](5-5)}{[2(5)-5](5-5)}\\\\\\f(5) = \dfrac{(35-1)(0)}{(10-5)(0)} = 0[/tex]

Since for the value of x=5, the function is defined and returns the value as 0. Thus, x=5 is not an asymptote.

[tex]f(x) = \dfrac{(7x-1)(x-5)}{(2x-5)(x-5)}\\\\\\f(\frac52) = \dfrac{[7(\frac52)-1](\frac52-5)}{[2(\frac52)-5](\frac52-5)}\\\\\\f(\frac52) = \dfrac{(16.5)(-2.5)}{(0)(-2.5)} = \dfrac{\infty}{0}[/tex]

Since the function is undefined for the value of x=(5/2). Thus, x=(5/2) is an asymptote.

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Considering the given linear equation, it is found that the correct statement is given by:

B. The graph of this equation is a vertical line.

It is:

Ax + By = C

Considering that A ≠ 0 and B = 0, the expression is represented by:

Ax = C

x = C/A.

Which means that the graph is a vertical line, hence option B is correct.

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The probability of getting exactly 8 hits in his next 20 at-bats is 0.153 (Round off to the nearest thousandth.).

The correct option is (c)

Binomial distribution can be thought of as simply the probability of a SUCCESS or FAILURE outcome in an experiment or survey that is repeated multiple times.

Probability= [tex]C^{n}_r\; p^{r} \;q^{(n-r)[/tex]

where, n= number of trial,

r= number of success desire,

p= probability of success,

q= probability of Failure

probability of success = 0.34

To find the probability of winning exactly 8 hits in next 20 at-bats we find

dbinom (8, 20, 0.34)

Since p= 0.34

q= 1-p

 = 1-0.34

 = 0.66

n= 20, r=8

Using Binomial Distribution, we get

Probability= [tex]C^{n}_r\; p^{r} \;q^{(n-r)[/tex]

                 =[tex]\frac{n!}{r!(n-r)!} p^{r}\; q^{(n-r)}[/tex]

                 = [tex]\frac{20!}{8!(20-8)!} (0.34)^{8}\; (0.66)^{(20-8)}[/tex]

                = 125970 x 0.0001785794 x 0.00683168

                = 0.1536830

                ≈ 0.153 (Round off to the nearest thousandth.)

Hence, the probability of getting exactly 8 hits in his next 20 at-bats is 0.153.

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Answer:

All of the rugs are the same size after making the cuts. The vertical line goes down the center of the rectangle, making two congruent parts. The diagonal line also splits the rectangle into two congruent parts because the area of a right triangle is exactly half the area of the rectangle.

Step-by-step explanation:

Answer:

$114.19

Step-by-step explanation:

7.25*15 = 108.75

108.75*1.05 = 114.1875

You can't have less than a cent, so it is $114.19

Answer: $114.19

Step-by-step explanation:

Answer:

Tom sits in the middle and he is 18

Step-by-step explanation:

On the table you will first mark off Tom from being in the rear, as well as being 19

You will mark off Tom and Roy from the 1st, which places Davis as 1st, you also know that Tom is neither 1st nor last, so he is in the middle.

Now you see that Roy is neither in the 1st nor middle, so he is last.

Last is also the 20 yr old, so Roy is 20yrs and last seat.

Tom is neither 19 or 20.

So Tom is in the middle and 18yrs old

The total number of children in Stephan's school prefer pepperoni pizza where 375 children in Stephan's school is 310.

Equivalent ratio is the ratio which is same in the value as the original ratio, but the numerator and denominator is different for both the ratios.

Stephan read that 62 out of every 75 children prefer pepperoni pizza. Thus, the ratio of children who prefer pepperoni pizza to the total children is,

[tex]n=\dfrac{62}{75}\\[/tex]

Let suppose there are x children in Stephan's school prefer pepperoni pizza. There are 375 children in Stephan's school. The ratio of children who prefer pepperoni pizza to total 375 children is,

[tex]\dfrac{x}{375}[/tex]

Both the above ratio are for the same condition, and are equivalent ratio. Thus,

[tex]\dfrac{x}{375}=\dfrac{62}{75}\\x=\dfrac{62}{75}\times375\\x=310[/tex]

Thus, the total number of children in Stephan's school prefer pepperoni pizza where 375 children in Stephan's school is 310.

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Answer:

m<ABC = 90 degrees  m<ABD = 57 degrees

Step-by-step explanation:

OMG this is soooooo easy I love geometry.

Answer:

x^14 y^9

Step-by-step explanation:

Add the exponent of the x's

(x^5) + (x^9) = x^14

Add the exponent of the y's

(y^7) + (y^2) = y^9

You can't combine different varibles so your answer will be x^14 y^9

The error in Courtney claims that Option 2 would result in the class using 270 gallons is that he multiplied rather than dividing.

From the information given, it should be noted that Courtney claims that Option 2 would result in the class using 270 gallons of water during 180 minutes of showering is incorrect because she should have divided and not multiplied. This will be:

= 270 / (3/2)

= 180 × 2/3

= 120

Therefore, 120 gallons will be used.

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Answer:

9.16

Step-by-step explanation:

350 = 12 (x + 20)

350 = 12x +240

350 = 12x +240

-240           -240

110 = 12x

_______

     12

9.16 or 9.17 = x

[tex]2x + 3y = 9\\3y = -2x + 9\\y = -\frac{2}{3}x + 3[/tex]

Look at the graph picture I attached

[tex]y = mx + c[/tex]

c is the intercept, which is why the graph crosses the y-axis at +3

to find where it crosses the x-axis, we make y = 0

[tex]y = 0\\\to -\frac{2}{3}x + 3 = 0\\-\frac{2}{3} = -3\\\frac{2}{3}x = 3\\2x = 9\\x = \frac{9}{2}\ \ (=4.5)[/tex]