A triangular brace has an angle measure of 30 degrees, with a side opposite this angle measuring 8 inches. The base of the triangular brace, which is adjacent to the given angle measure, is 11 inches in length. Which of the following statements is correct?

Answer:

[tex]\frac{1}{8}[/tex]

Step-by-step explanation:

Using the rules of exponents

•  [tex]a^{-m}[/tex] ⇔ [tex]\frac{1}{a^{m} }[/tex]

• [tex]a^{\frac{m}{n} }[/tex] ⇔ [tex]\sqrt[n]{a^{m} }[/tex]

Hence

[tex]16^{-\frac{3}{4} }[/tex] = [tex]\frac{1}{16^{\frac{3}{4} } }[/tex]

= [tex]\frac{1}{\sqrt[4]{16^{3} } }[/tex] = [tex]\frac{1}{2^{3} }[/tex] = [tex]\frac{1}{8}[/tex]

Answer:

yea its pi not pie, but he is right

Step-by-step explanation:

the answer is B) 128

if the diameter of the cylinder's base is 8, then its radius is half that, or 4.

[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=4\\ h=8 \end{cases}\implies V=\pi (4)^2(8)\implies V=128\pi[/tex]

Answer:

the answer is B. They are perpendicular because their slopes are negative reciprocals.

Step-by-step explanation:

Answer:

the answer is B.

Step-by-step explanation:

It makes the problem solve smoother.

Answer:

x:2x:√3x.

Step-by-step explanation:

I would write it as x:2x:√3x.

The hypotenuse is twice the length of the shorter leg and the longer leg is the square root of 3 times the shorter leg.

Answer:

The correct option is A) x : 2x : x√3

Step-by-step explanation:

Consider the provided information.

For a 30-60-90 triangle.

The side opposite to the 30° angle is x.

The side opposite the 60° angle is √3 x.

The side opposite the 90° angle is 2 x.

Side opposite to the 30° angle is the smallest side as 30° is the smallest angle among 30-60-90. Similarly the side opposite of 60° is the second largest side as 60° is the second largest angle and for the side opposite of 90° is the largest side as 90° is the largest angle.

Hence, the correct option is A) x : 2x : x√3

Answer:

c. pi/2

Step-by-step explanation:

The answer is the option c. pi/2.

You must know that y = sin(x) is an odd function and also that y = cos(x) is an even function.

Also, you should know that sin(x + pi/2) = cos(x).

You can show it using the definition of the functions sine and cosine in the unit circle or using the formula of the sine of a sum: sin(A + B) = sin(A)*cos(B) + cos(A)*sin(B).

When you substitute B with pi/2 you get sin (A + pi/2) = sin(A)*0 + cos(A)*1 = cos(A).

Then, given that cos(A) is even sin(A+pi/2) is even.

Answer:

option b

Step-by-step explanation:

We are given that [tex]y=sin \frac{1}{2}(x-C)[/tex] be an even function

We have to find the value of C for which given function is even function

We know that sin x is odd function and cos is even function

Odd function : when f(x)[tex]\neqf(-x) [/tex] then the function is called an odd function.

Even function : When f(x)=f(-x) then the function is called an even function.

Sin(-x)=-Sin x

Cos (-x)= Cos x

When we take C=[tex]2\pi[/tex]

Then , y=Sin[tex]\frac{x}{2}-\frac{2\pi}{2}[/tex]

y=[tex]sin(\frac{x}{2}-\pi)[/tex]

[tex]y=-sin\frac{x}{2}[/tex]  ( [tex]sin (x-\pi)=-sin x[/tex])

When x is replace by -x

Then, we get [tex]y=-sin(-\frac{x}{2})=sin\frac{x}{2}[/tex]

[tex]f(-x)\neq f( x)[/tex]

Hence, option a is false.

b.C=[tex]\pi[/tex]

[tex]y= sin (\frac{x}{2}-\frac{\pi}{2})[/tex]

[tex] y=-sin(\frac{\pi}{2}-\frac{x}{2})[/tex]

[tex]y=-cos \frac{x}{2}[/tex]

When x is replaced by -x then we get

[tex] y=-cos (-\frac{x}{2})=- cos \frac{x}{2}[/tex]

f(x)=f(-x) , Therefore, function is even,hence option b is true.

c.C=[tex]\frac{\pi}{2}[/tex]

[tex]y=sin (\frac{x}{2}-\frac{\pi}{4})[/tex]

[tex]Sin (A-B)=Sin A Cos B- Sin B Cos A[/tex]

[tex][y= sin \frac{x}{2} cos {\frac{\pi}{4}-cos\frac{x}{2} sin\frac{\pi}{4}[/tex]

[tex] sin\frac{\pi}{4}= cos \frac{\pi}{4}=\frac{1}{\sqrt2}[/tex]

[tex]y=\frac{1}{\sqrt2}(sin \frac{x}{2}- cos \frac{x}{2})[/tex]

When x is replaced by -x then we get

[tex]y=\frac{1}{\sqrt2}(-sin\frac{x}{2}-cos \frac{x}{2})[/tex]

[tex]f(x)\neq f(-x)[/tex]

Hence, function is odd .Therefore, option c is false.

Answer:

The answer isc

Step-by-step explanation:

C

Answer:

B. n = 65; p = 0.8

Step-by-step explanation:

Answer:

Option C

Step-by-step explanation:

Given

Mean= μ=60

and

Standard Deviation= σ=5

In order to calculate the percentage of students between 55 and 65, we have to calculate z-score for both

z-score for 55=(55-60)/5  

=(-5)/5

=-1

The area to the left of z-score -1 is 0.1587

z-score for 65=(65-60)/5  

=5/5

=1

The area to the left of z-score 1 is 0.8413

Area between z-scores of 55 and 65=0.8413-0.1587

=0.6826

Converting into percentage

=0.6826*100

=68.26%

Option C is the correct answer ..  

Answer:

c. 68

Step-by-step explanation:

The empirical rule states that, if a population is approximately normal then 68% of the observations will fall within 1 standard deviation of the mean.

Going by this definition, 65 is one standard deviation to the right of the mean while 55 is one standard deviation to the left of the mean. Therefore, the percent of students who have scored between 55 and 65 points will be about 68%.

The question requires an approximation, About what percent, not exact computation. Thanks

Answer:

1. The median.

Step-by-step explanation:

First arrange in ascending order:

5.8  6.1  6.1  6.2  6.2  6.2  6.3  6.8  6.8 7

The median = 6.2. On the box plot the median is marked at 6.3 so that is incorrect. All the others are correct

Answer:

3v+5+8u is written as a product of three factors is incorrect because factors are associated with multiplication and multiplication is only used twice within the problem and also they are all be add

3v+5+8u is written as a sum of three terms is correct because sum is associated with addition and three terms are being added together

8 is a coefficient is correct because a coefficient is a number being multiplied by a variable in this case and its still a variable in both ways of looking at it because terms are also single numbers

8u and 5 are like terms is incorrect because you cannot add them together

5 is a constant is correct because a constant is a single number

none of these are true is incorrect because there are correct answers

Answer:

it would be the 1st one

Step-by-step explanation:

Answer:

Letter (D), or y = -3x - 4

Step-by-step explanation:

A slope of -3 should be self explanatory, and y intercept is determined by the b value in the form y = mx + b. Since b is negative, we are looking for -4. Therefore, your answer is (D).

Hope this helps!

Look at the equations and see if the statements are true.

Company 1 and 4 do not charge the same rate per mile, company one charges 0.5 per mile and company 4 charges 0.06 per mile.

Company 2 and 3 do not charge the same.

Company 2 has an x in the equation so is not just a flat fee.

Company 3 does not have an x in the equation, so only charges a flat fee.

The correct answer is the last one.

Answer:

96 is a composite number. 96 = 1 x 96, 2 x 48, 3 x 32, 4 x 24, 6 x 16, or 8 x 12

Step-by-step explanation:

Answer:

(10 x 13) + (10 x 12) + (12 x 5 / 2) + (12 x 5 / 2) + (10 x 5)

360

The simplest basic geometric object is a point. It is named with a capital letter and symbolized by a dot. The correct option is C.

The simplest basic geometric object is a point. It is named with a capital letter and symbolized by a dot. A point has no size and solely represents the position (that is, zero length, zero width, and zero height).

Since a plane is a flat, endlessly long two-dimensional surface. A plane is a two-dimensional analog that can incorporate three dimensions of space, a line, and a point.

Now, the statement that will be true about the three points given is that only one plane can be drawn so it contains all three points.

Hence, the correct option is C.

The complete question is mentioned in the image below.

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Answer:

Third option

Step-by-step explanation:

Given expression is:

[tex]\sqrt[3]{32x^8y^{10}}[/tex]

Making the exponents multiples of 3

[tex]=\sqrt[3]{8*4*x^6*x^2*y^{9}*y}\\=\sqrt[3]{2^3*4*x^6*x^2*y^{9}*y}\\Applying\ radical\\=2^{(3*\frac{1}{3})} *4^{\frac{1}{3} }*x^{(6*\frac{1}{3})}*x^{(2*\frac{1}{3})}*y^{(9*\frac{1}{3})}*y^{\frac{1}{3}}\\=2x^2y^3\sqrt[3]{4x^2y}[/tex]

Hence,

Option No 3 is correct ..

Enter the given values into the equation and solve.

5800 = 4100e^(k*40)

Divide both sides by 4100 and simplify:

58 / 41 = e^(k*40)

Remove e by taking the logarithm of both sides:

ln(58/41) = k *40

Divide both sides by 40:

k = ln(58/41)/40

k = 0.00867

Now for the population to double set up the equation:

2*4100 = 4100e^kt

The 4100 cancels out on both sides:

2 = e^kt

Take the logarithm of both sides:

ln(2) = k*t

Divide both sides by k

t = ln(2) /k

replace k with the value from above:

t = ln(2) / 0.00867

t = 79.95

Rounded to the nearest tenth = 80.0 hours to double.

Answer:

Step-by-step explanation:

To answer the question, we first need to find the constant k, using the given information and the expression.

[tex]P=4100e^{kt} \\5800=4100e^{k(40)} \\\frac{5800}{4100}=e^{40k}\\e^{40k}=1.41\\lne^{40k}=ln1.41\\40k=0.34\\k=\frac{0.34}{40}\approx 0.0085[/tex]

Now that we have the constant. We can find the time it would take to double the population which would be 11600:

[tex]P=4100e^{kt}\\11600=4100e^{0.0085t}\\\frac{11600}{4100}= e^{0.0085t}\\e^{0.0085t}=2.83\\lne^{0.0085t}=ln2.83\\0.0085t=1.04\\t=\frac{1.04}{0.0085}\approx 122.35[/tex]

Therefore, it would take around 122 hours to double the population.

Answer:

D

Step-by-step explanation:

multiples of 6 : 6, 12, 18, 24, 30, 36, ....

multiples of 15 : 15, 30, 45, ......

From the lists the least common multiple is 30

[tex]6=2\cdot3\\15=3\cdot5\\\\\text{lcm}(6,15)=2\cdot3\cdot5=30[/tex]

Answer:

[tex]y=-3x+14[/tex]  or  [tex]3x+y=14[/tex]

Step-by-step explanation:

we have

[tex]y+1=-3(x-5)[/tex] ----> equation of the line into point-slope form

step 1

Convert to slope intercept form

The equation of the line into slope intercept form is equal to

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

so

[tex]y+1=-3(x-5)[/tex]

[tex]y+1=-3x+15[/tex]

[tex]y=-3x+15-1[/tex]

[tex]y=-3x+14[/tex] ----> equation of the line into slope intercept form

step 2

Convert to standard form

The equation of the line into standard form is equal to

[tex]Ax+By=C[/tex]

so

we have

[tex]y=-3x+14[/tex]

Adds 3x both sides

[tex]3x+y=14[/tex] ----> equation of the line in standard form

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

y = mx + b

m - slope

b - y-intercept

We have the equation y = 75x + 50.

Therefore

slope: m = 75

y-intercept: b = 50

Answer:

y+3=-6(x +9)

Step-by-step explanation:

equation represents a line that passes through (-9, -3) and has a slope of -6is:

y+3=-6(x +9)

because : The equation of a linear function in point-slope form is:                    y – y1 = m(x – x1) ....m : the slope

The point is A (x1 , y1)

you have m = - 6      x1 = -9      y1 = -3

The equation represents a line that passes through (-9, -3) and has a slope of -6 is y+3 = -6(x+9).

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, a line is passing through the point (-9, -3) and the slope of -6,

We need to determine the equation of the line,

The general formula of a line passing through a point (x', y') and have slope m is given by,

y-y' = m(x-x')

Here, (x', y') = (-9, -3), m = -6,

Therefore, the equation of the asked will be =

y-(-3) = -6(x-(-9))

y+3 = -6(x+9)

Hence, the equation represents a line that passes through (-9, -3) and has a slope of -6 is y+3 = -6(x+9)

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Answer:

it should be (based on the instructions we don't have) [tex]\frac{-3}{2}[/tex]

Step-by-step explanation:

because the "D" in the parenthesis has 2 negative signs, it inverts itself making it just what D equals, which on the number line is [tex]\frac{-3}{2}[/tex]

Answer:

990 feet

Step-by-step explanation:

Fabricator 4 recieved what's left after the rest were distributed

= 5,840 - 2,500 - 1,200 - 1,150 = 990

Answer:

990 feet.

Step-by-step explanation:

To calculate the feet of metal that the last fabricator will sell, you just have to substract from the total feet needed the amount of metal that have been already ordered to the other fabricators.

Total metal duct work= Fabricator 1+ Fabricator 2+ Fabricator 3+ Fabricator 4

If you clear the equation it would be:

F4= Total- F1- F2- F3

F4= 5840- 2,500- 1,200- 1150

F4= 990 ft.

Check the picture below.

since the larger cube has a volume of 6 cubic units, let's see what is the volume of one of the small cubes, and check how many times does that volume go into the other.

[tex]\bf \stackrel{\textit{volume of a cube}}{V=s^3}~~ \begin{cases} s=side's~ length\\ \cline{1-1} s=\frac{1}{2} \end{cases}\implies V=\left( \cfrac{1}{2} \right)^3\implies V=\cfrac{1}{8} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{how many times does }\frac{1}{8}\textit{ go into 6?}}{6\div \cfrac{1}{8}\implies \cfrac{6}{1}\div \cfrac{1}{8}\implies \cfrac{6}{1}\cdot \cfrac{8}{1}}\implies 48[/tex]

Answer:

Step-by-step explanation:

Answer:

-2+sqrt(3)

Step-by-step explanation:

When cos(angle)=sqrt(3)/2

then sin(of that angle)= + or - 1/2 depending on the quadrant

Anyways 330 degrees is in the 4 quadrant.  Cosine is positive there while sine is negative.

so sin(330)=-1/2

Formula for tan(x/2)=(1-cos(x))/sin(x)

Therefore  tan(165)=tan(330/2)=(1-cos(330))/sin(330)=(1-sqrt(3)/2)/(-1/2)

Multiply top and bottom by 2 to get

tan(165)=(2-sqrt(3))/-1

tan(165)=-2+sqrt(3)

Answer:

-1/5

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

A) a ≥ 3 + 2j; j ≥ 14, a ≤ 35

B) a ≤ 3 + 2j; j ≥ 14, a ≤ 35

C) a ≥ 3 + 2j; j ≤ 14, a ≤ 35

D) a ≤ 3 + 2j; j ≤ 14, a ≤ 35

All the system of linear inequalities which can be used to find the possible ages of Anna, a, and Jamie, j are,

a < 3 + 3j

j ≥ 14

a ≤ 35

We have to given that,

Anna is no more than 3 years older than 2 times Jamie’s age.

Jamie is at least 14 and Anna is at most 35.

Let us assume that,

Age of Anna = a

Age of Jamie's = j

Hence, system of linear inequalities which can be used to find the possible ages of Anna, a, and Jamie, j are,

For Anna is no more than 3 years older than 2 times Jamie’s age.

a < 3 + 3j

And, Jamie is at least 14 and Anna is at most 35.

j ≥ 14

a ≤ 35

Thus, All the system of linear inequalities which can be used to find the possible ages of Anna, a, and Jamie, j are,

a < 3 + 3j

j ≥ 14

a ≤ 35

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Answer:

4/5

Step-by-step explanation:

start with putting the decimal over ten

8/10

than divide numerator and denominator with the common denominator 2

8÷2=4 10÷2=5

4/5

Answer:

1. 13.98

2. 14.47

Step-by-step explanation:

The question is on sample standard deviation and population standard deviation

Arrange the data in increasing order

12,14, 16,16,17,19,21,26,35,37,42,43,45,46,56

n=15

Find the mean of the data set

[tex]mean = (12+14+ 16+16+17+19+21+26+35+37+42+43+45+46+56)/15[/tex]

mean= 29.67 ⇒30

Find the deviations

You subtract the value of mean from each of  the data set given

Deviations= -18, -16, -14, -14, -13,-11, -9,-4,5,7,12,13,15,16,26

Find squares of deviations

= 324, 256, 196, 196, 169, 121, 81, 16, 25, 49, 144, 196, 225, 256, 676

Find sum of squares of deviations

[tex]324+ 256+ 196+ 196+ 169+ 121+ 81+ 16+ 25+ 49+ 144+ 196+ 225+ 256+ 676 = 2930[/tex]

1. Treating the data set to represent an entire population then;

Variance= sum of squares of deviation/number of data set

Variance= 2930/15 = 195.33

Population standard deviation = √195.33 = 13.98

2. Treating the data set as a sample , the number of data set is reduced by one.i.e n= 15-1= 14

Sample Variance=2930/14 =209.29

sample standard deviation= √209.29 = 14.47