the red line in the figure is an altitude of triangle ABC. Using right angle trigonometry, write an equation involving sin C​

Answer:

-1/8

Step-by-step explanation:

[tex](-2)^-3 \\=\frac{-1}{2}^{3}\\=\frac{-1}{8}[/tex]

Answer:

-1/8

Step-by-step explanation:

[tex]\left(-2\right)^{-3}\\\\\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}\\\left(-2\right)^{-3}=\frac{1}{\left(-2\right)^3}\\\\=\frac{1}{\left(-2\right)^3}\\\\\left(-2\right)^3=-8\\\\=\frac{1}{-8}\\\\=-\frac{1}{8} \\\\\left(\mathrm{Decimal:\quad }\:-0.125\right)[/tex]

Answer:

t=r/d; t=0.2

Step-by-step explanation:

If d=r/t, then multiple both sides by t, to get td=r, then divide both sides by d, to get t=r/d. So t=8/40 t=0.2

B or C (both are correct just choose one)

B or C (both are correct).

Answer:

Only one solution

Step-by-step explanation:

[tex] |r - 6| = 0 \\ r - 6 = \pm \: 0 \\ r - 6 = 0 \\ r = 6[/tex]

Answer: P, T, Y

This is because the points on the line are straight

Option - A is the correct answer.

We have a geometrical figure given in the question.

We have to determine which set of points are collinear.

Three or more points are said to be collinear if they lie on a single straight line.

According to question -

It can be seen that only one set of points - (P, T, Y) lie on the same straight line. Of the options mentioned, one is - (P, T, Y)

Hence, the correct option is Option - A.

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Answer:

3/5^3

3/5^3 = 27

125

= 0.216

Step-by-step explanation:

Rules for expressions with fractions:

Fractions - use the slash “/” between the numerator and denominator, i.e. for five-hundredths enter 5/100. If you are using mixed numbers be sure to leave a single space between the whole number and fraction part.

The slash separates the numerator (number above a fraction line) and denominator (number below).

Mixed numerals (mixed fractions or mixed numbers) write as non-zero integer separated by one space and fraction i.e., 1 2/3 (having the same sign). An example of a negative mixed fraction: -5 1/2.

Because slash is both signs for fraction line and division, we recommended use colon (:) as operator of division fractions i.e., 1/2 : 3.

Decimals (decimal numbers) enter with a decimal point . and they are automatically converted to fractions - i.e. 1.45.

Colon : and slash / is the symbol of division. Can be used to divide mixed numbers 1 2/3 : 4 3/8 or can be used for write complex fractions i.e. 1/2 : 1/3.

An asterisk * or × is the symbol for multiplication.

Plus + is addition, minus sign - is subtraction and ()[] is mathematical parentheses.

The exponentiation/power symbol is ^ - for example: (7/8-4/5)^2 = (7/8-4/5)2

Calculator follows well-known rules for order of operations. Most common mnemonics for remembering this order of operations are:

PEMDAS - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

BEDMAS - Brackets, Exponents, Division, Multiplication, Addition, Subtraction

BODMAS - Brackets, Of or Order, Division, Multiplication, Addition, Subtraction.

GEMDAS - Grouping Symbols - brackets (){}, Exponents, Multiplication, Division, Addition, Subtraction.

Be careful, always do multiplication and division before addition and subtraction. Some operators (+ and -) and (* and /) has the same priority and then must evaluate from left to right.

Answer:

[tex]\frac{536}{15}[/tex] or [tex]35\frac{11}{15}[/tex] (they're the same)

Step-by-step explanation:

Answer:

x = 6

Step-by-step explanation:

Given that PQ = 3x + 14, QR = 7x - 10, and Q is the midpoint of PR, it means Q is equidistant from both endpoints of P and Q. In order words, the distance from P to Q is the same as the distance from Q to R.

Therefore, PQ = QR. Which is:

[tex] 3x + 14 = 7x - 10 [/tex]

Solve for x. Collect like terms

[tex] 3x -7x = - 14 - 10 [/tex]

[tex] -4x = -24 [/tex]

Divide both sides by -4x

[tex] x = 6 [/tex]

Answer:

200,000

Step-by-step explanation:

To solve this, you can divide the 2019 total projected employment (210,000) by 1 + the growth rate (.05) to find the 2009 total employment.

210,000 / (1 + .05) = 200,000

I hope this helps!

-TheBusinessMan

Answer:

B. 12 square ft C. 63 square ft

Step-by-step explanation:

Marlena places a square rug on her living room floor, which is also a square.

Now if a square rug is placed in her room, the area of the floor will definitely be the area if the square rug..

And area of a square it = length ²

The result will give s a perfect square for an integer number.

A. 9 square ft = perfect square

B. 12 square ft = not perfect square

C. 63 square ft =not perfect square

D. 81 square ft= perfect square

So the ones that are not perfect squares Is the answer to the question

The  area of her floor is NOT covered by the rug is 12 square ft and  81 square ft.

It is required to find the area of her floor is NOT covered by the rug.

A square is a four-sided polygon, whose all its sides are equal in length and opposite sides are parallel to each other. Also, each vertices of square have angle equal to 90 degrees.

Given:

Marlena places a square rug on her living room floor, which is also a square.

Now if a square rug is placed in her room, the area of the floor will definitely be the area if the square rug..

If the length of each side of the rug is equal to the length of each side of the room, there will be no area not covered.

According to given question we have,

And area of a square it = length ²

The result will give s a perfect square for an integer number.

A. 9 square ft = perfect square

B. 12 square ft = not perfect square

C. 63 square ft =not perfect square

D. 81 square ft= perfect square

Therefore, the  area of her floor is NOT covered by the rug is 12 square ft and  81 square ft.

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let the unknown no.be x

therefore, 76+122+92+x = 360

                 = 198+92+x = 360

                = 290+x = 360

                    x=360-290

                    x= 70degree

hope this is helpful,

^_^

Answer:

eds bageles are $.22 per bagel and best bagels are $.23 per bagel.

Step-by-step explanation:

We have [tex]h(p)=p^2+2p[/tex] and [tex]h(p)=3[/tex] which means we can equate:

[tex]p^2+2p=3[/tex].

Subtract 3 from both sides:

[tex]p^2+2p-3=0[/tex].

Then solve for p:

[tex]p^2+2p-3=0[/tex].

[tex](p-1)(p+3)=0[/tex].

So the product of two factors (p-1) and (p+3) is 0 which means at least one of the factors must be 0:

[tex]p-1=0\implies p_1=1[/tex].

Or

[tex]p+3=0\implies p_2=-3[/tex].

Hope this helps.

Answer:

The answer is B. sin A = 0.5

Step-by-step explanation:

Answer:

a + s = 394     total tickets sold is 394 s = a - 56       56 fewer student tickets than adult substitute a-56 in place of s in 1st equation and solve for a a + (a - 56) = 394 2a - 56 = 394 2a = 450 a = 225 adult tickets sold s = a-56 = 169 student tickets sold

Hoped I helped

Answer:

3^12

Step-by-step explanation:

(3^3/4(2) - 3/8) ^4/9

(3^6/8-3/8)^4/9

(3^3/8)^4/9

3^3/8(4/9)

3^27/72(32/72)

3^864/72

3^12

Sorry if it's hard to read...

Answer:

Step-by-step explanation:

The diagram is not given in this question, but we can proceed anyways.

from the problem statement we can observe that the radius of the arc is same as the width of the door

a. the radius is 4.2 cm

b. the length of the arc given that the central angle is 25°  can be gotten using the formula stated bellow

arc length = 2 π r *(∅/360)

substituting we have

arc length = 2*3.142*(225/360)

arc length= 6.284*0.625

arc length=3.92 cm

Answer:

  60°

Step-by-step explanation:

The definition of cosine tells you ...

  cos(β) = 3/6 = 1/2

  β = arccos(1/2) . . . . use the inverse cosine function to find the angle

  β = 60°

_____

The ratio of side lengths in a 30°-60°-90° triangle (one of the "special" triangles), is ...

  1 : √3 : 2

The 2 : 1 ratio of longest to shortest side in this right triangle is a clue that the largest acute angle is 60°. It also tells you that x = √3 times the short side length, so is x = 3√3.

Answer:

(a) The degrees of freedom; the relevant t distribution would have = n - 1 = 41 - 1 = 40.

(b) A 95% confidence interval for the mean speed of vehicles crossing the bridge is [79.92 km/hr, 82.78 km/hr] .

(c) We should not reject the hypothesis since 80 km/h is in the interval found in (b).

(d) Decrease the Type I error probability.

Step-by-step explanation:

We are given that the average speed for a sample of 41 vehicles was 81.35 km/h, with the sample standard deviation being 4.52km/h.

(a) Since here we don't know about population standard deviation, so the distribution that will be used here is t-distribution as the data also follows the normal distribution.

The degrees of freedom; the relevant t distribution would have = n - 1 = 41 - 1 = 40.

(b) Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                             P.Q.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~   [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample average speed of vehichles = 81.35 km/h

             s = sample standard deviation = 4.52 km/h

             n = sample of vehicles = 541

            [tex]\mu[/tex] = population mean  

Here for constructing a 95% confidence interval we have used a One-sample t-test statistics as we don't know about population standard deviation.

So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-2.021 < [tex]t_4_0[/tex] < 2.021) = 0.95  {As the critical value of t at 40 degrees of

                                               freedom are -2.021 & 2.021 with P = 2.5%}  

P(-2.021 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.021) = 0.95

P( [tex]-2.021 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]2.021 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

P( [tex]\bar X-2.021 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.021 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.021 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.021 \times {\frac{s}{\sqrt{n} } }[/tex] ]

                                      = [ [tex]81.35-2.021 \times {\frac{4.52}{\sqrt{41} } }[/tex] , [tex]81.35+2.021 \times {\frac{4.52}{\sqrt{41} } }[/tex] ]  

                                     = [79.92 km/hr, 82.78 km/hr]

Therefore, a 95% confidence interval for the mean speed of vehicles crossing the bridge is [79.92 km/hr, 82.78 km/hr] .

(c) The hypothesis given to us is;

Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 80 km/hr    {means that the mean speed of vehicles over the bridge would be the speed limit of 80 km/h}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 80 km/hr    {means that the mean speed of vehicles over the bridge would be the speed limit of different from 80 km/h}

Here, we should not reject the null hypothesis since 80 km/h is in the interval found in (b) which means that we are 95% confident that the mean speed of vehicles over the bridge would be the speed limit of 80 km/h.

(d) Decreasing the significance level of the hypothesis test above would decrease the Type I error probability because Type I error probability is represented by the significance level.

Answer:

[tex]y=-0.5x+4.5[/tex]

Step-by-step explanation:

The slope of [tex]y=2x-6[/tex] is:

The negative reciprocal of that slope is:

So the perpendicular line will have a slope of [tex]-1/2[/tex]:

And now put in the point [tex](1,5)[/tex]:

And that answer is OK, but let's also put it in [tex]y=mx+b[/tex] form:

Answer:

3 and 1/2  minus 2/3  minus 1/3 =

7/2 minus 2/3 minus 1/3 =

21/6 minus 4/6 minus 2/6 =

17/6 - 2/6 =

15/6 =    5/2 = 2 and 1/2

Optionally, you can think of it this way:

He used 2/3 yards for the pillow and 1/3 yard for the scarf.

So he used 1 yard

3 and 1/2 minus 1 = 2 and 1/2 = 5/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

cosine is negative in 2nd and 3rd quadrant.

cotangent is negative in 2nd and 4th quadrant.

In the second quadrant, both cosine and cotangent are negative.

In the first quadrant all trig functions are positive, In the second quadrant sine and sec are positive in the third quadrant tan and cot are positive, and in the fourth quadrant cos and cosec are positive.

We know there are four quadrants in an XY plane.

We also know that sine is positive on 1st and second quadrants and cosine is positive on the first and fourth quadrants.

tan = (sin/cos).

So, cot = 1/tan = cos/sing.

∴ cotangent is negative if any one of sine and cosine is negative which is in the second and fourth quadrants because in the third quadrant both sine and cosine are negative making cotangent positive.

∴ In the second quadrant cosine and cotangent, both are negative.

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Note. The original question with options given on the bottom

Answer:

F - 1, B -2, A - 3, D - 4, C - 5, E - 6

Step-by-step explanation:

F.  Sample

B. Population  

A. Statistic  

D. Parameter  

C. Data  

E. Variable  

========================================================

Question

A bank manager is interested in the average length of time that customers are willing to wait in line before they give up and leave the bank. Match the vocabulary word with its corresponding example.

---------------------

1. The 25 customers that the manager observed leave

2. All of the bank's customers

3. The average length of time that the 25 customers waited before leaving the bank

4. The average length of time that all customers will wait before leaving the bank

5. The list of times for the 25 customers who left the bank

6. The length of time a customer waits before leaving the bank

---------------------

Answer: x²-x+6

Step-by-step explanation:

(f+g)(x) means f(x)+g(x). Since we are given the values of f(x) and g(x), we can directly subtract them.

x²+1+(5-x)                     [distribute +1]

x²+1+5-x                      [combine like terms]

x²-x+6

Answer:

[tex]\huge\boxed{(f+g)(x) = x^2 - x+ 6}[/tex]

Step-by-step explanation:

[tex]\sf f(x) = x^2 + 1\\g(x) = 5-x[/tex]

Adding both functions

[tex]\sf (f+g)(x) = x^2 + 1+ 5 - x\\(f+g)(x) = x^2 - x+ 6[/tex]

Answer:

multiplication

Step-by-step explanation:

it seems the best

Answer:

7/4 = 1.75

Step-by-step explanation:

step 1: pick two points on the line that have nice integer coordinates.

--> (3,4) and (-1,-3)

step 2: calculate the y difference and the x difference

--> y difference: 4 - -3 = 7

    x difference: 3 - -1 = 4

step 3: the slope is y difference / x difference

--> slope = 7/4

Answer:

13°

Step-by-step explanation:

The smallest angle in a triangle is the angle opposite the shortest side.

In this case the angle opposite side 9

let the angle be x, then using the tangent ratio in the right triangle

tan x = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{9}{40}[/tex] , thus

x = [tex]tan^{-1}[/tex] ([tex]\frac{9}{40}[/tex] ) ≈ 13° ( to the nearest degree )

Answer:

[tex](x+4,y-5)[/tex]

Step-by-step explanation:

Studying the figures ABCD and A'B'C'D', we can look at just one point and figure out the transformation from that.

Point A is at (-7, 8)

Point A' is at (-3, 3)

If we look at the x values, -7 and -3, we can see that the value changed by 4. So [tex]x+4[/tex] will be what the x becomes.

Also looking at the y values, we can see that the values were 8 and 3 - that's a change of -5, so our y is [tex]y-5[/tex].

Combining these, we get [tex](x+4, y-5)[/tex].

Hope this helped!

Answer: A.  (x,y) → ( x+4,y-5)

Step-by-step explanation:

This a rigid transformation and is being translated to find the transformation you could use any vertex.

Using the image of B  and to get  to B prime we have to move  4 units to the right and 5 units down.

So we could describe the whole transformation as (x,y) → ( x+4,x-5)