write your answer in simplest radical form​

9514 1404 393

Answer:

  3. 42.21 in

  4. 4.38 cm

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationships between an angle in a right triangle and the basic trig functions. The triples of letters stand for ...

  Sin = Opposite/Hypotenuse

  Cos = Adjacent/Hypotenuse

  Tan = Opposite/Adjacent

where the terms "opposite" and "adjacent" refer to sides of the triangle that are opposite the angle of interest or adjacent to it, respectively.

In these problems, the measure of the hypotenuse is shown, and the problem requests the measure of the side opposite the given angle. The sine function is relevant.

__

3. sin(79°) = GE/GB = GE/(43 in)

   GE = (43 in)sin(79°) ≈ (43 in)(0.981627) ≈ 42.21 in

__

4. sin(26°) = BC/BA = BC/(10 cm)

  BC = (10 cm)sin(26°) ≈ (10 cm)(0.438371) ≈ 4.38 cm

Answer:

[tex]A(x) = 12500(1.054)^x[/tex]

Step-by-step explanation:

Exponential equation for population growth:

Considering a constant growth rate, the population, in x years after 2005, is given by:

[tex]A(x) = A(0)(1 + r)^x[/tex]

In which A(0) is the population in 2005 and r is the growth rate, as a decimal.

The initial population of the town was estimated to be 12,500 in 2005.

This means that [tex]A(0) = 12500[/tex]

The population has increased by about 5.4% per year since 2005.

This means that [tex]r = 0.054[/tex]

So

[tex]A(x) = A(0)(1 + r)^x[/tex]

[tex]A(x) = 12500(1 + 0.054)^x[/tex]

[tex]A(x) = 12500(1.054)^x[/tex]

Answer:

opposite angles

Step-by-step explanation:

They are formed in the intersection of lines AD and BD.

Answer:

opposite angles

Step-by-step explanation:

they are formed in the intersection of lines AD and BD. two figures are called similar if they have same shape however have different size.

Answer:

x = 27/8

Step-by-step explanation:

We can write a ratio to solve

x               3

------- = ----------

x+9           11

Using cross products

x*11 = 3(x+9)

11x = 3x+27

Subtract 3x from each side

8x = 27

8x/8 = 27/8

x = 27/8

Answer:

fx = 2xe^(x^2+y^2) + 3e^xy + 3xye^xy

fy = 2ye^(x^2+y^2) + 3x^2.e^xy

Answer:

25 miles (The pattern is m = 25g where m is miles and g is gallons.)

Pressure is force per unit area. If the block is sitting at rest on the surface, it applies a pressure of mg/A, where mg is the block's weight and A is the area of the face that makes contact with the surface.

The smaller the value of A, the larger the pressure. So the highest pressure the block can exert is achieved when it's resting on the face with the smallest dimensions.

If the block is a cube with side length 95 cm, then the pressure exerted by each face is the same.

Answer:

a. 1.44

Step-by-step explanation:

We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 40%.

At the null hypothesis, it is tested if the proportion is of at most 40%, that is:

[tex]H_0: p \leq 0.4[/tex]

At the alternative hypothesis, it is tested if the proportion is of more than 40%, that is:

[tex]H_1: p > 0.4[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.4 is tested at the null hypothesis:

This means that [tex]p = 0.4, \sigma = \sqrt{0.4*0.6}[/tex]

A random sample of 200 people was taken. 90 of the people in the sample favored Candidate A.

This means that:

[tex]n = 200, X = \frac{90}{200} = 0.45[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.45 - 0.4}{\frac{\sqrt{0.4*0.6}}{\sqrt{200}}}[/tex]

[tex]z = 1.44[/tex]

Thus the correct answer is given by option a.

Answer:

B

Step-by-step explanation:

z+z=6, z=3. z+y=5, y=2, x+y=10, x=8

Answer:

6:21

Step-by-step explanation:

We want to find the ratio of squares to shapes

So simply count the squares

There are 6 squares

And then find the total number of shapes

There are a total of 21 shapes

So for every 6 squares there are 21 total shapes

In other words the ratio of squares to shapes is 6:21

Answer:

Step-by-step explanation:

Given,

Number of squares = 6

Total no. of shapes = 21

Therefore,

Unsimplified ratio of squares to total shapes

= 6:21 (Ans)

Answer:

The set S could, but does not have to, span Rn   ( A )

Step-by-step explanation:

Assume S is a set of linearly dependent vectors in Rn

The best statement from the options is ; The set S could, but does not have to, span Rn

This is because S could span Rn ( as stated in option c ) but will  not necessary span Rn ( as seen in option D )

Answer:

207 tens

Step-by-step explanation:

If you mean

8,000 + 70 = 6000 + X tens

then it should be 207 tens

Answer:

x=5

Step-by-step explanation:

im so bad at explaining things but i hope this helped

Answer:

the answer would be 100,000,000

Greatest 8 Digit Number: 99,999,999

Adding 1 = 99999999+1

= 100,000,000

Must click thanks and mark brainliest

Graph is attached below ;

Answer:

Unit rate = 12 computers per day

Step-by-step explanation:

To obtain the unit rate of computers sold per day using the graph, we need to obtain the slope of the graph, which is the change in y per change in x

That is ; the gradient ;

Slope = change in y / change in x

Slope = (y2 - y1) / (x2 - x1)

y2 = 60 ; y1 = 36 ; x2 = 5 ; x1 = 3

Slope = (60 - 36) / (5 - 3) = 24 / 2 = 12

Slope = 12

Unit rate = 12 computers per day

Answer:

The total lateral surface of this cube is 4*e^2

Step-by-step explanation:

A cube is a figure with all the sides of the same length, so each face of a cube is a square.

Remember that the area of a square of sidelength L is:

A = L^2

Now, when we want to find the lateral surface of a figure, we ignore the bases of the figure.

So, if a cube has 6 faces, if we ignore the two bases, we are left with 4 square faces.

And if the edge length is e, then each one of these four faces has an area:

A = e^2

So the total lateral surface is 4 times that:

S = 4*e^2

The total lateral surface of this cube is 4*e^2

Answer:

4e2

Step-by-step explanation:

I got it correct on founders edtell

[tex]\sf\huge\underline\color{pink}{༄Answer:}[/tex]

What is the solution of the equation x^2 - 14x + 67 = 0?

[tex]\color{pink}{==========================}[/tex]

#CarryOnLearning

[tex]\sf\color{pink}{༄⁂✰Bae \: Yoonah}[/tex]

Answer:

0.4060

Step-by-step explanation:

To calculate the sample proportion, phat, we take the ratio of the number of preferred outcome to the total number of trials ;

Phat = number of times coin lands on head (preferred outcome), x / total number of trials (total coin flips), n

x = 406

n = 1000

Phat = x / n = 406/ 1000 = 0.4060

The estimate of the chance that this coin will land on heads is 0.406

If a coin is flipped 1000 times, the total outcomes will 1000

If it landed on the head 406 times, the expected outcome will be 406.

Pr(the coin lands on the head) = 406/1000

Pr(the coin lands on the head) = 0.406

Hence the estimate of the chance that this coin will land on heads is 0.406

Learn more on probability here: https://brainly.com/question/14192140

9514 1404 393

Answer:

  (d)  A = 14.28 in², P = 14.28 in

Step-by-step explanation:

The figure is wholly contained within a 4" square, which has an area of (4 in)² = 16 in², and a perimeter of 4(4 in) = 16 in. Since the figure is smaller in area and has a shorter perimeter (the top corners are rounded, not square), both answer values must be less than 16.

The only reasonable choice is the last choice: 14.28 in², 14.28 in.

__

If you want to figure this out in detail, you have the area of a rectangle that is 2 in by 4 in, and the area of a semicircle of radius 2 in. The total area is ...

  A = LW +1/2πr²

  A = (2 in)(4 in) + 1/2(3.14)(2 in)² = 8 in² +6.28 in²

  A = 14.28 in²

__

The perimeter is half that of a 4" square, plus half that of a 4" circle.

  P = 1/2(4(4 in) +π(4 in)) = (2 in)(4 +π) = 2(7.14) in

  P = 14.28 in

Answer: a

Step-by-step explanation:

If θ lies in the fourth quadrant, then sin(θ) < 0 and cos(θ) > 0. So we have from the Pythagorean identity,

sin²(θ) + cos²(θ) = 1   ==>   cos(θ) = +√(1 - sin²(θ)) = √21/5

Then

sec(θ) = 1/cos(θ) = 5/√21

and

tan(θ) = sin(θ)/cos(θ) = (-2/5)/(√21/5) = -2/√21

Answer:

Pencils = 325 ; Pens = 975 ; Markers = 650

Step-by-step explanation:

Let :

Number of Pencils = x

Number of pens = y

Number of markers = z

2 times as many markers as pencils

z = 2x

3 times as many pens as pencils

y = 3x

x + y + z = 1950

Write z and y in terms of x in the equation :

x + 3x + 2x = 1950

6x = 1950

Divide both sides by 6

6x / 6 = 1950 / 6

x = 325

Number of pencils = 325

Pens = 3 * 325 = 975

Markers = 2 * 325 = 650

Pencils = 325 ; Pens = 975 ; Markers = 650

Answer:

c = 4√2

Step-by-step explanation:

From the question given above, the following data were obtained:

Angle θ = 30

Opposite = 2√2

Hypothenus = c =?

We can obtain the value of c by using the sine ratio as illustrated below:

Sine θ = Opposite / Hypothenus

Sine 30 = 2√2 / c

½ = 2√2 / c

Cross multiply

c = 2 × 2√2

c = 4√2

Therefore, the value of c is 4√2.

Answer:

Y = -x + 2

Step-by-step explanation:

y = -x + 8

y = 1x + b

10 = 8 + b

b = 2

Answer:

y-y1=m(x-x1)

y-10=8(x-8)

y-10=8x-64

y-10+64-8x

y+54-8x

y-8x+54

Answer:

y = 3x

Step-by-step explanation:

abscissa is the x coordinate

ordinate is the y coordinate

y = 3x

Answer:

See explanation

Step-by-step explanation:

Given

See attachment for proper presentation of question

Required

Mean and Range

To do this, we simply calculate the mean and the range of each row.

[tex]\bar x = \frac{\sum x}{n}[/tex] ---- mean

Where:

[tex]n = 4[/tex] ---- number of rows

[tex]R = Highest - Lowest[/tex] --- range

So, we have:

Sample 1

[tex]\bar x_1 = \frac{1027+ 994 +977 +994 }{4}[/tex]

[tex]\bar x_1 = 998[/tex]

[tex]R_1 = 1027- 994[/tex]

[tex]R_1 = 33[/tex]

Sample 2

[tex]\bar x_2 = \frac{975 +1013 +999 +1017}{4}[/tex]

[tex]\bar x_2 = 1001[/tex]

[tex]R_2 = 1017 - 975[/tex]

[tex]R_2 = 42[/tex]

Sample 3

[tex]\bar x_3 = \frac{988 +1016 +974 +997}{4}[/tex]

[tex]\bar x_3 = 993.75[/tex]

[tex]R_3 = 1016-974[/tex]

[tex]R_3 = 42[/tex]

Sample 4

[tex]\bar x_4 = \frac{998 +1024 +1006 +1010}{4}[/tex]

[tex]\bar x_4 = 1009.5[/tex]

[tex]R_4 = 1024 -998[/tex]

[tex]R_4 = 26[/tex]

Sample 5

[tex]\bar x_5 = \frac{990 +1012 +990 +1000}{4}[/tex]

[tex]\bar x_5 = 998[/tex]

[tex]R_5 = 1012 -990[/tex]

[tex]R_5 = 22[/tex]

Sample 6

[tex]\bar x_6= \frac{1016 + 998 +1001 +1030}{4}[/tex]

[tex]\bar x_6= 1011.25[/tex]

[tex]R_6= 1030-998[/tex]

[tex]R_6= 32[/tex]

Sample 7

[tex]\bar x_7 = \frac{1000 +983 +979 +971}{4}[/tex]

[tex]\bar x_7 = 983.25[/tex]

[tex]R_7 = 1000-971[/tex]

[tex]R_7 = 29[/tex]

Sample 8

[tex]\bar x_8 = \frac{973 +982 +975 +1030}{4}[/tex]

[tex]\bar x_8 = 990[/tex]

[tex]R_8 = 1030-973[/tex]

[tex]R_8 = 57[/tex]

Sample 9

[tex]\bar x_9 = \frac{992 +1028 +991 +998}{4}[/tex]

[tex]\bar x_9 = 1002.25[/tex]

[tex]R_9 = 1028 -991[/tex]

[tex]R_9 = 37[/tex]

Sample 10

[tex]\bar x_{10} = \frac{997 +1026 +972 +1021}{4}[/tex]

[tex]\bar x_{10} = 1004[/tex]

[tex]R_{10} = 1026 -972[/tex]

[tex]R_{10} = 54[/tex]

Sample 11

[tex]\bar x_{11} = \frac{990 +1021 +1028 +992}{4}[/tex]

[tex]\bar x_{11} = 1007.75[/tex]

[tex]R_{11} = 1028 -990[/tex]

[tex]R_{11} = 38[/tex]

Sample 12

[tex]\bar x_{12} = \frac{1021 +998 +996 +970}{4}[/tex]

[tex]\bar x_{12} = 996.25[/tex]

[tex]R_{12} = 1021 -970[/tex]

[tex]R_{12} = 51[/tex]

Sample 13

[tex]\bar x_{13} = \frac{1027 +993 +996 +996}{4}[/tex]

[tex]\bar x_{13} = 1003[/tex]

[tex]R_{13} =1027 -993[/tex]

[tex]R_{13} =34[/tex]

Sample 14

[tex]\bar x_{14} = \frac{1022 +981 +1014 +983}{4}[/tex]

[tex]\bar x_{14} = 1000[/tex]

[tex]R_{14} = 1022 -981[/tex]

[tex]R_{14} = 41[/tex]

Sample 15

[tex]\bar x_{15} = \frac{977 +993 +986 +983}{4}[/tex]

[tex]\bar x_{15} = 984.75[/tex]

[tex]R_{15} = 993-977[/tex]

[tex]R_{15} = 16[/tex]

Answer:

$150

Step-by-step explanation:

0.2 X 750 = 150

hope this helps

Answer:

the probability of taking a clear picture of a California candor is .24

Answer:

It is E. radicand

Step-by-step explanation:

Answer:

Radicand

Step-by-step explanation:

Radicand is the number found inside the radicals

Example:

[tex]\sqrt[4]{5} ; 2\sqrt[4]{5}[/tex]  are like terms

5 -> radicand and 4 is the index