20. What area of the figure below if one square is 1cm x 1cm? a. 6 cm ² b. 8cm ² c. 10 cm². d. 12cm ²
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Answer:

[tex]\tan \theta=-\dfrac{\sqrt{5}}{2}[/tex]

[tex]\cos \theta=\dfrac{2}{3}[/tex]

[tex]\sin \theta=-\dfrac{\sqrt{5}}{3}[/tex]

Step-by-step explanation:

To find the exact values of the trigonometric functions of θ, we can use the following trigonometric identities:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Trigonometric Identities}\\\\$\sec x=\dfrac{1}{\cos x}$\\\\\\$\tan x=\dfrac{\sin x}{\cos x}$\\\\\\$\sin^2x+\cos^2x=1$\\\end{minipage}}[/tex]

In quadrant IV, cosine of the angle is positive, whereas sine of the angle is negative.

Given that sec θ = 3/2, and secant is the reciprocal of cosine:

[tex]\sec \theta=\dfrac{3}{2}[/tex]

[tex]\dfrac{1}{\cos \theta}=\dfrac{3}{2}[/tex]

[tex]\boxed{\cos \theta=\dfrac{2}{3}}[/tex]

To find sin θ, we can substitute the found value of cos θ into the Pythagorean identity:

[tex]\sin^2 \theta+\cos^2 \theta=1[/tex]

[tex]\sin^2 \theta+\left(\dfrac{2}{3}\right)^2=1[/tex]

[tex]\sin^2 \theta=1-\left(\dfrac{2}{3}\right)^2[/tex]

[tex]\sin \theta=\sqrt{1-\left(\dfrac{2}{3}\right)^2}[/tex]

[tex]\sin \theta=\dfrac{\sqrt{5}}{3}[/tex]

As sine of the angle is negative in quadrant IV:

[tex]\boxed{\sin \theta=-\dfrac{\sqrt{5}}{3}}[/tex]

Finally, substitute the values of sin θ and cos θ into the tan θ identity to find tan θ:

[tex]\tan \theta=\dfrac{\sin \theta}{\cos \theta}[/tex]

[tex]\tan \theta=\dfrac{-\frac{\sqrt{5}}{3}}{\frac{2}{3}}[/tex]

[tex]\boxed{\tan \theta=-\dfrac{\sqrt{5}}{2}}[/tex]

Therefore, the exact values of the trigonometric functions for θ are:

[tex]\tan \theta=-\dfrac{\sqrt{5}}{2}[/tex]

[tex]\cos \theta=\dfrac{2}{3}[/tex]

[tex]\sin \theta=-\dfrac{\sqrt{5}}{3}[/tex]

The m∠1 and m∠2 which are linear pairs of angles are 72° and 108°.

We know when a transversal intersects two parallel lines at two distinct points,

Two pairs of interior and alternate angles are formed such that the measure of interior angles are same and the measure of alternate angles is also the same.

We know that the sum of linear pair of angles is equal to 180°.

therefore, From the given information, (x + 36)° + 3x° = 180°.

4x + 36° = 180°.

4x = 144°.

x = 36°.

So, m∠1 = 72° and m∠2 = 108°.

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Answer:

Step-by-step explanation:

I think its A

The   length of the model is 2 feet

The model is  the actual size. This means that for every 6 feet measured on the actual car, the model will span 1 foot.

Note that the model length is in the numerator and the actual length is in the denominator.

Thus, if the car is 12 feet long and L represents the length of the model, then write the ratio as .

Set the two ratios equal to each other to obtain the proportion below.

The length of the model is given as 2 feet

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A line's point slope form equation is y - y1 = m. (x – x1). Consequently, y - 0 = m(x = 0), or y = mx, is the equation of a line passing through the origin with a slope of m.

Finding the slope between two points on a line and then solving for the y-intercept in the slope-intercept equation y=mx+b allow us to build an equation for that line.

The slope of the line passing through these points,

[tex]m=\frac{y2-y1}{x2-x1} \\\\m=\frac{7-9}{0} =infinity[/tex]

infinity slope means y axis.

The equation of line will be x=0.

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The area of the triangle ABC is 6√6 cm².

Triangle ABC is depicted in the given diagram, where AB = 7 cm, BC = 6 cm, and AC = 5 cm.

Heron's formula, which claims that the area is provided by: for a triangle with sides of lengths a, b, and c, can be used to determine the triangle's area.

(s(s-a)(s-b)(s-c)) = area

where s is the triangle's semi perimeter and is determined by:

s = (a + b + c)/2

Here are the facts:

7 cm for a and 6 cm for b.

c = 5 cm

The semi perimeter is as follows:

s = (7 + 6 + 5)/2 = 9

When we apply Heron's formula, we get:

Area = √(9(9-7)(9-6)(9-5)) = √(9 × 2 × 3 × 4) = √216

When we reduce the square root, we obtain:

= 6√6 cm²

As a result, the triangle ABC has a 6√6 cm² area.

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Answer:

  T〈-7,0〉

Step-by-step explanation:

You want a description of the transformation of triangle ABC to triangle A"B"C".

∆A"B"C" has the same orientation as ∆ABC, so no reflection is involved (eliminates choice B).

Point A" is 7 units to the left of point A, so the translation is 7 units left (and no units up or down).

The transformation is ...

  [tex]\boxed{T_{\langle-7,0\rangle}}[/tex]

The two values of y such that the barn is 50 yards from the well

The length of line in an ordered pair is calculated using the formula

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

where

d = distance between the points

x₂ and x₁ = points in x coordinates

y₂ and y₁ = points in y coordinates

distance between points  (-1, 1) and (-1,, y) is calculated to be 50 yards and hence we solve for y

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

50 =√{(-1 - -1)² + (1 - y)²}

50 =√{ (1 - y)²}

2500 = (1 - y) (1 - y)

2500 = 1 - 2y + y²

y² - 2y - 2499 = 0

solving the quadratic equation gives

y = 51 OR -49

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The simplification of the given estimate above would be = 3 21/40

To simply a mixed fraction, the mixed fraction should be converted to a single fraction. That is;

3⅝ = 29/8

Use the newly converted fraction to solve:

= 29/8 -1/10

Fine the Lowest common denominator = 49

= 145-4/40

= 141/40

= 3 21/40 ( convert to a mixed fraction)

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It is given that 2/5 of all patients admitted to ward 17.

Remining fraction is:

So 3/5 of patients admitted to ward 18.

Since 1/6 of all patients moved to another ward, and the reminder assigned as before, the initial fraction becomes:

Now, 3/5 of the new fraction, 5/6 is admitted to ward 18.

That is:

This is half of the patients.

The difference of the number of the patients admitted to ward 17 is the same fraction of the number of infected:

So the difference of patients is 4.

The expression when evaluated is 46552

From the question, we have the following parameters that can be used in our computation:

5,819 x 8.

Using the standard algorithm, we have:

5,819 x 8 = (5800 + 19) * 8

Open the brackets

So, we have the following representation

5,819 x 8 = 5800* 8 + 19 * 8

Evaluate

5,819 x 8 = 46400 + 152

So, we have

5,819 x 8 = 46552

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Answer:

Length = 10cm, Width = 9 cm

Step-by-step explanation:

Let's call the amount that both the length and width are increased by "x". So, the new length is 5 + x and the new width is 4 + x.

The original area of the rectangle was 5 * 4 = 20 cm2.

The new area of the rectangle after the increase is (5 + x) * (4 + x) = 20 + 70 + 2x^2.

Expanding the right-hand side, we have 20 + 70 + 2x^2 = 90 + 2x^2.

Equating the two areas, we get:

20 + 70 + 2x^2 = 90 + 2x^2

Subtracting 2x^2 from both sides:

20 + 70 = 90

Subtracting 20 from both sides:

70 = 70

So x^2 = 50 / 2 = 25.

Taking the square root of both sides, we get:

x = 5

So the length of the longer rectangle is 5 + x = 5 + 5 = 10 cm, and the width is 4 + x = 4 + 5 = 9 cm.

Answer:

102

Step-by-step explanation:

Answer:100 or it just means 10 times

Step-by-step explanation: you need to learn the angles when the number are put on each side and then your answer will come!

They reach their location at 9:24 the next morning.

The relative speed is the net speed of two different objects with respect to each other.

If two objects move in the same direction we take the difference between their speeds.

If two objects move in the opposite direction we take the sum of their speeds.

We can utilize the following parameters in our calculation based on the question,

Time = 4 pm

Distance = 64 km

Calculate how long it took the father to ride his horse and the son to walk the first 32 miles.

Time = Distance / (Difference between rates of father and son)

Time = 32 km / (8 km/h - 3 km/h)

Time = 32 km / 5 km/h

Time = 6.4 hours

Determine how long it will take the father to walk the final 32 miles and the son to ride the horse.

Time = Distance / (Difference in Speed)

Time = 32 km / (8 km/h - 4 km/h)

Time = 32 km / 4 km/h

Time = 8 hours

Therefore,

Total time = 6.4 hours + 8 hours + 3 hours break + 4 pm is 9:24 am the next day.

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Answer:

Part A: What percentage of the survey respondents do not like both hamburgers and burritos? (2 points)

25.6%. 54 out of 205 respondents do not like both hamburgers and burritos. 54/205 = 0.256 or 25.6%.

Part B: What is the marginal relative frequency of all customers that like hamburgers? (3 points)

50.2%. 110 out of 205 respondents like hamburgers. 110/205 = 0.502 or 50.2%.

Part C: Use the conditional relative frequencies to determine which data point has strongest association of its two factors. Use complete sentences to explain your answer. (5 points)

The data point with the strongest association between its two factors is that 29 out of 110 respondents who like hamburgers also like burritos. This is a conditional relative frequency of 26.4%, which is higher than any other combination of the two factors. This suggests that the respondents who like hamburgers are more likely to also like burritos than any other combination of the two factors.

Step-by-step explanation:

Answer: he will need an area of 6*4 fencing

Step-by-step explanation: if 6+4 is 10 times that by 2 and you have 20

I hope this helped

Answer: 1. 27/72 = 3/8,  2. 24/40 = 3/5,  3. 6/42 = 1/7

Step-by-step explanation:

1. 27/72 divided by 9/9 equals 3/8.

2. 24/40 divided by 8/8 equals 3/5.

3. 6/42 divided by 6/6 equals 1/7.

Answer:

D

Step-by-step explanation:

So the ratio is 8:6 right now and they want to sell 10 each. I can tell you now it's gonna change because neither 6 nor 8 goes into 10 evenly. Now to find out what it'll be

So currently, you found out Terrence has 36 and Jim has 48

So each is going to sell 10. That means...

Jim will have 38 and Terrence will have 26

[tex] \frac{38}{26} [/tex]

Now we'll just simplify until we can't anymore

[tex] \frac{38}{26} = \frac{19}{1 3} [/tex]

19 and 13 are prime numbers... that's the most I can go

Answer:

start by using the formula for the area of a rectangle:

Area = length × width

We know that the area of the farm is given as square miles, so we can write:

lw =

Solving for w, we can divide both sides by l:

w =

Therefore, the width of the rectangular farm is miles.

To simplify the expression, we can multiply the numerator and denominator by 2:

w =

So the width can also be expressed as the fraction __.

4.1.1 and 4.1.3 are discrete variables and 4.1.2 is a continuous variable.

What are discrete and continuous variables?

Discrete variables are those that have distinct, countable values. A continuous variable can be assigned to any value that falls inside a range, which has an infinite number of possible values.

4.1.1 "I am fifty years old"

It is a discrete variable because age is represented in whole numbers.

4.1.2 "I can drink 400.5 ml of juice in a minute"

It is a continuous variable because the amount of juice is consumed every minute so, we can obtain values even in fraction.

4.1.3 "I have 2 brothers and 1 sister"

It is a discrete variable because the given value is countable.

Hence, 4.1.1 and 4.1.3 are discrete variables and 4.1.2 is a continuous variable.

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The amount of water a tank can hold is 17155.86 cubuic ft.

Every three-dimensional object occupies some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

Finding an object's volume can help us calculate the quantity needed to fill it, such as the volume of water needed to fill a bottle, aquarium, or water tank.

Now in the given quetion, it is stated that ,

The amount of water that a spherical tank can hold varies directly as the cube of its radius.

Therefore,

[tex]V_1\alpha R^3\\\\\\V_1= aR^3\\\\a=\frac{1767}{7.5^3}[/tex]

Now , for the tank with radius 16 ft.

[tex]V_2\alpha R^3\\\\\\V_2= aR^3\\\\V_2=\frac{1767}{7.5^3}*16^3\\\\V_2=17155.86 ft^3[/tex]

Hence, the amount of water a tank can hold is 17155.86 cubuic ft.

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Answer:

The polygons are similar.

Step-by-step explanation:

The polygons are similar due to the SAS Similarity Theorem.

Hope this helped! :)

Answer:

[tex]x=42; \ y=14\sqrt{5}.[/tex]

Step-by-step explanation:

1. if the angles of the given triangle are 30-60-90°, then

2. y=0.5*28√5=14√5;

[tex]3. \ x=28\sqrt{5}*sin(60)=28\sqrt{3}*\frac{\sqrt{3} }{2}=42.[/tex]

4. finally, x=42; y=14√5.

Answer: The probability that a customer wins a prize 8.3%

Step-by-step explanation:

First off, the dice has twelve sides and only of the sides, 9, will allow a customer to win.

this means that there is a 1/12 chance that the customer will win a prize.

We can rewrite this into a decimal: 0.0833

and then to a percentage rounded to the nearest tenth: 8.3%

The probability that a customer wins a prize is 8.3% to the nearest tenth.

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Given that,

A clothing store has each customer roll a 12-sided die with faces numbered 1−12 to win a free T-shirt.

Customers who roll a 9 win.

Total possible outcomes = 12

Number of outcomes which results in a win = 1

Probability that a customer wins = 1/12

                                                       = 0.08333

                                                       = 8.3%

Hence the required probability is 8.3%.

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Answer:

okay have a nice day haha

Answer: E

Step-by-step explanation: Since this is a special right triangle(45,45,90), you know that the ratios of the leg to the hypotenuse is 1:1:sqrt2. 15 sort root two hold true to that rule and is the right answer.

Answer: Vegetable consumption per month is 17.33 pounds and fruits consumption per month is 10.47 pounds.

Step-by-step explanation:

Leonard gave the correct value of approximate average rate of change of function.

What is a function?

In mathematics, a function is an expression, rule, or law that specifies the relationship between an independent variable x and a dependent variable y.

The average rate of change of  function means the typical rate at which one quantity is changing in respect to another. A method that determines the amount of change in one item divided by the corresponding amount of change in another is known as an average rate of change function.

The formula for average rate of change of  function in the interval [a,b] is

[tex]\frac{f(b) - f(a)}{b-a}[/tex].

We are asked to find the rate of change when x = -3 to 6

From graph

when x = -3 , y = -2

when x = 6, y = 2

So average rate of change of function = [tex]\frac{f(6) - f(-3)}{6-(-3)} = \frac{2 - (-2)}{9} = \frac{4}{9}[/tex]

Therefore Leonard gave the correct value of approximate average rate of change of function.

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[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 140000\\ P=\textit{initial amount}\dotfill &16000\\ r=rate\to 67.2\%\to \frac{67.2}{100}\dotfill &0.672\\ t=years\\ \end{cases}[/tex]

[tex]140000 = 16000(1 + 0.672)^{t} \implies \cfrac{140000}{16000}=1.0672^t\implies \cfrac{35}{4}=1.0672^t \\\\\\ \log\left( \cfrac{35}{4} \right)=\log(1.0672^t)\implies \log\left( \cfrac{35}{4} \right)=t\log(1.0672) \\\\\\ \cfrac{\log\left( \frac{35}{4} \right)}{\log(1.0672)}=t\implies 33.35\approx t\qquad \textit{about 33 years and 128 days}[/tex]