Solve the following 28% of 300

Answer:

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

Taking the inverse tangent (arctan) of the given ratio 7/9.

Use a calculator or trigonometric table to find:

The approximate value of θ is 37.9°.

Answer:

8[tex]\sqrt[3]{2}[/tex]

Step-by-step explanation:

The cube root of -2 to the power of 10 is;

(-2)^10=2^10

2^10=(2^3)*(2^3)*(2^3)*2

You can factor out 2^3=8 of the cube root

So you get 8 times the cube root of 2

12/13 is the value of cosA is  in the triangle ABC

ABC is a right angle triangle

Angle B has a angle of 90 degrees

We know that the cosine function is a ratio of adjacent side and hypotenuse

The adjacent side of angle A is AB which we have to find

hypotenuse is 26

Cos A =AB/26

Let us find AB by using pythagoras theorem

10²+AB²=26²

100+AB²=676

Subtract 100 from both sides

AB²=576

Take square root on both sides

AB=√576

=24

Now plug in this value in cosA

CosA = 24/26

=12/13

Hence, the value of cosA is 12/13 in the triangle ABC

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Answer:

                                                                      250

                                                                     /       \

                                                   126            124

                                                           \        /     \

                 102                      24                87       57

                /     \                 /     \       /     \

             100     6          22     2          40     17

            /     /   \       /     /   \       /     /   \

         95     0     5      22     0      20     0      37

The frequency tree shows that 126 people arrived late, and 102 of them travelled by train. This means that 24 people arrived late and travelled by bus. There were a total of 250 people who attended the conference, so 124 people arrived on time. Of the people who arrived on time, 87 travelled by bus and 57 travelled by train.

Answer:

Step-by-step explanation:

Answer:

906.89 in²

Step-by-step explanation:

A regular dodecagon is a specific type of 12-sided polygon where all sides and angles are equal.

The formula for the area of a regular polygon is:

[tex]\boxed{\begin{minipage}{6cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{n\cdot s\cdot a}{2}$\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the length of one side.\\ \phantom{ww}$\bullet$ $a$ is the apothem.\\\end{minipage}}[/tex]

We know that the number of sides is 12 and that the length of one side is 9 inches, so in order to calculate the area, we first need to find the apothem.

The formula for the apothem of a regular polygon is:

[tex]\boxed{\begin{minipage}{6cm}\underline{Length of apothem}\\\\$a=\dfrac{s}{2 \tan\left(\frac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $a$ is the apothem.\\ \phantom{ww}$\bullet$ $s$ is the length of one side.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}[/tex]

Substitute s = 9 and n = 12 into the apothem formula, and solve for a:

[tex]a=\dfrac{9}{2 \tan\left(\frac{180^{\circ}}{12}\right)}[/tex]

[tex]a=\dfrac{9}{2 \tan\left(15^{\circ}\right)}[/tex]

[tex]a=\dfrac{9}{2 \left(2-\sqrt{3}\right)}[/tex]

[tex]a=\dfrac{9}{4-2\sqrt{3}}[/tex]

[tex]a=\dfrac{9}{4-2\sqrt{3}}\cdot \dfrac{4+2\sqrt{3}}{4+2\sqrt{3}}[/tex]

[tex]a=\dfrac{36+18\sqrt{3}}{4}[/tex]

[tex]a=\dfrac{18+9\sqrt{3}}{2}[/tex]

Now we have calculated the apothem, substitute this along with n = 12 and s = 9 into the area of a polygon formula

[tex]A=\dfrac{n \cdot s \cdot a}{2}[/tex]

[tex]A=\dfrac{12 \cdot 9 \cdot \frac{18+9\sqrt{3}}{2}}{2}[/tex]

[tex]A=\dfrac{108 \cdot \frac{18+9\sqrt{3}}{2}}{2}[/tex]

[tex]A=54 \cdot \dfrac{18+9\sqrt{3}}{2}}[/tex]

[tex]A=27\cdot (18+9\sqrt{3}})[/tex]

[tex]A=486+243\sqrt{3}[/tex]

[tex]A=906.89\; \sf in^2\;(nearest\;hundredth)[/tex]

Therefore, the area of a regular dodecagon with a side length of 9 inches is 906.89 in² (nearest hundredth).

Note: Please see the attached image for confirmation of the area using a graphic calculator.

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \pounds 2496\\ P=\textit{original amount deposited}\dotfill & \pounds1600\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years \end{cases} \\\\\\ 2496 = 1600[1+(0.08)(t)]\implies \cfrac{2496}{1600}=1+0.08t\implies \cfrac{39}{25}=1+0.08t \\\\\\ \cfrac{39}{25}-1=0.08t \implies \cfrac{14}{25}=0.08t\implies \cfrac{14}{25(0.08)}=t\implies 7=t[/tex]

Answer: C

Step-by-step explanation:

For box and whiskers plot the box is where the majority of the data is.  the whiskers(the lines on both sides will tell you where the range of numbers lie)

The middle line in the box is the median number.

The question is worded oddly where they want least likely to be more than 30 which means which one will have less than 30. (Double negative question)

You want the majority of the data to be less than 30, which is subway.  C

The correct answer is $28,100.

To calculate the difference between the costs of the accident and the premiums paid by the car owner, let's break down the expenses step by step:

(1) Annual Premium: The car owner pays an annual premium of $780 for automobile insurance. Over five years, the total premium paid is $780 * 5 = $3,900.

(2) Liability Coverage: The liability coverage provided by the insurance is up to $100,000. However, the other driver is claiming $32,000 in damages. Therefore, the insurance will cover the full amount of $32,000.

(3) Difference in Costs: To find the difference between the costs of the accident and the premiums paid, we subtract the insurance coverage from the total premium paid. In this case, the difference is $32,000 - $3,900 = $28,100.

Therefore, the costs of the accident were $28,100 more expensive than what the car owner paid in premiums.

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The vector shown in component form is (-4, -3)

We have to find the vector which is shown in the component form

To find this vector we have to find the difference of tail and head

Tail has coordinates (1, 2)

Head has coordinates (-3, -1)

We have to subtract  (-3, -1) from (1, 2)

(-3, -1)-(1,2)

We have to do this by subtracting x coordinates and y coordinates

(-3-1, -1-2)

(-4, -3)

Hence, (-4, -3) is the vector shown in component form

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To estimate the total distance traveled by the car in those 36 seconds, we can use the trapezium rule to approximate the area under the curve.

From the graph, we can see that the car's speed is constant between 0 and 30 seconds, and then it starts to decrease. Therefore, we can use a single trapezium to estimate the area under the curve for the first part.

The base of the trapezium is 30 seconds, and the height is the average of the speeds at 0 and 30 seconds. Let's denote the speed at 0 seconds as v0 and the speed at 30 seconds as v30.

The distance traveled in the first part can be estimated as:

Distance = 30 * (v0 + v30) / 2

To get a more accurate estimate, we need the specific values of v0 and v30 from the graph. Please provide the corresponding speed values for 0 and 30 seconds, and I can help you calculate the estimated distance.

Answer: 7.8

Step-by-step explanation: Identify the triangle as a 45-45-90 triangle.

Recognize that the sides of a 45-45-90 triangle are in a ratio of 1:1:√2.

Find the length of the hypotenuse of the triangle. In this case, the hypotenuse is 11 units.

Divide the length of the hypotenuse by √2 to find the length of the side opposite the 45-degree angle. In this case, the length of side x is 11/√2 = 7.77 units.

Round the length of side x to the nearest tenth. In this case, the length of side x is 7.8 units.

Answer:

= 10.4

Step-by-step explanation:

Here given is the right-angled triangle

For angle: = 60º

Perpendicular: = 9

Hypotenuse: =

Now using the trigonometry formula:

  = /

sin 60º = 9/

3√2 = 9/

= 18/3√

= 10.4(rounded to the nearest tenth)

Therefore required length is = 10.4

Answer:

0.0772 OR 0.95 OR 7.72

Step-by-step explanation:

A player makes 622 shots on goal and in that time scores 48 goals.

48 goals ÷ 622 shots = 0.0772.

This player’s shooting percentage is 0.0772, or 7.72%.

(a) The joint probability distribution of X and Y is 3/70.

(b) The value of P[(X,Y) € A), where A is the region that is given is 3/35.

(a) To find the probabilities, we consider the total number of ways to select 4 fruits out of 8:

Total number of ways to select 4 fruits out of 8 = C(8, 4) = 70

The probabilities for each combination of X and Y are as follows:

P(X = 0, Y = 0) = C(3, 0) * C(2, 0) * C(3, 4) / 70

P(X = 0, Y = 0) = 1 / 70

P(X = 0, Y = 1) = C(3, 0) * C(2, 1) * C(3, 3) / 70

P(X = 0, Y = 1)  = 2 / 70

P(X = 1, Y = 0) = C(3, 1) * C(2, 0) * C(3, 3) / 70

P(X = 1, Y = 0) = 3 / 70

P(X = 1, Y = 1) = C(3, 1) * C(2, 1) * C(3, 2) / 70

P(X = 1, Y = 1) = 18 / 70

P(X = 2, Y = 0) = C(3, 2) * C(2, 0) * C(3, 2) / 70

P(X = 2, Y = 0) = 9 / 70

P(X = 2, Y = 1) = C(3, 2) * C(2, 1) * C(3, 1) / 70

P(X = 2, Y = 1) = 18 / 70

P(X = 3, Y = 0) = C(3, 3) * C(2, 0) * C(3, 1) / 70

P(X = 3, Y = 0) = 3 / 70

The joint probability distribution of X and Y is as follows:

X\Y  0   1

0 1/70  2/70

1 3/70 18/70

2 9/70 18/70

3 3/70 0

(b) P[(X,Y) ∈ A], where A is given by ((a + v) | a + y < 2):

From the joint probability distribution table, we can see that the combinations (0, 0), (0, 1), and (1, 0) satisfy this condition.

P[(X, Y) ∈ A] = P[(0, 0)] + P[(0, 1)] + P[(1, 0)] = 1/70 + 2/70 + 3/70

P[(X, Y) ∈ A] = 6/70 or 3/35

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Answer:

True, True, False

Step-by-step explanation:

1. 8 ≥ 5-1 Is correct

2. 8 ≥ 5-4 is correct

3. 8 ≥ 5-(-4) is not correct

Answer:

x = 1 makes the inequality true

x = 4 makes the inequality true

x = -4 makes the inequality false

Step-by-step explanation:

We can determine whether x = 1, x = 4, and x = -4 makes the inequality by plugging in 1, 4, and -4 for x and seeing whether the inequality still holds true:

Step 1:  Plugging in 1 for x:

8 ≥ 5 - 1

8 ≥ 4

Because 8 is greater than 4, x = 1 makes the inequality true.

Step 2:  Plugging in 4 for x:

8 ≥ 5 - 4

8 ≥ 1

Because 8 is also greater than 4, x = 4 also makes the inequality true.

Step 3:  Plugging in -4 for x:

8 ≥ 5 - (-4)

8 ≥ 5 + 4

8 ≥ 9

Because 8 is not less than 9, x = -4 makes the inequality false

The given numerical data should be ordered from least to greatest as follows;

-11, -9, -8, -7, -2, 4, 5, 6, |-11|.

In Mathematics, a rational number can be defined a type of number which comprises fractions, integers, terminating or repeating decimals.

In Mathematics, an integer can be defined as a whole number that may either be positive, negative, or zero (0). This ultimately implies that, a positive integer simply refers to a whole number that is greater than or equal to one (1).

Next, we would order or sort the given numerical data from least to greatest as follows;

-11, -9, -8, -7, -2, 4, 5, 6, |-11|.

Note: |-11| is an absolute value that equals to 11.

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Answer:  it would take the cyclist 8.5 hours to travel 153 miles.

Step-by-step explanation: We can use proportions to solve this problem.

Let's define:

x = the time it would take for the cyclist to travel 153 miles.

Using proportions, we can set up the following equation:

45 miles / 2.5 hours = 153 miles / x

We can then cross-multiply and solve for x:

45 * x = 2.5 * 153

45x = 382.5

x = 382.5 / 45

x = 8.5

The coordinates of the focus obtained from the vertex form of the equation of the parabola is; (h, v) = (2, -7/4)

The vertex form of the equation of a parabola is; y = a·(x - h)² + k

The points on the parabola are;

(3, -1), and (2, -2)

The vertex of the parabola is; (2, -2)

Therefore, we get;

The vertex form of the equation of a parabola is; y = a·(x - h)² + k

Where;

(h, k) = The coordinates of the vertex, therefore;

y = a·(x - 2)² - 2

y + 2 = a·(x - 2)²

The point (3, -1), indicates that we get;

-1 + 2 = a·(3 - 2)²

(-1 + 2)/((3 - 2)²) = 1 = a

The equation of the parabola in focus form is; (x - h)² = 4·p·(y - k)

Therefore; (x - 2)² = 4·p·(y + k)

We get; (x - 2)² = (y + k)

(x - 2)²/(4·p) = y + k

(4·p) = a = 1

p = 1/4

The y-coordinates of the focus, v = -2 + 1/4 = -1 3/4 = -7/4

The coordinates of the focus, (h, v) is therefore;

(h, v) = (2, -7/4)

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Answer: To find the area of the region between the graph of y = x^2 + 1 and the x-axis on the interval [2, 4], we can integrate the function f(x) = x^2 + 1 with respect to x over the given interval. The definite integral represents the area under the curve between the specified x-values. Here's how to calculate it using integration:

∫[2,4] (x^2 + 1) dx

To integrate this function, we apply the power rule for integration. The power rule states that the integral of x^n with respect to x is (x^(n+1))/(n+1), where n is any real number except -1.

∫(x^2 + 1) dx = [(x^3)/3 + x] + C

Now, we can evaluate the definite integral over the interval [2, 4]:

[(4^3)/3 + 4] - [(2^3)/3 + 2]

= (64/3 + 4) - (8/3 + 2)

= (64/3 + 12/3) - (8/3 + 6/3)

= (76/3) - (14/3)

= 62/3

Therefore, the area of the region between the graph of y = x^2 + 1 and the x-axis on the interval [2, 4] is 62/3 square units.

Step-by-step explanation:

Answer:

Step-by-step explanation:

x=6/5,−4

Decimal Form:

x=1.2,−4

Mixed Number Form:

x=1  1/5,−4

Answer:

Since 1 fluid ounce is equal to 0.03125 quarts, we can convert the volume of water poured into the jar from ounces to quarts:

114 ounces x 0.03125 quarts/ounce = 3.5625 quarts

Therefore, Kenna pours 3 x 3.5625 = 10.6875 quarts of water to fill the jar three times. Rounding to the nearest whole number, we get 11 quarts.

So it takes 11 quarts of water to fill the jar.

The z-score corresponding to a sample mean capacity for 20 tanks of 8550 is 2.238.

To find the z-score corresponding to a sample mean capacity for 20 tanks of 8550, we need to use the formula for the z-score:

z = (x - μ) / (σ / √n)

Where:

x = sample mean capacity

μ = population mean capacity

σ = population standard deviation

n = sample size

Given:

x = 8550, μ = 8544, σ = 12 and n = 20

Substituting these values into the formula:

z = (8550 - 8544) / (12 / √20)

z = 6 / (12 / √20)

z = 6 / (12 / 4.472)

z = 6 / 2.683

z = 2.238

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Answer:

[tex]slope_{UF}[/tex] = - [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

calculate slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = U (3, - 5 ) and ( x₂, y₂ ) = F (- 1, - 4 )

m = [tex]\frac{-4-(-5)}{-1-3}[/tex] = [tex]\frac{-4+5}{-4}[/tex] = [tex]\frac{1}{-4}[/tex] = - [tex]\frac{1}{4}[/tex]

Hello !

1. A quadratic equation results in the form: ax² + bx + c

2. Calculate the discriminant: Δ = b² - 4ac

3. Calculate x with the dicriminant: (-b ± √Δ) / 2a

Example:

3x² + 7x - 2 = 0 is a quadratic equation.

x = (-b ± √(b² - 4ac)) / 2a

= (-7 ± √(7² - 4*3*(-2))) / (2*3)

= (-7 ± √73)/6

Answer:

First find the sales tax: $160 \times 0.0785 = $12.56.

Then add the sales tax to the price of the purchase to find the total cost: $160 + $12.56 = $172.56.

Next find the daily interest rate: $0.042\% = 0.00042$.

Then multiply the daily interest rate by the total cost to find the interest per day: $0.00042 \times $172.56 = $0.0725752$.

Finally, multiply the interest per day by 30 days to find the total interest and add it to the total cost to find the final answer: $0.0725752 \times 30 = $2.177256 + $172.56 = $174.737256 \approx $174.74.

So the answer is b.

Based on the information provided, we have an angle labeled as (4x-10)° and another angle labeled as K. It seems like we need to determine the relationship between these angles and find the value of x.

To determine the relationship between the angles, we need more context or information about the specific geometric configuration or properties mentioned in the task card. Without additional information, it is not possible to determine the relationship between (4x-10)° and K.

If you can provide further details or a description of the geometric setup or any additional instructions related to the angle relationship, I'll be glad to help you further.

The total area covered by the roll of wrapping paper is 3.6 square meters.

To calculate the total area covered by the wrapping paper, we need to find the surface area of each cube and then multiply it by the number of cubes.

The formula for the surface area of a cube is:

Surface Area = 6 * (side length)^2

Given that the length of each side of the cube is 20 cm (which is equal to 0.2 meters), we can substitute this value into the formula:

Surface Area = 6 * (0.2)^2

Surface Area = 6 * 0.04

Surface Area = 0.24 square meters

Now, we know that 15 cubes can be covered by the roll of wrapping paper. Therefore, the total area covered by the wrapping paper is:

Total Area = Surface Area * Number of Cubes

Total Area = 0.24 * 15

Total Area = 3.6 square meters

Therefore, the total area covered by the roll of wrapping paper is 3.6 square meters.

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To find the subtracted value, we need to calculate the multiplicative inverse of (4/3 - 4/9) and then subtract it from the sum of 7/12 and 7/8.

First, let's find the multiplicative inverse of (4/3 - 4/9):

Multiplicative inverse = 1 / (4/3 - 4/9)

To simplify the expression, we need a common denominator:

Multiplicative inverse = 1 / ((12/9) - (4/9))

= 1 / (8/9)

= 9/8

Now, we need to subtract the multiplicative inverse from the sum of 7/12 and 7/8:

Subtracted value = (7/12 + 7/8) - (9/8)

To perform this calculation, we need a common denominator:

Subtracted value = (7/12 * 2/2 + 7/8 * 3/3) - (9/8)

= (14/24 + 21/24) - (9/8)

= 35/24 - 9/8

To simplify further, we need a common denominator:

Subtracted value = (35/24 * 1/1) - (9/8 * 3/3)

= 35/24 - 27/24

= 8/24

= 1/3

Therefore, subtracting 1/3 from the sum of 7/12 and 7/8 will give you the multiplicative inverse of (4/3 - 4/9).

Answer:

[tex]\frac{6}{x+1}[/tex]

Step-by-step explanation:

I learned this like a month ago so I have notes abt it if you don't understand how it works. Just lmk if you need them

Step by Step Solution/ just copy and paste but if this is a test, the answer is 2.000

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    2*y-(4*x-5)=0

STEP

1

:Equation of a Straight Line

1.1     Solve   2y-4x+5  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  2y-4x+5  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is -5/2 so this line "cuts" the y axis at y=-2.50000

 y-intercept = -5/2  = -2.50000

Calculate the X-Intercept :

When y = 0 the value of x is 5/4 Our line therefore "cuts" the x axis at x= 1.25000

 x-intercept = 5/4  =  1.25000

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -2.500 and for x=2.000, the value of y is 1.500. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 1.500 - (-2.500) = 4.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     =  4.000/2.000 =  2.000

Geometric figure: Straight Line

 Slope = 4.000/2.000 = 2.000

 x-intercept = 5/4 = 1.25000

 y-intercept = -5/2 = -2.50000