Solve for x. Round to the nearest tenth of a degree, if necessary.

The Probability of drawing a card higher than an 8 from a regular 52-card deck is 5/13, or approximately 0.3846 (rounded to four decimal places).

There are a total of 52 cards in a regular deck, with 4 cards of each rank (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King) and 13 cards in each suit (hearts, diamonds, clubs, spades).

To determine the probability of drawing a card higher than an 8, we need to count the number of cards that satisfy this condition and divide it by the total number of cards in the deck.

There are 4 cards of each rank that are higher than an 8: 9, 10, Jack, Queen, King, and Ace. Therefore, there are a total of 5 x 4 = 20 cards that are higher than an 8 in the deck.

So, the probability of drawing a card higher than an 8 is:

P(higher than 8) = number of cards higher than 8 / total number of cards

P(higher than 8) = 20 / 52

Simplifying the fraction by dividing both the numerator and denominator by 4, we get:

P(higher than 8) = 5 / 13

Therefore, the probability of drawing a card higher than an 8 from a regular 52-card deck is 5/13, or approximately 0.3846 (rounded to four decimal places).

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Answer:

±80/289

Step-by-step explanation:

If you want to learn how to calculate 2tanθ/(1 + tan²θ), you need to follow these steps. But be warned, this is not a piece of cake. It's more like a piece of pi.

First, you need to find the value of sinθ by dividing both sides of the equation by 17:

Next, you need to find the value of cosθ by using the Pythagorean identity: sin²θ + cos²θ = 1. You can do this by rearranging the equation and taking the square root of both sides:

Then, you need to find the value of tanθ by using the ratio identity: tanθ = sinθ/cosθ. You can do this by plugging in the values of sinθ and cosθ and simplifying:

Finally, you need to find the value of 2tanθ/(1 + tan²θ) by plugging in the value of tanθ and simplifying:

So, the value of 2tantheta/(1 + tan²theta) is ±80/289. Note that there are two possible values because cosθ and tanθ can be positive or negative depending on the quadrant of θ.

Congratulations! You have just solved a trigonometric equation. You deserve a round of applause. Or maybe just a round pi.

Answer:

A

Step-by-step explanation:

You need to take a ruler and join the points for A and B. I can't do it here.. C and D are not right because they're incorrectly plotted. If A/B join as a straight line for all the points then it's linear. If they don't (and you find it a little curvy) it's a a quadratic. You can cross check as well but imo it's A.

C and D are out of question. Your only options are A and B. And I find the points joining a straight line so my answer would be A

To graph the inequality X < -5 on a number line, we start by drawing a number line and marking a point at -5.

We have,

To graph the inequality X < -5 on a number line, we start by drawing a number line and marking a point at -5.

Since the inequality is strict (X is less than -5), we will draw an open circle at -5 to indicate that -5 is not included in the solution set.

Next, we shade the portion of the number line to the left of -5, since any value of X less than -5 satisfies the inequality.

Note that the open circle at -5 indicates that X cannot be equal to -5, since the inequality is strict.

Any value to the left of -5 on the number line would satisfy the inequality.

Thus,

To graph the inequality X < -5 on a number line, we start by drawing a number line and marking a point at -5.

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Answer:

[tex]x + 2[/tex]

see the below process of the equation:

Step-by-Step Explaination:

Given, f(x)=x+1 and g(x)=x+1

∴g(g(x))=g(x+1)

=(x+1)+1

=x+2

-Thank You By MrIshaan

The area of the triangle is 17 cm square

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

The triangle

Where we have

Base = 5 cm

Height = 6.8 cm

Using the above as a guide, we have the following:

Area = 1/2 * Base * Heigt

Substitute the known values in the above equation, so, we have the following representation

Area = 1/2 * 5 * 6.8

Evaluate

Area = 17 cm square

hence, the area is 17 cm square

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Dakota's statement that his cat weighs 138 ounces is not correct.

To convert 13 pounds 8 ounces to ounces

we can multiply the number of pounds by 16 (since there are 16 ounces in a pound) and add the number of remaining ounces:

13 pounds x 16 ounces per pound = 208 ounces

8 ounces = 8 ounces

Total weight in ounces = 208 + 8 = 216 ounces

Therefore, Dakota's statement that his cat weighs 138 ounces is not correct.

It is significantly less than the actual weight of 216 ounces.

This may indicate that Dakota made a mistake in his calculation or misread the scale when weighing his cat.

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The solution is : 1/4 is the fraction which is equivalent to the shaded area of the rectangle.

Here, we have,

Since the rectangle is divided into 8 equal parts and two parts are shaded, this simply means that 2 out of 8 parts are shaded which is 2/8.

The fraction that's equivalent to the shaded area of the rectangle will be:

2/8 = (2 × 1) / (2 × 4)

      = 1/4

The equivalent fraction is 1/4

Hence, The solution is : 1/4 is the fraction which is equivalent to the shaded area of the rectangle.

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complete question:

A rectangle is divided into 8 equal parts. Two parts are shaded. What fraction is equivalent to the shaded area of the rectangle.

When writing a proof, we construct the first statement by copying the “given” statement(s) from the original problem. Hence, option D is correct.

When writing a proof, the first statement is typically either the "given" statement(s) or a previously proven result. Therefore, option D ("By copying the 'given' statement(s) from the original problem") is often the correct choice for constructing the first statement.

In some cases, option C ("By writing the next logical statement from the current one") may be a more appropriate choice. Regardless of which option is chosen, it is important to clearly justify each statement in the right column of the proof.

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Answer:

x²-x+6

Step-by-step explanation:

Use (f+g)(x) = f(x)+g(x), substitute and simplify

The volume of the square pyramid is 191.25 cm³

The volume of a square pyramid refers to the space enclosed between its five faces. The volume of a square pyramid is one-third of the product of the area of the base and the height of the pyramid. Thus, volume = (1/3) × (Base Area) × (Height).

We can write this mathematically as;

v = a² * (h/3)

v = 1/3 * 7.5² * 10.2

v = 765/4

v = 191.25 cm³

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The value of slope of the secant line is, 6

We have to given that;

The graph of line are shown in figure.

Now, Take two points on the secant line is,

⇒ (0, 0) and (0.1, 0.6)

Hence, The slope of the secant line is,

m = (0.6 - 0) / (0.1 - 0)

m = 0.6 / 0.1

m = 6/1

m = 6

Thus, The value of slope of the secant line is, 6

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The vocabulary term for segment a is called the apothem.

The area of the polygon is 319.8 cm²

To find the area of the polygon, we can use the formula:

Area = (1/2) × Perimeter × Apothem

The perimeter of the polygon can be found by multiplying the number of sides by the length of each side, so:

Perimeter = number of sides × length of each side

Perimeter = 6 × 14 cm (since it's a regular hexagon)

Perimeter = 84 cm

Finding the apothem, use the fact that it forms a right triangle with half of one side length and the apothem as the legs, and the apothem as the hypotenuse. Thus,

a² = s² - (s/2)²

a² = 196 - 49

a² = 147

a = √(147) = 7.65 cm

Now, we can plug in our values into the formula for the area:

Area = (1/2) × Perimeter × Apothem

Area = (1/2) × 84 cm × 7.65 cm

Area = 319.8 cm²

Rounding to the nearest tenth and including the correct units, we get:

Area ≈ 319.8 cm²

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Mean absolute deviation is 2.5.

The mean absolute deviation (MAD) measures how spread out a set of data is by calculating the average distance between each data point and the mean of the data set.

To find the MAD of the given data set {8,4,8,8,10,2,4,4}, we first need to find the mean of the data set.

Mean = (8+4+8+8+10+2+4+4)/8 = 6

Next, we need to find the absolute deviation of each data point from the mean:

|8-6| = 2

|4-6| = 2

|8-6| = 2

|8-6| = 2

|10-6| = 4

|2-6| = 4

|4-6| = 2

|4-6| = 2

To find the MAD, we need to take the mean of the absolute deviations:

MAD = (2+2+2+2+4+4+2+2)/8 = 2.5

Therefore, the mean absolute deviation of the data set {8,4,8,8,10,2,4,4} is 2.5. This means that, on average, the data points in the set are about 2.5 units away from the mean of the set.

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Answer:

A

Step-by-step explanation:

Answer :

Step-by-step explanation:

A.

[tex] \rightarrow \bigg(\dfrac{1}{3} \bigg )\bigg(\dfrac{ - 1}{2} \bigg ) \\ \\ \rightarrow \bigg(\dfrac{ - 1}{6} \bigg )[/tex]

B.

[tex] \rightarrow\bigg(\dfrac{ - 1}{4} \bigg )\bigg(\dfrac{ - 2}{3} \bigg ) \\ \\ \rightarrow\bigg(\dfrac{ 2}{12} \bigg ) \\ \\ \rightarrow \dfrac{1}{6} [/tex]

C.

[tex]\rightarrow\bigg(\dfrac{ - 12}{7} \bigg )\bigg(\dfrac{ - 2}{7} \bigg ) \\ \\ \rightarrow\dfrac{ - 12}{7} \times \dfrac{ - 7 }{2} \\ \\ \rightarrow 6[/tex]

D.

[tex]\rightarrow\bigg(\dfrac{ 12}{7} \bigg )\bigg(\dfrac{ - 2}{ 7} \bigg ) \\ \\ \rightarrow\dfrac{ 12}{ \cancel{7} } \times \dfrac{ \cancel{ 7 }}{ - 2} \\ \\ \rightarrow - 6[/tex]

Hence, Option D is the answer.

Answer:

Step-by-step explanation:

The sample space represents the set or collection of all possible outcomes. It's often written as S = [outcome1, outcome2, outcome3].

For this problem, there are 3 possible outcomes: red pen, blue pen or black pen. (The fact that Denato wants to pull a blue pen is irrelevant when defining the sample space bc we are just listing the possible outcomes.)

So the answer is [red, blue, black].

The value of k from the given trigonometric equation is 1.

Given that, sec²θ(1+sinθ)(1-sinθ)=k

Here, sec²θ(1-sin²θ)=k (∵(a+b)(a-b)=a²-b²)

sec²θ×cos²θ=k  (∵1-sin²θ=cos²θ)

We know that, secθ=1/cosθ

1/cos²θ ×cos²θ=k

k=1

Therefore, the value of k from the given trigonometric equation is 1.

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A wait time of 5 minutes would be considered unusual.

We have,

To find the z-score, we can use the formula:

z = (x - μ) / σ

where x is the value we are interested in, μ is the mean, and σ is the standard deviation.

Plugging in the values, we get:

z = (5 - 8) / 2 = -1.5

Rounding to two decimal places,

we get z = -1.50.

Since the z-score is more than 2 standard deviations below the mean, a wait time of 5 minutes would be considered unusual.

Thus,

A wait time of 5 minutes would be considered unusual.

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The probability that a randomly selected point within the circle would fall in the red- shaded area is 45. 833 %

The arc that is covered by the red - shaded area in the circle has a degree measure of 165 degrees. This is out of the total circle angle measure of 360 degrees.

This therefore means that the probability that a randomly selected point within the circle would fall in the red- shaded area can be found to be :

= Angle measure of red - shaped area / Total area x  100 %

= 165 / 360 x 100 %

=0. 45833 x 100 %

= 45. 833 %

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The measurement closest to the total surface area of the triangular prism is J) 393.6 [tex]in^{2}[/tex] .

To find the surface area of a triangular prism, we need to find the area of all its faces and add them up.

Looking at the net of the triangular prism, we can see that it has two congruent triangles and three rectangular faces.

The area of each triangular face can be found using the formula for the area of a triangle:

Area of a triangle = (1/2) x base x height

In this case, the base of each triangle is 12 inches and the height is 4 inches. So, the area of one triangular face is:

(1/2) x 12 x 4  = 24  [tex]in^{2}[/tex]

The area of each rectangular face can be found using the formula:

Area of a rectangle = length x width

In this case, the length and width of the rectangular faces are:

12 in. x 10.4 in.

12 in. x 12 in.

4 in. x 10.4 in.

So, the area of each rectangular face is:

12  x 10.4 = 124.8  [tex]in^{2}[/tex]

12  x 12  = 144  [tex]in^{2}[/tex]

4  x 10.4  = 41.6  [tex]in^{2}[/tex]

Therefore, the total surface area of the triangular prism is:

2 x 24  + 124.8  + 144  + 41.6  = 393.6 [tex]in^{2}[/tex]

So, the measurement closest to the total surface area of the triangular prism in square inches is J) 393.6  [tex]in^{2}[/tex] .

Correct Question :

The net of a triangular prism and its approximate dimensions are shown in the diagram, 4 in, 12 in, 10.4 in, 12 in, 12 in, 12 in. Which measurement is closest to the total surface area of the triangular prism in square inches?

F) 268.8  [tex]in^{2}[/tex]

G) 432  [tex]in^{2}[/tex]

H) 288  [tex]in^{2}[/tex]

J) 393.6  [tex]in^{2}[/tex]

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The domain of the function y = cos(z) is (-00,00)

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

y = cos(z)

The above equation means that

the variable y is a function of z

Also, we can see that the above function is a cosine function

In a cosine function. the input value can take any real value

This means that y can take any real value

And as such, the domain is the set of all real numbers

This is represented as (-00,00)

Hence, the domain of the function is (-00,00)

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The money loaned at 9% annual interest was 1500 and the money loaned at 11% annual interest was 19000.

Let the amount of money loaned at 9% be x

the amount of money loaned at 11% be y

According to the question,

Total money loaned = 20,500

Thus the equation formed is,

x + y = 20,500 ------ (i)

Simple interest is calculated by

I = P * r * t

where I is the simple interest

r is the rate of interest

t is the time

Thus, the interest on x = 0.09x

the interest on y = 0.11y

Total interest gained = 2,225

Thus the equation formed is,

0.09x + 0.11y = 2225 -------(ii)

Multiply (i) by 0.09

0.09x + 0.09y = 1845

Subtract the above from (ii)

0.02y = 380

y = 19000

x = 1500

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You will have $50,000 in your account after 50 years.

We have,

Simple interest formula is given by:

I = Prt

Where:

I = interest earned

P = principal amount (initial investment)

r = interest rate

t = time (in years)

Here,

P = $10,000

r = 8%

t = 50 years

So, the interest earned after 50 years will be:

I = Prt

= 10000 x 0.08 x 50

= $40,000

The total amount in the account after 50 years will be the initial investment plus the interest earned:

Total amount = $10,000 + $40,000 = $50,000

Therefore,

You will have $50,000 in your account after 50 years.

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Answer: The plane travelled 144 miles in 0.4 hours

Step-by-step explanation:

The plane travels at a speed of 360 miles/hour.

The speed is 360/60=6 miles per minute.

0.4 hours will be 0.4*60=24 minutes. To calculate how much the plane travels in 24 minutes, 24 will be multiplied by 6.

24*6= 144 miles.

Answer: 144

Step-by-step explanation: To solve this problem, we can use the formula:

distance = rate x times

where distance is the entire distance covered, rate denotes the plane's speed, and time denotes the length of the trip.

We can state that the plane is moving at a speed of 360 miles per hour (360 mph) given that it can fly 360 miles in an hour.

We need only enter the following variables into the formula and do a distance calculation to determine how far the plane can travel in 0.4 hours:

distance = rate × time

distance = 360 mph × 0.4 hours

distance = 144 miles

As a result, the aircraft can fly 360 miles per hour for 144 miles in 0.4 hours.

All tables that represent proportional relationship between x and y are:

B. table B.

E. table E.

In Mathematics and Geometry, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) by using various data points as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = (20 - 15)/(10 - 5) = (5 - 4)/(1 - 0)

Constant of proportionality, k = 1.

Therefore, the required linear equation is given by;

y = kx

y = x

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

a) The solution of the system of equations is, x = 30,000

b)  the equilibrium price is, p = 90

c) the equilibrium quantity is, p = 90

Given that;

The price (in S) of a cookbook is determined by the number of cookbooks x demanded by consumers and supplied by the publisher.

Supply: p=0.003.x

Demand: p = -0.007x+300

Hence, We can simplify as;

⇒ 0.003x = - 0.007x + 300

Solve for x;

⇒ 0.003x + 0.007x = 300

⇒ 0.01x = 300

⇒ x = 300/0.01

⇒ x = 30,000

Hence, the equilibrium price is,

p=0.003.x

p=0.003 × 30,000

p= 90

And, the equilibrium quantity is,

p = -0.007x+300

p = -0.007 × 30,000+300

p = - 210 + 300

p = 90

Thus, a) The solution of the system of equations is, x = 30,000

b)  the equilibrium price is, p = 90

c) the equilibrium quantity is, p = 90

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Answer:

B. (1,7)

Step-by-step explanation: