Please help me answer this question:

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Given:

The figure of a circle.

The measure of arc SR = 75 degrees.

Measure of angle RSQ = 95 degrees.

To find:

The measure of SQ.

Solution:

Let us consider, O be the center of the circle.

According to the central angle theorem, the measure central angle on an arc is twice of inscribed angle on the corresponding angle.

Using the central angle theorem, we get

\(m\angle QOR=2\times m\angle RSQ\)

\(m\angle QOR=2\times (95^\circ)\)

\(m\angle QOR=190^\circ\)

It is the central angle on major arc QR.

We know that the measure of complete central angle is 360 degrees.

The central angle on minor arc QR is:

\(360^\circ -190^\circ =170^\circ\)

It means the measure of arc RSQ is 170 degrees.

\(m(arc RS)+m(arc SQ)=m(arcRSQ)\)

\(75^\circ+m(arc SQ)=170^\circ\)

\(m(arc SQ)=170^\circ -75^\circ\)

\(m(arc SQ)=95^\circ\)

Therefore, the measure of arc SQ is 95 degrees.

Answer:162

Step-by-step explanation:

162

Answer:

The warranty the company should use is of 57,520 mile.

Step-by-step explanation:

Let X denote the tread life of a particular brand of tire.

It is provided that,  \(X\sim N(60,000, 1600^{2})\).

Also provided that the company wants 94% of the tires to outlast the warranty.

Let x denote the warranty .

That is, P (X > x) = 0.94.

⇒ P (X < x) = 0.06

⇒ P (Z < z) = 0.06

The corresponding value of z is -1.55.

*Use a z-table.

Compute the value of x as follows:

\(z=\frac{X-\mu}{\sigma}\\\\-1.55=\frac{x-60000}{1600}\\\\x=60000-(1.55\times 1600)\\\\x=57520\)

Thus, the warranty the company should use is of 57,520 mile.

Answer:

hdvbn

Step-by-step explanation:

nfshvjjnmmnjjmbm

Answer:

D) p > -2

Step-by-step explanation:

5 + p > 3

5 + p - 5 > 3 - 5

p > -2

Answer:

6/11

Step-by-step explanation:

Fraction that are girls

girls/ total

6/11

Answer:

6/11

Step-by-step explanation:

5+6=11 girls =6 so 6/11

The required amount invested in accounts with 8% and 12% are $1470 and $1820 respectively.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Lydia has money in two savings accounts one rate is 8% and the other is 12%  and the total interest is $336. Let the amount invest in accounts be x and y respectively.
According to the question,
0.08x + 0.12y = 336 - - - - - -(1)

Again,
she has $350 more in 12% account
y = x + 350 - - - - - -(2)

Put y in equation 1,
0.08x + 0.12[x + 350] =336
0.08x + 0.12x + 42 = 336
0.20x = 336 - 42
x = 294/0.20
x = $1470

Now

y = 1470 + 350
y = $1820

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Answer:

The function is increasing during the interval 0 < x < 5.

Step-by-step explanation:

“The domain on which the function is increasing” is just a fancy way of saying, over what X values is the f(x), or y, of the function increasing! When looking at a graph, whenever the function line is going up, that is when the function is increasing. All you need to to is find the X values over this time. Then, just format them in the [lowest x] < x < [highest x] format.

With this function, we can see that the f(x), or y, is increasing between X = 0 and X = 5. We would write 0 < x < 5. This shows that x is more than 0, but is less than 5 over the interval where it is increasing.

Let me know if you have any questions!

Answer:

subtract 4

isolating the variable (z)

Step-by-step explanation:

z=40

Answer:

Yes it is

Explanation:

If you check the number line youll see

Answer:

x = 4√3

Step-by-step explanation:

x² = 4(8 + 4) => tangent secant theorem

Solve for x

x² = 4(12)

x² = 48

Take the square root of both sides

√x² = √48

x = √(16 × 3)

x = 4√3

The growth rate of the population, given the initial population and the population after 10 years is 12. 5 % every 10 years.

To find the percent change or growth rate of a quantity between two different values, you can use the formula:

Percent change = ( new value - old value ) / old value x 100%

The new value would be the population of the village after 10 years which is 450 people.

The old value is the initial population of the village which is 400

The growth rate of the population is:
= ( 450 - 400 ) / 400 x 100 %

= 12. 5 %

The growth rate for the village is therefore 12. 5 % every ten years.

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Answer: (3, -2.333) or (3, -7/3)

Step-by-step explanation:

We're given an x value (x=3) when looking at the coordinate, so we're trying to find what y is equal to given the equation. We can plug in x=3 into 5x+3y=8 and isolate for y.

\(5(3)+3y=8\\15 + 3y=8\\3y=-7\\y=-\frac{7}{3}\)

Answer:

y= -2 1/3

Step-by-step explanation:

Since you have x, you put x into the equation and work through the problem.

5(3)+3y=8

15+3y=8, then subtract 15 from both sides

3y=(-7), then divide both sides by 3

y=(-7)/3 or (-2 1/3)

Answer:

  x = 31.2

Step-by-step explanation:

You want the solution to the proportion 12/x = 5/13.

You can eliminate the fractions by multiplying this equation by the least common denominator. That value is 13x, the product of these denominators. Multiplying by 13x, we have ...

  \(\dfrac{12}{x}\times13x=\dfrac{5}{13}\times13x\\\\\\12\cdot13=5\cdot x\qquad\text{simplified}\)

Now, the value of x is found by dividing both sides by its coefficient.

  \(\dfrac{12\cdot13}{5}=\dfrac{5x}{5}\\\\\\\dfrac{156}{5}=x\\\\\boxed{31.2=x}\)

__

Additional comment

The first step we did, multiplying by 13x, is also sometimes called "cross multiplication." The result of that step is that each numerator is multiplied by the opposite denominator.

Multiplying both sides of the equation by the same value (13x) is supported by the multiplication property of equality. The term "cross multiplication" is descriptive of the result, but is not a recognized property of equality. It is a good idea to keep the math operations you do grounded in the properties of equality.

You will notice that the steps we did were "multiply by 13x" and "divide by 5". These can be done at once by "multiply by 13x/5". Of course, that operation is done to both sides of the equation.

Any proportion can be written 4 ways:

  \(\dfrac{12}{x}=\dfrac{5}{13}\qquad\dfrac{x}{12}=\dfrac{13}{5}\qquad\dfrac{x}{13}=\dfrac{12}{5}\qquad\dfrac{13}{x}=\dfrac{5}{12}\)

These can be thought of as "upside down" and "sideways." We like the versions with the variable on top of a fraction, because the solution to that is simply multiplication by the variable's denominator.

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5th term of the sequence is -4

To find the 5th term in the sequence, we need to substitute n =  5 into the expression given

 \(a_5\) =  26- 6( 5)  

\(a_5\) =  26- 30

\(a_5\) = -4  

The formula given, an =  26- 6n, represents an  computation sequence with a common difference of-6.

This means that each term in the sequence is  attained by obtain 6 from the  former term.  

It's important to note that the formula is written in general form, meaning that it can be used to find any term in the sequence by simply plugging in the  matching value of  n.

 In this case, we were asked to find the 5th term, so we substituted n =  5 into the formula to get a5 = -4.

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Answer:

deez

Step-by-step explanation:

Answer:

Option B is correct.

Step-by-step explanation:

Trigonometry is defined as the branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles. There are three basic trigonometric ratios: sine, cosine, and tangent. Trigonometry and its functions have an enormous number of uses in our daily life. For instance, it is used in geography to measure the distance between landmarks, in astronomy to measure the distance of nearby stars and also in the satellite navigation system.

The trigonometric function of sine for an acute angle is the ratio between the leg opposite the angle when it is considered part of a right triangle and the hypotenuse while the cosine is the ratio of the base and the hypotenuse.

Here, \(sin 30\)° \(=\frac{4}{8}\)

\(sin 30\)° \(=\frac{1}{2}\)

\(cos 30\)° \(=\frac{4\sqrt{3}}{8}\)

\(cos30\)°\(=\frac{\sqrt{3} }{2}\)

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Answer:

The answer is 24.1 unit²

Step-by-step explanation:

Volume of prisms=cross sectional area×h

cross sectional area=Volume of prisms/height

A=216.9/9

A=24.1 unit²

Answer:

\({ \tt{ {x}^{2} + 4x + 3 = 0}} \\ { \tt{(x + 1)(x + 3) = 0}} \\ \\ { \tt{x = - 1 \: \: and \: \: - 3}}\)

Answer:

1/5x

Step-by-step explanation:

1/5x

the correct option is a. difference between the groups' averages, large absolute

I am trying to perform an A/B test to see if two samples come from the same underlying distribution. My alternative hypothesis is that the samples do not come from the same underlying distribution. The difference between the groups should be chosen as the test statistic averages  large absolute values of this statistic provide evidence in favor of the alternative hypothesis.

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The walkway is 12 feet 9 inches long.

To find the total length of the walkway, we need to add the lengths of the three boards together.

The first board is 3 feet 7 inches long, which can be written as 3'7".

The second board is 5 feet 4 inches long, which can be written as 5'4".

The third board is 3 feet 10 inches long, which can be written as 3'10".

Now, let's add the lengths together:

3'7" + 5'4" + 3'10"

When adding feet and inches, we need to carry over any extra inches beyond 12 to the feet.

Adding the inches first:

7" + 4" + 10" = 21"

Now, let's add the feet:

3' + 5' + 3' = 11'

So, the total length of the walkway is 11 feet 21 inches.

We need to convert the inches to feet by dividing by 12:

11' + 21" ÷ 12 = 11' + 1'9" = 12'9"

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The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.

To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.

Plugging in the coordinates of the point P = (1/2, y), we get:

(1/2)^2 + y^2 = 1

1/4 + y^2 = 1

y^2 = 1 - 1/4

y^2 = 3/4.

To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).

Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.

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The average speed during the trip is 11.9 miles per hour.

Speed is the ratio of distance and time.

It shows how fast an object is moving at a given time.

We have,

Total distance covered.

= 20 miles + 20 miles

= 40 miles

Total time.

= 2 hours + 22 minutes + 1 hour

= 3 hours 22 minutes

= 180 + 22 minutes

= 202 minutes

= 3.36 hours

Now,

Average speed.

= 40/3.36

= 11.9 miles per hour

Thus,

The average speed is 11.9 miles per hour.

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Considering the definition of an inequality, the inequality that can be used to determine x is 20x + 10≤ 80

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

An inequality contains one or more unknown values ​​called unknowns, in addition to certain known data.

Solving an inequality consists of finding all the values ​​of the unknown for which the inequality relation holds.

A rental car company charges $20 per day to rent a car and $0.10 for every mile driven.

Addison wants to rent a car, knowing that:

On the other hand, x represents the maximum number of days Alyssa can afford to rent for while staying within her budget.

Then, the inequality that can be used to determine x is:

20x + 0.1×100≤ 80

So:

20x + 10≤ 80

In summary, the inequality that can be used to determine x is 20x + 10≤ 80

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Given:

Total Population = 500  millions

Population Under 16 Years of Age or Institutionalized = 120 millions

Not in Labor Force = 150  millions

Unemployed = 23 millions

Now,

A) Labor force

= Total population – Population under 16 years of age – Not in labor force

= 500 – 120 – 150

= 230 millions

B) Unemployment rate \($=\frac{\text { Unemployment }}{\text { Labor force }} \times 100 \%$\)

or

Unemployment rate \($=\frac{23 \text { million }}{230 \text { million }} \times 100 \%$\)

or

Unemployment rate \($=10 \%$\)

The complete question is,

Assume the following data for a country:

Category Number of People (in Millions)

Total Population 500

Population Under 16 Years of Age or Institutionalized 120

Not in Labor Force 150

Unemployed 23

Part-Time Workers Looking for Full-Time Jobs 10

A) What is the size of the labor force (in millions)?

B) What is the official unemployment rate (in percentage)?

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The solution in interval notation is; (-∞,  49/2).

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

To solve the equation 5/16x - 7/4 < 3/4x + 21/2, we can simplify both sides:

5/16x - 7/4 < 3/4x + 21/2

Combining like terms:

5/16x  -3/4x  < 21/2 + 7/4

8/16x < 49/4

1/2x < 49/4

Simplifying the fraction;

x < 49/2

Therefore, the solution in interval notation is (-∞,  49/2).

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