What is the value of X?

Answer:

P (red) = 1/2

Step-by-step explanation:

It is given that a card is drawn from a well-shuffled deck of 52 cards and we are to find the probability of getting a red card.

We know that there are total 26 red cards in a deck (13 hearts and 13 diamonds).

Therefore, the probability of getting a red card P (red) = [tex] \frac { 2 6 } { 5 2 } [/tex] = 1/2

The probability of drawing a red card from a well-shuffled 52-card deck is 1/2 since half of the cards in the deck are red (26 out of 52)

This question pertains to the topic of probability in Mathematics. There are 52 cards in a standard deck, half of which are red (26 red cards: 13 hearts and 13 diamonds). Hence, the probability of drawing a red card is the number of red cards over the total number of cards in the deck.

So, the probability of drawing a red card from a well-shuffled 52-card deck is 26/52, simplified to 1/2. Hence the correct answer from the given choices is 1/2.

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Answer:

2

Step-by-step explanation:

Answer:

x = -1, 3

Step-by-step explanation:

so what you need to do is graph each one because that's what the questions ask. One way for you to check your answer is to set the two equations equal to each other.

-x + 5 = x^2 - 3x + 2

you want to end up with one equation and having the equation equal 0. So add x to both sides to cancel out the x on the left side and then subtract 5 from both sides to cancel out the 5 on the left side.

0 = x^2 - 2x - 3

now you factor

0 = (x - 3) (x + 1)

x = -1, 3

Answer:

[tex]5^{2}[/tex] = 25 :) hope this helps

Step-by-step explanation:

Answer:

The correct answer option is P(Both Work) =  435 / 703

Step-by-step explanation:

We are given that in a box of total 38 bulbs, 8 are the defective ones while the rest are good.

If Ken selects two bulbs at random from the box, we are to find the probability that they both work.

1st bulb: P (bulb works) =  [tex]\frac{30}{38} [/tex]

2nd bulb: P (bulb works) = [tex]\frac{29}{37} [/tex]

P (Both Work) = [tex]\frac{30}{38} \times \frac{29}{37}[/tex] = 435 / 703

Answer:

The correct answer is first option.   P(Both Work) =  435/703

Step-by-step explanation:

It is given that,

There are 8 burned bulbs and 30 good bulbs.

Therefore total number of bulbs = 8 + 30 = 38

To find the probability

We have to take two working bulbs from total bulbs.

Total bulbs = 38

The probability of taking two working bulbs = P(Both Work)

P(Both Work) = 30C₂/38C₂

  = (30 * 29)/(38 * 37) = 435/703

Therefore the correct answer is first option

Answer: option b.

Step-by-step explanation:

You must keep on mind the following identities:

[tex]csc\theta=\frac{1}{sin\theta}\\\\cot\theta=\frac{1}{tan\theta}[/tex]

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

Therefore, you can simplify the expression given in the problem as you can see below:

- Substitute identities:

[tex]\frac{csc\theta}{cot\theta}=\frac{\frac{1}{sin\theta}}{\frac{1}{tan\theta}}\\\\=\frac{tan\theta}{sin\theta}\\\\=\frac{\frac{sin\theta}{cos\theta}}{sin\theta}\\\\=\frac{sin\theta}{(cos\theta)(sin\theta)}\\\\=\frac{1}{cos\theta}[/tex]

By definition:

[tex]\frac{1}{cos\theta}=sec\theta[/tex]

The correct answer is B, or sec theta.

Just got it right on edge 2020, hope this helps!! :)

Answer:

D

Step-by-step explanation:

An equivalent expression is an expression which is equal to −(4 + 3i) + (2 + 2i). You can expand or simplify an expression to make an equivalent expression. Combine like terms - constants with constants and imaginary with imaginary - to simplify.

−(4 + 3i) + (2 + 2i) = -4 + 2 -3i + 2i = -2 - i

Answer:

The length is [tex]15\ ft[/tex]

The width is [tex]12\ ft[/tex]

Step-by-step explanation:

we know that

The area of rectangle is equal to

[tex]A=LW[/tex]

we have

[tex]A=180\ ft^{2}[/tex]

so

[tex]180=LW[/tex] -----> equation A

[tex]W=L-3[/tex] ------> equation B

substitute equation B in equation A and solve for L

[tex]180=L(L-3)[/tex]

[tex]180=L^{2}-3L[/tex]

[tex]L^{2}-3L-180=0[/tex]

using a graphing tool------> solve the quadratic equation

The solution is [tex]L=15\ ft[/tex]

see the attached figure

Find the value of W

[tex]W=15-3=12\ ft[/tex]

To find the dimensions of the rectangle given its area, we set up an equation using the length and width of the rectangle. Solving the equation will give us the dimensions. In this case, the length of the rectangle is 15 feet and the width is 12 feet.

To find the dimensions of the rectangle, let's assume the length of the rectangle is L feet. According to the problem, the width is 3 feet less than the length, so the width would be L - 3 feet. The area of the rectangle is given as 180 square feet, so we can set up the equation: L * (L - 3) = 180. Solving this equation will give us the dimensions of the rectangle.

Multiplying the binomials, we get L^2 - 3L = 180. Rearranging the equation, we have L^2 - 3L - 180 = 0. This is a quadratic equation that can be factored. Factoring, we have (L - 15)(L + 12) = 0. We can now solve for L by setting each factor equal to zero: L - 15 = 0 or L + 12 = 0. This gives us two possible solutions for L: L = 15 or L = -12.

Since we cannot have negative dimensions for a rectangle, we discard the negative solution. Therefore, the length of the rectangle is 15 feet. The width can be found by substituting this value back into the equation: Width = 15 - 3 = 12 feet. So, the dimensions of the rectangle are 15 feet by 12 feet.

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Answer:

The measure of arc KL is [tex]145\°[/tex]

Step-by-step explanation:

we know that

[tex]arc\ JK=arc\ KL=x\°[/tex]

so

[tex]2x+70\°=360\°[/tex] -----> complete circle

solve for x

[tex]2x=360\°-70\°[/tex]

[tex]2x=290\°[/tex]

[tex]x=145\°[/tex]

Answer: 40

Step-by-step explanation:

second train leaves 40 minutes after

Answer:

A) 0.5000; B) 0.9772; C) 0.9772; D) 0.8185; E) 0.9932; F) 1.0000

Step-by-step explanation:

For each of these, we will use a z score.  The formula for a z score is:

[tex]x=\frac{X-\mu}{\sigma}[/tex]

A) Our X is 5, our mean is 5 and our standard deviation is 0.2:

z = (5-5)/(0.2) = 0/0.2 = 0

Using a z table, the value to the left of this, less than, is 0.5000; this means the area to the right of this, greater than, is 1-0.5000 = 0.5000.

B) Our X is 5.4, the mean is 5 and the standard deviation is 0.2:

z = (5.4-5)/0.2 = 0.4/0.2 = 2

Using a z table, the value to the left of this, less than, is 0.9772.

C) The probability for this will be the same as for B; there is no distinction between "less than" and "less than or equal to" in z tables.

D) We find the z score for each of the endpoints of this interval, find the probabilities and subtract them:

z = (4.6-5)/0.2 = -0.4/0.2 = -2; the probability is 0.0228.

z = (5.2-5)/0.2 = 0.2/0.2 = 1; the probability is 0.8413.

The area between them is 0.8413-0.0228 = 0.8185.

E) X is 4.5, the mean is 5 and the standard deviation is 0.2:

z = (4.5-5)/0.2 = -0.5/0.2 = -2.5; the probability less than this is 0.0062.  This means the probability greater than this is 1-0.0062 = 0.9938.

F) X is 4, the mean is 5 and the standard deviation is 0.2:

z = (4-5)/0.2 = -1/0.2 = -5.  Everything in the z table is larger than this, so the probability is 1.000.

HERE'S HOW TO DO IT :)

A composite figure is made up of several simple geometric figures such as triangles, rectangles, squares, circles, and semicircles.

To find the area of a composite figure, separate the figure into simpler shapes whose area can be found. Then add the areas together.

(SEE EXAMPLE ATTACHED)

HERES WHAT WE KNOW ABOUT COMPOSITE FIGURES:

Composite Figures. A figure (or shape) that can be divided into more than one of the basic figures is said to be a composite figure (or shape). For example, figure ABCD is a composite figure as it consists of two basic figures

let me know if i can help more :)

See the attached picture for the answers:

Answer:

Step-by-step explanation:

You’re answer is 1/12

Answer:

1/12

Step-by-step explanation:

42 flats per table is your answer

Answer:

option(D)

x= 30 , y = 10√3

Step-by-step explanation:

Given in the question, a right angle triangle whose

hypotenuse = 20√3

We will use pythagorus theorem and trigonometry identities to find the value of x and y

Formula to use

sin(30) = y /  20√3

y = sin(30) x 20√3

y = 10√3

(20√3)² =  (10√3)² + x²

(20√3)² - (10√3)² = x²

x² = 900

x = √900

x = 30

so, the value of x = 30 and y = 10√3

Answer:

[tex]x=30,y=10\sqrt{3}[/tex]

Step-by-step explanation:

Recall the mnemonics SOH CAH TOA.

We use the cosine ratio to find the value of [tex]x[/tex].

[tex]\cos(30\degree)=\frac{Adjacent}{Hypotenuse}[/tex]

This implies that;

[tex]\cos(30\degree)=\frac{x}{20\sqrt{3}}[/tex]

[tex]\frac{\sqrt{3}}{2} =\frac{x}{20\sqrt{3}}[/tex]

Cross multiply to get;

[tex]2x=20\sqrt{3}\times \sqrt{3}[/tex]

[tex]2x=60[/tex]

[tex]x=30[/tex]

Using the sine ratio

[tex]\sin(30\degree)=\frac{y}{20\sqrt{3} }[/tex]

[tex]\frac{1}{2}=\frac{y}{20\sqrt{3} }[/tex]

Tis implies that;

[tex]y=\frac{1}{2} \times 20\sqrt{3}[/tex]

[tex]y=10\sqrt{3}[/tex]

The correct choice is D.

Answer:

4 out of 22 = 4/22

Step-by-step explanation:

ANSWER

a. 216

EXPLANATION

The given function is;

[tex]f(x) = {6}^{x} [/tex]

We want to find the value of this function when x=3.

We substitute this value into the function to obtain,

[tex]f(3) = {6}^{3} [/tex]

[tex]f(3) = 6 \times 6 \times 6[/tex]

[tex]f(3) = 216[/tex]

Answer:

The correct answer is option a.  216

Step-by-step explanation:

It is given that,

f(x) = 6ˣ for x = 3

To find the value of f(x)

f(x) = 6ˣ

when x = 3 we can write,

f(3) = 6³ = 6 * 6 * 6 = 216

Therefore the value of f(x) when x = 3 is 216

The correct answer is option a.  216

Answer:

option (B)

15 + 5√3

Step-by-step explanation:

In a 30-60-90 triangle, you can find the measure of any of the three sides, simply by knowing the measure of at least one side in the triangle.

Given in the question,

length of small leg = 5

As we know that

The hypotenuse is equal to twice the length of the shorter leg

The longer leg is equal to multiplying the shorter leg by the square root of 3

Perimeter of a triangle = sum of the length of three sides

                                     =  5√3 + 10 + 5

                                     = 15 + 5√3

Answer:

11/6 or decimal 1.8333... + 4.9 = 6.733333....

Step-by-step explanation:

Simplify the following:

(3 + 2/3)/2

Express 4/6 in its lowest form by cancelling out gcd(4, 6) = 2 from the numerator and denominator. 4/6 = (2×2)/(2×3) = 2/3:

(2/3 + 3)/2

Put 3 + 2/3 over the common denominator 3. 3 + 2/3 = (3×3)/3 + 2/3:

((3×3)/3 + 2/3)/2

3×3 = 9:

(9/3 + 2/3)/2

9/3 + 2/3 = (9 + 2)/3:

((9 + 2)/3)/2

9 + 2 = 11:

(11/3)/2

11/3×1/2 = 11/(3×2):

11/(3×2)

3×2 = 6:

Answer:  11/6 or decimal 1.8333... + 4.9 = 6.733333....

Answer:

It is  D.

Step-by-step explanation:

10^ 6  = 1,000,000 = 1 million.

So it is 6.794 million meters.

Answer:

a) 0.7486; b) 0.6518; c) No

Step-by-step explanation:

We use z scores to answer these questions.  The formula for a z score is

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

Our mean, μ, is 44; our standard deviation, σ, is 1.5.

For part a,

We want P(X > 43):

z = (43-44)/1.5 = -1/1.5 = -0.67

Using a z table, we see that the area under the curve to the left of this is 0.2514.  However, we want the area to the right; this means we subtract from 1:

1 - 0.2514 = 0.7486

For part b,

We want P(42 ≤ X ≤ 45):

z = (42-44)/1.5 = -2/1.5 = -1.3

z = (45-44)/1.5 = 1/1.5 = 0.67

Using a z table, the area under the curve to the left of z = -1.3 is 0.0968.  The area under the curve to the left of z = 0.67 is 0.7486.

The area between them is 0.7486 - 0.0968 = 0.6518.

For part c,

A response of 35 has a z score of

z = (35-44)/1.5 = -9/1.5 = -6

This is 6 standard deviations below the mean.  This is more than the amount required to make this an outlier, or an unlikely response.

Answer:

0.7325 to 5.6675 ug/dl

Step-by-step explanation:

The middle 90% will be 45% above the mean and 45% below the mean.  This means

0.5-0.45 = 0.05 and

0.5+0.45 = 0.95

We use a z table.  Look in the cells; find the values as close to 0.05 and 0.95 as we can get.

For 0.05, we have 0.0505 and 0.0495; since these are equidistant from 0.05, we use the value between them.  0.0505 is z=-1.64 and 0.0495 is z=1.65; this gives us z=-1.645.

For 0.95, we have 0.9495 and 0.9505; since these are equidistant from 0.95, we use the value between them.  0.9495 is z = 1.64 and 0.9505 is z=1.65; this gives us z = 1.645.

Now we use our z score formula,

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

Our two z scores are 1.645 and -1.645; our mean, μ, is 3.2; and our standard deviation, σ, is 1.5:

[tex]1.645=\frac{X-3.2}{1.5}[/tex]

Multiply both sides by 1.5:

[tex]1.5(1.645)=\frac{X-3.2}{1.5}\times 1.5\\\\2.4675 = X-3.2[/tex]

Add 3.2 to each side:

2.4675+3.2 = X-3.2+3.2

5.6675 = X

[tex]-1.645=\frac{X-3.2}{1.5}[/tex]

Multiply both sides by 1.5:

[tex]1.5(-1.645)=\frac{X-3.2}{1.5}\times 1.5\\\\-2.4675=X-3.2[/tex]

Add 3.2 to each side:

-2.4675+3.2 = X-3.2+3.2

0.7325 = X

Our range is from 0.7325 to 5.6675.

Final answer:

The range of arsenic blood concentrations corresponding to the middle 90% of healthy adults is approximately 0.765 ug/dl to 4.035 ug/dl.

Explanation:

The middle 90% of a Normally distributed data set falls within approximately two standard deviations of the mean. In this case, the mean is 3.2 ug/dl and the standard deviation is 1.5. To find the range of arsenic blood concentrations corresponding to the middle 90% of healthy adults, we can calculate the upper and lower boundaries.

First, we need to find the Z-scores that correspond to the 5th and 95th percentiles. The Z-score formula is:

Z = (x - mu) / sigma

Applying the formula, we get:

Z_lower = (x_lower - 3.2) / 1.5 = -1.53

Z_upper = (x_upper - 3.2) / 1.5 = 1.53

Next, we need to find the corresponding x values. Rearranging the Z-score formula, we can solve for x:

x = Z * sigma + mu

Plugging in the Z scores, we have:

x_lower = -1.53 * 1.5 + 3.2 = 0.765

x_upper = 1.53 * 1.5 + 3.2 = 4.035

Therefore, the range of arsenic blood concentrations corresponding to the middle 90% of healthy adults is approximately 0.765 ug/dl to 4.035 ug/dl.

The probabilities are;

a) 0.03

b) 0.691

c) 0.2.

How to calculate probability.

Given information

A company surveyed 1000 people on their age and the number of jeans purchased annually. The results of the poll are shown in the above table.

a) The person is over 25 and purchases 3

or more pairs of jeans annually

P(25 and 3 or Jeans)

[tex] = \frac{30}{1000} [/tex]

= 0.03

b) The person is older than 18 or purchases

1 pair of jeans annually.

[tex] = \frac{560 + 274 - 143}{100} [/tex]

[tex] = \frac{691}{1000} [/tex]

= 0.691

c) The person is 12 - 18 in the age group

and purchases at most 2 pairs of jeans annually

[tex] = \frac{17 + 61 + 122}{1000} [/tex]

[tex] = \frac{200}{1000} [/tex]

= 0.2

Complete question

A company surveyed 1000 people on their age and the number of jeans purchased annually. The results of the poll are shown in the table. A person is selected at random. Compute the probability of the following. The person is over 25 and purchases 3 or more pairs of jeans annually. The person is older than 18 or purchases 1 pair of jeans annually. The person is in the age group 12-18 and purchases at most 2 pairs of jeans annually.

Answer:

198

Step-by-step explanation:

If the ratio of adults to children is 6:11, then 6/17 of the people are adults and 11/17 of the people are children.

11/17 × 306 = 198

There are 198 children.

Answer:

x > -8

Step-by-step explanation:

First you distribute the -5 and get

-5x-35 < 10

Then you add 35 to both sides and get

-5x<45

Then dived by NEGATIVE 5 (since it is negative you flip the less than signs to greater than) and get

x> -8

Answer:

Choice C is correct

Step-by-step explanation:

The polar equation of the conic section is in standard form. The eccentricity is simply the coefficient of cos theta; thus e = 2

The eccentricity being more than 1 implies the conic section is a hyperbola.

To determine the directrix, divide 6 by 2 to obtain 3. The conic section opens to the left thus;

directrix; x = 3

Answer:

Choice C is correct

Final answer:

The probability of rolling a number less than 5 on a six-sided die is 2/3. When rolling the die 250 times, this probability suggests that a number less than 5 would be rolled approximately 167 times.

Explanation:

To predict the number of times you will roll a number less than 5 when rolling a standard six-sided die (with faces numbered 1 through 6), it's important to first understand the probability of rolling a number less than 5 for any single roll. Our numbers of interest here are 1, 2, 3, and 4.

The probability P of rolling any one of these four numbers on a six-sided die is 4 out of 6 (since there are 4 favorable outcomes and 6 possible outcomes in total), which simplifies to 2/3. This means that on any given roll, you have a 2/3 chance of rolling a number less than 5.

When rolling the die 250 times, we would expect this 2/3 probability to hold true on average. Therefore, we calculate the expected number of times a number less than 5 appears as follows:

Expected number of rolls less than 5 = Total number of rolls × Probability of rolling a number less than 5

Expected number of rolls less than 5 = 250 × 2/3

Expected number of rolls less than 5 = approximately 166.67

Since we cannot roll a die a fraction of a time, we would predict that you would roll a number less than 5 approximately 167 times out of 250 rolls.

The price and demand are inversely proportional to each other, When the price is less, the demand is higher. When the price is high, the demand is low.

So , as given, the gasoline prices has been decreased from $2.00 per gallon to $1.40 per gallon, so now the demand will increase. The quantity of gasoline that will be in demand will increase.

Answer:

The quantity of gasoline demanded will increase.

Step-by-step explanation:

We are asked to find the change in demand of gasoline, when price of gasoline decreased from $2 per gallon to $1.40.

We know that quantity of a product demanded is inversely proportional to supply of the product.

This means that an increase in price will decrease the quantity demanded, while a decrease in price will increase the demand.

Since the price of gasoline is decreased by $0.60 per gallon, therefore, the quantity of gasoline demanded will increase.

Answer:should be A

Step-by-step explanation:

I dunno

Answer:

it is A i just did it and i got it right so please trust me it is A

Step-by-step explanation: