find the probability of a freshman being called on in class if there are 12 sophomores, 10 juniors, 14 seniors, and 8 freshmen.

Assuming that the all the cards have the same probability of being drawn we get:

We have a deck of 52 cards.

A) The probability of drawing an even-numbered card is given by the quotient between the number of even-numbered cards and the total number of cards.

On the 52 card deck, there are 16 even cards (2, 4, 6, 8 for each type), so the probability is:

p = 16/52

Then the probability of drawing a face card is given in the same way, notice that now there are 51 cards in the deck and 12 face cards, so we get:

q = 12/51

The joint probability is the product of these two:

P = (16/52)*(12/51)  = 0.07

b) Both cards are 4 or larger.

There are 6 cards equal or larger than 4 for each type, so the probability for the first card is:

p = 24/52

For the second card, there is one card less in the deck (and one card less that is equal or larger than 4) so the probability is:

q = 23/51

The joint probability is:

P = (24/52)*(23/51) = 0.21

C) There are 6 black face cards, so the probability first is:

p = 6/52

Then there are 2 black cards with the number 5, so the probability is:

q = 2/51

The joint probability is:

P = (6/52)*(2/51) = 0.001

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Answer: Slope: 3

x-intercept(s): [tex](-\frac{1}{3} , 0)[/tex]

y-intercept(s): [tex](0,1)[/tex]

Answer:

25 customers

Explanation:

To find the number of people preferred cake, multiply the percentage by total customers.

People who preferred cake:

⇒ 35% × 71

⇒ 24.85

⇒ 25 (rounded to nearest whole number)

Answer:

(6.5,-6)

Step-by-step explanation:

(7+6)÷2= 6.5

(-5+-7)÷2=-6

Answer:

The second one is the correct answer

Step-by-step explanation:

There are more mammals on the list than birds and fish combined.

Answer:

  23.6 ft

Step-by-step explanation:

In the right triangle, an acute angle, the hypotenuse, and an adjacent side are marked. We went to know the length of the adjacent side. The trig relation involved is ...

  Cos = Adjacent/Hypotenuse

__

Filling in the given information, this relation tells us ...

  cos(29°) = x/(27 ft)

Solving for x, we get ...

  x = (27 ft)cos(29°) ≈ 23.614 ft

The value of x is about 23.6 ft.

Answer:

Part 1: See below ↓↓

You have two given data available here: the actual height of the Empire State Building measuring 1,450 feet, and the height of the block measuring 2 feet. To find how many blocks stacked together would make up 1,450 feet, just divide 1,450 by 2.

Number of blocks=1,450 feet * (1 block/2 feet)

Number of blocks = 725 blocks

Part 2 (kinda work)

What I did was I divided 1,450 by 5 and I got 290 so you would have to use 290 blocks to build the Empire State building out of blocks. The scale factor is 1 block per 5ft

Step-by-step explanation:

Answer:  The answer is 9

Answer:

9% of her monthly income is spent on 'Other expenses'

Step-by-step explanation:

[tex]900+120+80+100+320=1820[/tex]

but if you divide 180 by 2000 you'll get 0.09 but times that by 100 you'll get 9%

karen's conclusion is valid because the association does imply causation.

An association claim asserts that a particular level of one variable is expected to be related to a specific level of another variable. As two variables are related, they are said to be correlated, which means that when one variable varies, the other variable tends to change as well. 

An association claim must include at least two variables that are measured rather than manipulated.

While an association claim just acknowledges a connection between two variables, a causal claim goes a step further by claiming that one of the factors is responsible for altering the other.

Therefore, we can conclude that the claim which states that:

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Answer:

Association does not equal Causation, since Karen's theory does not have any evidence to prove causation, her theory is invalid.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The equation is solved by starting with the given equation, then performing inverse operations to undo what is done to the variable.

__

The equation shown is the same as the given equation.

  reason: given

The equation shown has the "-5" term missing. That happens when +5 is added to both sides of the equation. -5 +5 = 0, and 0 added to anything leaves the value unchanged.

  reason: addition property of equality

The equation shown has the "-6" coefficient of 'a' missing. That happens when the equation is multiplied by the multiplicative inverse of -6. That is, it is divided by -6.

  reason: division property of equality

_____

Additional comment

As we have noted in Step 3, division is the same as multiplication by the multiplicative inverse. The definition of multiplicative inverse tells you that the product of a number and its inverse is 1. The identity element property for multiplication tells you that multiplying by 1 leaves the value unchanged.

  (1/(-6))(-6a) = 1a = a

So, the reason for Step 3 could also be "multiplication property of equality."

Answer:

50 cm³

Step-by-step explanation:

Given volume of cylinder is 150 in³

we know that The volume of cone 1/3rd of cylinder.

Then volume of cone is 150/3 = 50 cm³

The median of the data is 64, the value of Q1 is 61.5, the value of Q2 is 71, and the value of Q3-Q1 is 9.5

A median is a middle number in a series of numbers that have been arranged to lift, and it might be more informative of the set of data than the average. When there are extremes in the sequences that might affect the average of the numbers, the median is sometimes employed instead of the mean.

We have data:

60, 60, 61, 62, 63, 63, 65, 65, 70, 72, 73, 98

The median = (63+65)/2 = 64

Q1 = (61+62)/2 = 61.5

Q2 = (70+72)/2= 71

Q3 - Q1 = 71 - 61.5 = 9.5

Thus, the median of the data is 64, the value of Q1 is 61.5, the value of Q2 is 71, and the value of Q3-Q1 is 9.5

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Answer:

Use the drop-down menus to identify the key values.

What is the median? ✔ 64

What is Q1, the median of the lower half of the data? ✔ 61.5

What is Q3, the median of the upper half of the data ✔ 71

What is the interquartile range, or Q3 – Q1? ✔ 9.5

Step-by-step explanation:

edge 2023

Using the distance formula, each side of the park is 13 units long

The vertices of the park are given as:

(26.5, 12), (38.5, 7), (26.5, 2), (13.5, 2), (1.5, 7), and (13.5, 12).

The length of each side is calculated using the following distance formula:

[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}[/tex]

Using any consecutive points, we have:

[tex]d = \sqrt{(13.5 - 1.5)^2 + (12 -7)^2} = 13[/tex]

Hence, each side of the park is 13 units long

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Answer:

values

x=17

AT = 49 units

OG = 21 units

The  increasing order of the horizontal widths of their asymptote rectangles is dependent on the values gotten from  y = ± x.

This is defined as a two-branched open curve formed by the intersection of a plane perpendicular to the bases of a double cone.

The rectangular hyperbola has two asymptotes which are defined as y = ± x in this scenario.

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The value of the constant of variation is 2,199 feet. The speed of the another rider is 87.96 feet/sec.

Let there are two variables p and q

Then, p and q are said to be directly proportional to each other if

 p = kq

where k is some constant number called the constant of proportionality.

This directly proportional relationship between p and q is written as

 p∝q  where that middle sign is the sign of proportionality.

In a directly proportional relationship, increasing one variable will increase another.

Now let m and n be two variables.

Then m and n are said to be inversely proportional to each other if

[tex]m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}[/tex]

(both are equal)

where c is a constant number called the constant of proportionality.

This inversely proportional relationship is denoted by

[tex]m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}[/tex]

As visible, increasing one variable will decrease the other variable if both are inversely proportional.

A.) The time it takes to complete a go-cart course is inversely proportional to the average speed of the go-cart. Therefore, the relationship can be written as,

Average speed ∝ (1/time)

Now, if the constant of variation is introduced then the relationship can be written as,

Average speed = k(1/time)

Substituting the values, we will get,

[tex]73.3\frac{ feet}{second}= k \times \dfrac{1}{30\ seconds}\\\\73.3 \frac{ feet}{second}\times 30\ seconds = k\\\\k = 2,199\ feet[/tex]

Hence, the value of the constant of variation is 2,199 feet.

B.) The speed of the another rider is,

Average speed = k(1/time)

Average speed = 2,199×(1/25) feet/sec

Average speed = 87.96 feet/sec

Hence, the speed of another rider is 87.96 feet/sec.

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The BTU required by the air conditioner/hour to cool the following structures is given as:

It is to be noted that the BTU required to cool per cubic foot of space is 4BTUs.

Since we are not given the dimensions of the structures, the required constant is thus, multiplied by the volume of the structures whose equations have been given above.

Note that:

Volume translates to enclosed space; and

BTU means British Thermal Unit.

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Answer:

Step-by-step explanation:

Answer:

14/24 is one expression equivalent to 7/12.

Answer:

14/24,21/36,28/48,35/60,42/72,49/84,56/96 are equivalent to 7/12...

Answer:

should be 78.5

Step-by-step explanation:

the formula for volume of a cone is V = pi^2 x H/3

so if you plug in the values you get V= 3.14 x5^2 x3/3 making the awsnser 78.5

Answer:

[tex]y=2x^2-4x-16[/tex]

Step-by-step explanation:

Factored form of a quadratic equation:

[tex]y=a(x-r_1)(x-r_2)[/tex]

where:

Given:

Substitute the given values into the formula and expand:

[tex]\implies y=2(x-4)(x-(-2))[/tex]

[tex]\implies y=2(x-4)(x+2)[/tex]

[tex]\implies y=2(x^2+2x-4x-8)[/tex]

[tex]\implies y=2x^2-4x-16[/tex]

Answer:

Could you possible line the numbers up a little bit, it'd be better to understand that way.

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

[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Given question:-}}}}[/tex]

             ❖ A number y increased by 5 is at least -21.

[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}[/tex]

          ❖ First, if you come across the word "increased" it means we

    "increase" a number, or add something to that number, like

y increased by 5 [tex]\longmapsto[/tex] [tex]\sf{y+5}[/tex]

Now, we are also given that this expression is at least -21, which means it can't be -21; it can be -21 or it can be greater than -21.

So we have

[tex]\longmapsto\sf{y+5\geq -21}}[/tex]

Solving for y

[tex]\longmapsto\sf{y\geq -21-5}[/tex]

[tex]\longmapsto\sf{y\geq -26}[/tex]

So the values of y greater than or equal to -26 will make this inequality true.

 [tex]\rule{300}{1}[/tex]

Answer:

y >= - 26

Step-by-step explanation:

your equation at first looks like this

y + 5 >= -21

then you subtract 5 to both sides

y >= -26

Answer:

Here is the ans...hope it helps

Answer: On a coordinate plane, 2 solid straight lines are shown. The first line is vertical to the x-axis at x = 20. Everything to the right of the line is shaded. The second line has a negative slope and goes through (0, 50) and (50, 0). Everything to the right of the line is shaded.

Step-by-step explanation:

x = # of stools = 20

y = # of recliners = 50-20 = 30

Answer:

On a coordinate plane, 2 solid straight lines are shown. The first line is vertical to the x-axis at x = 20. Everything to the right of the line is shaded. The second line has a negative slope and goes through (0, 50) and (50, 0). Everything to the left of the line is shaded.

Answer: A. 15 miles.

Step-by-step explanation: Did the math 22, 33 and got A. 15 miles.

Answer:

120% are sixth graders

But, If you meant to say 18 basketball players and 15 6th graders, the percentage would be around 83.3%

The linear equation is 3x + 5y = 75. Then the value of A, B, and C will be 3, 5, and 75 respectively.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The equation of a line is given as

y = mx + c

where m is the slope and c is the constant.

Then we have

y = (-3/5)x + c

The line is passing through (25, 0). Then we have

25 = c

Then we have

y = (-3/5)x + 25

On simplifying, we have

5y = -3x + 75

3x + 5y = 75

Then the value of A, B, and C will be 3, 5, and 75 respectively.

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Answer:

Its a linear function as there is a common difference of -9.

Step-by-step explanation:

x  y      Difference

1   4    

2  -5      -9

3 -14      -9

4 -23     -9

5 -32     -9

For a difference in x of we have a difference in y  of -9.

Answer:

A and c

Step-by-step explanation:

multiply the 3 to both parts of equation

Answer:

it's A and C, multiply 3 with 3x and 4y