A deck of cards contains RED cards numbered 1,2,3,4,5 and BLUE cards numbered 1,2,3,4. Let R be the event of drawing a red card, B the event of drawing a blue card, E the event of drawing an even numbered card, and O the event of drawing an odd card. Drawing the Red 5 is an example of which of the following events? Select all correct answers. Select all that apply: B OR E B OR O R AND E R OR E O′ B AND O

Answer:

[tex]\sf A. \quad -3.5 < -\dfrac{10}{3}[/tex]

Step-by-step explanation:

Convert -3.5 into a fraction:

[tex]\implies \sf -3.5=-\dfrac{35}{10}=-\dfrac{\diagup\!\!\!\!5 \times 7}{\diagup\!\!\!\!5 \times 2}=-\dfrac{7}{2}[/tex]

Rewrite both fractions so that they have the same denominator:

[tex]\implies \sf -\dfrac{7}{2}=-\dfrac{7 \times 3}{2 \times 3}=-\dfrac{21}{6}[/tex]

[tex]\implies \sf -\dfrac{10}{3}=-\dfrac{10 \times 2}{3 \times 2}=-\dfrac{20}{6}[/tex]

[tex]\textsf{As }\: -\dfrac{21}{6} < -\dfrac{20}{6} \textsf{ then}:[/tex]

[tex]\sf \implies -3.5 < -\dfrac{10}{3}[/tex]

Answer:

0.67

Step-by-step explanation:

Original price = $8.10

New price = $13.50

Increase in price = 13.50−8.10=$5.40

Ratio of the increase in price to the original price = 5.40 8.10=0.67

Answer: 62 + |−4| = 66°, 62° is the farthest from 0°

I believe this is the correct answer.

The one that shows how much warmer this location is in April than in December, and which temperature is the farthest away from 0°. will be B Option 62 - |−4| = 566°, 62° is the farthest from 0°

We have got an equation that can relate these three units of measurement of temperature, as given below:

[tex]\dfrac{C}{5} = \dfrac{F - 32}{9} = \dfrac{K - 273}{5}[/tex]

where C represents the measurement of a fixed temperature in celsius, F represents the measurement of that same intensity temperature in fahrenheit, and K represents the measurement of equally intense temperature in kelvin.

Based on the information given, the value of warmer will be;

= 62 - (-4)

= 62 + 4.

= 66

Therefore, the correct option will be option  B. 62 - |−4| = 566°, 62° is the farthest from 0°

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Answer:

32

Step-by-step explanation:

1-295/2

Answer:

x>22/3 or x<-32/3

Step-by-step explanation:

Step 1 - add 6 to both side

Step 2 - divide both sides by two

Step 3 - Solve Absolute Value

We know either x+ 5/3 >9 or x+5/3<-9

Subtract 5/3 from both sides

Answer:

[tex]\mathrm{a + 4 = |+All~real~numbers|}[/tex] (+∞)

Any concerns please notify me, and have a great day!

Answer:

a diamond ♦ it as acute angles

In this problem you have two unknowns: the weight of a bag of apples and the weight of a bag of oranges.

You have one given equation, which allows you to reduce the number of unknowns by one. This means that you will not be able to tell both the weight of the apples and the oranges, but find a line with possible solutions instead.

e.g. apples weigh 6+2x, oranges 7-3x where x is any real number.

You may narrow the problem down by assuming the weights to be non-negative, but to solve for x you need another piece of information that allows you to eliminate the last unknown.

Answer:

i want orange juice

Answer:

−5 > x > 10

Step-by-step explanation:

States from least population density (top) to greatest population density (bottom) are Colorado Arizona Minnesota Kentucky.

In the problem we are given with some datas

State      Population                 Land Area        

Arizona    6 . 83 × [tex]10^{6}[/tex]               113 , 594              

Colorado  5 . 46 × [tex]10^{6}[/tex]               103 , 642

Kentucky   4 . 43 × [tex]10^{6}[/tex]               39 , 486

Minnesota   5 . 45 × [tex]10^{6}[/tex]            79 , 627

population density are for

Arizona  (6 . 83 × [tex]10^{6}[/tex] )/113594=60.12

Colorado 52.68

Kentucky  112.19  

Minnesota   68.44

States from least population density (top) to greatest population density (bottom) are Colorado Arizona Minnesota Kentucky.

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Answer:

Step-by-step explanation:

Answer:

a farmer has 9 1/ 2 ha of land . He needs 11/4 ha for each crops

the no of different crop he can plant is ..

Step-by-step explanation:

The probability that the next spin will land on blue or green or purple as a fraction in simplest form is 44/71.

Given that, a spinner is divided into five coloured sections that are not of equal size: red, blue, green, yellow, and purple.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favourable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

The spinner results are as follows:

Colour        Frequency

Red                  19

Blue                 20

Green               14

Yellow               8

Purple               10

Total number of outcomes = 19+20+14+8+10=71

The probability of getting blue =20/71

The probability of getting green =14/71

The probability of getting purple =10/71

So, the probability of getting blue or green or purple = 20/71 + 14/71 + 10/71

=44/71

Therefore, the probability that the next spin will land on blue or green or purple as a fraction in simplest form is 44/71.

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Answer:29

Step-by-step explanation:14 multiplied by 29=406

Answer:

14 x 29 = 406

Step-by-step explanation:

so I believe it's 29

In linear equation, The value of the r is a P-q-s.

According to the statement

We have to find that the value of the r .

So, For this purpose, we know that the

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.

From the given information:

The equation is a :

P=q+r+s

This a type of the linear equation then

P=q+r+s

Now, rearrange the terms

P-q-s = r

Then the value of the r is

r = P-q-s .

So, In linear equation, The value of the r is a P-q-s.

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Answer: Equation for the line that passes through the points (6,-5) and (-4,1) is equal to 3x+5y+7 = 0.

Step-by-step explanation:

The equation of a line can be written in slope intercept form:  

y = mx + b   where m is the slope and b is the y-intercept

You can use the two points to find the slope m:

m = (y2 - y1 ) / ( x2 - x1 )

Given that points (6,-5) and (-4,1)

It represents the values are,

x1 = 6

y1 = -5

x2 = -4

y2 = 1

so,

Replace with x1, x2, y1, y2 values in this equation,

we can write,

m=(1-(-5)) / (-4-(6))

m = (1+5) / (-4-6)

m= 6/-10

m = 3/-5

Now you can select either point and substitute the coordinates in the equation to determine b, the y intercept.  Let's us (-4, 1):

y= mx + b

so, x = -4 and y = 1 and m = 3/-5

Replace with the values in this equation,

y= mx +b

1 = (-3/5)(-4) + b

1 = (0.6)(4) +b

1 = 2.4 +b

1-2.4 = b

-1.4 = b

b = -1.4

The equation will be:

y = mx +b

substitute m and b values,

Then,

y = (-3/5)x + (-1.4)

y = (-3/5)x -1.4

In standard form, the equation would be transformed as:

y = (-3x-7) / 5

5y = -3x-7

3x+5y = -7

3x+5y+7 = 0

In standard form, the equation would be transformed as: 3x+5y+7 = 0

Therefore,

Equation for the line that passes through the points (6,-5) and (-4,1) is equal to 3x+5y+7 = 0.

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Answer:

38

Step-by-step explanation:

[tex]3x {}^{2} y - x[/tex]

[tex] 3 \times ( - 2) { \\ }^{2} \times 3 - ( - 2)[/tex]

[tex]3 \times 4 \times 3+ 2[/tex]

[tex]36 + 2[/tex]

[tex]38[/tex]

Frequency Histogram for the data using a class width of 10 and using 95 as the lower limit of the first class.

A histogram is a bar graph type of data representation in this representation the width of the class size is represented by the rectangle shapes reaching a particular height which describes the the number of frequency distribution.

The girls scouted got their weight recorded. The weights of the girls recorded are 97 120 137 124 117 108 134 126 123 106 130 110 100 120 140.

All the weights are measured in pounds.

The histogram is represented in the x axis and the y axis. The weight of the girls is represented on the y axis. The number of girls is represented on the x axis.

Each girl's weight is represented by a different color to understand the graph easily.

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Approximately 733395 babies were born in the UK in 2018.

Given,

In the UK in 2018 a baby was born every 43 seconds.

We have to find the total number of babies in the UK in 2018.

A baby in every 43 seconds.

There is 3600 seconds in an hour.

There is 24 hours in a day.

In 2018 there were 365 days.

So, the total number of babies born in 2018 in the UK:

= (Seconds in an hour × hours in a day × total days in 2018) ÷ 43

= (3600 × 24 × 365) ÷ 43

= 31536000 ÷ 43

= 733395.3488

≈ 733395

That is, in the UK in 2018 approximately 733395 babies were born.

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If [tex]x[/tex] is positive, then [tex]\tan^{-1}(x)[/tex] is between 0 and π/2, which means [tex]\cos(\tan^{-1}(x))[/tex] is between 1 and 0.

Let [tex]\theta = \tan^{-1}(x)[/tex]. Then [tex]\tan(\theta) = x[/tex], and it follows from the Pythagorean identity that

[tex]\sin^2(\theta) + \cos^2(\theta) = 1 \implies \tan^2(\theta) + 1 = \sec^2(\theta) \\\\ ~~~~ \implies \sec(\theta) = \sqrt{1 + \tan^2(\theta)} \\\\ ~~~~ \implies \cos(\theta) = \dfrac1{\sqrt{1+\tan^2(\theta)}} \\\\ ~~~~ \implies \cos(\tan^{-1}(x)) = \boxed{\dfrac1{\sqrt{1+x^2}}}[/tex]

We took the positive square root when solving for [tex]\sec(\theta)[/tex] because we know [tex]\cos(\theta)[/tex] is non-negative, between 0 and 1.

Answer:

3.39x=y

Step-by-step explanation:

This is because the 'y' part is supposed to be the answer for how much the gallons of gasoline would be.

The 'x' part of the equation represents how much gallons of gasoline you got and you can treat it as a normal number.

Pretend that x is 2 and so you are to find out how much 2 gallons of gasoline costs and to work this out you would do this: 3.39 x 2.

You just basically treat x as a normal number like so and it would look like:

3.39 x x=3.39x

Answer:

The price of a senior citizen ticket to the fall musical is $6

The price of a student citizen ticket to the fall musical is $4

Step-by-step explanation:

C = the price of a senior citizen ticket to the fall musical

S = the price of a student citizen ticket to the fall musical

Day 1:

6C + 5S = 50

Day 2:

8C + 1S = 44

Manipulate the equations so that they have a common coefficient.

Multiple Day 2's equation by 5.

8C + 1S = 44

40C + 5S = 220

Subtract Day 2's equation from Day 1's

(40C + 5S = 220) - (6C + 5S = 50)

(40C + 5S) - (6C + 5S) = 220 - 50

(40C - 6C) + (5S - 5S) = 220 - 50

34C = 170

C = 5

Substitute C into either equation to solve for S.

Day 1:

6C + 5S = 50

6(5) + 5S = 50

30 + 5S = 50

5S = 50 - 30

5S = 20

S = 4

Day 2:

8C + 1S = 44

8(5) + 1S = 44

40 + 1S = 44

1S = 44 - 40

S = 4

We have the identity

[tex](a + b)^2 = a^2 + 2ab + b^2 = a^2 + ab + b (a + b) \\\\ ~~~~ \implies a + b = \sqrt{a^2 + ab + b (a + b)} \\\\ ~~~~ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{\cdots}}}}[/tex]

assuming [tex]a+b\ge0[/tex].

For the numerator, let [tex]b=1[/tex], so [tex]a\ge-1[/tex], which means

[tex]a^2 + a = x \implies a = \dfrac{-1 + \sqrt{1 + 4x}}2[/tex]

and so

[tex]\sqrt{x + \sqrt{x + \sqrt{x + \sqrt{\cdots}}}} = \dfrac{-1 + \sqrt{1 + 4x}}2 + 1 = \dfrac{1 + \sqrt{1 + 4x}}2[/tex]

For the denominator, let [tex]b=-1[/tex] so that [tex]a\ge1[/tex]. Now

[tex]a^2 - a = x \implies a = \dfrac{1 + \sqrt{1 + 4x}}2[/tex]

so that

[tex]\sqrt{x - \sqrt{x - \sqrt{x - \sqrt{\cdots}}}} = \dfrac{1 + \sqrt{1 + 4x}}2 - 1 = \dfrac{-1 + \sqrt{1 + 4x}}2[/tex]

So, in the integral we can simplify and evaluate it to

[tex]\displaystyle \int_0^{2021} \frac{\sqrt{x + \sqrt{x + \sqrt{x + \sqrt{\cdots}}}}}{1 + \sqrt{x - \sqrt{x - \sqrt{x - \sqrt{\cdots}}}}} \, dx \\\\ ~~~~~~~~ = \int_0^{2021} \frac{\frac{1 + \sqrt{1 + 4x}}2}{1 - \frac{1 - \sqrt{1+4x}}2} \, dx \\\\ ~~~~~~~~ = \int_0^{2021} \frac{1 + \sqrt{1 + 4x}}{1 + \sqrt{1 + 4x}} \, dx \\\\ ~~~~~~~~ = \int_0^{2021} dx = \boxed{2021}[/tex]

a > 4 for which the solutions of the inequality are all real numbers.

It is an expression mathematical that represents a non-equal relationship between a number or another algebraic expression. Therefore, it is common the use following symbols: ≤ (less than or equal to), ≥ (greater than or equal to), < (less than), and > (greater than).

The solutions for inequalities can be given by: a graph in a number line or numbers.

For solving this exercise, it is necessary to find a  for the given inequality.

a(x+3) < 5x+15-x

a(x+3) < 4x +15

ax+3a < 4x+15

Subtract 3a from both sides

ax+3a -3a< 4x+15-3a

ax < 4x+15-3a

ax-4x < 15-3a

x(a-4) < 15-3a

[tex]x < \frac{15-3a}{a-4}[/tex]

Like there is a variable a in the denominator, a-4 >0, then a>4.

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The required solution of the given expression is -9.

A straight line with numbers placed at equal intervals or segments along its length. Number line is a straight line with a "zero" point in the middle, with positive and negative numbers listed on either side of zero and going on indefinitely.

Given:

The given expression is

-2-(+7)

According to given question we have

Number line is a line with 0 in the middle, and then increasing positive numbers to the right of the 0 and decreasing negative numbers to the left of the 0. The line is infinite in length and it's not possible to show the whole line, but we will illustrate where on the line 9 and -9 are located.

-2-(+7)

=-2-7

=-9

Therefore, the required solution of the given expression is -9.

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The value of c from the equation is 2

The absolute value of a number can be defined as the non -negative value of a number irrespective of its sign.

It is known as the distance of a number from zero without consideration of its sign.

It is also known as the modulus of a number.

It is denoted with the symbol, " | | "

Given the expression;

∣−c+12∣= 14

find the absolute value

c + 12 = 14

collect like terms

c = 14 - 12

c = 2

Thus, the value of c from the equation is 2

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Macro bought 175 pens

The number of pens Macro bought can be calculated as follows

let x represent the number of pens bought

let y represent the number of pencils bought

x + y = 300.........equation 1

0.25x + 0.15y= 62.50.........equation 2

From equation 1

x + y= 300

x= 300-y

Substitute 300-y for x in equation 2

0.25(300-y) + 0.15y= 62.50

75 - 0.25y + 0.15y= 62.50

75 - 0.1y= 62.50

-0.1y= 62.50-75

0.1y= 12.5

y= 12.5/0.1

y= 125

Substitute 125 for y in equation 1

x + y= 300

x + 125= 300

x= 300-125

x= 175

Hence Marco bought 175 pens

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Answer:

Step-by-step explanation:

Compound Interest Formula

The Amount A after t years due to a principle P invested at an annual interest rate r compounded n times per year

Compounded Quartely means 4 times per year

A = P(1 + r/n)^nt

A= 13000(1 + 0.04/4)^4(7)

A = 13000(1 + 0.01)^28

A = 13000(1.01)^28

A = 13000(1.321290967)

A = 17176.78|257

A ≈ 17,176.78

Boys: 2, Girls: 5

There are 6 boys and 15 girls.

If there were 5 boys and 15 girls, the ratio would go to 1 to 3

But this is 6 boys to 15 girls

Final answer: 2:5

Work Shown:

x = number of people in week 3

280/x = 4/3

280*3 = 4*x

x = 280*3/4

x = 210

Answer:

0.5b + 4 = 2(b + 2)

0.5b + 4 = 2b + 4

0.5b - 2b = 4 - 4

-1.5b = 0

b = 0/-1.5

b = 0