8. Calculate the probability of getting red queen & probability of getting black card from a well suffled deck.​

Based on the mathematical statements, Zoe is 56 years old and Luke is 66 years old, now

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

30 years ago

Zoe was 2/3 as old as Luke

18 years ago

Zoe was 5/6 as old as Luke

Let their present ages be represented as

Zoe = x

Luke = y

So, we have the following representations

30 years ago

Zoe was 2/3 as old as Luke

x - 36 = 2/3(y - 36)

18 years ago

Zoe was 5/6 as old as Luke

x - 18 = 5/6(y - 18)

So, we have the following system of equations

x - 36 = 2/3(y - 36)

x - 18 = 5/6(y - 18)

Make x the subject in x - 18 = 5/6(y - 18)

x = 5/6(y - 18) + 16

Substitute x = 5/6(y - 18) + 16 in x - 36 = 2/3(y - 36)

5/6(y - 18) + 16 - 36 = 2/3(y - 36)

Open the brackets

5/6y - 15 + 16 - 36 = 2/3y - 24

Evaluate the like terms

5/6y - 35 = 2/3y - 24

Multiply through by 6

5y - 210 = 4y - 144

Evaluate the like terms

y = 66

Substitute y = 66 in x = 5/6(y - 18) + 16

x = 5/6(66 - 18) + 16

Evaluate

x = 56

Recall that

Zoe = x

Luke = y

So, we have

Zoe = x = 56

Luke = y = 66

Hence, they are 56 and 66 years, now

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Answer:

second option

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = - [tex]\frac{2}{3}[/tex] and (a, b ) = (1, - 7 ) , then

y - (- 7) = - [tex]\frac{2}{3}[/tex] (x - 1) , that is

y + 7 = - [tex]\frac{2}{3}[/tex] (x - 1)

Answer:i think the answer is 2/4 or 3/2

Step-by-step explanation:

Using the simplification, the value of u is 13/15.

In the given question we have to find the value of u.

The given expression is -1/2u+3/5=1/6

Simplifying the given expression to find the value of u.

-1/2u+3/5=1/6

Subtract 3/5 on both side, we get

-1/2u=1/6-3/5

Now equal the denominator to simplify

-1/2u=1/6 *30-3/5 *30

-1/2 *30u=5-3*6

-15u=5-18

-15u= -13

Divide by -15 on both side, we get

u = 13/15

Hence, the value of u is 13/15.

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Answer:

1.2

Step-by-step explanation:

3/2 ÷ 1 1/4

Answer:

1.2

Step-by-step explanation:

Just did it on khan academy.

The money spent by Mr. Dunston is $ 35.

Given that:-

Money spent by Mr. Dunston and Mr. Dolland = $ 45

Money spent by Mr. Dunston and Ms. Campbell = $ 65

Ms. Campbell spent 3 times as much as Mr. Dolland.

We have to find the money spent by Mr. Dunston.

Let the money spent by Mr. Dunston be $ x,

Let the money spent by Mr. Dolland be $ y and,

Let the money spent by Ms. Campbell be $ 3y

Hence, from the data given in the question, we can write,

x + y = 45  ...(1)

x + 3y = 65 ... (2)

By elimination method, we can write,

(2) - (1)

2y = 20

y = 10

x + 10 = 45

x = 45 - 10 = 35

x = 35

Hence, the money spent by Mr. Dunston is $ 35.

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The answer will be the graph of the straight line.

What is the equation straight line?

Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.

Using the equation we can plot the graph in 2D.

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The probability that a random sample of 20 second grade students from the city results in a mean reading rate of more than 97 words per minute is; 0.012676.

This z-score is used to tell us the number of standard errors that exists between the sample mean and the population mean.

The formula for z-score here is;

z = (x' - μ)/(σ/√n)

where;

x' is sample mean

μ is population mean

σ is standard deviation

n is sample size

We are given;

Sample mean; x' = 97

Population mean; μ = 91

Standard deviation; σ = 10

Sample size; n = 20

Thus;

z = (x' - μ)/(σ/√n)

z = (97 - 91)/(10/√20)

z = 2.236

From online p-value from z-score calculator, we have;

p = 0.012676

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Complete question is;

The reading speed of second grade students in a large city is approximately​ normal, with a mean of 91 words per minute​ (wpm) and a standard deviation of 10 wpm.

what is the probability that a random sample of 20 second grade students from the city results in a mean reading rate of more than 97 words per minute

Ray have to jog 1.53 hours to burn the calories he had taken by eating doughnut and latte.

Given,

The amount of calorie burns while jogging = 745 calories

The amount of calorie in Doughnut = 320 calories

The amount of calorie in latte = 820 calories

Here,

Total calorie intake by Ray = 320 + 820 = 1140

The calorie burnt while jogging = 745

Number of hours Ray needs to jog for burning 1140 calories;

1140/745 = 1.53 hours.

That is,

Ray have to jog 1.53 hours to burn the calories he had taken by eating doughnut and latte.

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The measure of the angle 1, angle 2, angle 3 is 68°, 94°, 25° respectively.

What is angle?

An angle is created where two straight lines or rays meet at a single point. The point from where two lines converge is known as an angle's vertex. The name "angle" comes from the Latin word "angulus," which meaning "corner."

Let's firstly find angle 1,

We  know that, the sum of the all three angles of a triangle is 180°.

So,

18° + 94° + angle 1 = 180°

112° + angle 1 = 180°

angle 1 = 180° - 112°

angle 1 = 68°

Now, we know that, opposite angle are always equal

Therefore,

angle 2 = 94°

Now, again applying the property of triangle that sum of all three angles are equal:

Therefore,

angle 3 + angle 2 + 61° = 180°

angle 3 + 94° + 61° = 180°

angle 3 = 25°

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Answer:

15 more appetizers

Step-by-step explanation:

A restaurant has 60 menu items. Of these menu items, main dishes outnumber appetizers by a ratio of 4:1. How many more appetizers would the restaurant have to add to the menu to bring the ratio to 2:1?

at a ratio of 4e:1a and having 60e: there are (60/4=15) 15 appetizers

at a ratio of 2e:1a and having 60e: there are (60/2=30) 30 appetizers

Because they already have 15 appetizers, they will need:

30 appetizers - 15 appetizers  = 15 more appetizers

lynn got the better deal than Roger.

percentage, a relative value indicating hundredth parts of any quantity.

Given,

lynn bought a new crash cymbal for her drum set. it costs 120$ but she received a 15% student discount.

Convert 15% to decimal form

15%=15/100=0.15

0.15×120=18

So 15% of 120 is 18.

Iynn bought crash cymbal for her drum set is 120-18=102

Roger bought the same crash cymbal from another store for$130

Roger applied coupon of $25.

So 130-25=$105

When we compare both Iynn and Roger, Iynn got the crash cymbal for a better deal.

Hence lynn got the better deal than Roger.

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Answer:

2

Step-by-step explanation:

This is because yes. If you add 1 and 1 (use your fingers) and count the two, you simply get 2.

The surface area of a cube with a side length of 10 cm is 600 [tex]cm^{2}[/tex].

Given:

The formula for finding the surface area of a cube is 6s2.

side length s = 10 cm.

Surface area of a cube =  6[tex]s^{2}[/tex] = 6*s*s

= 6 * 10 * 10

= 60 * 10

= 600 [tex]cm^{2}[/tex].

Therefore the surface area of a cube with a side length of 10 cm is 600 [tex]cm^{2}[/tex].

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The equation that represents the cost of the pizza is 10x where x is the cost of one slice of pizza and the value of x is $15.

According to the question,

We have the following information:

Tara eats 3 of the 10 slices and pays $4.50 for her share.

Now, let's take the cost of one slice of the pizza to be $x.

So, we have the following expression:

3x = 4.50

Dividing by 3 on both sides of the equation:

x = 4.50/3

x = $1.50

Now, there are 10 slices in pizza.

Cost of pizza = 10x

Cost of pizza = 10*1.50

Cost of the pizza = $15

Hence, the equation that represents the cost of the pizza is 10x where x is the cost of one slice of pizza and the value of x is $15.

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The calculation of the ratios, resulting from the square feet occupied by Departments A and B, and the amounts of allocated overhead costs to the two departments are as follows:

                           Ratio      Amount

Department A       1/5        $10,000

Department B      4/5       $40,000

The ratio is the relative value relationship shared by two or more numbers.

Ratios are fractional values depicted in fractions, decimals, and percentages.

Like proportions, ratios show how much a value or variable is contained in another.

Total overhead = $60,000

Department   Square Feet  Ratio    Amount of Overhead Allocated

Dept. A            10,000         A = 1      B = $15,000 ($60,000 x 1/4)

Dept. B            30,000         = 3     D = $45,000 ($60,000 x 3/4)

Ratios = 10,000:30,000

= 1:3

Sum of Ratios = 4

Thus, based on the ratios, Department A is allocated $15,000, while Department B will be allocated $45,000 of the distributable overhead costs.

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Answer:

v = 99

Step-by-step explanation:

given v varies directly as g then the equation relating them is

v = kg ← k is the constant of variation

to find k use the condition v = 36 when g = 4 , then

36 = 4k ( divide both sides by 4 )

9 = k

v = 9g ← equation of variation

when g = 11 , then

v = 9 × 11 = 99

Answer:

Step-by-step explanation:

Solution

Solve with the quadratic formula 

3k2+k−3=0    :    k=(−1+√376)/6 , k=(−1−√376 )/6   (Decimal:    k=0.84712…, k=−1.18046…)- Answer

Steps

3k2+k−3=0

Solve with the quadratic formula

For a quadratic equation of the form ax^2+bx+c=0,

the solutions are x1, 2=(−b±√b^2−4ac)/2a  where    a=3, b=1, c=−3 

Substituting we have

k1, 2= [(−1±√1^2−4· 3(−3)]/2· 3 

Apply rule 1^a=1 , therefore 1^2=1

=√1+4· 3· 3=√1+36

√1^2−4· 3(−3)=√37

Therefore,

k1, 2=(−1±√37)/2· 3 

k1, 2=(−1±√37)/6 

Separate the solutions

k1=(−1+√37)/6 

k2=(−1−√37)/6 

The solutions to the quadratic equation are:

k=(−1+√37)/6 , k=(−1−√37)/6 

k1=0.84712        k2=−1.18046

Any number between -7 and 7 can be located in the number line.

The number line is a horizontal line that has equally spread number increments.

Given a number line, suppose we plot -5 on it, which is between -7 and 7

Then, its position will be 5 units left of 0 on the number line.

Hence, -5 is the point between -7 and 7 on the number line, which is 5 units left on 0.

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Answer:

y = -338

Step-by-step explanation:

[tex]-26 = \dfrac{y}{13}[/tex]

Multiply by 13 on both sides.

[tex]-26 \cdot 13 = y[/tex]

[tex]-338 = y[/tex]

y = -338

Answer:

-338

Step-by-step explanation:

-26=y/13

cross multiplying

y=-26×13

y=-338

Answer:

36,288

Step-by-step explanation:

The percentage increase for each of the given figures are;

a) 6%

b) 6%

c) 12%

Percentage increase is simply defined as the percentage by which a figure increases. The formula to calculate percentage increase is;

Percentage increase = (Final value - Initial Value)/initial value) * 100%

a) We are given;

Original quantity = 100

New quantity = 106

Thus;

Percentage increase = (106 - 100)/100 * 100%

Percentage increase = (6/100) * 100%

Percentage increase = 6%

b) We are given;

Original quantity = 10

New quantity = 16

Thus;

Percentage increase = (16 - 10)/10 * 100%

Percentage increase = (6/10) * 100%

Percentage increase = 60%

c) We are given;

Original quantity = 50

New quantity = 56

Thus;

Percentage increase = (56 - 50)/50 * 100%

Percentage increase = (6/50) * 100%

Percentage increase = 12%

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Complete question is;

Find the percent increase for the given original and new quantities in parts a through c.

a) Original quantity:100 New quantity:106

b) Original quantity:10 New quantity:16

c) Original quantity:50 New quantity:56

The number of yes votes on whether to raise property taxes, using proportions, was of 3345, considering that 6183 total votes.

A proportion is a fraction of a total amount, and equations are built with these fractions and the rates in the context of a problem to find the desired measures in the problem using basic arithmetic operations such as multiplication and division.

One application of proportions is for ratio problems, as one ratio between two amounts a and b is given by the division of a by b, and over the total, these rates are:

The ratio of yes votes to no votes was 5 to 4, hence the fraction of yes votes is given as follows:

5/(5 + 4) = 5/9.

The total number of votes was of 6183, hence the number of yes votes is calculated as follows:

5/9 x 6183 = 3435 total yes votes.

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Answer:

3x-3:

(1/3)(9x-9)

(9/2x - 2) -(3/2x +1)

(3/2x-2) + (3/2x-1)

2x-1:

(7/2 x -2) - (3/2 x - 1)

1/2(4x-2)

Step-by-step explanation:

(7/2 x -2) - (3/2 x - 1)

7/2 x -2 -3/2 x +1 Distribute the negative sign to both terms

4/2 x -1 Combine like terms

2x-1

(1/3)(9x-9)

3x-3 Distributive property

(9/2x - 2) -(3/2x +1)

9/2x -2 -3/2x -1 Distribute negative sign

6/2x -3

3x-3

(3/2x-2) + (3/2x-1)

3/2x -2 +3/2x -1 Can just get rid of parenthesis since everything is added.

6/2x -3

3x-3

1/2(4x-2)

2x-1 Distribute the 1/2 to both numbers

Answer:  12/0

Step-by-step explanation:  (5−3)(2)+8

(2)(3)−7+1

=

(2)(2)+8

(2)(3)−7+1

=

4+8

(2)(3)−7+1

=

12

(2)(3)−7+1

=

12

6−7+1

=

12

−1+1

=

12

0

=

1

0

;)

120 ounces of 35% salt and 90 ounces of water is needed to obtain 210 ounces of a mixture that is 20% salt.

An equation shows the relationship between two or more numbers and variables.

Let x represent the amount of water and y represent the amount of 35% solution.

She wants to obtain 210 ounces of a mixture that is 20% salt. Hence:

x + y = 210   (1)

Also:

0% of x + 35% of y = 20% of 210

0.35y = 42

y = 120

x + y = 210

x + 120 = 210

x = 90

120 ounces of 35% salt and 90 ounces of water

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Answer:

1.342

Step-by-step explanation:

4^x+64^x=272

4^x+(4^3)^x=272

4^3x+4^x=272

(4^x)^3+4^x=272

(4^x)^3+4^x-272=0

u^3+u-272=0 ==> substitute 4^x with u

Now, use synthetic division to find roots:

[tex]\sqrt[3]{272}[/tex]31   |    1    0              1             -272

                       [tex]\sqrt[3]{272}[/tex]1     [tex]\sqrt[3]{272^2}[/tex]      272

                 1    [tex]\sqrt[3]{272}[/tex]1      [tex]\sqrt[3]{272^2}[/tex]       0

4^x=[tex]\sqrt[3]{272}[/tex]

log 4 (4^x)=log 4 ([tex]\sqrt[3]{272}[/tex])=1.342

If Jolyn scores 48 points, and the z-score of this value is 3, then her mean points in this normally distributed game is equal to 27.

In a normal distribution, the relative score or z-score can be calculated by using this formula:

[tex]z=\frac{x\;-\;u}{\sigma}[/tex]

Where:

Making mean (μ) the subject of formula, we have:

μ = x - zσ  x

Substituting the given parameters into the formula, we have;

Mean point, μ = 48 - (3 × 7)

Mean point, μ = 48 - 21

Mean point, μ = 27.

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For the given number of loaves of white and brown bread , the inequality representation of the problem is given by (x + y ) ≤ 900.

As given in the question,

Types of bread baked in bakery = 2 types

Let x represent the number of loaves of white bread

And y represent the number of loaves of brown bread

Total number of loaves which can be stored in the store room is less than or equal to 900.

For the given situation representation of inequality is given by:

x + y ≤ 900

Therefore, for the given number of loaves of white and brown bread , the inequality representation of the problem is given by (x + y ) ≤ 900.

The complete question is :

Betty's bakery bakes white bread and brown bread. The loaves of bread are then stored in a store room that can house only 900 loaves. The loaves are baked during the day, and in the evening they are delivered to convenience stores. At all times, the number of loaves in the store room must be less than or equal to 900. Part A Assuming x to be the number of loaves of white bread and y to be the number of loaves of brown bread, how would the problem be represented in the form of an inequality?

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