Jake had of a cake. He gave
6
2
4
of it to his friend at lunch. How
much more cake does Jake have
left?

Step-by-step explanation:

your question is strange.

first you tell us that 50 people like coffee, 25 like tea, and 13 like both.

and then you ask how many like coffee or tea or both.

is this a joke ? or do you rather mean how many like only coffee, or only tea, and how many don't like neither ?

since 13 people like coffee and tea, these 13 are also part of the group of 50 that like coffee, and of the group of 25 that like tea.

so, to get the number of people that like only one, we need to deduct the number of people, who like both from both groups.

the number of people that only like coffee is therefore

50 - 13 = 37

and the number of people that only like tea is

25 - 13 = 12

we know the number of people that like coffee and tea is 13.

together that are

37 + 12 + 13 = 62 people.

that means 70 - 62 = 8 people don't like neither coffee nor tea.

Answer: 62

Step-by-step explanation:

Those who like coffee only = 50 - 13 = 37. Those who like tea only = 25 - 13 = 12. Those who like either coffee, or tea, or both = 37 + 12 + 13 = 62.

In theory, the 70 people being surveyed could fall under any of the following four categories:

I have labelled the four categories 1, 2, 3 and 4 for convenient reference.

From the information provided in the question, category 1 contains 50 people, category 2 contains 25 people, while category 3 contains 13 people. We do not yet know how many people fall under category 4, but we shall calculate it.

We know from set theory that the four aforementioned categories are known formally as sets. A set is simply a group of objects or things that are similar in some way. Each of the objects in a set is called a member of that set. Two sets can intersect. The intersection of two sets is simply the collection of members that are in both of the two sets. Also, two sets can unite. The union of two sets is the collection of members that in either of the two sets.

For example, category 3 is the intersection of category 1 and 2. The question requires us to calculate the union of category 1 and 2.

Answer:

Slope is undefined. { Infinity }

Step-by-step explanation:

Formula we use,

→ Slope(m) = (y2 - y1)/(x2 - x1)

Now required slope will be,

→ m = (y2 - y1)/(x2 - x1)

→ m = (8 + 12)/(17 - 17)

→ m = 20/0

→ [ m = 0 ]

Hence, the slope is undefined.

The slope of the line passing through the points ( 17 , -12 ) and ( 17 , 8 ) is undefined

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 17 , -12 )

Let the second point be Q ( 17 , 8 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 8 - ( -12 ) ) / ( 17 - 17 )

On simplifying the equation , we get

Slope m = ( 8 + 12 ) / 0

Slope m = 20 / 0

So , the slope is undefined

Hence , the slope of the line is m = undefined

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Answer:

P=-15

Step-by-step explanation:

P-12=-27  |+27

P+15=0

P=-15

In the given equation, the coefficient of b is 183/23 and the constant coefficient is -30.

The given equation is 8b= b/23 +30.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Now, 8b= b/23 +30

⇒ 8b-b/23 -30=0

⇒ 8b-b/23 -30=0

⇒ 183b/23 -30=0

Here, the coefficient of b is 183/23 and the constant coefficient is -30.

Therefore, in the given equation, the coefficient of b is 183/23 and the constant coefficient is -30.

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Answer:

0.38

Step-by-step explanation:

imagine a circle, with C being the center, and 13 being the radius.

the triangle is then representing the trigonometric functions. remember, they are all multiplied by the radius as the circle is much higher than the norm circle (radius 1).

so,

5 = sin(C) × 13

sin(C) = 5/13 = 0.384615385... ≈ 0.38

Answer:

D) [tex]f^{-1}(x)=(x-3)^2+2[/tex]

Step-by-step explanation:

[tex]f(x)=\sqrt{x-2}+3 \implies x=\sqrt{f^{-1}(x)-2}+3 \\ \\ x-3=\sqrt{f^{-1}(x)-2} \\ \\ (x-3)^2=f^{-1}(x)-2 \\ \\ f^{-1}(x)=(x-3)^2+2[/tex]

Note we take the positive case because the domain of the original function is the same as the range of the inverse, and the domain of [tex]f(x)[/tex] is [tex][2, \infty)[/tex].

So our goal is to determine the mean test score, which we don't know, we know to raw scores, we know one raw score is 38 that's one standard deviation below the mean, which by definition of a Z score that Z equals negative one. one

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The values that make the inequality true are (a) 2.11 (c) 1.1 and (d) 1.63

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

0.3m ≥ 0.55-0.2m

Evaluate the like terms

0.5m ≥ 0.55

Divide both sides by 0.5

So, we have the following representation

m ≥ 1.1

This means that the true values are at least 1.1

In this case, they are 1.1, 1.63 and 2.1

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Answer:

Hope the picture will help you

Answer:

height = 4cm

Step-by-step explanation:

volume of right-circular cylinder = πr²h

h = r

so

πr²r or πr³

πr³ = 64π

r³ = 64

r = 4

h = 4

it would be inconsistent. Meaning it won't have a solution

Answer:

Step-by-step explanation:

13

Answer: 13

Step-by-step explanation:

I hope it helps

The slope of the line that passes through the given two points is m = 26/25.

Consider a line that passes through the points (x1, y1) and (x2, y2).

So, the slope of the line is calculated by

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

The given line passes through points (1, 3) and (26, 29).

So, we can consider (x1, y1) = (1, 3) and (x2, y2) = (26, 29).

Then, the slope of the line is

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

   = (29 - 3)/(26 - 1)

   = 26/25

Therefore, the slope of the given line is 26/25.

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Answer:

19°

Step-by-step explanation:

m<A + m<B + m<C = 180°

a + 17° + 49° + 5a = 180°

6a + 66° = 180°

6a = 114°

a = 19°

Answer: y = -5/6x - 23/6

(Read the explanation first to make sure it's correct)

Step-by-step explanation:

A parallel line means that it has the same slope as the equation:

5x + 6y = 11

Let's first convert this standard form equation into slope-intercept form:

y = -5/6x + 11/6

So that means that our new line also has a slope of:

-5/6

So far, for our new equation we have:

y = -5/6x + b

Next, let's plug in the values of our point to the equation:

-3 = 5/6 + b

So b = -23/6

So the equation in slope-intercept form is:

y = -5/6x - 23/6

The required values of x and y are x = 2 and y = 11.

We have been given that parallelogram PQRS which has:

PT = ​y, TR = 5x+​1, QT = 2​y, TS = 6x+10

We know that the diagonals of a parallelogram bisect each other.

So, PT = TR and QT = TS

Substitute the values and we have a system of equations:

y = 5x + ​1    ....(i)

2y = 6x + 10 ....(ii)

Substitute the value of the equation y = 5x + ​1 in equation (ii), and solve for x

2(5x + ​1) = 6x + 10

10x + 2 = 6x + 10

10x - 6x = 10 - 2

4x = 8

x = 8/4

x = 2

Substitute the value of x = 2 in equation (i), and solve for y

y = 5(2) + ​1

y = 10 + 1

y = 11

Therefore, the required values of x and y are x = 2 and y = 11.

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x=7/6

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

Answer: width is 13.5 cm

Step-by-step explanation:

9 x 2 +2x =45

45-18

2x=27

2x/2=27/2

x=13.5

width is 13.5 cm

The solution for this system of linear equations are x=-18 y=-71

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here: 3x+2y=1

                  −x+5y=−23

[tex]\left[\begin{array}{ccc}3&2\\-1&5&\\\end{array}\right][/tex]  . [tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex]  = [tex]\left[\begin{array}{ccc}1\\-23\\\end{array}\right][/tex]

                      [tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex]   =   [tex]\left[\begin{array}{ccc}5&1\\-2&3&\\\end{array}\right][/tex] . [tex]\left[\begin{array}{ccc}1\\-23\\\end{array}\right][/tex]

                       [tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-18\\-71\\\end{array}\right][/tex]

Hence, The solution for this system of linear equations are x=-18 y=-71

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The solution is, 12000 pound was the ball's actual weight.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

given that,

While on vacation in Missouri, Sue's family stopped to see the world's largest ball of nylon twine.

Before they got there, Sue predicted the ball would weigh 6,000 pounds.

Her prediction was 50% less than the actual weight of the ball.

let, the ball's actual weight = x

now, 50% of x = x/2

ATQ, x/2 = 6,000 pounds.

so, x = 12000

Hence, The solution is, 12000 pound was the ball's actual weight.

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Answer:

  yes

Step-by-step explanation:

You want to know if a function can have the characteristic that the limit at a point does not exist, but the function is defined at that point.

A function has no limit at a point if the limit from the left is different from the limit approaching from the right.

Consider the sign function ...

  [tex]\text{sign}(x)=\begin{cases}-1,&x < 0\\0,&x=0\\1,&x > 0\end{cases}[/tex]

The left limit as x → 0 is -1; the right limit as x → 0 is +1, so the limit as x → 0 "does not exist." However, the function is defined at x=0.

The function is defined everywhere, but the limit as x→0 does not exist.

The population of the city after eight years is 35,125,731,743

Population growth is the increase in the number of people in a population or dispersed group. The expression P(t) = P(o)(1+r)^t can be used to determine the growth rate of a population.

Where P(t) is the population at a particular time

P(o) is the initial population , t is the time and r is the growth rate.

Here the growth rate has been given, but we are to find p(t).

P(t) = 330,000(1+3.25)⁸

P(t) = 330,000(4.25)⁸

P(t) = 330,000× 106441.61

P(t) = 35,125,731,743( nearest billion)

Therefore the population of the city after 8years is 35,125,731,743

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Answer:10

Step-by-step explanation:3/5x10=6

The price of the pipette for company A and company B will be $480 and $420, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

A research facility supervisor was keen on purchasing another pipette. Organization A was selling 2 pipettes for £300 not as much as Organization B was selling 3 pipettes for. For a solitary pipette, Organization A was more costly by £60 than Organization B.

Let 'x' be the price of the pipette of company A and 'y' be the price of the pipette of company B. Then the equations are given as,

2x = 3y - 300         ...1

x = y + 60                 ...2

From equations 1 and 2, then we have

2(y + 60) = 3y - 300

2y + 120 = 3y - 300

y = 420

Then the value of x is given as,

x = 420 + 60

x = 480

The price of the pipette for company A and company B will be $480 and $420, respectively.

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The stated statement indicates that the takt time is 5.38 minutes for each section.

Takt time is calculated as the amount of manufacturing time that is available divided by the volume of orders. Takt time, for instance, is two minutes if a factory makes widgets for 480 minutes a day and clients need 240 widgets per day. Similar to this, the takt time is one week if clients desire two new goods per month.

Takt time depends on client demand and the amount of time that is available, and for many items, it is always changing as the demand from the market shifts. Takt time is unaffected by system changes, although cycle time is affected.

Available hours are 7 * 60 minutes, which is 420 minutes.

No. of parts = 78 units

Available time for work / No of parts = Takt time

               = 420/ 78

               = 5.38 minutes per part

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Answer:

Hope the picture will help you

The solution of the inequality will be;

⇒ x > 5

And, The solution is shown on number line.

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality is,

⇒ - 2/5x < - 2

Now,

Solve the inequality as;

⇒ - 2/5x < - 2

⇒ - 2x < - 2 × 5

⇒ - 2x < - 10

Multiply by - 1,

⇒ 2x > 10

⇒ x > 5

Thus, The solution of the inequality = x > 5

And, The solution is shown on number line in figure.

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After solving the equation, we can conclude that Callie should rent the bicycle for a maximum of 3 hours.

The equals sign is indeed a symbol used in mathematical formulas to denote the equality of two reactions.

Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions.

For example, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.

So, according to the given information, form the equation as follows:

12x + 10 = 45

Where x is the number of hours Callie rents the cycle.

Now, calculate for x as follows:

12x + 10 = 45

12x = 45 - 10

12x = 35

x = 35/12

x = 2.91

Rounding off: 3

Therefore, after solving the equation, we can conclude that Callie should rent the bicycle for a maximum of 3 hours.

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Complete question:

Callie is on vacation and wants to rent a bicycle to explore the town. She pays a $10 flat fee and then $12 per hour for the rental.

If Callie has $45 to spend, what is the greatest number of full hours she can rent the bicycle?

The factored form of the polynomial x + 9x + 20 is (x + 4)(x + 5). To obtain this form, we can use the factoring method known as "FOIL," which stands for "First, Outer, Inner, Last." This method involves multiplying the first terms, the outer terms, the inner terms, and the last terms of the two factors to obtain the original polynomial.

In this case, if we let the factors be (x + 4) and (x + 5), we can use FOIL to multiply them and obtain the following:

(x + 4)(x + 5) = (x * x) + (4 * x) + (x * 5) + (4 * 5)

This simplifies to:

(x + 4)(x + 5) = x^2 + 9x + 20

As we can see, the result is the original polynomial. Therefore, the factored form of x + 9x + 20 is (x + 4)(x + 5)

The value of the factored form of the polynomial are,

⇒ (x + 4) (x + 5)

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

The polynomial are,

⇒ x² + 9x + 20

Now, We can simplify as;

⇒ x² + 9x + 20

⇒ x² + 5x + 4x + 20

⇒ x (x + 5) + 4 (x + 5)

⇒ (x + 4) (x + 5)

Thus, The value of the factored form of the polynomial are,

⇒ (x + 4) (x + 5)

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