After a certain number of people entered an empty room, 2/3 of the people who’d entered the room leave. After 2 more people leave, 1/4 of the original number of people who entered the room remain. What was the original number of people who entered the empty room?

Answer:

SV = 13

Step-by-step explanation:

• the opposite sides of a parallelogram are congruent , so

UV = ST , that is

4x - 1 = 19 ( add 1 to both sides )

4x = 20 ( divide both sides by 4 )

x = 5

Then

TU = 2x + 3 = 2(5) + 3 = 10 + 3 = 13

SV = TU = 13

The 5:3 (5 to 3) ratio of the number of Almond Joys candy to Kit kats candy, and the 40 Almond Joys candies stashed, indicates that the number of Kit kandies also received are 24 Kit Kats candies.

A ratio is an indication of the number of times one quantity is contained within another item.

The ratio of the Almond Joys to the Kit Kats = 5 : 3

The number of Almond Joys obtained = 40

The number of Kit Kats obtained can be found as follows;

The number of Almond Joys received for every 3 Kit Kats received = 5

Let x represent the total number of candies collected, we get;

[tex]\frac{5}{5+3} \times x = 40[/tex]

Therefore;

5·x = 40 × (5 + 3) = 320

x = 320 ÷ 5 = 64

The total number of candies collected = 64

The number of Kit Kats = The total number of candies collected - The number of Almonds Joys received

Therefore; The number of Kit Kats received = 64 - 40 = 24

The number of Kit Kats received = 24 Kit Kats

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You will have 24 Kit Kats based on the information given.

A ratio is defined as the comparison of two or more quantities that indicates their sizes in relation to each other.

From the information, after a long night of begging for candy, the person ended up having a decent stash of Almond Joys and Kit Kals in the ratio of 5:3.

Since Almond Joys and Kit Kats  are in the ratio of 5:3 and you had Almond Joys. Let K represent the number of Kit Kats. Then we have:

5 : 3 = 40 : K

5/3 = 40/K

5K = 3 × 40

5K = 120

K = 120/5

K = 24

Thus, you will have 24 Kit Kats

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There are various rules for plotting a graph which includes having scale over X and Y axis.

The options for vertical bar charts are shown below. For horizontal bar charts, swap out "vertical" for "horizontal" and "horizontal" for "vertical."

1. A title ought to be at the top of the graph.

2. The vertical axis' scale has to be consistent and set to 0.

3. Utilise horizontal gridlines.

4. Each bar's definition ought to be listed on its label.

5. The label for the horizontal axis should include a description of the qualitative variable that the bar chart represents. In the event if the labels on each individual bar are sufficiently illustrative, a horizontal axis label is not required.

6. It should say "Count" or "Frequency" on the vertical axis.

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Answer:

25 cashiers

Step-by-step explanation:

To solve this, you can multiply the number of cashiers at 10:00 am (20) by 1 1/4, which is the same as multiplying by 5/4.

20 x 5/4 = 25

So, there are 25 cashiers at 4:00 pm.

You can confirm this by dividing 25 by 5/4 to see if it equals 20:

25 * 4/5 = 20

Therefore, there are 25 cashiers at 4:00 pm.

Answer:

y = [tex]\frac{6}{4}[/tex] or [tex]\frac{3}{2}[/tex]

Step-by-step explanation:

Since we are given x=1, we can plug that into the equation given:

-4y + [tex]\sqrt[3]{1}[/tex] = -6(1) + [tex]1^{2}[/tex]

-4y + 1 = -6 + 1

-4y = -6

y = [tex]\frac{-6}{-4}[/tex]

y = [tex]\frac{6}{4}[/tex] or [tex]\frac{3}{2}[/tex]

Answer:

Step-by-step explanation:

The solution of the inequality is x < -50.

And we can use the substitution method to find the solution of the inequality.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

An inequality 100 - 3x < -50.

Diego first solves the equation and sees that x = 50.

So, substituting the value of x to the inequality.

100 - 3(-50) < -50.

100 - 150 < -50

-50 < -50.

To find the solution of the inequality:

100 - 3x < -50.

-3x < -50 -100

x < - 50

Therefore, the solution of the inequality is x < -50.

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Part 1: The percentage of the purchase price to the sale price is 83.3%.

Part 2: The number of jackets the small store owner must sell to make $260 in total sales is 5.

The percentage refers to the ratio of one value compared to another.

Percentages are computed as the quotients of a numerator divided by the denominator, multiplied by 100.

Purchase price of coats per unit = $55

Selling price per unit = $66

Markup = $11 ($66 - $55) or 20% ($11/$55 x 100)

Margin = 16.7% ($11/$66 x 100)

Percentage of the purchase price to the sales price = 83.3% ($55/$66 x 100) or (100 - 16.7)

b) Cost of jackets per unit = $45

Markup = 20%

Sale price per unit = $54 ($45 x 1.20)

The total expected jacket sales ≥ $260

The number of jackets to sell at $54 each = 5 ($260/54)

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The logarithm of a number with respect to a base is the exponent to which the base must be raised to produce that number. In other words, log_b(x) = y means b^y = x.

To find log_7(x), we can use the change of base formula which is log_b(x) = log_c(x) / log_c(b).

So you can use the logarithm of base 10 (common logarithm) or base e (natural logarithm) and use the above formula to find log7

So for example, log7(49) = log10(49) / log10(7) or log7(49) = ln(49) / ln(7)

You can use a calculator or a logarithm table to find the result.

--The question is incomplete, answering to the question below--

"How can we find log₇(x)?"

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The surface area of the square pyramid is 45.

Given data :

H = 6ft.)

W = 3ft

L = 3ft.

2 × b × s +b. Volume of a Square Pyramid

= 45ft

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The evaluation of the average rate of change of the function for the cooling rate of the liquid can be presented as follows;

(c) The rate at which the liquid is cooling in the first half-hour is about 4.15 °F/min

The cooling rate in the second half-hour is about 0.11 °F/min

The average rate of change of a function f(x) between the values, x = a, and x = b, can be found as follows;

Average rate of change = [tex]\frac{f(b) - f(a)}{b - a}[/tex]

(c) The function for the temperature obtained from a similar question posted online is presented as follows;

[tex]T(m) = 128\cdot e^{-0.12\cdot m}+ 74[/tex]

The time duration of the cooling in minutes = m

Therefore, the initial temperature is the temperature at 0 minutes, which indicates that we get;

m = 0, [tex]T(0) = 128\cdot e^{-0.12\times 0}+ 74[/tex] = 202

The temperature of the liquid after 30 minutes, can be found as follows;

[tex]T(30) = 128\cdot e^{-0.12\times 30}+ 74[/tex] ≈ 77.50

The rate at which the liquid is cooling on average in the first half hour therefore, is; Cooling rate = (202 - 77.50)/(30) = 4.15

The average cooling rate in the second half hour is found as follows;

After the second half hour, the duration of cooling = 60 minutes

Therefore, we get;

[tex]T(60) = 128\cdot e^{-0.12\times 60}+ 74[/tex] ≈ 74.1

The average cooling rate in the second half-hour is therefore;

(77.50 - 74.1)/(60 -30) ≈ 0.11

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The multiplication theorem of probability is if  and  be two events associated with the sample space . Then, (∩) = ()⋅() and the addition theorem of probability is For two mutually exclusive events ,

(or ) = () + ().

According to the multiplication theorem of probability, the probability of both events and occurring is equal to the product of the probability of occurring and the conditional probability of event occurrence if event happens.

Let  and  are two events associated with the sample space . ∩ gives the simultaneous occurrence of two events  and

We know that the conditional probability of the event given that has occurred is given by (∣) and is given by

(∣) = (∩)(), () ≠ 0

We can write the above equation as

(∩) = (∣)⋅()⋯()

Also, we can write

(∣) = (∩)(), () ≠ 0

(∩) = (∣)⋅()

Combining () and (), we can write

(∩) = (∣)⋅() = (∣)⋅(), where (),() ≠ 0

According to the addition theorem, if two events and , are mutually exclusive, the probability of either or  occurring is the total of the individual probabilities of  and .

Let event happen in ways, and event happen in ways. Then the total number of happening of events is , which is = +

Thus, the probability of events happening is given by (or ).

By the definition of probability,

() = / and () = /

Adding,

() + () = / + / = + / = / = 1

Therefore,

(or ) = () + ()

--The given question is incomplete; the complete question is

"What is the multiplication and addition theorem of probability? Explain with suitable examples."--

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A set of numbers is co-prime numbers if and only if these have only one common factor i.e., one.

Co-Prime Numbers are a set of numbers where the common factor between them is 1. This means that the HCF or highest common factor should be 1 for these numbers. Co-prime numbers are also referred to as "relatively prime numbers". This means that if we consider x and y to be the set of co-primes, then the only common factor between the two numbers is 1. The properties of co-primes are :

Consider a set of two numbers : 16 and 15 The factors of 16 are 1, 2, 8 and 16. The factors of 15 are 1, 3, 5 and 15. The common factor of 16 and 15 is only 1. So 16 and 15 are Co-prime numbers.

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Complete question:

What are co-prime numbers?.

Answer:12.57

Step-by-step explanation:

Given that radius of the circle= 2km

as we know the formula of circumference of the circle as

Circumference of the circle= 2* pi * radius

circumference of the circle = 2*pi*2

                                               = 2* 22/7*2

                                               =88/7

                                                =12.57

Answer: Right Triangle

Step-by-step explanation: You can use the Pythagorean Theorem. a^2+b^2=c^2

You test if the equation is true. 21^2 x 20^2 = 29^2 which is 841 = 841

Answer: 1

Step-by-step explanation:

The reason why a chemical equation have to follow the law of conservation of mass is that the mass of the products and the mass of the reactants must be equal.

Antoine Lavoisier discovered in 1789 that mass is neither created nor destroyed in chemical reactions, which led to the formulation of the Law of Conservation of Mass. To put it another way, the mass of any one element at the start of a reaction will be equal to that element's mass at the end of the reaction. . When the total mass of atoms on both sides of a chemical reaction is equal, the reaction is said to be balanced.

According to the rule of conservation of mass, mass is neither generated nor destroyed during a chemical process. The carbon atom in coal, for instance

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The distance from the airplane to the end of the runway will be 45.89 miles.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

An airplane is 45 miles from the end of the runway, AB, and 9 miles high, AC, when it approaches the airport. Then the triangle ABC is a right-angle triangle. Then we have

AC² = AB² + BC²

AC² = 45² +  9²

AC² = 2025 + 81

AC² = 2106

AC = 45.89 miles

The distance from the airplane to the end of the runway will be 45.89 miles.

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To solve the 3 4 5 triangle method to find the sides of the right-angle triangle we use the Pythagoras theory.

One type of triangle that has one right (90°) angle is a right triangle.

The Greek mathematician Pythagoras is credited with creating a mathematical formula for calculating the length of the third side of a right triangle given the lengths of the other two sides.

The triangle's right angle is formed by the sides of variables a and b. Either side may utilize either variable. The side that is left, or the side that leans away from the right angle, is represented by the variable c. The hypotenuse, or side c, is the longest side and is always present.

Thus, To solve the 3 4 5 triangle method to find the sides of the right-angle triangle we use the Pythagoras theory.

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Equivalence is a relationship that exists between two statements such that if the two statements are both true or both false, then the affirmation of one and the negation of the other contradicts itself.

Equivalent generally refers to two numbers, terms, or expressions that have the same value. There are many ways to express equivalent quantities. It can be represented by bars or equal signs. "Equivalence" relies on a specific relationship called an equivalence relationship. Any two elements are said to be equivalent if there is an equivalence relation between them. Also, in mathematics, equality is different from equivalent. The same means the same in all respects, and equivalent means similar but not identical. For example, 2 is said to be equal to 2, but it is equivalent to 1 + 1.

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Yes, the trinomial 9z 30z + 25 is a perfect square. The square of the binomial equation can be used to construct a perfect square trinomial statement.

A trinomial of the form + bz + c is said to be a perfect square if and only if it satisfies the condition b = 4ac.In a perfect square trinomial, two of your words will be perfect squares. If two perfect square terms are absent, the trinomial is not a perfect square trinomial.

It is now necessary to calculate the square roots of each perfect square word, add the two square roots, and multiply the result by two. The square of this trinomial is perfect. Because both 922 = (3ae)° and 25 = 52 are perfect squares, the only thing left to decide is if the middle term matches when you square (3x-5).In order to at least produce a negative coefficient for the middle phrase, the minus sign was utilised.

Complete question:

What does the following equation, 9x2 30x 25, look like factored? . Is the trinomial 9x2 30x25 a perfect square?

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Miguel takes 1.6 hours to cover the distance of 84.8 miles with the given speed of 53 miles per hour.

Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.

here,
In the question, we are given a speed = 53 miles per hour and the distance traveled with the given speed is 84.8 miles, we have to determine the time for the same distance.
We know that,
Speed = distance/time
Speed = 84.8 / 53
Speed = 1.6 hours

Thus, the required time evaluated is 1.6 hours.

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Answer:

There are 150 pounds of Candy Corn and 350 pounds of Candy Pumpkins in the mixture.

Answer:

10.22 kilograms

Step-by-step explanation:

you do 1.48+8.74=10.22

The chef bought 10.22 kilograms of nuts in total.

To find the total amount of nuts the chef bought, we add the number of almonds to the number of pecans:

1.48 kg + 8.74 kg = 10.22 kg

So the chef bought 10.22 kilograms of nuts in total.

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The break - even point is 5.

C=15x + 150

R=45x

Here, C = R

15x + 150 = 45x

30x = 150

x = 5

The break - even point is 5

                                                 = 225

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Applying the linear pair theorem, the measure of angle KJG is: 55°.

According to the linear pair theorem, if two angles lie on a straight line, they form a pair of angles whose sum is equal to 180 degrees.

In the image attached below, angles IJG and KLG are both angles on a straight line, and ate therefore equal to 180 degrees when added.

This:

Measure of angle IJG = 125°

m<KLG = 180 - m<IJG

m<KLG = 180 - 125

m<KLG = 55°

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the height of the stamp is 2/5in.

What is a fraction?

If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.

Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.

Given that stamp of Height is 3in with 4 1/2 in width.

So 9/2 of width = 3 Height

1 of width = 3/(9/2) Height

So for 3/5 in wide = 3/5* 3/(9/2) = 2/5in

Hence the height of the stamp is 2/5in.

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A function which has the greater initial value include the following: linear function A.

In Mathematics, the y-intercept is sometimes referred to as an initial value and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

By critically observing the table of values for linear function A, we can reasonably and logically deduce that its y-intercept (initial value) is equal to 8 when the value of "x" is equal to zero (x = 0).

For linear function B, we would substitute the value of x with zero (0) as follows;

y = 3x + 2

y = 3(0) + 2

y = 0 + 2

y = 0.

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Answer:

To complete the same work in 48 days working 10 hours a day, 40 additional women must be added. This is calculated by multiplying the number of days (60) by the number of hours worked per day (9) and dividing it by the number of days required (48) multiplied by the number of hours worked per day (10). This gives a total of 80 women.