The gasoline gauge on a van initially read
1/4 full. When 12 gallons were added to the​ tank, the gauge read 3/4 full. How many more gallons are needed to fill the​ tank?

The principle of mathematical induction is a method of proof used in mathematics to prove that a statement is true for all natural numbers.

It is based on the idea that if the statement is true for one number, then it can be used to prove that it is true for the next number. Mathematical induction can be expressed mathematically as follows:

Let P(n) be a statement involving an integer n

Base Case: P(m) is true for some m

Induction Hypothesis: Assume P(k) is true for some k>m.

Induction Step: Show that P(k+1) is true.

Therefore, P(n) is true for all n>m

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the extended sheet  in Europe has a greater area than the standard letter size paper. The difference in area between the two is about 20 square cm, it can make a difference in certain applications.

area of rectangle = length * breath  

The standard sheet of paper commonly used in the United States and Canada is known as "Letter" size paper, which measures 8.5 inches by 11 inches (21.59 cm x 27.94 cm). To compare the area of this paper to the extended sheet of paper used in Europe, we need to convert the dimensions to centimeters.

So, the area of the standard letter size paper in centimeters would be:

21.59 cm x 27.94 cm = 603.78 square cm

On the other hand, the extended sheet of paper in Europe measures 21.0 cm by 29.7 cm. Therefore, its area would be:

21.0 cm x 29.7 cm = 623.70 square cm

the extended sheet of paper in Europe has a greater area than the standard letter size paper used in the United States and Canada. The difference in area between the two is about 20 square cm, it can make a difference in certain applications.

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Answer:This would be option letter C

Step-by-step explanation:The diagram is a gram of external geofram so the position Is fFX(4) ^N

Answer:

D

Step-by-step explanation:

f(x)= -x^2+4

Draw graph of -x^2 and shift it 4 units above

Answer:

118.4cm2

Step-by-step explanation:

Surface area of square :5×5=25

Surface area for one triangle:

square root of 9²+2.5²=9.340770846

Area of triangle 0.5×5×9.340770846=23.35192712

As there is 4 triangle do 23.35192712×4=93.40770846

After

25+93.40770846=118.4077085

1dp= 118.4cm²

Answer:

Step-by-step explanation:

This is a binomial distribution problem, where each person either has car insurance with Geico or doesn't have.

Let's denote the probability of a person having car insurance with Geico as p = 0.75, and the probability of not having car insurance with Geico as q = 0.25.

The probability of getting exactly k people out of n people who have car insurance with Geico is given by the binomial distribution formula:

P(k) = (n choose k) * p^k * q^(n-k)

where (n choose k) is the number of ways to choose k items out of n items, which is calculated by the formula:

(n choose k) = n! / (k! * (n-k)!)

where n! denotes the factorial of n.

We need to find the probability of getting at least 8 people out of 10 who have car insurance with Geico, which is the same as the probability of getting 8, 9, or 10 people who have car insurance with Geico. So, we can calculate this probability by adding the probabilities of these three cases:

P(at least 8) = P(8) + P(9) + P(10)

P(8) = (10 choose 8) * 0.75^8 * 0.25^2 = 0.002

P(9) = (10 choose 9) * 0.75^9 * 0.25^1 = 0.054

P(10) = (10 choose 10) * 0.75^10 * 0.25^0 = 0.056

Therefore, the probability of at least 8 people out of 10 having car insurance with Geico is:

P(at least 8) = P(8) + P(9) + P(10) = 0.002 + 0.054 + 0.056 = 0.112

So, the probability that at least 8 people out of 10 have car insurance with Geico is 0.112 or approximately 11.2%.

By adding all the numbers in the line plot, we conclude that she will have enough olive oil.

To check this, we just need to add the 13 numbers and see if it is more than 16.

Each point above the line plot means how many times that number will apear in our sum, then the sum will be:

(2*0 + 4*(4/8) + 3*(6/8) + 3*1 + (1 + 2/8))

Now we need to solve that:

(2*0 + 4*(4/8) + 3*(6/8) + 3*1 + (1 + 2/8))

= 2 + 9/4 + 3 + 1 + 1/4

= 2 + 3 + 1 + 9/4 + 1/4

= 6 + 10/4

= 6 + 8/4 + 2/4

= 6 + 2 + 1/2

= 8 + 1/2

That is the amount of ounces of oil that she needs for the 13 recipes, it is less than 16 ounces, so she will have enough oil.

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Answer:

The equation is in slope-intercept form, Y = MX + B, where M is the slope and B is the y-intercept. In this case, the slope is 100 and the y-intercept is 40.

I hope that helps!

Step-by-step explanation:

The equation for the word problem is Y = 100x + 40.

Where Y is the total cost of the summer camp, x is the number of weeks of camp, 100 is the cost per week of camp, and 40 is the registration fee.

The mean is 72, which is the center of the distribution, 50% of the students will score less than 72. The area to the right of z = 1, so approximately 15.87% of students will score above 80.

a) Since the mean is 72, and we want to know the percentage of students who scored less than 72, we need to find the area under the normal distribution curve to the left of the z-score that corresponds to 72. Since the standard deviation is 8, the z-score is:

z = (72 - 72) / 8 = 0

Using a standard normal distribution table or a calculator, we can find that the area to the left of z = 0 is 0.5. Therefore, 50% of students scored less than 72.

b) To find the percentage of students who scored above 80, we need to find the area under the normal distribution curve to the right of the z-score that corresponds to 80. The z-score is:

z = (80 - 72) / 8 = 1

Using a standard normal distribution table or a calculator, we can find that the area to the right of z = 1 is 0.1587. Therefore, approximately 15.87% of students scored above 80.

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After answering the provided question, we can conclude that As a probability  result, the answer is 3/11.

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating an unlikely event and 1 indicating an unavoidable event. Because there are two equally likely outcomes, switching a fair coin and coin flips has a probability of 0.5 or 50%. (Either heads or tails). Probability theory, a branch of mathematics, is concerned with the investigation of random events rather than their properties. It is used in a variety of fields, including statistics, finance, science, and engineering.

To calculate the likelihood that the next podcast Eliana listens to will be a cooking podcast, multiply the number of cooking podcasts she has listened to by the total number of podcasts she has listened to.

We can see from the list of topics that Eliana has listened to three cooking podcasts out of a total of 11 podcasts. As a result, the likelihood that Eliana's next podcast will be a cooking podcast is:

3/11

As a result, the answer is 3/11.

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Answer:

$25

Step-by-step explanation:

You round 44.95 to 45 and 68.49 to 70. 70 - 45 = 25.

The expressions that are polynomials include the following: E. 13x²² + x²³ + 7x¹⁹ + 12x²

In Mathematics, a polynomial function can be defined as a mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value.

Generally speaking, all of the variables with respect to a polynomial function would always have positive (non-negative) integer exponents. Additionally, a polynomial function does not have variables or numerical value under a radical, in its denominator, or as its argument (non-polynomial function).

In this context, we can reasonably infer and logically deduce that all of the given expression except 13x²² + x²³ + 7x¹⁹ + 12x² does not a polynomial function.

In conclusion, the polynomial function 13x²² + x²³ + 7x¹⁹ + 12x² has only positive (non-negative) integer exponents.

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Answer:  35 000 000mm

Step-by-step explanation:

The time it takes them to paint the living room together is 2 hours. Expressing this as a fraction reduced to lowest terms 2 hours is 2/1.

Time working together refers to the amount of time that two or more people need to work together to complete a certain task. It is often used in situations where people are working collaboratively or cooperatively to achieve a common goal.

Let's denote the time it takes Marie to paint the living room alone by M and the time it takes Fran to paint the living room alone by F.

From the problem, we know that:

M = 3 hours

F = 6 hours

To determine the time it takes them to paint the living room together, we can use the following formula:

1 / (time working together) = 1 / M + 1 / F

Substituting the values we have:

1 / (time working together) = 1 / 3 + 1 / 6

Simplifying the right-hand side of the equation:

1 / (time working together) = 2 / 6 + 1 / 6

1 / (time working together) = 3 / 6

1 / (time working together) = 1 / 2

Therefore, the time it takes them to paint the living room together is 2 hours. Expressing this as a fraction reduced to lowest terms:

2 hours = 2/1

So the answer is: 1 / (time working together) = 1 / 2, or equivalently, the time working together is 2/1.

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Answer:

B

Step-by-step explanation:

y = x ( 3-x) = 3x - x^2      the ' x^2 ' makes it nonlinear

Solution :

Zoe's ball pool is a cylinder with height 20 cm and diameter 90 cm.

Height = 20 cm

Diameter = 90 cm

Calculate :

(a) The Radius of the pool.

Answer :

We are given with Diameter of pool 90 cm.

We know that,

Radius = Diameter/2

Radius = 90/2 = 45 cm.

(b) The circumference of the pool .

Answer :

Circumference = 2 πr

[tex]2 \times \dfrac{22}{7} \times 45 \\ \\ \dfrac{ 44 \times 45}{7} \\ \\ \frac{1980}{7} \\ \\ 282.8 \: cm[/tex]

(c) The area of the base of the pool.

Answer :

Area of base = πr²

[tex] \dfrac{22}{7} \times {(45)}^{2} \\ \\ \frac{22}{7} \times 2025 \\ \\ 22 \times 289.28 \\ \\ 578.56 \: {cm}^{2} \\ [/tex]

(d) The volume of the pool

Answer :

Volume of cylinder = πr²h

[tex] \dfrac{22}{7} \times {(45)}^{2} \times 20 \\ \\ \dfrac{22}{7} \times 2025 \times 2 \\ \\ \dfrac{22}{7} \times 4050 \\ \\ \frac{89100}{7} \\ \\ 12728.57 \: {cm}^{3} [/tex]

Answer:

Step-by-step explanation:

297.754

Answer:

a. Since the half-life of the isotope is 8 hours, we know that the decay rate is exponential and we can use the formula:

A(t) = A0 * (1/2)^(t/8)

where A0 is the initial amount of the substance, t is the time elapsed, and A(t) is the amount of substance remaining after t hours.

Substituting the given values, we get:

A(t) = 7 * (1/2)^(t/8)

b. To find the rate at which the substance is decaying, we need to take the derivative of A(t) with respect to t:

A'(t) = -7/8 * (1/2)^(t/8) * ln(1/2)

Simplifying, we get:

A'(t) = -ln(2) * (7/8) * (1/2)^(t/8)

c. To find the rate of decay at 14 hours, we can plug in t=14 into the equation we found in part b:

A'(14) = -ln(2) * (7/8) * (1/2)^(14/8) ≈ -0.4346 grams per hour (rounded to four decimal places)

The coordinates of the point P on the directed line segment from A to B such that P is 2/3 the length of the line segment from A to B are (-1, 2).

The coordinates of point P are obtained applying the proportions in the context of the problem.

P is 2/3 the length of the line segment from A to B, hence the equation is given as follows:

P - A = 2/3(B - A)

Then the x-coordinate of P is obtained considering the x-coordinates of A and B as follows:

x - 9 = 2/3(-6 - 9)

x - 9 = -10

x = -1.

The y-coordinate of P is obtained considering the y-coordinates of A and B as follows:

y + 8 = 2/3(7 + 8)

y + 8 = 10

y = 2.

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The average ticket cost for each concert is given as follows:

The ticket costs are obtained by a system of equations, for which the variables are given as follows:

It cost a total of $1707 to purchase six tickets for concert A and six tickets for concert B, hence:

6a + 6b = 1707

a + b = 284.5.

Three tickets for concert B cost a total of $687, hence the cost for concert B is of:

3b = 687

b = 287/3

b = $95.67.

Replacing into the first equation, the cost for concert A is given as follows;

a = 284.5 - 95.67

a = $188.83.

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The radius of the circle with given circumference is 13.

What is circumference?

In mathematics, the circumference of any shape determines the path or boundary that surrounds it. In other words, the perimeter, also referred to as the circumference, helps determine how lengthy the outline of a shape is.

We are given that the circumference of a circle is 81.64 miles.

We know that circumference of a circle is given by 2πr.

So, using this we get

⇒ C  = 2πr

⇒ 81.64  = 2 * 3.14 * r

⇒ 81.64  = 6.28 * r

⇒ r  = 13

Hence, the radius of the circle with given circumference is 13.

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Step-by-step explanation:

Substituting the given values, we get:

a + b/c = 24 + 36/4

= 24 + 9

= 33

Therefore, a + b/c = 33 when a = 24, b =36, and c = 4.

The sum of the given fractions is (2x + 10)/x.

What is fraction ?

A fraction is a way of representing a part of a whole or a ratio between two quantities. It is written in the form of a numerator and a denominator separated by a horizontal line. The numerator represents the number of equal parts under consideration, while the denominator represents the total number of equal parts that make up the whole. For example, the fraction 3/4 represents three equal parts out of a total of four equal parts. Fractions can be added, subtracted, multiplied, and divided to perform various mathematical operations.

According to the question:
The given fractions can be added if they have a common denominator. In this case, the common denominator is 9x.

So, we need to write the fractions with 9x as the denominator:

2/1 * (9x/9x) = 18x/9x

10/1 * (9/9x) = 90/9x

Now, we can add these two fractions:

18x/9x + 90/9x = (18x + 90)/9x = 9(2x + 10)/9x = 2x + 10/ x

Therefore, the sum of the given fractions is (2x + 10)/x.

Q: Find K by Adding the fractions and simplify if possible k=(2*(9x))+(10*(9x))

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As a result, after translation and dilation, the initial quadrilateral's apex (5, 2) changes into the vertex (8, 10).

One quadrilateral is a circular shape with four sides. These geometric shapes are quadrilaterals: produced by Raphael. a quadrilateral form. There is only one pair of parallel edges to the form, and there are no right angles.

To find the coordinates of the vertices of the quadrilateral after translation and dilation, we can follow these steps:

Translate the vertex (5, 2) by subtracting 1 from the x-coordinate and adding 3 to the y-coordinate to get the new coordinates: (5-1, 2+3) = (4, 5).

Dilate the translated vertex by a factor of 2 with respect to the origin (0, 0) to get the final coordinates: (24, 25) = (8, 10).

Therefore, the vertex (5, 2) of the original quadrilateral is transformed into the vertex (8, 10) after translation and dilation.

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The complete question is: After translating a quadrilateral with a vertex at (5,2) to a new position given by (x-1, y+3) and then dilating it by a factor of 2, what are the coordinates of the new vertices of the quadrilateral?

Answer:

(8,10)

Step-by-step explanation:

Therefore, at two separate moments, x = 0.28 and x = 1.17, the ball stands at a height of 15 feet. (rounded to two decimal places).

The meaning of an equation in algebra is a mathematical assertion that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are split by the 'equal' symbol.

To find out when the ball is at a height of 15 feet, we need to solve the equation:

-16x² + 30x + 5 = 15

First, we can simplify the equation by subtracting 15 from both sides:

-16x² + 30x - 10 = 0

Now we can divide both sides by -2 to make the coefficient of the x² term positive:

8x² - 15x + 5 = 0

This is a quadratic equation in standard form, where a = 8, b = -15, and c = 5. Using the quadratic method, we can find x:

x = (-b ± √(b² - 4ac)) / 2a

Plugging in the values, we get:

x = (-(-15) ± √((-15)² - 4(8)(5))) / 2(8)

x = (15 ± √(225 - 160)) / 16

x = (15 ± √65) / 16

Therefore, the ball is at a height of 15 feet at two different times:

x ≈ 0.28 seconds and x ≈ 1.17 seconds (rounded to two decimal places).

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When event 1, 6, and 8 are checked, probability  P(X) equals 3/8.

When event 2, 3, 4,5, and 7 are checked, P(not X) equals 5/8.

Simply put, probability is the likelihood that something will occur. The study of events with a probability distribution is called statistics.

There are eight balls in the bag, numbered one to eight.

Five balls are grey, while the remaining ones are all white.

2,3,4,5, and 7 are the gray-colored balls.

The white coloured balls are 1, 6, and 8, and the probability of getting a grey ball is P(not X).

P(not X) = Chance of receiving a grey ball a) Calculate P(X) and P (not X)

1, 6, and 8 are verified for event X, and P(X) equals 3/8.

2,3,4,5, and 7 are tested for the event "not X," and P(not X) = 5/8.

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The following values are in No Mode: 51.63, 54, 45.63, 43, 30, 55.18, 57, 34, 39.09, 38.81, 47.5, 42.9, 50, 29 and 46. There is no Mode; the Median is 45.63; the Mean is approximately 44.99.

In order to determine the Mean, Median, and Mode for the provided data set:

Sort the information in ascending order:

29, 30, 34, 38.81, 39.09, 42.9, 43, 45.63, 46, 47.5, 50, 51.63, 54, 55.18, 57

Mean:

The mean is calculated as follows:

Mean is the average of all values (number of values)

Mean = (29 + 30 + 34 + 38.81 + 39.09 + 42.9 + 43 + 45.63 + 46 + 47.5 + 50 + 51.63 + 54 + 55.18 + 57) / 15

Mean ≈ 44.99

Median:

When the values are organised in order, the median is the middle value in the data set. The median is the value in the middle when there are an odd number of values. The median is the average of the two middle values when there are an equal number of values.

The median is the eighth value in the data set because there are 15 values total:

Average = 45.63

Mode:

The most prevalent value in a data set is referred to as the mode. There is no mode in this instance because no value appears more than once.

As a result, there is no Mode and the Mean is roughly 44.99, while the Median is 45.63.

No Mode | 51.63, 54, 45.63, 43, 30, 55.18, 57, 34, 39.09, 38.81, 47.5, 42.9, 50, 29 and 46.

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Answer:

0.266666

Step-by-step explanation:

1) Use the algorithm method.

       0 . 2 6 6 6 6 6

      ____________________________

15   |  4  .

        3   .  0

      __________

       1  . 0  0

            9  0

       _________

                 1  0  0

                    90

           ___________

                       1  0  0

                           9 0

           ___________

                             1 0 0

                               9  0

                          ______

                                1 0 0

                                    9 0

                                    ___

                                      10

2) therefore, 4/15 ≈0.266666.

0.266666

Step-by-step explanation:

To find the percentage that $4250 represents of $6500, we can use the following formula:

percentage = (part / whole) x 100%

where "part" is $4250 and "whole" is $6500.

Substituting these values into the formula, we get:

percentage = (4250 / 6500) x 100%

percentage = 0.6538 x 100%

percentage = 65.38%

Therefore, $4250 represents 65.38% of $6500.

Answer: It is approximately 65%

Step-by-step explanation: Divide $4,250 by $6,500 and your answer without rounding is 65.3846%

In this question, f is a one-to-one function and f(0)=7. Thus, f⁻¹(7)=0.

As we already know that f(0)=7,

then (f(0))⁻¹ = f⁻¹(7)=0.

Thus, (f(0))⁻¹=0.

These are important as they can be used to show the existence of an inverse function. A one-to-one function is a type of mathematical function that maps one element of its domain to exactly one element of its codomain. This means that for every element of the domain, there is a unique element of the codomain.

f⁻¹(7)=0

The inverse of a one-to-one function f is denoted by f⁻¹, and it is defined as the inverse of the function f.

In this question, f is a one-to-one function and f(0)=7.

This means that the inverse of f, f⁻¹, maps 7 to 0.

Thus, f⁻¹(7)=0.

(f(0))⁻¹=0

Since the inverse of a one-to-one function f is denoted by f⁻¹, then (f(0))⁻¹ is the inverse of f(0).

As we already know that f(0)=7, then (f(0))⁻¹ = f⁻¹(7)=0.

Thus, (f(0))⁻¹=0.

To summarize, f⁻¹(7)=0 and (f(0))⁻¹=0 since f is a one-to-one function and f(0)=7.

This is because the inverse of a one-to-one function f is denoted by f⁻¹ and it maps 7 to 0.

Thus, f⁻¹(7)=0 and (f(0))⁻¹=0.

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