with 12 gallons of gas, he notices that it costs him $50.28.


How much does one gallon of gas cost?

The average rate of change from 3 to 6 storms is $0.04 per unit. Hence, the option (A) 0.04 is the correct answer.

The given table shows the following data:

Number of storms predicted and the corresponding gas price: Number of storms predicted Gas price ($) 1 2.34 3 2.44 4 2.49 6 2.56 7 2.61We are to find the average rate of change from 3 to 6 storms. The average rate of change between any two quantities is equal to the ratio of the change in the value of the quantities to the change in their corresponding values, expressed as a rate per unit.

For this purpose, we will use the following formula:

Average rate of change = Change in value / Change in corresponding value Average rate of change from 3 to 6 storms will be: Average rate of change = (Gas price at 6 storms - Gas price at 3 storms) / (6 - 3)We are given that the Gas price at 3 storms = $2.44 and the Gas price at 6 storms = $2.56Therefore, substituting these values in the formula for the average rate of change we get, Average rate of change = ($2.56 - $2.44) / (6 - 3)= $0.12 / 3= $0.04

Thus, the average rate of change from 3 to 6 storms is $0.04 per unit. Hence, the option (A) 0.04 is the correct answer.

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Answer:

x = \(\frac{20}{7}\)

Step-by-step explanation:

\(\frac{3}{4}\) x - 5= \(\frac{1}{2}\) x + 2x - 10

multiply through by 4 ( the LCM of 4 and 2 ) to clear the fractions

3x - 20 = 2x + 8x - 40

3x - 20 = 10x - 40 ( subtract 10x from both sides )

- 7x - 20 = - 40 ( add 20 to both sides )

- 7x = - 20 ( divide both sides by - 7 )

x = \(\frac{-20}{-7}\) = \(\frac{20}{7}\)

Answer:

\(x=\frac{20}{7}\)

Step-by-step explanation:

Since x is on the right side of the equation, switch the sides so it is on the left side of the equation.

\(\frac{1}{2}x+2x-10=\frac{3}{4}x-5\)

Simplify the left side of the equation by combing \(\frac{1}{2}\) and \(x\).

\(\frac{x}{2}+2x-10=\frac{3}{4}x-5\)

To write \(2x\) as a fraction with a common denominator, multiply by \(\frac{2}{2}\).

\(\frac{x}{2}+2x*\frac{2}{2} -10=\frac{3}{4}x-5\)

Simplify terms by combining \(2x\) and \(\frac{2}{2}\). Combine the numerators over the common denominator.

\(\frac{x+2x*2}{2} -10=\frac{3}{4}x-5\)

Raise x to the power of 1.

\(\frac{x^1+2x*2}{2} -10=\frac{3}{4}x-5\)

Factor \(x\) out of \(x^1\).

\(\frac{x*1+2x*2}{2} -10=\frac{3}{4}x-5\)

Factor \(x\) out of \(x+2x*2\).

\(\frac{x*1+x(2*2)}{2} -10=\frac{3}{4}x-5\)

Factor \(x\) out of \(x*1+x(2*2)\)

\(\frac{x(1+2*2)}{2} -10=\frac{3}{4}x-5\)

Multiply 2 by 2.

\(\frac{x(1+4)}{2} -10=\frac{3}{4}x-5\)

Add 1 and 4.

\(\frac{5x}{2} -10=\frac{3}{4}x-5\)

Combine \(\frac{3}{4}\) and \(x\).

\(\frac{5x}{2} -10=\frac{3x}{4}-5\)

Move all terms containing \(x\) to the left side of the equation.

\(\frac{7x}{4}-10=-5\)

Move all terms not containing \(x\) to the right side of the equation.

\(\frac{7x}{4}=5\)

Multiply both sides of the equation by \(\frac{4}{7}\)

\(\frac{7x}{4}*\frac{4}{7} =5*\frac{4}{7}\)

Simplify both sides of the equation.

\(x=\frac{20}{7}\)

Answer:

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Step-by-step explanation:

eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

Factor using the perfect square rule.

( 3 y − 4 ) ^2

Answer: 3x+ 4 units

Step-by-step explanation:

9x^2 + 24x + 16 =(3x +4) (3x + 4)          

lenth of each side 3x+  units

Answer: x=3

Step-by-step explanation: 2x +4)° 2x-9)°​= 4x  2 +8x−9=3

 Pull out like factors :

  2x + 4  =   2 • (x + 2) (4 • (x + 2) • x) -  9

4x • (x + 2) -  9

Factoring  4x2+8x-9  

The first term is,  4x2  its coefficient is  4 .

The middle term is,  +8x  its coefficient is  8 .

The last term, "the constant", is  -9  

Step-1 : Multiply the coefficient of the first term by the constant   4 • -9 = -36  

Step-2 : Find two factors of  -36  whose sum equals the coefficient of the middle term, which is   8 .

     -36    +    1    =    -35  

     -18    +    2    =    -16  

     -12    +    3    =    -9  

     -9    +    4    =    -5  

     -6    +    6    =    0  

     -4    +    9    =    5  

     -3    +    12    =    9  

     -2    +    18    =    16  

     -1    +    36    =    35

x=3

The value of x for the given triangle is 37°.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

There are many types of triangles such that right-angle triangles, equilateral triangles, and much more.

The sum of all interior angles of a triangle is 180°.

So,

x + 2x +4 + 2x-9 = 180°

5x - 5 = 180°

x = 37°

Hence "The value of x for the given triangle is 37°".

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Given question is missing an image attached below;

The number of different spanning trees for each graph is: a) K3: 1, b) K4: 4, c) K2,2: 2 and d) C5: 5.

a) The complete graph K3 consists of 3 vertices, and in a spanning tree, we need to have exactly 3 vertices connected without forming any cycles. Therefore, K3 has only one possible spanning tree.

b) The complete graph K4 has 4 vertices. To form a spanning tree, we need to connect all 4 vertices without creating any cycles. K4 can be thought of as a tree with 4 branches extending from a central vertex. Each branch can be connected to any of the other vertices. Hence, there are 4 possible spanning trees for K4.

c) The complete bipartite graph K2,2 consists of 4 vertices divided into two sets, each containing 2 vertices. To form a spanning tree, we need to connect all 4 vertices without creating any cycles. Since there are only two possible edges between the two sets, there are only two possible spanning trees for K2,2.

d) The cycle graph C5 consists of 5 vertices arranged in a circular shape. To form a spanning tree, we need to connect all 5 vertices without creating any cycles. Removing any one of the edges from the cycle will result in a tree. Therefore, C5 has 5 different spanning trees.

Therefore, the number of different spanning trees for each graph is:

a) K3: 1

b) K4: 4

c) K2,2: 2

d) C5: 5  

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The equation so the system has no solution is (d) y = 3/2x + 8

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

y = 3/2x - 4

For a system of linear equation to have no solution, the equations must have the same slope but different intercepts

In this case, y = 3/2x + 8 has the same slope and different intercept with y = 3/2x - 4

Hence, the equation is (d)

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So, the given system will have a unique solution when k=,1

A system of linear equations in two variables will have a unique solution when the equations are consistent and independent.

In this case, the system of equations is kx + 3y = k and 3x + ky = k.

One way to check for consistency and independence is by using the determinant of the coefficient matrix and comparing it to the determinant of the system. The determinant of the coefficient matrix is (kk) - (3ky) = k^2 - 3ky and the determinant of the system is k^2 - k.

For the system to have a unique solution, the determinant of the coefficient matrix must be non-zero and equal to the determinant of the system.

Therefore, the system will have a unique solution when k^2 - 3ky = k^2 - k.

Which means that k=1.

This system will have a unique solution when k=1, and the pair of linear equations will be 1x + 3y = 1 and 3x + ky = 1.

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Answer:

To evaluate f(x)=1/2x-3 for each value of x, we substitute each value into the function and simplify:

(a) f(-8) = (1/2)(-8) - 3 = -4 - 3 = -7

(b) f(0) = (1/2)(0) - 3 = 0 - 3 = -3

(c) f(3) = (1/2)(3) - 3 = 1.5 - 3 = -1.5

(d) f(10) = (1/2)(10) - 3 = 5 - 3 = 2

Therefore, the values of the function for each value of x are:

(a) f(-8) = -7

(b) f(0) = -3

(c) f(3) = -1.5

(d) f(10) = 2

The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.

The statement that is true is: d. All of these are true.Explanation:A study may have various sources of variability, including participant selection, the setting in which the study is conducted, and the measure used. The following options are as follows:a. The study may be affected by a situational variable.b. The construction noise may contribute to variability in test scores.c. The study has a confounding variable. The groups differ in the time they are to report to the testing room.d. All of these are true.Therefore, all of these options are true. For example, the study may be affected by a situational variable if a natural disaster or other unforeseen event happens that causes the study to be disrupted. In this case, the study was disrupted by a noisy construction crew, which may have contributed to variability in test scores. The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.

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Answer:

Step-by-step explanation:

Slope =

\( \frac{change \: in \: y}{change \: in \: x} \)

X1=2 X2=7

Y1=-1 Y2=-1

hence

\( \frac{ - 1 - ( - 1)}{7 - 2} \)

\( \frac{ - 1 + 1}{7 - 2} \)

\( \frac{0}{5} \)

\(slope = 0\)

Answer:

220.8 ounces

Chulo weighs 220.8 ounces

Step-by-step explanation:

Simple

Total no of marbles = 6 + 4 + 8 = 18

Probability of red marble = 6 / 18 = 1/ 3

Puppy 1 has  1.31 lbs more than puppy 12

From the question, the given parameters are

The additional weight of puppy 1 is calculated by subtracting the weight of puppy 2 from the weight of puppy 1

This is represented as

Additional weight = Weight of puppy 1 - Weight of puppy 2

Substitute the known values in the above equation

So, we have

Additional weight = 8.4 lbs - 7.09 lbs

Evaluate the difference

Additional weight = 1.31 lbs

Hence, the additional weight of puppy 1 is 1.31 lbs

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If you rejecting the null hypothesis can lead to either a correct decision or to an error, either a type I error or a type II error. (option a).

A correct decision occurs when we reject the null hypothesis and the alternative hypothesis is actually true.

A type I error, also known as a false positive, occurs when we reject the null hypothesis when it is actually true. In other words, we conclude that there is a significant difference between two groups or that a certain parameter is different from what was assumed in the null hypothesis, when in reality, there is no difference. Type I errors can occur due to random chance, or if the sample size is too small, or if the significance level is too high.

A type II error, also known as a false negative, occurs when we fail to reject the null hypothesis when it is actually false. This means that we conclude that there is no significant difference between two groups or that a certain parameter is equal to the value assumed in the null hypothesis, when in reality, there is a difference. Type II errors can occur if the sample size is too small or if the significance level is too low.

Therefore, option (a) is the right one.

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Answer:

j

Step-by-step explanation:

Answer:

a.  a = 144, b = 67

Step-by-step explanation:

a + 36 = 180  they are consecutive interior angles, so they add up to 180

a = 180 - 36 = 144

b + 113 = 180  they are consecutive interior angles, so they add up to 180

b = 180 - 113 = 67

The goal of building one-to-many relationships between tables is to minimize redundant data.

Data redundancy is a regular occurrence in many businesses and occurs when an identical piece of data is stored in two or more different locations. As more businesses switch from using segregated data to a central repository, they discover that their database is full of inconsistent duplicates of the same entry. Understanding how to effectively manage and track data redundancy can help your business avoid long-term inconsistency problems, even though it can be difficult to reconcile — or even benefit from — redundant data entries.

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The goal of building one-to-many relationships between tables is to minimize redundant data.

Redundant data refers to data that is duplicated across multiple tables, which can lead to data inconsistencies and

increase the amount of storage space required.

By creating one-to-many relationships between tables, data is only stored once in the database, and each instance of

the data in other tables refer back to the original source, reducing the need for redundant data storage.

Therefore, The goal of building one-to-many relationships between tables is to minimize redundant data.

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Answer:

Step-by-step explanation:

The real area of the terrace is 300 square meters. If the scale of the drawing is 1:200, it means that 1 cm on the drawing represents 200 cm in real life. Therefore, to find the real dimensions of the terrace.

We need to multiply the dimensions on the drawing by 200.

The length of the terrace in real life is:

7.5 cm x 200 = 1500 cm

The width of the terrace in real life is:

10 cm x 200 = 2000 cm

The area of the terrace in real life is:

1500 cm x 2000 cm = 3,000,000 cm²

To convert the area to square meters, we need to divide by 10,000 (since 1 m² = 10,000 cm²):

3,000,000 cm² ÷ 10,000 = 300 m²

Therefore, the real area of the terrace is 300 square meters.

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They are the same

Step-by-step explanation:

Explanation: 3/4 and 6/8 are equal

Answer:

48

Step-by-step explanation:

Number of comedy = 6

Number of action = 4

Number of drama = 2

Selecting one of each ; total Number of possible combinations ;

nCr

Comedy = 6C1

Action = 4C1

Drama = 2C1

6C1 * 4C1 * 2C1 = 6 * 4 * 2 = 48

Answer:

the answer is -5,-7,-10,-14,-19

From Daniel's initial location from the campsite given the width of the

stream is 400 feet and Daniel swims to the boat ramp, we have;

1.) Please find attached the drawing of the situation

2.) 3.34 minutes

3.) 1,298.59 feet

4.) 3.69 minutes

1.) Please find attached a labelled diagram of the scenario created with MS Visio

2.) Daniel's average swimming rate (speed) = 150 feet per minute

\(The \ distance \ Daniel \ swims = \mathbf{\dfrac{400 \, feet}{sin(53^{\circ})}} \approx 500.85 \, feet\)

The time it takes him to swim to the boat ramp, t, is therefore;

3.) The distance, d₁, downstream of the boat ramp from Daniel is given as follows;

d₁ = √((500.85 feet)² - (400 feet)²) ≈ 301.41 feet

Therefore;

The distance from the boat ramp to the campsite, d₂, is therefore;

d₂ ≈ 1600 feet - 301.41 feet = 1,298.59 feet

The distance from the boat ramp to the campsite, d₂ ≈ 1,298.59 feet                              

4. The time, t₂, it will take Daniel to jog from the boat ramp to the campsite is given as follows;

\(t_2 = \mathbf{\dfrac{d_2}{v_2}}\)

Where;

v₂ = The rate at which Daniel can jog, which is 4 mph

Which gives;

\(t_2 = \mathbf{\dfrac{1298.59 \, feet}{4 \, mph}} = \dfrac{1298.59 \, feet}{4 \, mph} \approx \dfrac{1298.59 \, feet}{5.866142 \ feet/s} \approx \dfrac{221.37 \, s}{60 \, s/min} \approx 3.69 \, min\)

Therefore;

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Answer:

7.33

Step-by-step explanation:

The probability that no one enters between 12:00 and 12:05 is 0.082.

The probability that at least 4 people enter the casino during that time is 0.242

Given that people enter the casino at the rate of 1 every 2 minutes. A random variable X is defined as the number of people entering the casino between the time period of 12:00 and 12:05. Since we are given in the question that people enter the casino at the rate of 1 every minute, hence in the given time period they enter at the rate of 2.5.

P(X=0) = \(e^{-2.5}\) = 0.082

Hence the probability that no one enters between 12:00 and 12:05 is 0.082.

The required probability is simply

P(X≥4) = 1 - P(X=0) - P(X=1) - P(X=2) - P(X=3)

= 1 - \(e^{-2.5}\) - 2.5\(e^{-2.5}\) - (((2.5)² / 2)\(e^{-2.5}\) ) - (((2.5³)/3!)\(e^{-2.5}\))

= 0.242

Hence, the probability that at least 4 people enter the casino during that time is 0.242

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Answer:

x = 2

Step-by-step explanation:

In the given figure

∵ ABC is a triangle

∵ D is a point on side AB

∵ E is a point on side BC

∵ DE // AC

∵ AC is the third side of the triangle

→ That means DE divides the sides AB, BC into parts that have the same ratio

∴ \(\frac{BD}{DA}\) = \(\frac{BE}{EC}\)

∵ BD = 6 and DA = 4

∵ BE = x + 1 and EC = x

→ Substitute them in the ratio above

∴ \(\frac{6}{4}\) = \(\frac{x+1}{x}\)

→ By using the cross multiplication

∵ 6 × x = 4 × (x + 1)

∴ 6x = 4(x + 1)

∴ 6x = 4(x) + 4(1)

∴ 6x = 4x + 4

→ Subtract 4x from both sides

∵ 6x - 4x = 4x - 4x + 4

∴ 2x = 4

→ Divide both sides by 2 to find x

∴ x = 2

The parent factors are the colours white or gray

Below is an image to represent the Tree diagram

It shows that for a white shirt Marcus can buy either a white medium and white large sizes

It also shows that for a gray shirt Marcus can also buy a gray medium and a gray large shirt

With this information, we can conclude that the possible answer to the question is the last OPTION D

Answer:

8x+60

Step-by-step explanation:

4(2x+15)

=4×2x+4×15

=8x+60

expand brackets ;)