Convert 30 gallons to liters using an equivalent rate

Answer:

A.X+4

Step-by-step explanation:

3x2 + 18x + 24

A. x + 4

B. x - 4

C. x - 3

D. x + 3

Apex Answers

Answer:

  24

Step-by-step explanation:

The given age relationships can be used to reason about their ages.

__

When Holly was 4 times Spencer's age, the difference in their ages was 4-1=3 times Spencer's age. That is, Spencer was 51/3 = 17 years old, and Holly was 68.

That was 7 years ago, so Spencer is now 17+7 = 24 years old.

Answer:

All of them will double at the same time.

Step-by-step explanation:

The rule of 72 wa created to have an estimate of how long will an account that pays interests will take to double its value, in this case, as they all have the same interest rate, and the rule of 72 depends only on the interests that the account pays, there will be no difference between the doubling time of the accounts since eventhough they all have different amounts of money, having the same interest rate, will make them grow at the same rate.

Answer:

3 ways

Explanation:

We know that a parabola has a second degree equation), while a line has a first degree equation.

To get the points of intersection, we will need to solve both simultaneously.

Solving them, we can reach a maximum of two solutions, however, other scenarios are also possible.

Possible scenarios:

1- no intersection occurs as shown in the first attachment

2- one intersection occurs as shown in the second attachment

3- two intersections occur as shown in the third attachment

Based on the above, there are three ways where the line and parabola can intersect

Hope this helps :)

Answer:

0,1,2

Step-by-step explanation:

When both variables are standardized, the correlation coefficient remains the same. Scaling the variable by a constant factor doesn't change the relationship or correlation strength.

When both variables are standardized, the correlation coefficient between the standardized variables will always be the same as the correlation coefficient between the original variables. The standardization process does not change the relationship between the variables, but rather scales them to have a mean of 0 and a standard deviation of 1. Therefore, the correlation coefficient remains unchanged.

If median family income had been measured in thousands of dollars instead of dollars, the correlation would not change. Scaling the variable by a constant factor, such as thousands, would only change the units of measurement, but not the relationship between the variables or the strength of the correlation.

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The last two numbers of the given sequence are respectively gotten to be; 83 and 77

From the sequence, we see that;

From 98 to 97, there is a decrease of 1

From 97 to 95, there is a decrease of 2

From 95 to 92, there is a decrease of 3

From 92 to 88, there is a decrease of 4

The sequence pattern of decrease is seen to be: 1, 2, 3, 4

Thus, by inference we can say that the next decrease is 5. Thus,

Next number in sequence = 88 - 5 = 83

The number after that will be; 83 - 6 = 77

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The length of midsegment DE is going to be 38.

The correct answer is option C.

For a better understanding let us name the triangle as ABC and DE is the midpoint on side AB and Ac respectively.

We need to find the value of DE.

We are given that AD = 45 DB = 45 , AE = 55 EC = 55 DE = 6x + 2 and BC = 2x + 64

We need to find the value of midsegment which means we need to find the value of DE.

In order to find the value of DE we would first need to find the value of x.

So , for finding the value of x we would first use the concept of similarity of triangles.

In triangle ADE and triangle ABC

angleA = angleA ( common)

angleD = angleB ( as DE || BC, so the angles formed by parallel lines are going to be equal)

By AA similarity we can say that triangle ADE similar to triangle ABC.

So , now after proving that both of the triangles are similar we can say that all of the sides of the triangles are going to be equal.

AD/ AB = DE/BC = AE/AC

AD/AB = DE / BC

Substituting the required values in expression above.

45/ AB = 6x + 2/ 2x + 64

45/ 90 = 6x + 2 / 2x +64 (AB = AD + DB = 45 + 45 = 90)

Cross-multiplying :

90x + 2880 = 540x + 180

-450x = -2700

x = 6

So , the value of x is going to be 6.

As we have found the value of x now we can easily find the value of DE by substituing the value of x in expression :

DE = 6x + 2

DE= 6(6) + 2

DE = 36 + 2

DE = 38

So , the length of DE is going to be 38.

Therefore , from the given options the correct one is C.

The question probable may be:

9. Find the length of the midsegment The diagram is not to scale:

A. 18

B. 15.5

C. 38

D. 76

Answer:

'Sometimes' is the correct option

Step-by-step explanation:

We are given the statement,

'A kite is a rhombus'.

We know that,

Rhombus - is a parallelogram whose all four sides are equal and opposite angles are equal.

Kite - is a quadrilateral having two equal length adjacent sides and the angles where the pair of adjacent sides meet are equal.

So, we get that,

Thus, the kite is a rhombus when the all the sides of a kite are equal.

Hence, 'A kite is sometimes a rhombus'.

Answer:

Actually, it's never true.

Step-by-step explanation:

A kite is a quadrilateral defined to have no pairs of parallel sides.

A rhombus is a quadrilateral that has two pairs.

Answer:

25 cm hope whoever gets to see this has a great day :D

Answer: a. [tex]\dfrac{1}{6}[/tex]

Step-by-step explanation:

Given : Events X and Y are independent.

The probability of X occurring is [tex]\dfrac{1}{3}[/tex].

The probability of Y occurring is [tex]\dfrac{1}{2}[/tex].

Since both events are independent, then we have

[tex]\text{P(X and Y)}=\text{P(X)}\times \text{P(Y)}\\\\\Rightarrow\ \text{P(X and Y)}=\dfrac{1}{2}\times\dfrac{1}{3}=\dfrac{1}{6}[/tex]

Hence, [tex]\text{P(X and Y)}=\dfrac{1}{6}[/tex]

Thus , (a.) is the correct option.

Final answer:

The original fraction, based on the provided conditions, is found to be 3/8 by setting up an equation relative to the changes described and solving for the unknown numerator and denominator.

Explanation:

The question involves solving for the numerator and denominator of a fraction based on provided conditions. Let's denote the denominator as x and the numerator as x - 5, since the numerator is 5 less than the denominator. According to the given conditions, when the numerator is multiplied by 2 and the denominator is increased by 16, the fraction becomes smaller by 1/3 of its original value.

Original fraction: [tex]\(\frac{x - 5}{x}\)[/tex]. After the modifications: [tex]\(\frac{2(x - 5)}{x + 16}\)[/tex]. The condition that the fraction becomes smaller by 1/3 of its original value leads to the equation: [tex]\(\frac{x - 5}{x} - \frac{1}{3} \cdot \frac{x - 5}{x} = \frac{2(x - 5)}{x + 16}\)[/tex].

Simplifying this equation, we first express the reduced original fraction as [tex]\(\frac{2(x - 5)}{3x}\)[/tex]. Then, setting it equal to the modified fraction, we get[tex]\(\frac{2(x - 5)}{3x} = \frac{2(x - 5)}{x + 16}\)[/tex]. Canceling out [tex]\(2(x - 5)\)[/tex] from both sides and solving for x, we find that x = 8. Therefore, the original denominator is 8, and the numerator is 3, making the original fraction 3/8.

Given the points are A(3, 2) and B(6, 4).

If it is asking about the slope of the line AB, then we can use the slope formula as given by :-

[tex] Slope, \;m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex]

where (x₁, y₁) = A(3, 2) and (x₂, y₂) = B(6, 4)

[tex] m = \frac{4-2}{6-3} =\frac{2}{3} [/tex]

Hence, m = 2/3 would be slope of the line AB.

If it is asking about the y-intercept of the line AB, then we can use slope-intercept form as given by :-

y = mx + b

where m is the slope and b is the y-intercept.

we can plug the value of m = 2/3 and point A(3, 2) into the equation and solve for b.

[tex] 2=(\frac{2}{3} )(3) +b \\\\
2 = 2 + b \\\\
b = 0 [/tex]

Hence, b = 0 would be y-intercept of the line AB.

If it is asking for the equation of the line AB, then we can use slope-intercept form and put values of m = 2/3 and b = 0.

y = mx + b

[tex] y=\frac{2}{3} x+0 \\\\
y=\frac{2}{3} x \;\;
or\;\; 3y=2x [/tex]

Hence, [tex] y=\frac{2}{3} x \;\; or\;\; 3y=2x [/tex] would be equation of the line AB.

The probability that a randomly chosen student like at least two of the three styles of music will be 0.21.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences. Then the probability is given as,

P = (Favorable event) / (Total event)

A school radio station polled 500 students to find out what kind of music they appreciate. According to the study, 207 people prefer rock, 172 prefer country, and 126 choose jazz. Furthermore, 33 like rock and country, 27 prefer rock and jazz, 32 prefer country and jazz, and 13 prefer all three forms of music.

The number of favorable events is given as,

Favorable events = 33 + 27 + 32 + 17

Favorable events = 105

Then the probability is given as,

P = 105 / 500

P = 0.21

P = 21%

The probability that a randomly chosen student like at least two of the three styles of music will be 0.21.

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Answer:

D. -1

Step-by-step explanation:

All the variable terms are on the left, so subtract the constant on the left (5) from the equation and collect terms.

... 4t = -4 . . . . . . . variable term on one side; constant term on the other

Divide by the coefficient of t.

... t = -1

Answer:

For scientific notation, we write one number to the left of the decimal point and the other numbers are written as a power of ten.

2.)1,220,000,000

[tex]1.22\times10^{9}[/tex]

3.)0.0287

We can write this in fraction form as:

[tex]\frac{287}{10000}[/tex]

So, when 10000 will go up that is in numerator it will hold a negative power.

So, in scientific notation it will be [tex]2.87\times10^{-2}[/tex]