Lisa paid $46.58 for 16.7 gallons of gasoline. What was the cost per gallon, rounded to the nearest hundredth?

The approximate value of [tex]log_4128[/tex] is 3.5.

What is logarithm?

The opposite of exponentiation in mathematics is the logarithm. The exponent to which b must be raised in order to produce a number x is therefore the logarithm of a number x to the base b. For instance, since 1000 = 10^3, log10 of 1000 is 3, or log10 = 3.

Given: log 128≈ 2.1  and  log 4≈ 0.6

We have to find the approximate value of [tex]log_4128[/tex].

We know that,

[tex]log_ba = \frac{loga}{logb}[/tex]

Here,

[tex]log_4128 = \frac{log128}{log4}[/tex]

Plug the values of log 128 and log 4

⇒ [tex]log_4128 = \frac{log128}{log4} = \frac{2.1}{0.6} = 3.5[/tex]

Hence, the approximate value of [tex]log_4128[/tex] is 3.5.

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A. The relationship between the number of pounds of grapes sold (x) and the total price (y) can be described by the equation y = 2.25x.

The required details for pounds in given paragraph

This equation can be derived from the data in the table by substituting the values for x and y and solving for the coefficient 2.25. For example, for x = 2 pounds of grapes, we have y = $4.50, so 4.50 = 2.25 * 2. Similarly, for x = 4 pounds of grapes, we have y = $9.00, so 9.00 = 2.25 * 4. We can use this equation to find the total price for any number of pounds of grapes sold.

B. The total price of 17 pounds of red peppers is $31.60. The 1.80 in the equation p = 1.80r represents the price per pound of red peppers. In this case, 1.80 dollars is the price per pound of red peppers, and r is the number of pounds of red peppers that are being purchased. Therefore, the total price of r pounds of red peppers is equal to 1.80 dollars per pound multiplied by the number of pounds of red peppers being purchased.

C. The graphs representing the equations for the original and increased price per pound of grapes will share one point because the two equations will be tangent to each other at that point.

what is pound?

A pound is a unit of weight that is commonly used in the United States and some other parts of the world. It is defined as the weight of a standard reference object, called the international pound, which is kept at the International Bureau of Weights and Measures in France.

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Solve the inequality. v - (-5) < -9 the solution for the inequality is

Inequality, A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.

The given algebraic expression is v - (-5) < -9

This is solved as follows

v - (-5) < -9

v + 5 < -9

v < -9 - 5

v < -14

The value of v is -14

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The equations that passes through the points, (–4, –16) and (5, 2), are:

y – 2 = 2(x – 5)

y = 2x – 8

y + 16 = 2(x + 4)

To find the equation that passes through the points (–4, –16) and (5, 2), substitute each of the values of the points into the equations and see if it makes it true.

(–4, –16) = (x, y) into y + 4 = 2(x – 16):

-16 + 4 = 2(-4 – 16)

-12 = -40 [not true]

The equation does not passes through the point.

(–4, –16) = (x, y) into y – 2 = 2(x – 5):

-16 – 2 = 2(-4 – 5)

-18 = -18 [true]

The equation passes through the point.

(–4, –16) = (x, y) into y = 2x – 8:

-16 = 2(-4) - 8

-16 = -16 [true]

(–4, –16) = (x, y) into y + 16 = 2(x + 4):

-16 + 16 = 2(-4 + 4)

0 = 0 [true]

Therefore, the answers are:

y – 2 = 2(x – 5)

y = 2x – 8

y + 16 = 2(x + 4)

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Answer:

Step-by-step explanation:

The answer is (3,0)

You need to plug in the values of x and y to figure it out, because a coordinate is in the form (x,y) so in (3,0) 3 is the x value and 0 is the y value.

If you plug (3,0) into the first inequality y > -2x+3 you get 0 > -3 which is true

steps

-2(3) +3 = -3

And if you plug (3,0) into the second inequality y < x-2 you get 0 <  1 which is also true

So basically just plug in the values of x and y into the inequality and test if it works on one of the inequalities you've been given if it doesn't try the next order pair, if it does try it on the other inequality and check if it works on it to.

Answer:

b. [tex]y = -0.03x + 18.4[/tex]

explanation:

is just some logic. we see the second unit on the x-axis is 4, so let's try that. -0.03 * 4 = -0.12. -0.12 + 18.4 = 18.28. 18.28 lines up with the 18.3 measurement we see. the next closest option brings us to 17.8, so we'll go with b.

the probability to get two consecutive reds will be 19.75%.

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

A fair spinner has 9 equal sections: 4 red, 3 blue and 2 green.

The probability of not getting two consecutive red is  1  minus the probability of getting two consecutive greens. Since the spinner is fair, the probability of getting a green on any one spin is  4/9

Since consecutive spins are independent, the probability of getting two consecutive red is (4/9)² = 16/81= 19.75%

Hence the probability to get two consecutive reds will be 19.75%.

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Answer:

64 possible outcomes

Step-by-step explanation:

Since the bag contains four red cards, four white cards, and four black cards, each with a unique number from 1 to 4, there are a total of 4 * 4 * 4 = <<444=64>>64 possible outcomes in the sample space. This means that there are 64 possible cards that could be chosen, and each of these is an equally likely outcome.

All symmetry, reflexivity, and transitivity are required for an equivalence relationship.

In mathematics, equivalence refers to the quality of elements of a group or in a set that share common features.

To have an equivlance relationship, three requirement are needed:

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Answer:

x = 0.47

Step-by-step explanation:

[tex] {7}^{(1 - x)} = {2}^{(1 + x)} \\ apply \: log \: of \: base \: 7 \: to \: both \: sides \\ log_{7}(7)^{(1 - x)} = log_{7}(2)^{(1 + x)} \\ (1 - x) log_{7}(7) = (1 + x) log_{7}(2) \\ 1 - x = 0.36(1 + x) \\ 1 - x = 0.36 + 0.36x \\ 0.36x + x = 1 - 0.36 \\ 1.36x = 0.64 \\ x = \frac{0.64}{1.36} \\ x = 0.47[/tex]

Answer:

Two-thirds

Step-by-step explanation:

slope is

∆y/∆x = (y2-y1) divided by (x2-x1)

= (-8-(-6)) divided by (-6-(-3))

= -2 divided by -3

= 2/3

The required equation of line is x - 4y + 8 = 0, and graph is shown below.

A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.

The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.

Given that,

That line passes through the point (4, 3),

And the slope of the line is 1/2.

To determine the graph of the line,

First find equation of line,

By using formula of line that passes through point (x₁, y₁) and whose slope is m,

y - y₁ m (x - x₁)

Substitute the values here,

y - 3 = 1/4(x - 4)

4y - 12 = x - 4

x - 4y - 4 + 12 = 0

x - 4y + 8 = 0

The required equation is x - 4y + 8 = 0,

The graph of the equation of line is shown below.

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Answer:

Solve for X: -3x + 5y=13 is x=5/3y + −13/3

(Solve for y: 3/5x + 13/5)

Solve for X: x+4y=-10 is x= −4y−10

(solve for y: y= −1/4x + −5/2)

Step-by-step explanation:

Solve for X in  -3x + 5y=13:

Step 1: Add -5y to both sides.

−3x+5y+−5y=13+−5y

−3x=−5y+13

Step 2: Divide both sides by -3.

−3x/−3 = −5y + 13/−3

x = 5/3y + −13/3

Solve for Y in -3x + 5y=13:

Step 1: Add 3x to both sides.

−3x + 5y + 3x = 13 + 3x

5y = 3x + 13

Step 2: Divide both sides by 5.

5y/5 = 3x + 13/5

y = 3/5x + 13/5

Solve for X in  x+4y=-10:

Step 1: Add -4y to both sides.

x + 4y + −4y = −10 + −4y

x = −4y −10

Solve for Y in x+4y=-10:

x+4y=−10

Step 1: Add -x to both sides.

x + 4y+ −x = −10 + −x

4y=−x−10

Step 2: Divide both sides by 4.

4y/4 = −x − 10/4

y = −1/4x + −

Answer:

Equation of line A: y = 4

Equation of line B: x = 8

Step-by-step explanation:

I am not sure how to explain this but those are your answer.

Vertical angles are pairs of angles that are located on opposite sides of a line and are equal in measure, the value of k is 9.

Vertical angles are pairs of angles that are located on opposite sides of a line and are equal in measure. They are formed when two lines intersect, and they are always congruent, or equal in measure.

That if one angle measures 130°, the measure of its vertical angle must also be 130°.

If the other angle has a measure of (8k + 58)°, and it is a vertical angle to the angle that measures 130°, then it must also have a measure of 130°.

We can set up the equation 130 = 8k + 58 and solve for k to find the value of k.

Subtracting 58 from both sides gives us 72 = 8k. Dividing both sides by 8 gives us k = 9.

Therefore, the value of k is 9.

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Step-by-step explanation:

A school dance club is selling bottled water at a football game to raise funds. The club has raised $26 so far and has the goal of raising $100. If each bottle of water earns the club an additional $2, which equation can be used to find the number of bottles of water w that the club needs to sell to reach their goal?

equation:

100 = 2w - 26

solving:

100 = 2w - 26

74 = 2w

w = 37 more bottles

Answer:

m∠ x is 130° and m∠ y is 130°

Step-by-step explanation:

Based on the drawn example I gave would explain why

So because ∠AGF = ∠CHF that would make these two angles Corresponding angles and corresponding angles are congruent

Thus making ∠AGH or m∠ x equals 130°

Now we look at ∠DHE and ∠AGF these two angles would be classified as Alternate interior angles which would make them congruent to each other aswell

Thus making ∠DHG or m∠ y equals 130°

Reason also includes the fact that m∠ x and m∠ y would be alternate interior angles also

An electronic health record (EHR) is a document that contains information about a patient that has been securely authorised. Medical providers can enter data and update a new encounter using an electronic health record.

By enabling appropriate access to and secure electronic sharing of a patient's critical medical information, the electronic health information exchange (HIE) helps to increase the efficiency, effectiveness, safety, and affordability of patient care.

The "blueprint" of a database, or how the data may link to other tables or other data models, is known as a database schema. The schema does not, however, actually hold any information. A database instance is a sample of data from a database at a specific point in time.

An electronic health record (EHR) is a document that contains information about a patient that has been securely authorised. Medical providers can enter data and update a new encounter using an electronic health record.

Microsoft uses a document format called DOC. A document called a DOC file includes formatted text, graphics, tables, graphs, and charts, among other things.

Data that can be entered in free text style is referred to as unstructured data. Structured data is a type of data that includes check boxes, graphics, tables, and other options that the user can select from.

Since the DOC system uses free text, the EHR's data is structured.

Therefore,

An electronic health record (EHR) is a document that contains information about a patient that has been securely authorised. Medical providers can enter data and update a new encounter using an electronic health record.

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Answer: 259.2

Step-by-step explanation:

If you take the 324 seniors and divide it by 5 then multiply by four

Answer:x-25=y

Step-by-step explanation:

u just subtract and put it into equation form

For the question "A new washer and dryer set costs $1250 with an annual expenditure of $100 for electricity..." None of the options are correct

The statement "The annual cost of the washer-dryer set will never exceed $100 during the life of the set" is false because the function C(n) is defined as C(n) = (1250 + 100(n))/n,

A washer-dryer set has an average lifetime of 10ten years

But given the function

C(n) = (1250 + 100(n))/n,

even after 5000 years, the washer-dryer set will still be above $100 as shown below

[tex]C(5000)=\frac{1250+100\left(500000\right)}{500000}[/tex]

C(5000)=100.0025

b) For the given function C(n) = (1250 + 100n) / n, the highest power of x is 1 in both the numerator and denominator. The leading coefficient of the numerator is 100 and the leading coefficient of the denominator is 1, so the horizontal asymptote is the line y = 100.

To find the vertical asymptotes of a rational function, we need to look for values of x that make the denominator equal to 0, but the numerator not equal to 0. These values of x will be the vertical asymptotes of the graph.

For the given function C(n) = (1250 + 100n) / n, the denominator is n, so the vertical asymptotes are x = 0.

Therefore, the asymptotes of the graph of C(n) = (1250 + 100n) / n are the horizontal asymptote y = 100 and the vertical asymptote x = 0.

The statement "The asymptotes of the function are at x = –12.5 and y = 100" is false because a function does not have asymptotes if it is defined for all values of x. In this case, the function C(n) is defined for all positive values of n, so it does not have asymptotes.

c)  The statement "The annual cost after 10 years is $225 assuming only purchase and electricity expenses" is false because the annual cost after 10 years is given by

C(10) = (1250 + 100*10)/10

C(10)=225

But

= 225 + 100 (10)

=225000

Therefore, the annual cost after 10 years is $225000, not $225.

Hence given this none of the Options are correct

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CQ

A new washer and dryer set costs $1250 with an annual expenditure of $100 for electricity.

The function C(n) =1250+100n/n represents the annual cost of operating the washer-dryer set (besides the $100 for electricity) as a function of n years of owning the set.

Which of the following statement(s) about the function is true?

I. The annual cost of the washer-dryer set will never exceed $100 during the life of the set.

II. The asymptotes of the function are at x = –12.5 and y = 100.

III. The annual cost after 10 years is $225 assuming only purchase and electricity expenses.

F I only

G I and II only

H I and III only

J I, II, and III

The dependent variable represented on the graph is the Total Cost

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

As a general rule:

The variable represented on the y-axis is the dependent variable

From the given parameters, we have

This means that

y-axis = Dependent variable

This can also be expressed as

Dependent variable = Total Cost

This means that the dependent variable is Total Cost

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Answer:

x = -522 19/30

Step-by-step explanation:

To solve for x, distribute the 3/5. This gives us 3/5x - 21/50 = -314. Add over 21/50 to the other side, allowing for 3/5x to equal -313 29/50. Divide by 3/5 on both sides and we get x equal to -522 19/30. This is the final answer as a mixed number and is also in simplest form.

By rounding to 1 significant figure, estimate answer is 40

What is significant figures?

Significant figures of a number in positional notation area unit digits within the number that area unit reliable and necessary to point the number of one thing.

Main  body:

1) 40.73 to 1 significant figure = 40.

2) 1.06 to 1 significant figure = 1.

3) Therefore, we just multiply 40 by 1, which equals 40.

FURTHER EXPLANATION (IF NEEDED):

With significant figures, whole numbers such as 10, 20, 50 etc. have 1 significant figure. This is because the 0 does not count as a significant figure.

With decimals, all numbers after the decimal point are also included as significant figures (even 0). E.g. 40.73 has 4 significant figures and 1.06 has 3 significant figures.

EXAMPLES (IF NEEDED):

Rounding to 2 significant figures:

40.73 = 42

1.06 = 1.1

Rounding to 3 significant figures:

40.73 = 40.7

1.06 = 1.06 (because it's already in 3 significant figures)

Rounding to 4 significant figures:

40.73 = 40.73 (already in 4 significant figures)

1.06 = 1.060 (0 is counted as a significant figure if there is a decimal or another number comes after that 0)

E.g. 1006 has 4 sig figs, while 1060 would have 3 sig figs because the last 0 is not counted as a significant figure. 10.60 would have 4 sig figs because of the decimal.

Hence , By rounding to 1 significant figure, estimate answer is 40.

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Answer:

Irrational

Step-by-step explanation:

[tex]\sqrt{8} =\sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2}[/tex] and this is irrational

So [tex]\sqrt{8} + \sqrt{8} = 2\sqrt{8} = 2 \cdot 2\sqrt{2} = 4\sqrt{2}[/tex] which is irrational

(adding an irrational number to anything gives an irrational number)

The 7th term of the geometry sequence is 2,097, 152. Hence option C is the correct option.

What is a term of a sequence?

A phrase is used to describe each number in the series. The first term in the order 1, 3, 5, 7, 9,... is 1, the second is 3, the third is 5, and so on.

A geometric sequence is sequence such that the pervious term is multiplied by a constant number to get next term. The constant number is known as common ratio.

Given pattern is  8, 64, 512, 4,096, ..

The common ratio is 64/8 = 512/64 = 4096/512 = 8.

The first term of the sequence is 8.

The nth term of geometric sequence is ar^(n-1), where a is the first term, r is the common ratio.

The 7th term of the sequence is 8(8)⁷⁻¹ = 8(8)⁶ = 2,097, 152.

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The order from least to greatest is −2.3, −0.2, 0.7, 2.2. The correct option is A.

When numbers are arranged in ascending order, they are done so from smallest to largest. We must first compare the numbers before we can arrange them in any order. Compare first, then order. Numbers are arranged in ascending order.

Given that the numbers are 0.7, −0.2, 2.2, and −2.3. The numbers in ascending order will be arranged as,

0.7, −0.2, 2.2, −2.3

-2.3 > -0.2 > 0.7 > 2.2

Hence, the ascending order of the given data is -2.3 > -0.2 > 0.7 > 2.2.

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The expression is simplified to -105

An integer can be defined as a whole number, with no fractional or decimal form which can be positive, negative or zero.

Negative integer values are  the additive inverses of their corresponding positive numbers.

Integers are a collection of whole numbers and negative values.

The types of integers are;

From the information given, we have;

10(-3)(4) - (-15)

expand the bracket

10(-12) - ( -15)

expand further

-120 + 15

Add the values

-105

Hence, the value is -105

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