Select the number line that plots these numbers.5, -2, 1, –4

The estimates  for [tex]6\frac{1}{9}. 1\frac{5}{7}[/tex] is [tex]10\frac{10}{21}[/tex]

The actual answer of [tex]6\frac{1}{9}. 1\frac{5}{7}[/tex] is [tex]10\frac{30}{63}[/tex]

The estimated answer of the fraction can be done as follows:

[tex]6\frac{1}{9}. 1\frac{5}{7}[/tex]

Hence,

[tex]6\frac{1}{9} = \frac{55}{9}[/tex]

[tex]1\frac{5}{7} = \frac{12}{7}[/tex]

Therefore, the actual answer of the fractions is as follows:

[tex]\frac{55}{9}.\frac{12}{7} = \frac{660}{63} = 10\frac{30}{63}[/tex]

Hence, the estimated answer of the fractions can be calculated as follows

[tex]\frac{55}{9}.\frac{12}{7} = \frac{660}{63} = \frac{220}{21} = 10\frac{10}{21}[/tex]

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A. The relationship between number of towers and number of customers is proportional.

B. 12 customers.

A proportional relationship between two variables, x and y, is a relationship whereby the ratio y/x is the same all through the table of values.

Thus, the value of y/x is constant, and is referred to as the unit rate or constant of proportionality, k.

Part A:

Given the table of values, we have:

Constant of proportionality (k) = y/x = 252/5.25 = 300/6.25 = 348/7.25 = 444/9.25 = 48.

Therefore, it is a proportional relationship because it has a constant of proportionality, k = 48.

Part B:

Substitute k = 48 into y = kx (proportional relationship)

y = 48x.

The equation for the relationship is, y = 48x. Substitute y = 576 into the equation to find the value of x, number of customers:

576 = 48x

Divide both sides by 48

576/48 = 48x/48 [division property of equality]

12 = x

x = 12

The number of customers is 12.

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16 fresh coffee are needed to obtain 14 2/25 lb of roasted coffee.

Coffee loses 12% of it's weight when it is roasted

The number of fresh coffee that is needed to obtain 14 2/25 lb of roasted coffee can be calculated as follows

let y represent the number of fresh coffee needed

100%-12%

= 88%

= 88/100

= 0.88

14 2/25

= 352/25

= 14.08

The number of fresh coffee can be calculated as follows

0.88y= 14.08

y= 14.08/0.88

y= 16

Hence to obtain 14 2/25 lb of roasted coffee, 16 fresh coffee is required.

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Answer:

16 lbs

Step-by-step explanation:

The sum of complementary angles = 90°

The angle shown is a right angle

Therefore:

k + 54.3 = 90

k = 90 - 54.3

k = 35.7°

Answer:

-1

Step-by-step explanation:

Correct option is A)

Given,

f(x)=5x−1

To find: f(0)

Put x=0 in the given eqation.

Therefore, we get

f(0)=5(0)−1

=0−1

=−1

A method of notation in which digits are divided into groups of three by commas is known as the standard form of a number.

When a number has three digits, these groups are termed periods?

The periods are separated by commas.

Large numbers have three spots between each group of digits. Periods are the names of the groups.

The periods are typically separated by commas.

number follows 100000 and 100001

nonetheless, does not include decimals, negative integers, or fractions. Let's first express the quantity in numerical form, so 100,000 represents 100,000. The next whole number after 100,000 is the one obtained by adding 1 to the previous amount. As a result, 100000 + 1 Equals 100001, the following whole number.

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The cost of one hotdog based on the given situation is $5

The correct answer option is Option C

let

Family A:

3h + 5w = 20

Family B:

6h + 3w = 33

Solve the two equations simultaneously:

3h + 5w = 20

6h + 3w = 33

Multiply (1) by 2

6h + 10w = 40

6h + 3w = 33

Substract the equations to eliminate h

10w - 3w = 40 - 33

7w = 7

divide both sides by 7

w = 7/7

w = 1

Substitute w = 1 into

3h + 5w = 20

3h + 5(1) = 20

3h + 5 = 20

3h = 20 - 5

3h = 15

divide both sides by 3

h = 15/3

h = 5

So therefore, the cost of one hotdog and one bottle water is $5 and $1 respectively.

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Answer: the answer is 5 dollars

Step-by-step explanation:

The equation of the line that passes through the points (0, 3) and (2, - 1) in point-slope form is y - 3 = - 2 · x, that is equivalent to y = - 2 · x + 3 (m = - 2, b = 3).

According to Euclidean geometry, a line can be constructed by knowing the location of two distinct points on a plane. Then, we can determin the slope of the line from the two points. First, determine the slope of the line by using the secant line formula:

m = (- 1 - 3) / (2 - 0)

m = - 4 / 2

m = - 2

Second, substitute all the variables in the equation of the line in point-slope form:

y - 3 = - 2 · x (Point-slope form)

y = - 2 · x + 3 (Slope-intercept form)

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Answer:

5.   [tex]\bold{(g \circ f)(-3) = 16}}[/tex]

6.   [tex]\bold{h(h(-3x)) = -12x + 15 }}[/tex]

7.   [tex]{\bold{f\left(g\left(x-3\right)\right):\quad 3x-21}}[/tex]

8.   [tex]\bold{\text \bold g(f(-3x)) = -36x + 15}}[/tex]

Step-by-step explanation:

These are examples of composite functions.

What is a composite function?
A function by definition is a process that takes a collection of inputs and produces a corresponding collection of outputs in such a way that the process produces one and only one output value for any single input value.

Since we consider a function a process it makes sense to think of two functions acting in sequence to produce a single output. The output from one function is fed into the second function.

Note that we can have [tex]f[/tex][tex]g[/tex] as the outer function, in which case the notation will be [tex](g \circ f)(x)[/tex] or [tex]g(f(x))[/tex]

Problem Solution

5.     [tex]g(x) = x + 3 \;\text and\; f(x) = 3x + 4[/tex]
       Find  [tex](g \circ f)(-3) = g(f(-3))[/tex]

6.   [tex]h(x) = 2x + 5[/tex]
     Find [tex]h(h(-3x))[/tex]

 [tex]7.\;\;\;g\left(x\right)\:=\:x-\:3,\:f\left(x\right)\:=\:3x\:-\:3\\\\\text{Find } \:f\left(g\left(x-3\right)\right)[/tex]

.[tex]\bold{8.\;\;g(x) = 3x + 3, f(x) = 4x + 4}\\\\\bold{\text{Find } g(f(-3x))}[/tex]

It is known that that the median divides the range into half.

And the first and third quartiles are the landmark for 25% and 75% of the data values.

Therefore, a dot plot is divided into 4 parts, each of ehich represents 25% of the population.

In the given dot plot diagram, it is observed that the mean of the construction worker's salary, coincide with the upper quartile of the salary., at $45,000

It means that 50% population of construction workers is getting at most $45,000 while 75% population of teachers is getting at most $45,000.

So if a construction worker is making the median salary i.e. $45,000, so he/she will be making more than 75% of the teachers.

Metric system:

Centiliter

Miligram

Kilometer

U.S. Customary System:

Yard

Pound

Mile

Buying 12 pack is better as it is cheaper than 4 pack.

A problem can be solved using the unitary method by first determining the value of a single unit, and then multiplying that value to determine the required value. The unitary method involves determining the value of a single unit before determining the value of the necessary quantity of units.

Given Data

Protein bars come in a 4 pack box or a 12 pack box

4 pack costs 7.68 and the 12 pack costs 22.32

In 4 pack

4 pack = 7.68

1 pack = 1.92

In 12 pack,

12 pack =  22.32

1 pack = 1.86

4 pack > 12 pack

Buying 12 pack is better as it is cheaper than 4 pack.

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Option (c)

Given:

The measure of pantry shelf is 3 yard by 3/7 yrds.

The objective is to find the area of the pantry shelf.

The area of shelf can be calculated as,

Hence, option (c) is the correct answer.

Denmark uses kroner as its currency. Before a trip to Denmark. Mia will get 8670 Kroner in exchange for $ 1700.

bank A

Dollars ($)     Kroner

80                  408

100                 510

120                 612

Since $ 80 = 408 Kroner

=>       $ 1    = 408 / 80 = 5.1 Kroner   . . . . . . conversion rate of $ to Kroner)

=>   $ 1700 = 1700 x 5.1 = 8670 Kroner

Hence Mia will get 8670 Kroner in exchange for $ 1700

The exchange rate of conversion from $ to Kroner is arrived at by applying Unitary System of calculation in arithmetic (mathematics).

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Answer:

[tex]\textsf{A.} \quad f(x)=\dfrac{1}{x-4}[/tex]

Step-by-step explanation:

An asymptote is a line that the curve gets infinitely close to, but never touches.

A vertical asymptote occurs when the denominator of a rational function is zero.

From inspection of the given graph, there is a vertical asymptote at [tex]x=4[/tex] .  

Therefore, the denominator of the rational function must equal zero when [tex]x=4[/tex] .

Therefore, the only solution where the denominator is zero when [tex]x=4[/tex] is:

[tex]\boxed{f(x)=\dfrac{1}{x-4}}[/tex]

Answer:

[tex]y=2x^2+4x[/tex]

Step-by-step explanation:

Given table:

[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5} x & -3 & -2 & -1 & 0\\\cline{1-5} f(x) & 6 & 0 & -2 & 0\\\cline{1-5}\end{array}[/tex]

The x-intercepts of a quadratic function are when f(x) = 0.

Therefore, the x-intercepts are:  x = -2 and x = 0.

Intercept form of a quadratic equation

[tex]y=a(x-p)(x-q)[/tex]  

where:

Substitute the found x-intercepts and one of the points from the table into the formula and solve for a:

[tex]\begin{aligned} y&=a(x-p)(x-q)\\\\\implies6&=a(-3-(-2))(-3-0)\\6&=a(-1)(-3)\\6&=3a\\a&=\dfrac{6}{3}\\\implies a&=2\end{aligned}[/tex]

Substitute the x-intercepts and the found value of a into the formula:

[tex]\implies y=2(x+2)(x-0)[/tex]

Expand to standard form:

[tex]\implies y=2(x+2)(x-0)[/tex]

[tex]\implies y=2x(x+2)[/tex]

[tex]\implies y=2x^2+4x[/tex]

Given:

1.1.1 The equation of the reflection of g(x) in the x-axis is of the form:

The rule for the reflection in the x-axis:

Applying the rule:

Hence, g'(x) = 4-3x

1.1.2 The equation of the reflection of h(x) in the y-axis.

The rule for reflection in the y-axis:

Applying the rule:

Hence, h('x) = 2/-x

1.1.3 The values of k for which :

Re-arranging:

Using the rule that for an equation to have non-real roots, the discriminant (D) must be less than zero.

Simplifying we have:

Hence, the values of k for which the equation has non-real roots is that k must be less than -8

1.1.4 The average gradient of f(x) between x=-4 and x=0:

First, we need to find the value of f(x) at x=-4.

Next, we must find the value of f(x) at x=0:

Using the average gradient formula:

Hence, the average gradient is -12

Answer:

Explanation:

Here, we want to estimate the rabbit population after 5 years

From the question, there was an approximate increase in the rabbit population by 150 (from 150 to 300) in a space of 2 years

Let us have an exponential relationship for this:

Let us get the value of t

P is the current population at 300

I is the initial

a is ?

t is the number of years which is 2

Mathematically, we have it that:

Now, for the 5 years tenor, we substitute 5 for t

We have that as:

From the option, we have an approximate value of 800 rabbits

SOLUTION

From the question, since the coordinates of the mid-points JK and JL has been given as M (2,16) and M, (-3, 5), respectively.

To find the distance between these two mid-points, we simply use the distance formula to do that.

The distance formula is given as

Applying these to the points M (2,16) and M, (-3, 5), we have

Hence the answer is 12.1 units

SOLUTION

Recall that a quadratic equation is of the form

The possible number of zeros of a quadratic function is 2The zeroes of a quadratic function could be real or complex

Therefore a quadratic function can have zero real roots

or 1 real root or 2 real roots.

The circumference of a circle whose radius is 15 inches measures 94.2 inches.

For a circle of radius R, the circumference is given by the formula:

C = 2*pi*R

Where pi is 3.14

In this case, we know that the radius is 15 inches, then we can write:

R = 15 in

Replacing that in the circumference formula we get:

C = 2*3.14*15 in = 94.2 inches.

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Answer: [tex](-16, -6) \cup (-2, 8)[/tex]

Step-by-step explanation:

[tex]||x+4|-7| < 5\\\\-5 < |x+4|-7 < 5\\\\2 < |x+4| < 12\\\\1. -2 < x+4 < 2 \implies -6 < x < -2\\\\2. -12 < x+4 < 12 \implies -16 < x < 8\\\\\therefore (-16, -6) \cup (-2, 8)[/tex]

To solve this equatio you use the next property:

Subtraction Equal Property: it is used in expressions with adds. State that you can substract the same amount from both sides of the equation and maintain euality.

In this case, to solve r you substract 18 in both sides of the equation:

As 18-18 is 0;

1. The least number of hours that.Kee can work is 7 hours.

2. The maximum number of miles that Julie will drive will be 272 miles.

1. Lee makes $64 per hour and he wants to make no less than $400 each hours for the trip. The number of hours will be:

Let the number of hours = h

64h >= 400

Divide

h >= 400/64

h >= 6.25

The least hour should be 7 hours.

2. The maximum number of miles that Julie will drive will be:

44(3) + 0.25m = 200

m = number of miles

132 + 0.25m = 200

0.25m = 200 - 132

0.25m = 68

m = 68 / 0.25

= 272

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The answer is 5

Step-by-step explanation:

-3=z-8

put +8 underneath -8. Then cross it out.

Put +8 underneath -3. -3+8=5

The answer is 5.

I hope this helped you!

The graph for the function (y = -(1/4)x + 3) is given in the attached image. See the explanation below.

Step 1 Find (x,y) pairs
Step 2: plot the points

Step 3 Draw the line on the graph.

Let's look at Step 1.

Using the graph as an example, our first pair of x,y is (0, 3)

This is obtained by substituting 0 in the equation y = -(1/4)x + 3

⇒ y = -(1/4)0 + 3

y = 0 +3

y = 3, where x = 0

If we repeat this process with x = 1, x = 2, x = 3, we will get the corresponding y for case.

Step 2: Plotting the x,y pairs will give us points on the graph.

Step 3: connecting the dots will give us the same line in the graph that is attached.

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So C receives py/(x+y)(p+q) share of money out of the total money

The ratio of money shared between A and B = x:y

Sum of the ratios is x+y

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorize ratios.

B' share of money = y/(x+y)

The ratio of money between C & D = p:q

Sum of the ratio = p+q

B's share of the money is further divided among C & D in the ratio of p:q therefore:

C's share of money = y/(x+y)*p/(p+q)

= py/(x+y)(p+q)

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