Tara has 4 and 4 over 5 feet of rope.

part a: how many 2 over 5 foot pieces can tara cut from the 4 and 4 over 5 feet of rope? show your work. (5 points)

part b: using the information in part a, interpret the meaning of the quotient in terms of the two fractions given. (5 points)

the answer box is a writing thing so might have to explain it differently

Answer:

C

Step-by-step explanation:

Distribute the negative, (2x^2 + 5) + (-4x+3)

Add like terms, 2x^2 - 4x +(5+3)

2x^2-4x+8

a. The continuous growth rate of the bacteria is 21%

b. The initial population of bacteria is 715

c. The culture will contain 2043 bacteria after 6 × 10⁻⁴ years

Since [tex]n(t) = 715e^{0.21t}[/tex] represents the number of bacteria in the culture.

This function is similar to an exponential function of the form  [tex]y(t) = Ae^{\lambda t}[/tex] where λ = growth rate

Comparing n(t) and y(t), we see that λ = 0.21

So, the continuous growth rate of the bacteria is 0.21 = 0.21 × 100 %

= 21%

So, the continuous growth rate of the bacteria is 21%

Since [tex]n(t) = 715e^{0.21t}[/tex] represents the number of bacteria in the culture, the initial population of bacteria is obtained when t = 0.

So, [tex]n(t) = 715e^{0.21t}[/tex]

[tex]n(0) = 715e^{0.21(0)} \\= 715e^{0} \\= 715 X 1\\= 715[/tex]

So, the initial population of bacteria is 715

To find the time when the number of bacteria will be 2043, this means n(t) = 2043.

Since  [tex]n(t) = 715e^{0.21t}[/tex]

Making t subject of the formula, we have

t = ㏑[n(t)/715]/0.21

So, substituting n(t) = 2043 into the equation, we have

t = ㏑[n(t)/715]/0.21

t = ㏑[2043/715]/0.21

t = ㏑[2.8573]/0.21

t = 1.05/0.21

t = 4.99

t ≅ 5 hours

Converting this to years, we have t = 5 h × 1 day/24h × 1 year/365 days

= 5/8760

= 5.7 × 10⁻⁴ years

≅ 6 × 10⁻⁴ years

So, the culture will contain 2043 bacteria after 6 × 10⁻⁴ years

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Substitute -6 in a and -5 in b

5(-6) + 5(-5)

-30+(-25)

=-55

Hope it helps!

Answer:

-55

5x-6 = -30

5 x -5 = -25

-25 + -30 = -55

Step-by-step explanation:

hope this helps

The volume of the given solid is 6322.75 cubic units.

What is the volume of the given figure?

It is given that,

The area of the regular pentagonal base, a = 35 units

Altitude of the given pyramid, h = 9 units

The formula for the volume of a pyramid with regular pentagonal base is given by,

V = (5/12) × tan(54°)ha²

Substituting the given values of a and h, we get the volume as,

V = (5/12) × tan(54°) × 9 × (35)²

V = (5/12) × (1.376) × 9 × 1225

V = (5/4) × (1.376) × 3 × 1225

V = (5/4) × 5056.8

V ≈ 6322.75 units³

Thus, the volume of the given figure comes out to be approximately equal to 6322.75 cubic units.

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The correct option is the third one:

-1 ≤ y - 3 and y - 3 ≤ 1

Which compound inequality represents the absolute value inequality?

Here we have:

|y - 3| - 4 ≤ -3

We can rewrite it to:

|y - 3| ≤ -3 + 4

|y - 3| ≤ 1

This can be decomposed in two inequalities, which are:

(y - 3) ≤ 1

(y - 3) ≥ -1

Then we can see that the correct option is the third one, as both inequalities must be meet.

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It is false to state that " If neither variation in an A/B is statistically better, you pick the variation you like best and proceed to make the change."

A/B testing compares two variations of a website element, often by evaluating users' responses to variant A vs. variant B and determining which of the two variants is more successful.

When the variation seems to be equal, then another factor must be introduced into the metric analysis that helps to make the testing objective.

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After 39 years, the value of this quantity is 1,023.35

Here we know that:

Then the exponential equation is:

[tex]A(t) = 570*(1 + 0.35)^{t/20}[/tex]

Where t is the time in years.

So, after 39 years, the value of this quantity is given by:

[tex]A(39) = 570*(1 + 0.35)^{39/20} = 1,023.35[/tex]

After 39 years, the value of this quantity is 1,023.35

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If two squares have different perimeters, the one with the larger perimeter will have a larger area. If two polygons have the same perimeter, then they must have the same shape. If two polygons have the same shape but are different sizes, then they must have different perimeters.

If two squares have equal areas, they will also have sides of the same length. But although "equal areas mean equal sides" is true for squares, it is not true for most geometric figures.

In order to find the perimeter or distance around the rectangle, we need to add up all four side lengths. This can be done efficiently by simply adding the length and the width, and then multiplying this sum by two since there are two of each side length.

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The median value of x is 2.

According to the statement

we have given the values of x at some points then

and we have to find the median for the x.

We know that the median formula is {(n + 1) ÷ 2}th, where “n” is the number of items in the set and “th” just means the (n)th number.

and after put the values in this formula we get our median value for x.

So,

we have given that the f(x) is 0.2 when x is from -1 to 0

and f(x) is 0.2 +1.2x when x is grater than 0 but less than 1

and f(x) is 0 when x is less than -1 or grater than 1

From these statements it is clear that the the f(x) is only exist when the x lies in between from the -1 to 1.

So, the total value of x becomes is -1,0,1

Then according to the median formula

median = (n + 1) ÷ 2

median = (3+1) / 2

median = 2.

So, The median value of x is 2.

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A conclusion which can be derived from these random samples is that: E. Cars are faster than SUVs.

A median can be defined as the middle number (center) of a sorted data set, which is typically when the data set is arranged in from the least to greatest or the greatest to least.

In Mathematics, the median of a data set is generally considered to be a better measure of center than the mean when there's an outlier in the data set.

Based on the information provided for these random samples from the race, we can infer and logically conclude that Cars are faster than SUVs because a median speed of 132 is greater than a median speed of 115.

In conclusion, it is important to note that the Cars used in this survey (research) are faster than SUVs because the median for the SUVs in Sample 2 is equal to 115 while the median for the Cars in Sample 1 is equal to 132.

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Answer:

its not 15 points ):

Step-by-step explanation:

The domain and range of the function is D) Domain: (-∞, ∞); Range: (-∞, ∞)

The domain is the input values, or the x values. We can put in any x values for this function.

Domain : (-∞, ∞)

The range is the output values or the y values. We can get any output values for this function

Range: (-∞, ∞)

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Complete question:

What are the domain and range of the function below?

A) Domain: (-∞, -5)

Range: (5, ∞)

B) Domain: (-5, -10)

Range: (5, 10)

C). Domain: (-5, 10)

Range: (-10, 5)

D) Domain: (-∞, ∞)

Range: (-∞, ∞)

The total earnings for the year is $18,900.

The total earnings is a sum of the annual salary, commission and Christmas bonus.

Commission = 6% x (160,000 - 20,000) =

6% x $140,000

0.06 x 140,000 =  $8,400

Total earnings =  $8,400 + 10,000 + $500 = $18,900

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the necessary steps to predict data not included in a data set using a scatter plot and line of best fit are Options 2, 3, 4

In using the line of best fit also known as the slope, they following steps are involved;

In using scatterplot, they following steps are involved;

This explains that the average of the set of data is found from the scatter plot and line of best fit.

Thus, the necessary steps to predict data not included in a data set using a scatter plot and line of best fit are Options 2, 3, 4

Graph the data in a scatter plot

Extend the line of best fit beyond the data

Find the average of the data

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Answer:

This has nothing to do with math

Step-by-step explanation:

I don't know what this even means

A conclusion which can be derived from these random samples is that: B. the students in grades 11 and 12 scored higher than the students in grades 9 and 10.

A median can be defined as the middle number (center) of a sorted data set, which is when the data set is arranged in from the greatest to least or the least to greatest.

In Mathematics, the median of a data set is generally considered to be a better measure of center than the mean when there's an outlier in the data set.

Based on the information provided for these samples, we can logically conclude that the students in grades 11 and 12 scored higher than the students in grades 9 and 10 because a median score of 86 is greater than a median score of 79.

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The area of the square will be 196cm².

It should be noted that the perimeter of a square is the addition of all its sides. Therefore, the length of the side will be:

= 56/4

= 14

Therefore, the area of the figure will be:

= 14²

= 14 × 14

= 196cm²

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Answer:

The exponent of the first term must have twice the value of the exponent of the second term.

Step-by-step explanation:

Based on the information in the table, an example of independent events is  the: P(policer officer and chooses car).

An independent event can be defined as an event that isn't dependent on other events. Thus, it isn't affected by any previous event.

Based on the information provided, we can infer and logically deduce that an example of independent events is  the probability of being a policer officer and chooses a car because they aren't overlapping probabilities.

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Some of the metrics that I would look at to determine whether or not a new feature will be successful are as follows:

It should be noted that metrics are the measures of quantitative assessment used for comparing, and tracking performance or production.

Metrics are heavily relied on in the financial analysis of companies to make decisions.

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The measure of the indicated angle to the nearest degree is 47°.

Given the data in the question;

From trigonometric ratio, Cosθ = Adjacent / Hypotenuse

Cosθ = 36/53

θ = cos⁻¹( 36/53 )

θ = 47°

Therefore, the measure of the indicated angle to the nearest degree is 47°.

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Answer:

0.1363636... = 3/22

Step-by-step explanation:

Let x = 0.1363636...

           100x = 13.6363636...

  (-)            x =   0.1363636...

------------------------------------------

              99x = 13.5

x = 13.5/99

x = 135/990

x = 27/198

x = 9/66

x = 3/22

0.1363636... = 3/22

0.1363636... is not equal to 1/33.

1/33 = 0.030303...

The canonical expression equivalent to sinusoidal model y(t) = 2 · sin (4π · t) + 5 · cos (4π · t) is y(t) = (√ 29) · sin (4π · t + 0.379π) .

Herein we have a simple harmonic motion model represented by a sinusoidal expression of the form y(t) = A · sin (C · t) + B · cos (C · t), which must be transformed into its canonical form, that is, y(t) = A' · sin (C · t + D). We proceed to perform the procedure by algebraic and trigonometric handling.

The amplitude of the canonical function is determined by the Pythagorean theorem:

A' = √(2² + 5²)

A' = √ 29

The angular frequency C  is the constant within the trigonometric functions from the non-canonical formula:

C = 4π

Then, we find the initial position of the weight in time: (t = 0)

y(0) = 2 · sin (4π · 0) + 5 · cos (4π · 0)

y(0) = 5

And now we calculate the angular phase below: (A' = √ 29, C = 4π, y = 5)

5 = √ 29 · sin (4π · 0 + D)

5 / √ 29 = sin D

D ≈ 0.379π rad

The canonical expression equivalent to sinusoidal model y(t) = 2 · sin (4π · t) + 5 · cos (4π · t) is y(t) = (√ 29) · sin (4π · t + 0.379π) .

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The number of individuals who participated in the entire experiment was 80.

In the question, we are informed that an Independent group experiment or between-subjects experiment comparing four treatment conditions produces 20 scores in each treatment condition.

We are asked to find the number of individuals who participated in the entire experiment.

The number of treatment conditions in the experiment is given to be 4.

The scores in each treatment condition for the experiment is given to be 20.

The total number of individuals who participated in the experiment will be the product of the number of treatment conditions in the experiment and the scores in each treatment condition for the experiment.

Thus, the number of individuals who participated in the entire experiment = 4*20 = 80.

Thus, the number of individuals who participated in the entire experiment was 80.

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The commission rate exists at $8,493 with a rate of 9.5%.

Jorge earns 9% from all his sales, so his commission exists

89400 × 0.09 = $8046

Harris made $447 more than that, so his commission exists

8046 + 447 = $8493

To estimate his commission rate, we can utilize the subsequent equation

89400 × rate percentage = 8493

Rate percentage = 8493 / 89400

Rate percentage = 0.095

Rate percentage = 9.5%

So Harris' commission exists at $8,493 with a rate of 9.5%.

Therefore, the commission rate exists at $8,493 with a rate of 9.5%.

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Based on the Roni using a lawn mower and Allie pushing one, Roni would be able to mow 0.71 of the field.

Assume that the part of the field that Roni would mow is x.

The relevant equation would be:

x/30 + x/75 = 1

5x/150 + 2x/150 = 1

7x / 150 = 1

x = 21.43

In 30 minutes, Roni would have mowed:

= 21.43 / 30

= 0.71

Full question is:

Roni and Allie are mowing the grass at the soccer field. Roni has a riding lawn mower and can mow the field in 30 minutes. Allie is pushing a lawn mower and can mow the field in 75 minutes.

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The equation of the graph is [tex]f(x) = -\sqrt{x -2[/tex]

The graph is added as an attachment

The form of the graph is

[tex]f(x) = a\sqrt{x + b[/tex]

The graph passes through the points (2, 0) and (6, -2).

So, we have:

[tex]0 = a\sqrt{2 + b[/tex] and [tex]-2 = a\sqrt{6 + b[/tex]

Solve for b in [tex]0 = a\sqrt{2 + b[/tex]

Divide both sides by a

[tex]0 = \sqrt{2 + b[/tex]

Square both sides

0 = 2 + b

Subtract 2 from both sides

b = -2

Substitute b = -2 in [tex]-2 = a\sqrt{6 + b[/tex]

[tex]-2 = a\sqrt{6 -2[/tex]

[tex]-2 = a\sqrt{4[/tex]

Evaluate the square root

-2 = 2a

Divide by 2

a = -1

Substitute b = -2 and a = -1 in [tex]f(x) = a\sqrt{x + b[/tex]

[tex]f(x) = -\sqrt{x -2[/tex]

Hence, the equation of the graph is [tex]f(x) = -\sqrt{x -2[/tex]

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The range of values of y is -1.6 < y < 7

The complete question is added as an attachment

From the attached image, we have the following sides

4y + 15 and 5y + 8

Both sides must be greater than 0.

So, we have:

4y + 15 > 0 and 5y + 8 > 0

Rewrite as:

4y > -15 and 5y > - 8

Solve for y

y > -3.75 and y > -1.6

If y is less than -1.6, the side 5y + 8 would be negative.

So, we make use of the inequality y > -1.6 as one of the range

Also, 4y + 15 is greater than 5y + 8.

So, we have:

4y + 15 > 5y + 8

Evaluate the like terms

-y > -7

Divide by -1

y < 7

So, we have:

y > -1.6 and y < 7

Combine both inequalities

-1.6 < y < 7

Hence, the range of values of y is -1.6 < y < 7

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Answer: [tex]\theta=\frac{8}{3} \text{ radians}[/tex]

Step-by-step explanation:

[tex]8=3\theta\\\\\theta=\frac{8}{3} \text{ radians}[/tex]

The equation that represents the situation is,

y = x + 15

Given Information

It is given  that the students complete a 15-point extra-credit assignment in order to raise their test scores.

The new test score is 15 more than the old test score.

We have to find an equation for this situation. A mathematical equation is a formula that uses the equals sign to connect two expressions in order to express their equality.

Forming Equation

Original Score = x

New Score = y ................... (1)

Thus, after the test, the score is raised by 15 points.

⇒ New score = x + 15 .................... (2)

The following equation can be deduced from (1) and (2)

y = x + 15

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