Enacting a modeled response depends on your ability to reproduce the response by converting your stored mental images into overt behavior.

Alex bought 24.75 gallons of paint to use for the house painting.

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the amount of paint bought by Alex, hence:

(1/3)x + 3/2 + 2(3/2) + 12 = x

X = 24.75 GALLONS

Alex bought 24.75 gallons of paint to use for the house painting.

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The solution of the differential equation dy/dx=[tex]2xy/(x^{2} -1)[/tex] is y=[tex]-x^{2} +1[/tex].

Given a differential equation dy/dx=[tex]2xy/(x^{2} -1)[/tex].

We are required to find the solution of the differential equation when y(0)=1.

dy/dx=[tex]2xy/(x^{2} -1)[/tex]

Taking y to left side and dx to right side.

1/y dy=2x/[tex](x^{2} -1)[/tex] dx

Integrating both sides.

[tex]\int\limits {1/y} \, dy[/tex]=[tex]\int\limits {2x/(x^{2} -1)} \, dx[/tex]----------1

log y=[tex]\int\limits {2x/(x^{2} -1)} \, dx[/tex]

Solving right side.

[tex]\int\limits {2x/(x^{2} -1)} \, dx[/tex]

let [tex]x^{2} -1[/tex]=z

differentiating both sides with respect to x.

2x=dz/dx

2x dx=dz

Put 2x dx=dz in 1.

[tex]\int\limits {1/y} \, dy[/tex]=[tex]\int\limits {1/z } \, dz[/tex]

log y=log z+log c

Put z=[tex]x^{2} -1[/tex]

log y=log([tex]x^{2} -1[/tex])+log c

log y=log [{[tex]x^{2} -1[/tex])c]

y=([tex]x^{2} -1[/tex])c------------2

Put x=0 and y=1

1=(0-1)c

1=-c

c=-1

Put c=-1 in 2 to get the solution.

y=-1([tex]x^{2} -1[/tex])

y=[tex]-x^{2} +1[/tex]

Hence the solution of the differential equation dy/dx=[tex]2xy/(x^{2} -1)[/tex] is

y=[tex]-x^{2} +1[/tex].

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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: (-∞, ∞)

Answer:

a. The free throw percentage obtained by the Lions is of 81.25%.

b. The free throw percentage for the Eagles was of 37.04%.

c. The field goal percentage for the Lions was of 56.01%.

d. The field goal percentage for the Eagles was of 34.43%.

e. The Lions scored 96 points.

f. The Eagles scored 64 points.

Solution:

a. The lions attempted 16 free throws and made 13, which means lions scored 13 out of 16,

The free throw percentage obtained by the Lions = [tex]\frac{13}{16}[/tex] × 100 = 81.25%

The free throw percentage obtained by the Lions is 81.25%

b. The eagles attempted 27 free throws and made 7 which means 7 out of 27, so:

The free throw percentage obtained by the eagles = [tex]\frac{7}{27}[/tex] × 100 = 25.92 %

The free throw percentage obtained by the eagles is 25.92 %

c. The lions attempted 51 two-point shots and made 22, and attempted 16 three-point shots and made 10.

Total attempted = 51 + 16 = 67

Total shots made = 22 + 10 = 32

The field goal percentage (two-point and three-point shots combined) for the Lions = [tex]\frac{32}{67}[/tex] × 100 = 47.76 %

The field goal percentage for the Lions was of 47.76 %.

d. The eagles attempted 41 two-point shots and made 19, and attempted 16 three-point shots and made 7.

Total attempted = 41 + 19 = 60

Total shots made = 19 + 7 = 26

The field goal percentage (two-point and three-point shots combined) for the eagles= [tex]\frac{32}{67}[/tex] × 100 = 43.33 %

The field goal percentage for the eagles was of 43.33 %.

e. Total goals secured by lions 13 free throws, 22 two's and 10 three's. So

Total points = 10 × 1 + 22 × 2 + 10 × 3 = 84

The Lions scored 84 points.

f. Total goals secured by eagles 7 free throws, 19 two's and 7 three's. So

Total points = 7 × 1 + 19× 2 + 7 × 3 = 66

The eagles scored 66 points.

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

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The number of employees is 91.

According to the statement

Given that the standard deviation = 24.5

The width in the question = 13

We solve for the margin of error E.

E = width / 2

E= 13/2 = 6.5

At 90%

Alpha = 1-0.90

= 0.1

Alpha/2 = 0.1/2 = 0.05

Z 0.05 = 1.576

Now find the Sample size n

= ((1.576x24.5)/2)²

= 90.8

= 91

So, The number of employees is 91.

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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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Answer:

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

Step-by-step explanation:

Beau can wrap 32 inches of ribbon outside the mirror.

Area of Beau Thai's mirror is 60 sq. inches.

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

The word "area" refers to a free space. A shape's length and width are used to compute its area.

Given information:

Length of mirror = 6 inches

Width of mirror = 10 inches

To Find:

The amount of ribbon Beau could wrap around the outside of the mirror.

Perimeter of the mirror = 2(6+10)

                                       = 2(16)

                                       = 32 inches

The area of Beau Thai's mirror.

Area of the mirror = 6*10

                              = 60 sq. inches

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Answer: 8r + 9.8s + 8.1

Step-by-step explanation:

   Given:

-(-8r-9.8s)+8.1

   Distribute:

   ↳ A - times a - becomes a +, a -times a + stays a -

8r + 9.8s + 8.1

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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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Answer:

d; y - 1 = 4/5(x + 2)

Step-by-step explanation:

the equation for a point-slope form line is y - y1 = m(x - x1)

plug in the points and you will get your answer

y - 1 = 4/5(x + 2)

that is your answer

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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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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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 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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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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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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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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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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The distance between the points (-8, -3) and (-2, -5) is √40 units

Using distance formula,

d = √(x₂ - x₁)² + (y₂ - y₁)²

Therefore, using (-8, -3) and (-2, -5).

x₁ = -8

x₂ = -2

y₁ = -3

y₂ = -5

d =  √(-2 + 8)² + (-5 + 3)²

d = √(6)² + (-2)²

d = √36 + 4

d = √40

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The symbolic representation for the given statement " If two angles are not congruent, then they have the same measure" is ~q → p. So, option A is correct.

It is given that,

p - "Two angles have the same measure"

q - "The angles are congruent"

Statement: " If two angles are not congruent, then they have the same measure"

So, symbolically it is written as,

The hypothesis "two angles are not congruent" is represented by ~q and the conclusion "they have the same measure" is represented by p.

That is,

The representation is "If ~q then p i.e., ~q → p. So, option A is correct".

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The probability that all of the cards drawn are red is 0.0253.

A standard deck of playing cards has 52 cards.

Of the 52 cards, 26 of the cards are red cards.

When we draw the first card, the probability of getting red is 26/52.

When we draw the second card, the probability of getting red is 25/51.

When we draw the third card, the probability of getting red is 24/50.

When we draw the fourth card, the probability of getting red is 23/49.

When we draw the fifth card, the probability of getting red is 22/48.

Therefore, the probability of drawing 5 red cards without replacement is

= [tex]\frac{26}{52}* \frac{25}{51}* \frac{24}{50} *\frac{23}{49}* \frac{22}{48}[/tex]

= 26*25*24*23*22/52*51*50*49*48

= 0.0253

Therefore, we have found that the probability that all cards drawn are red is 0.0253.

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Using it's concepts, the domain and the range of the graph are given as follows:

In this graph, have that the function is defined for all values of x except x = -1, and assumes all real values, hence the domain and the range of the graph are given as follows:

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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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The shortest possible time to perform the tasks is 30 minutes, these activities would be performed in this time by the couple made up of you and your aunt 1.

To calculate the shortest time to complete the wedding tasks, we must carefully observe the information in the table and identify the time that each person takes to complete the tasks. Subsequently, we must identify the people who take the shortest time, in this case it is you and your aunt 1 as shown below:

You

aunt 1

Additionally, we must subtract the two values, to know how long it will take in total for both people to perform the three required activities.

According to the above, the most efficient couple is your aunt 1 and you because you will take 30 minutes to complete the activities.

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Answer:

27.7 m²

Step-by-step explanation:

     In regular polygon, all the sides and angles are equal. The polygon in the picture is a equilateral triangle.

 a = 8 m

 √3 = 1.732

   [tex]\sf \boxed{\bf Area \ of \ equilateral \ triangle= \dfrac{\sqrt{3}a^2}{4}}[/tex]

                                                       [tex]\sf =\dfrac{1.732 * 8 * 8 }{4}\\\\ = 1.732*2*8\\\\= 27.71\\\\= 27.7 \ m^2[/tex]

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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[tex]\textbf{Heya !}[/tex]

the denominators are equal, so subtracting these two fractions is a piece of cake:-

[tex]\sf{\cfrac{21}{15}-\cfrac{9}{15}}[/tex]

[tex]\sf{\cfrac{21-9}{15}}[/tex]

[tex]\sf{\cfrac{12}{15}}[/tex]

`hope it's helpful to u ~

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 required order of the number from least to greatest square root is

1/√3 < √1 < √2 < √2.5

Which number is greatest in value:

In the above numbers 1, 1/3 and 2.5 do not have square roots.

So, we will write 1, 1/3 and 2.5 inside the square root as shown below.

√1 = 1

√(1/3) = 1/√3 = 0.577350269

√2.5 = 1.58113883

√2 = 1.414

Arranging these numbers according to their value, we get the order as-

0.577350269 < 1 < 1.414  < 1.581138831

Hence, the required order of the number from least to greatest square root is 1/√3 < √1 < √2 < √2.5.

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