find the z-score for which the area under the standard normal curve to its left is 0.96. round to two decimal places

Answer:

no real roots

Step-by-step explanation:

0 has one square root which is 0. Negative numbers have no square roots since a square is either positive or 0.

The total sale after 15 months is 30 million and the rate of change in total sales every month is 2√10 million dollars.

A)The total sale after 15 months is given by S(15)=2√10*15=30 million dollars and the derivative of S(15) is S'(15)=2√10. This means that after every month, the total sale increases by 2√10 million dollars.

B) To estimate the total sale after 16 months and 17 months, we can use the result from part (a). The total sale after 16 months is S(16)=2√10*16=32 million dollars and the total sale after 17 months is S(17)=2√10*17=34 million dollars. Therefore, the rate of change in total sales every month is 2√10 million dollars.

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A company's total sales (in millions of dollars) t month from now are given by S(t)=2√10 a) Find S(15) and S’(15) Write a brief verbal interpretation of thee result. B) Use the result in part (a) to estimate the total ale after 16 months and after 17 months

Team B will need to sell a minimum of 192 candies to reach its goal.

Since each term in a linear equation has an exponent of 1, graphing an algebraic equation always yields a straight line. It is called a "linear equation" because of this.

There are linear equations with one variable and those with two variables.

Given total amount to be raised by each team is $100,

Team B wants to sell cotton candy,

rent of candy machine = $25

total cost to be earned for team B = $100 + $25 = $125

let the number of candies sold be x

cost used in each candy sticks = $0.10

cost used by x candy sticks = $0.10x

the selling price of each candy = $0.75

the selling price of x  each candy  = $0.75x

total gain from selling x candies = $0.75x - $0.10x

total gain from selling x candies = $0.65x

minimum candies to be sold to reach the goal

$0.65x = $125

x = 125/0.65

x = 192.30

x = 192 (approx)

Hence to reach the goal, at least 192 candies are to be sold by team B.

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Answer:

x° = 54

y = 14

Step-by-step explanation:

Sum of interior angles of a triangle = 180, therefore:

79 + 16 + m∠P = 180

m∠P = 180 - 79 - 16 = 54

m∠RPQ = m∠UST = x° = 54°

64/16 = 28/(y-7)    solve for y:

64(y-7) = (28)(16) = 448

y - 7 = 448/64 = 7

y = 7 + 7 = 14

In Smithville, the gas station is located at Point Zero and the laundromat is 2/5 of a mile south of the gas station. The sandwich shop is 2/5 of a mile south of the convenience store and the day care is 3/5 of a mile south of the sandwich shop.

All of these locations are easily accessible and provide convenience services to the local Smithville community. The gas station offers fuel and other automotive services, while the laundromat provides laundry and dry cleaning services. The sandwich shop provides quick food and snacks, while the day care offers a safe and nurturing environment for children.

All of these locations are within a close proximity to one another and provide a convenient way for the Smithville community to access essential services.

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The "data view" of a dataset with two groups that each contain 40 people will have 80 rows.

A data set is a collection of data that is organized and processed to provide useful information. In a data set, each row represents a single observation or record. In the case where a data set contains two groups, each group represents a separate set of observations or records.

If each group has 40 people, this means that there are 40 separate observations or records in each group. Therefore, the total number of rows in the "data view" of the data set will be equal to the sum of the number of rows in each group, which is 40 + 40 = 80.So, the "data view" of a data set with two groups that each have 40 people will have 80 rows, with each row representing a single observation or record from one of the two groups.

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Answer: y ≤ -4x - 1.

Step-by-step explanation:

Hello!  

The first thing you know is that since the shaded region is to the (left) or below the line, you will have to use the symbol for equal to or less than (≤).  If the line was a dotted line, then you would use the symbol (<).  If the line was a dotted line and the shaded region was above or to the right of the line, then you would use the symbol (>).  If the line was a regular line like in the picture and the shaded region was to the right of the line instead of to the left like in the picture, then you would use the symbol (≥).  

Secondly, you know that the y-intercept is -1 and the slope is -4 using the equation (y2 - y1)/(x2 - x1) with the coordinates (0, -1) and (1, -5).  Substitute this information into the slope formula, y = mx + b.

y = -4x + (-1) or y = -4x - 1

You now have the equation:

y = -4x - 1.  Use the sign you figured out earlier for the equation in place of the equal sign.  Here is what the final equation should look like:

y ≤ -4x - 1.

Using the ratios we know that the required kilograms of corn and beef is 3.5kg and 1.4kg respectively

A ratio in mathematics demonstrates how many times one number is present in another.

For instance, if a dish of the fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.

The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.

Ratios contrast two figures by ordinarily dividing them.

A/B would be your formula if you were comparing one data point (A) to another data point (B).

This indicates that you are multiplying information A by information B.

For instance, your ratio will be 5/10 if A is 5 and B is 10.

So, we have the ratio:

corn:beef:rice = 5:2:7

Rice is 4.9kg.

We know that 5+2 = 7.

Then,

4.9/7 = 0.7

Corn: 0.7 * 5 = 3.5kg

Beef: 0.7 * 2 = 1.4kg

Therefore, using the ratios we know that the required kilograms of corn and beef is 3.5kg and 1.4kg respectively

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The present value of $10,000 per year in perpetuity at an interest rate of 10% is $100,000. Therefore, correct answer will be B.$100,000.

This is because the present value of an annuity, or a series of payments, is equal to the sum of the present value of each payment. In this case, the payment is $10,000 and the interest rate is 10%. Therefore, the present value of each payment is $10,000/(1+0.1)^1, which is $9,090.

Since the payments are perpetual, the present value of the annuity is equal to the present value of each payment multiplied by the number of payments, which is infinite. Therefore, the present value of the annuity is $9,090 multiplied by infinity, which is $100,000.

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Answer:

B

Step-by-step explanation:

The symbol > means greater than, so the number line points to the right
Because it is not [tex]\geq[/tex] (greater than or equal to), the circle should be open

Answer:

81

Step-by-step explanation:

Mean means the average

Mean = (sum of #s) / amount of #s

sum of numbers = 90 + 87 + 58 + 79 +91 = 405

amount of #s = 5

405/5 = 81

Answer:

81

Step-by-step explanation:

Mean is the sum of all numerical data values over the number of data. In this problem, we have total of 5 numerical data. Therefore:

[tex]\displaystyle{\bar{x} = \dfrac{\sum x}{N}}\\\\\displaystyle{\bar{x} = \dfrac{90+87+58+79+91}{5}}\\\\\displaystyle{\bar{x} = \dfrac{405}{5}}\\\\\displaystyle{\bar{x} = 81}[/tex]

Note:

[tex]\bar{x}[/tex] is mean value, [tex]\displaystyle{\sum x}[/tex] is sum of data, N is number of data

The candle will take nearly 33.2 minutes to burn out completely at the same rate.

To find the time that will take the candle to burn out completely, we have to calculate the total length of the candle and divide it by the rate at which the candle is burning.

Let us take the time it takes to burn the whole candle = T.

The total length of the candle = 22 cm.

The burning rate of the candle is 22 cm - 5.5 cm = 16.5 cm per 11 minutes.

So, T = 22 cm / (16.5 cm/11 minutes) = 22 cm * 11 minutes / 16.5 cm = 33.2 minutes.

Therefore, the candle will take nearly 33.2 minutes to burn out completely at the same rate.

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The solution of the given differential equation is = y=2x2. on initial value problem y(1)=2.

A differential equation in mathematics is an equation that includes one or more functions and their derivatives. The rate of change of a function at a point is determined by the derivatives of the function. It is mostly employed in disciplines like physics, engineering, biology, and others. Studying equation-satisfying solutions and the solutions' characteristics is the main goal of differential equations.

differential equations have several applications in different fields such as applied mathematics, science, and engineering. Apart from the technical applications, they are also used in solving many real life problems. Let us see some differential equation applications in real-time.

1) Differential equations describe various exponential growths and decays.

2) They are also used to describe the change in return on investment over time.

3) They are used in the field of medical science for modelling cancer growth or the spread of disease in the body.

4) Movement of electricity can also be described with the help of it.

5) They help economists in finding optimum investment strategies.

The given differential equation is -

[tex]x\frac{dy}{dx}=2y , IVP\ is\ y(1)=2,[/tex]

we can solve it by variable separable,

[tex]\int \frac{dy}{2y}=\int \frac{dx}{x}\\\\0.5logy=logx+logc\\y={xc}^2\\y(1)=2\\2=1c^2\\c=\sqrt2\\\\the\ solution\ of D.E \ is\-\\y=2x^2[/tex]

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The solution for x of the expression 3x - 4 + 6x = 112 is given as follows:

x = 12.89.

The expression for this problem is defined as follows:

3x - 4 + 6x = 112

The first step is combining the like terms at the left side of the expression, hence:

3x + 6x = 9x.

Then the expression is given as follows:

9x - 4 = 112.

Isolating the variable x, the solution for x of the expression is given as follows:

9x = 116

x = 116/9

x = 12.89.

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In mathematics, the empirical rule speaks that, in a normal data set, nearly every piece of data will fall within three standard deviations of the mean. The mean is the average of all of the numbers within the set.

The empirical rule advance about because the same shape of distribution curves continued to appear over and over to statisticians.

approximately normal, meaning that the data follows a bell-shaped curve regular around the mean.

The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations.

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To reach $1,830, for an initial investment of $770 at a 6.1% continuously compounded interest rate, it would take approximately 7 years and 8 months.

Continuously compounded interest is a method of calculating interest on a deposit where interest is added to the original deposit as soon as it is earned, and the process is repeated continuously. This means that instead of compounding the interest once or twice a year, as with traditional compound interest, the interest is compounded an infinite number of times in each year.

The formula for continuously compounded interest is:

A = P × [tex]e^{rt}[/tex]

where A is the Accrued amount, P is the Principal amount, r is the interest rate, t is the time in years.

1,830 = 770 × [tex]e^{(0.061)(t)}[/tex]

t = ln(1,830/770) / 0.061

t = ln(2.397) / 0.061 = 7.71 years

Therefore it would take about 7.71 years or 7 years and 8 months for the value of the account to reach $1,830.

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Answer:

answer is 12

12 because 5x12+5 = 65 and 180-115=65 meaning x=65

All the components of the question are solved below.

(a) 2πd is not a valid expression to calculate a distance because d is not a distance, it is a position.

(b) x+Δr could be a valid expression to calculate a distance because x is a distance and Δr is a position difference, so their sum is also a distance.

(c) x+y2 is not a valid expression to calculate a distance because the units of x and y2 are not consistent with each other.

(d) x2+y2 is a valid expression to calculate a distance because both x and y are distances and their sum squared represents the Pythagorean theorem, which is commonly used to calculate distances in physics.

(e) A+z is not a valid expression to calculate a distance because A is an area and z is a distance, so their sum does not have a physical interpretation as a distance.

(f) vΔt2 is not a valid expression to calculate a distance because v is a velocity and Δt is a time difference, so their product does not have a physical interpretation as a distance.

(g) aΔt2 is a valid expression to calculate a distance because a is an acceleration and Δt is a time difference, and their product represents the displacement of an object under constant acceleration, which is a distance.

Therefore, all the components of the question are solved above.

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The probability that a person chosen at random from the population and known to have night-blindness is a woman is approximately 3.78, or 378%.

Let's call the number of men in the population "m" and the number of women in the population "w". We know that m = 2w and that 2.3% of men have night blindness and 2.8% of women have night blindness.

Let's call the probability that a randomly chosen person with night-blindness is a woman "P(Woman)". We want to find the value of P(Woman).

We can use Bayes' Theorem to solve for P(Woman). Bayes' Theorem states that:

P(A | B) = P(B | A) * P(A) / P(B)

where P(A | B) is the probability of event A given that event B has occurred, P(B | A) is the probability of event B given that event A has occurred, P(A) is the probability of event A, and P(B) is the probability of event B.

In this case, A is the event that the person chosen is a woman and B is the event that the person chosen has night-blindness. So, P(A) is the probability that a randomly chosen person is a woman and P(B) is the probability that a randomly chosen person has night-blindness.

P(A) can be calculated as follows:

P(A) = w / (m + w) = w / (2w + w) = w / (3w) = 1/3

P(B) can be calculated as follows:

P(B) = (2.3% * m + 2.8% * w) / (m + w) = (2.3% * 2w + 2.8% * w) / (3w) = (4.6% + 2.8%) * w / (3w) = 7.4% / 3

Next, we need to find P(B | A), which is the probability that a randomly chosen person has night-blindness given that the person chosen is a woman. We know that 2.8% of women have night-blindness, so:

P(B | A) = 2.8%

Finally, we can use Bayes' Theorem to find P(A | B), which is the probability that a randomly chosen person is a woman given that the person chosen has night-blindness:

P(A | B) = P(B | A) * P(A) / P(B) = 2.8% * 1/3 / (7.4% / 3) = 0.28 / 0.074 = 3.78

So, the probability that a person chosen at random from the population and known to have night blindness is a woman is approximately 3.78, or 378%.

Therefore, The probability that a person chosen at random from the population and known to have night-blindness is a woman is approximately 3.78, or 378%.

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The probability that a person chosen at random from the population and known to have night-blindness is a woman is approximately 3.78, or 378%.

Let's call the number of men in the population "m" and the number of women in the population "w". We know that m = 2w and that 2.3% of men have night blindness and 2.8% of women have night blindness.

Let's call the probability that a randomly chosen person with night-blindness is a woman "P(Woman)". We want to find the value of P(Woman).

We can use Bayes' Theorem to solve for P(Woman). Bayes' Theorem states that:

P(A | B) = P(B | A) * P(A) / P(B)

where P(A | B) is the probability of event A given that event B has occurred, P(B | A) is the probability of event B given that event A has occurred, P(A) is the probability of event A, and P(B) is the probability of event B.

In this case, A is the event that the person chosen is a woman and B is the event that the person chosen has night-blindness. So, P(A) is the probability that a randomly chosen person is a woman and P(B) is the probability that a randomly chosen person has night-blindness.

P(A) can be calculated as follows:

P(A) = w / (m + w) = w / (2w + w) = w / (3w) = 1/3

P(B) can be calculated as follows:

P(B) = (2.3% * m + 2.8% * w) / (m + w) = (2.3% * 2w + 2.8% * w) / (3w) = (4.6% + 2.8%) * w / (3w) = 7.4% / 3

Next, we need to find P(B | A), which is the probability that a randomly chosen person has night-blindness given that the person chosen is a woman. We know that 2.8% of women have night-blindness, so:

P(B | A) = 2.8%

Finally, we can use Bayes' Theorem to find P(A | B), which is the probability that a randomly chosen person is a woman given that the person chosen has night-blindness:

P(A | B) = P(B | A) * P(A) / P(B) = 2.8% * 1/3 / (7.4% / 3) = 0.28 / 0.074 = 3.78

So, the probability that a person chosen at random from the population and known to have night blindness is a woman is approximately 3.78, or 378%.

Therefore, The probability that a person chosen at random from the population and known to have night-blindness is a woman is approximately 3.78, or 378%.

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The graph of the function is f⁻¹ ( x ) is plotted

Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.

Identify the even and odd multiplicities of the polynomial functions' zeros.

Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.

The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities

Given data ,

Let the x values of the function be represented as

x = { -3 , -2 , -1 , 0 , 1 , 2 , 3 }

Let the y values of the function be represented as

y = { -6.4 , -2.6 , -1.2 , -1 , -0.8 , 0.6 , 4.4 }

The value of the equation is plotted in the graph

Now , the inverse function is f⁻¹ ( x ) , you basically swap the numbers, all x values would equal y

So , y = { -3 , -2 , -1 , 0 , 1 , 2 , 3 }

And , x = { -6.4 , -2.6 , -1.2 , -1 , -0.8 , 0.6 , 4.4 }

Hence , the graph is plotted and the function is f⁻¹ ( x )

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Answer: 11.25 kmph or 6.99 mph

Step-by-step explanation:

take the speed equation s=d/t (speed equals distance over time)

s=72/6.4 (15 min is 0.4 of an hour)

your final answer will be S= 11.25 kilometers per hour or 6.99 miles per hour

No, the set s is not a basis for R3. A basis for R3 must contain three linearly independent vectors.

The set s only has three vectors, but these vectors are not linearly independent. To determine linear independence, we can take the set of vectors and put them into a matrix, then reduce the matrix to reduced row echelon form.

Let A be the matrix whose columns consist of the vectors in s:

A =

[tex]\begin{bmatrix} 0 & 4 & -8 \\ 4 & 0 & 20 \\ -1 & 3 & -11\end{bmatrix}[/tex]

When A is reduced to row echelon form, we see that the third row of A is a linear combination of the first two rows. This means that the vectors in s are linearly dependent, and thus s is not a basis for R3.

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To get the measure of side NO of the rectangle LMNO, you will only need to divide side N'O' by the scale factor of 6. Then you'll get 4, which is the actual measure of side NO.

Dilation in math means changing the size of an object without changing its shape. The size of the object may be decreased or increased based on the scale factor. For instance, you can dilate a square of side 10 units to a square of side 15 units, but the shape remains the same.

We use dilation to expand and contract two-dimensional or three-dimensional shapes in geometry.

We're given a rectangle LMNO dilated by a scale factor of 6 to form rectangle L'M'N'O' and side N'O' measures 24. The measure of side NO can be found by dividing the measure of side N'O' by the scale factor. 26 : 6 = 4, so 4 is the measure of side NO.

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By applying the unit of time concept, it can be concluded that the order from the shortest to longest work time is Rafael, Leanne, and Ray.

A unit of time is a specific time interval, which is used as a standard way of measuring or expressing duration.

Units of time that are often used daily are hours, minutes, and seconds, where 1 hour = 60 minutes and 1 minute = 60 seconds

A report on workout time is displayed as follows:

Name           Time

Rafael           75 minutes

Ray               1 3/4 hours

Leanne         1 hour 25 minutes

To sort names based on their workout time, we must first equate the time unit. For this case, we want to make them all in minutes.

Rafael: 75 minutes

Ray: 1 3/4 hours = 60 + (3/4 * 60)

                          = 60 + 45

                          = 105 minutes

Leanne: 1 hour 25 minutes = 60 + 25

                                             = 85 minutes

Thus the order from the shortest to longest work time is Rafael, Leanne, and Ray.

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Using the definition of a triangle's incenter, the measurements in the triangle ABC, where G is the incenter, are as follows: GC = 20.4

Triangle ABC's measurements are as follows using the concept of a triangle's incenter:

[tex]- $\mathrm{m} \angle \mathrm{ABG}=20^{\circ}$[/tex]

[tex]- $\mathrm{m} \angle \mathrm{BCA}=22^{\circ}$[/tex]

[tex]- $\mathrm{m} \angle \mathrm{BAC}=118^{\circ}$[/tex]

[tex]- $\mathrm{m} \angle \mathrm{BAG}=59^{\circ}$[/tex]

DG = 4

BE = 10.99

BG = 11.7

GC = 20.4

The intersection of the three angle bisectors, which split each angle vertex into two, defines the incenter of a triangle.

The incenter is a point that is at a right angle and equally distant from each of the triangle's three sides.

The measurements in the image can be determined as indicated below by applying the aforementioned properties.

- Given:

[tex]& m \angle E B G=20^{\circ} \\[/tex]

[tex]& m \angle E C G=11^{\circ} \\[/tex]

CF = 20

EG = 4

BD = 11

Find [tex]$m \angle A B G$[/tex]

[tex]$m \angle A B G=m \angle E B G$[/tex]  (angle bisector definition)

- Substitute

[tex]\mathrm{m} \angle \mathrm{ABG}=20^{\circ}$$[/tex]

Find [tex]$m \angle B C A$[/tex] :

[tex]$m \angle B C A=2(m \angle E C G)$[/tex] (angle bisector definition)

- Substitute

[tex]& m \angle B C A=2(11) \\[/tex]

[tex]& \mathbf{m} \angle \mathbf{B C A}=\mathbf{2 2}^{\circ}[/tex]

Find [tex]$m \angle B A C$[/tex]

[tex]$m \angle B A C=180-(m \angle C B A+m \angle B C A)$[/tex] (sum of triangle definition)

- Substitute

[tex]& m \angle B A C=180-(40+22) \\[/tex]

[tex]& \mathbf{m} \angle \mathbf{B} \mathbf{A C}=\mathbf{1 1 8}^{\circ}[/tex]

Find [tex]$m \angle B A G$[/tex]

[tex]$m \angle B A G=\frac{1}{2}(m \angle B A C)$[/tex]  (angle bisector definition)

- Substitute

[tex]& m \angle B A G=\frac{1}{2}(118) \\[/tex]

[tex]& \mathrm{m} \angle \mathbf{B A G}=\mathbf{5 9}^{\circ}[/tex]

Find DG :

DG = EG (Perpendicular bisectors of the sides of a the triangle are equal in length from the incenter of a triangle) (Perpendicular bisectors of the sides of a the triangle are equal in length from the incenter of a triangle)

- Substitute

DG = 4

Find BG:

[tex]$B G=\sqrt{B D^2+D G^2}$[/tex] (Pythagorean Theorem)

- Substitute

[tex]& B G=\sqrt{11^2+4^2} \\[/tex]

[tex]& B G=\sqrt{137} \\[/tex]

[tex]& \mathbf{B G}=11.7[/tex]

Find BE :

[tex]B E=\sqrt{B G^2-E G^2}[/tex] (Pythagorean Theorem) }

- Substitute

[tex]& B E=\sqrt{11.7^2-4^2} \\[/tex]

[tex]& B E=\sqrt{120.89} \\[/tex]

[tex]& \mathbf{B E}=\mathbf{1 0 . 9 9}[/tex]

Find GC:

[tex]$G C=\sqrt{C F^2+F G^2}$[/tex] (Pythagorean Theorem)

- Substitute

[tex]$$ GC=\sqrt{20^2+4^2}[/tex]

[tex]G C=\sqrt{416}[/tex]

GC = 20.4

In conclusion, using the definition of a triangle's incenter, the measurements of triangle ABC, where G is the incenter, are as follows:

[tex]- $\mathrm{m} \angle \mathrm{ABG}=20^{\circ}$[/tex]

[tex]- $\mathrm{m} \angle \mathrm{BCA}=22^{\circ}$[/tex]

[tex]- $\mathrm{m} \angle \mathrm{BAC}=118^{\circ}$[/tex]

[tex]- $\mathrm{m} \angle \mathrm{BAG}=59^{\circ}$[/tex]

DG = 4

BE = 10.99

BG = 11.7

GC = 20.4

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The types of triangles that describe the park, that is, Triangle ABC are:

An equilateral triangle is a triangle where all three sides are equal in length. An isosceles triangle is a triangle where two sides are equal in length.

A scalene triangle is a triangle where all three sides have different lengths. A right triangle is a triangle where one of the angles measures 90 degrees. An acute triangle is a triangle where all angles measure less than 90 degrees. An obtuse triangle is a triangle where one of the angles measures more than 90 degrees.

For example, if the park outline is a triangle with all three sides of equal length, then the triangle would be an equilateral triangle. If the park outline is a triangle with one angle measuring more than 90 degrees, then the triangle would be an obtuse triangle.

Complete Question:

"Triangle ABC makes the outline of a new park. Select all the types of triangles that describe the park?"

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Answer:

The value of (y+6) is greater in 4(y+6).

Step-by-step explanation:

This is because the higher number of y's there are, the higher number you have to divide by, therefore in the end the number is smaller.

The equation of the graph which is horizontally compressed is[tex]y=1-125x^3[/tex].

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here the given graph equation is y = 1-[tex]x^3[/tex] .

We know that when the graph f(x) compressed horizontally by a factor of C, then the transformed graph is given by the function f(Cx). Then

So, when the graph [tex]y=1-x^3[/tex] is compressed horizontally by a factor of 5 then,

=> y = [tex]1-(5x)^3[/tex]

=> [tex]y=1-125x^3[/tex]

Hence the compressed graph is  [tex]y=1-125x^3[/tex].

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Answer: g(0) = 4

Step-by-step explanation:

Given that, g(x) = 3 + x + ex

g'(x) = 1 + ex > 0

⇒ g(x) is an increasing function.

g(0) = 3 + 0 + e0

g(0) = 3 + 1

g(0) = 4

When g(0) = 4, the inverse of the function g(x) = 3 + x + e^x is g^-1(4) = 0.

A function from a set X to a set Y allocates precisely one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain. Originally, functions were the idealization of how a variable quantity depended on another quantity. A function is an equation with just one solution for y for every x. A function produces exactly one output for each input of a certain type. Instead of y, it is usual to call a function f(x) or g(x). f(2) indicates that we should discover our function's value when x equals 2.

Here,

Given that, g(x) = 3 + x + e^x

g'(x) = 1 + e^x > 0

g(x) is an increasing function.

g(0) = 3 + 0 + e^0

g(0) = 3 + 1

g(0) = 4

g^-1(4) = 0

The inverse of function g(x) = 3 + x + e^x is g^-1(4) = 0 when g(0) = 4.

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Answer: L= 8 miles D= 22

Step-by-step explanation:

Divided 206 by 9 get 22.8. 22 is for the days that it took the construction workers to pave the road. and 8 for 8 miles left that needs to be paved.