Write the quadratic function g (x) = x² - 2x - 5 in vertex form.

The ant population will reach 38.2 thousand in about 3.25 years, assuming a growth rate of 5% per year.

To answer this question, we need to know the growth rate of the ant population. Let's say the growth rate is 5% per year. This means that each year, the population will increase by 5% of its current size. To calculate the population size after a certain number of years, we can use the formula:

P = P0 * (1 + r)^t

where P is the population size after t years, P0 is the initial population size, r is the growth rate as a decimal, and t is the number of years.

Assuming the initial population size is 30 thousand, we can plug in the values to find when the population will reach 38.2 thousand:

38.2 = 30 * (1 + 0.05)^t

Solving for t, we get t = 3.25 years. However, it's important to note that the actual growth rate may be different, so this calculation is just an estimate.

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The correct matrices are:

Matrix:

7 1 5

1 5 7

5 7 1

Matrix:

9   18  27

27 -9  18

18  27 9

Matrix:

8 1 6

6 8 1

1 6 8

Matrix:

7 1 5

1 5 7

5 7 1

[tex]Diagonal elements of A^2 are: 7^2 + 1^2 + 5^2[/tex]

Matrix:

9   18  27

27 -9  18

18  27 9

[tex]Diagonal elements of A^2 are: 9^2 + 27*18 + 18*27 or (-9)^2[/tex]

Matrix:

8 1 6

6 8 1

1 6 8

[tex]Diagonal elements of A^2 are: 8^2 + 6*1 + 1*6[/tex]

Matrices play an instrumental role in mathematics due to their versatility as an array of numbers or symbols arranged in rows and columns within a rectangular configuration.

The extensive application extends beyond just math into other areas like computer science or physics.

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The expected count of women who ranked the dark-skinned model as the most beautiful is 100.

Since there are three models, we would expect 100/3 = 33.33% of the women to have ranked each model as the most beautiful if there were no relationship between skin color and beauty judgements. Thus, we can calculate the expected count of women who ranked the dark-skinned model as the most beautiful as follows:

Expected count = 300 * 33.33% = 100

Therefore, we can expect that 100 women out of the 300 sampled would have ranked the dark-skinned model as the most beautiful if there were no relationship between skin color and beauty judgements. The observed count of 55 women who ranked the dark-skinned model as the most beautiful is higher than the expected count, which suggests that there may be a relationship between skin color and beauty judgements. However, further statistical tests would be needed to confirm this.

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As the function f is defined piecewise with different rules on different intervals, we need to check the continuity of f at each point of its domain.

In order for a function to be continuous, it needs to be defined and have no breaks, jumps, or holes in its graph. Let's consider the function f with a positive constant k.

The function f can be written as:

f(x) = {

kx^2, if x < 2,

4k - 3x, if x >= 2

}

To determine the value of k for which f is continuous, we need to ensure that the two cases defined for f match at the point x = 2.

When x < 2, the function is defined as kx^2. At x = 2, this becomes k(2)^2 = 4k.

When x >= 2, the function is defined as 4k - 3x. At x = 2, this becomes 4k - 3(2) = 4k - 6.

For the function f to be continuous, the values of 4k and 4k - 6 must be equal at x = 2. Therefore, we have the equation 4k = 4k - 6.

Simplifying the equation, we find that -6 = 0, which is not true for any value of k.

Since the equation has no solution, it means that there is no specific value of k for which f is continuous. However, we can note that for all positive values of k, the function will still be defined in both cases and continuous within each individual case. Therefore, the function f will be continuous for all positive values of k.

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Answer:

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

To calculate the variance for this set of data, you simply need to square the sample standard deviation.

In this case, the sample standard deviation is 7.79.

The variance for this set of data is 60.68.

For the given data with standard deviation of 7.79, the variance is 60.68.

The given sample standard deviation for the number of new vehicles sold per month for a sample of 6 car dealerships is 7.79, we have to calculate the variance for this set of data. The formula to calculate variance is:

Var(X) = s2 = (Σ(X - μ)2) / N

Where, X = each value of the dataset, μ = mean of the dataset, N = total number of values in the dataset

Given that,

Standard deviation (s) = 7.79, Sample size (n) = 6, Variance (s²) = ?

We know that, variance = (standard deviation)²

Variance = 7.79²

Variance = 60.6841 ≈ 60.68

Hence, the variance for the given set of data is 60.68 (approx).

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The incorrect statement is

1: The transformation can be represented by (x, -y).

In geometry reflection is a transformation that produces the mirror image of a figure across a line or a plane.

The line or plane across which the figure is reflected is called the line of reflection. The image produced by reflection is a congruent image of the original figure

the reflection depicted is over the y axis and the reflection rule in this case is

(x, y) →  (-x, y)

Other options are true as the pre image is in the fourth quadrant and is congruent with the image.

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The system of the equations that describes the situation can be represented as: j + g = 23, j - 2g = - 4

A system of equation is a linear algebraic expression that are represented in variables with their coefficients. A system of equation usually comprises of two equation and these equation are attached to their individual constant.

This implies that, we can have a system of equations where x and y are the variables and the constant can be any number. From the given information, let's assume that the variable for Jodi is "j" and Jerry is "g", then:

j + g = 23

If Jodi buys 4 less than twice number of Jerry's games, then we can have:

j = 2g - 4

j - 2g = - 4

Therefore, the system of the equations can be represented as:

j + g = 23        ------- (1)

j - 2g = - 4     --------- (2)

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The baby bird's initial height above the ground would be 10 meters when it jumped.

I understand you would like to know the height of the baby bird above the ground when it jumped, using the function "f" that models its height (in meters) as a function of time (in seconds).
To find the bird's initial height above the ground when it jumped, we need to evaluate the function f at the time when the bird just jumped, which is at time t = 0 seconds.
Step 1: Plug t = 0 into the function f(t).
f(0) = (height of the bird at time t = 0 seconds)
Since you didn't provide the specific function f, I cannot give you the exact height value. However, once you have the function f(t), simply substitute t = 0 and calculate f(0) to find the bird's initial height above the ground when it jumped.
For example, if the function were f(t) = 10 - 2t, you would do:
f(0) = 10 - 2(0) = 10
the baby bird's initial height above the ground would be 10 meters when it jumped. Make sure to use your given function f(t) to find the accurate height for your problem.

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The maximum height above the ground attained by the bird is 16 meters

The curve showing the travel path of the bird from a tree is a parabola.

Examining the graph attached in the problem, the maximum height reached with is same as the vertex of the parabola, is at point (2, 16)

hence we can say that the height reached by the bird is equal to 16 m

The attached graph shows the point marking the height the bird traveled

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Answer: 22

Step-by-step explanation:

Ok, so the way I do it I multiply then divide.

For Monday I did: ?/220=55/100. what you would do is multiply across then divide by the other number, so 220x55 which is 12100 then you will divide it by 100. So 121 people voted on Monday

For Tuesday: Using the same method. ?/220=45/100 you will multiply 45x220 giving you 9900 then you will divide by 100 giving you 99. 99 people voted on Tuesday.

So to find the DIFFERENCE you need to subtract, so 121-99 leaving you with 22. Also, if you are confused how on where I got 100 from you put the percentage over 100, because percentages go from 0%-100% so you put the partial percentage over the maximum (100)  

Answer:

sec θ

Step-by-step explanation:

cos θ + sin θ tan θ

= cos θ + sin θ (sin θ / cos θ)

= cos θ + (sin²θ)/cos θ

= cos θ + (1 - cos²θ) / cosθ

= cos θ + 1/cos θ - cos²θ/cos θ

= cos θ + 1/cos θ - cos θ

= 1/cos θ

= sec θ

The volume of the tool box is 2,052 cubic inches.

To find the volume of a rectangular solid, we need to multiply its length, width, and height. In this case, the length is 19 inches, the width is 12 inches, and the height is 9 inches. So, we can use the formula:

Volume = length x width x height

Volume = 19 in. x 12 in. x 9 in.

Volume = 2,052 cubic inches

Therefore, the volume of the tool box is 2,052 cubic inches.

Conclusion: The tool box has a volume of 2,052 cubic inches, which means it can hold that much space or stuff inside it.
The volume of the toolbox is 2052 cubic inches.


To calculate the volume of a rectangular solid, you multiply the length, width, and height of the solid. In this case, the dimensions of the toolbox are 19 inches (length), 12 inches (width), and 9 inches (height).

Step 1: Multiply the length, width, and height:
Volume = Length × Width × Height

Step 2: Substitute the given dimensions:
Volume = 19 inches × 12 inches × 9 inches

Step 3: Perform the multiplication:
Volume = 2052 cubic inches

The volume of the rectangular solid toolbox with sides of 19 inches, 12 inches, and 9 inches is 2052 cubic inches.

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The equation that represents the grade for the assignments is:

Y = 6(X) + 50

The general formula for the equation of a line in slope intercept form is expressed as:

y = mx + c

where:

m is slope

c is y-intercept

We are told that they give 6 points each for each assignment done and a base grade of 50. Thus, using the format of linear equation in slope intercept form, we have the equation as:

Y = 6(X) + 50

Here 6 is the slope.

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The probability of drawing a green candy and a blue candy from the bag, one at a time and without replacement, is approximately 0.077 or 7.7%.

To calculate the probability of drawing a green candy and a blue candy from the bag without replacement, we need to determine the total number of candy combinations and the favorable combinations (green and blue candies).

The total number of candies in the bag is 3 blue + 4 green + 6 red = 13 candies.

When drawing the first candy, there are 13 candies to choose from. If a green candy is drawn, there are 4 green candies remaining out of the 12 candies left in the bag. Now, if a blue candy is drawn as the second candy, there are 3 blue candies remaining out of the 11 candies left in the bag.

The probability of drawing a green candy and a blue candy can be calculated as follows:

Probability = (Number of favorable combinations) / (Total number of candy combinations)

Number of favorable combinations = 4 (number of green candies) * 3 (number of blue candies) = 12

Total number of candy combinations = 13 (total candies) * 12 (remaining candies) = 156

Probability = 12 / 156 ≈ 0.077 or 7.7% (rounded to the nearest tenth)

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Answer:

A histogram would be the most appropriate graph to display the distribution of scores and identify clusters and gaps.

Step-by-step explanation:

Simplifying the expression, 7x + 9 - 3x + 4, we can combine the like terms to get: 4x + 13.

Like terms are terms that have the same degree or are of the same variable, for example, 3x and 7x are like terms, 9 and 4 are like terms as well because they are constants.

Given the expression, 7x + 9 - 3x + 4, we can simplify the expression by combining like terms as shown below:

Rearrange the expression:

7x - 3x + 9 + 4 [note that 7x and 3x are like terms while 9 and 4 are also like terms]

Combine like terms:

4x + 13

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Mr. Adam Bought 15 cookies and 10 muffins.

Variables to represent the number of muffins and cookies that Mr. Adam bought. We'll let x be the number of muffins and y be the number of cookies. Then we can set up two equations based on the information given:

Equation 1: x + y = 20   (the total number of muffins and cookies is 20)

Equation 2: 0.5y = 1.5x + 5   (the cost of the cookies is $5 more than the cost of the muffins)

Let's simplify Equation 2 by dividing both sides by 0.5:

y = 3x + 10

Now we can use substitution to solve for one of the variables. We can rearrange Equation 1 to solve for x:

x = 20 - y

Then we can substitute this expression for x in Equation 2:

y = 3(20 - y) + 10

Simplifying this equation, we get:

y = 50 - 3y

Adding 3y to both sides, we get:

4y = 50

Dividing both sides by 4, we get:

y = 12.5

This means that Mr. Adam bought 12.5 cookies. However, we can't have a fraction of a cookie, so let's check whether our solution makes sense in the context of the problem.

If Mr. Adam bought 12.5 cookies, he must have bought 7.5 muffins (since x + y = 20). But we can't have a fraction of a muffin either.

Therefore, it's likely that there was an error in the problem setup. One possibility is that Mr. Adam actually bought a total of 25 muffins and cookies (instead of 20). In this case, the equations would be:

Equation 1: x + y = 25

Equation 2: 0.5y = 1.5x + 5

Following the same steps as before, we would get:

y = 15 and x = 10

Therefore, Mr. Adam bought 15 cookies and 10 muffins.

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Hello

9¹⁴ x 9² ÷ 9⁵

= 9¹⁴⁺² ÷ 9⁵

= 9¹⁶ ÷ 9⁵

= 9¹⁶⁻⁵

= 9¹¹

The unknown exponent "x" is equal to 11. So the simplified expression is 9¹¹ - 9¹¹.

Let's begin by applying the rules of exponents to simplify the given expression:

Step 1: Combine the exponents when multiplying the same base.

[9¹⁴ x 9²] can be simplified to 9¹⁴⁺² = 9¹⁶.

Step 2: Calculate 9⁵.

9⁵ = 9 x 9 x 9 x 9 x 9 = 59,049.

Step 3: Now we have the expression: 9¹⁶ / 59,049 - 9ˣ.

We need to find the value of the unknown exponent that completes the expression. Let's denote the unknown exponent as "x."

Step 4: Subtract the exponents when dividing the same base.

9¹⁶ / 59,049 can be written as 9¹⁶⁻⁵ = 9¹¹

Step 5: So, the simplified expression is 9¹¹ - 9ˣ.

Now, we want to find the value of "x."

Step 6: To do this, we can set the exponents equal to each other since they have the same base.

We have: 11 = x.

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The resulting confidence interval will give you the range of values within which the true slope of the line is likely to fall, with a 90% level of confidence.

To find a 90% confidence interval for the slope of the true line describing the association between Math and Verbal scores, we would need to conduct a regression analysis on the data. This would allow us to estimate the slope of the line and calculate a confidence interval around that estimate.

Assuming that we have already conducted the analysis and obtained the necessary statistics, let's say that our estimate for the slope is 0.8 with a standard error of 0.2. Using a t-distribution with n-2 degrees of freedom (where n is the sample size), we can calculate a 90% confidence interval around our estimate by multiplying the standard error by the appropriate t-value (in this case, 1.645) and adding and subtracting the resulting value from our estimate.

Thus, our 90% confidence interval for the slope would be (0.8 - (1.645*0.2), 0.8 + (1.645*0.2)) = (0.452, 1.148). This means that we can be 90% confident that the true slope of the line describing the association between Math and Verbal scores falls somewhere within this interval.

In this context, our confidence interval tells us how uncertain we are about the true relationship between Math and Verbal scores. Specifically, it tells us that there is a 90% chance that the true slope of the line falls within the range of 0.452 to 1.148. This means that we cannot be absolutely certain about the direction or strength of the relationship between these two variables, but we can be reasonably confident that it falls within this range.

a) To find a 90% confidence interval for the slope of the true line describing the association between Math and Verbal scores, follow these steps:

Step 1: Obtain the data for both Math and Verbal SAT scores.

Step 2: Perform a linear regression analysis to obtain the sample slope (b) and its standard error (SE).

Step 3: Determine the critical value (t) for the 90% confidence level. This can be found using a t-table or a calculator with the appropriate degrees of freedom (n-2, where n is the number of data points).

Step 4: Calculate the margin of error by multiplying the standard error (SE) by the critical value (t).

Step 5: Create the confidence interval by adding and subtracting the margin of error from the sample slope (b).

The resulting confidence interval will give you the range of values within which the true slope of the line is likely to fall, with a 90% level of confidence.

b) In this context, the 90% confidence interval for the slope means that we are 90% confident that the true slope of the line describing the association between Math and Verbal scores falls within the calculated range. This gives us an indication of the strength and direction of the relationship between the two variables. If the interval contains only positive values, it suggests a positive association between the scores; if it contains only negative values, it suggests a negative association; and if it includes zero, we cannot conclude that there is a significant association between Math and Verbal scores at the 90% confidence level.

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Answer:

8 decimeter are 800 millimeters

Step-by-step explanation:

Just multiply the length value by 100

Hope this helps :)

Pls brainliest...

Answer: 8 decimeters equals 800 millimeters.

Step-by-step explanation:

We know that,

1 decimeter = 100 millimeter

Therefore, To convert decimeters to millimeters, we have to multiply it by 100.

Hence, mm= dm*100

                   = 8*100

                   = 800

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The length of the room (h) is 18 feet. The width of the room is (h - 4), so the width is 18 - 4 = 14 feet.The dimensions of the room are 18 feet by 14 feet.

Let's denote the length of the room as h. According to the problem, the width is four feet less than the length, so the width can be represented as (h - 4).

The area of a rectangle is given by the formula: area = length * width. In this case, the area is given as 252 square feet. Therefore, we can write the equation:

252 = h * (h - 4)

To solve this equation, we need to put it in standard quadratic form, which is ax² + bx + c = 0. Expanding the equation and rearranging terms, we have:

h² - 4h - 252 = 0

Now we can solve this quadratic equation. It can be factored or solved using the quadratic formula. Factoring it, we find:

(h - 18)(h + 14) = 0

Setting each factor equal to zero, we have two possible solutions:

h - 18 = 0 or h + 14 = 0

Solving for h, we find:

h = 18 or h = -14

Since the dimensions of a room cannot be negative, we discard the solution h = -14.

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Answer:

2 there we have the second quadrant

So the equation of the tangent line to the graph of y = x + cos x at the point (0, 1) is y = x + 1.

To find the equation of the tangent line to the graph of y = x + cos x at the point (0, 1), we need to find the slope of the tangent line at that point. The slope of the tangent line is given by the derivative of the function y = x + cos x evaluated at x = 0:

y' = 1 - sin x

y'(0) = 1 - sin 0 = 1

So the slope of the tangent line at the point (0, 1) is 1. Using the point-slope form of the equation of a line, we can write the equation of the tangent line as:

y - 1 = 1(x - 0)

Simplifying, we get:

y = x + 1

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Answer: 4.97

Step-by-step explanation:

h(0.1) means value of h(x) when x = 0.1

Plug in x = 0.1 into h(x): h(0.1) = -3*(0.1)^2+5 = -3*0.01+5 = -0.03+5 = 4.97

the equation of the ellipse in standard form with the given properties is:

x²/16 + y²/16 = 1

What is ellipse?
An ellipse is a closed curve that is symmetric about its center. It is a type of conic section, which is formed by intersecting a cone with a plane. An ellipse is defined as the set of all points in a plane for which the sum of the distances to two fixed points (called the foci) is constant.

To write the equation of an ellipse in standard form with the center at the origin, foci at (-1, 0), and co-vertices at (0, -4), we can use the following information:

Center: (h, k) = (0, 0) (since the center is at the origin)

Foci: (c, 0) = (-1, 0)

Co-vertices: (0, b) = (0, -4)

Let's denote "a" as the distance from the center to the vertices and "c" as the distance from the center to the foci.

From the given information, we can deduce that:

a = 4 (since the distance from the center to the co-vertices is 4)

c = 1 (since the distance from the center to the foci is 1)

The standard form equation for an ellipse with a horizontal major axis and center at the origin is:

x²/a² + y²/b² = 1

Substituting the values we found:

x²/4² + y²/(-4)² = 1

Simplifying the equation:

x²/16 + y²/16 = 1

Thus, the equation of the ellipse in standard form with the given properties is:

x²/16 + y²/16 = 1

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Answer:

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

Both angles PQS and PRS intercept same arc PS, hence they have same measure:

Substitute values and solve for x:

Plug in the value of x into either angle measure:

The intercepted arc is twice the inscribed angle measure:

Answer:

130

Step-by-step explanation:

Answer:

Cylinder:  π r² h

Cone:  V=1/3hπr²

Sphere: V = 4/3 πr³

One-third of the volume of a cylinder

Step-by-step explanation:

Your welcome

Mrs. Coleman can make 20 dresses from the remaining fabric.

To determine how many dresses Mrs. Coleman can make from the remaining fabric, we need to calculate the available fabric after she used 3 meters for her skirt and convert it to centimeters.

Given:

Total fabric received = 25 meters

Fabric used for Mrs. Coleman's skirt = 3 meters

Remaining fabric = Total fabric received - Fabric used for the skirt

Remaining fabric = 25 meters - 3 meters

Remaining fabric = 22 meters

Now, we need to convert the remaining fabric from meters to centimeters:

1 meter = 100 centimeters

Remaining fabric in centimeters = Remaining fabric in meters * 100 centimeters/meter

Remaining fabric in centimeters = 22 meters * 100 centimeters/meter

Remaining fabric in centimeters = 2200 centimeters

To calculate the number of dresses Mrs. Coleman can make, we divide the remaining fabric in centimeters by the fabric needed per dress:

Number of dresses = Remaining fabric in centimeters / Fabric needed per dress

Number of dresses = 2200 centimeters / 110 centimeters per dress

Number of dresses = 20 dresses

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Option B is correct, 2/3 is the scale factor of the dilation.

Triangle A'B'C' is the dilated form of the triangle ABC

By the translation of dilation an object becomes larger or smaller

Scale factor is the size by which the shape is enlarged or reduced.

Let us consider the side AB which has 12 units

When it is multiplied with 2/3 we get 8 which is length of A'B'

Similarly let us check for other sides of the triangle, which gives 2/3 as a scale factor

Hence, 2/3 is the scale factor of the dilation.

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