Why did Michael Gallin begin making tweaks to

the way he taught math to his students?

The equation for the described function can be written as:

y = cos(x - π) - 9/2

Let's break down the components of the equation:

The cosine function, cos(x), produces a periodic wave with an amplitude of 1.

The period of the cosine curve is determined by the coefficient in front of the angle, which is 1 in this case. A period of 1 corresponds to one complete cycle of the cosine curve.

The left phase shift of π shifts the entire curve to the right by π units.

The vertical translation down by 9/2 units shifts the entire curve downwards by 9/2 units.

Therefore, the equation y = -cos(x - π) - 9/2 represents a cosine curve with the given characteristics.

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Answer:

picture ?

Step-by-step explanation:

Answer:

Hope it helps...

Step-by-step explanation:

Answer:

-10/7

Step-by-step explanation:

Use slope formula

[tex]\frac{y2-y1} {x2-x1}[/tex]

x1= -3

y1 = 5

x2 = 4

y2 = -5

[tex]\frac{-5-5}{4--3}[/tex]

[tex]\frac{-10}{7}[/tex]

Similar to the univariate t-test, the bivariate t-test has all of the mentioned characteristics, so, E. All of the above.

The univariate and bivariate t-tests are different in the fact that while one measures only one variable, the other measures two variables.

The similarities between these tests include the fact that they both require ratio or interval data, they are both drawn from populations with normal distributions and they are useful for analyzing large sample sizes. Also, the two tests ate useful when the population's standard deviation is known.

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The correct boxes to check are x = 1 and x = 2.

To identify the vertical asymptotes of the function f(x) = (x - 8) / ([tex]x^{2}[/tex]- 3x + 2), we need to determine the values of x for which the denominator of the function becomes zero. These values will give us vertical asymptotes.

Breaking the denominator into the factors :

[tex]x^{2}[/tex] - 3x + 2 = (x - 1)(x - 2)

Setting the denominator equal to zero:

x - 1 = 0 --> x = 1

x - 2 = 0 --> x = 2

So, the vertical asymptotes of the function are:

x = 1 and x = 2.

Now, let's check for diffrent values of x:

x = -8 (This is not a vertical asymptote as it is not related to the function's denominator.)

x = -2 (This is not a vertical asymptote as it is not associated with the function's denominator.)

x = -1 (This is not a vertical asymptote as it is not related to the function's denominator.)

x = 1 (This is a vertical asymptote.)

x = 2 (This is a vertical asymptote.)

x = 8 (This is not a vertical asymptote as it is not related to the function's denominator.)

Therefore, the correct boxes to check are x = 1 and x = 2.

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The correct question is given below -

Identify the vertical asymptote(s) of each function. Check all of the boxes that apply. f(x)=x-8/[tex]x^{2}[/tex]-3x+2

x = -8

x = -2

x = -1

x = 1

x = 2

x = 8

Answer:

D and E for the first one. B and D for the second one

Step-by-step explanation: edg is stinky, i hope this helped a little

Hello!

This is a question about ratios and relating them to multiples of the ratio.

We are given that a recipe for cooking rice requires 14 cups of boiling water for every 8 cups of rice.

Then we are asked how many cups of rice are needing to be added if we have 28 cups of boiling water.

Since 28 is two times 14, and assuming that this ratio is proportional, we can multiply the cups of rice by 2 to find the equal ratio.

That means that 16 cups of rice should be added if we have 28 cups of boiling water.

In terms of ratios, we can set up the following proportion.

[tex]\frac{14}{8}=\frac{28}{x}[/tex]

Then here, we can cross multiply and solve for [tex]x[/tex].

[tex]14x=224[/tex]

[tex]x=16[/tex]

Hope this helps!

A converging lens with a focal length of 6.70 cm forms an erect image of a 4.80 mm tall real object positioned to the left of the lens. The resulting image is 1.50 cm tall.

A converging lens is a lens that bulges in the middle and causes light rays to converge. In this case, the lens has a focal length of 6.70 cm, which means that parallel rays of light incident on the lens will converge to a point 6.70 cm away from the lens. The object, positioned to the left of the lens, has a height of 4.80 mm. When the light rays from the object pass through the lens, they refract and intersect at a point to form the image. The image formed is erect, meaning it is in the same orientation as the object. The height of the image is 1.50 cm.

The magnification of the image can be calculated using the formula: magnification = height of image / height of object. In this case, the magnification is 1.50 cm / 4.80 mm. To convert the height of the object to centimeters, we divide 4.80 mm by 10, which gives us 0.48 cm. Therefore, the magnification is 1.50 cm / 0.48 cm, which equals approximately 3.125.

Since the image is erect and the magnification is greater than 1, we can determine that the image is larger than the object. The positive magnification indicates that the image is virtual, which means it cannot be projected onto a screen. The image is formed on the same side of the lens as the object, which is the left side in this case. The image distance can be calculated using the lens formula: 1/f = 1/v - 1/u, where f is the focal length, v is the image distance, and u is the object distance. Since the image is formed on the same side as the object, the object distance is negative (-u). By plugging in the values, we can solve for the image distance. However, additional information, such as the object distance, would be needed to calculate the exact position of the image.

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Answer:

2 of the 3 answers in picture

Step-by-step explanation:

Answer:

The answers are 2, 3, and 1 only

Step-by-step explanation:

This is the correct answer for plato users

Answer:

c) $43.81

Step-by-step explanation:

= $25.00 + ($0.09 × 209)

= $25.00 + $18.81

= $43.81

Answer:

ree kid it is 3409,3567

Step-by-step explanation:

Answer:

no solution

Step-by-step explanation:

Answer:

472

Step-by-step explanation:

break it up into two rectangles

1) 12x18=216 in

2) 8x32=256

Hope this helped

Answer:

472 in²

Step-by-step explanation:

The figure is composed of 2 rectangles , then

area = area of lower rectangle + area of upper rectangle, that is

area = (8 × 32) + (12 × 18) = 256 + 216 = 472 in²

Answer:

2 - x^2

Step-by-step explanation:

By using the property of CPCTC (corresponding parts of congruent triangles are congruent) he can prove ∠DEF ≅ ∠ABC.

Which statement best explains why Ben uses the width BI to create the arc JK from point E?

A.  ∠DEF ≅ ∠ABC when BH = EK, BI = JK, and HI = EJ.

B.  BI = JK when ∠DEF ≅ ∠ABC.

C.  BI = EJ when ∠DEF ≅ ∠ABC.

D.  ∠DEF ≅ ∠ABC when BH = EJ, BI = EK, and HI = JK.

The statement Ben explains why Ben uses the width BI to create the arc JK from point E is  ∠DEF ≅ ∠ABC when BH = EJ, BI = EK, and HI = JK.

The correct option is (D).

Ben ensuring that for making an arc JK,

BH = EJ

BI = EK

HI = JK

These are the three congruent corresponding sides for making an arc.

then, he will use the congruence criteria to ΔDEF ≅ ΔABC.

By using the property of CPCTC (corresponding parts of congruent triangles are congruent) he can prove ∠DEF ≅ ∠ABC.

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Which statement best explains why Ben uses the width BI to create the arc JK from point E.

Answer:

1.

centre(h,k)=(-13,9)

radius (r)=6

we have

equation of the circle is

(x-h)²+(y-k)²=r²

(x+13)²+(y-9)²=6²

x²+26x+169+y²-18y+81=36

x²+y²+26x-18y+169+81-36=0

x²+y²+26x-18y +214=0

is a required equation of the circle.

2.

centre(h,k)=(1,-1)

radius (r)=11

we have

equation of the circle is

(x-h)²+(y-k)²=r²

(x-1)²+(y+1)²=11²

x²-2x+1+y²+2y+1=121

x²+y²-2x+2y=121-2

x²+y²-2x+2y=119

is a required equation of the circle.

There is a high level of confidence that the true proportion lies within the interval of 22% to 27%

The proper interpretation of a 95% confidence interval of a proportion of U.S. adults who own a sports car with an upper limit of 27% and a lower limit of 22% is:

I am 95% confident that the true proportion of U.S. adults who own a sports car is between 22% and 27%.

This interpretation accurately conveys the meaning of a confidence interval. It means that if we were to take multiple random samples and calculate 95% confidence intervals using the same methodology, approximately 95% of those intervals would contain the true proportion of U.S. adults who own a sports car. Therefore, there is a high level of confidence that the true proportion lies within the interval of 22% to 27%.

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Answer:

IQR=13 im pretty sure

Step-by-step explanation:

The measure interquartile range is 13 option (B) IQR= 13 is correct.

A box and whisker plot is a method of abstracting a set of data that is approximated using an interval scale. It's also known as a box plot. These are primarily used to interpret data.

We have a box plot, and the data from a survey of ages of people taking an exercise class was skewed to the left.

We know on the left side skewed has more data on the right and on the left side, there are fewer data.

From the dot plot, the end point is not given, so we are assuming the end point is 58.

IQR = 58 - 45 = 13

Thus, the measure interquartile range is 13 option (B) IQR= 13 is correct.

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Answer:

32. (E)stopped at 2pm

33. (A)

Step-by-step explanation:

32. on the graph you go across the x axis and find where the straight line starts and look for the time

33. look at the y-axis and see what line and the number it is on

The 90% confidence interval for the mean number of calories is 155.3 to 158.4

From the question, we have the following parameters that can be used in our computation:

The dataset

The mean is calculated as

x = sum/count

So, we have

x = (186 + 181 + 176 + 149 + 184 + 190 + 158 + 139 + 175 + 148 + 152 + 111 + 141 + 153 + 190 + 157 + 131 + 149 + 135 + 132) / 20

x = 156.85

Calculate the margin of error using

E = t * σ/√n

Where t = 1.729 i.e. the critical value

So, we have

E = 1.729 * 4/√20

Evaluate

E = 1.55

The confidence interval is then calculated as

CI = x ± E

So, we have

CI = 156.85 ± 1.55

Evaluate

CI = 155.3 to 158.4

Hence, the 90% confidence interval for the mean number of calories is 155.3 to 158.4

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Answer:

12.5

Step-by-step explanation:

Answer:

d: 83

e: 97

f: 83

Step-by-step explanation:

d: We first have to find out f, so f and d can be alternate interior angles, which means they can be congruent to each other.

e: e is a vertical angle to the given angle, which means they are congruent, making it also 97 degrees.

f: f is a supplementary angle to the given angle, which means we can subtract 97 from 180 to give us 83.

Going back to angle d, now that we know f is 83 degrees, then d is an alternate interior angle, so d=f, meaning d is also 83 degrees.

Hope this helps! :)

The weight of each bag of the mixture can be determined by using a tape diagram. Given that Linda mixed 5.15 lb of cashews with 4.32 lb of pistachios, and after filling up 6 bags that were the same size with the mixture, he had 0.05 lb of nuts left.

A tape diagram is a bar model that is used to represent fractions and ratios visually. It is useful when comparing different quantities that are related to each other.Tape DiagramTo solve the problem using a tape diagram, we begin by representing the total weight of the mixture and the weight of each bag using a single length unit. For example, we can choose 1 inch to represent the weight of 1 pound.

In this case, we would represent the total weight of the mixture as 5.15 + 4.32 = 9.47 inches. Next, we divide the total length by the number of bags to find the length of each bag. If the total length of the mixture is 9.47 inches and there are 6 bags, then the length of each bag is:9.47 ÷ 6 = 1.578 inches. Finally, we convert the length of each bag back to pounds by multiplying by the weight of 1 pound, which is 1 inch in our tape diagram. Thus, the weight of each bag is:1.578 × 1 = 1.578 lb. Therefore, the weight of each bag of the mixture is 1.578 lb.

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The  radius of convergence for the Maclaurin series of f(x) is R = 1.

To obtain the Maclaurin series for the given function f(x) = 2ex + e6x, we can use the Maclaurin series expansions of the exponential function. The Maclaurin series for ex is given by e^x = Σ(x^n/n!) from n=0 to infinity, with a radius of convergence of R = ∞.

Using this, we can rewrite the given function as f(x) = 2e^x + e^6x. Substituting the Maclaurin series expansion of ex into the first term and the Maclaurin series expansion of e^6x into the second term, we get:

f(x) = 2(Σ(x^n/n!)) + (Σ((6x)^n/n!))
= 2Σ(x^n/n!) + Σ((6^n)(x^n)/n!)

Now we can combine the two series by collecting like terms and coefficients. The resulting Maclaurin series for f(x) is:

f(x) = Σ((2/n! + (6^n)/n!)(x^n))

The radius of convergence of this series will be determined by the smaller of the radii of convergence of the individual series used, which is R = 1 for the series of ex and R = 1 for the series of e^6x. Therefore, the radius of convergence for the Maclaurin series of f(x) is R = 1.

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Answer:

It's the one right under the first one

The point on the line that passes through point H and is perpendicular to line FG is (–6, 10).

First, we need to find the slope of line FG. The slope of a line can be calculated by dividing the change in the y-coordinate by the change in the x-coordinate. In this case, the change in the y-coordinate is 10 and the change in the x-coordinate is 3, so the slope of line FG is 10/3.

Since the lines are perpendicular, their slopes are negative reciprocals of each other. The negative reciprocal of 10/3 is -3/10.

Now, we need to find the equation of the line that passes through point H and has a slope of -3/10. The general equation of a line is y = mx + b, where m is the slope and b is the y-intercept. In this case, we know that m = -3/10 and the y-coordinate of point H is 10. Plugging these values into the equation, we get y = -3/10*x + 10.

To find the x-coordinate of the point we are looking for, we can substitute in the y-coordinate of point H. 10 = -3/10*x + 10, so x = –6.

Therefore, the point on the line that passes through point H and is perpendicular to line FG is (–6, 10).

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The values p = 3 and q = -7 would make the expression (3 – 7i)(p + qi)i equal to 58i.

Let's expand the expression:

(3 - 7i)(p + qi)i = (3 - 7i)(pi - q)

Using the distributive property, we have:

= 3pi - 7pi^2 - 3qi + 7qi^2

Since i^2 is equal to -1, we can substitute -1 for i^2:

= 3pi - 7p - 3qi - 7q

Now, equating the imaginary part to 58i:

-7p - 7q = 58

Dividing both sides by -7:

p + q = -8

From the given options, only p = 3 and q = -7 satisfy this equation:

3 + (-7) = -4

Therefore, the values p = 3 and q = -7 would make the expression (3 – 7i)(p + qi)i equal to 58i.

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Answer:

2 2/5=5/5+5/5+2/5=12/5

3 3/4= [(3•4)+3]/4=15/4

(12/5) / (15/4)= 12/5 • 4/15=12•4/5•15=

48/75 kilometers in 1 minute

Step-by-step explanation:

How that this helps! :)

Have a great rest of your day/night!