What is the equation of the line that passes through the points (4, 5) and (7, 3)

As per given by the question,

(a) There are given that diameter of the ice cream cone is 3.5 cm, and height is 6 cm.

Now,

Ftom the formula of the volume of the ce cream.

So,

Then,

There are given tha a diameter is 3.5,

So, Radius of the ice cream cone is,

Now,

Substitute the value in above formula,

So,

Hence, the 19.23 cm ice cream fit in the cone.

(b). There are given that diameter of 1 scoop ice cream is 3.5 cm.

Then,

The formula of the one scoop ice cream is,

Now,

The radius is,

So,

Hence, the volume of the one scoop ice cream is 22.44 cm.

In ridge regression, the penalty strength parameter, represented by \lambda», controls the trade-off between fitting the training data well and keeping the model coefficients small.

When a very large penalty strength is chosen, it results in a higher degree of shrinkage of the regression coefficients towards zero. This means that the model becomes less complex and less likely to overfit the training data. However, it also means that the model may become too biased towards the null hypothesis, leading to underfitting and decreased predictive power. Therefore, choosing the right value of \lambdaλ is crucial for achieving optimal performance in ridge regression.
In ridge regression, choosing a very large λ (lambda) penalty strength results in a higher regularization effect, which helps to reduce overfitting by shrinking the coefficients of the independent variables towards zero. This helps to create a more generalized model by controlling the complexity of the model. However, choosing a λ value that is too large can also result in underfitting, as the model may become too simple to capture the underlying relationships in the data effectively.

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The factorized form of each expression is given below:

a. (x - 5)(x + 5)

b. (y - 6)(y + 6)

c. (x - 1)(x - 13)

d. (s + 2)(s + 5)

e. (q - 4)(q - 3)

f. (r + 1)(r + 12)

g. (x - 5)(x + 4)

h. (y + 2)(y + 3)

i. (b - 3)(b + 4)

j. (k - 2)(k - 3)

a. x² - 25:

The difference of squares formula is a² - b² = (a - b)(a + b).

Here, a = x, b = 5. So, x² - 25 = (x - 5)(x + 5).

b. y² - 36:

Again, using the difference of squares formula, a = y, b = 6. So, y² - 36 = (y - 6)(y + 6).

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The correct formula for the revenue generated by the item is Revenue = 200p - 5p^2.

The revenue generated by the item can be calculated by multiplying the price (p) by the unit sales (200 - 5p). Therefore, the correct formula for the revenue generated by the item is:

Revenue = Price x Unit Sales
Revenue = p(200 - 5p)
Revenue = 200p - 5p^2

The revenue generated by the item is a quadratic function of the price (p). To find the maximum revenue, we need to differentiate the function with respect to p and set it equal to zero:

dRevenue/dp = 200 - 10p = 0
10p = 200
p = 20

Therefore, the maximum revenue is generated when the price of the item is $20. Substituting p = 20 in the revenue formula, we get:

Revenue = 200(20) - 5(20^2) = $2000

Hence, the correct formula for the revenue generated by the item is Revenue = 200p - 5p^2, and the maximum revenue is achieved when the price of the item is $20, generating a revenue of $2000.

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Answer:

So starting off with 1a f(4)

We simply substitute x with 4 for the function

f(4)=2(4)-5

f(4)=8-5

f(4)=3

Next 1b, here it's a little different since you have to multiply the functions I think ( please correct me if I'm wrong).

gf(4), basically means functions g and f are being multiplied and their variables are being substituted with 4.

g(4)=4^2+3

g(4)=16+3

g(4)=19

and we also know from before that f(4)=3, so we'll do 19 times 3 which is 57

For the next two, I may be wrong, but I'm still going to try:

anything to the power of a negative is a fraction so for f^-1(x)=2x-5 we'll have 1/f(x)=x/2+5/2

And then for g^-1, we'll have 1/g(x)=\(\sqrt{x-3} \sqrt{x-3}\)

Hope I helped :)

Answer:

3

Step-by-step explanation:

Answer:

M = (2500 + 193.25) / 24 = $113.03

We can use the monthly payment to calculate the finance charge over the life of the loan, which is equal to 24 times the monthly payment minus the principal amount:

Finance charge = 24 * M - 2500 = 24 * 113.03 - 2500 = 193.25

Now that we have the finance charge, we can calculate the APR:

APR = (Finance charge / Principal amount) * (12 / Number of months) * 100%

APR = (193.25 / 2500) * (12 / 24) * 100%

APR = 7.73%

So, the APR of this loan is 7.73%.

Answer:

A. d ÷ 11

Explanation:

The quotient of two terms is the division of the first term by the other term.

If we say the quotient of d and 11​, we write it mathematically as:

The correct choice is A.

The part of the graph that would show no change in distance is when Mary stopped and waited for the traffic light to turn green.

Statement B is correct.

We know that during this time, Mary did not move forward or cover any distance. Hence, the graph would show a flat line at this point, indicating no change in distance.

Distance is described as a numerical or occasionally qualitative measurement of how far apart objects or points are.

In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria.

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Answer:

i believe it's B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The row of the table that reveals the x-intercept of the function f is given as follows:

Second row.

A function has two intercepts, which are listed as follows:

The definition of each type of intercept is given as follows:

From the second row of the table, we have that when x = -4, f(x) = 0, hence the x-intercept of the function is of x = -4.

The y-intercept is of y = -16, as from the fourth row, when x = 0, y assumes a value of 16.

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The distance around the track along the inside edge of each lane is shown below.

We have to use

Perimeter = 2 x longer dimension+ π x shorter dimensions

So, Distance between lanes

= 20/8

= 2.5 yards

Now, the perimeters are

Lane 1:

= 2 x 80 + π x 56

= 335.84 yards

Lane 2:

= 2 x 80 + π x (56+ 2 x 2.5)

=  351.54 yards

Lane 3:

= 2 x 80 + π x (56+ 4 x 2.5)

=  367.24 yards

Lane 4:

= 2 x 80 + π x (56+ 6 x 2.5)

= 382.94 yards

Lane 5:

= 2 x 80 + π x (56+ 8 x 2.5)

= 398.64 yards

Lane 6:

= 2 x 80 + π x (56+ 10 x 2.5)

= 414.34 yards

Lane 7:

= 2 x 80 + π x (56+ 12 x 2.5)

= 430.04 yards

Lane 8:

= 2 x 80 + π x (56+ 14 x 2.5)

= 445.74 yards

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9f =49.6-3.7

9f=45.9

f = 5.1

Step-by-step explanation:

Basically the area of sphere is 4πr² where r is radius whose value is distance from centre to the edge of the given sphere whereas π (pi) whose value is 3.14 or 22/7. It is defined as the ratio between circle's circumference and it's diameter. But are you aware about the area of circle?? Actually that is πr². If you notice carefully you'll find that area of sphere is 4 times the area of circle. So, if you're provided with the area of circle you can simply multiply the value with 4 to get the area of sphere. But if not, then simply plugin the value of radius and pi in 4πr² to find out the area of sphere.

But since the formula is almost same then how they're different? Well the difference between a sphere and a circle is because of two-dimensional and three-dimensional shape. A circle is a two-dimensional flat shape figure whereas a sphere is a three-dimensional shape.

Talking about the unit of sphere. The unit we use is always the same as the units of radius i.e. cm or m. Since, it is the square of the radius in the given formula, then the unit is also the square of the units, or cm² or m².

The formula is given by

\(\\ \rm\hookrightarrow Area=\pi r^2\)

Answer:

20% off 45.00 is 36.00

Step-by-step explanation:

The difference is $9.00

Answer:

$36

Step-by-step explanation:

20% of $45 is $9.

$45 - $9 = $36

For an Arithmetic sequence of numbers with sum of three consecutive terms is equals to the 6 and sum of their cubes is 132 are equal to either -1, 2, 5 or 5,2, -1.

An arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding is equals to a constant number say d. It is also known as an arithmetic progression. We have sum of three consecutive terms in an arithmetic sequence is equals to 6 and the sum of their cubes is 132. Let the three consecutive terms in an arithmetic sequence be \(a_1, a_2, a_3\). So, \(a_1 + a_2 + a_3 = 6 \) -----(1) and a₁³ + a₂³ + a₃³ = 132 ------(2)

We have to determine the three numbers. Now, \(a_1 = a \), \(a_2 = a + d\), \(a_3 = a + 2d \).

Substitute all values in equation(1), a + a + d + a + 2d = 6

=> 3a + 3d = 6

=> a + d = 2

=> a = 2 - d ----(3)

From (3), (2 - d)³ + ( 2 -d +d)³ + (2 - d + 2d)³ = 132

=> (2 - d)³ + 2³ + ( 2 + d)³ = 132

=> 2³ - d³ - 3× 2²d + 6d² + 2³ + 2³ + d³ + 3× 2²d + 6d² = 132

=> 3× 2³ + 2×6d² = 132

=> 12d² + 24 = 132

=> 12d² = 108

=> d² = 9

=> d = ± 3

so, either a = 2 - 3 = -1 , ( d = 3) or a = 2 + 3 = 5 (d = -3)

Hence, required value either -1, 2, 5 or 5,2, -1.

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Based on the residual plot, it is possible to determine whether a regression model is a good fit or not.

A residual plot is a scatterplot of the residuals (the differences between the actual values and the predicted values) against the predicted values. A good regression model should have residuals that are randomly distributed around zero and have roughly equal variance across the range of predicted values.

If the residuals form a pattern, such as a U-shape or a curve, it indicates that the model is not a good fit for the data. Additionally, if there are outliers or extreme values in the residual plot, it suggests that the model may not be appropriate for those observations.

Correct Question :

Based on the residual plot, how do you think that regression model is a good fit?

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Answer:

Step-by-step explanation:

A midsegment connecting two sides of a triangle is parallel to the third side and is half as long.

Answer:

Step-by-step explanation:

x            y

1            2

2           4

3           9

4           16

This sounds like a quadratic equation of f(x)=x^2, thus, the range is:

Answer:

I'm not completely sure but I do know that 7/5 x 15 equals 21 and that there is a difference of 6 so that may help you

Answer:

x=256

Step-by-step explanation:

Answer:

x=256

Step-by-step explanation:

In this case you have a linear equation of the form:

y=mx+b

To graph a line we only need to specify two points of the line and then join them.

b the intercept is zero in this case, and the slope of your line is -1/2. Since the intercept is zero, this means that the line crosses the origin, so the point (0,0) is included in the line, to find other poin of the line we just have to replace a value of x and calculate the value of y, for example let's take x equals 2.

Now, we know that the line crosses the points (0,0) and (2,-1), let's graph them.

Answer:

Step-by-step explanation:

y - 21 = 1/7(x + 7)

y - 21 = 1/7x + 1

y = 1/7x + 22

Answer:

I believe the answer is y=1/7x+22

Step-by-step explanation:

The area of the region R above is given by A = 1. The volume of the solid under the surface f(x, y) = 3x^2 + 4y^3 over the region R is given by V = 3x^2/2 + 1/5

(a) To compute the volume of the solid under the surface f(x, y) = 3x^2 + 4y^3 over the region R = {(x, y) : 1 ≤ x ≤ 2, 0 ≤ y ≤ 1}, we can set up a double integral over the region R.

The volume V is given by the double integral of the function f(x, y) over the region R:

V = ∬R f(x, y) dA

Since f(x, y) = 3x^2 + 4y^3, the volume integral becomes:

V = ∫[1, 2] ∫[0, 1] (3x^2 + 4y^3) dy dx

Now, let's evaluate the integral:

V = ∫[1, 2] [3x^2y + 4y^4/4] dy

  = ∫[1, 2] (3x^2y + y^4) dy

  = [3x^2y^2/2 + y^5/5] |[0, 1]

  = (3x^2/2 + 1/5) - (0 + 0)

Simplifying further, we have:

V = 3x^2/2 + 1/5

Therefore, the volume of the solid under the surface f(x, y) = 3x^2 + 4y^3 over the region R is given by V = 3x^2/2 + 1/5.

(b) To compute the area of the region R above using an iterated integral, we can set up a double integral over the region R.

The area A is given by the double integral of 1 (constant) over the region R:

A = ∬R 1 dA

Since we have a rectangular region R, we can express the area as:

A = ∫[1, 2] ∫[0, 1] 1 dy dx

Now, let's evaluate the integral:

A = ∫[1, 2] [y] |[0, 1] dx

  = ∫[1, 2] (1 - 0) dx

  = [x] |[1, 2]

  = 2 - 1

Therefore, the area of the region R above is given by A = 1.

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The area A of the region bounded by the functions f(x) = 2x\(x^{2}\)2/3 - x - 4 and g(x) = x\(x^{2}\)2 - 2x/3 - 6 can be calculated using the integral: A = int_[−2, 4] f(x) - g(x) dx. The integral evaluates to A = 65/3 units.

To evaluate the integral, we will first use u-substitution with u = x\(x^{2}\)2/3 and du = 2x/3dx. This substitution simplifies the integral to A = int_[−2\(x^{2}\)3, 4\(x^{2}\)3] (2u/3 - u - 4) du.

Next, we use integration by parts with u = 2u/3 - u - 4 and dv = du. This gives us A = (2u/3 - u - 4)v - int_[−2\(x^{2}\)3, 4\(x^{2}\)3] vdu.

We can now find the integral for v by integrating du, giving us v = u + C. Since v must equal zero when u = −2\(x^{2}\)3, we can set C = -2\(x^{2}\)3 and simplify the integral to A = (2u/3 - u - 4)(u + -2\(x^{2}\)3) - int_[−2\(x^{2}\)3, 4\(x^{2}\)3] (u + -2\(x^{2}\)3)du.

Finally, we can find the integral for u + -2\(x^{2}\)3 by integrating du again, giving us (u + -2\(x^{2}\)3) = 3u\(x^{2}\)2/2 + 2\(x^{2}\)3u + C. We can set C = 0 since u + -2^3 must equal zero when u = −2\(x^{2}\)3, and simplify the integral to A = (2u/3 - u - 4)(u + -2\(x^{2}\)3) - int_[−2\(x^{2}\)3, 4\(x^{2}\)3] (3u\(x^{2}\)2/2 + 2\(x^{2}\)3u) du.

Evaluating this integral gives us A = (2u/3 - u - 4)(u + -2\(x^{2}\)3) - 3(4\(x^{2}\)5/2 + 8\(x^{2}\)4)/2 + 2\(x^{2}\)3(4\(x^{2}\)3 + 8\(x^{2}\)2)/2. Substituting in u = 4\(x^{2}\)3 and u = -2\(x^{2}\)3 gives us A = 65/3 units.

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Answer:

6,750 pounds

Step-by-step explanation:

3 3/8 tons = ? pounds

there are 2,000 pounds in 1 ton so:

3 3/8 * 2,000 = 6,750 pounds

Answer:

96,000 people

Step-by-step explanation:

convert the length from miles to feet.

2.5 miles = 13,200 feet

Area = 13,200× 8

Area = 105,600 square feet

but the fans will be on both sides of the sidewalk,hence,

the area will be twice.

105,600 square feet ×2= 211,200 square feet.

1 fan = 2.2 square feet

x = 211,200 square feet

therefore number of fans will be = 96,000 people.

The most appropriate choice for Percentage will be given by

What is percentage?

Suppose there is a number and the number has to be expressed as a fraction of 100. Then that number is called percentage.

For example, 2% means \(\frac{2}{100}\)

Here,

Let the number be x

On increasing x by 10%, result = \(x + \frac{10}{100} \times x\)

                                                  = \(x + \frac{x}{10}\)

                                                  = \(\frac{10x +x}{10}\)

                                                  = \(\frac{11x}{10}\)

Now on increasing his answer by 10 %, result =

                                                                            \(\frac{11x}{10}+\frac{10}{100}\times \frac{11x}{10}\\\frac{11x}{10} + \frac{11x}{100}\\\frac{110x + 11x}{100}\\\frac{121x}{100}\)

Total increase in number = \(\frac{121x}{100} - x\)

                                           = \(\frac{121x-100x}{100} \\\)

                                           = \(\frac{21x}{100}\)

Percentage increase = \(\frac{\frac{21x}{100}}{x} \times 100\)

                                   = 21%

Percentage increase overall = 21 %

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1) In this question, we can notice that theta is in Quadrant IV. In this quadrant, the cosine of theta yields a positive value.

2) So, let's make use of a Pythagorean Identity to find the value of the cosine of theta, given the sine of that same angle:

3) Thus the cosine of theta is 4/5 for in Quadrant IV cosine is positive.