an imaginary circle that goes through both retinae and the fixation point is known as

Answer:

Step-by-step explanation:

sugar: half - 1/6 cup , double - 2/3 cup

mirin: half - 1/8 cup , double - 1/2 cup

shoyu: half - 6 Tbsp , double 1 1/2 cup

flour: half - 5/8 pound , double 2 1/2 pounds

chicken: half - 1 1/4 pounds , double: 5 pounds

To find the exact area of the surface obtained by rotating a curve about the x-axis, we can use the formula for the surface area of revolution. In the first problem, the curve x = (1/3)*(y^2 + 2)^(3/2) is rotated about the x-axis. In the second problem, the curve x = 1 + 3y^2 is also rotated about the x-axis. We will calculate the surface areas for each problem.

Problem 1:

To find the surface area of the first curve, we can integrate the formula 2πy * √(1 + (dx/dy)^2) over the given interval. Taking the derivative of x with respect to y, we get dx/dy = (2/3)*y*(y^2 + 2)^(1/2). Plugging this into the formula and integrating from y = 1 to y = 2, we can calculate the exact surface area of the resulting surface.

Problem 2:

For the second curve, we again integrate the formula 2πy * √(1 + (dx/dy)^2) over the given interval. Differentiating x with respect to y gives us dx/dy = 6y. Substituting this into the formula and integrating from y = 1 to y = 2 will yield the exact surface area of the rotated surface.

By evaluating these integrals, we can find the exact surface areas for both curves when rotated about the x-axis. These calculations will provide the precise values of the surface areas for each problem.

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Answer:

Option D) 302= 77+5x

Step-by-step explanation:

Number of hours he worked = 5hrs

Take 'x' as cost per hour,

Then total cost of labor = 5x

Additional charge for parts = $77

Total amount she spent = $302

Equation for her spending= 5x+ 77 = 302

This can also be written as 302= 77+5x

Hope this helps.

Answer:

Step-by-step explanation:

The triangle would end up back where it started.  It is hard to explain without a graph.  If you have graph paper, you might want to try drawing this out.  Say that the original points are at A (1,2) B (2,0) and C(0,0).  Now, when we reflect the points over the x axis, they will be the same distance below the x that the points original were about the x axis.  Since A was 2 units above the axis, it will now be 2 units below at (1, -2).  Points B and C will stay on the x axis and will remain in place at B(2.0) and C(0,0).  Since these points are on the line, they were not above the x axis, so they will now not be below the x axis.

Now, we are going to reflect the triangle over the y axis.  Since C (0,0) is already on the y axis, it will not move.  It will remain there.  Since B(2,1) is two units to the right of the y axis, when we flip it, it will now be 2 units to the left of the y axis B (-2,0).  Point C will move one unit to the left of the y axis to become (-1,2).

The last thing left it to rotate this final triangle 180 degrees.  Since a circle is 360 degrees and 180 is half of a circle, it does not matter if we rotate clockwise or counter-clockwise.  If you could trace our new triangle and put a plus sign at the origin (0,0).  You would put your pencil on the origin  and rotate the two turns at the plus sign.  This would put your triangle right back to the beginning.  So the original value of B would be the same.  In this case C ((2,0)

The point B' would be at point B. The position of point won't change.

A reflection is a type of transformation that involves flipping a shape, known as the preimage, over a line, known as the line of reflection, to produce a new shape (called the image). You can picture what would happen if you flipped the form over the line in order to graph a reflection.

Given:

Triangle ABC is reflected over the x‐axis, reflected over the y‐axis, and rotated 180 degrees.

Let (x, y) be the coordinates of B.

To find B':

If a figure reflected over x-axis, then

(x, y) → (x, -y)

So, let point B₁ is  (x, -y).

If a figure reflected over y-axis, then

(x, y) → (-x, y)

So, (x, -y) → (-x, -y)

So, let point B₂ is  (-x, -y).

If a figure rotated 180 degrees about the origin, then

(x, y) → (-x, -y)

(-x, -y) → (x, y)

So the B' is (x, y).

Therefore, the position of point won't change.

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The sum of the numbers is 2.115 * 10^14

The sum expression is given as:

(2.1 × 10^14) + (1.5 × 10^12)

Express 1.5 as 0.015 * 10^2

(2.1 × 10^14) + (0.015 * 10^2 × 10^12)

Evaluate the product

(2.1 × 10^14) + (0.015 * 10^14)

Factor out 10^14

10^14 *(2.1 + 0.015)

Evaluate the sum

10^14 * 2.115

Rewrite as:

2.115 * 10^14

Hence, the sum of the numbers is 2.115 * 10^14

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Make same exponent

Use distributive law ab+ac=a(b+c)

Option C

Answer:

6x8=48

Step-by-step explanation:

Another way you can find the volume by counting all the squares/every one of them and make sure you count them correctly, so you don't miscount.

Answer:

  (d)  x = 4

Step-by-step explanation:

You want the solution to the system of equations using the given graph.

The solution to the equation f(x) = g(x) is the x-coordinate of the point(s) on their graphs where the curves intersect.

The graph shows the point of intersection of the two functions is (4, 1). This is the solution you have marked in the supplied image.

  x = 4

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To maximize its profit, a monopolist would choose option d: q = 30 and p = 60.

To maximize profit, a monopolist would choose the outcome that corresponds to the highest profit level.

Profit is calculated as total revenue minus total cost.

Let's analyze each option:

a. q = 45 and p = 45:

In this case, the monopolist produces a quantity of 45 units and sets the price at $45.

To determine if this is the optimal choice, we need to compare the revenue and cost associated with this outcome with the other options.

b. q = 60 and p = 30:

Here, the monopolist produces a higher quantity of 60 units but sets a lower price of $30.

c. q = 30 and p = 30:

This option represents a lower quantity of 30 units and a price of $30.

d. q = 30 and p = 60:

In this scenario, the monopolist produces a lower quantity of 30 units but sets a higher price of $60.

To determine the optimal outcome, we need to consider the monopolist's cost structure.

Without information about costs, we cannot definitively identify the optimal choice.

The monopolist would consider both revenue and cost implications to maximize profit.

However, we can make some general observations:

Option a (q = 45 and p = 45) and option c (q = 30 and p = 30) result in the same price and may have similar revenue implications.

The choice between these options would depend on the cost structure and profit margins.

Option b (q = 60 and p = 30) could result in higher revenue due to the higher quantity sold, but the lower price may affect profit margins.

Option d (q = 30 and p = 60) may result in higher prices and potentially higher profit margins, but the lower quantity sold may affect revenue.

Ultimately, the monopolist would need to assess the revenue, cost, and profit implications of each option to determine the optimal outcome for maximizing profit.

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Answer:

The x intercepts are x = 4, x = -1, and x = 3.

Step-by-step explanation:

\(g(x)=(2x-8)(x+1)(9-3x)^{2}\\(2x-8)(x+1)(9-3x)^{2}=0\\2x-8-0\\2x=9\\x=4\\x+1=0\\x=-1\\9-3x=0\\3x=9\\x=3\\\)

Answer:

Step-by-step explanation:

m∠AOB = 72°

m∠A = 54°

The area of one petal of the polar curve r = 5 sin 2θ would be 25π/4.

Supposing that there is no direct formula available for deriving the area, we can derive the area of that region by dividing it into smaller pieces, whose area can be known directly.

Then summing all those pieces' area gives us the area of the main big region.

The polar curve r = 5sin 2θ

When r = 0, θ = 0, π/2 which corresponds to one loop.

We need the limits to provide r=0 or cos(5x) =0 so:

Therefore the area of the region enclosed by this curve is

\(A = \dfrac{1}{2} \int\limits^a_b {r^{2} } \, d\theta \\\\\\A = \dfrac{1}{2} \int\limits^{\pi /2}_0 {25sin^{2}2\theta } \, d\theta \\\\\\A = \dfrac{1}{2} \times 25\int\limits^{\pi /2}_0 {sin^{2}2\theta } \, d\theta \\\\\\A = \dfrac{1}{2} \times 25\int\limits^{\pi /2}_0 \dfrac {1-cos^{2}4\theta } {2}\, d\theta\\ \\\\A = \dfrac{25}{2}( \theta - \dfrac {sin4\theta} {2})\, d\theta |^{\pi /2}_0\\\\\\A = \dfrac{25}{2} \times \dfrac{\pi }{2} \\\\\\A = \dfrac{25\pi }{4}\)

Thus, the area of one petal of the polar curve r = 5sin 2θ would be 25π/4.

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The shift that  are found by the naive string matcher in searching for the pattern is in the text Mississippi are options (b) 1 and (e) 4

The naive string matcher is a simple algorithm for searching a pattern within a text. It works by comparing the pattern with all possible substrings of the text and returning the starting indices of the matches. The algorithm starts by aligning the first character of the pattern with the first character of the text and then checks if all the characters in the pattern match the corresponding characters in the text.

If a mismatch is found, the algorithm moves to the next starting position in the text and repeats the process. The algorithm continues until all possible starting positions in the text have been checked.

Assuming that the pattern being searched is "issi", the shifts found by the naïve string matcher in searching for the pattern in the text "Mississippi" are

shift of 1: "issi" matches at position 1 in the text "Mississippi"

shift of 4: "issi" matches at position 4 in the text "Mississippi"

Therefore, the correct options are (b) 1 and (e) 4

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In a 2 x 2 x 2 factorial design, you need to test a total of seven possible effects: three main effects (A, B, and C) and four interaction effects (A x B, A x C, B x C, and A x B x C).

In a 2 x 2 x 2 factorial design, there are three independent variables, each with two levels. The possible effects to test include main effects and interaction effects.

The main effects are the individual effects of each independent variable on the dependent variable. In this design, there are three main effects to test: the effect of the first independent variable (A), the effect of the second independent variable (B), and the effect of the third independent variable (C).

Interaction effects occur when the effect of one independent variable on the dependent variable depends on the level of another independent variable. In a 2 x 2 x 2 design, there are three possible two-way interaction effects to test: A x B, A x C, and B x C. Additionally, there is one three-way interaction effect to test: A x B x C.

In summary, in a 2 x 2 x 2 factorial design, you need to test a total of seven possible effects: three main effects (A, B, and C) and four interaction effects (A x B, A x C, B x C, and A x B x C).

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Answer:

Step-by-step explanation:

kacie has paid $175 after being in the cooking class for two months

the expression 25x + 25 represents the total cost that kacie has paid after x months

Answer:

A = 101250 meter²

Step-by-step explanation:

Answer:

Maximum area enclosed will be 101250 meter².

Step-by-step explanation:

Let the length of the rectangular plot is x meters and the width is y meters.

900 meters is the length of the fence which represents the length of the three sides of the plot.

Therefore,

x + 2y = 900

y =  meters

Now the area of the rectangular plot will be

A = Length × Width

  = (x)(y)

  = 

  = 450x - 

We know for the maximum area we will differentiate the area and equalize it t the zero.



= 450 - x

For the maximum area, 

Therefore, 450 - x = 0

x = 450

and y = 

y = 

y = 450 - 225

  = 225 meters

Now the area enclosed A = 450 × 225

A = 101250 meter²

For the function, \(h(x) = \frac{50}{5.5 + 8e^{-0.9x} }\), the value of h(4) is h(4) ≈ 8.7

From the question, we are to determine the value of h(4) in the given function.

The given function is

\(h(x) = \frac{50}{5.5 + 8e^{-0.9x} }\)

To determine the value of h(4), substitute 4 for x in the given function

\(h(x) = \frac{50}{5.5 + 8e^{-0.9x} }\)

\(h(4) = \frac{50}{5.5 + 8e^{-0.9(4)} }\)

\(h(4) = \frac{50}{5.5 + 8e^{-3.6} }\)

\(h(4) = \frac{50}{5.5 + 8(0.0273237) }\)

\(h(4) = \frac{50}{5.5 + 0.21859 }\)

\(h(4) = \frac{50}{5.71859 }\)

h(4) = 8.7434

h(4) ≈ 8.7

Hence, the value of h(4) is 8.7

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Answer:

i think thats an obtuse triangle

Step-by-step explanation:

Answer: its an obtuse triangle

Step-by-step explanation:

Answer:

8/18

Step-by-step explanation:

the probability of the marble being red is 5/9 and it being blue is 4/9

so the probability of it being a blue marble two times is

4/9 + 4/9

=

8/18

The y-intercept is the point where the regression line crosses the vertical axis of the scatterplot.

A scattergram is also called a point where the predicted value of Y (the dependent variable) is 0. In other words, it is the value of Y when all independent variables in the model are equal to 0. The y-intercept is an important parameter in linear regression analysis because it provides information about the initial value of the dependent variable before changes in the independent variables occur. It is also used to calculate the slope of the regression line, which represents the rate of change in Y for each unit change in the independent variable.

The Y-intercept is the point where:

C) the regression line intersects the vertical axis of the scatterplot.

On a graph, the Y-intercept represents the value of the dependent variable (Y) when the independent variable (X) is equal to zero. This is an important concept in linear regression and helps to understand the relationship between two variables.

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Answer:

The system 800x+1300y=12300 and y = x+3 can be used to determine the number of associate assigned to the case and the number of partners assigned to the case where x represent the number of associates and y represent the number of partner

Step-by-step explanation:

Per day charge of each associate = $800

Per day charge of each partner = $1300

Total charged per day = $12300

Let,

x be the number of associates

y be the number of partners

According to given statement;

800x+1300y=12300        Eqn 1

y = x+3              Eqn 2

The system 800x+1300y=12300 and y = x+3 can be used to determine the number of associate assigned to the case and the number of partners assigned to the case where x represent the number of associates and y represent the number of partners

Answer:

1.   x< 3

2.   x>12

have a great day :)

Step-by-step explanation:

H0: p1 ≥ p2 (Null hypothesis: Proportion of ADHD-diagnosed students in School A is equal to or greater than in School B)

Null Hypothesis: The proportion of students diagnosed with ADHD in School A is equal to or greater than the proportion of students diagnosed with ADHD in School B.

Symbolically, the null hypothesis can be stated as:

H0: p1 ≥ p2

Where:

H0: Null Hypothesis

p1: Proportion of students diagnosed with ADHD in School A

p2: Proportion of students diagnosed with ADHD in School B

In other words, the null hypothesis assumes that there is no significant difference or that School A may have an equal or higher proportion of students diagnosed with ADHD compared to School B.

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Answer:

It's quite easy

Step-by-step explanation:

people less than 30 years = frequency of people 0 to 15 + 15 to 30 = 8+15 =23

Therefore there are 23 people less than 30 years old.

pls mark me as brainliest pls.

Answer:

53+14.5=67.50

Step-by-step explanation:

You have to add the two values to find the correct answer.

Length of the shorter diagonal of the parallelogram will be 18.46 feet

Let the Parallelogram ABCD with BD and AC as it’s diagonal

According to the question,

AB = 17 feet

AD = 11 feet

As the opposite sides of a parallelogram are parallel and equal

Therefore, AB = CD = 17 feet

                AD = BC = 11 feet

Also the longer diagonal, BD = 22 feet

In triangle BCD, using cosine formula

\(BD^{2}\) = \(CD^{2}\) + \(BC^{2}\)- 2BC.CD.CosC

\(22^{2}\) = \(17^{2}\) + \(11^{2}\) - 2(11)(17)Cos C

484 = 289 + 121 - 374CosC

-0.197 = Cos C

C = arc Cos(-0.197)

Therefore, C = \(110^{0}\)

Now ∠C + ∠D = \(180^{0}\)

101+  ∠D = 180

∠D = \(79^{0}\)

Now, in triangle ADC

\(AC^{2}\) = \(AD^{2}\) + \(CD^{2}\) - 2AD.CD.CosD

 \(AC^{2}\) = \(11^{2}\) + \(17^{2}\) - 2(11)(17)Cos79

\(AC^{2}\) = 121 + 289 - 374Cos79

\(AC^{2}\) = 410 -364(.19)

\(AC^{2}\) = 340.84

AC = sqrt(340.84)

AC = 18.46

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A. statistically significant difference in the mean blood hemoglobin levels between breastfed infants and formula-fed infants at α = 0.05.

B. the 95% confidence interval for the difference in population means between breast-fed infants and formula-fed infants is (−0.06, 1.18).

C. Both the hypothesis test and the confidence interval lead to the same conclusion that there is a difference in the mean blood hemoglobin levels between the two feeding regimens.

What is null hypothesis?

In statistics, the null hypothesis (H0) is a statement that assumes that there is no significant difference between two or more groups, samples, or populations.

(a) To test the hypothesis that there is a difference in the population means between breast-fed infants and formula-fed infants, we can use a two-sample t-test with equal variances. The null hypothesis is that the population means are equal, and the alternative hypothesis is that they are not equal. Using α = 0.05 as the significance level, the critical value for a two-tailed test with 40 degrees of freedom is ±2.021.

The test statistic can be calculated as:

t = (x1 - x2) / (Sp * √(1/n1 + 1/n2))

where x1 and x2 are the sample means, Sp is the pooled standard deviation, and n1 and n2 are the sample sizes. The pooled standard deviation can be calculated as:

Sp = √(((n1 - 1) * s1² + (n2 - 1) * s2²) / (n1 + n2 - 2))

where s1 and s2 are the sample standard deviations.

Plugging in the values from the table, we get:

t = (13.3 - 12.4) / (1.776 * √(1/23 + 1/19)) = 2.21

Since the absolute value of the test statistic is greater than the critical value, we reject the null hypothesis and conclude that there is a statistically significant difference in the mean blood hemoglobin levels between breastfed infants and formula-fed infants at α = 0.05.

(b) To construct a 95% confidence interval for the difference in population means between breast-fed infants and formula-fed infants, we can use the formula:

(x1 - x2) ± tα/2,Sp * √(1/n1 + 1/n2)

where tα/2,Sp is the critical value of the t-distribution with (n1 + n2 - 2) degrees of freedom and α/2 as the significance level.

Plugging in the values from the table, we get:

(x1 - x2) ± tα/2,Sp * √(1/n1 + 1/n2)

= (13.3 - 12.4) ± 2.021 * 1.776 * √(1/23 + 1/19)

= 0.56 ± 0.62

Therefore, the 95% confidence interval for the difference in population means between breast-fed infants and formula-fed infants is (−0.06, 1.18).

(c) The hypothesis test and the confidence interval both lead to the conclusion that there is a difference in the mean blood hemoglobin levels between breast-fed infants and formula-fed infants. In part (a), we rejected the null hypothesis that the population means are equal, which means we concluded that there is a difference. In part (b), the confidence interval does not contain 0, which means we can reject the null hypothesis that the difference in means is 0 at the 95% confidence level.

Therefore, both the hypothesis test and the confidence interval lead to the same conclusion that there is a difference in the mean blood hemoglobin levels between the two feeding regimens.

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Given:

There are given that the arc of BC is 182 degrees and the measure of arc AC is 78 degrees.

Explanation:

To find the value of the angle of 1, we need to use the circle properties:

So,

From the properties:

Then,

Put the values into the above formula:

So,

Final answer:

Hence, the correct option is A.

The amount due on the note with the cost of $7800 , 10% promissory note for 60 days is equal to $7930.

As given in the question,

Cost of purchase a plumbing components  = $7,800

Valley spa signed promissory note for 60 day

Percentage of promissory note = 10%

Condition: For the note is dishonored :

Amount due,  

Due Interest on the note

= 7800 × (10 /100) × ( 60 /360)

= 78 × 10 × ( 1/6)

= 13 × 10

= $130

Total amount due

= original cost + interest

= $(7800 + 130)

= $7930

Therefore, for the dishonored note  the amount due on the note is $7930.

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Answer:

±2 sqrt(2) / 3

Step-by-step explanation:

cos theta = adj / hyp

cos theta = 1/3

Using the Pythagorean theorem

a^2 + b^2 = c^2

opp ^2 + adj ^2 = hyp ^2

opp ^2 + 1 ^2 = 3^2

opp ^2 +1 = 9

opp ^2 = 9-1

opp ^2 = 8

Taking the square root of each side

opp = ± sqrt(8)

opp = ±2 sqrt(2)

sin theta = opp / hyp

               = ±2 sqrt(2) / 3