After the cataract took Euler's sight, he

The value of angle V which is ∠V is calculated as:  64.01°

The trigonometric ratios are used to find the angles and lengths of a right angle triangle.

Some of the trigonometric ratios are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

The parameters given are:

∠W = 90°

UW = 39

WV = 80

VU = 89

Thus, using trigonometric ratios, we have:

∠V = tan⁻¹(80/39)

∠V = 64.01°

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The work done pulling the bucket to the top of the well of depth 76 feet is equals to the 346.56 pounds/ feet.

Work is the product of force and distance, W=F×d. A Riemann Sum is a collection of rectangles used to approximate the area underneath a curve. In this case the "height" of the rectangle will be the force being exerted, and the "width" of the rectangle will be the amount of distance it moved. The work done by the force on the object can be expressed as an integral, [tex]W = \int_{a}^{b}F(x)dx[/tex]

Weigh of bucket = 5 pounds

A rope with negligible weight is used to draw water from a well. The depth of well = 76 feet.

Initially, Water in bucket = 37 pounds

Rate of pulling rope = 1.8 feet per second

Rate of water leaking in bucket = 0.25 pounds per second

Changing rate of leaking from pounds/sec to pounds/ feet : Q = 0.25/1.8 pounds/feet

= 0.139 pounds per feet

Thus, the rate of water leak from bucket hole is 0.12 pounds per feet. Let 'x' be height of bucket in feet from bottom of well. So, the total water leaked from hole = 0.12x

After leakage Remaining water in bucket = (37 - 0.12x )pounds

Also, add the weigh of buket in above expression. The limits of integration varies with depth of well that is 0 to 76 feet. Using Riemann sum method, work done pulling the bucket to the top of the well, [tex]W = \int_{0}^{76} ( 37 - 0.12x + 5 ) dx [/tex]

=>[tex]W = \int_{0}^{76} ( 42 - 0.12x ) dx [/tex]

=> [tex]W = [0 - \frac{0.12x²}{2}]_{0}^{76} \\ [/tex]

=> [tex]W = \frac{0.12×76²}{2} - 0 [/tex]

=> W = 0.12× 38×76 = 346.56 pounds/ feet. Hence required work done is 346.56 pounds/ feet.

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Answer:

the last 3 are true

Step-by-step explanation:

hope this helps

Step-by-step explanation:

(1/6²)⁵ = 1/6¹⁰ = 6^-10

because in the case of exponent of an exponent the exponents are multiplied with each other.

and 1/n = n^-1

(6^-5)² = 6^-10

because as above the exponents are multiplied with each other.

6^-3 / 6⁷ = 6^(-3 - 7) = 6^-10

a^n × a^m = a^(n+m)

a^n / a^m = a^(n-m)

the others are not 6^-10 :

6^-5 × 6² = 6^(-5 + 2) = 6^-3

6⁵×6^-3 / 6^-8 = 6^(5 - 3 - -8) = 6^(5 ‐ 3 + 8) = 6¹⁰

Answer:

use long divison  ike this

      16

  -------

8 | 132

    8

  -----

    52

    48

  -----

     4

Step-by-step explanation:

Answer:

Step-by-step explanation:

                                         132/8 = 16 with 4 leftover

                                             32 divided by 8 is 4, 96 divided by 8 is 12, the                                                                  

                                                  extra 4 left over

Using differentials to estimate the relative error in the calculated area of the disk of disk with radius 15 cm is equals to the 3.192%.

We have, a disk with radius of 15 cm.

Maximum error = 0.25

We have to determine the area of the disk. Area is a two dimensional quantity. It is defined as the space occupied by figure or any two dimensional shape. Here, formula for area of disk, A = πr² --(1)

here, r = 15 cm , dr = 0.25

Relative error is defined as the ratio of absolute error in measurement to the oringnal measurement. Differentating the equation (1) with respect to r, dA = d( πr²)

=> dA = 2πr dr

Substitutes the known values, in above formula, dA = 2× π × 15 ×0.25

=> dA = 7.50 × π = 23.55

So, absoulte error in area = 22.55

Original value of area = π(15)² = 706.5 cm²

Now, relative error % = (∆A/A)×100

= (22.55/706.5)×100

= 0.031917 × 100

= 3.1917 ~ 3.192 %

Hence, required value is 3.192%.

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Complete question:

the radius of a disk is given 15 cm as with a maximum error of 0.25 . use differentials to estimate the relative error in the calculated area of the disk. please enter your answer in decimal format with three significant digits after the decimal point.

The sample size required to estimate a population proportion with a desired level of confidence and margin of error depends on the size of the population and the confidence level desired. In this case, the population proportion is unknown and the desired confidence level is 99.5% with a margin of error of 4%.

To determine the sample size required, we can use the formula:

n = (Z² * p * q) / E²

where n is the sample size, Z is the Z-score corresponding to the desired level of confidence (which for a 99.5% confidence level is 2.81), p is the estimated population proportion (which is 0.5 as we have no reasonable estimate), q is 1-p, and E is the margin of error (which is 0.04).

Plugging in these values, we get:

n = (2.81² * 0.5 * 0.5) / 0.04² ≈ 1381

Therefore, a sample size of at least 1381 is required to estimate the population proportion with 99.5% confidence and a margin of error of 4%.

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The appropriate statistical test for whether the mean rating of guilts are greater for unattractive defendants than for attractive is:

B. 1 tailed t-test.

At the null hypothesis, it is tested if the mean rating of guilt will not be higher for unattractive defendants than for attractive defendants, that is:

H0  : uU <=uA

At the alternative hypothesis, it is tested if the rating is greater, that is:

H1 : uU> uA

We are comparing the means, hence a t-test is used. We are testing if one is greater than other(not different), hence a 1-tailed test is used, and option B is correct.

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Answer:

3 inches

Step-by-step explanation:

area of a rectangle

12×5

To succeed in an i-Ready mastery check, it is essential to review the materials covered in the lessons thoroughly, actively engage in the learning process, and ask questions if anything is unclear.

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i-Ready is an online adaptive learning platform that offers personalized learning experiences for students in reading and mathematics.

Mastery checks play a crucial role in ensuring that students fully understand the concepts being taught before progressing to more advanced topics.

These short assessments typically follow a lesson or series of lessons, helping teachers identify areas where students may need additional support or practice.

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The required fraction for the given condition is [tex]\frac{1}{3}[/tex]

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

Give shape contain 12 squares out of then four squares are shaded.

so, required fraction can be determine as

[tex]$Fraction=\frac{4}{12}[/tex]

[tex]$Fraction=\frac{1}{3}[/tex]

Thus, required fraction is [tex]\frac{1}{3}[/tex]

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Complete question;

The circumference of the bottle cap is nothing but the circumference of a circle and it is 9.42 cm.

The circumference of a circle or other curved geometric form refers to the space encircling it. It is a boundary's one-dimensional linear measurement.

The diameter of the circle is given, D = 3cm

Therefore the radius of the circle, r = D/2 = 3/2 cm

Circumference of circle = 2[tex]\pi[/tex]r

                                         = 2 * 3.14 * 3/2

                                         = 3.14 * 3

                                         = 9.42 cm

Therefore the circumference of the bottle cap is 9.42 cm.

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Elijah incorrectly combined the constant terms 4 and 8 to get -8. The correct simplification of the expression should be 4 + 8 - 3x - 10x, which simplifies to 12 - 13x.

To simplify the expression 4 - 3x + 8 - 10x, we first combine the like terms -3x and -10x to get -13x. Then we combine the constant terms 4 and 8 to get 12. So the simplified expression is 12 - 13x.

However, Elijah made a mistake by combining the constant terms 4 and 8 as if they had opposite signs. This resulted in a term of -8 that is not present in the original expression. The rest of his simplification is correct.

Therefore, the correct simplification of the expression is 4 + 8 - 3x - 10x, which simplifies to 12 - 13x.

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Complete Question:

Elijah is simplifying the expression 4 - 3x + 8 - 10x. He arrived at the answer 4 - 8 - 3x + 10x - 4 = 7x,

where did elijah go wrong?

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Answer: 112 ft²

Step-by-step explanation:

The area of a triangle can be found with the equation

[tex]A=\frac{1}{2} bh[/tex], where b is the base (bottom line of the triangle) and h is the height (the distance of the line from the peak of the triangle that forms a right angle with the base).

In this problem we are given the base and height: the base is 16 feet, and the height is 14 ft.

Therefore, the area is [tex]\frac{1}{2} *16*14[/tex], which is 112 ft²

Answer:

?=45 degrees

Step-by-step explanation:

All of the angles are congruent.

So the equation is:45+90+?=180

?=45 degrees

Answer: 45 degrees

Step-by-step explanation:

we can solve the given equation by taking log to get answer as x = log₈(25)

what is  an equation ?

An equation is a mathematical statement that contains an equal sign, indicating that two expressions have the same value. It is a way of expressing the relationship between different variables or quantities.

In the given question,

Taking the logarithm of both sides with base 8, we get:

log₈(8ˣ) = log₈(25)

Using the logarithmic property that logₐ(b^c) = c logₐ(b), we can simplify the left-hand side to:

x log₈(8) = log₈(25)

Since log₈(8) = 1, we have:

x = log₈(25)

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The correct comparison between the t-distribution and z-distribution is:

The density curve of the t-distribution is more spread out than the density curve of the z-distribution, especially for small sample sizes.

Both t-distribution and z-distribution have symmetric density curves.

However, for small sample sizes, the t-distribution curve is more spread out and has heavier tails compared to the z-distribution curve.

The area under both curves is equal to 1, as they represent probability distributions.

As the sample size increases, the t-distribution curve approaches the z-distribution curve in shape.

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Answer: A (0.5)

Step-by-step explanation:

Determine by dividing total number of popcorn sold by the attendance. Use the plotted points to help you.

a) We would expect approximately 0.2325 × 200 = 46.5 vehicles

to fail in their first 2 years. Since we cannot have a fraction of a vehicle

failing, we would expect around 46 or 47 vehicles to fail in their first 2

years.

b) The approximate probability that 50 or more vehicles fail in

the first 2 years is 0.0004.

c) The approximate probability that no more than 10 of the remaining

vehicles fail in their first 2 years, given that 30 have already failed, is 0.0002.

a) The average lifespan of the vehicle is 8 years, and it follows an

exponential distribution, which has a probability density function of

[tex]f(x) = (1/θ) \times e^(-x/θ)[/tex],

where θ is the mean of the distribution. Thus, θ = 8.

The probability that a vehicle fails in the first 2 years can be found by

integrating the exponential probability density function from 0 to 2:

P(X ≤ 2) = ∫[0,2] f(x) dx = ∫[0,2] (1/8) × e^(-x/8) dx

Using a calculator or a table of integrals, we can find this probability to

be approximately 0.2325.

b) The number of vehicles that fail in the first 2 years follows a Poisson

distribution with parameter λ = 200 × P(X ≤ 2) = 200 × 0.2325 = 46.5.

The probability that 50 or more vehicles fail in the first 2 years can be

found using the Poisson distribution with parameter λ = 46.5:

P(X ≥ 50) = 1 - P(X < 50)

Using a Poisson distribution table or a calculator, we can find that P(X <

50) is approximately 0.9996.

Thus, P(X ≥ 50) = 1 - 0.9996 = 0.0004 (approximately).

c) Given that 30 vehicles have already failed in under 2 years, we need

to find the probability that no more than 10 of the remaining 170 vehicles

fail in their first 2 years.

The number of vehicles that fail in the first 2 years follows a Poisson

distribution with parameter λ = 170 × P(X ≤ 2) = 170 × 0.2325 = 39.525

(rounded to 40).

Thus, we need to find P(Y ≤ 10), where Y is a Poisson random variable

with parameter λ = 40.

Using a Poisson distribution table or a calculator, we can find that P(Y ≤

10) is approximately 0.0002.

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The total number of ways to assign the guests to the rooms is 126 ways

We can solve this problem by using a combination. We have 5 friends and 5 rooms, so we can think of the friends as stars and the rooms as bars that separate them. The number of ways to assign the friends to the rooms is equal to the number of ways to arrange the 5 stars and 4 bars (since there are 4 spaces between the bars).

We can choose any 4 positions out of 9 (5 stars and 4 bars) to place the bars, so the number of ways to assign the friends to the rooms is equal to the binomial coefficient.

[tex]${9 /\choose 4} = \frac{9!}{4!5!} = 126$.[/tex]

Therefore, there are 126 ways for the innkeeper to assign the 5 friends to the 5 rooms.

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In the proportion, Mr.Balewa needs  9 cups to makes 12 dozen cookies.

A percentage is created when two ratios are equal to one another. We write proportions to construct equivalent ratios and to resolve unclear values. a comparison of two integers and their proportions. According to the law of proportion, two sets of given numbers are said to be directly proportional to one another if they grow or shrink in the same ratio.

Here  

He uses 4 1/2 cups of flour to make six dozen cookies then to makes 12 dozen cookies the x cups of flour .

Now using proportion,

= (4 1/2) / 6 = x / 12

= (9/2) / 6 = x/12

x = (9*12)/(2*6) = 9

= 9 cups.

Hence Mr. Balewa needs  9 cups to makes 12 dozen cookies.

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Since the total amount of kids who participated in the survey is 150, 100% of the pie is equal to 150 kids.

We know that 46% of the 150 kids like video games so the number of kids that like video games is 0.46 * 150 = 69.

Similarly, 14 + 16 = 30% of 150 kids like reading and art so the number of kids that like reading and art is 0.3 * 150 = 45.

Your second question is quite hard to understand. But you know that 120 kids like video games and those kids make up 40% of the total so mathematically you can say,

40% * number of total students = 120

number of total students = 120/40% = 300

Answer: a ≤ 2

Step-by-step explanation:

How to write an inequality statement:

Step 1: Write the two values being compared in the problem.

Step 2: Determine whether the first value is larger or smaller than the second value.

Step 3: Express the inequality with the right symbols:

≤ = less than or equal to

≥ = greater than or equal to

Therefore, the answer would be a≤2.

Hope this helped!

Answer:

a = 127° , b = 12° , c = 115°

Step-by-step explanation:

a and 53° are same- side interior angles and sum to 180° , that is

a + 53° = 180° ( subtract 53° from both sides )

a = 127°

c and 115° are alternate angles and are congruent , then

c = 115°

53° , b and c lie on a straight line and sum to 180°

53° + b + c = 180°

53° + b + 115° = 180°

b + 168° = 180° ( subtract 168° from both sides )

b = 12°

then a = 127° , b = 12° , c = 115°

Answer:

a = 127; b = 12; c = 115

Step-by-step explanation:

c =115

b = 180 - 115 - 53

b = 12

a = b + c

a = 12 + 115

a = 127

Answer:

x^4 - mx^2 + n^2 = 0

Step-by-step explanation:

We can use algebraic manipulation to solve for m and n. First, we can square the equation xy = n to get:

(x^2)(y^2) = n^2

Since we also have x^2 + y^2 = m, we can substitute y^2 with m - x^2 to get:

x^2(m - x^2) = n^2

Expanding the left side of the equation, we get:

mx^2 - x^4 = n^2

Multiplying both sides by 16, we get:

16mx^2 - 16x^4 = 16n^2

Adding 32xy to both sides, we get:

16mx^2 + 32xy - 16x^4 = 16n^2 + 32xy

Substituting n for xy, we get:

16mx^2 + 32n - 16x^4 = 16n^2 + 32n

Rearranging the equation, we get:

16mx^2 - 16x^4 - 16n^2 = 0

Dividing both sides by -16, we get:

x^4 - mx^2 + n^2 = 0

Answer:

(4x+4y)²

Step-by-step explanation:

Given x²+y² = m ,xy=n.

Now 16m+32n = 16(m+2n)

= 16(x²+y²+2xy) = 4²(x+y)²[ x²+y²+2xy= (x+y)²]

(4x+4y)².