Number 4. I need help finding the value please help

Answer:

Step-by-step explanation:

4.  a) tan x=17/12=1.416

       x=54.8≈55

b)sin  b=78/132=0.59

  b=36.2≈36

cos 28=x/82

x=82*cos 28=82*0.9=73.8

The cut-out from each corner that maximizes the volume is 3 inches.

The dimensions are given as:

\(\mathbf{Length = 15}\)

\(\mathbf{Width = 24}\)

Assume the cut-out is x.

So, the dimension of the board is:

\(\mathbf{Length = 15 - 2x}\)

\(\mathbf{Width = 24 - 2x}\)

\(\mathbf{Height = x}\)

The volume (V) is calculated as:

\(\mathbf{V = Length \times Width \times Height}\)

So, we have:

\(\mathbf{V = (15 - 2x) \times (24 - 2x) \times x}\)

Expand

\(\mathbf{V = 360x - 78x^2 + 4x^3}\)

Differentiate

\(\mathbf{V' = 360 - 156x + 12x^2}\)

Set to 0

\(\mathbf{ 360 - 156x + 12x^2 = 0}\)

Divide through by 12

\(\mathbf{ 30 - 13x + x^2 = 0}\)

Rewrite as:

\(\mathbf{ x^2 - 13x + 30 = 0}\)

Using a calculator, we have:

\(\mathbf{x = \{3, 10\}}\)

The value of x = 10 is greater than the dimensions of the box.

So, we have:

\(\mathbf{x = 3}\)

Hence, the cut-out from each corner that maximizes the volume is 3 inches.

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The measure of arc BC is 720 times the measure of angle BAC.

Given that AC is the diameter of the circle and AB is a chord with a length of 16 units, we need to find BC (the length of the other chord) and mBC (the measure of angle BAC).

To find BC, we can use the property of chords in a circle. If two chords intersect within a circle, the products of their segments are equal. In this case, since AB = BC = 16 units, the product of their segments will be:

AB * BC = AC * CE

16 * BC = 2 * r * CE (AC is the diameter, so its length is twice the radius)

Since the area of the circle is given as 289 square units, we can find the radius (r) using the formula for the area of a circle:

Area = π * r^2

289 = π * r^2

r^2 = 289 / π

r = √(289 / π)

Now, we can substitute the known values into the equation for the product of the segments:

16 * BC = 2 * √(289 / π) * CEBC = (√(289 / π) * CE) / 8

To find mBC, we can use the properties of angles in a circle. The angle subtended by an arc at the center of a circle is double the angle subtended by the same arc at any point on the circumference. Since AC is a diameter, angle BAC is a right angle. Therefore, mBC will be half the measure of the arc BC.

mBC = 0.5 * m(arc BC)

To find the measure of the arc BC, we need to find its length. The length of an arc is determined by the ratio of the arc angle to the total angle of the circle (360 degrees). Since mBC is half the arc angle, we can write:

arc BC = (mBC / 0.5) * 360

arc BC = 720 * mBC

Therefore, the length of the arc BC equals 720 times the length of the angle BAC.

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Answer:

2072

Step-by-step explanation:

Multiply 14 x 37

518 x 4

2072

Answer: $2,072 a month

Step-by-step explanation:

multiply 14 by 37 to see her weekly rate which is $518 a week. then multiply  518 by 4 (because there are about 4 weeks in a month). then you get the answer of $2,072

Answer:

1.  Benny had 266 dollars to spend on 9 books.  After buying them, he had 14 dollars.  How much did each book cost?

The books cost $28 dollars each.

how to calculate...

$266 - $14 = $252

then take $252 divided by 9 = $ 28

2.  Oceanside Bike Rental Shop charges 14 dolars plus 9 dollars an hour for renting a bike.  Sally paid 86 dollars to rent a bike.  How many hours did she pay to have the bike checked out?

8 hours

how to calculate...

take 86 - 14 = 72

then 72  divided 9 = 8 hours

3.  The sum of three consecutive numbers is 132.  What is the smallest of the three numbers?

43 is the smallest of the 3 numbers

calculation...

x + (x+1) + (x+2) = 132

3x + 3 = 132 -3

3x=129

x=129/3

x=43  (answer for the 1st number)

43+1=44 (answer for the 2nd number)

43+2=45 (answer for the 3rd number)

add them all to make sure they equal to 132

43+44+45=132

132=132

4.  Sandy sold half of her comic books and then bought 8 more.  She now has 16.  How many did she begin with?

x= how many Sandy started with

1/2 x + 8 = 16

1/2x = 16 - 8

1/2x = 8 * 2

x = 16 comics books

Step-by-step explanation:

The mean score has an equal probability of occurring of the scores in the uniformly distributed quiz is 5.5.

In a uniform distribution where the scores range from 1 to 10, each possible score has an equal probability of occurring. To find the mean (or average) of the scores, we can use the formula:

Mean = (Sum of all scores) / (Number of scores)

In this case, the sum of all scores can be calculated by adding up all the individual scores from 1 to 10, which gives us:

Sum of scores = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55

The number of scores is 10 since there are 10 possible scores from 1 to 10.

Plugging these values into the formula, we get:

Mean = 55 / 10 = 5.5

Therefore, the mean of the scores in this quiz is 5.5.

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The question is -

Suppose a professor gave a quiz where the scores are uniformly distributed from 1 to 10. What is the mean of the scores?

What will the dimensions of some cross-sections of a cuboid be when cutting depends on the viewpoint.

We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.

Suppose we have a cuboid shape of a wooden block.

The height of the wooden block is h, the width of the wooden block is w and the length of the wooden block is l.

Now if we cut the wooden block along the red line a look at it from the top it will look like a rectangle width width 'w' and length 'l'.

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Answer: A. A rectangle 4 inches by 2 inches

Step-by-step explanation:

Answer:

7020

Step-by-step explanation:

2÷390,702,468

2÷195,351,234

3÷

1). 15 days

2). 115.2 pounds.

3). 500 meters

1. To find out when the couple will have another day off together, we need to find the least common multiple (LCM) of their work schedules. The LCM of 3 and 5 is 15, so the couple will have another day off together after 15 days.

2. The weight W of an object above the earth varies inversely as the square of the distance D from the center of the earth.

This means that W = k/D^2, where k is a constant.

To find k, we can plug in the values given in the question: 180 = k/4000^2.

Solving for k gives us k = 180*4000^2 = 2880000000. Now we can plug in the new distance, 4000 + 1000 = 5000 miles, to

find the new weight: W = 2880000000/5000^2 = 115.2 pounds.

3. To find the total distance traveled by the fly, we need to find out how long it takes for the turtles to meet.

The combined rate of the turtles is 10 + 20 = 30 m/s, so it will take them 150/30 = 5 seconds to meet.

The fly travels at a constant rate of 100 m/s, so in 5 seconds it will have traveled 100*5 = 500 meters.

Therefore, the total distance traveled by the fly is 500 meters.

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The equation of the parabola will be;

y = (x - 3)² + 1

What is mean by Parabola?

A parabola is a set of points in the plane which are equidistant from the directrix and focus.

Given that;

The vertex of the parabola = (3 , 1)

A parabola passes through the point (2,2).

Now,

Since, The equation of parabola in vertex form is;

y = a (x - h)² + k

Where, (h , k) are vertex of the parabola.

So, The equation of parabola with vertex (3, 1) will be;

y = a (x - 3)² + 1

And, It passes through the point (2,2).

So we substitute the value of (2, 2) in place of (x, y) as;

2 = a (2 - 3)² + 1

2 = a + 1

a = 2 - 1

a = 1

Substitute the value of a in above equation, we get;

The equation of parabola as;

y = (x - 3)² + 1

Therefore, The equation of the parabola will be;

y = (x - 3)² + 1

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Answer:

????

Step-by-step explanation:

Where's the equation? diagram?

Answer:

How we supposed to answer with no equation

Step-by-step explanation:

Answer:

9m

Step-by-step explanation:

18-12=6

15-6=9

Answer:

X:15=12:18

X=12x15 /18

X=180/18

X=10

Answer:

4 units

Step-by-step explanation:

The complete question is

BD and AC are chords that intersect at point Y. A circle is shown. Chords B D and A C intersect at point Y. The length of B Y is 3, the length of Y D is 8, the length of A Y is x, and the length of Y C is 6. What is the length of line segment AY?

The picture of the question in the attached figure

we know that

The Intersecting Chord Theorem states that:  When two chords intersect each other inside a circle,the products of their segments are equal.

do

In this problem

substitute the given values

solve for x

therefore

The length of segment AY is 4 units

The solution of pair of equation 2x + y = 5 and 3x - 2y = 4 is x = 2 and y = 1.

The set of equations given is linear equations that can be solved simultaneously to find the values of variables x and y.

2x + y = 5------->(1)

3x - 2y = 4------->(2)

Multiply equation (1) by 2 and then add it to equation (2)

4x + 2y = 10

3x -  2y =   4

7x + 0  = 14

7x = 14

x = 2

Putting x = 2 in (1),

2(2) + y = 5 

y = 5 - 4 = 1

Therefore, the values of x and y obtained are 2 and 1, respectively. 

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Answer:

I believe the answer is 45.

Step-by-step explanation:

This is just my opinion. However I could be wrong.

Answer:

5.4

Step-by-step explanation:

Scale factor = 2.7/3 = 0.9

x = 6*0.9 = 5.4

Answer:

x=4

Step-by-step explanation:

There

Step-by-step explanation:

first u start by writing it in

figure as stated in the question

6017

Answer:

Step-by-step explanation:

The word "sine" (Latin "sinus") comes from a Latin mistranslation by Robert of Chester of the Arabic jiba, which is a transliteration of the Sanskrit word for half the chord, jya-ardha.

Answer:

\(x = 10 \: and \: y \: = 70.\)

Step-by-step explanation:

\(if \: from \: the \: sine - cosine \: rule : \\ \sin( \beta ) = \cos(90 - \beta ) \\ \cos( \beta ) = \sin(90 - \beta ) \\ then \: if : \\ sin(x+20)°=cos(y−10)° \\ let \: x + y = 80 \\ if \: x = 10. \\ y = 70. \\ \)

The International System of Units (SI) is the modern form of the metric system and is the world's most widely used measurement system. It defines seven base units for measuring physical quantities, from which all other SI units can be derived. The three fundamental base units for length, mass, and volume are as follows:

Length: The base unit for length in the SI system is the meter (m). It is defined as the distance traveled by light in a vacuum during a time interval of 1/299,792,458 of a second. The meter is used to measure distances ranging from the size of atoms to astronomical distances.

Mass: The base unit for mass in the SI system is the kilogram (kg). It is defined as the mass of a particular cylinder of platinum-iridium alloy that is kept at the International Bureau of Weights and Measures in France. The kilogram is used to measure the mass of objects ranging from subatomic particles to planets.

Volume: The base unit for volume in the SI system is the cubic meter (m³). It is defined as the volume occupied by a cube with edges of one meter in length. The cubic meter is used to measure volumes ranging from the size of molecules to large bodies of water.

Other derived units for length, mass, and volume include centimeters, millimeters, grams, liters, and cubic centimeters. These units are commonly used in everyday life and scientific research.

In conclusion, the base units for length, mass, and volume in the SI system are meter, kilogram, and cubic meter respectively. These units provide a standardized and internationally recognized system for measuring physical quantities.

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Answer:

C.264,508,625,645

Step-by-step explanation:

the arrangement is from the least number to the greatest

The solution of the inequality 2|5 - 2x| - 3 ≤ 15 is x ≤ 7 and x ≥ - 2. The interval notation can be written as -2 ≤ x ≤ 7.

The given inequality 2|5 - 2x| - 3 ≤ 15 can be solved as,

2|5 - 2x| - 3 ≤ 15

Add 3 on both sides.

2|5 - 2x| - 3 + 3 ≤ 15 + 3

2|5 - 2x|  ≤ 18

Divide by 2 on both sides.

|5 - 2x|  ≤ 9

The two conditions when resolving modulus are given by,

5 - 2x ≤ 9 and 5 - 2x ≥ - 9

Solve the two conditions to get the solution.

5 - 2x ≤ 9

- 2x ≤ 9 - 5

-2x ≤ 4

-x ≤ 2

Therefore, x ≥ - 2.

Next, 5 - 2x ≥ - 9

- 2x ≥ - 9 - 5

- 2x ≥ - 14

- x ≥ - 7

Therefore, x ≤ 7.

The solution to the inequality lies between the interval -2 ≤ x ≤ 7.

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The radius of the smaller cone created when a horizontal plane passes through the cone at exactly 4 feet from the base is 6.6 feet.

To determine the radius of the smaller cone created when a horizontal plane passes through the cone at exactly 4 feet from the base, we can use similar triangles.

The given cone has a height of 10 feet and a diameter of 22 feet. The radius of the given cone is half of the diameter, so it is 22/2 = 11 feet.

When a horizontal plane passes through the cone at exactly 4 feet from the base, it divides the cone into two parts: the smaller cone and the frustum (the remaining part of the cone).

The height of the smaller cone is the distance from the 4-feet mark to the top of the cone, which is 10 - 4 = 6 feet.

Since the two cones are similar, their corresponding dimensions are proportional. The ratio of the corresponding heights is the same as the ratio of the corresponding radii.

So, we can set up the following proportion:

(r_small / r_given) = (h_small / h_given)

Substituting the values we have:

(r_small / 11) = (6 / 10)

Cross-multiplying:

10 * r_small = 11 * 6

r_small = (11 * 6) / 10

r_small = 66 / 10

r_small = 6.6 feet

Therefore, the radius of the smaller cone created when a horizontal plane passes through the cone at exactly 4 feet from the base is 6.6 feet.

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The value of x is found as 3 using the method of substitution.

For the given expression, use substitution method to solve.

2x + y = 7  ........eq 1

y = 2x - 5  ........eq 2

Substitute the value of y from eq 2 in eq 1.

2x + 2x - 5 = 7

Solving;

4x = 7 + 5

4x = 12

x = 3

Thus, the value of x is found as 3.

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Friday's practice session was 3 and 153/896 hours longer than

To find out how much longer Friday's practice session was than Wednesday's, we need to subtract Wednesday's practice time from Friday's practice time.

Friday's practice time is 2 3/7 hours. To make it easier to subtract, we can convert this mixed number to an improper fraction:

2 3/7 = (2 × 7 + 3) / 7 = 17/7

Now we can add this to Wednesday's practice time, which is already in improper fraction form:

1 1/8 = (1 × 8 + 1) / 8 = 9/8

Adding these two fractions, we get:

17/7 + 9/8

To add these fractions, we need to find a common denominator. The smallest number that both 7 and 8 divide into is 56, so we can convert both fractions to have 56 as the denominator:

17/7 × 8/8 = 136/56

9/8 × 7/7 = 63/56

Now we can add the numerators:

136/56 + 63/56 = 199/56

This is the total practice time for both Wednesday and Friday. To find out how much longer Friday's practice session was than Wednesday's, we need to subtract Wednesday's practice time from this total:

199/56 - 9/8

To subtract fractions, we need to find a common denominator again:

199/56 - 9/8 = (199/56) × (8/8) - (9/8) × (7/7) = 1425/448 - 63/56

Now we can subtract the numerators:

1425/448 - 63/56 = 2841/896

This is the difference between Friday's practice time and Wednesday's practice time, expressed as an improper fraction. To convert this back to a mixed number, we can divide the numerator by the denominator:

2841 ÷ 896 = 3 with a remainder of 153

So the answer is Friday's practice session was 3 and 153/896 hours longer than Wednesday's practice session.

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The smallest set of independence or conditional independence relationships we need to assume for the given scenarios are P(A|B) = P(A), P(A,B) = P(A)P(B), P(A|B,C) = P(A|B)P(A|C), P(A,B|C) = P(A|C)P(B|C), and P(A,B,C) = P(A)P(B)P(C).

The smallest set of independence or conditional independence relationships we need to assume for the following scenarios are as follows:

(i) In this scenario, we need to assume the conditional independence relationship P(A|B) = P(A). This means that A is independent of B given the condition that B is true.

(ii) In this scenario, we need to assume the independence relationship P(A,B) = P(A)P(B). This means that A and B are independent of each other.

(iii) In this scenario, we need to assume the conditional independence relationship P(A|B,C) = P(A|B)P(A|C). This means that A is independent of B and C given the condition that both B and C are true.

(iv) In this scenario, we need to assume the conditional independence relationship P(A,B|C) = P(A|C)P(B|C). This means that A and B are independent of each other given the condition that C is true.

(v) In this scenario, we need to assume the independence relationship P(A,B,C) = P(A)P(B)P(C). This means that A, B, and C are independent of each other.

In summary, the smallest set of independence or conditional independence relationships we need to assume for the given scenarios are P(A|B) = P(A), P(A,B) = P(A)P(B), P(A|B,C) = P(A|B)P(A|C), P(A,B|C) = P(A|C)P(B|C), and P(A,B,C) = P(A)P(B)P(C).

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Overestimating the economic impact can stem from exaggerated multipliers and overlooking leakage, while underestimating can result from neglecting indirect effects and a limited time frame for analysis.

Overestimating the economic impact of a sporting event can occur due to several reasons:

Exaggerated multiplier effect: The multiplier effect suggests that spending on a sporting event will lead to additional rounds of spending, generating more income for the local economy. However, these multipliers are often overestimated, leading to an exaggerated economic impact.

Ignoring leakage: Leakage occurs when money spent on a sporting event leaves the local economy, such as when profits go to national or international corporations. Overestimating economic impact can happen if leakage is not taken into account.

On the other hand, underestimating the economic impact of a sporting event can be caused by:

Failure to consider indirect effects: Sporting events can have indirect effects on the local economy, such as increased tourism and job creation. Underestimating the economic impact may occur if these indirect effects are not considered.

Limited time frame: Economic impact studies often focus on the immediate impact of a sporting event, but fail to capture the long-term effects. This can result in an underestimation of the true economic impact.

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