The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.74
5.74
millimeters and a standard deviation of 0.07
0.07
millimeters. Find the two diameters that separate the top 5%
5
%
and the bottom 5%
5
%
.

length of side AB is approximately 5.74 units when rounded to the nearest hundredth

To find the value of x in triangle ABC,

Applying the law of sines in triangle ABC, we have:

sin(A)/AB = sin(B)/AC

where AB is the length of side AB, and sin(A) and sin(B) are the sines of angles A and B, respectively.

Substituting the given values, we get:

sin(36)/AB = sin(180-36- angle C)/7

simplifying the equation, we get:

AB = 7sin(36)/sin(C)

To find the angle C, we can use the fact that the sum of the angles in a triangle is 180 degrees:

angle C = 180 - angle A - angle B

Substituting the given values, we get:

angle C = 180 - 36 - 90 = 54 degrees

Substituting the values of sin(36) and sin(54) into the equation for AB, we get:

AB = 7sin(36)/sin(54) = 5.74 (rounded to the nearest hundredth)

Therefore, the length of side AB is approximately 5.74 units when rounded to the nearest hundredth.

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The length of the extension ladder that is against the outside wall of the house is 22.58 feet.

What is the length of the ladder?

The ladder forms a right triangle when it is placed up against a home. The hypotenuse of a ladder is its length. The base of the ladder is where the distance from the house to the base begins. The length is the distance from the home.

Here, we have

Given: An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 22 feet up. The ladder makes an angle of 77

To find the length of the ladder, Sin would be used:

Sin = opposite / hypotenuse

Sin77 = 22 / h

h = 22 / 0.9743 = 22.58 feet

Hence, the length of the extension ladder that is against the outside wall of the house is 22.58 feet.

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Triangle DEF as shown ion figure D(-4, 6), E(2,6), F(0,8) translate by a factor of 1/2, So the new vertex are: D' (-2, 3), E' (1, 3), F' (0, 4)

Triangle is commonly represented by a graph in which the three points are labeled as A, B, and C, and the three line segments are labeled as AB, AC, and BC. The graph of a triangle typically looks like below figure.

The new coordinates of each vertex of the triangle after scaling by 1/2.

For vertex D:

x-coordinate = -4, y-coordinate = 6

New x-coordinate = (1/2) × (-4) = -2

New y-coordinate = (1/2) × 6 = 3

So the new coordinates for D' are (-2, 3)

For vertex E:

E (2, 6) ⇒ 1/2 × (2, 6) ⇒ (1, 3)

So the new coordinates for E' are (1, 3)

For vertex F:

F (0, 8) ⇒ 1/2 × (0, 8) ⇒ (0, 4)

So the new coordinates for F' are (0, 4)

D(-4, 6), E(2,6), F(0,8)  ⇒   D' (-2, 3), E' (1, 3), F' (0, 4)

Finally, plot the new points on the same coordinate plane and connect them to form the new triangle. You should see that the new triangle is a smaller version of the original triangle, with all sides and angles scaled down by a factor of 1/2.

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Answer:

C

Step-by-step explanation:

9x+2+4x+10+x=180

14x=180-2-10

14x=168

x=168/14=12

m∠Q=9x+2=9×12+2=108+2=110°

Answer:

To calculate the amount in the IRA at retirement, we can use the formula for the future value of an annuity:

S = PMT * (((1 + r)^n - 1) / r)

Where:

PMT = the monthly payment (in dollars)

r = the monthly interest rate (APR/12)

n = the number of months (45 years * 12 months/year)

Substituting the given values, we get:

PMT = $50

r = 0.06/12 = 0.005

n = 45 * 12 = 540

S = $50 * (((1 + 0.005)^540 - 1) / 0.005) = $204,055.57

So the IRA will contain $204,055.57 at retirement.

The total deposits made over the time period is:

Total deposits = 540 * $50 = $27,000

Therefore, the amount in the IRA at retirement ($204,055.57) is significantly higher than the total deposits made over the time period ($27,000). This demonstrates the power of compound interest over a long time horizon

Step-by-step explanation:

If u have other qstns too, feel free to ask me on my sn ap

The correct option is (b) i.e. area of rectangle is [tex]x^{3} y^{4}[/tex].

What is rectangle?

The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. the two sides come together at a straight angle  at each corner ,The rectangle differs from a square because its two opposite sides are of equal length.

Given : width of rectangle : xy

            length of rectangle : [tex]x^{2} y^{3}[/tex]

we know that,  area of rectangle = length × breadth

                                                      =  x²y³ × xy

Now, adding power of terms which has same base.    

we get, [tex]x^{3} y^{4}[/tex]                                                                

so, the correct option is (b).

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Answer:

360

Step-by-step explanation:

.05n = 18

n = 360 campers

The limits [tex]\lim_{x \to 0 } f(x)[/tex] exists and the function f(x) is continuous at x = 0

Other solutions are shown below

The domain of a function is the set of all possible input values, while the range is the set of all possible output values.

From the graph, we have the domain and the range to be:

From the graph, we have the values of the function to be

f(-4) = 1 and f(-6) = 2

From the graph, we have the values of the limits to be

[tex]\lim_{x \to 4^{-} } f(x) = -2[/tex]

[tex]\lim_{x \to 4^{+} } f(x) = 2[/tex]

Yes, the limit  [tex]\lim_{x \to 0 } f(x)[/tex]

To check if a function is continuous at x=0, you need to check three conditions:

Hence, the function is continuous at x = 0

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We can conclude by answering the provided question that We get a equation sample size of 579 people by rounding up to the closest whole number. To be 90% sure that the sample percentage is within 1.5

An equation in mathematics is a declaration that states the equivalence of two expressions. An equation is made up of two parts that are separated by a mathematical equation (=). For example, the argument "2x + 3 = 9" asserts that the sentence "2x + 3" equals the number "9." The objective of equation solution is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more variables. The variable x is elevated to the second degree in the equation "x2 + 2x - 3 = 0." Lines are used in many different areas of mathematics, such as algebra, calculus, and geometry.

To calculate the sample number required for this poll, use the following formula:

[tex]n=(Z^{2} *P*Q/E^{2}[/tex]

[tex]n=(1.645^{2} *0.5*0.5)/0.015^{2} a578.98[/tex]

We get a sample size of 579 people by rounding up to the closest whole number. To be 90% sure that the sample percentage is within 1.5 percentage points of the actual population percentage, we would need to poll at least 579 randomly chosen air passengers.

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The coordinate of the figure after translation and reflection is A"(-12, 2), B"(-8, 6) and C'(-7, 13)

To translate the points A(12, -7), B(8, -3), and C(-7, 4) 9 units up, we simply add 9 to the y-coordinate of each point. The new coordinates of the translated points are:

A'(12, 2)

B'(8, 6)

C'(-7, 13)

To reflect the translated points across the y-axis, we simply negate the x-coordinate of each point. The final coordinates of the reflected and translated points are:

A"(-12, 2)

B"(-8, 6)

C'(-7, 13)

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The triangle proportionality theorem indicates that Maria and Juan properly divides the plot of land

The triangle proportionality theorem which is known as Thales Theorem states that the segment drawn joining two of the sides of a triangle and parallel to the third side divides the other two sides proportionately.

The parallel lines with which Maria and Juan uses to divide the 300 feet long side into six sides of the same length, indicates that length of each division on the Shady Lane is 50 feet, therefore, the length of each division on the Oak Creek will also be the same.

The slope of the the divisions on Maria's Plan is steeper than the slopes on the division on Juan's Plan such that the length of each division on Oak Lane is longer for Juan, than for Maria.

However, the triangle proportionality theorem, and the width of each division on Shady Lane indicates that the width of each division is 50 feet.

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The buyer were to opt for the builder's offer, the total payments over the life of the loan would be $248,110. This includes interest payments of $165,110. So, while the reduced payments may seem like a good deal in the short-term, buyers need to carefully consider the long-term implications before making a decision.

The builder's Mortgage offer seems attractive, as it significantly reduces the payments for the first two years. However, it's important to consider the long-term implications of this offer.

While the reduced payments may be helpful for buyers who are facing financial constraints in the short-term, they may end up paying more over the life of the loan.

Let's look at the numbers. With the builder's offer, the payments for the first year would be $377.11 per month, and $565.67 per month for the second year. This means that the total payments for the first two years would be $13,165.52. After that, the regular monthly payments of $754.22 would kick in, and the buyer would need to pay this amount for the remaining 23 years of the loan.

If the buyer were to opt for the fully amortizing loan with monthly payments of $754.22 for the entire 25-year term, the total payments over the life of the loan would be $226,266. This includes interest payments of $143,266.

On the other hand, if the buyer were to opt for the builder's offer, the total payments over the life of the loan would be $248,110. This includes interest payments of $165,110. So, while the reduced payments may seem like a good deal in the short-term, buyers need to carefully consider the long-term implications before making a decision.

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The equation of its axis of symmetry is x = 4.

What is axis of symmetry?

The axis of symmetry is a line that divides a symmetrical object or shape into two mirror-image halves. In mathematics, the axis of symmetry is often used in the context of graphs of equations, particularly quadratic equations

The axis of symmetry of a quadratic function is a vertical line that passes through the vertex of the parabola.

If a quadratic equation has zeros at x = 3 and x = 5, then its factored form is:

(x - 3)(x - 5) = 0

Expanding this expression, we get:

x^{2} - 8x + 15 = 0

This is the standard form of a quadratic equation: ax^{2} + bx + c = 0, where a = 1, b = -8, and c = 15.

To find the x-coordinate of the vertex of the parabola, we can use the formula:

x = -b/2a

Substituting the values of a and b, we get:

x = -(-8)/(2*1) = 4

Therefore, the axis of symmetry is a vertical line passing through x = 4. The equation of this line is simply:

x = 4

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1. The diagonal of the base of the box is shorter than the length of the wind chime. 2. The interior diagonal of the box shorter than the length of the wind chime. 3.  The wind chime will not fit in the box.

A diagonal is a line segment that connects two polygonal corners (vertexes), although it is not an edge (side). In other words, it connects any two polygonal vertices that are not neighboring. So, when we directly link any two vertices that are not connected by any sides, we may draw the diagonals in a polygon. A diagonal is a line that runs straight across the vertices of a polygon and joins its opposing corners. In other terms, a line segment connecting any two non-adjacent corners is a polygon's diagonal. Depending on how many sides a polygon has, distinct polygons may have a variable number of diagonals.

Given that the length of the wind chime is 16 inches thus,

1.  diagonal of base of the box = √10²+8² = √164 = 12.8

Hence, the diagonal of the base of the box is shorter than the length of the wind chime.

2.  interior diagonal of the box = √6²+8²+10² = √200 = 14.14

The interior diagonal of the box shorter than the length of the wind chime

3.  The wind chime will not fit in the box

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The approximate diameter of the sphere is 29.3 cm, the correct option is C.

To find the approximate diameter of the sphere, we can use the formula for the volume of a sphere and solve for the diameter.

The following equation determines a sphere's volume:

V = [tex]\frac{4}{3} \pi r^{3}[/tex]

where r is the sphere's radius and V is its volume.

We are given the volume of the sphere as 3600 cubic centimeters. If we use this value as a substitute in the formula, we get:

3600 = [tex]\frac{4}{3} \pi r^{3}[/tex]

Multiplying both sides by [tex]\frac{3}{4}\pi[/tex], we get:

r³ = ([tex]\frac{3}{4}\pi[/tex]) × 3600

r³ = 8100

If you take the cube-root of both sides, you get:

r = [tex]8100^{1/3}[/tex]

r ≈ 14.6 cm

So, the radius of the sphere is approximately 14.6 cm.

The sphere's diameter is twice its radius. Therefore, the approximate diameter of the sphere is:

d = 2r

d= = 2 × 14.6

d ≈ 29.3 cm

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The complete question is:

The volume of a sphere is 3600 cubic centimeters. What is the approximate diameter of this sphere?

Volume of the sphere = [tex]\frac{4}{3} \pi r^{3}[/tex]

A) 9.5 cm

B) 19 cm

C) 29.3 cm

D) 14.6 cm

Answer:

[tex]x = \frac{18}{ \sqrt{2} } = \frac{18 \sqrt{2} }{2} = 9 \sqrt{2} [/tex]

Each leg is 9√2 cm long.

Bella will put 10 spikes on each Beetlebot, since she has a total of 80 spikes and 8 Beetlebots.

A division sentence is a mathematical sentence that expresses the relationships between numbers, when the operation of division is being applied.

The total number of spikes Bella has is 4 packs x 20 spikes per pack = 80 spikes. She wants to put the same number of spikes on each of the 8 Beetlebots. Let's call the number of spikes she puts on each Beetlebot "x".

The division sentence that represents this situation is:

80 spikes ÷ 8 Beetlebots = x spikes per Beetlebot

Simplifying this division sentence, we get:

10 spikes per Beetlebot = x spikes per Beetlebot

Therefore, Bella will put 10 spikes on each Beetlebot, since she has a total of 80 spikes and 8 Beetlebots and wants to distribute the spikes evenly.

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Answer:

-57

Step-by-step explanation:

matrix multiplication

This is an example of a survey or sampling technique called systematic sampling. The students are selecting every 10th student from the population (in this case, the population is the entire student body) to survey.

This technique can be useful when the population is too large to survey everyone or when a random sample is difficult to obtain. By using systematic sampling, the students can obtain a representative sample of the student body without having to survey every single student.

However, it's important to note that systematic sampling can introduce bias if there is a pattern or structure in the population that is related to the sampling interval. For example, if every 10th student is in a particular grade level or section of the school, this could skew the results of the survey. To mitigate this potential bias, researchers should ensure that the sampling interval is random and that they are not selecting every nth person based on any identifiable characteristics.

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Answer:

yES

Step-by-step explanation:

From the calculation, we have the total area of the figure as shown to be 86 cm^2.

The area of a triangle is the amount of space that is enclosed within the three sides of a triangle. It can be calculated using the formula:

A = 1/2 * b * h

where A is the area of the triangle, b is the length of the base of the triangle, and h is the height of the triangle, which is the perpendicular distance from the base to the opposite vertex.

We know that;

Tan 45 = h/10

h = 10 cm

Then;

Tan 30 = 10/10 + x

0.58 = 10/10 + x

0.58(10 + x) = 10

5.8 + 0.58x = 10

x = 7.2 cm

Thus;

The area of the first triangle = 1/2 * 10 * 10

= 50 cm^2

The area of the second triangle = 1/2 * 7.2 * 10

= 36cm^2

Total area = 86 cm^2

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Hence, equation of parabola is  option b, y = -2(x + 3)² - 2

A parabola is a U-shaped curve that is created by graphing a quadratic function.

It is a type of conic section, which is formed when a plane intersects a cone.

The general equation of a parabola is given by y = ax^2 + bx + c, where a, b, and c are constants.

The value of the parameter a determines the shape and orientation of the parabola. If a > 0, the parabola opens upwards and has a minimum point. If a < 0, the parabola opens downwards and has a maximum point.

The equation of parabola is:-

y = a(x - h)² + k

hence applying value in given equation-

y = -2(x - (-3))² - 2

y = -2(x + 3)² - 2

hence option b y = -2(x + 3)² - 2 is the correct answer.

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The complete question is :-

Hence, equation of parabola is  option b, y = -2(x + 3)² - 2

A quadratic function graphed as a U-shaped curve is called a parabola.

It is a particular kind of conic section that is created when a plane crosses a cone.

Y = ax² + bx + c is the general equation of a parabola, where a, b, and c are constants.

The parabola's shape and orientation depend on the value of the parameter a. The parabola has an upward opening and a minimum point if a > 0. The parabola has a maximum point and opens downward if a 0.

The equation of parabola is:-

y = a(x - h)² + k

hence applying value in given equation-

y = -2(x - (-3))² - 2

y = -2(x + 3)² - 2

hence option b y = -2(x + 3)² - 2 is the correct answer.

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complete question is:

Answer:

To find the cost of filling Binaya's water tank, we need to calculate the volume of the tank first. The tank is in the shape of a cylinder surmounted by a hemisphere, so we can find the volume by calculating the volumes of the cylinder and hemisphere separately and adding them together.

The formula for the volume of a cylinder is V_cyl = πr^2h, where r is the radius and h is the height.

Given that the internal radius of the tank is 90 cm and the total height is 3.8 m, we convert the height to cm to match the radius unit and get 380 cm in height.

So, the volume of the cylinder part of the tank will be V_cyl = π(90)^2(380) = 9147600 cm^3.

The formula for the volume of a hemisphere is V_hem = (2/3)πr^3, where r is the radius of the hemisphere. By halving the internal radius of the cylinder, we get the radius of the hemisphere as 45 cm.

So, the volume of the hemisphere part of the tank will be V_hem = (2/3)π(45)^3 = 95325π cm^3.

The total volume of the tank will be the sum of the volumes of the cylinder and hemisphere:

V_total = V_cyl + V_hem = 9147600 + 95325π = 9457589.25 cm^3.

To convert this volume to litres, we divide by 1000:

V_total_l = 9457.59 l.

The cost of filling the tank with water at the rate of 20 paisa per litre will be:

Cost = 9457.59 x 0.20 = 1891.52 paisa = 18.92 rupees (rounded to two decimal places).

Therefore, it will cost Binaya 18.92 rupees to fill his water tank with water at the given rate.

Imagine you are waiting at the bus stop for a friend to get off a bus from the north. Three buses from the north and four buses from the south arrive about the same time. What is the probability that your friend will get off the first bus? Will the first bus come from the north?

A "verb" is defined as "a word or group of words that express an action (such as eat), an event (such as happen), or a state (such as exist)" in the Oxford Learners' Dictionary. A verb is defined as "a word or phrase that describes an action, condition, or experience" by the Cambridge Dictionary.

Imagine you are waiting at the bus stop for a friend to get off a bus from the north. Three buses from the north and four buses from the south arrive about the same time. What is the probability that your friend will get off the first bus? Will the first bus come from the north?

Note: The verb "arrive" is in the Present Simple tense because it is a general statement about buses arriving at the same time. The verb "is" is in the Present Simple tense because it is a general question about the probability. The verb "come" is in the Present Simple tense because it is a general question about the first bus. The verb "is" could also be in the Present Continuous tense, i.e., "Will the first bus be from the north?" depending on the context and intended meaning. However, in this case, both Present Simple and Present Continuous are grammatically correct. The correct tense to use depends on the specific context and meaning intended. Please provide more context or clarify if you have a specific intended meaning or scenario in mind. I'll be happy to help you further.

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Answer:

Two

Step-by-step explanation:

Trangles are labled n named alphabetically therefore on the bigger triangle D comes first than E and E comes forsr than R wich means that itvis triangle DER not any ather way around.

On the second triangle A comes first than N and N comes first then T thetefore it is triangle ANT

Answer:

Option A is the correct answer

Triangle RED IS SIMILAR TO TRIANGLE TAN

Answer:

x=1

Step-by-step explanation:

To solve this equation, you must substitute. The equation for y is given. To use substitution, you have to put the y equation into the second one. In this case it would look something like this:

2(3x-4)=6x-8

(distribute)

6x-8=6x-8

(add 8)

6x=6x

(divide by 6)

x=x

In this circumstance, x is equal to 1.

Step-by-step explanation:

[tex] \frac{ \frac{1}{7} }{ \frac{2}{5} } = \frac{1}{7} \times \frac{5}{2 } = \frac{5}{14} \\ [/tex]

Answer: 5/14

Step-by-step explanation:

It would help if you used the KCF (Keep, Change, Flip) method. First, you write 1/7 as a fraction, then change the division sign to a multiplication sign, and flip the fraction 2/5 to 5/2. Then multiply 1/7 by 5/2 to get 5/14.

You can expect to run out of cash on approximately 39.45% of the days in a month when withdrawing $8,350 every day.

To determine the percentage of days in a month where you can expect to run out of cash, we'll need to consider the following terms: daily withdrawal, monthly cash usage, and average days in a month.

1. Daily withdrawal: This is the amount of money you withdraw from the ATM each day. In this case, you withdraw $8,350 every day.

2. Monthly cash usage: This is the total amount of money you will withdraw in a month. To calculate this, multiply the daily withdrawal by the number of days in a month. Since the average number of days in a month is approximately 30.42 (365 days in a year / 12 months), the monthly cash usage would be $8,350 x 30.42 ≈ $253,507.

3. Average days in a month: As mentioned earlier, this is approximately 30.42 days.

Now, we need to determine the number of days you would run out of cash. To do this, divide your monthly budget by the daily withdrawal amount. Let's assume you have a budget of $100,000:

Days without cash = $100,000 / $8,350 ≈ 11.98 days.

Since you can't have a fraction of a day, round it up to 12 days.

4. Calculate the percentage: To find the percentage of days you would run out of cash, divide the number of days without cash by the average number of days in a month and multiply by 100:

Percentage = (12 days / 30.42 days) x 100 ≈ 39.45%.

So, you can expect to run out of cash on approximately 39.45% of the days in a month when withdrawing $8,350 every day.

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Total weight of piece of leaf which both ant carries can be calculated by summing both the weight of leaf is 1.48×10⁻².

what is weight?

In the context of physics and engineering, weight refers to the force with which an object is attracted towards the Earth or any other celestial body due to gravity. The weight of an object is equal to the product of its mass and the acceleration due to gravity.

In the given question,

we need to just add both weight of leaf to get total weight

total weight= weight₁  of leaf +weight₂ of leaf

=1.25×10⁻² +2.3×10⁻³

=1.25×10⁻² +0.23×10⁻²

=1.48×10⁻²

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