Write the fifteenth term of the binomial expansion of (a³+d) 24.

The value that Helen wants to use is Pi = C/D. The lower bound value is 3.065, and the upper bound for Helen's value is 3.165.

What is circumference?

The circumference is the perimeter of the circle.

Given, the circumference, C, at 405 mm to three significant numbers.

She correctly estimates the diameter, d, to be 130 mm to two significant numbers.

Helen wants to find the value of Pi using the formula pi=C/D

We have, the circumference of the circle = C = 405 mm

The diameter of the circle = d = 130 mm

Pi = C/D

= 405 mm / 130 mm

= 405 / 130

= 3.115

3.115, measured to the nearest 0.1.

The degree of accuracy is nearest 0.1.

0.1/2 = 0.05

Upper bound = 3.115 + 0.05 = 3.165

Lower bound = 3.115 - 0.05 = 3.065

Therefore, the lower bound and upper bound for Helen's value are 3.165, and 3.065.

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Using the roller coaster as an example, draw a right triangle.

Use h to symbolize the horizontal distance.

The following expression can be used to get h given that roller coaster serves as a representation of the hypotenuse side length.

30² = h² + 25².

Assemble similar phrases.

h² = 30² - 25².

horizontal separation

In (a), there is:

h² = 30² - 25².

This results:

h² = 275

Take both sides' roots.

h = 16.58

Consequently, 16.58 feet are the horizontal distance.

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Answer:

70.5%

Step-by-step explanation:

If a continuous random variable X is normally distributed with mean μ and variance σ², it is written as:

[tex]\large\boxed{X \sim\text{N}(\mu,\sigma^2)}[/tex]

Given:

Therefore, if the weights of the 12-month-old baby boys are normally distributed:

[tex]\boxed{X \sim\text{N} \left(22.5,2.2^2 \right)}[/tex]

where X is the weight of the baby boy.

To find the percentage to the nearest tenth of 12-month-old baby boys who weigh between 19.7 and 24.4 pounds find P(19.7 ≤ X ≤ 24.4).

Calculator input for "normal cumulative distribution function (cdf)":

[tex]\implies \text{P}(19.7 \leq X \leq 24.4)=0.704548741[/tex]

[tex]\implies \text{P}(19.7 \leq X \leq 24.4)=70.5\%[/tex]

Therefore, the percentage of 12-month-old baby boys who weigh between 19.7 and 24.4 pounds is 70.5% (nearest tenth).

Based on the above, the number of 3-points that they make is 25.

Simultaneous equation is a form of two equations that have to be solved at the same time. Thus, the number of 2 points made is 17, while that of 3 points is 25.

A set of equations that has to be solved simultaneously so as to determine the values of the unknown variables is termed simultaneous equation.

The given question would result to a simultaneous equation as follows;

let the number of 2 points made by represented by m, and that of 3 points by n.So that;

m + n = 42  ..................

i2m + 3n = 109  ...............

ii multiply equation 1 by 3 and equation 2 by 1 to have;3m + 3n = 126 ............

iii 2m + 3n = 109 .............

iv subtract eqaution iv from iii

m = 17

substitute the value of m in equation 1 to have:

m + n = 4217 + n = 42n = 42 - 17   = 25m = 17, n = 25

Thus the number of 2 points made was 17, while that of 3 points made was 25.

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The original cardboard measures 25 cm by 40 cm. By cutting out a 10 cm by 10 cm corner square, the new measurement of the cardboard will be 15 cm by 30 cm. The volume of the container will be 4500 cm^3.

The goal of this project is to build a container out of a rectangular piece of cardboard measuring 25 cm by 40 cm. To do this, a square must be cut out of each corner of the cardboard and the sides must then be bent up. In order to produce a container with the most internal volume, the corner square should be 10 cm by 10 cm. This will result in four equal sides and a larger internal volume. The larger internal volume will allow the container to hold more material, thus making it more efficient for the project.

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What the slope and the y-intercepts represent are;

Slope means that the rate at which the number of miles people in the U.S. traveled per year increased was 0.048

y-intercept means that the number of vehicle-miles traveled in 1975 is; 1.345 (in trillions)

A reasonable prediction for the number of miles people in the U.S. will travel in 2022 is; 3.601 (in trillions)

The equation for the line of best fit is given as;

y = 0.048x + 1.345

where;

x is the number of years since 1975

y is the number of vehicle-miles traveled in trillions

The equation of a line in slope intercept form has the general form as;

y = mx + c

where;

m is slope

c is y-intercept

Thus;

Slope = 0.048 which is the rate at which the number of miles people in the U.S. traveled per year increases.

y-intercept = 1.345 (in trillions) which is the number of vehicle-miles traveled in 1975

The year 2022 will be 47 years since 1975 and so the prediction is;

y = 0.048(47) + 1.345

y = 3.601 (in trillions)

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In  linear equation, He travels at a greater speed from his friend's house, at a rate of 0.6667 miles per minute, that is, 2 miles in 3 minutes.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.  

                             Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Using linear function concepts, it is found that:

Seth starts closer to the school in the bus.

He travels at a greater speed from his friend's house, at a rate of 0.6667 miles per minute, that is, 2 miles in 3 minutes.

From the graph of the bus, when he takes the bus, he is 13 miles from the school, as he starts at position 4 and ends at 17.

At his friend house, he is 13 miles from the school only after 3 minutes, which means that the bus will be closer.

The scenario with the greater speed is the one with the higher slope, that is, higher rate of change, which is the change in distance divided by the change in time.

In the bus, change of 13 miles in 24 minutes, thus

       mᵇ = 13/24 = 0.5417

   From the friend's house, change of 2 miles in 3 minutes, thus

   mf = 2/3 = 0.6667

Thus, he travels at a greater speed from his friend's house, at a rate of 0.6667 miles per minute, that is, 2 miles in 3 minutes.

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Answer: The circumference itself can be considered a full circle arc length. Arc Measure: In a circle, the degree measure of an arc is equal to the measure of the central angle that intercepts the arc. Arc Length: In a circle, the length of an arc is a portion of the circumference.

An arc length is a portion of the circumference of a circle. You can use the measure of the arc (in degrees) to find its length (in linear units). In a circle, the ratio of the length of a given arc of the circumference is equal to the ratio of the measure of the arc to 360°.

It will help you.

Step-by-step explanation:

Answer:

y = 3x + 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (- 2, - 2) ← 2 points on the line

m = [tex]\frac{-2-4}{-2-0}[/tex] = [tex]\frac{-6}{-2}[/tex] = 3

the line crosses the y- axis at (0, 4 ) ⇒ c = 4

y = 3x + 4 ← equation of line

Answer:

y=3x+4

Step-by-step explanation:

The formula used is point slope, or y=mx+b

here, the m is the slope, and the b is the y-intercept

The y-intercept is where the graph crosses the y-axis, also known as when x=0

In this case, the y intercept is at the point (0,4) so you'd plug in 4 for the 'b' in the equation

To find the slope, use the rise over the run of the graph.

To do this, pick two points along the graph, and count how many units up/down, and to the left/right between the two points

The units up/down goes on top, being positive if they're up, and negative if they're down

The units left/right go on bottom, being positive if they're right, and negative if they're left

In this case you go 3 units up, and 1 unit right, so the slope would be 3/1 or 3

Step-by-step explanation:

come on, use some common sense.

length to breadth = 3/2.

so, when the breadth is 24, what is the factor compared to the original 2 of 3/2 ? 12.

2 × 12 = 24 cm

and then, we need to multiply the other ratio part by the sand factor

3 × 12 = 36 cm

when the length = 60 cm, then the factor compared to the original 3 of 3/2 is 20.

3 × 20 = 60 cm

and multiplying the other ratio part by the same factor

2 × 20 = 40 cm

when the breadth is 52, the factor compared to the original 2 of 3/2 is 26.

2 × 26 = 52 cm

and multiplying the other ratio part by the same factor

3 × 26 = 78 cm

Answer:

y=-2/3x+4

Step-by-step explanation:

Rise/run (from the y-intercept to the next point you go down 2 and then to the right 3)

Y-intercept (where the line touches the y-axis) 4

After solving the percentage the distance through which Nakeiha fell asleep along the trip is 72miles.

Percentage is a number expressed as a fraction of 100. The % sign means to divide the number by 100.

To solve this question, we will do 18% x 400.

= (18/100) x 400

= 72 miles

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Five water glasses each minute, one minute to fill the cooler.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. what kinds of values and units

Let's say you go to the store to buy six apples.

You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples. Recognizing the units and values is crucial when using the unitary technique to a problem.

Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things.

We are aware of the quantity of apples and the amount of money in the aforesaid problem.

According to our question-

divide 150 by 30 equal 5

= 5

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Answer:

Yes, the lines are parallel. This is because the lines have the same slope. The slope of a line is a measure of how steep the line is, and it is calculated by taking the difference of the y-coordinates of two points on the line and dividing it by the difference of the x-coordinates of the same two points. In this case, the slope of line a is -1, and the slope of line b is also -1. Because the lines have the same slope, they are parallel to each other.

Answer:

2(x+8)=126

Step-by-step explanation:

GD is the bisector of CGE and 126 and the angle CGE are equal

Answer:

£54

Step-by-step explanation:

Write 45% as

45

100

Since finding the fraction of a number is the same as multiplying the fraction with the number, we have

45

100

of 120 =

45

100

× 120

Therefore, the answer is 54

If you are using a calculator, simply enter 45÷100×120 which will give you 54 as the answer.

Answer:

£90

Step-by-step explanation:

1 friend = £30

all together there are 3 friends

30 x 3 = 90

or you can simplify and do 3x3 which is 9

and add the 0 at end (90)

each person = 30($)

people = 3

cost($) * number of people

[tex]30\times3[/tex]

[tex]=\fbox{90}[/tex]

The segments in the blank provided is GH/FH=IH/JH so that the equation is true

Similar triangles differ in size but have the same form. Corresponding angles are identical in comparable triangles. Similar triangles have corresponding sides that have the same ratio. The ratio of the square of any two of their corresponding sides to any identical triangle's area is the same.

The triangle similarity criteria are:

AA (Angle-Angle)

SSS (Side-Side-Side)

SAS (Side-Angle-Side)

In the given question

<GHP=<IHJ (vertically opposite angles)

<JIH=<HPG (alternate angles)

From AA similarity critera

triangles JHI ~ triangle GHP

Hence

GH/FH=IH/JH

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Answer:

Step-by-step explanation: Step 1: Tyler correctly states that rhombuses have all sides congruent.

Step 2: Tyler correctly states that dilating a rhombus by a scale factor will result in sides of the same length, but he does not provide a justification for why he chose the scale factor of WX/AB.

Step 3: Tyler correctly states that if all sides in two figures are proportional, then the figures are similar, but he does not provide a justification for why this is true.

Step 4: Tyler correctly states that he will translate A'B'C'D' by the directed line segment A'W, but he does not provide a justification for why this will result in A'' and W coinciding.

Step 5: Tyler correctly states that he will rotate A"B"C"D" by the angle B"WX, but he does not provide a justification for why this will result in B'' and X coinciding.

Step 6: Tyler correctly states that he will reflect A"B''C''D'' over segment WX if needed, but he does not provide a justification for why this will result in D'' and Z coinciding.

The length of second lawn is found as the 36 sq. m.

For the stated question-

First lawn:

Area = length x width

A = 6 x 4 = 24 sq. m.

Second lawn:

A2 = length x width

6 x A = L x 4

6 x 24 = L x 4

L = 6 x 6

L = 36 sq. m

Thus, the length of the second lawn is found as the 36 sq. m.

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Answer:

Step-by-step explanation:

36 is the answer

Answer:

y=-3

Step-by-step explanation:

A line of symmetry is the line where a function can be folded in half evenly. Here it occurs at y=-3

line of symmetry, the line at which point the graph begins to mirror itself, Check the picture below.

We require a more accurate and objective measure to determine the association between the two variables because visual exams are primarily subjective. We employ the linear correlation coefficient to express the degree and direction of the association between two variables:

[tex]r=\frac{\sum \frac{\left(x_i-\bar{x}\right)}{s_x} \frac{\left(y_i-\bar{y}\right)}{s_y}}{n-1}[/tex]

where the sample means and standard deviations of the x's are x and sx, respectively, and the y's are y and sy, respectively. n is the sample size. .

A different method of calculating the correlation coefficient is:

[tex]r=\frac{S_{x y}}{\sqrt{S_{x x} S_{y y}}}[/tex]

[tex]\begin{aligned}& \text { where } S_{x x}=\sum x^2-\frac{\left(\sum x\right)^2}{n} \\& S_{x y}=\sum x y-\frac{\left(\sum x\right)\left(\sum y\right)}{n} \\& S_{y y}=\sum y^2-\frac{\left(\sum y\right)^2}{n}\end{aligned}[/tex]

In honor of Karl Pearson, who created the linear correlation coefficient in the first place, it is also known as Pearson's product moment correlation coefficient. This metric quantifies the strength of the linear, or straight-line, relationship between the two variables as well as its positive or negative direction.

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The set of all possible y-x values is between 3 and 6, excluding both endpoints.

===================================================

Explanation:

The y-x value is smallest when:

I recommend to draw out a number line. The idea is to place x and y as close as possible to each other.

Based on those two conditions, we use y = 10 and x = 7 respectively. That gives y-x = 10-7 = 3 as the smallest possible difference. Keep in mind we can't actually reach this value so we would write y-x > 3 which is the same as 3 < y-x.

--------------------

Similarly, y-x is largest when:

Like earlier, use a number line to see why this would be the case. We're trying to space x and y out as far as possible.

The largest y value and smallest x value are y = 12 and x = 6 in that order. So the upper bound is y-x = 12-6 = 6. Like before, we can't actually reach this number which means we write y-x < 6.

--------------------

Recap:

Put those two results together in a tidy compound inequality to get the final answer    3 < y-x < 6

It says: The expression y-x is between 3 and 6, excluding both endpoints.

If it takes a printer seconds to print a single lyer, and it took 75 seconds to print a batch of lyers without stopping, the number of lyers in the batch is 75 / . This is because if it takes seconds to print a lyer, and we have 75 seconds available to print lyers, we can divide the total time available by the time it takes to print each lyer to find out how many lyers we can print.

For example, if it takes 3 seconds to print a single lyer, the number of lyers in the batch is 75 / 3 = 25. If it takes 2 seconds to print a single lyer, the number of lyers in the batch is 75 / 2 = 37.5.

Therefore, the number of lyers in the batch depends on the time it takes to print a single lyer. To find the exact number of lyers in the batch, we need to know the time it takes to print a single lyer.

Answer:

y = –5x/4 + 7

Step-by-step explanation:

x1 = 8 ,x2 = 4, y1 = –3 , y2 = 2

lets find the slope(m)

m = y2–y1/x2–x1

m = 2 – (–3)/ 4 – 8

m = 5/ –4

m= –5/4

to find the equation of a line using this as our guider y = mx + b

we will make use of one coordinate

(8,–3)

using the formula for one point

y – y1 = m(x – x1)

y – (–3) = –5/4(x – 8)

y + 3 = –5x/4 + 10

y = –5x/4 + 10 –3

y = –5x/4 + 7

i hope i helped pls rate the answer as brainliest if i deserve it

thanks

By using the formula for area of rectangle, it can be calculated that Area of the median is 2400 sq. feet

What is area of rectangle?

The area of a rectangle is calculated by multiplying the length by the width. For example, if a rectangle has a length of 10 feet and a width of 6 feet, the area would be 10 x 6 = 60 square feet. The area of a rectangle is a two-dimensional measurement and is typically expressed in units squared, such as square feet or meters squared. Other shapes, such as a triangle or a circle, also have areas and are calculated differently.

If l is the length of the rectangle and b is the breadth of the rectangle, then area of rectangle is calculated by the formula

Area = [tex]l \times b[/tex]

Length of the median = 300 feet

Width of the median = 8 feet

Area of the median = 300 [tex]\times[/tex] 8 = 2400 sq. feet

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Answer:

The value of n in this equation is 5.

Step-by-step explanation:

This can be determined by using the property of exponents that states that x^n * x^m = x^(n+m). In this case, 10^n * 10^5 = 14,521, so 10^(n+5) = 14,521. Solving for n, we get n = 5.

The properties of the triangles created from the original triangle based on triangle congruency rules are as follows;

SSS: The triangle created using the lengths of the three sides of the original should have the same length and angles as the original

The triangle formed using SSS is a unique triangle and no other triangle has similar dimensions

SAS: The lengths of the sides and the measure of the angles should be the same

The triangle created using SAS is a unique triangle and there is not a way to have a third side that has a different length

ASA; The triangle formed using the ASA of the original triangle should have the same length as the same lengths and angles as the original triangle

The triangle formed using ASA is a unique triangle and there is not a way to create a triangle that has a different side length.

Two triangles are congruent if the lengths of the three sides of one triangle are congruent to the three sides of the other triangle or if they meet the other conditions of triangle congruency.

Length of first measured side of the triangle = 52 units

Angle made by the first measured side with the horizontal = 41°

Length of the second measured side of the triangle = 87 units

Angle the second measured side makes with the horizontal = 33°

Length of the third measured side of the triangle = 113 units

Angle the third side makes with the horizontal ≈ 6.5°

Let the vertices of the first side be A and B, we get;

∠A = 180° - (41° + 33°) = 106°

∠C = 33° - 6.5° = 26.5°

∠B = 41° + 6.5° = 47.5°

SSS: The SSS (Side-Side-Side) congruency postulate states that if the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.

Therefore, the lengths of the sides and the measures of the angles of the triangle created using the lengths of the three sides of the original triangle will be the same as the original triangle.

The SSS congruency postulate indicates that the triangle created using the same lengths of the three sides of the original triangle is a unique triangle and there are no other triangles having the same side lengths but different angles

SAS: The Side-Angle-Side, SAS, congruency postulate states that if the adjacent sides and an included angle of a triangle are congruent to two adjacent sides and an included angle of another triangle, then the two triangles are congruent.

Therefore, the triangle formed using two sides of the original triangle and the included angle between them will have the same length as the sides of the original triangle, and the triangle formed using the SAS of the original triangle is unique

The length of the third side of the triangle created using the SAS measurement is always the same as the length on the original triangle

ASA: The Angle-Side-Angle, ASA, congruency postulate states that if two angles and the included side of one triangle are congruent to two angles and an included side of another triangle, then the two triangles are congruent.

The triangle formed using the ASA is a unique triangles and therefore and there is no way to create a triangle that has a different side length

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The height of the desk for the doll according to conversion scale given is 1.5in.

Based on the information provided, the height of Katelyn’s actual desk is 3 feet. She wants to build a desk for her doll and she wants to use a scale of 0.5 in: 1feet to convert the measurements. A conversion scale refers to a scale which indicates the relationship between two different units of measurement.

According to the given conversion scale,

1 feet = 0.5in

If the height is 3 feet, the measurement in inches would be:

3 feet = 3 feet * 0.5 in/ 1 feet = 1.5 in

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