2 cos^2(pi/8) -1= ,
x=(2n + 1) π/4 + π/8, where n is an integer.
What is meant by integer?
An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction.Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers that are not integers are some examples.The Latin word integer, from the prefix in ("not") plus tangere, means "whole" or (literally) "untouched" ("to touch").An integer is any number that may be expressed without using any fractions. Since there are no fractions in integers, they are essentially entire numbers that can be positive, zero, or negative.An integer field can have 3, 5, 10, or 20 digits, with length being defined in terms of the number of digits. One byte of storage is required for a 3-digit field.x=(2n + 1) π/4 + π/8, where n is an integer.
We use the double angle identity 2[tex]cos^{2}[/tex]A−1 = cos2A
if x − π/8 =A, then 2[tex]cos^{2}[/tex] (x− π/8) −1 = cos(2(x − π/8)) = cos(2x − π/4)
Hence cos(2x − π/4) = 0
and 2x − π/4 = (2n + 1) π/2, where n is an integer
or 2x = (2n+1) π/2 + π/4
or x = (2n + 1) π/4 + π8, where n is an integer.
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Determine whether AB←→ and CD←→− are parallel, perpendicular, or neither. A(1, 5), B(4, 4), C(9, -10), D(-6, -5)
The lines [tex]\overleftrightarrow{AB}[/tex] with points on the line A(1, 5), and B(4, 4) and the line [tex]\overleftrightarrow{CD}[/tex] with points C(9, -10), D(-6, -5), have equal slopes and are therefore; parallel
[tex]\overleftrightarrow{AB}[/tex] is parallel to [tex]\overleftrightarrow{CD}[/tex]
What are parallel lines?Parallel lines are lines in which the distance between them remain the same as they extend contionuously.
The two lines are parallel, perpendicular, or neither, depending on their slope.
The lines [tex]\overleftrightarrow{AB}[/tex] and [tex]\overleftrightarrow{CD}[/tex] are parallel, if their slope are the same
The lines [tex]\overleftrightarrow{AB}[/tex] and [tex]\overleftrightarrow{CD}[/tex] are perpendicular if the slope of [tex]\overleftrightarrow{AB}[/tex] is the negative reciprocal of the slope of [tex]\overleftrightarrow{CD}[/tex]
The lines [tex]\overleftrightarrow{AB}[/tex] and [tex]\overleftrightarrow{CD}[/tex] are neither parallel nor perpendicular if their slope are neither equal nor the negative inverse of the other.
The slope of a line passing through the points (x₁, y₁), (x₂, y₂) can be found using the formula;
[tex]Slope=\frac{y_2 - y_1}{x_2 - x_1}[/tex]
The slopes of the line [tex]\overleftrightarrow{AB}[/tex] and line [tex]\overleftrightarrow{CD}[/tex] are therefore
The slope of line [tex]\overleftrightarrow{AB}[/tex] = (4 - 5)/(4 - 1) = -1/3
Slope of [tex]\overleftrightarrow{CD}[/tex] = (-5 - (-10))/(-6 - 9) = -1/3
The slope of the lines [tex]\overleftrightarrow{AB}[/tex] and [tex]\overleftrightarrow{CD}[/tex] are the same therefore, the lines [tex]\overleftrightarrow{AB}[/tex] and [tex]\overleftrightarrow{CD}[/tex] are parallel
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153,300 is 3/2 of what number?
pleaseee I really need it
Answer:
X = 229,950
Step-by-step explanation:
Lets convert the sentence into an equation.
We can write "3/2 of what number?" as (2/3)X, where X is "what number."
"153,300 is" can be rephrased as "is 153,300", or = 153,300.
Put these together:
(2/3)X = 153,300
Solve:
(2/3)X = 153,300
(3/2)*(2/3)X = (3/2)*153,300
X = (3/2)*153,300
X = 3*(76,650)
X = 229,950
====
CHECK: Is (2/3) of 229,950 = 153,300? YES
The point of intersection of concurrent lines is called the?
The point of intersection of concurrent lines is called the point of concurrency.
Concurrent lines are lines that intersect at a single common point. This point of intersection is also known as the point of concurrency.
It can also be said that concurrent lines are lines that pass through a common point and this point is known as the point of intersection or point of concurrency.
In geometric figures, there are some special point of concurrency. For example, in a triangle, there are three special point of concurrency: the incenter, the circumcenter, and the orthocenter. The incenter is the center of the inscribed circle, the circumcenter is the center of the circumcircle and orthocenter is the point where the three altitudes of the triangle intersect.
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Please help quickly! TV is a medsegment of UWX
if WX=3s+77 and TV=2s+42, what is TV
The length of TV is 40 units.
What is Triangle Midsegment theorem?The section connecting a triangle's two sides at their midpoints is parallel to and only half as long as the third side.
Given a triangle ABC, let's draw a line segment connecting the midpoints of two of the sides, say AB and BC.
Then by Triangle Midsegment Theorem,
DE = (1/2)AC. DE is parallel to AC
Given:
WX = 3s+ 77 and TV = -2s + 42
As, we know a midsegment connecting two sides of a triangle is parallel to the third side and is half as long.
VT = 1/2 WX
-2s + 42 = 1/2 ( 3s + 77)
-4s + 84 = 3s + 77
84- 77= 3s + 4s
7 = 7s
s = 1
Hence, length of TV = -2(1)+ 42 = 40 units
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If a point is chosen inside the large circle, what is the probability that it will also be inside the small circle?
[?]%
A point near the center of a circle can be situated under the area covered by radius R/2.
So, the favourable outcomes = [π x (R/2)^2]
Now, a point inside a circle can be situated under area covered by radius R.
So, total outcomes = [π x ( R) ^2]
Hence, required probability,
= [ π x (R/2)^2]/[π x (R) ^2]
=1/4
=2.5
RadiusRadius is defined as a line segment joining the center to the boundary of a circle or a sphere. The length of the radius remains the same from the center to any point on the circumference of the circle or sphere. It is half of the length of the diameter.
What is RadiusIn geometry, the radius is defined as a line segment joining the center of the circle or a sphere to its circumference or boundary. It is an important part of circles and spheres which is generally abbreviated as 'r'. The plural of radius is "radii" which is used when we talk about more than one radius at a time. The largest line segment in a circle or sphere joining any points lying on the opposite side of the center is the diameter, and the length of the radius is half of the length of the diameter. It can be expressed as d/2, where 'd' is the diameter of the circle or sphere.
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A customer buys a reusable mug at a coffee shop for $8.65 and pays an additional $0.99 for each coffee refill ordered with the reusable mug. If the customer spends a total of $21.52 on the reusable mug and x coffee refills, how many refills does the customer order?
Simplify the following.
Answer:
27√2
Step-by-step explanation:
9√18
9√9√2
27√2
6x7!!!!!!!!!!!!!!!!!
Answer:42
Step-by-step explanation:
Hi there! So I think you're asking for 6 x 7. That's 42.
6 + 6 + 6 + 6 + 6 + 6 + 6
That's 6, written seven times.
7 + 7 + 7 + 7 + 7 + 7
That's 7, written six times.
Solving these, both are 42. You can use this method if you're ever needing to do a quick problem. Then you'll just memorize it! :D
27
of the students in
100
6th grade said they
have one sibling. What
27
percent is equal to?
100
11»
>>> FRACTION, DECIMAL, PERCENT
E
The 27 percent is equal to 27/100 as a fraction, 0.27 as a decimal and 27% as a percentage.
What is percentage?
A percentage is a way of expressing a number as a fraction of 100. It is often used to express a proportion or ratio of one number to another, usually with respect to a whole. A percentage is denoted by the symbol "%". It can be represented as a decimal or a fraction.
27 out of 100 students in 6th grade said they have one sibling.
As a fraction, this is 27/100.
As a decimal, this is 0.27
As a percentage, this is 27%
Hence, 27 percent is equal to 27/100 as a fraction, 0.27 as a decimal and 27% as a percentage.
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The distribution of age for players of a certain professional sport is strongly skewed to the right with mean 26.8 years and standard deviation 4.2 years. Consider a random sample of 4 players and a different random sample of 50 players from the population. Which of the following statements is true about the sampling distributions of the sample mean ages for samples of size 4 and samples of size 50 ? A Both will be skewed to the right, and the mean for size 50 will be closer to 26.8 than the mean for size 4. B Both will be skewed to the right, and the standard deviation for size 50 will be closer to 4.2 than the standard deviation for size 4. Both will be approximately normal, and the mean for size 50 will be closer to 26.8 than the mean for size 4. Only the sampling distribution for size 4 will be approximately normal, and the standard deviation for both will be 4.2. E Only the sampling distribution for size 50 will be approximately normal, and the mean for both will be 26.8.
Both will be approximately normal, and the mean for size 50 will be closer to 26.8 than the mean for size 4.
Step 1: Calculate the mean of the population.
The mean of the population is 26.8 years.
Step 2: Calculate the standard deviation of the population.
The standard deviation of the population is 4.2 years.
Step 3: Calculate the mean of the sample.
The mean of the sample is the average of all the values in the sample.
Step 4: Calculate the standard deviation of the sample.
The standard deviation of the sample is the square root of the sum of the squares of the differences between each value and the mean.
Step 5: Calculate the sampling distribution of the sample mean. The sampling distribution of the sample mean is the probability distribution of the mean of a sample drawn from the population. It is typically modeled as a normal distribution with the same mean as the population and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
Step 6: Determine if the sampling distributions for size 4 and size 50 are approximately normal.
The sampling distributions for size 4 and size 50 are both approximately normal. The mean for size 50 will be closer to 26.8 than the
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a buyer for a specialty clothing manufacturer must buy at least 2000 bales of cotton that weigh at least 420 kilograms per bale. a cotton broker has a shipment of 100,000 bales with weights that are normally distributed with a mean of 376 kilograms and a standard deviation of 22 kilograms. how many bales should the buyer purchase to ensure that he has at least 2000 bales that weigh 420 kilograms each?
The buyer should purchase 87913 bales to ensure that he has at least 2000 bales that weigh 420 kilograms each.
For having a bale of 420 and above,
we calculate standard deviation using below information
(420 - 376 /22) = 0.02275 = 2.275% chance of having a bale of 420+ kg
To find out the number of bales to pe precise,
2000/0.02275 = 87912.1 so you'll need at the very least 87913 bales to be reasonably certain.
The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
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Which function is shown on the graph?
Of(x)= -1/2 sin x
Of(x)= 1/2 sinz x
O f(x)= -1/2 cos x
O f(x) = 1/2 cos x
To graph sine, cosine, and tangent functions, use values on the unit circle.
Which function is shown on the graph?Create a table of values with the angle and the value of the trigonometric function and make note of where a function is undefined. Then plot and connect the points on a graph with the angle as the x-axis and the trigonometric value as the y-axis.
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What is 871.816 divided by 7618.882 ?
Answer:
-0,8777 the answer is at least it seems
Step-by-step explanation:
0.1144283374 is its answer..
Help me ;-;
Enter a number in each box so that the expressions are equivalent.
(A) 0.8 (2x + x) + 3(7 - 4.1x) = x + 21
(B) 12
1
2
(6x + 22y) = x + y
(C) (3x - ) - (6x + 1) = -3x - 2
(D) 112
1
2
x + 27y = (12
1
2
x + 9y)
Therefore , the solution of the given problem of linear equation is x's coefficient is -9.9,x's coefficient is 75 and y's coefficient is 275.
How a linear equation is defined ?A model of linear regression is one that applies the formula y=mx+b. B is the slope, and m is the y-intercept. Ignoring the fact that while both y and y are distinct components, the previous sentence is frequently referred as a "mathematical formula with two variables." Bivariate linear equations only have two variables. The application domains of linear equations have zero solutions in all cases.
Here,
Given :
=>0.8 (2x + x) + 3(7 - 4.1x) = __x + 21
=>0.8(3x) + 21 - 12.3x = __x + 21
=>2.4x + 21 - 12.3x = __x + 21
=>-9.9x + 21 = __x + 21
=> -9.9
=> 12 1/2 (6x + 22y) = x + y
=> 75x + 275y = x + y
Therefore , the solution of the given problem of linear equation is x's coefficient is -9.9,x's coefficient is 75 and y's coefficient is 275.
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3 pounds of potatoes makes 8 servings of mashed potatoes. How many servings of mashed potatoes would 12 pounds of potatoes make? Show your work using equivalent ratios.
As you answer the following questions, write explanations for why your current answer is correct
Answer:
We can use equivalent ratios to solve this problem.
We know that 3 pounds of potatoes makes 8 servings of mashed potatoes.
This can be expressed as a ratio: 3 pounds of potatoes : 8 servings of mashed potatoes
We can use this ratio to find the number of servings of mashed potatoes that 12 pounds of potatoes would make.
To do this, we'll keep the ratio of potatoes to servings of mashed potatoes the same, while scaling up the quantity of potatoes.
We can start by cross multiplying:
3 pounds of potatoes * x servings of mashed potatoes = 8 servings of mashed potatoes * 12 pounds of potatoes
3 * x = 8 * 12
Next, we'll solve for x by dividing both sides of the equation by 3
x = 8*12/3
x = 32
So, 12 pounds of potatoes would make 32 servings of mashed potatoes.
This answer is correct because the ratio of potatoes to servings of mashed potatoes is the same in both cases and we just scaled up the quantity of potatoes while keeping the ratio the same.
Identify the properties used in solving the inequality.
The inequality is resolved using the addition and division characteristics.The addition, subtraction, multiplication, and division operations all function as methods for solving equations.
Determine the attributes that were used to solve the inequality ?Describe inequality.The addition, subtraction, multiplication, and division operations all function as methods for solving equations.
Finding the value of the unknown variable might be as easy as adding, subtracting, multiplying, or dividing the two sides of an equation.
Inequality is the relationship between two expressions or values that are not equal to one another.
3x - 2 > -4 is the inequality that is given.
Greater than minus four is three times x minus two.
The addition property is used to add +2 on both sides.
3x – 2 +2 > -4+2
3x>-2
By dividing +3 on both sides, we can be employing the division property.
x>-2/3
Therefore, the inequality is resolved using the addition property and division property.
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Over the next 17 months you have to read more than 102 books. You have to read x books per month. The inequality 17x > 102 represents this situation. Solve the inequality to find the number of books you have to read per month.
how many books do you have to read more than per month
Hello! I won't be putting the answer to this question, not sure what format this is (test/homework.) Just want to be clear! So I'll be explaining what to do but the answer is for you to find. ;)
Step-by-step explanation: 17x > 102, divide both sides by 17 to isolate the x.
17x/17 > 102/17
I'll leave you with that! ;D
Answer:
More than 6 books per month.
Step-by-step explanation:
Given variable:
Let x be the number of books you have to read per month.Given information:
Over the next 17 months you have to read more than 102 books.Therefore, the inequality to represent the given information is:
17x > 102To solve the inequality, divide both sides by 17:
⇒ 17x ÷ 17 > 102 ÷ 17
⇒ x > 6
Therefore, you have to read more than 6 books per month.
complete the empty cells in the table
can someone help me with those 2 tables pls
Mackenzie is trying to find the height of a radio antenna on the roof of a local
building. She stands at a horizontal distance of 29 meters from the building.
The angle of elevation from her eyes to the roof (point A) is 24° and the
angle of elevation from her eyes to the top of the antenna (point B) is 32°. If
her eyes are 1.71 meters from the ground, find the height of the antenna (the
distance from point A to point B). Round your answer to the nearest meter if
necessary.
The antenna Is[tex]$4.6 \mathrm{~m}$[/tex] high
Steps on how to determine the radio antennas' height?Height of the base station antenna (h1) is 30.48 metres (100 ft) At the antenna, base-station power is 10 watts (40 dBm) Gt = 6 dB more than the dipole gain for the base-station antenna (6 dBd). The FM band can be operated more effectively with short antennas that are coiled or have a coil at the base. The AM broadcast band requires long and growing antennas. Basically, they are lengthy conductors—the longer, the better.To find the distance H, we make use of the relationship
[tex]& \frac{H}{33 m}=\tan 33^{\circ} \\[/tex]
[tex]& \Longrightarrow H=33 m \cdot \tan 33^{\circ}[/tex]
To find the distance h, we make use of the relationship
[tex]& \frac{h}{33 m}=\tan 27^{\circ} \\[/tex]
[tex]& \Longrightarrow h=33 m \cdot \tan 27^{\circ}[/tex]
Thus, the distance H - h, or the height of the radio antenna, can be found as follows
[tex]& H-h=33 m \cdot \tan 33^{\circ}-33 m \cdot \tan 27^{\circ} \\[/tex]
[tex]& =33 m \cdot\left(\tan 33^{\circ}-\tan 27^{\circ}\right) \\[/tex]
[tex]& =33 m \cdot(0.6494-0.5095) \\[/tex]
[tex]& =33 m \cdot 0.1399 \\[/tex]
[tex]& =4.6167 m \approx 4.6 m[/tex]
The antenna Is[tex]$4.6 \mathrm{~m}$[/tex] high
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I really need help with this ☹️
Slope: 7
Y-intercept: 15
Equation: y = 7x + 15
To find the slope, start with finding the change in y and change in x.
If you look at the table, you can see the x values constantly change by 1. You can also see that the y values constantly change by 7.
Slope = change in y ÷ change in x
Slope = 7 ÷ 1
Slope = 7
To find the y-intercept, look at the table and see what y is when x is 0, which is 15.
The standard form of a linear equation is y = mx + b, m being the slope and b being the y-intercept. We have already found those values, so we can substitute them in to get y = 7x + 15.
How old is the king, how many children has he, and how long is his boat? Given that the product of three positive integers gives 32118 which answers these questions. The length of his boat is given in metres, the king has sons and daughters, he has more years than his children, but he is not yet one hundred years old. please help fast
please
If the product is a positive integer is 32118, then the king's age is 53. There will be children is 6 and the length of the boat is 101 m.
What are integers?The Latin term "Integer," which implies entire or intact, is where the word “integer” first appeared.
The puzzle demands three numbers - x, y, z which represent the king's number of children, age, and length of the boat respectively.
(r1), x, y, and z are positive integers different from 1 and such that -
XYZ = 32118
(r2) 4 ≤ x < y < 100
Begin with (r1) which leaves only a finite number of possibilities, whereas (r2), which does not restrict z at all, leaves an infinite number.
Therefore, we examine (r1). Now, 32118 is divisible by 6, and so we easily decompose it into prime factors:
32118 = 2 × 3 × 53 × 101
For a decomposition into three factors, we have to combine two of the four primes. Therefore, there are only six different ways to decompose the number 32118 into a product of three factors, all different from 1:
6 × 53 × 101
3 × 101 × 106
3 × 53 × 202
2 × 101 × 159
2 × 53 × 303
2 × 3 × 5353
Of these six possibilities, the remaining requirement (r2) rejects all except the first one, and so we obtain -
x = 6 , y = 53 and z = 101.
Therefore, there will be children is 6 and the length of the boat is 101 m.
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7. A toy is made up of cylindrical rings stacked
on a base, as shown in the diagram. The
diameter of Ring 1 is 87% of the diameter of the
base. For Ring 2 through Ring 7, the diameter
of each ring is 87% of the diameter of the ring
directly below it.
7
G
2
The diameter of the base is 5 inches. Which
function can be used to find the diameter in
inches of Ring r, wherel≤r≤7 ?
F d(r) = 5(0.87)
G_ d(r) = 0.87(r-5)
H_ d(r) = 0.87(5)
J d(r) = 5(r-0.87)
The function that can be used to find the diameter in inches of Ring r, is option F: d(r) = 5× (0.87)^r.
What is diameter?
A circle is a 2D form in geometry in which all of the points on its surface are equally spaced from its centre. The radius is the length from any point on the surface to the centre. Similar to this, the diameter of a circle is defined as the distance through its centre between any two points on its surface.
It is given that the diameter of base is 5 inches.
The diameter of ring 1 is 87% of diameter of base -
⇒ diameter of ring 1 = 87% of 5 inch
= 5 × 87/100
Diameter of ring 1 = 5 × 0.87 inch
Now, diameter of ring 2 is 87% of diameter of ring 1
⇒ diameter of ring 2 = 87% of 5 × 0.87 inch
= 5 × 0.87 ×87/100
= 5 × 0.87 × 0.87
Diameter of ring 2 = 5× (0.87)²
Now, diameter of ring 3 is 87% of diameter of ring 2
⇒ diameter of ring 3 = 87% of 5 × (0.87)² inch
= 5 × (0.87)² ×87/100
= 5 × (0.87)² × 0.87
Diameter of ring 3= 6× (0.9)³
Therefore, the diameter of ring r = 5× (0.87)^r.
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A survey of 169 law firms in a country found that the average hourly billing rate for partners was $607 what is the population and the sample?
The population in this case would be all of the law firms in the country.
The sample is the group of law firms that were surveyed, which is 169 firms.
The average hourly billing rate of $607 is the sample statistic.
In statistics, a population is the entire group of individuals or objects that we are interested in studying. In this case, the population would be all of the law firms in the country. The population can include all possible values, characteristics, and attributes of interest.
A sample, on the other hand, is a subset of the population that we actually collect data from. In this case, the sample is the group of 169 law firms that were surveyed. The sample is used to represent the population and to make inferences about the population.
Also, the sample statistics such as the average hourly billing rate of $607, is an estimate of the population parameters such as population mean, which is the average hourly billing rate of all law firms in the country.
In summary, population represents the entire group of law firms in the country, and the sample is a subset of law firms surveyed and the sample statistic such as the average hourly billing rate of $607 is an estimate of the population parameter such as population mean.
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What is a quotient example?
Answer: A quotient is an answer to a division problem
Step-by-step explanation: Exaple: 2/3=0.6666666666666.... in this problem 0.66666666666666666666666666666666666 is the quotient
HELP pls will mark you the brainliest
4) The complete table is,
Kites purchased Total cost for Kites
0 8
1 12
4 4 × 4 + 8 = 24
7 4 × 7 + 8 = 36
10 4 × 10 + 8 = 48
5) The equation for the total cost y in terms of the number of kites purchased x, is
⇒ y = 4x + 8
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
4) We have to given that;
Multiply the number of kites by 4 and add 8 to get the cost of kites.
Hence, We get the complete table as;
Kites purchased Total cost for Kites
0 8
1 12
4 4 × 4 + 8 = 24
7 4 × 7 + 8 = 36
10 4 × 10 + 8 = 48
5) The equation for the total cost y in terms of the number of kites purchased x, is
Let two points are (0, 8) and (1, 12)
Hence, We get;
⇒ y - 8 = (12 - 8) / (1 - 0) (x - 0)
⇒ y - 8 = 4x
⇒ y = 4x + 8
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A height of 26 feet and a diameter of 5. 6 feet. What is the volume of the geode, rounded to the nearest tenth?
The volume of the geode rounded to the nearest tenth is equals to the 640.1 feet³.
Geodes are approximately cylindrical structures with an internal cavity lined with mineral materials. They have a durable outer wall that is more resistant to weathering than the surrounding bedrock. This allows the geode to survive intact as the surrounding bedrock weathers.. The volume of cylinderical body is represented as, V = πr² h
where, r --> radius of cylinder
h --> height of cylinder
π --> maths specific constant , π = 3.14
We have a geode rock with height 26 feet and diameter 5.6 feet. As we know diameter of is double the radius. Let radius of geode be "R" .
And R = diameter/2 = 5.6/2 = 2.8 feet.
Volume of geode, V = πr²h
= 3.14 × ( 2.8)² feet² × 26 feet
= 640.0576 ~ 640.1 feet³
Hence , required volume is 640.1 feet³.
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4. Write a function that Alan can use to estimate his take-home pay, where x represents gross pay and y represents net pay.
function estimateNetPay (x, y) { // calculate estimated take-home pay let takeHomePay = x - y; // return estimated take-home pay return takeHomePay;}
What is function?Function in math is a rule that assigns one unique output to each input of a given set of inputs. This means that for every input there is one, and only one, corresponding output. Functions can be represented in a variety of ways, such as equations, graphs, tables, and verbal descriptions. Functions can also be combined to form more complex functions.
// Example:
let grossPay = 1000;
let netPay = 200;
let estimatedTakeHomePay = estimateNetPay(grossPay, netPay);
console.log(estimatedTakeHomePay); // 800
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what is the area of a triangle whose vertices are A(4,-1), B(9,2), and C(4, -6)
Answer: 12.5
Step-by-step explanation: Plotting the points and then finding their sides, and then using Herons formula, you can get the answer 12.5
In a certain chemical, the ratio of zinc to copper is 4 to 19. A jar of the chemical contains 741 of copper. How many grams of zinc does it contain?
Using the ratio formula the amount of zinc in the jar of chemical containing 741 grams of copper is 156 grams.
What is ratio?
Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorise ratios. Part to whole ratio is one, and part to part ratio is the other.
The amount in ratio of zinc in a chemical is = 4
The amount in ratio of copper in a chemical is = 19
The actual weight of copper in the jar of the chemical is = 741
The actual weight of zinc in the jar of the chemical is = x
Use the formula for ratio -
A : B = A' : B'
Substitute the values in the equation -
4 : 19 = x : 741
4/19 = x/741
Simplify the equation to get the amount of zinc -
19 × x = 4 × 741
19x = 4 × 741
x = (4 × 741)/19
x = 4 × 39
x = 156
Therefore, the amount of zinc in the jar is 156 grams.
To learn more about ratio from the given link
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consider the more realistic case where students choose how much time to spend in a preparation course, and you can only randomly sample sat and hours from the population. write the population model as sat
In this scenario, the population model would be written as:
SAT = β0 + β1 * Hours + ε
where:
SAT represents the SAT score of the studentsHours represents the number of hours the students spend in the preparation courseβ0 is the intercept termβ1 is the slope coefficient representing the relationship between the number of hours spent in the preparation course and the SAT scoreε is the error term, representing the unpredictable factors that affect SAT scores and are not explained by the number of hours spent in the preparation course.This model represents the underlying relationship between SAT scores and the number of hours spent in the preparation course for the entire population. By randomly sampling data from this population, you can use this model to make inferences about the population parameters (β0, β1) and make predictions about SAT scores based on the number of hours spent in the preparation course.
You can learn more about population model at
https://brainly.com/question/25630111
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