Step-by-step explanation:
This is the equation for a circle in the form :
(x-h)^2 + (y-k)^2 = r^2 where h,k is the center and r is the radius
center = 5.2,-3.7 and radius = sqrt (49) = 7
Which statement correctly explains the association of the scatter plot? Since the Y values increase as the X values increase the Scatter plot shows a positive association. Sense to Weibo use decrease as the X values increase the scatter plot shows a positive association.
The correct statement regarding the association in the scatter plot is given as follows:
Since the y-values decrease as the x-values increase, the scatter plot shows a negative association.
How to classify the association between variables?There can either be a positive association between variables or a negative association between variables, as follows:
Positive association happens when both variables have the same behavior, that is, as one increases the other increases, and as one decreases the other also decreases.Negative association happens when the variables have opposite behavior, as one variable is increasing the other is decreasing, or as one variable is decreasing, the other is increasing.In this problem, we have a decreasing scatter plot, hence there is a negative association between the variables.
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2)
A high school basketball team won exactly 65 percent
of the games it played during last season. Which of
the following could be the total number of games the
team played last season?
A) 22
B) 20
C) 18
D) 14
Answer:
To find the answer, we can use the formula:
number of won games / total number of games played = percentage won
Let x be the total number of games played. We know that the percentage won is 65%, or 0.65 as a decimal. So we can set up the equation:
number of won games / x = 0.65
To solve for x, we can cross-multiply:
number of won games = 0.65x
We want to find a whole number value for x that makes sense. One way to do this is to try each answer choice and see if it gives a whole number value for the number of won games. Let's start with choice A:
If the team played 22 games, then the number of won games is:
number of won games = 0.65 * 22 = 14.3
This is not a whole number value, so we can rule out choice A.
We can repeat this process for each answer choice. When we try choice C, we get:
number of won games = 0.65 * 18 = 11.7
This is also not a whole number value, so we can rule out choice C.
When we try choice D, we get:
number of won games = 0.65 * 14 = 9.1
This is also not a whole number value, so we can rule out choice D.
Therefore, the only remaining answer choice is B, which gives us:
number of won games = 0.65 * 20 = 13
This is a whole number value, so the team could have played 20 games in total last season.
50 Points! Multiple choice geometry question. Photo attached. Thank you!
area of equilateral triangle =
[tex]( \sqrt{3 } \div 4) \times a {}^{2} [/tex]
(C) area = 84.9 in²
3. (1) The population of a city was 1,20,000 in the year 2078 and the population growth rate was 4.5% 20,000 people migrated here from other places in the year 2079
(a) Find the population reached in the year 2079.
(b) What will be the total population in the year 2081?
The population reached in the year 2079 is 1,65,400 and the total population in the year 2081 would be 1,80,623.
To find the population reached in the year 2079, we need to consider the initial population and the growth rate, as well as the number of people who migrated.
The initial population in 2078 was 1,20,000. The population growth rate is 4.5%, which means the population will increase by 4.5% each year.
To calculate the population in 2079, we first need to calculate the increase in population due to the growth rate:
Population increase due to growth rate = 1,20,000 * (4.5/100) = 5,400
Then we add the number of people who migrated:
Total population in 2079 = Initial population + Population increase due to growth rate + Number of migrants
= 1,20,000 + 5,400 + 20,000
= 1,45,400 + 20,000
= 1,65,400
To calculate the total population in the year 2081, we need to consider the growth rate and the population in 2080.
The population in 2080 would be the population in 2079 plus the population increase due to the growth rate:
Population increase due to growth rate in 2080 = 1,65,400 * (4.5/100) = 7,444
Total population in 2080 = 1,65,400 + 7,444
= 1,72,844
To calculate the total population in 2081, we need to consider the growth rate and the population in 2080:
Population increase due to growth rate in 2081 = 1,72,844 * (4.5/100) = 7,779
Total population in 2081 = Population in 2080 + Population increase due to growth rate in 2081
= 1,72,844 + 7,779
= 1,80,623
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HELP!!! what is the answer!!!!
Answer:
Step-by-step explanation:
the of of 50 percent of people is married
Help me a123 sq ft
B61 sq ft
C49sq ft
D110 sq ft
The area of the required shaded portion is 123 ft²
Given is figure having some shaded portion we need to find the area of the same,
So, the shaded portion is two right isosceles triangles with equal side measuring 14 ft and 7 ft,
So, to find the same, we will calculate the area of the triangles and add them,
Area of a triangle = 1/2 x base x height
Area of the shaded portion = 1/2 x 7 x 7 + 1/2 x 14 x 14
= 122.5 ft²
≈ 123 ft²
Hence the area of the required shaded portion is 123 ft²
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What is the 10th term of the geometric sequence where a1 = 384 and a7 = 6?
0.75
3
6
1.5
Answer:
(a) 0.75
Step-by-step explanation:
You want the 10th term of the geometric sequence with a1 = 384 and a7 = 6.
N-th termThe equation for the n-th term can be written ...
an = a1·b^(n-1)
Using a1 = 384, we can find b from ...
a7 = 6 = 384·b^(7-1)
(6/384)^(1/6) = b
10th termThen the 10th term is ...
a10 = 384·(6/384)^((10-1)/6) = 0.75
The 10th term of the sequence is 0.75.
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If (2x-7), (x-1), 3x, x, (x+2), 30 and 10
1. Find the value of x
2. Find the value of the largest angle
PLEASE HELP ME ASAP
The value of x in arithmetic progression is 5/3 and the largest angle is 30.
The given sequence is: (2x-7), (x-1), 3x, x, (x+2), 30, 10.
In an arithmetic progression, the common difference (d) between consecutive terms remains constant.
The common difference between the terms = (x - 1) - (2x - 7) = x - 1 - 2x + 7 = 6 - x
6 - x = 3x - (x - 1)
6 - x = 3x - x + 1
6 - x = 2x + 1
-x - 2x = 1 - 6
-3x = -5
x = -5 / -3
x = 5/3
Therefore, the value of x is 5/3.
2x-7 = 2 ×5/3 -7 = -3.66
x-1 = 5/3-7 = -5.33
3x = 3 × 5/3 = 5
x + 2 = 5/3+2 =3.66
Thus, the largest angle is 30.
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Your question is incomplete, most probably the full answer is:
If (2x-7), (x-1), 3x, x, (x+2), 30 and 10 are in AP, then
1. Find the value of x
2. Find the value of the largest angle
What is 4∑5n=1 equal to? (See picture below)
Did I get it right?
The summation of 5 to power of n (where n starts from 1) is determined as 625.
What is the sum of the number?The sum of the expression given is calculated by using the defined expression as sated in the question to perform the summation.
The given summation expression include;
∑5ⁿ
where;
n is defined to start from 1. (this written as n = 1)So we are going to sum the number 5ⁿ 4 times.
The expression becomes;
5ⁿ x 5ⁿ x 5ⁿ x 5ⁿ = 5⁴ⁿ
where;
n = 1
The summation becomes;
5⁴ⁿ = 5⁴ = 625
Thus, the summation of 5 to power of n (where n starts from 1) is determined as 625.
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In the year 2000, population
In the year 2000, it was estimate that the population of the world was 6, 082, 966, 429 people.
What was the world population in 2000 ?Based on data provided by the table give, the global population in the year 2000 was estimated to be around 6, 082, 966, 429 individuals. This remarkable figure, serving as a testament to the expansive tapestry of humanity, reflects the vastness and intricacy of our interconnected world during that period.
Within the context of demographic analysis, the United Nations diligently compiled and analyzed extensive data to derive this population estimate for statistical reasons.
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The full question is:
In the year 2000 the world population was
Please I need solution and steps
Answer:
Refer to the step-by-step, follow along carefully.
Step-by-step explanation:
Verify the given identity.
[tex]\frac{\sin(x)}{1-\cos(x)} -\frac{\sin(x)\cos(x)}{1+\cos(x)} =\csc(x)(1+\cos^2(x))[/tex]
Pick the more complicated side to manipulate, so the L.H.S.
(1) - Combine the fractions with a common denominator
[tex]\frac{\sin(x)}{1-\cos(x)} -\frac{\sin(x)\cos(x)}{1+\cos(x)}\\\\\Longrightarrow \frac{\sin(x)(1+\cos(x))}{(1-\cos(x))(1+\cos(x))} -\frac{\sin(x)\cos(x)(1-\cos(x))}{(1+\cos(x))(1-\cos(x))} \\\\\Longrightarrow \frac{\sin(x)+\sin(x)\cos(x)-\sin(x)\cos(x)+\sin(x)\cos^2(x)}{(1+\cos(x))(1-\cos(x))} \\\\\Longrightarrow \boxed{\frac{\sin(x)+\sin(x)\cos^2(x)}{(1+\cos(x))(1-\cos(x))}} \\\\[/tex]
(2) - Simplify the denominator
[tex]\frac{\sin(x)+\sin(x)\cos^2(x)}{(1+\cos(x))(1-\cos(x))}\\\\\Longrightarrow \frac{\sin(x)+\sin(x)\cos^2(x)}{1-\cos(x)+\cos(x)-\cos^2(x)}\\\\\Longrightarrow \boxed{\frac{\sin(x)+\sin(x)\cos^2(x)}{1-\cos^2(x)}}[/tex]
(3) - Apply the following Pythagorean identity to the denominator
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Pythagorean Identity:}}\\\\1-\cos^2(\theta)=\sin^2(\theta)\end{array}\right}[/tex]
[tex]\frac{\sin(x)+\sin(x)\cos^2(x)}{1-\cos^2(x)}\\\\\Longrightarrow \boxed{\frac{\sin(x)+\sin(x)\cos^2(x)}{\sin^2(x)}}[/tex]
(4) - Simplify the fraction and split it up
[tex]\frac{\sin(x)+\sin(x)\cos^2(x)}{\sin^2(x)}\\\\\Longrightarrow \frac{1+\cos^2(x)}{\sin(x)}\\\\\Longrightarrow \boxed{\frac{1}{\sin(x)}+\frac{\cos^2(x)}{\sin(x)}}[/tex]
(5) - Apply the following reciprocal identity
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Reciprocal Identitiy:}}\\\\\csc(\theta)=\frac{1}{\sin(\theta)} \end{array}\right}[/tex]
[tex]\frac{1}{\sin(x)}+\frac{\cos^2(x)}{\sin(x)}\\\\\Longrightarrow \csc(x)+\frac{1}{\sin(x)}\cos^2(x) \\\\\Longrightarrow \csc(x)+\csc(x)\cos^2(x) \\\\\therefore \boxed{\boxed{\csc(x)(1+\cos^2(x))}}[/tex]
Thus, the identity is verified.
Prove of the expression sin x / (1 - cos x) - [sin x cos x ] / (1 + cos x) by using trigonometry formula is shown below.
We have to given that,
Expression to verify is,
⇒ sin x / (1 - cos x) - [sin x cos x ] / (1 + cos x)
Now, We can simplify as,
⇒ sin x / (1 - cos x) - [sin x cos x ] / (1 + cos x)
⇒ sin x [ 1 / (1 - cos x) - cos x / (1 + cos x)]
⇒ sin x [1 + cos x - cos x (1 - cos x )] / (1 - cos²x)
⇒ sin x [1 + cos x - cos x + cos²x] / sin²x
⇒ (1 + cos²x) / sin x
⇒ cosec x (1 + cos²x)
Thus, Prove of the expression sin x / (1 - cos x) - [sin x cos x ] / (1 + cos x) by using trigonometry formula is shown above.
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solve each equation 1/3a= -15
The solution to the equation 1/3a = -15 is a = -45
How to determine the solution to the equationfrom the question, we have the following parameters that can be used in our computation:
1/3a = -15
Multiply 3 to both sides of the equation
so, we have the following representation
3 * 1/3a = -15 * 3
When the products are evalated, we have
a = -45
Hence, the solution to the equation is a = -45
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What is the meaning of "If dom(f) = [tex]X^{n}[/tex], then f is an n-ary function on X"?
The statement "If dom(f) = Χ, then f is an n-ary functionon X" means that if the domain of the function f is equal to the set X, then f is considered an n-ary function on X.
How is this so?In other words, for each element in X, the function f can take n arguments or inputs to produce aunique output. The term "n-ary" indicates the number of arguments that the function can accept.
A statement in mathematics is a declarative utterance that is either true or untrue but not both. A proposal is anothername for a statement. The main point is that there should be no uncertainty.
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Answer:
The statement "If dom(f) = X, then f is an n-ary function on X" means that if the domain of a function f is equal to the set X, then f is a function that takes n arguments or inputs from the set X, where the value of n depends on the specific function.
Step-by-step explanation:
The statement "If dom(f) = X", then f is an n-ary function on X" means that if the domain of the function f is equal to the set X, then f is an n-ary function on X.
Here's a breakdown of the terms used in the statement:
- dom(f): The domain of a function f refers to the set of all possible input values for the function. It represents the set of values for which the function is defined.
- X: In this context, X represents a set. It could be any set, and it serves as the domain for the function f.
- n-ary function: An n-ary function is a function that takes n arguments or inputs. The value of n represents the number of inputs the function expects.
Therefore, the statement is saying that if the domain of the function f is equal to the set X, then f is an n-ary function on X. It implies that the function f takes n inputs from the set X, where n is determined by the specific function.
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer:
13cm
Step-by-step explanation:
The area of a trapezoid is given by the formula:
Area = ½*(b1+b2)*h
where:
b1 and b2 are the lengths of the bases of the trapezoid h is the height of the trapezoidIn this problem, we are given that b1 = 6 cm, b2 = 15 cm, and Area = 136.5 square centimeters.
Plugging these values into the formula, we get:
136.5 = ½*(6 + 15)*h
Solving for h, we get:
136.5=10.5h
h = 136.5/10.5=13centimeters
Therefore, the height of the trapezoid is 13 centimeters.
The aquarium has 10 more red fish than blue fish. 60 percent of the fish are red. How many blue fish are in the aquarium? Show your work. (10 points)
Answer:
There are 20 blue fish in the aquarium.
Step-by-step explanation:
If 60% of the fish are red than 40% are blue. That means that 20% fish is 10 fish. 20% = 10 fish. 40% = 20 fish.
Factor the following and then fill in the blanks. 2x²7x-15 = (2x + )(x- Blank 1: Blank 2:
Answer:
(2x + 3)(x - 5)
Step-by-step explanation:
2x² - 7x - 15
consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 2 × - 15 = - 30 and sum = - 7
the factors are - 10 and + 3
use these factors to split the x- term
2x² - 10x + 3x - 15 ( factor the first/second and third/fourth terms )
= 2x(x - 5) + 3(x - 5) ← factor out (x - 5) from each term
= (2x + 3)(x - 5) ← in factored form
Blank 1 is 3
Blank 2 is 5
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What scale factor was applied to the first rectangle to get the resulting image?
Enter your answer as a decimal in the box.
Answer:
2.5
Step-by-step explanation:
the length has increased by 7.5/3 = 2.5.
so the scale factor is 2.5
(4x-12) + ( 1/2x y -10) for x=4 and y=6
Answer: (4x-12) + ( 1/2x y -10) = 6
Step-by-step explanation:
First, input 4 for x and 6 for y into the equation so it looks like this:
(4(4)-12) + (1/2(4)(6)-10)
Now solve inside the parentheses starting with the first one. 4 * 4 = 16 so the inside of the first parentheses should look like (16 - 12) which equals 4.
For the second set of parentheses, 1/2 * 4 * 6 = 12, so the inside of that parentheses would look like (12 - 10), which equals 2.
At this point, the equation should look like this: (4) + (2). If you add those two together, your answer should be 6.
The consistency of the diameters of wheel bearings is vital to the operation of the wheel. The specifications require that the variance of these diameters be no more than 0.0015 centimeter squared. The diameter is continually monitored by the quality-control team. Twenty subsamples of size 10 are obtained every day. One of these subsamples produced bearings that had a variance of 0.00317 centimeter squared. Conduct a hypothesis test to determine if the quality control team should advise management to stop production and search for causes of the inconsistency of the bearing diameters. Use a significance level of 0.05.
A hemisphere has a
surface area of 768
square feet. Find
the diameter of the
hemisphere.
The diameter of the hemisphere is 39.1918 feet.
The surface area of a hemisphere is given by the formula:
Surface Area = 2πr²
We have,
surface area of the hemisphere is 768π square feet,
So, 2πr² = 768π
Dividing both sides of the equation by 2π, we get:
r² = 384
To find the diameter, we need to double the radius.
Taking the square root of both sides of the equation, we get:
r = √384
r ≈ 19.5959
Now, Diameter ≈ 2 x 19.5959 ≈ 39.1918
Therefore, the diameter of the hemisphere is 39.1918 feet.
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Find x to the nearest hundredth.
16
X
40°
OA. x = 24.89
OB. x = 13.43
O C. x 10.28
OD. x = 12.26
Sin 40° = x/16
0.6428 = x/16
x = 0.643 × 16
x = 10.2848
x = 10.28
So, the value of x is 10.28 (C)
That's it :)
There are thirteen boys and fifteen girls in a class. The teacher randomly selects one student to answer a question. Later, the teacher selects a different student to answer another question. What is the probability that the first student is a boy and the second a girl? Explain.
Step-by-step explanation:
To solve this problem, we need to calculate the probability of the first student being a boy and the second student being a girl.
There are a total of 13 boys and 15 girls in the class, making a total of 28 students.
The probability of the first student being a boy is given by:
P(boy) = Number of boys / Total number of students = 13 / 28
After the first student is selected, there are now 27 students remaining (since one student has already been selected). Out of these 27 students, there are still 15 girls remaining.
The probability of the second student being a girl, given that the first student was a boy, is given by:
P(girl|boy) = Number of girls / Remaining number of students = 15 / 27
To find the probability of both events occurring (the first student being a boy and the second student being a girl), we multiply the individual probabilities:
P(boy and girl) = P(boy) * P(girl|boy) = (13/28) * (15/27)
Calculating this expression:
P(boy and girl) ≈ 0.2041
Therefore, the probability that the first student is a boy and the second student is a girl is approximately 0.2041 or 20.41%.
If 2 pints = 1 quart and 1 quart = 1 pint then how many pints are 2 quarts?
Step-by-step explanation:
1 qt = 2 pts multiply both sides by two
2 qt = 4 pints
25. Three students contributed a total of $200 towards a building for the aged. Azar contributed 50% of it, Sunil 25% and the rest was contributed by a girl Becky. How much money did Becky contribute? rice he lost 25% of its weight
Becky contributed $50 towards the building for the aged.
Let's calculate the amounts contributed by each student:
Azar contributed 50% of the total amount:
Amount contributed by Azar = 50% of $200
= (50/100) × $200
= $100
Sunil contributed 25% of the total amount:
Amount contributed by Sunil = 25% of $200
= (25/100) × $200
= $50
Now, we can calculate the amount contributed by Becky:
Total contribution by Azar and Sunil = $100 + $50 = $150
The remaining amount contributed by Becky can be found by subtracting the total contribution by Azar and Sunil from the total amount:
Amount contributed by Becky = Total amount - Total contribution by Azar and Sunil
= $200 - $150
= $50
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Find the missing dimension of the cylinder. Round your answer to the nearest whole number.
Volume = $\ 10,000\pi\ $ in.3
A cylindrical piece of a log is shown. The diameter of its base is 32 inches and height is h.
$h\ \approx$
in.
The nearest Whole number, the missing dimension (height) of the cylinder is approximately 39 inches.
The missing dimension of the cylinder, we can use the formula for the volume of a cylinder:
Volume = π * r^2 * h
Given that the volume is 10,000π in³ and the diameter of the base is 32 inches, we can determine the radius (r) of the cylinder.
The diameter is twice the radius, so the radius is half of the diameter:
r = 32 inches / 2 = 16 inches
Substituting the known values into the volume formula, we have:
10,000π in³ = π * (16 in)^2 * h
Cancelling out the common factor of π, we get:
10,000 = 16^2 * h
Simplifying further:
10,000 = 256 * h
To isolate h, we divide both sides of the equation by 256:
h = 10,000 / 256
Calculating the value of h:
h ≈ 39.06
Rounded to the nearest whole number, the missing dimension (height) of the cylinder is approximately 39 inches.
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A sample of 318 students at a university is surveyed. The students are classified according to gender ("female" or "male"). They are also classified according major ("biology", "business", "engineering", "mathematics", or "computer science"). The results are given in the contingency table below. Biology Business Engineering Female Male 47 37 20 36 What is the relative frequency of biology majors in the sample? Round your answer to two decimal places. 43 15 Mathematics 29 35 Computer science 20 36
50 Points! Multiple choice geometry question. Photo attached. Thank you!
The angle ABC in the circle is 70 degrees.
How to find the angle in a circle?The intercepted arc is the arc that is inside the inscribed angle and whose
endpoints are on the angle. The arc angle is half the the inscribed angle.
The intercepted arc that is formed is equal to the inscribed angle,
multiplied by two (intercepted arc measure = inscribed angle × 2).
Therefore, let's find the arc angle ABC as follows:
∠ ABC = 1 /2 (360 - 120 - 100)
∠ ABC = 1 /2 (360 - 220)
∠ ABC = 1 /2 (140)
Therefore,
∠ ABC = 70 degrees
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#8: Expand the logarithm shown below. *
log981xy
In order to expand the properties of logarithms log981x:
log981x = log98 + log1x
One must know that loga + logb = log(ab), and loga + logb = log(ab) may also be represented as loga(b) or logab.
Using this property, we can simplify the expression further:
log981x = log98 + log1x = log9 + log8 + log1 + logx
We know that log9 = 2 and log1 = 0, so we can simplify even further:
log981x = log9 + log8 + log1 + logx = 2 + log8 + 0 + logx = 2 + log8x.
Therefore, the expanded value would be log981x to 2 + log8x.
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2x + y ≤ 2
a. change the inequality into slope-intercept form, and then change it into an equation.
b. create a table. Use the x-values indicated
c. Graph the points and draw a line.
d. Shade the solution area.
e. Check your solution. Use (0,0) as your test point and see if it satisfies the conditions of the original inequality.
Please help ASAP 7p-13p+4-5p
Hello!
[tex]7p-13p+4-5p\\\\= 7p-13p-5p+4\\\\= -6p-5p+4\\\\\Large\boxed{= -11p + 4}[/tex]