There are 404 numbers between 1 and 2020 inclusive that can be the side of the hypotenuse given that three sides of the right triangle have integral lengths which form an arithmetic sequence. This can be obtained by forming the arithmetic sequence, equating by Pythagoras theorem and finding numbers divisible by the integral.
Find the value of hypotenuse?Let the arithmetic sequence be (a - d), a, (a+d)
Using Pythagoras theorem,
(a - d)² + a² = (a+d)²
a² -2ad + d² + a² = a² + 2ad + d²
2a² - 2ad + d² = a² + 2ad + d²
2a² - a² + d² - d² = 2ad + 2ad
a² = 4ad
a = 4d
Thus hypotenuse will be (a + d) = 4d + d = 5d
How many numbers between 1 and 2020 inclusive can be the side of the hypotenuse?Since the value of hypotenuse is 5d, the total numbers divisible by 5 between 1 and 2020 will be the number of possible sides of the hypotenuse.
There are 2020 numbers between 1 and 2020 inclusive
The numbers divisible by 5 = 2020/5 = 404
Hence there are 404 numbers between 1 and 2020 inclusive that can be the side of the hypotenuse given that three sides of the right triangle have integral lengths which form an arithmetic sequence.
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A science test, which is worth 100 points, consist of 24 questions. Each question is worth either 3 points or 5 points. If X is the number of 3 point questions and why is the number of 5 point questions, the system shown represents this situation. X+y=24, 3x+5y=100. What does the solution of this system indicate about the questions on the test?
Answer:
x= 10 y=14 : 10 3 point, 14 5 point
Step-by-step explanation:
Write your equation down vertically,
3x + 5y = 100
x + y = 24
Next find multiply bottom equation by one number from the tops opposite,
3x + 5y = 100
(-3)x +(-3)y = (-3)24
3x + 5y = 100
-3x - 3y= -72
Add the two functions to isolate y
2y= 28 y=14
Plug y back into original and solve
3x +5(14) =100 --> 3x + 70 =100 --> 3x = 30 x=10
How much wood is needed to replace the entire roof of this gazebo that is in the
shape of a right pyramid on top of a regular octagon? (Note: The roof's base does
not require wood.)
can someone please help me
Answer:
Cos (3pi/4) =0.999154554
Sin (3pi/4)=0.041111762
Step-by-step explanation:
On your calculator there should be SIN and COS next to each other
#1 tap COS
#2 put your given numbers, in this case
COS(3pi/4) = 0.999154554
same goes for SIN
SIN (3pi/4)=0.041111762
Given: Circle X with Radius r and circle Y with radius s
Prove: Circle X is similar to Circle Y
It can be proved that Circles X and Y are similar.
How can we prove that the circles are similar?We were told that circle Y have a radius of s
And X have the Radius r
Going with the theorem that Similar shapes are proportional, we can find the scale factor from circle X to circle Y by making a division on the radii of both circles.
Then the scale factor is [tex]\frac{s}{r}[/tex] which implies that circle Y will gotten by dilation of circle Y.
Therefore, both circles are similar
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Decide whether the triangles are similar. if so, determine the appropriate expression to solve for x. triangles abc and edf; triangle abc has angle a measuring 53 degrees, angle c measuring 62 degrees, side ac labeled as y, side ab labeled as w, and side bc labeled as x; triangle edf has angle d measuring 61 degrees, angle f measuring 53 degrees, side de labeled z, side ef labeled u, and side df labeled r.
Answer:
Step-by-step explanation:
Similar Triangle:
Two triangles are comparable if they have the same ratio of corresponding sides and equal pairs of corresponding angles.If more figures have the same shape, but their sizes are different, then such objects are referred to as similar figures. Consider a hula hoop and wheel of a cycle, the shapes of each of those gadgets are much like every other as their shapes are equal.
Triangle ABC has angles of 53 and 62 degrees....the sum is 115 degrees. The third angle must be 180 - 115 = 65 degrees.
A triangle with one angle = 61 degrees cannot be similar
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Answer: The triangles are not similar; no expression for x can be found.
help me with this pls asap
Answer:
your picture is blank if you can fix it i will be glad to help you
Step-by-step explanation:
Answer:
First option
Step-by-step explanation:
The line corresponds to the f(x).
Hope this helps
Solve 5x=125 using the one-to-one property of exponents.
A) X=In(125)
B) x = 1
C) x = 3
OD) x = 5
Anyone is here
Answer:
Step-by-step explanation:
hello :
A) X=In(125)
Select the correct answer. Identify the expression equivalent to 4(x + x + 7) - 2x + 8 - 4 by substituting x= 1 and x = 2.
A. 6x + 11
B. 3(x + 7)
C. 2(3x + 16)
D. 3x + 16
Answer:
C is correct
Step-by-step explanation:
I'm not sure what the substituting part has to do anything, but here is how I got the answer
4(x+x+7)-2x+8-4
4(2x+7)-2x+4
8x+28-2x+4
6x+32
Factor and you get
2(3x+16), which is answer choice C
You can check that the answer is right by plugging in x=1 and x=2 into the original equation and the answer choice, which may be what that is asking.
(FIRST TO ANSWER GETS BRAINLIEST OR 5 STARS) For consecutive weeks, the manager of a local restaurant collected data on the number of cheese pizzas sold each week. The data is shown in the scatterplot below.
(scatterplot is below)
Can the given line be used to make reasonable predictions of the number of cheese pizzas that will be sold in upcoming weeks? Explain your reasoning.
Yes, the line can be used to make reasonable predictions of the number of cheese pizzas that would be sold in the upcoming weeks. This is because the line is the line of best fit
Line of best fitFrom the question, we are to determine if the line can be used to make reasonable predictions of the number of cheese pizzas that would be sold in the upcoming weeks
In the graph, we have a scatterplot.
The line drawn is the line of best fit
Hence,
Yes, the line can be used to make reasonable predictions of the number of cheese pizzas that would be sold in the upcoming weeks. This is because the line is the line of best fit.
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5. The two rectangles are similar. Which is the correct proportion that can
be used to find the missing side?
12/4=x/20
12/4=x/8
12/8=x/4
4/12=x/8
Answer:
The second choice.
Step-by-step explanation:
Correspond sides are in the same ratio
12/4 = x/8
.
the cost of 4 ice cream cones from the snack bar was $10.40. if each ice cream costs the same amount, which model correctly illustrates the relationship? check all that apply
twice a certain number is 58. 4 times that number will be
a) 4x58 b) 58 + 4 c) 58x2 d)8x58
Answer:
c) 58x2
Step-by-step explanation:
Twice the number 29 is 58
So, 29 is related to 58
Therefore 29*4 = 58*2
Consider the function f(x)=x2 bx c. if the minimum of this function is located at point (2,0), then what are the values of b and c?
The values of b and c are -4 and 4 respectively
How to determine the values of b and c?The function is given as:
f(x) = x^2 + bx + c
Differentiate f(x)
f'(x) = 2x + b
Set to 0
2x + b = 0
Solve for b
b = -2x
The minimum is (2, 0).
So, we have:
b = -2 * 2
b = -4
Substitute b = -4 in f(x) = x^2 + bx + c
f(x) = x^2 - 4x + c
Substitute (2, 0)
0 = (2)^2 - 4(2) + c
This gives
0 = 4 - 8 + c
Evaluate
c = 4
Hence, the values of b and c are -4 and 4 respectively
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The graph of the piecewise function f(x) is shown.
On a coordinate plane, a piecewise function has 2 connecting lines. The first line has a closed circle at (negative 2, negative 5) and goes up to a closed circle at (2, negative 1). The second line has a closed circle at (2, negative 1) and goes down to an open circle at (4, negative 2).
What is the range of f(x)?
{x | −2 ≤ x < 4}
{x | −2 < x ≤ 4}
{y | −5 < y < −1}
{y | −5 ≤ y ≤ −1}
Answer: {y | −5 ≤ y ≤ −1}
Step-by-step explanation:
The extreme values are -5 and -1.
There is a closed circle at (-2, -5), so -5 is in the range.There is a closed circle at (2, -1), so -1 is in the range.So, the answer is {y | −5 ≤ y ≤ −1}.
a carpool contains three kindergartners and five first-graders. if two children are ill, find the probability tyhat at lease one of them
The probability that at least one of them is a kindergartner; 0.643.
What is probability?Calculating or estimating how likely something is to occur is what probability is all about. The likelihood of an event occurring can be expressed using words like "certain," "impossible," or "probable."
Probabilities are always expressed in mathematics as fractions, decimals, or percentages with values ranging from 0 to 1.
Calculation for the probability of the one of them is a kindergarden;
The total number of children is 8.
The total number of kindergarden are 3.
The total number of first graders are 5.
Let 'P' be the probability that at least one of them is kindergarden.
P(at least one kindergartner) = 1 - P(no kindergartner) = 1 - P(all first-graders)
The probability that all are first-graders = (5/8)×(4/7)
= 5/14
Therefore, P(at least one kindergartner) = 1 - (5/14)
= 9/14
= 0.643
Therefore, if two children are ill then, the probability that at least one of them is a kindergartner is 0.643.
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The correct question is-
A carpool contains three kindergartners and five first-graders. if two children are ill, find the probability that at least one of them is a kindergartner.
The programmer at a local public radio station is compiling data on listeners who stream podcasts. an executive for the national broadcaster has communicated that the overall population mean is 20,500 with a standard deviation of 2,180. the local programmer has a sample of 30 podcasts for her station. by the central limit theorem, which interval do about 99.7% of the sample means fall within?
The interval in which 99.7% of the sample means fall within 3 standard deviations of the mean is 19,306 to 21,694.
What is the central limit theorem?According to the central limit theorem,
Sample mean = Population mean = μ
Sample standard deviation = (Population standard deviation)/√n = σ/√n
where n is at least 30.
Calculation:It is given that,
The overall population mean = 20,500
Population standard deviation σ = 2180
Sample size n = 30
Since n = 30, the central limit theorem can be applied.
According to the Empirical rule(68-95-99), 99.7% of the sample means fall within the 3 standard deviations of the mean.
So, the interval is calculated by
Sample mean = Population mean = μ = 20500
Standard deviation(sample) = σ/√n
⇒ S = 2180/√30 =398.011 ≅ 398
Thus,
The lower bound = 20500 - 3 × 398 = 19,306
The upper bound = 20500 + 3 × 398 = 21,694
Therefore, the required interval is from 19,306 to 21,694.
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The function f is defined by f(x)=2-x. If 2f(p)=8, what is f(2p)?
If function 'f' is defined by f(x)=2-x and 2f(p)=8 then the value of f(2p) is 6.
Given, f(x) = 2-x
Solve this problem by making a series of substitutions.
First, find the value of p.
Then use the definition of the function f to find the value of f(2p).
We are given
f(x) = 2 - x
Multiply both sides by 2, and simplify.
2f(x) = 2(-x +2)
2f(x) = -2x + 4
Let x = p.
2f(p) = -2(p) + 4
We are given that 2f(p) = 8.
Substitute 20 for 2f(p).
8 = -2p + 4
2p = -4
p = -2
Now we know that p = -2, so we can find f(2p).
f(x) = -x + 2
f(2p) = -2p + 2
Substitute -2 for p.
f(2p) = -2(-2) + 2
f(2p) = 4 +2
f(2p) = 6
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A survey was conducted in the class about their favorite subjects. 35% of the class voted for Math and Science. 45% of the class voted for Math. Find the percent of the class who voted for Math also voted for Science.
The percent of the class who voted for Math also voted for Science is 38.8%
How to find the percent who voted math and also voted for science?Therefore,
1 = p(m) + p(s) - p(m ∩ s)
Hence,
p(m) = 45% = 0.45
p(s) = ?
p(m ∩ s) = 35% = 0.35
Therefore,
1 = 0.45 + p(s) - 0.35
1 - 0.45 + 0.35 = p(s)
p(s) = 0.9
Therefore,
p(m | s) = 0.35 / 0.9 = 0.38888888888 = 38.8%
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P(x) · Q(x) = R(x); if P(x) = x + 1 and R(x) = 2x³ + 2x²- 3x-3, what is Q(x)?
A. 2x² - 3
B. 2x² - 2
C. 2x² + 2
D. 2x² + 3
Answer: A
Step-by-step explanation:
[tex]P(x) Q(x)=R(x)\\\\(x+1)Q(x)=2x^3 + 2x^2 - 3x-3\\\\Q(x)=\frac{2x^3 + 2x^2 - 3x-3}{x+1}\\\\Q(x)=\frac{2x^2 (x+1)-3(x+1)}{x+1}\\\\Q(x)=2x^2 - 3[/tex]
Select the correct answer.
What is the zero of the function represented by this graph?
x = 5
x= -6
x=-5
x=6
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here's the explanation ~
Zeros or roots of a function is the value of independent variable (usually x - coordinate or absicca) where the value of dependent variable (y - coordinate or ordinate) is 0.
That is :
The point where it cuts the x - axis, it has an x - coordinate = -6
Therefore, we can conclude that The zero of given function is -6
Answer:
x = -6.
Step-by-step explanation:
It is where the graph cuts the x-axis (where the function is zero).
That is -6.
How do you find
arcsin (-1)
By the definition of inverse functions, we will get:
[tex]arcsin(-1) = -pi/2[/tex]
How to find the arcsin of -1?The function arcsin(x) is the inverse of the sine function, such that, if:
[tex]sin(x) = y\\\\arcsin(y) = x[/tex]
Now, we know that:
[tex]sin( -pi/2) = -1[/tex]
Where pi = 3.14
Then, using the above rule:
[tex]arcsin(-1) = -pi/2[/tex]
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Question 20
Points 3
The height of a lighthouse is 98 meters and the distance between the top of the lighthouse and boat is 125 meters. Find the distance
between the bottom of the lighthouse and the boat.
O 125 m
O 77.6 m
The distance between the bottom of the lighthouse and the boat is 77.6m.
What is the distance between the bottom of the lighthouse and the boat?
The lighthouse and the boat would form a right triangle. The height would be the height of the lighthouse. The distance between the top of the lighthouse and boat would be the hypotenuse. The distance between the bottom of the lighthouse and the boat would be the base.
In order to determine the required distance, Pythagoras theorem would be used.
The Pythagoras theorem: a² + b² = c²
where:125² = 98² + b²
b² = 125² - 98²
b = √(25² - 98² )
b = 77.6m
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find the volume of a sphere with a raduis of 3 in.
Answer:
V≈113.1in³.
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Evaluate. (-3 2/3)^2
Answer:
answer is 121/9
Step-by-step explanation:
13.4444444444 (decimal form)
121/9 (improper fraction form)
13 4/9 (mixed fraction form)
Maria is creating a round stained glass window like the one below. She needs to cut the dark pink glass to the correct size to fit into the frame. At what angle (x) should she cut the glass so that it fits if she knows the arc measure of a is 35º and the arc measure of b is 45º. What does x equal?
Applying the angle of intersecting chords theorem, the value of x is: 40º.
What is the Angle of Intersecting Chords Theorem?According to the angle of intersecting chords theorem the following equation is true:
x = 1/2(a + b).
Given the following:
a = 35º
b = 45º
Plug in the values
x = 1/2(35 + 45)
x = 1/2(80)
x = 40º
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Jay went to an amusement park. the park charges an entrance fee of $10.50 and $4.50 for every ride. jay spent $46.50 on entrance fees and rides. which fuction can be used to find the number of rides he went on? f (x) = 4.5 x + 10.5 f (x) = 4.5 x f (x) = 4.5 x minus 10.5 f (x) = negative 4.5 x
The function that can be used to find the number of rides Jay went on is, f(x) = 4.5x + 10 = 46.5. Hence, the first option is the right choice.
Also, on solving the function we get that, Jay went on 8 rides.
We assume the number of rides Jay spent to be x.
The cost of each ride is given to be $4.50.
Thus, the total amount Jay spent on rides = $4.50x.
The entrance fee to the park is given to be $10.50.
Thus, the total expenditure of Jay can be shown as $(4.5x + 10.5).
But, in the question we are given that Jay spend $46.50 altogether.
Thus, the function to find the number of rides Jay went on can be shown as:
f(x) = 4.5x + 10 = 46.5.
Hence, the first option is the right choice.
To find the number of rides he went, we can solve this function as:
4.5x + 10 = 46.5,
or, 4.5x = 46.5 - 10.5 = 36,
or, x = 36/4.5 = 8.
Thus, Jay went on 8 rides.
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Given the series below, find S29.
{13+4+(−5)+(−14)+(−23)+...}
Select one:
a. -2,480
b. -2,752
c. -3,016
d. -3,277
Answer:
d
Step-by-step explanation:
there is a common difference between consecutive terms in the series, that is
4 - 13 = - 5 - 4 = - 14 - (- 5) = - 23 - (- 14) = - 9
this indicates the series is arithmetic with sum to n terms
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
here a₁ = 13 and d = - 9 , then
S₂₉ = [tex]\frac{29}{2}[/tex] [ (2 × 13) + (28 × - 9) ]
= 14.4(26 + (- 252))
= 14.5(26 - 252)
= 14.5 × - 226
= - 3,277
what’s ten times ten
uppose you want to test the value of the mean in a population. You collect a random sample of 60 which yields a sample mean and sample standard deviation. You only know sampled information to perform the test. What type of procedure is appropriate for your data
To test the value of the mean in a population when only sample mean and sample deviation are known to perform the test then it is appropriate to use z-test procedure.
What is a Z-test?
A statistical method of testing a hypothesis is the z-test where either:
We are aware of the population variance, which is equal to 2.Despite the fact that we are unsure of the population variance, our sample size, n 30, is sizable. In this instance, we estimate the population variance using the sample variance.A t-test unlike of z-test must be used if the sample size is less than 30 and the population variance is unknown.Additional prerequisites for using the z-test include the following:
Data must follow a normal distribution.Independent data points are required.The variances for each sample must be equal.To know more about the z-test..........
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Point W is on line segment \overline{VX} VX . Given VX=4x,VX=4x, VW=3x,VW=3x, and WX=5,WX=5, determine the numerical length of \overline{VX}. VX .
The numerical length of VX is undefined
How to determine the numerical length of VX?The given parameters are
VX = 4x
VW = 3x
WX = 5x
Point W is on line segment VX
So, we have
VX = VW + WX
This gives
4x = 3x + 5x
Evaluate
4x= 8x
The above equation is false
Hence, the numerical length of VX is undefined
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