Answer:
Step-by-step explanation:
From the series, 2, 8, 18, 32, 50,...
By observation and by trial and error.
The first term, n = 1 = 2*1*1 = 2
Second term, n =2, = 2*2*2 = 8
Third, n =3, = 2*3*3 = 18
Third term, n = 4, = 2*4*4 = 32
Fourth term, n =5, 2 * 5* 5 = 50
For nth term, 2 *n *n = 2n²
Therefore nth term = 2n²
I hope this helps.
Find the missing factor.
||
x 10² = 19,500
Answer: x=195
Step-by-step explanation:
Find the value of 10²: 10² =100
Divide 19,500÷100: 19,500÷100=195
Missing factor is 195
Write 18/7 as a mixed number
Answer:
2 4/7 is the correct answer
Answer:
42 --- 7Step-by-step explanation:
7x2=14=2
18-14=4
So 18/7 equals 2 4/7
how to find slope intercept form?
Slope intercept form is y = mx + b
Y = the y-value [ for example, in the pair (9, 8), 8 would be the y-value
M = slope [ to find slope, use the equation (y2-y1)/(x2-x1) ]
X = the x-value [ for example, in the pair (9, 8), 9 would be the x-value
B = the y-intercept; when x is 0, whatever y is, that's your y-intercept
Now that you know what the variables mean, plug them into your equation.
A bisector which divides the line segment into two parts
The perpendicular bisector is a line that bisects the line segment into two equal halves and forms a right angle with the line segment.
What is a Perpendicular bisector?
A line that divides another line segment into two equal halves by intersecting it perpendicularly is known as a perpendicular bisector. A rule, compass, and pencil can be used to draw a perpendicular bisector. When two lines cross at right angles or 90 degrees, they are said to be perpendicular to one another. A line that splits a line into two equally sized parts is known as a bisector. A line segment's perpendicular bisector suggests that it meets the segment at a 90-degree angle and splits it into two equal halves.
So, In the given question, We can say that A bisector that divides the line segment into two parts is called a perpendicular bisector;
We can also, find the proof of it: as: It divides AB into two equal halves or bisects it. It makes right angles with (or is perpendicular to) AB.
Every point in the perpendicular bisector is equidistant from points A and B.A ruler and compass are needed. The process for creating a line segment's perpendicular bisector is as follows:
Draw the first segment of the line PQ.
Step 2: Set the compass to a length that is a little longer than half of PQ's length.
Draw arcs above and below the line by positioning the compass pointer at point P in step 3.
Step 4: Set the compass pointer at point Q while maintaining the same length. Draw two arcs above and below the line, in the same manner, maintaining the compass's pointer at Q.
Hence, The perpendicular bisector is a line that bisects the line segment into two equal halves and forms a right angle with the line segment
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if 2/3 kg of beef cost p160 then how much will 6 2/5 kg of beef cost
Please solve it with solution i need this ASAP thank u :)
Answer:
1536 p
Step-by-step explanation:
6 2/5 kg / ( 2/3 kg/160 p) = 1536 p
Maggie brought oranges and sandwiches to a picnic. The number of oranges was three more than twice the number of sandwiches. Maggie brought 9 oranges to the picnic. How many sandwiches did she bring?
Maggie brought 3 sandwiches to the picnic .
In the question ,
it is given that
Maggie bought oranges and sandwiches to a picnic .
given the number of oranges = 9
also given that , number of oranges was three more than twice the number of sandwiches
let the number of sandwiches Maggie brought to a picnic be x .
So , the number of oranges is = 2x + 3
So , 2x + 3 = 9
Subtracting 3 from both the sides ,
we get ,
2x = 9 - 3
2x = 6
On dividing both sides by 2,
we get ,
x = 6/2
x = 3
Therefore , the number of sandwiches = 3 .
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An experimenter would like to construct a 99% confidence interval with a width at most 0. 5 for the average resistance of a segment of copper cable of a certain length. If the experimenter knows that the standard deviation of such resistances is 1. 55. How big a sample should the experimenter take from the population? what happens if the standard deviation and the width of the confidence interval are both doubled?.
A big sample that should the experimenter take from the population is 256 and if the standard deviation and the width of the confidence interval are both doubled then the sample is also 256.
In the given question,
The confidence level = 99%
Given width = 0.5
Standard deviation of resistance([tex]\sigma[/tex])= 1.55
We have to find a big sample that should the experimenter take from the population and what happens if the standard deviation and the width of the confidence interval are both doubled.
The formula to find the a big sample that should the experimenter take from the population is
Margin of error(ME) [tex]=z_{\alpha /2}\frac{\sigma}{\sqrt{n}}[/tex]
So n [tex]=(z_{\alpha /2}\frac{\sigma}{\text{ME}})^2[/tex]
where n=sample size
We firstly find the value of ME and [tex]z_{\alpha /2}[/tex].
Firstly finding the value of ME.
ME=Width/2
ME=0.5/2
ME=0.25
Now finding the value of [tex]z_{\alpha /2}[/tex].
Te given interval is 99%=99/100=0.99
The value of [tex]\alpha[/tex] =1−0.99
The value of [tex]\alpha[/tex] =0.01
Then the value of [tex]\alpha /2[/tex] = 0.01/2 = 0.005
From the standard table of z
[tex]z_{0.005}[/tex] =2.58
Now putting in the value in formula of sample size.
n[tex]=(2.58\times\frac{1.55}{0.25})^2[/tex]
Simplifying
n=(3.999/0.25)^2
n=(15.996)^2
n=255.87
n≈256
Hence, the sample that the experimenter take from the population is 256.
Now we have to find the sample size if the standard deviation and the width of the confidence interval are both doubled.
The new values,
Standard deviation of resistance([tex]\sigma[/tex])= 2×1.55
Standard deviation of resistance([tex]\sigma[/tex])= 3.1
width = 2×0.5
width = 1
Now the value of ME.
ME=1/2
ME=0.5
The z value is remain same.
Now putting in the value in formula of sample size.
n[tex]=(2.58\times\frac{3.1}{0.5})^2[/tex]
Simplifying
n=(7.998/0.5)^2
n=(15.996)^2
n=255.87
n≈256
Hence, if the standard deviation and the width of the confidence interval are both doubled then the sample size is 256.
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Given the points (-4,r) and (-8,3) find the value of r that results in a slope of -10
Answer:
r = -37
Step-by-step explanation:
Step 1: Write out what is known
Points are (-4,r) and (-8,3)Slope = m = -10[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]Step 2: Set up an equation to solve for r
[tex]m=\frac{3-r}{-8-(-4)} =-10[/tex]Step 3: Solve for r
[tex]\frac{3-r}{-8-(-4)} =-10\\[/tex][tex]\frac{3-r}{-8+4} =-10[/tex][tex]\frac{3-r}{-4} =-10[/tex][tex](-4)\frac{3-r}{-4} =-10(-4)[/tex][tex]3-r=40[/tex][tex]-r=37[/tex][tex]r=-37[/tex]29
Write the answer in the blank.
What number is 267 more than 190?
Answer:
457
Step-by-step explanation:
190 + 267 = 457
In 1910 the population of the village of Stambridge was 4620; by 2010 this had
increased to 12 246 residents.
What is the percentage increase?
Answer:
165.065% increase
Step-by-step explanation:
Or Lelie climb a 10-meter tower to ride a traight water lide. After landing in the plah pool, he walk 24 meter back to the bae of the tower. How far did he travel in all?
The total distance traveled by him is 60 ft
In this question, apply the Pythagorean relationship
Let's assume, the climbing, sliding and walking back to the base form a right-angle triangle
The tower height = the height of the triangle, h=10f
The sliding lane= the hypotenuse of the triangle=?
The distance covered to the base= base of the triangle=24f
Applying the relation ;
a²+b²=c²
10²+24²=c²
100+576=c²
676=c²
[tex]\sqrt{626}[/tex]=c
26=c
Distance traveled in all=26+24+10=60 feet
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this is due in 30 mins
11) The pre-image, R at the point (-2, 3) on the grid shown produces an image following the reflection across the line y = 2·x - 3 as follows;
I. The line [tex]\overline{RR'}[/tex] which is obtained from the image R' following a reflection across the line y = 2·x - 3, is perpendicular to the line y = 2·x - 3, because the points R and R' are vertically opposite each other, therefore, the slope is the negative inverse of the slope of y = 2·x - 3, which is -0.5
II. Please find attached the graph made using MS Excel showing the points R and R'
What is a reflection transformation?A reflection transformation is one in which a point is reflected across a line such that the distances of the image and the pre-image from the line are the same and the line acts like a mirror producing an image of the object.
The coordinates of point R = (-2, 3)
The equation of the line of reflection is; y = 2·x - 3
The coordinates of the image of a point, (x₁, y₁) reflected across a line, a·x + b·y + c = 0, is found as follows;
The image of is found using the formula;
[tex]\dfrac{x - x_1}{a} =\dfrac{y-y_1}{b} = -\dfrac{2\cdot (a\cdot x_1+b\cdot y_1+c)}{a^2+b^2}[/tex]
The equation, y = 2·x - 3, can be expressed in the form a·x + b·y + c = 0, as follows;
y = 2·x - 3
0 = 2·x - 3 - y
Therefore;
a = 2, b = -1, and c = -3
(x₁, y₁) = (-2, 3)
[tex]\dfrac{x - (-2)}{2} = -\dfrac{2\times (2\times (-2)- 3-3)}{2^2+(-1)^2}=4[/tex]
[tex]\dfrac{x +2}{2} = 4[/tex]
x = 2× 4 - 2 = 6
x = 6
[tex]\dfrac{y-3}{-1} = 4[/tex]
y = 4 ×(-1) + 3 = -1
The coordinates of the image, (x, y) = (6, -1)
The slope of the line is -(1/2)
The equation of the perpendicular line is therefore;
(y - 3) = -0.5·(x - (-2)) = -0.5·x - 1
y = -0.5·x - 1 + 3 = -0.5·x + 2
Equation of the perpendicular line through R; y = -0.5·x + 2
The intersection point is therefore;
-0.5·x + 2 = 2·x - 3
2.5·x = 5
x = 5 ÷ 2.5 = 2
y = 2×2 - 3 = 1
y = 1
The point is therefore, (2, 1)
The difference in the x-values = 2 - 2 = 4
The difference in the y-value = 1 - 3 = -2
Therefore, 4 is added to the x-value of the point (2, 1) and 2 is subtracted to get the image as follows;
(x, y) = (2 + 4, 1 - 2) = (6, -1)
The slope of [tex]\overline{RR'}[/tex] = (3 - (-1))/(-2 - 6) = -0.5
b. Graphically, the equation of the line [tex]\overline{RR'}[/tex] can be used to find the point R', by adding the horizontal distance and subtracting the vertical distance of the point R from the the point of intersection of the two lines.
Please find attached the graph showing R and the image R' created with MS Excel.
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What is the awnser. Thank you
Answer:
Henry is correct
Step-by-step explanation:
add 4 to each sides of the equation
2x=16
Divide each side of the equation by 2
X=8
2x - 4 = 12
add 4 to both sides:
2x - 4 + 4 = 12 + 4
2x = 16
divide both sides by 2:
2x/2 = 16/2
x = 8
so Henry is correct.
What is 18% more than 61
Answer: I think the answer is 71.98
Step-by-step explanation:
the scale on a map is stated as 1: 100 000 on the map jennifer estimates that the distance to her destination is 8cm is shes correct in her estimate ,how many kilometers are there to her destination
By using unitary method it is obtained that Jennifer is at a distance of 8 km to her destination
What is unitary method?
Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity
Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.
Here unitary method is used
The scale on a map is stated as 1: 100 000
So 1 cm on the map is equivalent to 100000 cm on the ground
8 cm on the map is equivalent to 100000 [tex]\times[/tex] 8 cm on the ground
8 cm on the map is equivalent to 800000 cm on the ground
8 cm on the map is equivalent to [tex]\frac{800000}{1000 \times 100}[/tex] km on the ground
8 cm on the map is equivalent to 8 km on the ground
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What is the image point of (-8,-6) after the transformation R90° T-4,-4?
The image point of the given parent point (-8,-6) after the transformation R 90° and T-4,-4 is (10, -12).
What is a meaning of the term transformation?When one figure is relocated from one place to the next without altering its structure, shape, or orientation, a transition known as translation takes place. If we are aware of the direction and magnitude of the figure's movement, we may draw the translation in the coordinate plane.For the given question.
Let the given point be;
P --> (-8, -6)
Translation the function by T-4,-4.
P'--> (-8 - 4, - 6-4)
P'--> (-12, - 10)
Now, rotation the function by 90 degrees.
The new coordinates be-
P' (x, y) ----> P''(-y, x)
P''(-y, x) = (10, - 12)
Thus, the image point of the given parent point (-8,-6) after the transformation R 90° and T-4,-4 is (10, -12).
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Please provide an explanation please
Step-by-step explanation:
First we need to write down something
X*x+8*x+6*x=240msquares
X2+14x=240
X2+14x-240=0
So now we use discriminant formula
196-4(1*240)=-44
-14-+(root of 44)
_____________. = answer
2
Find the area of the triangle if the perimeter of the triangle is 144 ft.
Answer:
I think it is 671
Step-by-step explanation:
The 2 sides are the same length because of those dashes on them so 61 + 61 = 122.
144 - 122 = 22 which is the base
Area is "Base times height divided by two"
The height is 61
so the area is (22 x 61) / 2
22 x 61 = 1,342
1,342 divided by 2 is 671
I think this is right, im sorry if it is wrong.
What is the y intercept of 3y+2x+5=4x+2y+15
100pts
Jesus planted tomatoes and peppers in his garden. All together, he planted a dozen plants. If he planted three times as many peppers as tomatoes, how many peppers did he plant?
Answer:
9 peppers
Step-by-step explanation:
A dozen is 12
so 3t + t = 12
4t=12 /3
t=3
He planted 9 peppers
Answer:
tomatoes are T so T3 is how many peppers he planted.
PS: if you are looking for a direct question you need to give the number of tomatoes or peppers.
Step-by-step explanation:
The sampling distribution of the sample mean will always have the same _________ as the original distribution.
The sampling distribution of the sample mean will always have the same the mean of the original non-normal distribution, as the original distribution.
What is distribution?
Each of these samples contains a mean, and if we add up all of the means, we can construct a probability distribution that explains the distribution of the means. As long as we have sufficient samples, as will be discussed later, this distribution is always normal and is referred to as the sampling distribution of the sample mean.
Since the sample mean's sampling distribution is normal, we can naturally calculate the distribution's mean and standard deviation and utilise that information to analyse probability questions.
Here, The sample variance is equal to the population variance divided by the sample size if the population is infinite and the sampling is random, or if the population is finite but we are sampling with replacement.
So we need to use the mean of non-normal distribution.
Hence the answer will be the mean of the original non-normal distribution.
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The measure of a single interior angle in a regular octagon is (4x + 12)0. Find the value of x, rounding your answer to the nearest tenth.
Answer:
x ≈ 30.8
Step-by-step explanation:
You want the value of x if the measure of an interior angle of a regular octagon is (4x +12)°.
Interior anglesThe sum of interior angles of an n-gon is 180°×(n -2), where n is the number of sides. An octagon has 8 sides, so the sum of angles is ...
180°×(8 -2) = 1080°
The angles of a regular n-gon are congruent, so one interior angle of a regular octagon is ...
1080°/8 = 135°
ApplicationThe given angle expression is equal to 135°, so we have ...
(4x +12)° = 135°
4x = 123 . . . . . . . divide by ° and subtract 12
x = 30.75 . . . . . . divide by the coefficient of x
The value of x is about 30.8.
HELP PLS
A bird was sitting 2 meters from the base of an oak tree and flew 6 meters to reach the top of the tree. How tall is the tree?
THIS NEEDS PYTHAGOREM THEORAM
Answer: I don't know if I'm 100% spot on but I belive it may be 6.32.
There are calculators for this online, try get home (unless it's a test) and use them.
1. (9x+3y) +(-7x)
2. (8m-6n) + (7m)
Answer:
1. 2x + 3y
2. 15m -6n
Step-by-step explanation:
Combine like terms.
Answer:
1) 2x+3y
2) 15m-6n
Step-by-step explanation:
Lets first simplify 1.
1) open parentheses
9x+3y-7x
2)combine like terms
2x+3y
Simplify 2.
1) open parentheses
8m-6n+7m
2) combine like terms
15m-6n
8.
In parallelogram ABCD, diagonals AC and BD intersect at point E, AE = 7x -21, and CE = 4x.
What is AC?
Enter your answer in the box.
AC =
The required length of the diagonal AC is given as 56 units.
Given that,
In parallelogram ABCD, diagonals AC and BD intersect at point E, AE = 7x -21, and CE = 4x.
A parallelogram is a quadrilateral consisting of pairs of parallel sides.
Here,
in a parallelogram, diagonals bisecting each other means that a diagonal intersects another diagonal at a midpoint.
So,
AE = CE
7x - 21 = 4x
x = 7
Now,
CE = 4 {7} = 28
AC = 28 + 28 = 56
Thus, the required length of the diagonal AC is given as 56 units.
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Answer:56
Step-by-step explanation: TRUST ME
What expression is equivalent to -2(3x + 5y)
The expression equivalent to the given expression -2(3x + 5y) is
y = 3x / 5How to find the expression equivalent to the given expressiongiven that
-2(3x + 5y)
expanding the parenthesis
-6x - 10y = 0
10y = 6x
y = 6x/10
y = 3x / 5
we can conclude that y = 3x/5 is equivalent to -2(3x + 5y)
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please help ty i struggle with angles so
The area of a rectangle with length of 4 ft. and width of 9 ft. is 36 ft²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The area of a figure is the amount of space occupied in a two dimensional shape or object.
The area of a rectangle is the product of its length and width. Hence:
Area = length * width
From the diagram:
Area = 4 ft. * 9 ft. = 36 ft²
The area is 36 ft²
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Answer:
Perimeter: 26 ft
Step-by-step explanation:
To find perimeter, you add all the side measurements together.
Since the left side (4 ft) is congruent to the right, the right side is also 4 ft. Add both and you get 8 ft.
Since the bottom side (9 ft) is congruent to the top, the top side is also 9 ft. Add both and you get 18 ft.
8 + 18 = 26
So the perimeter is 26 ft.
a solid right circular cone has radius 5 cm and height 12 cm as shown. what is the probability that a randomly chosen point inside this cone is a distance of at least 1 cm away from the closest point on the surface of the cone? express your answer as a decimal to the nearest thousandth.
Answer:
47
Step-by-step explanation:
Can sb help me find the final balance
The final balance after 1 year with initial value $1000 if the interest is compounded quarterly will be $1215.5
What is compound interest?
Compound interest is computed as interest on the initial principal plus any accrued interest from prior periods. The power of compound interest is the creation of "interest on interest."
We are given that she initially invested $1000 and that she get 5% and interest is compounded quaterly.
After 3 months the interest will be
I = 1000*(5/100)
I = 50
So the total amount becomes
$1050 after 3 months
Now after 3 months again 5% interest will be credited
Hence the amount becomes
I1 = 1050*(5/100)
I1 = 52.5
Hence the total amount becomes
1102.5 after 6 months
After 9 months the interest will be
I2 = 1102.5*(5/100)
I2 = 55.12
Hence the total amount becomes
$1157.62 after 9 months
After 1 years the interest will be
I3 = 1157.62*(5/100)
I3 = 57.88
Hence the total amount becomes $1215.5
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Hailey is making floral centerpieces for a wedding. Each centerpiece has 17 flowers. She has 430 flowers for the project. She estimates that she can make between 20 and 30 complete centerpieces. Is her estimate reasonable? Use your knowledge of place value and division to explain the reasonableness of her answer.
Hailey's estimation is reasonable, because she can make 25 centerpieces using 430 flowers
Number of flowers in each centerpieces = 17 flowers
The total number of flowers that she has = 430 flowers
She estimates that she can make between 20 and 30 complete centerpieces
Number of centerpieces that she can make = The total number of flowers that she has / Number of flowers in each centerpieces
Substitute the values in the equation
Here we have to use division
Number of centerpieces that she can make = 430 / 17
= 25.29
≈ 25 centerpieces
Hence, Hailey's estimation is reasonable, because she can make 25 centerpieces using 430 flowers
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