The missing terms of the arithmetic sequence -13, - 6, 1 , 8 , 15, 22.
an = a1, a2, a3, a4, a5, a6
formula for nth term is :
an = a + (n - 1)d
where
an = last term
a = a1 = first term
n = number of terms
d = difference between two terms
here
a2 = a + d
- 6 = a + d ....(1)
a5 = a + 4d
15 = a + 4d .......(2)
on solving equation we get :
- 6 = a + d ....(1)
15 = a + 4d .......(2)
(-) (-) (-)
- 21 = - 3d
d = 21/3
d = 7
using the value of d in equation the value of a is :
- 6 = a + d
-6 = a + 7
a = -6 -7 = -13
then
a1 = a = -13
a2 = a + d = -13 + 7 = -6
a3 = a + 2d = -13 +2 x 7 = 1
a4 = a + 3d = -13 + 3 x 7 = 8
a5 = a + 4d = -13 +4 x 7 = 15
a6 = a + 5d = -13 +5 x 7 = 22
The missing terms of the arithmetic sequence -13, - 6, 1 , 8 , 15, 22.
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l need help to solve this practice question
Confidence interval to estimate the population mean is 81.592< μ <96.408.
Confidence = 95%
Z-value = Z = 1.960
No. of sample = n = 28
Mean = X = $89
Standard deviation = S = 20
Confidence interval = CI = [tex]X+Z*(\frac{S}{\sqrt{N}})[/tex] or [tex]X-Z*(\frac{S}{\sqrt{N}})[/tex]
= [tex]89+1.96(\frac{20}{\sqrt{28}})[/tex] or [tex]89-1.96(\frac{20}{\sqrt{28}})[/tex]
= 89 + 7.408 or 89 - 7.408
= 96.408 or 81.592
Hence, interval is 81.592< μ <96.408.
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Y=x-700
2x - y = 800
Answer:
X=
Step-by-step explanation:
first you should substitute for X
Y=X-700
2X-y=800
2X-(X-700]=800
X+700=800
X=100
then you substitute for Y
Y=100-700
Y=-600
last you put in the equations to make sure all the numbers are right.
-600=100-700 good
200--600=800 good
X=100
Y=-600
math geometry help help
Answer:
x = 18
Step-by-step explanation:
ABCD ∼ JKLM
AB = 12 JK = x
AD = 6 JM = 9
6/9 = 12/x
2/3 = 12/x
2/3 = 12/18
2/3 = 2/3
Sara wants to estimate the number of bees in a beehive. She catches 100 bees from the hive and marks each one with a dye. She then lets the bees go. The next day, Sara catches 50 bees from the hive. 10 of these bees have been marked with dye. a) Using this information, what is a good estimate for the number of bees in the beehive? b) Write down any one assumption you have made.
As per the given percentage of 20, the total number of bees is 200 and on the second day, he caught 40 unique bees so the total unique bees are 140
Percentage:
Percentage refers the amount of something is expressed as if it is a part of the total which is a hundred. and the ratio can be expressed as a fraction of 100.
Given,
Sara wants to estimate the number of bees in a beehive. She catches 100 bees from the hive and marks each one with a dye. She then lets the bees go. The next day, Sara catches 50 bees from the hive. 10 of these bees have been marked with dye.
Here we need to determine the number of bees in the beehive.
Let us consider she catches 100 bees from the hive and marks each one with a dye. And then lets the bees go.
Then the next day, she catches 50 bees from the hive. 10 of these bees have been marked with dye.
So, the percentage of the dye bees in the hive will be
P = 10/50 x 100
P = 20%
Now, let the total number of the bees be x, then the total number of the bees will be
=> 100 x 2 = 200
Therefore, the total number of bees is 200.
Now, the number of unique bees will be
Unique bees = 100 + (50 - 10)
Then, the number of unique bees = 100 + 40
Therefore, the number of unique bees is 140.
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Parallelogram ABCD is shown. A is at negative 5, 1. B is at negative 4, 3. C is at negative 1, 3. D is at negative 2, 1. Parallelogram ABCD is rotated 90° counterclockwise. What rule shows the input and output of the rotation, and what is the new coordinate of A′? (x, y) → (−x, −y); A′ is at (5, −1) (x, y) → (−y, x); A′ is at (−1, −5) (x, y) → (y, −x); A′ is at (1, 5) (x, y) → (x, −y); A′ is at (−5, −1)
For the rotation in 90° counter clockwise, the rule that shows input and out of the of the rotation is (−y, x) and the new coordinates are (-1, -5)
Rotation:
Rotation defines the transformation in which the object is rotated about a fixed point.
Given,
Parallelogram ABCD
A is at (-5,1)
B is at (-4,3)
C is at (-1,3)
D is at (-2, 1).
Parallelogram ABCD is rotated 90° counterclockwise.
Now, we have to find the rule shows the input and output of the rotation, and what is the new coordinate of A′.
Here we need to find the rotation of A alone.
So, we have to take the point (-5,1) alone.
The rule, that is used for 90° counterclockwise rotation is states that "When rotating a point 90 degrees counterclockwise about the origin then the point A(x, y) becomes A'(-y, x)."
Based on the this rule, we have written the following as,
=> (-5,1) => (-(1), -5)
=> (-1, -5)
Therefore, the new coordinate of A' is (-1, -5)
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Homework: 4.2 Apply Pythagorean Theorem
Date
Find the missing side of each triangle. Round your answers to the nearest tenth if necessary.
Need help with this math please
Step-by-step explanation:
try this option; all the details are in the attachment.
Need help with both of these
Answer: SUCK
Step-by-step explanation:
FREE BRAINLIEST IF CORRECT
Multiply and combine like terms to determine the product of these polynomials.
2x2(4x−7xy+5)(3y−2)
Step-by-step explanation:
[tex]4(12xy - 8x - 21xy ^{2} + 14xy + 15y - 10)[/tex]
[tex]4( - 21 {xy}^{2} + 26xy - 8x + 15y - 10)[/tex]
[tex] - 84 {xy}^{2} + 104xy - 32x + 60y - 40[/tex]
1. Approximately 75% of light bulbs are good. If 15 light bulbs are chosen
(a) What is the probability that 10 or more are good?
(b) What is the probability that 5 or more are good?
(c) What is the probability that all are good?
Answer:
Step-by-step explanation:
(a) The probability that 10 or more are good is 1/10
(b) The probability that 5 or more are good is 1/25
(c) The probability that all are good is 3/25
Probability:
Basically, the possibility of the outcome of any random event is known as probability.
Given,
Approximately 75% of light bulbs are good.
Here we need to find If 15 light bulbs are chosen, then
(a) The probability that 10 or more are good
(b) The probability that 5 or more are good
(c) The probability that all are good
Let us consider that the total number of light bulbs are 100.
And 75% of the bulbs are good.
Which means there are 75 good bulbs in it.
So, the defective bulbs are
=> 100 - 75
=> 25
So, the probability that 10 or more are good is calculated as,
=> 10/100
=> 1/10
Similarly, the probability that 5 or more are good is
=> 5/100
=> 1/25
And the probability that all are good is,
=> 15/100
=> 3/25
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From a research paper, it is known that the number of soldiers who died annually by being kicked by a horse followed a Poisson distribution with an average of 0.61 death in an army corps each year.
(a) Find the standard deviation of death in an army corps each year.
(b) Find the probability of exactly 3 deaths in an army corps in a given year.
(c) Find the probability of at most 2 deaths in an army corps over an 8-year period.
As per the concept of Poisson distribution ,
(a) The standard deviation of death in an army corps each year is 0.781
(b) The probability of exactly 3 deaths in an army corps in a given year is 0.069
(c) The probability of at most 2 deaths in an army corps over an 8-year period is 0.3425
Poisson distribution:
Basically, the process of estimating the occurrence of a specified event that happens during a particular period of time is known as Poisson distribution.
Given,
From a research paper, it is known that the number of soldiers who died annually by being kicked by a horse followed a Poisson distribution with an average of 0.61 death in an army corps each year.
Here we need to find the following:
(a) The standard deviation of death in an army corps each year
(b) The probability of exactly 3 deaths in an army corps in a given year
(c) The probability of at most 2 deaths in an army corps over an 8-year period
As per the given question, we have identified the following value,
The Poisson distribution average λ = 0.61
So, the standard deviation of the death
=> σ = √0.61
Therefore, the standard deviation is 0.781.
The probability of exactly 3 deaths in an army corps in a given year is calculated as,
=> P(X = 3) = e⁻⁰°⁶¹ x (0.61³/3!)
=> P(X = 3) = e⁻⁰°⁶¹ x (0.2269/6)
=> P(X = 3) = e⁻⁰°⁶¹ x 0.0378
=> P(X = 3) = 1.8404 x 0.0378
=> P(X = 3) = 0.069
Therefore, the probability of exactly 3 deaths in an army corps in a given year is 0.069
Now, the probability of at most 2 deaths in an army corps over an 8-year period is calculated as,
=> P(X = 2) = e⁻⁰°⁶¹ x (0.61²/2!)
=> P(X = 2) = e⁻⁰°⁶¹ x (0.3721/2)
=> P(X = 2) = e⁻⁰°⁶¹ x 0.1861
=> P(X = 2) = 1.8404 x 0.1861
=> P(X = 2) = 0.3425
Therefore, the probability of at most 2 deaths in an army corps over an 8-year period is 0.3425
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Option 1: Sample vs. Population
Compare and contrast the terms population and a sample that were reviewed in this unit. How do you decide on which group to use when creating a study or experiment? How can you avoid bias and be sure the study you are executing is accurate?
The best way to decide on which group we should experiment with the population sample is through a random selection.
What are the population and sample?The terms population and sample are often used interchangeably, but there is a subtle difference between the two.Population refers to the entire group of individuals that you want to study. A sample is a subset of the population that you actually study.When creating a study or experiment, you need to decide whether to use a population or a sample. If you want to study a large group of people, it may not be practical to study the entire population. In this case, you would use a sample. However, you need to be careful when selecting a sample, because it is easy to introduce bias.(B) Avoid bias and be sure the study you are executing is accurate:
It is also important to avoid bias when choosing a population or sample for research.The best way to do this is to use a random selection process. This means that every member of the population has an equal chance of being selected for the sample.Therefore, the best way to decide on which group we should experiment with the population sample is through a random selection.
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Simplify the expression to a + bi form:
-√4+√-72+√64-√-98
The expression to a + bi form is [tex]=10-\sqrt{2i}[/tex]
Simply put, what is linear algebra?
The subject of linear algebra is linear combinations. To build new columns and arrays of numbers, arithmetic is used to arrays of numbers called matrices and columns of numbers called vectors. The study of the planes and lines, vector spaces, and mappings needed for linear changes is referred to as algebra.
What is nonlinear equations?
A nonlinear equation is one whose graph is not a straight line and whose greatest power of the variables is not 1.
Step-by-step explanation:
Given:
[tex]-\sqrt{4} + \sqrt{-72}+\sqrt{64}+\sqrt{-98}=2+8-7\sqrt{2i}+6\sqrt{2i}[/tex]
[tex]=10-\sqrt{2i}[/tex]
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A sweet potato pie with a diameter of 8 inches is cut into 6 equal slices. To
the nearest square inch, what is the area of each slice?
OA. 34 in²
OB. 8 in2
OC. 14 in²
OD. 4 in²
Answer: 8 in²
Step-by-step explanation:
A diameter of a sweet potato pie is 8 inches
Hence a radius of a sweet potato pie is 8/2=4 inches
A=πr²
π=3.14159≈3
r=4 inches
Hence,
A=3(4²)
A=3(4*4)
A=3(16)
A=48 in²
The area of each slice is:
48:6=
8 in²
mary wants to order some packs o mini cupcakes for her daughters birthday party. Mary has $200 to spend. Each pack costs $12.75. The total shipping will be $14.50. Determine the number of packs Mary can order
The number of packs of mini cupcakes ordered by Mary are 15 approximately if she has $200 to spend and the cost of each pack is $12.75 and shipping cost is $14.50.
Total amount, Mary can spend = $200
Cost of one pack = $12.75
Total shipping cost = $14.50
Amount remaining after shipping cost = $200 - $14.50 = $185.50
Total packs Mary can order = $185.50/$12.75 = 14.54
Hence, Mary can order approximately 15 packs of mini cupcakes.
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Find the area under the standard normal curve which lies:
(a) to the left of z= -2.07
(b) between z= -0.56 and z=1.2
(c) between z= 0.08 and z=2.84
(d) to the right of z=0.96
The area under the standard normal curve that lies to:
(a) to the left of z= -2.07
= 0.019226
(b) between z= -0.56 and z =1.2
= 0.17267
(c) between z = 0.08 and z =2.84
= 0.46586
(d) to the right of z =0.96
= 0.83147
What is standard normal curve?The standard normal distribution, commonly known as the z-distribution, is a unique type of normal distribution in which the mean is 0 and standard deviation is equal to 1.
Any normal distribution's values can be transformed into z scores to standardize it.
Z scores indicate the number of standard deviations each result is from the mean.
The area under the standard normal curve is gotten using the z table for the scores and the values are as follows
(a) to the left of z= -2.07
= 0.019226
(b) between z = -0.56 and z = 1.2
= z = -0.56 - z = 1.2
= 0.28774 - 0.11507
= 0.17267
(c) between z= 0.08 and z=2.84
= z = 0.08 - z = 2.84
= 0.46812 - 0.00226
= 0.46586
(d) to the right of z = 0.96
= 1 - z = 0.96
= 1 - 0.16853
= 0.83147
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a
=
730
rounded to the nearest 10
b
=
20.8
rounded to 1 DP
Find the maximum (to 2 DP) of
a
÷
b
The maximum of a/b to two decimal points after rounding off is 35.10.
According to the question,
We have the following information:
a = 730 (rounded to nearest 10)
b = 20.8 (rounded to 1 decimal point)
Now, we have to find the value of a divided by b and then we have to round off the final result to two decimal points.
So, we have the following expression for division:
a/b
730/20.8
35.0961
Now, when we will round off to two decimal points, we will increase 9 by adding 1 because the right next digit to 9 is greater than 5.
35.10
Hence, the maximum of a/b to two decimal points is 35.10.
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5. In a science experiment, Bacteria A gains 3 more bacteria each day, and * Bacteria B triples in size each day. Which bacteria is growing faster over time? Explain your thinking.
Please help will mark Brainly
Answer: B and D
Step-by-step explanation:
y-4 = 2/3 (x-1)
y = 2/3 x - 2/3 + 4
y = 2/3 x - (-10)/3
y= 2/3x + 10/3
10/3 = 3 1/3
so the answers are B and D.
4. (02.02 MC) The following are beginning salaries for a certain industry in different areas: $56,250.00 $79,150.00 $61,360.00 $57,120.00 $57,120.00 $63,190.00 $65,370.00 $59,160.00 Find the median of the data set. (2 points) $57,120.00 $60,260.00 $62,396.00 $120,970.00
the median of the data set is $60,260.00.To find the median of a set of data, we first need to put the values in order from lowest to highest. Then, if the number of values is odd, the median is the middle value.
what is median ?
In statistics, the median is a measure of central tendency that represents the middle value of a dataset. To find the median, you need to first arrange the values in order from lowest to highest (or from highest to lowest).
In the given question,
To find the median of a set of data, we first need to put the values in order from lowest to highest. Then, if the number of values is odd, the median is the middle value. If the number of values is even, the median is the average of the two middle values.
In this case, the values in order from lowest to highest are:
$56,250.00
$57,120.00
$57,120.00
$59,160.00
$61,360.00
$63,190.00
$65,370.00
$79,150.00
There are eight values, which is an even number, so we need to take the average of the two middle values, which are $59,160.00 and $61,360.00.
The average of these two values is:
($59,160.00 + $61,360.00) / 2 = $60,260.00
So the median of the data set is $60,260.00.
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Please help me out! I will give brainliest answer!
The values of x =11.3° and y =10° as of given diagram.
A straight angle and a right angle are measured at 90° and 180°, respectively.
In the given diagram, ∠VRT = Right angle= 90°
i.e., (4y)° + (5y)° = 90°
(9y)° = 90°
y = 10°
∴ 4y = 40°
5y = 50°
Then, the line SRU is a straight line. The angle will be 180°;
i.e., (4y)° + (12x - 4)° = 180°
40° + (12x - 4)° = 180°
12x - 4 = 180° - 40°
12x = 140° - 4°
x = 136° / 12
x = 11.3
Hence, the value of x =11.3° and y =10°
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A farmer with 350 meters of fencing wants to enclose a rectangular plot that borders on a river. If the farmer does not fence the side along the river, what is the largest area that can be enclosed? What are the dimensions of the enclosed area?
The width, labeled x in the figure, is ____
(Type an integer or decimal rounded to the nearest tenth as needed.)
The length, labeled 350-2 x in the figure, is ____
(Type an integer or decimal rounded to the nearest tenth as needed.)
The largest area that can be enclosed is _______
(Type an integer or decimal rounded to the nearest tenth as needed.)
The solution to the questions are:
The width, labelled x in the figure is 87.5 metersThe length, labelled 350-2 x in the figure, is 175 metersThe largest area that can be enclosed is 15312.5 square metersHow to determine the width and the length of the rectangle?From the question, we have the following parameters that can be used in our computation:
Length = 350 - 2x
Width = x
The area of a rectangle is the product of its dimensions
So, we have
Area = Length x Width
Substitute the known values in the above equation, so, we have the following representation
A = (350 - 2x) * x
Evaluate
A = 350x - 2x²
Differentiate and set to 0
350 - 4x = 0
So, we have
4x = 350
Divide by 4
x = 87.5
Recall that
Length = 350 - 2x
So, we have
Length = 350 - 2 x 87.5
Evaluate
Length = 175
The area is then calculated as
Area = Length x Width
So, we have
Area = 175 x 87.5
Evaluate
Area = 15312.5 square meters
Hence, the area is 15312.5 square meters
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Oliver borrowed $2,000 to purchase a riding lawn mower for his lawn care business. The bank offered him an interest rate of 13% for 9 months. Calculate the simple interest using I = prt.
$195
$260
$1,500
$2,340
Answer:
i think D hope this helps :D
Step-by-step explanation:
Answer:
195
Step-by-step explanation:
helpppppppppppppppppppppppppppppppp
Answer:
10
Step-by-step explanation:
put 20 as the value for x and solve the equation:
(4/5) * 20 -6
= 4*20/5 - 6
= 80/5 - 6
= 16 - 6
= 10
Answer:
[tex]\huge\boxed{\sf f(20)=10}[/tex]
Step-by-step explanation:
Given function:[tex]\displaystyle f(x)=\frac{4}{5} x-6[/tex]
Put x = 20
[tex]\displaystyle f(20)=\frac{4}{5} (20)-6\\\\f(20)=4 \times 4 - 6\\\\f(20)=16-6\\\\f(20)=10\\\\\rule[225]{225}{2}[/tex]
Please help me asap!!!!!!!
Answer:
46 = .90x + 2(.70x)
x = 20
Step-by-step explanation:
46 = .90x + 2(.70x)
46 = .90x + 1.4x
46 = 2.3x
20 = x
O and R are the subsets of a Universal set, U, such that U={22,23,24,25,26,27,28,29,30} 0={ prime numbers } {R}={ even numbers } a) Draw a Venn diagram to represent this information.
b) List the elements of.
i) ( O U R )'
ii) ( O ∩ R)'
iii) O ∩ R
The elements of (OUR)', (O∩R)', and O∩R will be {23, 29}, {22, 23, 24, 26, 28, 29, 30}, and {null}, respectively.
What are Sets?Sets are groups of clearly specified components. The number of items in a finite set is denoted by a curly bracket.
O and R are the subsets of a Universal set, U, such that
U = {22,23,24,25,26,27,28,29,30}
O = {prime numbers} = {23, 29}
R = {even numbers} = {22, 24, 26, 28, 30}
The elements of (OUR)' will be given as,
(OUR)' = {23, 29}
The elements of (O∩R)' will be given as,
(O∩R)' = {22, 23, 24, 26, 28, 29, 30}
The elements of O∩R will be given as,
O∩R = 0
The elements of (OUR)', (O∩R)', and O∩R will be {23, 29}, {22, 23, 24, 26, 28, 29, 30}, and {null}, respectively.
The Venn diagram is given below.
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I need help right with this thanks..
Applying vertical or opposite angles theorem the values of m∠1, m∠3 and m∠4 are 141°, 141° and 39° respectively
Angles at a pointAngles around a point describes the sum of angles that can be arranged together so that they form a full turn. Angles around a point add to 360 °. The sum of the angles is 360° and they have made a full turn, and so the angles around a point add to equal 360° .
This implies that m∠1, m∠2, m∠3 and m∠4 all sum up to 360°
However, m∠2 = 39°
This can be used to find m∠4
m∠2 = m∠4 (Opposite or vertical angles are equal)
Therefore, m∠4 = 39°
But m∠1 and m∠3 are also equal by applying vertical angles theorem too.
Let them be represented by x
x + 39 + x + 39 = 360
Reason : Sum of angles at a point equals 360°
2x + 78 = 360
2x = 282
x = 141°
The values of m∠ 1 and m∠3 are 141° respectively
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if 848 m long iron wire is required to fence a square field 4 times,find the length of the square field
Answer:
53 m
Step-by-step explanation:
4 times around a square means 16 sides
848 /16 = 53 m per side
Solve for (A) current ratio, (B) acid test (quick), (C) average day's collection (D) asset turnover, and (E) profit margin on sales. Round to nearest hundredth or hundredth percent as needed. Current Assets $ 21,000 Accounts Receivable 4,200 Current Liabilities 16,000 Inventory 3,500 Net Sales 41,000 Total Assets 32,000 Net Income 6,000
From the calculation below, we have:
A) Current ratio = 1.31
(B) Acid test (quick) = 1.09
(C) Average day's collection = 37.39 days
(D) Asset turnover = 1.28 times
(E) Profit margin on sales = 14.63%
How we calculate current ratio and others?The requirements can be solved as follows:
A) Current ratio = Current Assets / Current Liabilities = $21,000 / $16,000 = 1.31
(B) Acid test (quick) = (Current Assets - Inventory) / Current Liabilities = ($21,000 - $3,500) / $16,000 = 1.09
(C) Average day's collection = (Accounts Receivable / Net Sales) * 365 = ($4,200 / $41,000) * 365 = 37.39 days
(D) Asset turnover = Net Sales / Total Assets = $41,000 / $32,000 = 1.28 times
(E) Profit margin on sales = Net Income / Net Sales = ($6,000 / $41,000) * 100 = 14.63%
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1. Find the slope of the line through
(-2,1) and (4,-2).
Answer: ________________________________________________
f(x) = -1/2x
Answer:
Step-by-step explanation:
slope = y2-y1/x2-x1
-2-1/4-(-2)=-3/6=-1/2 or -0.5
A LADDER IS 5 FEET 6 inches tall how tall is it in inches?
Answer:
66 inch
Step-by-step explanation:
have great day
