The equation of the line with a slope of one third and passes through (-2, 1) is y = one-third x + five-thirds.
How to find the equation of a line?The equation of a line can be represented in a slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the equation of the line has a slope of 1 / 3. Let's find the y-intercept using the coordinates (-2, 1)
y = 1 / 3 x + b
1 = 1 / 3 (-2) + b
1 + 2 / 3 = b
b = 3 + 2 / 3
b = 5 / 3
Therefore, the equation is y = 1 / 3 x + 5 / 3
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A statistician proposed a new method for constructing a 90 percent confidence interval to estimate the median of assessed home values for homes in a large community. To test the method, the statistician will conduct a simulation by selecting 10,000 random samples of the same size from the population. For each sample, a confidence interval will be constructed using the new method. If the confidence level associated with the new method is actually 90 percent, which of the following will be captured by approximately 9000 of the confidence intervals constructed from the simulation?
(A) The Sample Mean
(B) The Sample Median
(C) The Sample Standard Division
(D) The Population mean
(E) The Population Median
The measure that will be captured by approximately 9000 of the confidence intervals is given as follows:
(E) The Population Median.
What is the interpretation of a x% confidence interval?The interpretation of a x% confidence interval is that it is x% likely that the population parameter(mean/proportion/standard deviation/median) is between a and b, which are the bounds of the confidence interval.
The bounds of the confidence interval are obtained by the estimate plus/minus the margin of error.
The measure for which the confidence intervals are calculated in this problem is given by:
Median.
The sample median for each sample is used for the estimes, and then these estimates are inferred for the population median, which is the population parameter, hence option e is correct.
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a rectangle is drawn so the width is 49 inches longer than the height. if the rectangle's diagonal measurement is 61 inches, find the height.
Refer to the attachment for figure:
The height of the rectangle = 11 inches
What is rectangle?
A rectangle is a type of quadrilateral with parallel sides equal to each other and four equal 90-degree vertices. Because of this, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.
Let x= height
Width becomes x+49
Diagonal BD=61 inches
By pythagoras theorem,
BD²=BC²+CD²
61²= (x+49)²+x²
3721=x²+98x+2401+x²
On simplification,
x²+49x-660=0
Find the factors
(x+60)(x-11)=0
x=-60, x=11
Consider positive value for height
height = 11 inches
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If robert reads 2pages per minute, how many pages could she read in 1 1/2 hours?
Robert can read 180 pages in [tex]1\frac 12[/tex] hours
How to determine the number of pages?The given parameters in the question are:
Speed = 2 pages per minute
Number of hours = [tex]1\frac 12[/tex] hours
The number of pages to read in this time can be calculated using the following equation
Number of pages = Speed * Number of hours
Substitute the known values in the above equation So, we have the following equation
Number of pages = 2 * [tex]1\frac 12[/tex]
Convert the units
Number of pages = 2 * [tex]1\frac 12[/tex] * 60
Evaluate
Number of pages = 180
Hence, the number of pages is 180 pages
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For which value of does the matrix have one real eigenvalue of algebraic multiplicity ?.
the matrix has one real eigenvalue of algebraic multiplicity.
[1-λ k
1 -7-λ] =(1-λ)(-7-λ)-(1)(k) = λ² +6λ -(k+7)
Mathematics has several different subfields, including algebra. Algebra is the study of mathematical symbols and the rules for using them in formulas; it is a common thread that runs through practically all of mathematics.
Since many applications of mathematics include the manipulation of variables, which are frequently represented by Roman letters, elementary algebra is a prerequisite. For the most part in education, the study of algebraic structures like groups, rings, and fields is referred to as abstract algebra (the term is no more in common use outside the educational context). In contemporary presentations of geometry, linear algebra—which deals with linear equations and linear mappings—is used.
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485.2635 Find the digits in the hundreds place, in the tenths place, and in the ten thousandths place for the following number.
Answer:
Hundreds: 6 Tenths: 2 Ten Thousands: 5
Step-by-step explanation:
Hundreds are 2 decimal places (0.02)
Tenths are 1 decimal place (0.1)
Ten Thousands are 4 decimal places (0.0004)
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Malik's budget for chocolate chips for the week is $25. How many whole pounds of chocolate chips can he order
Given a budget of $25, the whole pounds of chocolate chips that Malik can order is 11 pounds of chocolate.
How to find the chocolate chips ordered?For up to 3 pounds, the supplier will charge Malik $4 per pound. This means that after buying 3 pounds of chocolate chips, the amount Malik would be left with it:
= Malik budget - (Price of 4 pounds x 4 pounds)
= 25 - (4 x 3)
= $13
The number of pounds of chips that Malik an buy at $1.50 per pound is:
= 13 / 1 .50
= 8 whole pounds
The total number of whole pounds that Malik can order is:
= 3 + 8
= 11 pounds
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Johnny has some nickels and dimes in his pocket, and the change is worth $0.75. He has twice as many dimes as nickels. How many of each type of coin does Johnny have?
| BTW this is a system of equations question
The number of dimes and nickels that Johnny has are 6 and 3 respectively.
How to calculate the value?The following should be noted:
Nickel = 5 cent = 0.05
Dime = 10 cents = 0.10
Let the number of nickels = n
Let the number of dimes = 2n
Total worth = $0.75
This will be illustrated as:
0.05(n) + 0.10(2n) = 0.75
0.05n + 0.20n = 0.75
0.25n = 0.75
Divide
n = 0.75/0.25
n = 3
Number of nickels = 3
Number of dimes = 2n
= 2 × 3
= 6
Number of dimes = 6
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Evaluate-2(^-6)(2^3)
Answer:
-1/8
Step-by-step explanation:
-2³/2⁶ negative exponents go in the denonimator
-1/2³ subtract exponents since the denonimator is larger
-1/8 simplify
Is the following statement a good definition?
An equilateral triangle is a triangle with all sides congruent.
yes
or
no
Answer: Yes
Step-by-step explanation:
An equilateral triangle has three equal sides and angles, therefore all of the sides are congruent.
6. Your parent promises to make you a smoothie using
the blender while you're mowing the lawn. The blender
makes a sound that is 88 decibels. What is the intensity
of the sound of the blender?
The intensity of the sound that is 88 decibels of the blender is 6.3×10⁻⁴ W/m².
Decibels:
Decibel is unit used to measure the intensity of a sound or the power level of an electrical signal by comparing it with a given level on a logarithmic scale.
Given,
Your parent promises to make you a smoothie using the blender while you're mowing the lawn. The blender makes a sound that is 88 decibels
Here we need to find the intensity of the sound of the blender
In order to find the intensity, we have to do the following steps,
First, we have to divide the decibel level by 10.
=> 88/10 = 10/10 log (x / 1 x 10⁻¹²)
Now, we have to use that value as the exponent of the ratio.
=> 8.8 = log (x / 1 x 10⁻¹²)
Finally, we have to use that power of ten to find the intensity in Watts per square meter.
=> 6.3×10⁻⁴ .
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Dimples is a dominant trait (D). The Punnett square shows a cross for this trait between two parents.
What is the probability that the offspring will have dimples?
25%
50%
75%
100%
Answer: 50%
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A survey was given to people who owend a certain type of car. What percent of the people surveyed were completely sastified with the car?
Write the correct function in the table below
HELP ASAP
The function that represent the given table is f(x) = 2n+1.
In the given question we have to write the correct function for the table given below.
The given table is
x y
0 3
1 5
2 7
3 9
We can write it as
x y
0 3=1+2
1 5=3+2
2 7=5+2
3 9=7+2
So we can see that in each odd number we are adding 2.
So the function should be
f(x) = (2n−1)+2
f(x) = 2n−1+2
f(x) = 2n+1
Hence, the function that represent the given table is f(x) = 2n+1.
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Erica worked 14 hour lat week and 20 hour thi week. If he earn $9 per hour how much did he earn during thee two week?
Answer:
$306
Step-by-step explanation:
we know that
Erika earns 9$ per hour
so
By proportion
Find how much she earn during the total hours of two weeks
The total hours of two weeks is equal to
[tex]14+20=34 hours[/tex]
[tex]\frac{9}{1} \frac{money}{hour} = \frac{x}{34} \frac{money}{hours}[/tex]
[tex]x =34[/tex]×[tex]9[/tex]
x = 306$
therefore
the answer is
$306
In this triangle, angle W equals (3x-24) degrees, and angle C equals (4x-11) degrees, and angle T equals 2x degrees, what does angle W equal?
Traingle is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
The sum of the three angles is equal to 180 degrees.
The value of angle W is 47.67
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
In this triangle:
angle W = (3x-24) degrees.
angle C = (4x-11) degrees.
angle T = 2x degrees.
Now,
The sum of the three angles is equal to 180 degrees.
3x - 24 + 4x - 11 + 2x = 180
9x - 35 = 180
9x = 180 + 359x = 215
x = 215/9
Now,
The angle W.
= 3x - 24
= (3 x 215/9) - 24
= 215/3 - 24
= 71.67 - 24
= 47.67
Thus,
The value of angle W is 47.67
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So if I get paid every 12 days and I put 80$ back every 12 days how long would it take to get to 2000 dollars
It will take 300 days to get to 2000 dollars.
According to the question,
We have the following information:
One gets paid every 12 days and one puts back $80 every 12 days.
Now, the total amount of dollars is $2000.
Now, we have the following progression:
80, 160, 240, ...
This is an arithmetic progression.
an = a+(n-1)d where a is the first term and d is the common difference
2000 = 80+(n-1)80
2000 = 80+80n-80
2000 = 80n
n = 2000/80
n = 25
Now, the number of days one is paid is after 12 days.
So, the number of days to get 2000 dollars:
25*12
300 days
Hence, it will take 300 days to get to 2000 dollars.
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Write an equation of the line passing through point
P(-8, 0) that is perpendicular to the line y=-3
The equation of line passing through the point P(-8,0) that is perpendicular to the line y=-3 is y=0 which can be found out from slope intercept formula.
It is given to us that -
The point is P(-8,0)
The line is represented as y=-3
The point P is perpendicular to the given line.
We have to find out the equation of the line passing through P which is perpendicular to the given line.
We know that the equation of a line is given by -
y = mx + c
where, (x, y) = coordinates of the point
m = slope of the line
c = a constant
Comparing this with the equation of the given line, we have
m=0 and c =-3
This implies that the slope of the perpendicular is also equal to 0.
The slope intercept formula for the perpendicular line can be represented as -
y = mx + c
Using the coordinates of P(-8,0), we have
0 = 0*(-8) +c
=> c = 0.
Thus, the equation of line passing through the point P(-8,0) that is perpendicular to the line y=-3 is y=0.
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tossing a fair coin 20 times and counting the number of heads (x). what is the chance that the number of heads is 13 or more?
By using Binomial Distribution of probability, it is obtained that
Probability that the number of heads is 13 or more = [tex]137980(\frac{1}{2})^{20}[/tex]
What is Binomial Distribution?
Binomial distribution is a discrete type probability distribution whose probability mass function is
P(X = k) = [tex]{n \choose k} p^k(1 - p)^{n-k}[/tex]
p is the probability of success.
Here Binomial distribution of probability is used
P(X [tex]\geq[/tex] 13) = P(X = 13) + P(X = 14) + ........ + P(X = 20)
P(X = 13) = [tex]{20 \choose 13} (\frac{1}{2})^{13}( 1 - \frac{1}{2}})^{20-13}[/tex]
= [tex]{20 \choose 13} (\frac{1}{2})^{13}( \frac{1}{2}})^{7}[/tex]
=[tex]{20 \choose1 3} (\frac{1}{2})^{20}[/tex]
P(X = 14) = [tex]{20 \choose14} (\frac{1}{2})^{20}[/tex]
P(X = 20) = [tex]{20 \choose20} (\frac{1}{2})^{20}[/tex]
Total Probability = [tex]({20 \choose 13} + {20 \choose 14} + .... {20 \choose 20})(\frac{1}{2})^{20}[/tex]
= (77520 + 38760 + 15504 + 4845 + 1140 + 190 + 20 + 1)[tex](\frac{1}{2})^{20}[/tex]
= [tex]137980(\frac{1}{2})^{20}[/tex]
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Do the following three lengths form a right triangle? 10, 10, 20
Answer:
No, these three sides can't form a triangle====================
Triangle inequality theorem states that the sum of any two sides must be greater than the remaining side.
We see 10 + 10 = 20, so this is contradicting the mentioned theorem, therefore these lengths are not good to form a triangle.
We see 10 + 10 = 20, so this is contradicting the mentioned theorem, therefore these lengths are not good to form a triangle.
Given,
The lengths of triangle is given as:
10 , 10 and 20
To check the following three lengths form a right triangle.
Now, According to the question:
What is triangle inequality theorem ?
The triangle inequality theorem describes the relationship between the three sides of a triangle. According to this theorem, for any triangle, the sum of lengths of two sides is always greater than the third side.
So, The length of triangle are 10, 10, 20
10 + 10 = 20
We see 10 + 10 = 20, so this is contradicting the mentioned theorem, therefore these lengths are not good to form a triangle.
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What effect do you think the sample size have on the mean of the sampling distribution of the mean?.
The effect of the sample size on the mean of the sampling distribution is that it effects the variations .
In the question ,
If the sample size is increased ,
that is if the number of sample is increased then the errors in the sampling distribution becomes less .
and if the sample size is decreased then it will lead to the increase in the errors of the distribution .
The formula for relationship between variation and sample size is given as ,
σx = σ / sqrt (n)
we can see that variation and sample size are inversely proportional .
that means increase in the sample size results in reduction of variation.
Therefore , The effect of the sample size on the mean of the sampling distribution is that it effects the variations .
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It takes 20 hours and $400 to interview a candidate, and it takes 120 hours and $3600 to train an employee.
A company has less than $95000 to interview and train employees, and it wants to spend at most 470 hours to do so.
Let C denote the number of candidates they interview and E the number of employees they train.
Write an inequality that represents the condition based on the number of dollars the company can spend.
Write an inequality that represents the condition based on the number of hours the company wants to spend.
Leroux health insurance is considering changing the options in one of their health care plans (plan a) based on customer feedback that prescriptions and regular visits to the doctor are too expensive for the insured individual. How can leroux reduce the costs of regular health care without driving up the price of their health care plan? leroux health insurance plan a cost: monthly premium: $248. 00 annual deductible: $5,500. 00 co-pays: brand-name prescriptions $35. 00 generic prescriptions $15. 00 visits: primary care physician: $40. 00 specialist: $60. 00 urgent care: $125. 00 emergency room: $325. 00 a. Reduce the monthly premium but increase the co-pay amounts to compensate for the lower premium. B. Reduce the annual deductible, but increase the co-pay amounts so that the monthly premium can stay the same. C. Reduce the co-pay amounts but increase the annual deductible so that the monthly premium can stay the same. D. Reduce the co-pay amounts but increase the monthly premium to compensate for the lower deductible.
Leroux can reduce the costs of regular health care without driving up the price of their health acre plan by : (c) Reducing the co-pay amounts but increase the annual deductible so that the monthly premium can stay the same.
Since the customers are complaining that the cost of regular visits and prescriptions ($15) are too expensive for them based on the plan they choose, this means that the purpose of the health insurance plan which is to reduce the overwhelming cost burden on individuals when trying to access proper healthcare is not be implemented successfully.
The co-pay amount which is usually known as the out-of-pocket amount that insurers pay whenever they go for regular doctor visits ( covered service in the insurance package ) and reducing this amount will reduce the immediate cost which makes the customers to complain about how expensive assessing a doctor on regular visits are.
The effect of the increased annual deductible is one way to push the immediate burden of paying a higher co-pay amount by the customer.
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A cereal company packs cereal boxes into large cardboard boxes. The large boxes are 12 inches long and 8 inches wide. How tall are the large boxes if the volume is 3,456 cubic. In.?
The height of the large boxes is 36 inches when the volume of box is 3456 cubic inches.
According to the question,
We have the following information:
A cereal company packs cereal boxes into large cardboard boxes. The large boxes are 12 inches long and 8 inches wide.
Volume of box = 3456 cubic inches
We know that the box is in the shape of cuboid.
Following formula is used to find the volume of cuboid:
Volume = length*width*height
12*8*height = 3456
96*height = 3456
Dividing both sides by 96:
Height = 3456/96
Height of the box = 36 inches
Hence, the height of the large boxes is 36 inches when the volume of box is 3456 cubic inches.
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27x + 35y = -105
what is x and what is y
Answer:
x-intercept: -([tex]\frac{35}{9}[/tex],0)
y-intercept: (0,-3)
Step-by-step explanation:
Please help
Which function includes all ordered pairs in the table
Answer:
the correct answer is A. y = - x - 4
Step-by-step explanation:
Just insert the graph into a calculator and solve.
every time x goes up two, so does y. except the y is 4 units lower than the x.
The perimeter of a garden is 40 feet. The length is two more than four times the width. Write a system of equations where x represents the width and y represents the length.
Answer:
2(x+y) = 40y = 2 +4xStep-by-step explanation:
You want a system of equations for the width (x) and length (y) of a rectangle with a perimeter of 40 feet and length 2 more than 4 times the width.
EquationsOne equation can give the relation for the perimeter:
2(x +y) = 40
The other can express the relation between width and length:
y = 2 +4x
Your system of equations is 2(x+y) = 40, and y = 2+4x.
__
Additional comment
The solution is (x, y) = (3.6, 16.4) feet.
The ratio of the number of red cubes to the total number of small plastic cubes in a classroom is 3:14. How many red cubes are there if there are 560 cubes altogether?
Answer:
red cubes = 99, plastic cubes = 462
Step-by-step explanation:
total number of cubes/total ratio
= 560/17
= 33 (approximately)
red cubes
= 33 × 3
= 99
plastic cubes
= 33 × 14
= 462
Though 462 + 99 equals 561 rather than 560, I had to approximate the values because if not, the result will be 461 which is a prime number.
12.) Find m22 if m2XVW = 64°.
V
2
W
P
X
The value of the angle ∠2 = 32° using angle bisector.
What is angle bisector?
In geometry, the ray, line, or segment that divides a given angle into two equal pieces is known as the angle bisector. For instance, a 60-degree angle will be split into two angles of 30 degrees each by an angle bisector. It splits one angle into two smaller congruent angles, to put it another way.
An angle in a triangle is divided into two equal or congruent angles by a straight line known as the angle bisector. Each triangle can have one angle bisector for each of its three vertices. The intersection of these three angle bisectors in a triangle is referred to as the triangle's incenter.
The given angle ∠XVW = 64°
VP is a bisector,
So the angle ∠XVW will be divided equally.
So ∠2 = 32°
Hence the angle of the bisector ∠2 = 32°.
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X i a poitive integer 33 divided by x i a poitive interger write 4 poible value of x
531/4
Please give step by step explanation, must be long division.
Answer: 132.5
Step-by-step explanation:
Answer:
132.75
Step-by-step explanation:
*in picture below*