Answer:
Point of intersection:
[tex]3x - y = 8 - - - (a) \\ x + 2y = 5 - - - (b) [/tex]
2 × equation(b) + equation (a):
[tex]7x = 21 \\ x = 3 \\ \\ y = 3x - 8 \\ y = 1[/tex]
Point of intersection = (3, 1)
Perpendicular line:
[tex]3x + 6y - 11 = 0 \\ 6y = - 3x + 11 \\ y = - \frac{1}{2} x + \frac{11}{6} [/tex]
General equation of line:
[tex]y = mx + c \\ 1 = (2 \times 3) + c \\ c = - 5[/tex]
Value of m:
[tex]m \times m {}^{i} = - 1 \\ m \times - \frac{1}{2} = - 1 \\ m = 2[/tex]
An organization consists of 8,684 employees. They decided to conduct a survey about their new vacation policies. The organization surveyed 884 of their employees and found that 36% of those surveyed disliked the new vacation policies. Assuming a 95% confidence level, which of the following statements holds true?
Answer:
A. As the sample size is appropriately large, the margin of error is ±0.032.
Step-by-step explanation:
The margin of error is ±0.032 and the sample size is appropriately large. Therefore, the correct option is A.
SOMEONE PLEASE HELP ME WITH THIS AND EXPLAIN EACH ONE AND HOW YOU DID IT PLEASE MY TEACHER SUCK AND ILL GIVE YOU BRAINLY IF U GET IT RIGHT!!!!
Answer:
a)
d)
Step-by-step explanation:
It's easiest to reduce each statement to its simplest form for comparison
Our test statement can be reduced by combining like terms
16x - 12 -24x + 4 = -8x - 8
this becomes our new gold standard
a) 4 + 16x - 12(1 + 2x)
apply the distributive property by multiplying terms in parenthesis by -12
4 + 16x - 12 - 24x
combine terms
-8x - 8 Yeaah, We have a winner as it exactly matches our gold standard.
b) 40x - 16 is already in simplest terms and does NOT match the gold standard.
c) 16x - 24x - 4 + 12
has the same cardinal values as the original, but differing signs, reducing gives -8x + 8
Not quite the same as a plus sign occurs where a negative exists in our gold standard.
d) -8x - 8 is already in simplest terms and exactly matches our gold standard. Yeah!
e) 10(1.6x - 1.2 - 2.4x + 4)
apply distributive property by multiplying each term in parenthesis by 10
16x - 12 - 24x + 40
combine like terms
-8x + 28 does NOT match our gold standard
Identify the pair numbers
Answer:
D. 212 degrees Fahrenheit and 100 degrees Celsius.
Step-by-step explanation:
The boiling point of water in Celsius is 100.
The way to calculate Celsius to Fahrenheit:
F = (C × 9/5) + 32
So we plug in 100 for C.
F = (100 × 9/5) + 32
F = 180 + 32
F = 212
Therefore, the numbered pair is 212 degrees F and 100 degrees C.
Find m2 ABD.
A
D
40°
B
C
In the graph above, which vertical line (V) and horizontal line (H) can be used to graph point A?
A)
V: x = 1; H: y = 4
B)
V: x = 4; H: y = 1
C)
V: y = 4; H: x = 1
D)
V: x = 1; H: y = –4
Answer:
V: x = 1; H: y = 4
Step-by-step explanation:
Point A is at x = 1 and y = 4
A vertical line at x=1 and a horizontal line at y = 4
through: (3, - 3); slope = 2/3
Answer:
y=2/3x - 5
Step-by-step explanation:
Since we have the slope and a point, we can make an equation in point intercept form (y=mc+b) by using the point slope form formula (y-y1)=m(x-x1), where (x1,y1) is the point you plug in.
(y-y1)=m(x-x1)
m=2/3
y1=-3
x1=3
y- -3=2/3(x-3)
y+3=2/3(x-3)
Distribute 2/3 with (x-3) by multiplying
y+3=2/3x - 2
Subtract 3 from both sides
y=2/3x - 5
Find the answer for x and y
Answer:
x = 57
y = 57
Step-by-step explanation:
because of the two parallel lines :
41+y+8+74 = 180 add like terms
y + 123 = 180 subtract 123 from both sides
y = 57
x - 3 + 41 + y + 8 = 180 because they make a straight line
x + y + 46 = 180
x + 57 + 46 = 180
x + 123 = 180 subtract 123 from both sides
x = 57
Becky Anderson must pay a lump sum of $6000 in 5 yr. If only $5000 is available to deposit right now, what annual interest rate is necessary for the money to increase to $6000 in 5 yr?
Hello!
Out equation is: [tex]A=P(1+\frac{r}{n} )^t^n[/tex]
A= 6000
P=5000
N=1
T=5
R= What we are trying to find
This means we will have [tex]6000=5000(1+r)^5[/tex]
Divide both sides by 5000:
[tex]\frac{6000}{5000} = (1+r)^5[/tex]
Move the power to the other side by rooting both sides:
[tex]\frac{6000}{5000} ^1^/^5 = 1+r[/tex]
Subtract 1 from both sides:
[tex]\frac{6000}{5000} ^1^/^5 -1 = r[/tex]
Now we just need to calculate: R = 0.03713728...
I don't know how many decimal places you can have, but I will round to 2. This will give you an Interest Rate of 3.71%.
I hope this helps! :)
PLEASE HELPPPPPP!!!!! THIS IS DUE ASAP PLEASEEE
Answer:
1
Step-by-step explanation:
list the numbers that are odd or greater than 2
1,2,3,4,5,6
aka every single outcome
therefore the answer is just 1
Answer:
5/6
Step-by-step explanation:
The possible outcomes are 1,2,3,4,5,6
Odd numbers are 1,3,5
Greater than 2 are 3,4,5,6
Good solutions are 1,3,4,5,6 = 5 outcomes
P( odd or greater than 2) = good solutions / total
= 5/6
Four friends bought books at a bookstore. The person who got the best deal has the lowest ratio of cost to number of books purchased. Book Purchases Name Total Cost Number of Books Jo $9 4 Kei $12 8 Kate $30 16 Bryn $8 4
Answer:
Kei got the best deal.
Explanation:
The ratio of cost to number of books purchased for all of four friends will be.....
Jo ⇒ [tex]\frac{9}{4}[/tex], Kei ⇒ [tex]\frac{12}{8}[/tex] , Kate ⇒ [tex]\frac{30}{16}[/tex], Bryn ⇒ [tex]\frac{8}{4}[/tex]
From here you have to find the common denominator in this case is 16.
[tex]\frac{9}{4} =\frac{9*4}{4*4} =\frac{36}{16}[/tex]
[tex]\frac{12}{8} =\frac{12*2}{8*2} =\frac{24}{16}[/tex]
[tex]\frac{30}{16} =\frac{30*1}{16*1} =\frac{30}{16}[/tex]
[tex]\frac{8}{4} =\frac{8*4}{4*4} =\frac{32}{16}[/tex]
As you could tell the lowest is [tex]\frac{24}{16}[/tex] so the lowest is Kei.
Find the least common multiple of 14 and 22.
Given that
[tex] log(3) f = a[/tex]
and
[tex] log(3) g = b[/tex]
express
[tex] log(9) ( \frac{ \sqrt{f} }{g})[/tex]
in terms of a and b.
Answer:
(a-2b)/4
Step-by-step explanation:
log 9 (sqrt(f)/g) = 0.5*log 9 (f(x)) - log 9 (g(x))= 0.5*0.5*log 3 f(x) - 0.5*log 3 g(x) = a/4 - b/2=(a-2b)/4
Can you tell which 3-D shape this would make?
Answer:
the answer is A
Step-by-step explanation:
you can see the image dont have stand. so it cannot be 3d. 3d need right left up down to fullfil the box
Dosen"t fold to make a 3D shape.
What is 3D shape?3D shapes exist in forms with three dimensions, such as width, height, and depth. An example of a 3D shape exists as a prism or a sphere. 3D shapes exist as multidimensional and can be physically held.
A 2D shape includes two dimensions- length and breadth. A 3D shape contains three dimensions- length, breadth, and height.
The figure doesn't fold to make a 3-D shape as it doesn't have all the specified number of sides for any given shapes.
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There is a circle with a center of 0,0 on a coordinate plane. There is one point on the circle's circumference in which the x:y ratio is 3:1. What is a possible coordinate?
Answer:
(3, 1)
Step-by-step explanation:
A circle with radius √10 and centre at (0, 0) will have a point (3, 1) on its circumference.
Dean Halverson recently read that full-time college students study 20 hours each week. She decides to do a study at her university to see if there is evidence that students study an average of more than 20 hours each week. A random sample of 35 students were asked to keep a diary of their activities over a period of several weeks. It was found that the average number of hours that the 35 students studied each week was 21.1 hours. The sample standard deviation of 4.3 hours.
Find the p-value.
The p-value should be rounded to 4-decimal places.
Answer:
0.0698
Step-by-step explanation:
Given :
Population mean, μ = 20
Sample mean, xbar = 21.1
Sample standard deviation, s = 4.3
Sample size, n = 35
The hypothesis :
H0 : μ = 20
H0 : μ > 20
The test statistic :
(xbar - μ) ÷ (s/√(n))
T = (21.1 - 20) ÷ (4.3/√(35))
T = 1.1 ÷ 0.7268326
Test statistic = 1.513
Using the Pvalue calculator :
df = n - 1 = 35 - 1 = 34
Pvalue(1.513, 34) = 0.06976
Pvalue = 0.0698 (4 decimal places)
The p-value is 0.0698 if rounded to 4-decimal places.
It is given that students study an average of more than 20 hours each week and the random sample of 35 students was asked to keep a diary of their activities over a period of several weeks.
The average number of hours that the 35 students was 21.1 hours.
The sample standard deviation is 4.3 hours.
It is required to find the p-value.
What is the standard deviation?It is defined as the measure of data dispersement, It gives an idea about how much is the data spread out.
We can test the hypothesis using the Z test, the formula for the Z-test is given below:
[tex]\rm Z= \frac{(x-u)}{\frac{S}{\sqrt{n} } }[/tex]
Where x is the sample mean
u is the population mean
s is the standard deviation
n is the sample size.
The hypothesis are: H0 : μ = 20 V/s H1 : μ > 20
We have x = 21.1
u = 20
s = 4.3
n = 35
Putting these values in the above formula, we get:
[tex]\rm Z= \frac{(21.1-20)}{\frac{4.3}{\sqrt{35} } }\\\\\rm Z= \frac{(1.1)}{\frac{4.3}{\sqrt{35} } }\\\\[/tex]
Z = 1.513
difference or df = n -1 ⇒ 35-1 ⇒ 34
P-value at (1.513, 34) = 0.06976 (From the p-value calculator)
P-value = 0.0698 (Rounded to 4-decimal places)
Thus, the p-value is 0.0698 if rounded to 4-decimal places.
Learn more about the standard deviation here:
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Lainey is looking for a new apartment and her realtor keeps calling her with new listings. The calls only take a few minutes, but a few minutes here and there are really starting to add up. She's having trouble concentrating on her work. What should Lainey do? a) Tell her realtor she can only receive text messages O b) Limit the time spent on each call O c) Turn off her phone until she is on a break O di Call her realtor back when customers won't see her on the phone
a...cause she's having trouble concentrating,for her to work she needs to tell her realtor she can only receive text messages it enables her to know the process of the house hunt
Given a mean score of 1150, standard deviation of 90, and 500 participants, solve the following problem. Using this data and the z-score distribution provided in class. Be sure to give your answer in the units requested. Only place your answer in the box.
1. What is the score for someone in the 15th percentile?
2. What is the percentile rank of someone with a score of 1100?
3. How many students have scores of 1060 or greater?
4. How many students scored between 1200 and 1250?
Answer:
1. 1056.67
2. 29th percentile.
3. 79
4. 77
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean score of 1150, standard deviation of 90
This means that [tex]\mu = 1150, \sigma = 90[/tex]
1. What is the score for someone in the 15th percentile?
This is X when Z has a p-value of 0.15, so X when Z = -1.037.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.037 = \frac{X - 1150}{90}[/tex]
[tex]X - 1150 = -1.037*90[/tex]
[tex]X = 1056.67[/tex]
2. What is the percentile rank of someone with a score of 1100?
This is the p-value of Z when X = 1100. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1100 - 1150}{90}[/tex]
[tex]Z = -0.555[/tex]
[tex]Z = -0.555[/tex] has a p-value of 0.29, so 29th percentile.
3. How many students have scores of 1060 or greater?
The proportion is 1 subtracted by the p-value of Z when X = 1060. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1060 - 1150}{90}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a p-value of 0.1587.
Out of 500:
0.1587*500 = 79
79 is the answer.
4. How many students scored between 1200 and 1250?
The proportion is the p-value of Z when X = 1250 subtracted by the p-value of Z when X = 1200. So
X = 1250
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1250 - 1150}{90}[/tex]
[tex]Z = 1.1[/tex]
[tex]Z = 1.1[/tex] has a p-value of 0.8643.
X = 1200
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1200 - 1150}{90}[/tex]
[tex]Z = 0.555[/tex]
[tex]Z = 0.555[/tex] has a p-value of 0.7106
0.8643 - 0.7106 = 0.1537
Out of 500:
0.1537*500 = 77
77 is the answer.
find the value of trigonometric ratio
6. If gallon A has 8L of water and gallon B has 800 ml of water, calculate the total volume of water in both the gallons.
Answer:
send me again I can't understand question
Which is the graph of f(x) = 1/4(4)*?
5
40.4)
5 4 3
(4,4)
4 *04)
3
2
(2,1)
1
3 2
2
2
3.2)
(1.1)
543-24
1 2 3 4
-5 -4 -3 -2 -14
2 3
1 2 3
4 5
х
-5 -4 -3 -2 -14
-2
- 2
-3
-2
-3
-3
4
4
-5
-5
45
o
o
5
(2.4)
Answer:
(2,3)
Step-by-step explanation:
The graph of the given function is attached to the solution.
What is function?A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given is a function f(x) = 1/4(4)ˣ, we need to graph this,
Put x = 0
f(x) = 1/4
(0, 1/4)
Put x = 1
f(x) = 1
(1, 1)
Put x = 2
f(x) = 4
(2, 4)
Plot these points on a graph, the graph will be the graph of the function,
Since, the function is an exponential function therefore, we will get a curve.
Hence, the graph of the given function is attached to the solution.
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A chef is going to use a mixture two different brands of Italian dressing the first spring and days 5% vinegar the second brain contains 15% vinegar the sheriff wants to make 390$ ml addressing that is 9% vinegar how much of each brand should she use
I guess the chef is making the mixture for the sheriff... Let x be the amount of dressing with 5% vinegar that is required, and y the amount of 15% vinegar dressing (both amounts in mL).
The sheriff wants 390 mL of the mixed dressing, so that
x + y = 390
x mL of the 5% dressing contains 0.05x mL of vinegar, while y mL of the 15% dressing contains 0.15y mL of vinegar. The resulting mixture should have a concentration of 9% vinegar, so that it contains 0.09 (390 mL) = 35.1 mL of vinegar. This means
0.05x + 0.15y = 35.1
Solve for x and y :
y = 390 - x
0.05x + 0.15 (390 - x) = 35.1
0.05x + 58.5 - 0.15x = 35.1
23.4 = 0.10x
x = 234
y = 156
Four- sevenths of the children in class earned A's on the last math test. 18 children did not earn an A. How many earned A's? SHOW ALL WORK!!!
Answer: 24 people earnt As
Step-by-step explanation:
1. We know that 18 people are the other 3/7 of the class
2. We first find out 1/7, which is calculated by dividing 3/7 by 3, which is 18 / 3 so 6
3. We can then find 4/7 by multiplying the amount of 1/7 by 4, so 6 x 4 = 24
While organizing the magazines at the doctor's office, Camille put 12 magazines in the first pile, 15 magazines in the second pile, 18 magazines in the third pile, 21 magazines in the fourth pile, and 24 magazines in the fifth pile. If this pattern continues, how many magazines will Camille put in the sixth pile?
Answer:
27
Step-by-step explanation:
since you are adding 3 to the pile each time, on the 6th pile you would have 27 because 24 + 3 = 27
find the value of z, secant and tangent angles
Answer:
z = 110
Step-by-step explanation:
The measure of an angle created by the intersection of two secants outside a circle is half the difference of the angles it intercepts. In this it would be:
2x + 15 = 1/2 * (10x + 20 - 80)
We can now solve:
4x + 30 = 10x - 60
30 = 6x - 60
6x = 90
x = 15
This means the values of 10x + 20 is 10(15) + 20, which is 170.
Now, we can add up all the arcs in a circle, which sum to 360 degrees:
360 = z + 170 + 80
360 = z + 250
z = 110
Answer:
[tex]A)\ \ z = 110[/tex]
Step-by-step explanation:
One is given a circle with two secants. Please note that a secant is a line that intersects a circle in two places. The secant exterior angle theorem states that when two secants intersect each other outside of a circle, the measure of the angle formed is half the of the positive difference of the intersecting arcs. One can apply this theorem here by stating the following:
[tex]2x+15=\frac{(10x+20)-(80)}{2}[/tex]
Simplify,
[tex]2x+15=\frac{(10x+20)-(80)}{2}[/tex]
[tex]2x+15=\frac{10x-60}{2}[/tex]
[tex]2x+15=5x-30[/tex]
Inverse operations,
[tex]2x+15=5x-30[/tex]
[tex]15=3x-30[/tex]
[tex]45=3x[/tex]
[tex]15=x[/tex]
Substitute this value into the equation for one of the intersecting arcs to find the numerical value of that intersecting arc:
[tex]10x+20\\x = 15\\\\10(15) + 20\\= 150 + 20\\= 170[/tex]
The sum of all arc measures in a circle is (360) degrees. One can apply this here by stating the following:
[tex]80 + 170 + z = 360[/tex]
Simplify,
[tex]80 + 170 + z = 360[/tex]
[tex]250 + z = 360[/tex]
Inverse operations,
[tex]250 + z = 360[/tex]
[tex]z = 110[/tex]
Is this a function or not ?
Answer:
No, this is not a function as the curve is inappropriately drawn and the presence of variables is absent.
helppppp giving brainly too
Step-by-step explanation:
[tex] {p}^{2} + 2pq - 3 {q}^{2} [/tex]
[tex]( \frac{1}{4} {)}^{2} + 2( \frac{1}{4} )( \frac{2}{3} ) - 3( \frac{2}{3} {)}^{2} [/tex]
[tex] \frac{1}{16} + \frac{1}{ 3} - \frac{4}{3} [/tex]
[tex] \frac{ - 15}{16} [/tex]
Find the slope of the line through the pair of points. (7.-10) and (-6, -3)
Answer:
Fraction form: 7/-13
Decimal form:-0.53846153846154
If the point C is located at (5, 4) and C' is the image of C after being translated right 2. What are the
coordinates of C'?
Answer:
(7, 4)
Step-by-step explanation:
If point C is being translated to the right 2, the x coordinate will increase by 2. But, the y coordinate will stay the same.
Find the coordinates of C' by adding 2 to the original x coordinate:
5 + 2 = 7
The y coordinate will still be 4.
So, the coordinates of C' will be (7, 4)
Simplify the expression. Express your answer as an improper fraction in simplest form.
Answer:
Step-by-step explanation:
3/40 is the correct answer
Solve for x.
−4x + 60 < 72 OR 14x + 11 < −31
Choose 1 answer:
A) x < -3 or x > -3
B) x > -3
C) x <- 3
D) There are no solutions
E) All values of x are solutions
Answer:
A. x < -3 or x > -3
Step-by-step explanation:
Let's start with the equation -4x + 60 < 72.
-4x + 60 < 72
First using the order of operations, subtract 60 from both sides.
-4x + 60 - 60 < 72 - 60
- 4x < 12
Next we want to divide -4 from both sides to isolate the variable.
-4x/-4 < 12/-4
x > -3
When you divide a negative number, always make sure the change the sign.
Solve the next equation, 14x + 11 < -31, the same way we solved the last.
14x + 11 < -31
Subtract 11 from both sides.
14x + 11 - 11 < -31 -11
14x < -42
Divide 14 from both sides.
14x/14 < -42/14
x < -3
The equations have different signs.
A. x < -3 or x > -3
