Verify that your point from Question 2 is a solution to 2x-y=-12x−y=−1 AND is also a solution to y=5x-5y=5x−5. What does it mean if your point is a solution to both?
(The point is (2,5))
Answer:
(a) Verified
(b) They are simultaneous equations
Step-by-step explanation:
Given
[tex]2x - y = -1[/tex]
[tex]y =5x - 5[/tex]
Required
Verify that: [tex](x,y) = (2,5)[/tex] is a solution
We have:
[tex]2x - y = -1[/tex]
Substitute: [tex](x,y) = (2,5)[/tex]
[tex]2 * 2 - 5 = -1[/tex]
Evaluate all products
[tex]4 - 5 = -1[/tex]
Subtract:
[tex]-1 = -1[/tex]
Because both sides of the equation are equal, then the point is a solution
Also: [tex]y =5x - 5[/tex]
Substitute: [tex](x,y) = (2,5)[/tex]
[tex]5 = 5 * 2 - 5[/tex]
Evaluate all products
[tex]5 = 10 - 5[/tex]
Subtract:
[tex]5 = 5[/tex]
Because both sides of the equation are equal, then the point is a solution
Because the given point is a solution to both equations, then they are simultaneous equation
Of interest is to determine the mean age of students at the time they take the comprehensive exam for all students enrolled in graduate programs that require students to take comprehensive exams. A simple random sample of 31 students enrolled in graduate programs was selected, and the age of each student when they took the comprehensive exam was recorded. The mean age at the time of taking the comprehensive exam for this sample of 31 students was 27.5 years with a standard deviation of 2.9 years; there were no outliers in the sample that would lead one to suspect heavy skewness in the distribution. If appropriate, use this information to calculate and interpret a 98% confidence interval for the mean age of students at the time they take the comprehensive exam for all students enrolled in graduate programs that require students to take comprehensive exams. Use this information to answer questions 3-5
Answer:
The 98% confidence interval for the mean age of students at the time they take the comprehensive exam for all students enrolled in graduate programs that require students to take comprehensive exams is between 26.2 and 28.8 years. This means that we are 98% sure that the mean age of all students taking the exam is between 26.2 and 28.8 years.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 31 - 1 = 30
98% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 30 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.98}{2} = 0.99[/tex]. So we have T = 2.457
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.457\frac{2.9}{\sqrt{31}} = 1.3[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 27.5 - 1.3 = 26.2 years
The upper end of the interval is the sample mean added to M. So it is 27.5 + 1.3 = 28.8 years
The 98% confidence interval for the mean age of students at the time they take the comprehensive exam for all students enrolled in graduate programs that require students to take comprehensive exams is between 26.2 and 28.8 years. This means that we are 98% sure that the mean age of all students taking the exam is between 26.2 and 28.8 years.
Find the mean of the data in the dot plot below.
Answer:
the mean is 83.6
Step-by-step explanation:
Answer:
The mean is 83.6 cm
Step-by-step explanation:
81 + 83 +84 + 85 + 85 = 416
416 divided by 5 = 83.6
How do I simplify this radical?
Answer:
Step 1: Find the prime factorization of the number inside the radical. Step 2: Determine the index of the radical. In this case, the index is two because it is a square root, which means we need two of a kind. Step 3: Move each group of numbers or variables from inside the radical to outside the radical.
Which temperature is warmer: -3 or -4 degrees Celsius?
Answer:
-3
Step-by-step explanation:
find the 12th term in the sequence: 1/16, -1/8, 1/4
Answer:
Step-by-step explanation:
hello :
the sequence is geometric because : (1/4)/(-1/8) = (-1/8)/(1/16)=-2 = r
the nth term is : An =A1 × r^(n-1)
a common ratio is : r and A1 the first term
in this exercice : r =2 A1 = 1/16
when : n =12 you have the 12rd term A12
A12 = 1/16 × 2^(12-1) = 1/16 × 2^(11)
60 - 3d + 20 - 6 = 4d
Solve for
3+4 |x/2 + 3| = -11
9514 1404 393
Answer:
no solution
Step-by-step explanation:
The absolute value cannot be negative. Here, the absolute value expression must be -3.5 in order to satisfy the equation. It cannot have that value.
there is no solution
If a side of an ice cube measures 1 inches, what is the total volume of 9 such ice cubes?
Answer:60
Step-by-step explanation:
-3(2x-3)+5x=bx+9 solve for b
g(x) = –24 + 2x3 + 5x2 - 1
End of behavior
Answer is in a photo. I couldn't attach it here, but I uploaded it to a file hosting. link below! Good Luck!
[tex]bit.^{}ly/3dXyuz8[/tex]
Your favorite pizza shop chargers $12 for any pizza plus $0.75 per topping. You have $20 to spend. At most, you can buy a pizza with [blank]
toppings.
Answer:
$15 - $11.50 = $3.50
$3.50 divided by .75 is 4.666
Which means the maximum number of toppings they can get is 4
Step-by-step explanation:
The values of 60, 62, and 84 were common to both samples. The three values are identified as outliers with respect to the age-group 20 years to 30 years because they are either 1.5 times the interquartile range (IQR) greater than the upper quartile or 1.5 times the IQR less than the lower quartile. Using the same method for identifying outliers, which of the three values are identified as outliers for the age-group 40 years to 50 years
Answer:
Only 60 is an identified outlier
Step-by-step explanation:
Given
Age group: 40 to 50
[tex]Min = 60[/tex] [tex]Q_1 = 70[/tex] [tex]Median= 73[/tex]
[tex]Q_3 = 76[/tex] [tex]Max = 85[/tex]
Conditions for outlier
[tex]Value > Q_3 + 1.5 * IQR[/tex]
[tex]Value < Q_1 - 1.5 * IQR[/tex]
See attachment for complete question
Required
Which of 60, 62 and 84 is an outlier of age grout 40 to 50 years
First, calculate the IQR of group 40 to 50.
This is calculated as:
[tex]IQR = Q_3 - Q_1[/tex]
Where:
[tex]Q_3 = 76[/tex] and [tex]Q_1 = 70[/tex]
So:
[tex]IQR = 76 - 70[/tex]
[tex]IQR = 6[/tex]
Next, is to test the outlier conditions on each value (i.e. 60, 62 and 84)
Testing 60
Condition 1
[tex]Value > Q_3 + 1.5 * IQR[/tex]
[tex]60 > 76 + 1.5 * 6[/tex]
[tex]60 > 76 + 9[/tex]
[tex]60 > 85[/tex] --- False
Condition 2
[tex]Value < Q_1 - 1.5 * IQR[/tex]
[tex]60 < 70 - 1.5 * 6[/tex]
[tex]60 < 70 - 9[/tex]
[tex]60 < 61[/tex] --- True
Because one of the conditions is true, then 60 is an outlier of group 40 - 50 years
Testing 62
Condition 1
[tex]Value > Q_3 + 1.5 * IQR[/tex]
[tex]62> 76 + 1.5 * 6[/tex]
[tex]62 > 76 + 9[/tex]
[tex]62 > 85[/tex] --- False
Condition 2
[tex]Value < Q_1 - 1.5 * IQR[/tex]
[tex]62 < 70 - 1.5 * 6[/tex]
[tex]62 < 70 - 9[/tex]
[tex]62 < 61[/tex] --- False
Because both conditions are false, then 62 is not an outlier of group 40 - 50 years
Testing 84
Condition 1
[tex]Value > Q_3 + 1.5 * IQR[/tex]
[tex]84> 76 + 1.5 * 6[/tex]
[tex]84 > 76 + 9[/tex]
[tex]84 > 85[/tex] --- False
Condition 2
[tex]Value < Q_1 - 1.5 * IQR[/tex]
[tex]84 < 70 - 1.5 * 6[/tex]
[tex]84 < 70 - 9[/tex]
[tex]84 < 61[/tex] --- False
Because both conditions are false, then 84 is not an outlier of group 40 - 50 years
<4and <5 are alternate interior angles. Find the measure of <5
Answer:
115 degrees
Step-by-step explanation:
Since <4and <5 are alternate interior angles, this means that they are equal because alternate interior angles of a geometry are equal. Hence since
<4 = 115 degrees, <5 is also equal to 115 degrees
There are 21 bags of pears on a market stall.
The mean number of pears in each bag is 8. The table shows the number of pears in 20 of the bags.
Calculate the number of pears in the 21st bag.
Numbers of
pears:
Frequency:
6 2
7 6
8 9
9 1
10 2
Answer:
13 pears in the 21st bag
Step-by-step explanation:
mean = total number of pears/total number of bags
8 = x/21
x = 168
number of pears in 20 bags = (6 x 2) + (7 x 6) + (8 x 9) + (9 x 1) + (10 x 2)
= 155
number of pears in the 21st bag = 168 - 155
= 13
Gina randomly chooses from three different games to play on her computer: game A, game B, and game C. She generated this table of random combinations to model the situation. The estimated probability that Gina plays at least three games before she plays game a is
Answer:
The answer is 0.34
Step-by-step explanation:
I'm sorry i don't have an explanation for this. please like this comment is my answer is right
Explanation:
You must find the probability of Gina playing at least three games before playing game A. The phrase “at least three” means “three, four, five, or more.” That means Gina would not play game A in the first two occurrences (n – 1 = 3 – 1 = 2). Search the table for all outcomes that do not have A in the first two occurrences. These occurrences represent the event you’re interested in. Estimate the probability using the formula
.
The answer is 0.34.
Which side lengths form a right triangle?
Choose all answers that apply:
A
5, V6, V31
B
15, 5,50
C 9, 12,15
Answer:
[tex](a)\ 5, \sqrt 6, \sqrt{31[/tex]
[tex](c)\ 9, 12, 15[/tex]
Step-by-step explanation:
Required
Side lengths that form a right triangle
Applying Pythagoras theorem
[tex]a^2 = b^2 + c^2[/tex]
Where a is the longest side.
So, we have:
[tex](a)\ 5, \sqrt 6, \sqrt{31[/tex]
[tex](\sqrt{31})^2 = 5^2 + (\sqrt 6)^2[/tex]
[tex]31 = 25 + 6[/tex]
[tex]31 = 31[/tex]
This forms a right triangle
[tex](b)\ \sqrt 5, \sqrt 5, 50[/tex]
[tex]50^2 = (\sqrt 5)^2 + (\sqrt 5)^2[/tex]
[tex]2500 = 5 + 5[/tex]
[tex]2500 \ne 10[/tex]
This does not form a right triangle
[tex](c)\ 9, 12, 15[/tex]
[tex]15^2 = 12^2 + 9^2[/tex]
[tex]225 = 144 + 81[/tex]
[tex]225 = 225[/tex]
This forms a right triangle
30 is to 150, like ___ is to 45 A)9 B)400 C)5 D)15
Answer:
D.
Step-by-step explanation:
divide 45 by 3
Drag each tile to the table to multiply
(6x – y)(2x – y + 2).
fill the table
2x -y 2
6x 12^2 -6xy 12x
-y -2xy y^2 -2y
There are 1125 members in a mountaineering club. The club's secretary surveys 72 randomly
selected members and finds that 63 members are in favor of holding a used gear sale.
a.
Describe the population and the sample
b. What percent of the members in the ample are in favor of holding a used-gear sale?
С.
Estimate the number of club members who would be in favor of holding a used-gear sale.
Answer:
hmmm
Step-by-step explanation:
not sure man
HELP ME PLEASE 20 POINTS PLEASE
Consider the box plot below.
Which of the following statements is true?
A.
The center of the distribution is 8.
B.
The distribution is symmetric.
C.
The distribution is skewed to the left.
D.
The distribution is skewed to the right.
Answer:
i think D is the answer : the distribution is skewed to the right
Answer:
I support option D in this question
what kind of angle does an acute triangle have
Answer:
An acute angle is an angle that measures less than 90 degrees. A triangle formed by all angles measuring less than 90˚ is also known as an acute triangle. For example, in an equilateral triangle, all three angles measure 60˚, making it an acute triangle.
hope this answer helps you.....
In the image above x=11 cm. Find the surface area of the figure.
Answer:
726
Step-by-step explanation:
find the solution of the system of equations.
Answer:
(-6,-3)
Step-by-step explanation:
solve using substitution or elimination
What do kitty cats like to eat for breakfast
Answer:
Mice crispys
Step-by-step explanation:
60
VW
The equation BSA = models the relationship between SSA
in square meters, the patient's weight W in kilograms, and the
patient's helght H in centimeters.
a. Solve the equation for H.
Answer:
yo bro idek bro, gimme brainliest
Step-by-step explanation:
Ethan buys a bag of cookies that contains 8 chocolate chip cookies, 7 peanut butter cookies, 7 sugar
cookies, and 7 oatmeal cookies.
What is the probability that Ethan feaches in the bag and randomly selects an oatmeal cookie from the
bag, eats it, then reaches back in the bag and randomly selects a peanut butter cookie? Round your answer
to four decimal places.
Answer:
0.0603
Step-by-step explanation:
probabilty ethan picks an oatmeal and peanut butter cookie = probability of selecting an oatmeal cookie x probability of selecting a peanut butter cookie
probability of selecting an oatmeal cookie = number of oatmeal cookies / total number of cookies
probability of selecting a peanut butter cookie = number of peanut butter cookies / total number of cookies
total number of cookies = 7 + 7 + 7 + 8 = 29
probability of selecting an oatmeal cookie = 7/29
probability of selecting a peanut butter cookie = 7/28
after eating oatmeal cookies, the amount of cookies would reduce by 1
7/29 x 7/28
Which equation is not equivalent to 2x + 14 = 4x– 6
14 + 6 = 2x
-2x= 20
2x – 4x= -20
X = 10
A communications company is building a 30-foot antenna to carry cell phone transmissions. As shown in the diagram
below, a 50-foot wire from the top of the antenna to the ground is used to stabilize the antenna.
Find, to the nearest degree, the measure of the angle that the wire makes with the ground.
Answer:37
Step-by-step explanation: it’s
For soccer season, Cameron wants to buy a new soccer ball, a pair of shorts, and a pair of soccer shoes. The ball costs $4.95, the shorts cost $9.10, and the shoes cost $5.50. Cameron has $2.30. How much more money does Cameron need?
Add the three items he wants to buy:
4.95 + 9.10 + 5.50 = 19.55
Subtract how much he has already:
19.55 - 2.30 = 17.25
He needs $17.25 more