Answer:
[tex]\sum_{i=1}^n w_i *X_i = 2.8*24 = 67.2[/tex]
And for this case we want a gpa of 3.0 taking in count that in this semester he/ she is going to take 16 credits so then the new mean would be given by:
[tex] \bar X_f = \frac{\sum_{i=1}^n w_i *X_i+w_f *X_f }{24+16} = 3.0[/tex]
And we can solve for [tex]\sum_{i=1}^n w_f *X_f [/tex] and solving we got:
[tex] 3.0 *(24+16) =\sum_{i=1}^n w_i *X_i +\sum_{i=1}^n w_f *X_f [/tex]
And from the previous result we got:
[tex] 3.0 *(24+16) =67.2 +\sum_{i=1}^n w_f *X_f[/tex]
And solving we got:
[tex] \sum_{i=1}^n w_f *X_f =120 -67.2= 52.8[/tex]
And then we can find the mean with this formula:
[tex] \bar X_2 = \frac{\sum_{i=1}^n w_f *X_f}{16}= \frac{52.8}{16}=16=3.3[/tex]
So then we need a 3.3 on this semester in order to get a cumulate gpa of 3.0
Step-by-step explanation:
For this case we know that the currently mean is 2.8 and is given by:
[tex] \bar X = \frac{\sum_{i=1}^n w_i *X_i }{24} = 2.8[/tex]
Where [tex] w_i[/tex] represent the number of credits and [tex]X_i[/tex] the grade for each subject. From this case we can find the following sum:
[tex]\sum_{i=1}^n w_i *X_i = 2.8*24 = 67.2[/tex]
And for this case we want a gpa of 3.0 taking in count that in this semester he/ she is going to take 16 credits so then the new mean would be given by:
[tex] \bar X_f = \frac{\sum_{i=1}^n w_i *X_i+w_f *X_f }{24+16} = 3.0[/tex]
And we can solve for [tex]\sum_{i=1}^n w_f *X_f [/tex] and solving we got:
[tex] 3.0 *(24+16) =\sum_{i=1}^n w_i *X_i +\sum_{i=1}^n w_f *X_f [/tex]
And from the previous result we got:
[tex] 3.0 *(24+16) =67.2 +\sum_{i=1}^n w_f *X_f[/tex]
And solving we got:
[tex] \sum_{i=1}^n w_f *X_f =120 -67.2= 52.8[/tex]
And then we can find the mean with this formula:
[tex] \bar X_2 = \frac{\sum_{i=1}^n w_f *X_f}{16}= \frac{52.8}{16}=16=3.3[/tex]
So then we need a 3.3 on this semester in order to get a cumulate gpa of 3.0
The phone company Blurizon has a monthly cellular plan where a customer pays a flat
fee for unlimited voice calls and then a certain amount per GB of data used. If a
customer uses 12 GB, the monthly cost will be $105. If the customer uses 34 GB, the
monthly cost will be $237.
A) Find an equation in the form y = mx + b, where is the number of GB of data
used in a month and y is the total monthly cost of the Blurizon plan.
Answer: y =
B) Use your equation to find the total monthly cost if 14 GB are used.
Answer: If 14 GB are used, the total cost will be____
dollars.
Answer:
(a)y=6x+33
(b)$117
Step-by-step explanation:
If a customer uses 12 GB, the monthly cost will be $105.
If the customer uses 34 GB, the monthly cost will be $237.
given that
x is the number of GB of data used in a month; and y is the total monthly cost of the Blurizon plan.We have the pairs: (12, 105) and (34, 237)
(A)To determine the straight-line equation, we first determine the slope, m.
[tex]m=\dfrac{237-105}{34-12}\\\\=\dfrac{132}{22}\\\\m=6[/tex]
Substitution into y = mx + b, we have: y=6x+b
Next, we determine the value of b
When y=105, x=12
105=6(12)+b
b=105-6(12)=33
Therefore, an equation in the form y = mx + b is:
y=6x+33
(B)
Total Cost, y=6x+33
When 14 GB are used, i.e. x=14
y=6(14)+33
y=$117
If 14 GB are used, the total cost will be 117 dollars.
Please answer this correctly
Answer:
I want to say 9 but im preety sure it's 6
Step-by-step explanation:
you have 54 times to pick it
you have 9 marbles,
54 divided by 9= 6
answer is 6
hope this helped:))))
have a grate dayy
Answer:
1
this is because I see only one marble present which is orange
If it takes 4 hours for 2 men to mow a sports field,how long would it take 6 men working at the same rate to do the job?solution plis
Answer:
4/3 hours
Step-by-step explanation:
[tex]\frac{4*2}{6}\\=\frac{8}{6} \\= 4/3 hours[/tex]
Suppose you will perform a test to determine whether there is sufficient evidence to support a claim of a linear correlation between two variables. Find the critical values of r given the number of pairs of data n and the significance level α. n = 12, α = 0.01
Answer:
[tex]t=\frac{r \sqrt{n-2}}{\sqrt{1-r^2}}[/tex]
And is distributed with n-2 degreed of freedom. df=n-2=12-2=10
The significance level is [tex]\alpha=0.01[/tex] and [tex]\alpha/2 = 0.005[/tex] and for this case we can find the critical values and we got:
[tex] t_{\alpha/2}= \pm 3.169[/tex]
Step-by-step explanation:
In order to test the hypothesis if the correlation coefficient it's significant we have the following hypothesis:
Null hypothesis: [tex]\rho =0[/tex]
Alternative hypothesis: [tex]\rho \neq 0[/tex]
The statistic to check the hypothesis is given by:
[tex]t=\frac{r \sqrt{n-2}}{\sqrt{1-r^2}}[/tex]
And is distributed with n-2 degreed of freedom. df=n-2=12-2=10
The significance level is [tex]\alpha=0.01[/tex] and [tex]\alpha/2 = 0.005[/tex] and for this case we can find the critical values and we got:
[tex] t_{\alpha/2}= \pm 3.169[/tex]
Tell whether the following set is an empty set or not? A = { A quadrilateral having 3 obtuse angles}
Answer:
No.
Step-by-step explanation:
A quadrilateral with 3 obtuse angles is possible. You could have 100°+100°+100°+60° quadrilateral or whatever. As long as it's inner angles add up to 360°, it is possible.
Answer:
[tex]\boxed{\mathrm{It \: is \: not \: an \: empty \: set}}[/tex]
Step-by-step explanation:
A quadrilateral with 3 obtuse angles is possible.
A obtuse angle has a measure of more than 90 degrees and less than 180 degrees.
Let’s say three angles are measuring 91 degrees in a quadrilateral.
91 + 91 + 91 + x = 360
x = 87
The measure of the fourth angle is 87 degrees which is less than 360 degrees and is a positive integer, so it is possible.
Express the number using scientific notation: 0.000000067
Select one:
O a. 67 x 10-7
O b. 6.7 x 10-7
O c. can not be written in scientific form
O d. 6.7 x 10 -8
Answer: D
Step-by-step explanation:
To express this number in scientific notation, we want to move the decimal so that it goes past the first nonzero integer. In this case, we would move it to the right 8 times.
6.7×10⁻⁸
The only reason why the 8 is negative is because when you write the scientific notation in standard form, you will need to move the decimal to the left in order to get 0.000000067. Negative means moving to the left. Therefore, 6.7×10⁻⁸ is our correct answer.
Please answer this correctly
Answer:
9 bags
Step-by-step explanation:
130, 134, 136, 145, 145, 147, 147, 151, 154
9 bags had at least 130 peanuts.
I need help urgent plz someone help me solved this problem! Can someone plz help I’m giving you 10 points! I need help plz help me! Will mark you as brainiest!
Answer:
[tex]g(2) = 4(2) + 6 = 14[/tex]
[tex]f(2) = 2(2) + 3 = 7[/tex]
[tex](g - f)(2) = 14 - 7 = 7[/tex]
problem decoded dude
thank and follow meh
A lottery is conducted using three urns. Each urn contains chips numbered from 0 to 9. One chip is selected at random from each urn. The total number of sample points in the sample space is:_______ a) 30 b) 100 c) 729 d) 1,000"
Answer: Option d.
Step-by-step explanation:
Ok, we have 3 urns.
Each urn can give a number between 0 and 9, so each urn has 10 options.
And as the urns are different, the outcome in the first urn does not affect the outcomes in the others, and the same happens for the outcome in the second urn, so the events are independent.
The total number of combinations is equal to the product of the number of options for each event (here each urn is one event)
then the number of combinations is:
C = 10*10*10 = 10^3 = 1000
Then the correct option is d.
This applet illustrates 95% confidence intervals for samples from a normal distribution with known variance.
When taking 100 samples of size 30 or greater from a population, exactly 95 of them will create a confidence interval that contains the true population mean.
a. True
b. False
Which statement is the correct interpretation of the confidence interval in this illustration
a. The probability the true mean is between 76.08 and 83.92 is 0.95 or 95%.
b. We are 95% confident that the true mean is between 76.08 and 83.92.
Answer:
1- b. False
2 b. We are 95% confident that the true mean is between 76.08 and 83.92.
Step-by-step explanation:
Confidence Interval is the estimated value that is computed from the statistic of data which is observed. The range value is plausible for unknown parameters. To find the critical value the confidence interval value is observed through the t-value table.
I think of number. Add 2. Then Multiply it by 6. After that I square it. Assume the number as x. Write the correct algebraic form.
Answer:
[tex] {(6x+12) }^{2} \\
=36x^2+64x+144 [/tex]
Step-by-step explanation:
Thinked number
[tex]x[/tex]
Add 2
[tex]x + 2 \\ [/tex]
multiply it by 6
[tex]6(x+2) \\ [/tex]
square it
[tex] {(6x+12)}^{2} \\
= 36x^2+64x+144[/tex]
hope this helps
Answer:
36x^2 + 144x + 144
Step-by-step explanation:
Say the number youre think of is x
You do x + 2 as you're adding 2
Then you do x + 2 times 6 or 6 (x + 2) = 6x +12
6x + 12 squared = 36x ^ 2 + 144 x + 144
Mighty Casey hits two baseballs out of the park. The path of the first baseball can be described by the displacement (distance and direction) vector,
b1 = 100 i ^ + 10 j ^. The path of the second baseball can be described by the displacement vector b2 = 90 i ^ + (−20) j ^.
(a) How much farther did the first ball travel than the second? (Round your final answer to the nearest tenth.)
(b) How far are the baseballs apart? (Round your final answer to the nearest tenth.)
Answer:
a) 8.3 units of length
b) 31.6 units of length
Step-by-step explanation:
a) The distances traveled by each ball are given by:
[tex]d_1^2=100^2+10^2=10,100\\d_1=100.5\\\\d_2^2=90^2+(-20^2)=8,500\\d_2=92.2[/tex]
The diference between the distance traveled by both balls is:
[tex]d_1-d-2=100.5-92.2\\d_1-d_2=8.3[/tex]
The first ball traveled 8.3 units of length farther than the second ball.
b) The distance between both balls is:
[tex]d^2=(i_1-i_2)^2+(j_1-j_2)^2\\d^2=(100-90)^2+(10-(-20))^2\\d^2=1,000\\d=31.6[/tex]
The balls are 31.6 units of length apart.
standard form of line that passes thru (-3,5) and (-2,-6)
Answer:
11x + y = -28
Step-by-step explanation:
Step 1: Find slope
(6-5)/(-2--3) = -11
Step 2: Find y-intercept
y = -11x + b
5 = -11(-3) + b
5 = 33 + b
b = -28
Step 3: Write in slope-intercept form
y = -11x - 28
Step 4: Convert to standard form
11x + y = 28
And we have our final answer!
6• 2hen+3pens-5anchors
Answer:
[tex]180[/tex]
Step-by-step explanation:
[tex]6 \times 2 \times 3 \times 5[/tex]
[tex]12 \times 15[/tex]
[tex]=180[/tex]
Steps to solve:
6 * 2 + 3 - 5
~Multiply
12 + 3 - 5
~Add
15 - 5
~Subtract
10
Best of Luck!
Timmy received $50 for his birthday following the birthday party his parents promised him 5$ each week for completing his chores. Assuming Timmy completes all chores uses a linear equation to determine the number of dollars Timmy will have in 7 weeks
Answer:
$85
Step-by-step explanation:
Let y represent Timmy's money after x weeks. If we assume that the only money Timmy has is what is mentioned in the problem statement, then ...
y = 50 +5x . . . . . $50 initially plus $5 for each week
After 7 weeks, x = 7, so Timmy's fortune will be ...
y = 50 +5(7) = 50 +35
y = 85
Timmy will have $85 in 7 weeks.
Levi would like to use a credit card to make a $3000 purchase. He is considering two credit options. The first requires
a down payment of $1000 followed by monthly payments of $125. The second requires a down payment of $1300
followed by monthly payments of $110. The two options accumulate the same amount of interest and require the
same number of monthly payments.
What is the amount of interest for this loan?
Answer:
The amount of interest for this loan is 16.6%.
Step-by-step explanation:
Since Levi will make a purchase for $ 3000 with your credit card, you should explore the two options you have:
-On the one hand, a down payment of $ 1000, with fees of $ 125.
-on the other, a down payment of $ 1,300, with fees of $ 110.
In both cases, the fees are the same, and the interest too. Therefore, to determine the amount of installments and interest, the difference between the down payment of one option and the other must be taken and divided by the difference between the value of the installments of either option.
Thus, the difference of the down payment of 300 (1300 - 1000) must be divided by 15 (125 - 110). This yields a result of 20 (300/15), with which that will be the total of quotas until both have paid the same amount of money.
Thus, given that 1300 + 110 x 20 = 3,500, and that 1000 + 125 x 20 = 3,500, in both cases the total value to be paid is $ 3,500. Since 500 is 16.6% of 3000, the total purchase interest will be 16.6%.
Please answer this correctly
Answer:
sorry about that that was my sister . the correct answer is yes
Step-by-step explanation:
please mark as brainliest
Find an equation of the plane that passes through the point P0(- 3,3,1) with a normal vector n = (1,4, -3). Which of the following equations is an equation of the plane that passes through the point P0( - 3,3,1) with a normal vector n (1,4, -3)?
a. An equation for the plane is -3x+3y + Z = 6.
b. An equation for the plane is x+ 3y +z = 19.
c. An equation for the plane is x + y+ z = 26.
d. An equation for the plane is x +4y - 3z= 6.
Take an arbitrary vector (x, y, z), which goes from the origin to some point (x, y, z) on the plane we want to find.
Subtract from this vector, the vector that points to [tex]P_0[/tex], which is (-3, 3, 1). This translates the first vector so that it starts at the point [tex]P_0[/tex] and is directed at some point (x, y, z). We get a new translated vector, (x + 3, y - 3, z - 1), which lies in the plane.
The normal vector to the plane is orthogonal to every vector in the plane. So taking the dot product of any vector in the plane with the normal to the plane will always result in 0. We use this to find the plane's equation:
[tex]\vec n\cdot((x,y,z)-P_0)=(1,4,-3)\cdot(x+3,y-3,z-1)=0[/tex]
[tex]\implies(x+3)+4(y-3)-3(z-1)=0[/tex]
[tex]\implies x+4y-3z=6[/tex]
and so the answer is D.
Use the diagram to find the angle measures that satisfy each case. Find the measures of all four angles if 3·(m∠1+m∠3) = m∠2+m∠4.
Answer:
m∠1=45 degreesm∠2=135 degreesm∠3=45 degreesm∠4=135 degreesStep-by-step explanation:
Given that: 3(m∠1+m∠3) = m∠2+m∠4.
From the diagram:
m∠1=m∠3 (Vertical Angles)m∠2=m∠4 (Vertical Angles)Therefore:
3(m∠1+m∠1) = m∠2+m∠2
3(2m∠1)=2m∠2
Divide both sides by 2
3m∠1=m∠2
m∠1+m∠2=180 (Linear Postulate)
Therefore:
m∠1+3m∠1=180
4m∠1=180
Divide both sides by 4
m∠1=45 degrees
Since m∠1=m∠3
m∠3=45 degrees
Recall: m∠1+m∠2=180 (Linear Postulate)
45+m∠2=180
m∠2=180-45
m∠2=135 degrees
Since m∠2=m∠4
m∠4=135 degrees
match the term with the definition
Answer:
1 - c
2 - a
3 - e
4 - d
5 - b
Answer: c, a, e, d, b
Step-by-step explanation:
1. Angle: (c) A figure consisting of two rays with the same endpoint.
2. Circle: (a) The set of all points in a plane that are a given distance from a point. That distance is called the radius.
3. Point: (e) A location, has no size.
4. Ray: (d) The portion of a line that starts at one point and goes off to infinity.
5. Vertex: (b) A point where two or more rays or "arms" of an angle meet.
9+9+3=21
1234+1234+1234= 30
9+1224+12=?
Answer:
9+1224+12=1245
Hope this helps
Answer:
Mathematically,
9+1224+12 = 1245
But, Logically, here:
9+1224+12 = 21
Which is the cosine ratio of
Answer:The answer is B
Step-by-step explanation:
Answer:
Option B
Step-by-step explanation:
Cos A = [tex]\frac{Adjacent}{Hypotenuse}[/tex]
Where Adjacent = 28, Hypotenuse = 197
Cos A = [tex]\frac{28}{197}[/tex]
Do all systems of linear inequalities have solutions? If not, write a system of inequalities that has no solution. What would the graph of a system of linear inequalities with no solution look like?
Answer: There are systems with no solutions, and the graphs may show two regions with no intersections (as you know, the solution set is in the intersection of the sets of solutions for each inequality)
Step-by-step explanation:
Ok, suppose that our system is:
y > x
and
y < x.
This system obviously does not have any solution, because y can not be larger and smaller than x at the same time.
The graph of y > x is where we shade all the region above the line y = x (the line is not included)
and the graph of y < x is where we sade all the region under the line y = x (the line is not included)
So we will look at a graph where we never have a region with the two shades overlapping (so we do not have a intersection in the sets of solutions), meaning that we have no solutions.
I would really appreciate it if you could help me please
Answer:
Yes, triangle GYK is similar to triangle BAK.
Step-by-step explanation:
The sides of each triangle are proportional to each other.
Take the longest side of each triangle. You are comparing line AK with line KY.
The proportion is 15/25.
Now, take the shortest side of each triangle. You are comparing line KB with GK.
The proportion is 6/10.
To determine if the triangles are proportional, we can see if the two proportions are equal to each other:
15/20=6/10
3/5=6/10
Correct! 3/5 equals to 6/10. Therefore, the two triangles are similar because their sides are proportional.
Hope this helps :)
Answer:
O Yes!
Step-by-step explanation:
We would check whether the proportionality of their sides is equal
Taking proportionality
= [tex]\frac{6}{10} = \frac{15}{25}[/tex]
Cross Multiplying
6 × 25 = 15 × 10
150 = 150
So, ΔABK is similar to ΔGKY
5. A worker can do a piece of
piece of wook
in 14 days.
How much coook does he do ini day!
. How much work does he do in 7 days?
lijIt he works for 2 days and leaves,
how much work is left to finish it?
Answer:
therefore the left work of worker will be 6/7 part of work
When a ladder of length 2.5 m leans against the
of 55° with the ground. When the ladder leans
top edge of a window of a building, it forms an
angle
against the lower edge of the same window,
it forms an angle of 38° with the ground. Find the
height of the window, giving your answer in
centimetres.
Answer: window = 0.50 m
Step-by-step explanation:
First, draw a picture (see image below).
Then set up two equations that eventually you can set equal to each other.
Given: Ladder (hypotenuse) = 2.5
Angle to Top edge of window = 55°
Angle to Lower edge of window = 38°
[tex]\sin \text{Top}=\dfrac{opposite}{hypotenuse}\qquad \qquad \sin \text{Lower}=\dfrac{opposite}{hypotenuse}\\\\\\\sin 55^o=\dfrac{h+y}{2.5}\qquad \qquad \qquad \sin 38^o=\dfrac{y}{2.5}\\\\\\\underline{\text{Solve both equations for y:}}\\2.5\sin 55^o-h=y\qquad \qquad 2.5\sin 38^o=y\\\\\\\underline{\text{Set the equations equal to each other and solve for h:}}\\\\2.5\sin 55^o-h=2.5\sin 38^o\\2.5\sin 55^0-2.5\sin 38^o=h\\\large\boxed{0.50=h}[/tex]
SOMEONE PLEASE HELP ME ASAP PLEASE!!!
Answer:
A = 45 units^2
Step-by-step explanation:
This is a trapezoid
A = 1/2 (b1+b2) h
b1 is the top = 7
b2 is the bottom = 11
h = 5
A = 1/2 ( 7+11) *5
A = 1/2 ( 18)*5
A = 45 units^2
The personnel department of a large corporation wants to estimate the family dental expenses of its employees to determine the feasibility of providing a dental insurance plan. A random sample of 12 employees reveals the following family dental expenses (in dollars). See Attached Excel for Data. Construct a 97% confidence interval estimate for the average family dental expenses for all employees of this corporation.
The data cited is in the attachment.
Answer: 308.2±106.4
Step-by-step explanation: To construct a confidence interval, first calculate mean (μ) and standard deviation (s) for the sample:
μ = Σvalue/n
μ = 308.2
s = √∑(x - μ)²/n-1
s = 147.9
Calculate standard error of the mean:
[tex]s_{x} = \frac{s}{\sqrt{n} }[/tex]
[tex]s_{x}[/tex] = [tex]\frac{147.9}{\sqrt{12} }[/tex]
[tex]s_{x}[/tex] = 42.72
Find the degrees of freedom:
d.f. = n - 1
d.f. = 12 - 1
d.f. = 11
Find the significance level:
[tex]\frac{1-0.97}{2}[/tex] = 0.015
Since sample is smaller than 30, use t-test table and find t-score:
[tex]t_{11,0.015}[/tex] = 2.4907
E = t-score.[tex]s_{x}[/tex]
E = 2.4907.42.72
E = 106.4
The interval of confidence is: 308.2±106.4, which means that dental insurance plan varies from $201.8 to $414.6.
30 students, along with some of their parents, are going to a trip to Washington DC. Some of the adults are driving cars, and each car can accommodate up to 5 people including the driver. What is the smallest number of adults that should be invited on the trip to get all 30 students to Washington?
Answer:
Minimum 08 adults / drivers
Maximum 10 adults / drivers
Step-by-step explanation:
Total students are 30
Each car can take total 5 incl. drive
There needs to be 7 cars taking the 30 students, which also means there have to be minimum 7 drivers / adults.
Min. passengers = 30 + 7
Of course, there will be space for 3 more in the 8th car since 5 x 8 = 40
Given the vector (4|3) and the transformation matrix (0|1|-1|0), which vector is the imagine after applying the transformation to (4|3)? A. (4|-3)
B.(-3|4)
C.(3|-4)
D.(-4|3)
Answer:
C.(3|-4)
Step-by-step explanation:
Given the vector:
[tex]\left[\begin{array}{ccc}4\\3\end{array}\right][/tex]
The transformation Matrix is:
[tex]\left[\begin{array}{ccc}0&1\\-1&0\end{array}\right][/tex]
The image of the vector after applying the transformation will be:
[tex]\left[\begin{array}{ccc}0&1\\-1&0\end{array}\right]\left[\begin{array}{ccc}4\\3\end{array}\right]\\\\=\left[\begin{array}{ccc}0*4+1*3\\-1*4+0*3\end{array}\right]\\\\=\left[\begin{array}{ccc}3\\-4\end{array}\right][/tex]
The correct option is C
The image after applying the transformation to the matrix is [tex]\begin{bmatrix}3\\ -4\end{bmatrix}[/tex].
What is a matrix ?Matrix, a set of numbers arranged in rows and columns so as to form a rectangular array. The numbers are called the elements, or entries, of the matrix.
It is given that the vector is
[tex]\begin{bmatrix}4\\ 3\end{bmatrix}[/tex]
and the transformation matrix is
[tex]\begin{bmatrix}0 &1 \\ -1 &0 \end{bmatrix}[/tex]
The image after applying the transformation
[tex]\begin{bmatrix}4\\ 3\end{bmatrix}\begin{bmatrix}0 &1 \\ -1 &0 \end{bmatrix}[/tex]
[tex]\begin{bmatrix}0*4+0*3 \\-1*4+0*3 \end{bmatrix}[/tex]
[tex]\begin{bmatrix}3\\ -4\end{bmatrix}[/tex]
Therefore the image after applying the transformation to the matrix is [tex]\begin{bmatrix}3\\ -4\end{bmatrix}[/tex].
To know more about Matrix
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