Original mean = 64
standand deviation = 13
Explanations:Let the value of of the originalmean be X. If after 6 points have been added to every score in a sample, the mean is found to be M = 70, then;
X + 6 = 70
Subtract 6 from both sides
X + 6 - 6 = 70 - 6
X = 70 - 6
X = 64
Hence the mean of the original sample will be 64.
The standard deviation of the data will remain unchanged since the distance from the mean will remain the same no matter the change in mean. Therefore the standard deviation of the sample will be 13.
What expression shows 50 + 30 written as a product of 2 factors?
(A)5(10+ 7)
(B)5(10+ 3)
(C)10(5+ 2
(D)10(5+ 3)
need answers fast pleazz
Answer:
D
Step-by-step explanation:
distribute the 10 to (5+3) and you get 50+30
A gets you 50+35
B gets you 50+15
C gets you 50+20
D gets you 50+30
What is the product of 8V 5 and 5/10 in simplest radical form?
Given the numbers:
[tex]8\sqrt[]{5},5\sqrt[]{10}[/tex]The product of the numbers will be:
[tex]\begin{gathered} 8\sqrt[]{5}\times5\sqrt[]{10}=8\times5\sqrt[]{5\times10}=40\sqrt[]{50} \\ \\ 50=25\times2=5^2\times2 \\ \\ 40\sqrt[]{50}=40\sqrt[]{5^2\times2}=40\times5\sqrt[]{2}=200\sqrt[]{2} \end{gathered}[/tex]So, the answer will be:
[tex]200\sqrt[]{2}[/tex]I have been struggling with this problem for around 2 hours and can’t seem to get it
the quotient rule say:
[tex](\frac{f(x)}{g(x)})^{\prime}=\frac{g(x)\cdot f^{\prime}(x)-f(x)\cdot g^{\prime}(x)}{(g(x))^2}[/tex]now we defined:
[tex]\begin{gathered} f(x)=-4x^2+16 \\ g(x)=(x^2+4)^2 \end{gathered}[/tex]and the derivative:
[tex]\begin{gathered} f^{\prime}(x)=-8x \\ g^{\prime}(x)=2\cdot(x^2+4)\cdot2x \\ g^{\prime}(x)=4x(x^2+4) \end{gathered}[/tex]so now we can replace on the quotient rule:
[tex]\frac{(x^2+4)^2\cdot(-8x)-4x(x^2+4)\cdot(-4x^2+16)}{(x^2+4)^4}[/tex]now we can use properties, like:
[tex](x^2+4)^2=x^4+8x+16[/tex]When given two points and asked to find the equation of the line in slope-intercept form, what are the correct steps? Place a number next to the step to put them in order.
Given
given two points and asked to find the equation of the line in slope-intercept form
Find
what are the correct steps? Place a number next to the step to put them in order.
Explanation
to find the equation of the line in slope intercept form form given two points.
step 1 :
find the slope.
step 2
write equation in point slope form
step 3.
pick a point form the given points , substitue it into the point slope form
step 4.
write the equation in slope intercept form by simplifying
Final Answer
Hence , the correct order is 2 , 1 , 4 , 3
If 8% of the sheet aluminum is lost to scrap when forming a fuel tank, what is the weight of the tank if the raw sheets of aluminum weigh 200 pounds?
Solution:
Step 1: Calculate 8% of the raw sheets of aluminum :
[tex]200\text{ x 0.08 = 16}[/tex]This is the weight that is lost in the production of the fuel tank.
Step 2: Calculate the weight of the tank :
200 pounds - 16 pounds = 184 pounds.
So that, we can conclude that the correct answer is:
184 pounds.
Write the equation containing the points (-2,4) and (1,10).
Answer:
y=2x+8
Explanation:
Given the two points:
[tex]\begin{gathered} (x_1,y_1)=(-2,4) \\ \mleft(x_2,y_2\mright)=\mleft(1,10\mright) \end{gathered}[/tex]In order to find the equation of the line connecting them, we employ the use of the two-points formula given below:
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]Substitute the values:
[tex]\frac{y-4}{x-(-2)}=\frac{10-4}{1-(-2)}[/tex]Next, simplify:
[tex]\begin{gathered} \frac{y-4}{x+2}=\frac{6}{3}=2 \\ \implies y-4=2(x+2) \\ \implies y=2(x+2)+4 \\ \implies y=2x+4+4 \\ \implies y=2x+8 \end{gathered}[/tex]The equation containing the points (-2,4) and (1,10) is y=2x+8.
QuestionA cylinder has height 6 meters and radius 5 meters. Find the a. volume and b. surface area. Use 3.14 for. Do not round.
Problem: A cylinder has a height 6 meters and a radius 5 meters. Find the a. volume and b. surface area. Use 3.14 for. Do not round.
Solution:
Remember that the volution of cylinder is given by the following equation:
[tex]V\text{ =}\pi\text{r}^2h[/tex]where r is the radius of the cylinder and h is the height of the cylinder. In this case, we have that:
[tex]V\text{ =}\pi\text{r}^2h=\pi5^2\text{ x 6 = 150}\pi\text{ = 471.23}[/tex]So we can conclude that the volume of the cylinder is 471.23
Now, for surface area, remember that the surface area for the cylinder is given by the following equation:
[tex]V=2\pi r^2+\text{ }2\pi rh[/tex]where r is the radius of the cylinder and h is the height of the cylinder. In this case, we have that:
[tex]V=2\pi r^2+\text{ }2\pi rh\text{ = 2}\pi(5)^2\text{ + 2}\pi(5)(6)\text{ = 110}\pi\text{ = 345.57}[/tex]So we can conclude that the surface area for the cylinder is 345.57
Question 7 of 10Use the properties of logarithms to expand the following expression.(√log(x+4)5x³Your answer should not have radicals or exponents.You may assume that all variables are positive.
We have:
[tex]\begin{gathered} log(\sqrt{\frac{(x+4)^5}{x^3}}) \\ =log(\frac{(x+4)^2\sqrt{x+4}}{x\sqrt{x}} \end{gathered}[/tex]Applying properties of logarithms:
[tex]\begin{gathered} =log((x+4)^2\sqrt{x+4})-log(x\sqrt{x}) \\ =2log(x+4)+log(\sqrt{x+4})-logx-log\sqrt{x} \end{gathered}[/tex]Prepare an amortization schedule for the first three months on a loan of $87000 at 6% for 20 years
First, we need to calculate the value of the monthly payments. We can use the general ordinary anuity formula:
[tex]PV=\text{PMT}\cdot\lbrack\frac{1-(1+i)^{-n}}{i}\rbrack[/tex]Where PV=$87000
n=20
i=0.06
Replace the given values and solve for PMT:
[tex]\begin{gathered} 87000=\text{PMT}\cdot\lbrack\frac{1-(1+0.06)^{-20}}{0.06}\rbrack \\ 87000=\text{PMT}\cdot\lbrack\frac{1-0.3118}{0.06}\rbrack \\ 87000=\text{PMT}\cdot\lbrack\frac{0.6882}{0.06}\rbrack \\ 87000=\text{PMT}\cdot11.4699 \\ \text{PMT}=\frac{87000}{11.4699} \\ \text{PMT}=7585.06 \end{gathered}[/tex]Now that you have the payment, you can construct the table of the amortization schedule with the know information:
To calculate the missing information, start by calculating the interest component of the payment (interest paid) by multiplying the periodic interest by the remaining principal.
The monthly interest is the yearly interest divided by 12, then:
[tex]MI=\frac{0.06}{12}=0.005[/tex]And the interest paid is then:
[tex]\begin{gathered} IP=MI\cdot\text{ Remaining principal} \\ IP=0.005\cdot87000\text{ (for the first payment)} \\ IP=435 \end{gathered}[/tex]Now, calculate the principal paid by subtracting the interest paid from the payment amount:
[tex]\text{ Principal paid=7585.06-435}=7150.06\text{ (first payment)}[/tex]Then, by putting the values on the amortization schedule:
The remaining principal is 87000-7150.06 (principal paid).
Now for the second payment, calculate the interest paid with the new remaining principal:
[tex]\begin{gathered} IP=0.005\cdot79849,94\text{ (for the second payment)} \\ IP=399,25 \end{gathered}[/tex]And the principal paid is:
[tex]\text{ Principal paid=7585.06-399.25}=7185.81\text{ (second payment)}[/tex]The remaining principal is:
[tex]RP=79849.94-7185.81=72664.13[/tex]Thus:
And for the third month, you apply the same calculations and the amortization schedule is:
The following is the cost function for natural gas for the city where Greg lives. Greg's natural gas bill last month was $51.54. How many therms did Greg use last month? Round the answer to the nearest tenth of a therm (one decimal place). Only input the number. Do not input any unit. Example: 89.3
Kauro, this is the solution:
This is the cost function for natural gas for the city where Greg lives:
• c (t) = 16.74 + 0.742t
Now we replace c (t) by 51.54 to solve for t, as follows:
51.54 = 16.74 + 0.742t
Subtracting 16.74 at both sides:
51.54 - 16.74 = 16.74 + 0.742t - 16.74
34.8 = 0.742t
Dividing by 0.742 at both sides:
0.742t/0.742 = 34.8/0.742
t = 46.9 therms
The correct answer is 46.9
Which of the following is the graph of the quadratic function y = x2 - 6x -
Therefore,
From the graph above,
The correct answer is OPTION C
the cost of 3D movie tickets is $12 for 1 ticket, $24 for 2 tickets, and $36 for 3 tickets. determine whether the cost is proportional to the number of tickets by graphing on the coordinate plane. explain your reasoning
Explanation
1 ticket =$12
2 ticket =$24
3 ticket =$36
I worked on this and I can't seem to find the answer
1 liter = 1000 milliliters.
thus, 75791 liters =
[tex]75791\times1000=75791000[/tex]thus, 75791000 milliters.
Given: _A and B form a linear pair,_B and C are complementary, and m_A = 103°Prove: m C = 13°Statement:Reason:1. _A and B form a linear pair 1. Given2. m A+ m B = 180°2. Postulate3. mA = 103°3. Given4. 103° + m B = 180°4. Substitution5. m2B = 77°5.[?]6. B and C are complementary 6. Given7. m B + m C = 90°7. Definition8. 77° + m2 = 90°8. Substitution9. m C = 13°9.Select the reason that bestsupports Statement 5 in thegiven proof.A. Multiplication Property of EqualityB. Subtraction Property of EqualityC. Division Property of EqualityD. Addition Property of Equality
SOLUTION
Statement 4, states that
[tex]103^o+mPR = 9x -31 and QR = 43: Find xQ is the midpoint of PR
We can model the situation as:
Since Q is the midpoint of PR, QR and PQ have the same length, so PQ is also equal to 43.
Now, we can formulate the following equation:
PR = PQ + QR
So, replacing PR by 9x-31, PQ by 43 and QR by 43, we get:
9x - 31 = 43 + 43
9x - 31 = 86
Solving for x:
9x - 31 + 31 = 86 + 31
9x = 117
9x/9 = 117/9
x = 13
Answer: x = 13
Michael and Larry scored 18 points in a basketball game. Michael scored twice as many points as Larry. How many points did Larry score?6 8 10 12
Let Larry score x, Michael scored 2x
x + 2x = 18
3x = 18
x = 18/3 = 6 points.
Therefore, Larry scored 6 points. Option A
A circular pool with a radius of 3 m sits in a rectangular yard that is 14 m by 8 m. What area of the yard is NOT covered by the pool?
SOLUTION:
Step 1:
In this question, we are given the following:
A circular pool with a radius of 3 m sits in a rectangular yard that is 14 m by 8 m. What area of the yard is NOT covered by the pool?
Step 2:
The area of the yard that is NOT covered by the pool is given as :
[tex]\text{Area of the Rectangular yard - Area of the circular pool}[/tex][tex]\text{( Length }X\text{ Breadth ) - ( }\pi r^2\text{ )}[/tex][tex]\begin{gathered} (\text{ 14 X 8 ) - (}\frac{22}{7}X\text{ 3 X 3 )} \\ =\text{ 112 - (}\frac{198}{7}) \\ =\text{ 112 - 28.28571429} \\ =\text{ 83.71428571} \\ \approx83.71m^2\text{ ( 2 decimal places)} \end{gathered}[/tex]CONCLUSION:
The area of the yard NOT covered by the pool is:
[tex]83.71m^2\text{ ( 2 decimaal places)}[/tex]Given the parallelogram TVWY shown above, determine how triangles TUZ and WXV can be shown to be similar. A. Since ZTU VWX and VX = XW, the triangles are similar by angle-side. B. Since TUZ WXV and TU = UZ, the triangles are similar by angle-side. C. Since TUZ VWX and ZTU WXV, the triangles are similar by angle-angle. D. Since TUZ WXV and ZTU VWX, the triangles are similar by angle-angle.
Notice that triangles TUZ and WXV have an angle with the same measure; therefore, we need two additional corresponding similar angles, or two corresponding similar sides, or one side and an angle to prove similarity.
Options A is not possible since it would imply that triangle TUZ has two 90°-inner angles.
Option B states a relation between two sides of triangle TUZ, not between two sides (one of each triangle). Option B cannot be the answer.
According to the figure, angles TUZ and WXV have to be congruent; therefore, option C cannot be the answer.
The only valid alternative is option D, option D is the answer.
John was asked to place the numbers shown below in order from greatest to least. 0.2 , -0.3, 1.6, 120%, -2%, 3.8, --33, 3.14 After ordering the numbers from greatest to least, what number would John have in the 3rd position?
Let's begin by listing out the information given to us:
0.2, -0.3, 1.6%, 120%, -2%, 3.8, -33, 3.14
In sorting the numbers from the greatest to the least, we must bear the following in mind:
I. Any number having a negative parenthesis is lower than zero
II. % means 100; any number having % means the real value of the number is multiplied by 100
0.2 = 0.2
-0.3 = -0.3
1.6% = 1.6 * 100 = 160
120% = 120 * 100 = 12000
-2% = -2 * 100 = -200
3.8 = 3.8
-33 = -33
3.14 = 3.14
Rearranging from the greatest to the least, we have it thus:
120%, 1.6%, 3.8, 3.14, 0.2, -0.3, -33, -200
The number in the third position is 3.8
9Find the percentage change from the first quantity to the second quantity:From 60 km/h to 45 km/h.Answer:%
To calculate the percentage change;
From 60km/h to 45km/h is a decrease
So we will calculate the decrease = 60 - 45 =15
Divide 15 by the original value which is 60 and then multiply by 100%
That is;
Percentage change = 15/60 x100%
=25%
Hi i need some help on question 11 b and c. I have already done a
ANSWER:
a. 16.27 cm^3
b. 4.3 cm
c. 325.4 seconds
STEP-BY-STEP EXPLANATION:
The first thing is to calculate the value of the volume, which is the sum of the volume of each part, like this:
[tex]\begin{gathered} V=V_t+V_c+V_s \\ r=\frac{d}{2}=\frac{2.6}{2}=1.3 \\ V_t=A_b\cdot\frac{h}{3}=\pi\cdot(r)^2\cdot\frac{h}{3}=3.14\cdot(1.3)^2\cdot\frac{1.2}{3}=2.12cm^3 \\ V_c=A_b\cdot h=\pi\cdot(r)^2\cdot h=3.14\cdot(1.3)^2\cdot1.8=9.55m^3 \\ V_s=\frac{4}{6}\cdot\pi\cdot r^3=\frac{4}{6}\cdot3.14\cdot(1.3)^3=4.6cm^3 \\ V=V_t+V_c+V_s \\ V=2.12+9.55+4.6 \\ V=16.27cm^3 \end{gathered}[/tex]The volume of the upper container is 16.27 cm^3, and being symmetrical, it is the same for the bottom container.
At the moment that all the sand finishes going to the bottom container, the height will be the sum of the heights in each case.
Then:
[tex]\begin{gathered} h=1.2+1.8+1.3 \\ h=4.3\text{ cm} \end{gathered}[/tex]Therefore, the height is 4.3 centimeters
To reach that height, all the sand had to be passed from one side to the other, therefore, we can calculate the time as follows:
[tex]\begin{gathered} t=\frac{16.27cm^3}{0.05\frac{cm^3}{s}} \\ t=325.4\text{ sec} \end{gathered}[/tex]It would take a time of 325.4 seconds
Solve the equation for y in terms of x. In other words, algebraically rearrange the equation so that the y variable is by itself one side of the equation. Type your answer in the form y=mx+b. If you have a value that is not an integer then type it rounded to the nearest hundredth. Do not put spaces between your characters.5x+2y=0y=Answer
we have the equation
5x+2y=0
solve for y
step 1
subtract 5x on both sides
5x+2y-5x=0-5x
simplify
2y=-5x
step 2
Divide by 2 on both sides
2y/2=-5x/2
y=-(5/2)x
y=-2.50xcan someone help me with this one ? list the first 15 perfect cubes:
We have the following exercise
What is a cube of a number x?
The answer is to multiply this number or quantity 3 times. For example:
1^3 = 1 x 1 x 1 = 1,
2^3 = 2x 2 x 2 = 8
4^3 = 4x4x4 = 64
and so on.
Equivalently, let represent with a stick a unity 1: so for example
So if we want 2^3, is the same to say:
that is 2^3 = 8
Find the length of AB.6 in A30°BAB = [ ?Round your answer to the nearest hundredth.
(-4, 6); slope = - 3/4write the linear equation in slope intercept form given
We know the slope = -3/4 and a point = (-4, 6) of a line, and we wnat to find the equation in the slope-intercept form, so:
[tex]\begin{gathered} \text{The general slope-intercept form of a line is:} \\ y=mx+b \\ \text{Where m is the slope and b is the value of y-intercept} \end{gathered}[/tex]In this case, m=-3/4 and evaluating the point (-4, 6) we can find the value of b:
[tex]\begin{gathered} \text{With m=-3/4 and the point (x, y) = (-4, 6):} \\ 6=-\frac{3}{4}(-4)+b \\ 6=3+b \\ b=6-3 \\ b=3 \end{gathered}[/tex]We found that b = 3, so the equation of the line is:
[tex]y=-\frac{3}{4}x+3[/tex]Solve the equation for the variable. 5.3 = 2 - 2.7 I
We are asked to solve for the variable in the equation:
5.3 = z - 2.7
SO we need to isolate the variable "z" on one side of the equal sign. for that we add 2.7 to both sides:
5.3 + 2.7 = z - 2.7 + 2.7
combining like terms we get:
8 = z + 0
8 = z
Therefore z is 8.
input is complete.A parallelogram has a base of 9 units and an area of 12 square units. What is the corresponding height for that base? Remember: Area parallelogram = b × h
As written in the Question Tab, the area of the parallelogram can be solved by multiplying the base and the height. Since we already have the base = 9 units and its area which is 12 square units, the first and last thing to do is divide the area by the base to solve the height of the parallelogram. See computation below:
[tex]\begin{gathered} \text{area = base}\times\text{height} \\ 12=9\times h \\ Divide\text{ both sides by 9.} \\ \frac{12}{9}=\frac{9h}{9} \\ \frac{4}{3}or\text{ 1.33 = h} \end{gathered}[/tex]Therefore, the height of the parallelogram is 4/3 or 1.33 units.
It used to cost $33.00 to buy a case of 23 bottles of Sriracha. Because of the shortage, each case is now $50.00. How MUCH MORE is each bottle of Sriracha?
The amount of money that each bottle of sriracha would cost more would be = $0.82
What is product shortage?Product shortage is definitely as the decrease in the availability of a product in the market or decrease in its production.
The cost of a case of sriracha = $33.00
The amount of a case after the shortage = $50.00
The amount of bottles that is found in case = 23
The amount of each bottle before shortage = 23/33 = $0.70
The amount of each bottle after shortage = 50/33 =
$1.52
The amount of money that each bottle of sriracha would cost more = 1.52 - 0.70 = $0.82
Learn more about cost price here:
https://brainly.com/question/25491204
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The shaded area is 120T cm?, and the radius is 24 cm. Find X.
We will have the following:
[tex]A=(\frac{x}{2})\cdot r^2\Rightarrow120\pi=(\frac{x}{2})(24)^2[/tex][tex]\Rightarrow\frac{x}{2}=\frac{5\pi}{24}\Rightarrow x=\frac{5\pi}{12}[/tex][tex]\Rightarrow x\approx1.31[/tex]So, the value of x is approximately 1.31.
To adopt a dog from an animal shelter, you must pay $90 for vaccinations, $75 to spay or neuter the dog, and $40 for a wellness exam by a veterinarian. a. Write an expression in simplest form that represents the amount (in dollars) it costs to adopt x dogsb. What does the coefficient of the expression in part (a) represent?
1) Gathering the data
pay $90 for vaccinations,
$75 to spay or neuter the dog,
and $40 for a wellness exam
Let x be the price of the dog.
2) Since all of these expenses represent money out, or less money in your wallet. And all of these prices refer to the adoption of one dog then We can state
C=(90+75+40)x
C= 205x