Answer:
11
Step-by-step explanation:
3p²q+pq²=3×1/4×4+1/2×16=3+8=11
Which ordered pair is a solution to the system of inequalities?
y > –x
y ≤ x + 1
A) (0,5)
B) (4,–1)
C) (1,3)
D) (–4,0)
9514 1404 393
Answer:
B) (4,–1)
Step-by-step explanation:
A graph can help you figure this out. The point (4, -1) is in the doubly-shaded area, so is a solution to this system.
==========================================================
Explanation:
Choice A can be ruled out because
[tex]y \le x+1\\\\5 \le 0+1\\\\5 \le 1\\\\[/tex]
which is false.
Choices C and D are similar, so they can be ruled out as well.
---------------------
Choice B is the answer because it makes both inequalities true.
If we plug the coordinates of (4,-1) into the first inequality, we get
[tex]y > -x\\\\-1 > -4[/tex]
which is a true statement because -1 is to the right of -4 on the number line.
Now try the other inequality
[tex]y \le x+1\\\\-1 \le 4+1\\\\-1 \le 5\\\\[/tex]
that's true also. So again, (4,-1) makes both inequalities true, and that's why choice B is the answer.
What sum of money, invested at 9%
interest per year, is needed to provide an
income of $45 per year?
Answer:
$500
Step-by-step explanation:
Intrest = P. A * Intrest Rate * Time
Time = 1 year, Intrest Rate = 9%, P. A. is what we need to find, Intrest is 45
45=x*9/100*1, x=500
Answer:
500
Step-by-step explanation:
I = PRT where I is the interest, P is the amount invested, R is the rate and T is the time
We want 1 year at 9% to get 45 dollars in interest
45 = P ( .09) (1)
45 = .09P
Divide each side by .09
45/ .09 = P
500 =P
How many solutions on the interval {0, 2020} sin 2x + 1 + sin x + cos x have?
Answer:
0
Step-by-step explanation:
Instructions are in the picture
Answer:
123123 3213123 12312 dasdsd aw dasd sda asdasd
Step-by-step explanation:
Choose the correct answer.
The History Activities were about ___ and ___. They were both from ___. One of them had a ___ named after him. The other had a ___ named after him. The work they did together on a problem they got from a ___ laid the foundation for probability theory.
A. Pascal, Decartes, England, graph, book, relative
B. Luniz, Kolmogrov, Germany, church, square, teacher
C. Fermat, Luniz, England, law, diagram, priest
D. Pascal, Fermat, France, triangle, theorem, gambler
Answer:
I say Its letter d
Step-by-step explanation:
I hope this help
f(x) = x - 1. Find the inverse of f(x).
Answer:
f^-1 (x) = x+1
Step-by-step explanation:
f(x) = x-1
y = x-1
Exchange x and y
x = y-1
Solve for y
Add 1 to each side
x+1 = y-1+1
x+1 = y
The inverse is x+1
f^-1 (x) = x+1
Can someone check my answers if they are correct or incorrect? If it is incorrect, please let me know why it is incorrect please.
Expand (2+x)^-3
....
Answer:
1/(x^3 + 6x^2 + 12x + 8)
Step-by-step explanation:
The first thing we do is rationalize this expression. (2+x)^-3 is written as
1/(2+x)^3
Then from there we can foil out the denominator. It is easiest to foil (2+x)(2+x) first and then multiply that product by (2+x).
(2+x)(2+x) = 4 + 4x + x^2
(4+4x+x^2)(2+x) = 8+8x+2x^2+4x+4x^2+x^3.
Then we combine like terms and put them in order to get:
x^3 + 6x^2 + 12x + 8
And of course we can't forget that this was raised to the negative third power, so our answer is 1/(x^3 + 6x^2 + 12x + 8)
Answer:
Hello,
Step-by-step explanation:
[tex](a+x)^n=a^n+\left(\begin{array}{c}n\\ 1\end{array}\right)*a^{n-1}*x+\left(\begin{array}{c}n\\ 2\end{array}\right)*a^{n-2}*x^2+\left(\begin{array}{c}n\\ 3\end{array}\right)*a^{n-3}*x^3+\left(\begin{array}{c}n\\ 4\end{array}\right)*a^{n-4}*x^4+...+\left(\begin{array}{c}n\\ n\end{array}\right)*a^{n-n}*x^n[/tex]
[tex]with \\\\\left(\begin{array}{c}n\\ 1\end{array}\right)=n\\\\\left(\begin{array}{c}n\\ 2\end{array}\right)=\dfrac{n(n-1)}{2!} \\\\\left(\begin{array}{c}n\\3 \end{array}\right)=\dfrac{n(n-1)(n-2)}{3!} \\\\...\\[/tex]
[tex]\dfrac{1}{(2+x)^3} =\dfrac{1}{8} +3*\dfrac{x}{4}+3\dfrac{x^2}{2}+x^3\\\\[/tex]
help pls!!! Classify the following question: “President, vice president, and secretary are being chosen for the Environmental Club. In how many different ways can these three offices be filled from a list of ten members?”
the answer is: combation
please help, will give brainliest!!!!
Answer:
3
Step-by-step explanation:
3 - 3/x
----------------
1 - 1/x
Multiply the top and bottom by x
x(3 - 3/x)
----------------
x(1 - 1/x)
3x -3
------------
x-1
Factor the numerator
3(x-1)
-------
x-1
Cancel like terms
3
-----
1
3
At the beginning of a basketball season, the Spartans won 35 games out of 98 games. At this rate, how many games will they win in a normal 116 game season?
The stemplot below represents the number of bite-size snacks grabbed by 37 students in an activity for a statistics class.
A stemplot titled Number of snacks has values 12, 12, 13, 13, 14, 14, 15, 15, 15, 15, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 20, 20, 21, 21, 21, 21, 22, 23, 25, 25, 28, 32, 38, 42, 45.
Which of the following statements best describes the distribution?
The distribution of the number of snacks grabbed is skewed right with a center around 18 and varies from 15 to 45. There are no outliers.
The distribution of the number of snacks grabbed is symmetric with a center around 18 and varies from 12 to 45. There are possible outliers at 38, 42, and 45.
The distribution of the number of snacks grabbed is skewed left with a center around 18 and varies from 12 to 45. There are possible outliers at 38, 42, and 45.
The distribution of the number of snacks grabbed is skewed right with a center around 18 and varies from 12 to 45. There are possible outliers at 38, 42, and 45.
Answer:
The distribution of the number of snacks grabbed is skewed right with a center around 18 and varies from 12 to 45. There are possible outliers at 38, 42, and 45.
Step-by-step explanation:
First, we can see if the graph is symmetric. A symmetric graph is even on both sides of the center. As there are a lot more students that grabbed a small number of snacks, and the data is not even around the center (which is somewhere around 20 or 30 snacks). This means that the graph is not symmetric, making the second answer incorrect.
Next, we can check if the graph is skewed right or left. If the left of the graph represents a smaller amount of snacks and the right of it represents a higher number of snacks, we can see that most of the data is on the left of the graph. There are a few values to the right, but the overwhelming amount of data is on the left, making the distribution skewed to the right. This keeps the first and last answers possible
Moreover, we can find the center of the distribution. This is generally equal to the median, which is 18, so the center is around 18
After that, we can see what the values vary from. The lowest tens value is 1, and the lowest ones value in that is 2, making the lowest value 12. Similarly, the highest tens value is 4, and the highest ones value there is 5, making the range 12 to 45. This leaves the last answer, but we can check the outliers to make sure.
With the data, we can calculate the first quartile to be 15, the third quartile to be 21.5, and the interquartile range to be 21.5-15 = 6.75 . If a number is less than Q₁ - 1.5 * IQR or greater than Q₃ + 1.5 * IQR, it is a potential outlier. Applying that here, the lower bound for non-outliers is 15 - 6.5 * 1.5 = 5.25, and the upper bound if 21 + 6.5 * 1.5 = 30.75. No values are less than 5.25, but there are four values greater than 30.75 in 32, 38, 42, and 45. There are possible outliers at 38, 42, and 45, matching up with the last answer.
Find the equation (in terms of x) of the line through the points (-2,-3) and (4,-1)
Answer:
y = 1/3x - 7/3
Step-by-step explanation:
y2 - y1 / x2 - x1
-1 - (-3) / 4 - (-2)
2/6
= 1/3
y = 1/3x + b
-1 = 1/3(4) + b
-1 = 4/3 + b
-7/3 = b
Find an equation equivalent to r = 1 + 2 sin 0 in rectangular coordinates.
Answer:
C
Step-by-step explanation:
r=1+2sin(theta)
r^2=r+2*r*sin(theta)
x^2+y^2=±sqrt(x^2+y^2)+2y
Instructions: Find the area of the trapezoid
and round to the nearest tenth.
10.2 mi.
7 mi.
4.2 mi.
Area:
mi?
Answer:
299.88 mi. !!!!!
you just multiple all of them together to get the area!!!
Step by step explanation need it
Answer:
8/17
Step-by-step explanation:
The sine of an angle is defined as the opposite side to the reference angle divided by the hypotenuse.
The side opposite the angle is always the side not connected to the reference angle. In this case the opposite side = ZY
The hypotenuse = XZ
Sin(X) = ZY/XZ
Sin(X) = 1634 = 8 / 17
solve the equation 7*2=?
Answer:
7*2=14
Step-by-step explanation:
7*2=14 because is multiplication
Answer:
14 because it is multiplication
Which of the following is a quadratic function
A quadratic a function has a form of,
[tex]f(x)=ax^2+bx+c,a\neq0[/tex]
The first function has a term [tex]x^3[/tex] which doesn't fit the profile of a quadratic function. The highest exponent on x inside a quadratic function can be 2, but here we have 3 so this is not a quadratic function, but rather a cubic function.
The second function fits the form of a quadratic function perfectly.
The third function is a bit tricky. While technically the third function could be considered quadratic if the leading term would be something like [tex]0x^2[/tex] and we did't even see it written out because multiplying with 0. But when we specified the form of a quadratic function, we strictly said that the number before [tex]x^2[/tex] aka [tex]a[/tex] cannot equal to zero. So the last function is not a quadratic function but rather a linear function.
Hope this helps :)
Step-by-step explanation:
f(x) = 4x² + x - 3
[tex]f(x) = 4x {}^{2} + 3 - 2[/tex]
r3t40 is correct
Copy center charges $0.08 a page for machine fed copies and $0.20 for hand fed copies.If Logan's bill for 80 copies of his movie script is $13, how many copies of each type were made?
Answer:
machine fed copies = 25, hand fed copies = 55
Step-by-step explanation:
let machine fed = x, hand fed = y
0.08x+0.2y = 13 (1)
x+y = 80
x= 80-y (2)
sub (2) into (1)
0.08(80-y)+0.2y=13
6.4-0.08y+0.2y=13
0.12y=6.6
y = 55
sub y=55 into eqn 2
x = 80-55 = 25
What is the perimeter of CDE?
A. 37.8 units
B. 39 units
C. 32.5 units
D. 35.6 units
This value is approximate.
=============================================================
Explanation:
To find the perimeter, we simply add up the lengths of the three external sides.
The horizontal side from D to E is 16 units long since |-10-6| = 16. I subtracted the x coordinates of the points and applied absolute value. You could also count out the spaces and you should count 16 spaces from D to E.
Unfortunately, the diagonal lengths aren't as straight forward. We have two options here: The pythagorean theorem, or the distance formula.
I'll go with the distance formula.
Let's find the distance from C to D, aka the length of side CD
[tex]C = (x1,y1) = (-1,-2)\\\\D = (x2,y2) = (-10,0)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-1-(-10))^2 + (-2-0)^2}\\\\d = \sqrt{(-1+10)^2 + (-2-0)^2}\\\\d = \sqrt{(9)^2 + (-2)^2}\\\\d = \sqrt{81 + 4}\\\\d = \sqrt{85}\\\\d \approx 9.2195\\\\[/tex]
Side CD is roughly 9.2195 units long.
Repeat this idea to find the length of CE
[tex]C = (x1,y1) = (-1,-2)\\\\E = (x2,y2) = (6,0)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-1-6)^2 + (-2-0)^2}\\\\d = \sqrt{(-7)^2 + (-2)^2}\\\\d = \sqrt{49 + 4}\\\\d = \sqrt{53}\\\\d \approx 7.2801\\\\[/tex]
Side CE is roughly 7.2801 units long
The perimeter of triangle CDE is approximately...
P = DE+CD+CE
P = 16 + 9.2195 + 7.2801
P = 32.4996
This then rounds to 32.5 units. The answer is choice C.
round 12.5478 to the nearest hundredths
Answer:
12.04
Step-by-step explanation:
Find the number in the hundredth place 4 and look one place to the right for the rounding digit 1 . Round up if this number is greater than or equal to 5 and round down if it is less than 5 .
Algebra II Part 1
On your paper, graph these coordinates:
(-1, 1), (-5, 2)
Type the correct equation of the line.
Note: Do not use fractions in your answer.
Answer:
4y+x-3=0
Step-by-step explanation:
The equation is y=mx+b
1) Use the coordinates from the first point
(-1,1)
1= -m+b
2) Use the coordinates frm the second point
(-5,2) (y=mx+b, use x=-5, y=2)
2=-5m+b
You have the system of equations
1=-m+b (multiply by -1) -1= m-b
2=-5m+b
Add the first equation (multiplied by -1) and the second one
-1+2= m-b-5m+b
1= -4m
m=-0.25
2=1.25+b
b=0.75
y=-0.25x+0.75
4y= -x+3
4y+x-3=0
Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles. Find the probability that the first marble is white and the second marble is blue.
Answer:
3/56
Step-by-step explanation:
Probability is the ratio of the number of possible outcome to the number of total outcome.
Given that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles.
The total number of marbles in the box
= 1 + 3 + 2 + 2
= 8 marbles
The probability that the first marble is white and the second marble is blue
= 3/8 * 1/7
= 3/56
I need to know the answer ASAP
Answer:
Step-by-step explanation:
is f(x)=sqrt{x}+3x an exponential function?
The least-squares regression equation
y = 968 – 3.34x can be used to predict the amount of monthly interest paid on a loan after x months. Suppose the amount of monthly interest after 30 months was $865.93.
What is the residual for the amount of monthly interest paid on a loan after 30 months?
–202.27
–1.87
1.87
202.27
Answer:
-1.87 (B)
865.93 - [968-3.34(30)] = -1.87
ED2021
FX) is defined by the equation f(x) = 4x2 - 2x +17. What effect will multiplying
f(x) by 0.5 have on the graph?
A. The graph will be stretched horizontally.
B. The graph will be compressed horizontally.
C. The graph will be stretched vertically.
D. The graph will be compressed vertically.
Step-by-step explanation:
the graph will be compressed vertically
One card is randomly selected from a deck of cards. Find the odds against drawing a black 10.
The odds against drawing a black ten are ___:___.
(Simplify your answers.)
Answer:
25/26 or 26/27 depending on free hands.
The first is if you don't use jokers/free cards
There is 13 cards in a single set, and a single 10 card.
Two sets are black and two sets a red.
Hearts, Spades, Clubs, and Diamonds
There is only 2 black tens out of 52 or 54 cards, so we can set it up as
50/52 or 52/54 which is simplified to
25/26 or 26/27 depending on free hands.
Step-by-step explanation:
Can you please help me
Answer:
Step-by-step explanation:
⅝ - 5/9 = 5/72
A large soda-pop manufacturer wants to introduce a new design for the label on one of its signature soda-pop drinks. The manufacturer selects a random sample of 150 customers from people who purchase the drink at a large sporting event. Each selected customer is asked whether or not he or she prefers the new design. If the manufacturer were to take a second random sample of 150 customers at the sporting event, the two samples would give somewhat different results in the proportion who prefer the new design. This variation is a source of
Answer:
This variation is a source of
response error.
Step-by-step explanation:
A response error shows the lack of accuracy in the customer responses to the survey questions. A response error can be caused by a questionnaire that requires framing improvements, misinterpretation of questions by interviewers or respondents, and errors in respondents' statements. Some responses are influenced by the answers provided to previous questions, which introduces response bias.
