Step-by-step explanation:
Let the husband's income be x
Wife's income be x + 9000
X + X + 9000 = 81000
2X + 9000 – 9000 = 81000 – 9000
2X= 72000
X = 36000
Husband, 36000,
Wife, 9000+36000, 45000
State if the scenario involves a permutation or a combination. Then find the number of possibilities.
The student body of 290 students wants to elect a president and vice president.
Permutation/Combination:
Answer:
Answer:
Permutation. ; 83810 ways
Step-by-step explanation:
Permutation and combination methods refers to mathematical solution to finding the number of ways of making selection for a group of objects.
Usually, selection process whereby the order of selection does not matter are being treated using permutation, while those which takes the order of selection into cognizance are calculated using combination.
Here, selecting 2 members (president and vice president) from 290 ; since order of arrangement does not matter, we use permutation ;
Recall :
nPr = n! ÷ (n - r)!
Hence,
290P2 = 290! ÷ (290 - 2)!
290P2 = 290! ÷ 288!
290P2 = (290 * 289) = 83810 ways
33. The population of Canada, y (in millions), can be approximated by the relation y=
0.146x + 31, where x represents the number of years since 2000.
a. Approximate the population of Canada in the year 2006.
b. In what year did the population of Canada reach approximately 32,752,000?
Answer:x=6573/500,x=13(73/500
Step-by-step explanation:
It will takes 12 years to reach approximately 32,752,000.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
y = 0.146x + 31
where x represents the number of years since 2000.
a) The population of Canada in the year 2006
x= 6
y= 0.146 x 6 + 31
y = 31.876
b) The population of Canada reach approximately 32,752,000 in
y = 32.752
0.146x + 31= 32.752
0.146x = 1.752
x= 1.752/0.146
x= 12
Hence, it will takes 12 years to reach approximately 32,752,000.
Learn more about Equation here:
https://brainly.com/question/10413253
#SPJ2
Q:
To which axis is the line passing through A(4,3) and B(4,-2) parallel to?
Answer:
y-axis.
Step-by-step explanation:
The x coordinate of both points is 4, so it is parallel to they-axis.
What is the name of this prism?
A. trapezoidal prism
B. pentagonal prism
C. sphere
D. hexagonal prism
Luis was worried about his Spanish final exam grade. The test had 200 questions, and he got
175 of them correct. His sister Marina took her French final exam, and she got 130 out of 150
questions. Who got the better percent score (round to the nearest tenths)?
Answer:
Luis:
[tex] \frac{175}{200} \times 100\% = 87.5\%[/tex]
Marina:
[tex] \frac{130}{150} \times 100\% = 86.6\%[/tex]
Answer: Marina got the better percent score than Luis
Marina:
At a hockey game, a vender sold a combined total of 192 sodas and hot dogs. The number of sodas sold was two times the number of hot dogs sold. Find the
number of sodas and the number of hot dogs sold.
Answer:
they sold 64hotdogs and 128 sodas
Step-by-step explanation:
2x+x=192 3x=192 x=64
How many ways are there to rearrange the letters of the word: COMBINATION?
Answer: 4,989,600 different ways
Step-by-step explanation:
How does the area below the mean compare to the area above the mean in a normal distribution?
A. the areas are always equal regardless of the mean
B. the areas are sometimes equal depending upon the standard deviation of the distribution
C. the area above the mean is larger since the values are larger as you move above the mean
D. the areas are sometimes equal depending upon the value of the mean
Answer:
A.
Step-by-step explanation:
that is the definition of "mean". it cuts the possible outcomes weighed with their probabilities (actual occurrences vs. possible occurrences) in 2 halves.
The areas are always equal regardless of the mean.
option (a) is correct.
What is normal distribution?A probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.
The standard normal distribution is a probability distribution, so the area under the curve between two points tells you the probability of variables taking on a range of values. The total area under the curve is 1 or 100%.
Therefore ,the areas are always equal regardless of the mean.
Learn more details about normal distribution:
https://brainly.com/question/24273691
#SPJ5
sold 72 books, if ratio of books to bookmarks sols was 9:2, how many bookmarks sold?
16 book marks has been sold
Answer:
16 bookmarks
Step-by-step explanation:
9/72 = 2/x
72/9 = 8
2 x 8 = 16
hope this helps
The number of perpendicular bisectors a segment can have is:
1 point
a) 0
b) 1
c) 3
d) 10
Answer:
0
Step-by-step explanation:
0co
What are the degree and leading coefficient of the polynomial?
- 3v² - 2v^3+ 6-8v
9514 1404 393
Answer:
degree: 3leading coefficient: -2Step-by-step explanation:
The highest degree term is -2v^3. Its degree is 3, so the degree of the polynomial is 3. Its coefficient is -2, so the leading coefficient is -2.
If you are given odds of 6 to 7 in favor of winning a bet, what is the probability of winning the bet?
The probability is ___.
(Type an integer or a simplified fraction.)
Answer: 6/13
Step-by-step explanation: a/a+b = 6/6+7 = 6/13
If you are given odds of 6 to 7 in favor of winning a bet, the probability of winning the bet would be 6/13.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
P(E) = Number of favorable outcomes / total number of outcomes
Given; If you are given odds of 6 to 7 in favor of winning a bet, we need to find the probability of winning the bet.
P = a/a+b
P = 6/6+7
P = 6/13
Therefore, If you are given odds of 6 to 7 in favor of winning a bet, the probability of winning the bet would be 6/13.
Learn more about probability here;
https://brainly.com/question/11234923
#SPJ2
*20 points*
A rancher’s herd of 250 sheep grazes over a 40-acre pasture. He would like to find out how many sheep are grazing on each acre of the pasture at any given time, so he has some images of the pasture taken by the state department of agriculture’s aerial photography division. Here are three samples of the images.
Sample 1: 4
Sample 2: 1
Sample 3: 9
How do the sample statistics compare to the population mean and standard deviation?
There will be about 6.25 sheep on each acre.
250/40 = 6.25
Given that f(x) = 2x + 9, find the value that makes f(x) = 27.
Answer:
9
Step-by-step explanation:
f(x) = 2x+9
f(x) = 27
so, you get:
2x+9=27
2x=18
x=9
Express the area of the entire rectangle.
Your answer should be a polynomial in standard form.
please answer quick i need to go to my friends to get my joy con fixed
The area is just the base times the height. In this case, the base is (x+4) and the height is (x+6), and then you just distribute to get x^2 +4x+6x+24 which is x^2+10x+24.
If my savings of $x grows 10 percent each year, how much will i have in 2 years?
Answer:
20 percent
Step-by-step explanation:
Each year is 10 percent so 10x2 or 10+10 will equal 20
?
What is the equation of a parabola whose focus is (-4, -1)
and whose directrix is
y = -5?
x²
y = + x – 1
8
o
y = -
x²
--X+1
8
y?
x =
+ у - 1
8
y2
X = -
8 Y+1
Answer:
1st option,
y = x²/8 + x - 1
Answered by GAUTHMATH
Let a submarine be at a constant depth of 5 km. It is headed in the direction of a lighthouse. If the distance between the submarine and the base of the lighthouse is decreasing at a rate of 24 km/h when the sub is 13 km away from the base, then what is the speed of the submarine
Answer:
24 km/h
Step-by-step explanation:
Given:
Constant speed of submarine = 24 km/h
Depth under sea = 5 km
Distance of submarine from lighthouse = 13 km
Find:
Speed of the submarine
Computation:
At steady speed, the distance between both the submarine and the lighthouse base decreases at a rate of 24 km/hr.
So, when it is 13 kilometres from its starting point, the speed remains constant at 24 kilometres per hour.
I'm interval notation please
9514 1404 393
Answer:
(-2, 4]
Step-by-step explanation:
-21 ≤ -6x +3 < 15 . . . . given
-24 ≤ -6x < 12 . . . . . . subtract 3
4 ≥ x > -2 . . . . . . . . . . divide by -6
In interval notation, the solution is (-2, 4].
__
Interval notation uses a square bracket to indicate the "or equal to" case--where the end point is included in the interval. A graph uses a solid dot for the same purpose. When the interval does not include the end point, a round bracket (parenthesis) or an open dot are used.
Please helppppp!!!!!!!
Answer:
[tex](x-2)^2+(y+2)^2=9[/tex]
Step-by-step explanation:
The general equation for a circle is the following:
[tex](x-a)^2+(y-b)^2=c[/tex]
Where (a, b) is the center of the circle and ([tex]\sqrt{c}[/tex]) is the radius of the circle. In order to shift the function to the right, one has to add to the (a) value; to move it to the left one has to subtract from it. Similarly, to move the function up, one has to add to the (b) value, to move it down, one has to subtract from it. Apply this to the given function:
[tex](x+1)^2+(y-2)^2=9[/tex]
The center of this circle is (-1, 2). The circle is shifted to the right by (3) units, and down by (4). Thus the center is also shifted by these values:
(-1, 2)
Right by (3): (-1 + 3) = 2
Down by (4): (2 - 4) = -2
Substitute back into the function:
[tex](x-(2))^2+(y-(-2))^2=9\\\\(x-2)^2+(y+2)^2=9[/tex]
To mix weed killer with water correctly, it is necessary to mix 18 teaspoons of weed killer with 3 gallons of water. How many gallons of water are needed to mix with the entire box if it contains 24 teaspoons of weed killer
determine if it is a function, find the domain and the range.
{(9,−3),(4,−2),(1,−1), (0,0),(1,1),(4,2),(9,3)}
Answer:
it is not function
Step-by-step explanation:
because,
first of all,what do mean function
A function is a relation in which each element of the domain corresponds to exactly one
element of the range.
based on this description
Since the domain element 1 is assigned to two different values in the range, -1 and 1, so that it is
not a function
Please show work. The way that you solve for surface area and vol confuse me.
Answer:
search up the formula
Step-by-step explanation:
Please Help!
Use the function f(x) to answer the questions
f(x) = 5x^2 + 2x - 3
Part A: What are the x-intercepts of the graph of f(x)? Show your work (5 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show
your work (5 points)
Part 2: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph (5 points)
9514 1404 393
Answer:
A: -1, 3/5
B: (-1/5, -3 1/5)
2: plot the given points and draw a curve through them.
Step-by-step explanation:
Part AThe x-intercepts are most easily found from a graph of the function. I like the Desmos graphing calculator for this purpose. The x-intercepts are -1 and 3/5.
You can also find the x-intercepts by factoring the function.
f(x) = 5x^2 +5x -3x -3 = 5x(x +1) -3(x +1) = (5x -3)(x +1)
The x-intercepts are the values of x that make the factors zero:
5x -3 = 0 ⇒ x = 3/5
x +1 = 0 ⇒ x = -1
__
Part BThe vertex is on the axis of symmetry, which is the vertical line at the value of x halfway between the zeros. (-1 +3/5)/2 = (-2/5)/2 = -1/5
The value of f(x) there is ...
f(-1/5) = (5(-1/5) +2)(-1/5) -3 = (-1 +2)(-1/5) -3 = -1/5 -3 = -3 1/5
The vertex is (-1/5, -3 1/5).
__
Part 2The easiest step to take to graph the function is to type it into a graphing calculator (see attached).
If you're graphing this by hand, the three points given in parts A and B will be on the graph. The leading coefficient in the function is 3, so the x^2 parent function is vertically stretched by a factor of 3. This can make it a little more difficult to find points that lie on the graph.
Recognizing that the vertex form equation is ...
f(x) = 3(x +1/5) -3 1/5
I might choose x-values that are -1/5 ± 1/2 to get y-values that are -3 1/5 + 3/4. And, x = -1/5 ± 1 ⇒ y = -3 1/5 +3.
How many proportional relationships are shown in the coordinate plane below?
Answer:
The answer is B) There is one proportional relationship
Step-by-step explanation:
The green line (the one at the top) does not go through the origin. This is not a proportional relationship.
Problem: It does not go through 0,0
----------------------------------------------------------------------------------------------------------------
The blue line (the one in the middle) is a straight line through the origin. This is a proportional relationship.
Reason: It goes through 0,0
----------------------------------------------------------------------------------------------------------------
The purple line (the one at the bottom) does not go through the origin. This is not a proportional relationship.
Problem: It does not go through 0,0
----------------------------------------------------------------------------------------------------------------
Conclusion: Since the green and purple lines are not proportional but the blue line is, this means only 1 line is proportional.
Note:
I know my answer is very late but I wanted to help anyone who needs it for future reference.
c) The exponential model A = 513.5e0.009t describes the population, A, of a
country in millions, t years after 2005. Use the model to determine when the
population of the country will be 602 million.
Answer:
zotfnKhxitfupoydkfslfndckv
Find the missing side round to the nearest tenth
======================================================
Work Shown:
sin(angle) = opposite/hypotenuse
sin(29) = x/24
24*sin(29) = x
x = 24*sin(29) ..... exact value
x = 11.635430885912 .... approximate value
x = 11.6
To get the approximate value, you'll need a calculator. Make sure the calculator is in degree mode.
4. Jack started packing the box shown with 1-centimeter cubes.
- cubic centimeter
Select all the true statements below.
A. Jack needs to add 2 more layers to fill the box.
B. Jack packed 16 cubes into the bottom of the box.
The box is 8 centimeters long.
The box is 3 centimeters high.
E.) The volume of the box is 32 cubic centimeters.
F. The volume of the box is 16 centimeters.
Answer:
if I am not mistakedn the answe id e
CAN SOMEONE HELP ME PLEASE CAN YOU FIGURE OUT WHERE I PUT 4 PI ON THE NUMBER LINE
Answer:
see below
Step-by-step explanation:
Pi is approximately 3.14
4*3.14 =12.56
So about halfway between 12 and 13
The polygons in each pair are similar. Find the missing side length.
Let missing side be x
If both polygons are similar
[tex]\\ \sf\longmapsto \dfrac{3}{4}=\dfrac{18}{x}[/tex]
[tex]\\ \sf\longmapsto 3x=4(18)[/tex]
[tex]\\ \sf\longmapsto 3x=72[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{72}{3}[/tex]
[tex]\\ \sf\longmapsto x=24[/tex]
