what is the sum of a and b?
Answer:
a=13, b=7
Step-by-step explanation:
You can use the exponent rule
[tex]3x^{a-5}y^{9-b}=3x^{8}y^{2}[/tex]
so [tex]x^{a-5}=x^{8}[/tex] so
a-5=8
a=13
[tex]y^{9-b} =y^{2}[/tex] so
9-b=2
b=7
Getaway Travel Agency surveyed a random sample of 454545 of their clients about their vacation plans. Of the clients surveyed, 212121 expected that they would go on 333 vacations in the next year. There are 516516516 Getaway Travel Agency clients.
Based on the data, what is the most reasonable estimate for the number of Getaway Travel Agency clients who expect to go on 333 vacations in the next year?
Answer:
The most reasonable estimate for the number of Getaway Travel Agency clients who expect to go on 3 vacations in the next year is 241.
Step-by-step explanation:
The best estimate for the proportion of clients who expect to go on 3 vacations is the same proportion of the sample.
Sample:
45 clients.
Of those, 21 expected to go on 3 vacations in the next year.
21/45 = 0.4667
Out of the 516 clients:
0.4667*516 = 240.8
Rounding up
The most reasonable estimate for the number of Getaway Travel Agency clients who expect to go on 3 vacations in the next year is 241.
A box contains 20 different balls numbered from 1 to 20 (different balls have different numbers). At each step, we select a ball uniformly at random, record the number on it, and put it back in the box. This experiment is repeated 10 times. Find the probability that all the numbers recorded were distinct.
Answer:
P = 0.0655
Step-by-step explanation:
First, we are going to calculate the number of ways in which we can select the 10 balls. This is calculated using the rule of multiplication as:
[tex]T=20*20*20*20*20*20*20*20*20*20\\T=20^{10}\\T=1.024*10^{13}[/tex]
Because we have 20 different balls every time and the experiment is repeated 10 times.
Then, from that [tex]1.024*10^{13}[/tex] ways, there are C ways where all the numbers recorded are distinct. It is calculated as:
[tex]C = 20*19*18*17*16*15*14*13*12*11\\C = 6.704*10^{11}[/tex]
Because, the first time, we have 20 options, the second time, we can just select 19 balls because we can not repeat the numbers, the third time, we can just select 18 balls and we need to keep doing this until get to the 10th time.
Finally, the probability that all the numbers recorded were distinct is calculated as C/T and it is equal to:
[tex]P=\frac{C}{T}=\frac{6.704*10^{11}}{1.024*10^{13}} =0.0655[/tex]
Factorize x squared - 1x +10 =0
Answer:
no solution exists:
Step-by-step explanation:
x²−1x+10=0
Step 1: Simplify both sides of the equation.
x²−x+10=0
Step 2: Subtract 10 from both sides.
x²−x+10−10=0−10
x²−x=−10
Step 3: The coefficient of -x is -1. Let b=-1.
Then we need to add (b/2)^2=1/4 to both sides to complete the square.
Add 1/4 to both sides.
x²−x+ 1/4=−10+ 1/4
x²−x+ 1/4=−39 /4
Step 4: Factor left side.
(x -1/2)² = −39 /4
Step 5: Take square root.
x −1 /2 =±√ −39 /4
Step 6: Add 1/2 to both sides.
x =−1/2 + 1/2 = 1/2 ±√ -39/4
x = 1/2 ±√ -39/4
No real solutions.
There are 8 sophomores on the academic team. At the last competition, they each took the math test. Their scores were 82%,
92%, 76%, 72%, 92%, 74%, 80%, and 78%. What was the median math score of the sophomores?
79%
82%
87%
92%
Answer:
79%
Step-by-step explanation:
median is the middle no.
arrange the scores in descending order
72,74,76,(78,80),82,92,92
78+80, divide 2= 79%
The expression (3x2 + 2xy + 7) − (6x2 − 4xy + 3) is Equivalent to −3x2 − 2xy + 4 3x2 − 2xy + 4 −3x2 + 6xy + 4 3x2 − 6xy − 4
Answer:
[tex]-3x^2+6xy+4[/tex]
Step-by-step explanation:
[tex](3x^2+2xy+7)-(6x^2-4xy+3)=\\\\3x^2-6x^2+2xy+4xy+7-3=\\\\-3x^2+6xy+4[/tex]
Hope this helps!
Answer:
3x2-6xy
Step-by-step explanation:
I think i dont know
you are emailing your cousin a care package in a box shaped like a cube. Each side of the box is 6 inches long. You mist cover the box with brown wrapping paper in order for the post office to accept it. What is the minimum amount of brown wrapping paper you will need in order to completely cover the box
==========================================================
Work Shown:
x = side length of cube = 6 inches
SA = surface area of cube
SA = 6x^2
SA = 6*6^2
SA = 6*36
SA = 216 square inches
------------
side note: if you have a rectangular box that isn't a cube (ie the length, width, and/or height aren't all the same), then you would use this formula to get the surface area
SA = 2*(L*W+L*H+W*H)
where L,W,H are the length, width and height respectively.
37 POINTS pls help time limit 13 minute left...
Answer:
first 3
Step-by-step explanation:
Answer:
A B C and D are all true not the last one!
Step-by-step explanation:
Pls ANSWER LOOK AT THE PHOTO ANSWER ASAP
Answer:
Answer number one, x < 7/12
Answer:
A
Step-by-step explanation:
If you make he denominators equal to each other (in this case 12) the new fractions would be 3/12 and 10/12. Then you would subtract 3/12 from both sides making 7/12 on the right side. The inequality remains facing the same direction, making the answer A or x<7/12.
Find the value of this expression if X=-7
Answer:
-9
Step-by-step explanation:
[tex](-7)^{2}[/tex] = 49
when you have a negative number to any power make sure you plug it in correctly into the calculator.
[tex]\frac{49+5}{-7+1}[/tex] = [tex]\frac{54}{-6}[/tex]
54÷-6= -9
I hope this helps
Answer:
[tex]-9[/tex]
Step-by-step explanation:
[tex]\frac{x^2+5}{x+1}[/tex]
If [tex]x=-7[/tex] then:
[tex]\frac{-7^2+5}{-7+1} =\\\\\frac{49+5}{-6} =\\\\\frac{54}{-6} =\\\\-9[/tex]
The expression equals [tex]-9[/tex] if [tex]x=-7[/tex]
Complete the statements about series A and B. Series A: 10+4+ 8/5 + 16/25 + 32/125 + ... Series B: 1/5+ 3/5 + 9/5 + 27/5 + 81/5 + ... Series ____ has an r value of ___ where 0 < |r| < 1 . So, we can find the sum of the series. The sum of the series is ___.
Answer:
Series "A" has an r value of "2/5" where 0 < |r| < 1 . So, we can find the sum of the series. The sum of the series is "50/3".
Step-by-step explanation:
To find the r (rate) of each series, we can divide one term by the term before:
Series A: 4 / 10 = 2/5
Series B: (3/5) / (1/5) = 3
So the series A has an r value between 0 and 1, so we can find the sum of the series.
The sum is given by the formula:
Sum = a1 / (1 - r)
Where a1 is the first term. So we have that:
Sum = 10 / (1 - (2/5))
Sum = 10 / (3/5)
Sum = 10 * (5/3) = 50/3
Answer:
Series "A" has an r value of "2/5" where 0 < |r| < 1 . So, we can find the sum of the series. The sum of the series is "50/3".
Find the equation of a line parallel to y = 2x + 4 that goes through the point (2,5)
Answer:
y= 2x+1
Step-by-step explanation:
Line parallel to y = 2x + 4
And that goes through the point (2,5)
-----------
Parallel lines have equal slope, so it will be in the form of y= 2x+b
Let's find the value of y-intercept (b) by using the given point:
5= 2*2+bb= 5-4b= 1So the line is: y= 2x+1
The list shows numbers in order from least to greatest. Negative 34, negative 2 and three-fourths, blank, negative 1.5, 0, 2.3, 10, 25 and one-fifth Which is an integer that can be inserted on the blank line in the list?
Options
-2.5-2[tex]-1\dfrac{9}{10}[/tex]-1Answer:
(B) -2
Step-by-step explanation:
Given the list
[tex]-34.-2\dfrac{3}{4} ,x, -1.5,0,2.3,10,25\dfrac15[/tex]
This list has been arranged in order from the least to the greatest.
We are required to find an Integer that can be inserted on the blank line (I have used x) in the list.
An integer is defined as a positive or negative whole number.
Out of the given options, only -1 and -2 are integers. However:
-1 is greater than -1.5Therefore, it cannot be our result.
The correct answer is -2.
Answer:
-2 i did i what he said then revewied my quiz and it was right
Step-by-step explanation:
The point-slope from of a line that has a slope of -2 and passes through the point (5,-2)
Step-by-step explanation:
y + 2. = -2(x - 5)
y + 2 = -2x + 10.
y = -2x + 8
find the value of each trigonometric ratio part 3
Answer:
hope this helps you
Solve the equation.
-9x + 1 = -x + 17
Answer:
The value of [tex]x[/tex]:
[tex]x = -2[/tex]
Step-by-step explanation:
Find the value of [tex]x[/tex]:
[tex]-9x + 1 = -x + 17[/tex]
-Add both sides by [tex]x[/tex]:
[tex]-9x + 1 + x = -x + x + 17[/tex]
[tex]-8x + 1 = 17[/tex]
-Subtract both sides by [tex]1[/tex]:
[tex]-8x + 1 - 1 = 17 - 1[/tex]
[tex]-8x = 16[/tex]
Divide both sides by [tex]-8[/tex]:
[tex]\frac{-8x}{-8} = \frac{16}{-8}[/tex]
[tex]x = -2[/tex]
So, the final answer would be [tex]x = -2[/tex] .
Answer:
x=−2
Step-by-step explanation:
−9x+1=−x+17
Add x to both sides.
−9x+1+x=−x+17+x
−8x+1=17
Subtract 1 from both sides.
−8x+1−1=17−1
−8x=16
Divide both sides by -8.
−8x/-8 = 16/-8
Answer:
x=−2
use factoring to solve
x^2-2x-35=0
Answer:
I'm sorry I don't have an answer but for all future math work you should download photomath on your phone it's rly good
Answer:
The solution set of the quadratic equation is
x = {7, -5}
Step-by-step explanation:
Given the quadratic equation
[tex]$ x^2 - 2x -35 = 0 $[/tex]
We need to factor this equation
So you need two numbers such that
a + b = -2
and
a×b = -35
How about -7 and 5?
-7 + 5 = -2
-2 = -2
and
-7×5 = -35
-35 = -35
(x - 7)(x + 5) = 0
(x - 7) = 0
x = 7
and
(x + 5) = 0
x = -5
Therefore, the solution set of the quadratic equation is
x = {7, -5}
Verification:
Plug 7 into the quadratic equation
[tex]x^2 - 2x -35 = 0 \\\\(7)^2 - 2(7) -35 = 0 \\\\49 - 14 - 35 = 0 \\\\49 - 49 = 0\\\\0 = 0[/tex]
Plug -5 into the quadratic equation
[tex]x^2 - 2x -35 = 0 \\\\(-5)^2 - 2(-5) -35 = 0 \\\\25 + 10 - 35 = 0 \\\\35 - 35 = 0\\\\0 = 0[/tex]
please help me thankyou lol
Answer:
Yes, they are congruent
Step-by-step explanation:
They are congruent because they both have same length sides
f(x) is a function true or false
Answer:
Depends on the x value
Step-by-step explanation:
f(x) can only be a function if the x values are not repeating.
The set of ordered pairs (–1, 8), (0, 3), (1, –2), and (2, –7) represent a function. What is the range of the function?
Answer:
{y: y = –7, –2, 3, 8}
Step-by-step explanation:
On a coordinate plane, a parabola opens upward. It has a vertex at (0, 0), a focus at (0, 1.5) and a directrix at y = negative 1.5. Which equation represents the parabola shown on the graph? y2 = 1.5x x2 = 1.5y y2 = 6x x2 = 6y
Answer:
d) The equation of the standard parabola
x² = 6 y
Step-by-step explanation:
The given directrix is y= -31.5
The equation of the parabola is of the form x² =4 a y
Given focus (0,1.5) , Here a= 1.5
The equation of the standard parabola
x² = 4 a y
x² = 4 (1.5)y
x² = 6 y
Conclusion:-
The equation of the standard parabola
x² = 6 y
The equation that represents the parabola shown on the graph is x∧2 = 6 y
What is a parabola?
A parabola is known as a plane curve that starts from a point and moves such that its distance from a fixed point is equal to its distance from a fixed line.
The graph shows a vertical parabola opened upwards with the vertex at the origin.
How to determine the equation
The equation of the parabola from the graph is;
x∧2 = 4ay
The equation of the directrix;
y = -a = -1. 5
Thus, the value of a = 1.5
Then, substitute the value of a = 1.5 in the equation deduced from the graph
x∧2 = 4 × (1.5) × y
x∧2 = 6 y
Therefore, the equation that represents the parabola shown on the graph is x∧2 = 6 y
Learn more on parabola here:
https://brainly.com/question/4061870
#SPJ2
−4x−6=−5y+2 Write a formula for g(x) in terms of x
Answer:
4/5x + 8/5 = g(x)
Step-by-step explanation:
−4x−6=−5y+2
Solve for y
Subtract 2 from each side
−4x−6-2=−5y+2-2
-4x -8 = -5y
Divide each side by -5
-4x/-5 -8/-5 = -5y/-5
4/5x + 8/5 = y
Replace y with g(x)
4/5x + 8/5 = g(x)
You have $60 and your sister has $120. You are saving $14 per week and your sister is saving $10 per week. How long will it be before you and your sister have thr same amount of money? What amount would you have the same ?
Answer:
15 weeks
The amount of money is 270
Step-by-step explanation:
You: 60 +14x
Sister: 120+10x
Set them equal to each other
60+14x = 120+10x
Subtract 10x from each side
60+4x= 120
Subtract 60 from each side
4x= 60
Divide by 4
4x/4 = 60/4
x = 15
15 weeks
The amount of money is 120+10*15 = 120+150 = 270
Answer:
15 weeks
$270
Steps:
1: 60+14x=120+10x
2: 4x=60
3: x=15 weeks
4: Amount= 60+14*15= $270
Description:
The first step is to get the money u have that is $60 plus it with the saving u have that is $14 answer will equal as 120+10x as a equation. Now simplify the equation 4x=60. You will get x=15 that will be the weeks. And now get 60+14 times it by 15 answer will equal as $270. So 15 weeks and $270 is the answer.
Please mark brainliest
Hope this helps.
I need help please! I’m really confused about it
The answer is 1 and 3
2 prime factorization of 44
Answer:
2*2*11
Step-by-step explanation:
44 = 4*11
But 4 isn't prime
= 2*2*11
All of these are prime
What is the average rate of change for this exponential function for the
interval from x = 2 to x = 4?
it is two i think. hope i could help
The value of zlatans house has increased by 7% his house is now valued at £749 000 work out the value of the house before the increase
Answer:
Let x be the value of the house before increase
Since it's increases add 7% to the overall 100%
107/100x = 749000
x = 700000
The value of the house before increase is £700000.
Hope this helps.
Can anyone help me. Please
Answer:
how can I help?
Step-by-step explanation:
with what?
If 14x = 6(–4 + x), then x = ?
Answer:
Step-by-step explanation:
Expand first
-24+6x=14x
-6x on both sides
-24=8x
/x on both sides
X=-3
Answer: [tex]x=-3[/tex]
Step-by-step explanation:
You want to apply the distributive property. Or, you could just divide by 6 on both sides. Ill just apply the distributive property:
[tex]14x = -24 +6x[/tex]
Now subtract 6x from both sides to get:
[tex]8x = -24[/tex]
Divide both sides by 8 to get x = -3
If f(x) = 1 - X, which value is equivalent to [f(I)]?
О0
0 1
O v2
Ov-1
Answer:
0
Step-by-step explanation:
Here, given the function f(x), we want to calculate f(1)
Mathematically, this means we shall substitute 1 for the value of x in that function.
Thus, given F(x) = 1-x
Then F(1) would be = 1-1 = 0