The nth term of a sequence is n²+20
a) Work out the first three terms of the sequence.?
b) How many terms in the sequence are less than 50 ?
In a Science class, there are thirty students. Ten are males and twenty are females. On the last quiz, three males and six females earned an A. What is the approximate probability of selecting a male or a student that earned an A on the quiz?
0.53
0.10
0.43
0.63
At what values of x does the graph of y=e−x+2xe−x+x2e−x have a point of inflection?
Where the voice rises and falls. But inflection also describes a departure from a normal or straight course.
What is inflection point and how to find an inflection point?
Inflection points for the given equation x^2e^{-2x} are
f'(x) =[tex]2x2xe^{(-2x)}-2{(x2)} e^{(-2x)}[/tex]
f'(x) =[tex]-2(x-1)xe {(^-2x)}[/tex]
The point of inflection, also known as the inflection point, is when the function's concavity changes. Changing the function from concave down to concave up, or vice versa, signifies that. In other words, an inflection point is the location at which the rate of slope shift from a growing to a decreasing way, or vice versa, occurs. There is no doubt that those positions are neither local maxima nor minima. They are fixed points.On a curve, an inflection point is when the concavity changes, according to definition. (i.e., a shift in the sign of curvature). We are aware that the function is concave up if f " > 0, and that it is concave down if f " 0. The point of inflection on a graph is where the function switches from positive to negative, or from negative to positive, at a particular value of x = c.x= -b±√(b^2 - 4ac)/2a
x=4±√(16+16)4
x=4±4√2/4
x=[tex]\sqrt{2+2/2}[/tex]
x=[tex]\sqrt{2-2/2}[/tex]
We get,
x=[tex]\sqrt{(2+2)/2^{2}*\sqrt{2+2}[/tex]
so, inflection points are,
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the perimeters of the square and the rectangle below are the same. Write and solve an equation to find the value of x area= 121inches squared the rectangle is 3x and x-2
the area of the square is 121 in. Squared.
The equation is written as 3x + x - 2 = 11(2). Then the value of the variable 'x' is 6.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The borders of the square and the square shape underneath are something similar.
Perimeter of the square = Perimeter of the rectangle
4a = 2(L + W)
2a = L + W
If the area of the square is 121 square inches. Then the side length of the square is given as,
a² = 121
a = 11 inches
And the dimension of the rectangle is 3x and x - 2. Then the equation is given as,
3x + x - 2 = 11 (2)
4x - 2 = 22
4x = 24
x = 6
The equation is written as 3x + x - 2 = 11(2). Then the value of the variable 'x' is 6.
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the first term of an arithmetic sequence is -27. the common difference of the sequence is 6. What is the sum of the first 50 terms
Answer: 6000
Step-by-step explanation:
The formula for the first [tex]n[/tex] terms of an arithmetic sequence with first term [tex]a[/tex] and common difference [tex]d[/tex] is [tex]S_n=\frac{n}{2}[2a+(n-1)d][/tex].
In this question, [tex]a=-27, d=6, n=50[/tex].
So, [tex]S_{50}=\frac{50}{2}[2(-27)+(50-1)(6)]=6000[/tex].
Write a
system of equations with the solution (4, -3).
Answer:
A (0, -3) translated to the right 4 units.
Step-by-step explanation:
If you go right 4, you get (4, -3)
PLS HURRY The chances of finding a rare card in a pack of trading cards can be represented with the equation y equals one-fifteenth times x, where y represents the number of rare trading cards and x represents the number of packs of trading cards. Determine how many rare trading cards you would find if you bought 90 packs of trading cards.
6
15
1,350
one-fifteenth
If you bought 90 packs of trading cards then Rare trading cards are 6
What is probability?The number of favorable events to all the events in an experiment is the ratio that makes up the probability formula. Theoretical probability, Experimental probability, and Axiomatic probability are the three categories into which probability can be divided.
If the conditions are met, Y = 1/15 * X = 90 , then Y = 1/15 x 90 Y = 6.
A deck of cards has 52 cards. Therefore, 52 outcomes overall.
The number of positive results is 4 (as there are 4 kings in a deck)
Hence, there is a chance that this will happen.
P(E) = 4/52 = 1/13.
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using excel lookup functions, add new fields to the invoice data by bringing in information from the other data sheets
To pull values from another worksheet, we need to follow these steps:
Select cell C3 and click on it.
Insert the formula: =VLOOKUP(B3,'Sheet 2'!$ B$3:$C$7,2,0)
Press enter.
Drag the formula down to the other cells in the column by clicking and dragging the little “+” icon at the bottom-right of the cell.
How do I add a LOOKUP field in Excel?
Open Design View on the table. Click a cell in the Field Name column in the first available empty row, and then type a field name for the lookup field. Select Lookup Wizard from the drop-down list by clicking the arrow after clicking in the Data Type column for that row.
To compute values in several columns, the VLOOKUP function may be used in conjunction with other functions like the Sum, Max, or Average. Since this is an array formula, all we need to do to make it function is hit CTRL+SHIFT+ENTER at the conclusion of the formula.
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Express with an exponent.
125 =
A
5/3
с 3/5
B 5/5
Answer:A
Step-by-step explanation: 5 to the power of 3 is 5x5x5 which is 25x5 which then equals 125
which ordered pair is the solution y=(1/3)x-4
To find the ordered pair that is the solution to the equation y = (1/3)x - 4, we need to solve the equation for x.
To do this, we can first add 4 to both sides of the equation to get y + 4 = (1/3)x. Then, we can multiply both sides of the equation by 3 to get 3y + 12 = x.
Therefore, the ordered pair that is the solution to the equation y = (1/3)x - 4 is (12, 3y).
Note that the value of y is unknown in this solution. In order to find the exact solution, we would need to know the value of y. For example, if y = 2, then the ordered pair that is the solution to the equation y = (1/3)x - 4 is (12, 6).
The distance it takes to stop a car varies directly as the square of the speed of the car. If it takes 112 feet for a car traveling at 40 miles per hour to stop, what distance is required for a speed of 65 miles per hour?
*
The distance it takes to stop a car varies directly as the square of the speed of the car. If it takes 112 feet for a car traveling at 40 miles per hour to stop, what distance is required for a speed of 65 miles per hour?
*
Answer:
182 feet
Step-by-step explanation:
Taking the fact that 112/40 = 2.8, you would need to multiply the miles per hour by 2.8 to get the feet needed.
Why is that, well I cant really explain...its just math and it works out /:
A random sample of size 36 is taken from a population with mean µ = 15 and standard deviation σ = 8. What is the probability that the sample mean is greater than 16?
Answer:
Below
Step-by-step explanation:
Deleted
Data regarding fuel efficiency of an 18-wheel truck were collected. The graph shows the correlation between the average speed above 40 miles per hour (in miles per hour) and the money spent on gas (n dollars): Estimate the average rate of change from x = 5 to x = 9.
The average rate of change of the function at the interval x = 5 to x = 9 is 1.25
How to determine the average rate of changeThe interval is given as
x = 5 to x = 9
From the question (see attachment), we have the following parameters that can be used in our computation:
x = 5 and y = 15
x = 9 and y = 20
This means that
f(5) = 15 and f(9) = 20
The average rate of change is then calculated as
Average rate of change = [f(9) - f(5)]/[9 - 5]
Substitute the known values in the above equation, so, we have the following representation
Average rate of change = [20 - 15]/[9 - 5]
Evaluate
Average rate of change = 1.25
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If the difference follows the Normal model, what's the probability that the small bowl contains more cereal than the large one?
The probability that the small bowl contains more cereal than the large one is 0.0228.
Given :
The amount of cereal that can be poured into a small bowl varies with a mean of 1.5 ounces and a standard deviation of 0.3 ounces. A large bowl holds a mean of 2.5 ounces with a standard deviation of 0.4 ounces. You open a new box of cereal and pour one large and one small bowl.
we know that,
z = x - μ / σ
here
x = 0
μ = 1
σ = 0.5
= 0 - 1 / 0.5
= -1/0.5
= -1 / 05 / 10
= -1 * 10 / 5
= -10 / 5
= -2
if z = -2 then p value = 0.0228
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Full question :
The amount of cereal that can be poured into a small bowl varies with a mean of 1.5 ounces and a standard deviation of 0.3 ounces. A large bowl holds a mean of 2.5 ounces with a standard deviation of 0.4 ounces. You open a new box of cereal and pour one large and one small bowl.
If the difference follows the Normal model, what's the probability that the small bowl contains more cereal than the large one?
Triangle congruence
Will give brainliest
Thank you so much, I have a test tomorrow so I really appreciate it. Answering again so I can give you brainliest.
What’s the slope for x<-3
Answer:As you can see, this line is vertical! It goes directly up. We know that because the equation says that X is equal to -3. It is telling us that no matter what the Y value is, X will be -3.
Step-by-step explanation:
The equation to find slope is to take two points
(A,B) and (C,D) and to do the following equation: D−B
______
C−A
So, let's take two points. Let's say that Y is equal to 3 and 2. In that case, since X is always -3, our points would be (−3,2) and (−3,3).
Now, let's substitute into our formula.
3−2 1 1
------ = ----- = ---
3 (−3) (subtract) -3 + 3 0
As you can see, the final slope is 1/0
. If you put that into your calculator, it will come out as undefined, because any number divided by zero is undefined. And so your slope for any vertical line is undefined.
hi if someone wouldn’t mind doing this that would be great!!! 100 points im just desperate i need a whole bunch of stuff done tomorrow, thank you! :)
Answer:
1. y=2x−5
2. y=-x-4
3. y=-1/2x+1
Step-by-step explanation:
First Question:
We are given (3, 1) and (1, -3)
The slope is the difference of y-values over x-values. From this we get:
(1−−3)/(3−1)=4/2=2
Now, we want to find the y-intercept. To do this, we plug our slope and one of our points into the slope intercept equation: y=mx+b
Plugging in (3, 1) gives us 1=3∗2+b ⇒ b=1−6 = −5
We have our slope and y-intercept now, so the equation is y=2x−5.
Second Question:
We are given (-4, 0) and (1, -5)
The slope is
(-5-0)/(1--4)=-5/5=-1
Now, we want to find the y-intercept. To do this, we plug our slope and one of our points into the slope intercept equation: y=mx+b
Plugging in (-4, 0) gives us 0 = -1∗-4+b ⇒ b = -4
We have our slope and y-intercept now, so the equation is y=-x-4.
Third Question:
We are given (-6, 4) and (-2, 2)
The slope is
(4-2)/(-6--2)=2/48=-1/2
Now, we want to find the y-intercept. To do this, we plug our slope and one of our points into the slope intercept equation: y=mx+b
Plugging in (-2, 2) gives us 2 = -1/2∗-2+b ⇒ b = 2-1 = 1
We have our slope and y-intercept now, so the equation is y=-1/2x+1
can someone help quick? someone gave me the answer but didn’t explain. what’s the inequality? where do i graph this? please give the right answers only
An inequality that represents the height h, in inches, of a person allowed to ride rollar coaster is h ≥ 48
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.
Let h represent for the height of any member allowed to ride rollar coaster
From the question we know that everyone's height must be greater that 48 inches.
It means the inequalities would be
h ≥ 48 tall inches
Thus, an inequality that represents the height h is h ≥ 48
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If g'(x) = (2-x)x² So how many extreme points does the function g(x) has?
There are 3 extreme points does the function g(x) = (2 - x) x².
What is Function?A relation between a set of inputs having one output each is called a function.
Given that;
The function is,
⇒ g ' (x) = (2 - x) x²
Now,
Since, The function is,
⇒ g ' (x) = (2 - x) x²
We know that;
The extreme points are find as;
⇒ g ' (x) = 0
So, We get;
⇒ g ' (x) = 0
⇒ (x - 2) x² = 0
This gives two values as;
⇒ (x - 2) = 0
⇒ x = 2
And, x² = 0
⇒ x = 0, 0
Thus, The extremes values are;
⇒ x = 2 , 0, 0
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Sum of 3x + 2 and 8x
If u(x) = -2x² +3 and V(x) =
X
what is the range of (u.v)(x)?
The range of u(x) = {-15, -5,1,3,1, -5, -15} and range of v(x)= {-3,-2, -1,0,1,2,3} for the domain of x = { -3,-2,-1,0,1,2,3}
What is domain and range?The domain of a function is defined by the set of the values of independent variables and the ranges are the set of values of dependent variables.
The domains act as an input of function where ranges act as an output.
How to find domain and range?We select domain randomly as domain are the set of independent variables. But how will be the ranges must depend on the function given us.
we are given 2 function u(x) = -2x²+3 and v(x)
for the 1st function the set of domain and ranges are different, but the domain and ranges have the same values for the 2nd function.
we select domain x= {-3, -2, -1, 0, 1, 2, 3}
the ranges for u(x) ={ -15, -5, 1, 3, 1, -5 , -15}
because, u(-3) = -2(-3)²+3 = -15
u(-2) = -2(-2)²+3 =-5
u(0) = 3
similarly, for the same set of x value, v(-3) = -3
v(-2) = -2
v(0) =0
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Ramesh took a loan of Rs 50,000 from Urmila at the rate of 10% p.a. If he paid a
half of the principal and all the interest at the end of 3 years, in how many years
should he pay the remaining amount with total interest of Rs 20,000 from the
beginning?
Answer:
Below
Step-by-step explanation:
In three years the interest will be
50 000 * .1 * 3 = 15 000
He pays this and 25 000 so his remaining loan is 25 000
we want to know how long will it be before this remaining loan
incurs 5 000 interest ( for a total of 20 000)
25000 * . 1 * n = 5000 shows n = 2 years more
( 5 years from original loan date)
What is the solution to x2 – 9x < –8?
x < 1 or x > 8
x < –8 or x > 1
1 < x < 8
–8 < x < 1
Answer:
1 < x < 8
Step-by-step explanation:
x² - 9x + 8 < 0
(x-8)(x-1) = 0
x = 8
x = 1
these are the points where the parabola intercepts the x axis. We have to find when it is under x axis
1 < x < 8
1. Todd purchased a jumper for his infant son. The jumper clamps to the top of a door frame and has a spring from which the body of the jumper hangs to allow the infant to jump up and down. Included with the jumper are small weights, each identical in weight and size. The weights allow the user to adjust the initial height of the jumper by stretching the spring a certain distance. Todd adds 8 of the weights and notes the spring stretches 2 centimeters.
(a) According to Hook's Law, the amount that a spring is stretched, s, varies directly with the force applied to the spring by the weights, $F$. Write an equation that relates F and s for the spring on the jumper. (3 points)
F=ks 8=k 2
k=8/2 F=4 x
The equation that relates F and s for the spring on the jumper will be F=4x.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that, Todd increases the weights by 8 and observes a 2 cm spring extension. According to Hook's Law, the force exerted on a spring by the weights directly affects how much it is stretched, or s.
The equation that relates F and s for the spring on the jumper is obtained as,
F=ks
8=k×2
k=8/2
F=4 x
Thus, the equation that relates F and s for the spring on the jumper will be F=4x.
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12. The number of liters of fuel used on a trip
varies directly with the number of miles traveled. If
a 120 mile trip requires 12.5 liters of fuel, how
many liters are required for a 504 mile trip?
Answer:
Step-by-step explanation:
The graph shows a system of inequalities.
Graph of two inequalities.
Which system is represented in the graph?
y > x2 + 4x – 5
y > x + 5
y < x2 + 4x – 5
y < x + 5
y ≥ x2 + 4x – 5
y ≤ x + 5
y > x2 + 4x – 5
y < x + 5
The system of inequalities shown by the graph are
y > x² + 4x – 5y > x + 5How to identify inequality graphsThere are some points that help in interpreting inequality graphs.
The first part is to arrange the equation in the form so that y is the subject of the formula and to the left
Then watch out for dashed lines or solid lines
dashed lines means there is no equality sign in the inequality > OR <solid line means there is equality in the inequality ≤ OR ≥Another part is the shaded portion
shading above the line defines greater thanshading below the line defines less thanEquipped with tis information, it is clear that the two lines of the graph are both dashed and shaded above the line,
Hence we look out for equations having no equality sign in the inequality and due to the shading must be greater than.
This makes the first option the best choice
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Write a linear function f with f (0)
7 and f(3) = 1.
f(x) =
Answer:
f(x) = -2x +7
Step-by-step explanation:
The 2-point form of the equation for a line is suitable for this. For points (x1, y1) and (x2, y2), the equation is ...
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
For the given points (0, 7) and (3, 1), the equation is ...
y = (1 -7)/(3 -0)(x -0) +7
y = -6/3x +7 . . . . . . . . simplify.
We can use f(x) for y to get ...
f(x) = -2x +7
[tex]-16x^{\frac{-3}{2}[/tex]
The expression -16x^(-3/2) represents a term that has a coefficient of -16 and a variable x raised to the power of -3/2.
What is an expression?Generally, The expression -16x^(-3/2) represents a term that consists of a coefficient of -16 and the variable x raised to the power of -3/2.
In general, the exponentiation operator (^) represents the idea of raising a number (called the base) to a certain power (called the exponent). For example, x^2 means "x raised to the power of 2" and can be calculated as x * x = x^2.
Similarly, x^3 means "x raised to the power of 3" and can be calculated as x * x * x = x^3.
The exponent -3/2 means that the base (in this case, x) is raised to the power of -3/2. This can be simplified as follows:
x^(-3/2) = 1 / x^(3/2) = 1 / (x^(3/2))
The expression -16x^(-3/2) can then be simplified as follows:
-16x^(-3/2) = -16 * 1 / x^(3/2) = -16 / x^(3/2)
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The complete Question was not found
Solve the following inequalities 1/2 x ≥ 3
x[tex]x\geq 6[/tex].
Step-by-step explanation:1. Write the expression.[tex]\frac{1}{2}x \geq 3[/tex]
2. Divide both sides by 1/2.[tex]\frac{\frac{1}{2}}{\frac{1}{2} } x\geq \frac{3}{\frac{1}{2} }[/tex]
Dividing by a fraction of the same as multiplying by its multiplicative inverse. Since the multiplicative inverse of 1/2 is 2/1, we may rewrite as:
[tex]\frac{2}{1} *\frac{1}{2} x\geq \frac{2}{1} *3[/tex]
3. Simplify.[tex](1)x\geq(6)\\ \\x\geq6[/tex]
4. Verify.[tex]\frac{1}{2}(6) \geq 3\\ \\3\geq 3[/tex]
Correct!
5. Express the final result.x[tex]x\geq 6[/tex].
PLEASE HELP!!
At school athletic events you can buy 3 drinks and 2 hot dogs for $4.80, or you can buy 1 drink and 1 hot dog for $2.00. How much does 1 hot dog cost?
A. $0.80
B. $0.96
C. $1.00
D. $1.20
1 hot dog cost is $1.20 .
What is costs?
A cost is the value of money that has been expended to produce something or provide a service and is therefore no longer available for use in production, research, retail, and accounting. In the case of an acquisition cost, the money spent on the acquisition is considered the cost.
Let's say that each drink costs $x and each hot dog costs $y.
Using the provided information, 3 drinks and 2 hot dogs cost $4.80. In equation form, it reads as follows:
3 x+2 y=4.80
1 drink and 1 hot dog costs $2.00. In equation form, we can write it as:
x+y=2
x=2-y
Using this value of x in first equation, we get:
3(2-y)+2 y=4.80
6-3 y+2 y=4.80
6-y=4.80
y=6-4.80
y=1.20
Thus the cost of one hot dog is 1.20$
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