r should be 4/7. You're comparing the given series to a geometric series that converges. By the limit comparison test, you have
[tex]\displaystyle\lim_{n\to\infty}\frac{\frac{4^n+7}{7^n}}{\frac{4^n}{7^n}}=\lim_{n\to\infty}\frac{4^n+7}{4^n}=\lim_{n\to\infty}\left(1+\frac7{4^n}\right)=1[/tex]
and since this limit is positive and finite, and the series you're comparing to is convergent, then the first series must also be convergent.
Solve the system of equations.
y = x + 4
y = x2 + 2
Answer:
(2,6) and (-1,3)
Step-by-step explanation:
Hi there!
We're given the system of equations:
y=x+4
y=x²+2
and we need to solve the system
You may first notice that both equations are equal to y, so we can set them to equal each other via a property known as transitivity (if a=b and b=c, then a=c)
x²+2=x+4
subtract x from both sides
x²-x+2=4
subtract 4 from both sides
x²-x-2=0
we can factor the polynomial
the numbers that add up to -1 and multiply to get -2 are -2 and 1
(x-2)(x+1)=0
solve
x=2, x=-1
both values of x work- so we'll have 2 solutions in this case
now we need to solve for y; we can do this by substituting the value of x into one of the equations to solve for y
let's use y=x+4
so if we'll use x=2,
y=2+4
y=6
one solution will be (2,6)
and if we use x=-1
y=-1+4
y=3
and the other will be (-1,3)
Hope this helps! :)
The owner of a small deli is trying to decide whether to discontinue selling magazines. He suspects that only 9.8% of his customers buy a magazine and he thinks that he might be able to use the display space to sell something more profitable. Before making a final decision, he decides that for one day he will keep track of the number of customers that buy a magazine. Assuming his suspicion that 9.8% of his customers buy a magazine is correct, what is the probability that exactly 5 out of the first 10 customers buy a magazine? a) 0.00136008 b) 0.000796803 c) 0.002090 d) 0.00142299 e) 0.000882963 f) 0.000404963
Answer:
a) 0.00136008
Step-by-step explanation:
For each customer, there are only two possible outcomes. Either they buy a magazine, or they do not. The probability of a customer buying a magazine is independent of any other customer. Thus, the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
9.8% of his customers buy a magazine
This means that [tex]p = 0.098[/tex]
What is the probability that exactly 5 out of the first 10 customers buy a magazine?
This is [tex]P(X = 5)[/tex] when [tex]n = 10[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{10,5}.(0.098)^{5}.(0.902)^{5} = 0.00136008[/tex]
Thus, the correct answer is given by option A.
Solve the system useing elimination 4x+8y=16 6x-8y=4
Answer:
x=2 and y=1
Step-by-step explanation:
Add the two equations to remove "y" and solve for x:
4x+8y=16
6x-8y=4
________
10x=20
x=2
Plug x=2 into one of the original equations to get the value of "y":
4x+8y=16
4(2)+8y=16
8+8y=16
8y=8
y=1
Therefore, x=2 and y=1
what is 300+45-9x2+22-1+2
Answer:
350
Step-by-step explanation:
Use PEMDAS.
[tex]300+45-9*2+22-1+2[/tex]
300+45-18+22-1+2
345-18+22-1+2
327+22-1+2
349-1+2
348+2
350
Which expression is equivalent to 6/g^5 , if g >0
Answer:
The choose (D)
[tex] {g }^{ \frac{5}{6} } [/tex]
The expression equivalent to [tex]\sqrt[6]({g}^{5})[/tex] is [tex]g^{\frac{5}{6} }[/tex].
What is an exponent?The number of times a number has been multiplied by itself is referred to as an exponent. It could be an integer, a fraction, a negative integer, or a decimal. Powers or indices are other names for exponents. For instance, 6⁵ indicates that we are multiplying 6 by five. It is 6 × 6 × 6 × 6 × 6 in its expanded form.
How to solve this problem?The expression is [tex]\sqrt[6]({g}^{5})[/tex].
[tex]\sqrt[6]{g}[/tex] can be written as [tex]g^{\frac{1}{6} }[/tex].
Then the given expression can be written as [tex]g^{\frac{5}{6} }[/tex].
Therefore, the expression equivalent to [tex]\sqrt[6]({g}^{5})[/tex], g > 0 is [tex]g^{\frac{5}{6} }[/tex]. So, option D is correct.
Learn more about exponents here -
https://brainly.com/question/27850853
#SPJ2
Which of the following represents the factorization of the polynomial below? 2x^2+5x+3
Answer:
(2x + 3)(x + 1)
Step-by-step explanation:
you didn't show them, the factors are
(2x + 3)(x + 1)
Answer:
[tex](x+1)(2x+3)[/tex]
Step-by-step explanation:
[tex]2x^{2} +5x+3[/tex]
[tex]2x^{2} +3x+2x+3[/tex]
[tex]x(2x+3)+2x+3[/tex]
[tex](x+1)(2x+3)[/tex]
Given that X = {April, August}, then ξ = {months that begin with the letter A}. True or False?
Answer:
False
Step-by-step explanation:
hi I need help on this
if a =(2/3)and m is any scalar find ma
Answer:
[tex]ma = \frac{2m}{3}[/tex]
Step-by-step explanation:
Multiplication of an scalar by a fraction:
We consider the multiplication of a fraction by a symbolic scalar the same as the multiplication of a fraction by any other numbers, that is, multiplication of the numerators divided by the multiplication of the denominators.
In this question:
Fraction 2/3
Scalar m
[tex]\frac{2}{3} \times m = \frac{2m}{3}[/tex]
So
[tex]ma = \frac{2m}{3}[/tex]
Two cubical dice each have removable numbers 1 through 6. The twelve numbers on the two dice are removed, put into a bag, then drawn one at a time and randomly reattached to the faces of the cubes, one number to each face. The dice are then rolled and the numbers on the two top faces are added. What is the probability that the sum is 7?
a. 3/8 b. 2/11c. 2/3d. 1/3e. 2/9
Answer:
it might be 3 but I'm not sure
Please answer! Really need help! ASAP! Giving brainliest
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Explanation:
The y is a placeholder for a number. In this case, we'll replace it with 4.
So [tex]5y^2 - 10[/tex] becomes [tex]5(4)^2-10[/tex]
Use the order of operations PEMDAS to simplify
[tex]5(4)^2-10\\\\5(16)-10\\\\80-10\\\\70\\\\[/tex]
Therefore, [tex]5y^2-10\\\\[/tex] evaluates to 70 when y = 4.
Put another way, the equation [tex]5y^2-10 = 70\\\\[/tex] has one solution that is y = 4.
Please someone help me plz help
Answer:
x = 5
Step-by-step explanation:
Angles in a triangle add up to equal 180
Hence, 10x - 1 + 78 + 53 = 180
( Note that we just created an equation that we can use to solve for x )
We now solve for x using the equation we created
10x - 1 + 78 + 53 = 180
Combine like terms
10x + 130 = 180
Subtract 130 from both sides
10x = 50
Divide both sides by 10
x = 5
Please help! 15 points!
Suppose the sample space for a continuous random variable is 0 to 200. If the area under the density graph for the variable from 0 to 50 is 0.25, then the area under the density graph from 50 to 200 is also 0.25. O A. True B. False SUBMIT
Answer:
I guess it's False...Hope it helps you.
Answer:
true
Step-by-step explanation:
slope of 3,-4 and 5,8
Answer:
Slope = 6
Step-by-step explanation:
Use the slope formula:
[tex]m=\frac{y_1-y_2}{x_1-x_2}\\m=\frac{-4-8}{3-5}\\m=\frac{-12}{-2}\\m=6[/tex]
Answer:
6
Step-by-step explanation:
(3,-4) and (5,8)
To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)
Plug in these values:
(8 - (-4)) / (5 - 3)
Simplify the parentheses.
= (8 + 4) / (5 - 3)
= (12) / (2)
Simplify the fraction.
12/2
= 6
This is your slope.
Hope this helps!
Plot 1 4/5 and 2 3/10
Answer:
You could change 1 4/5 to 1 8/10 to make it easier to plot.
Please help I will give you Brainlyest
Answer:
below
Step-by-step explanation:
Clare's mistake was the writing of 4000 in standard form
he wrote 4 ×10²
instead of 4 ×10³
Answer:
Step 1
Step-by-step explanation:
I believe Claire's mistake is when she tries to simplify 4000
She says that 4000 = 4 × 10²
4000 is actually equal to 4 ×10³
Bill makes $240 per hour for a standard 40 hour work week. He earns time- and - a - half for every overtime hour he works. Bill earned a total of$11,400 in one week,how many overtime hours did her work?
Answer:
5 overtime hours
Step-by-step explanation:
Given that :
Pay per hour = 240
Overtime pay = 1 1/2 * pay per hour = 1 1/2 * 240 = 360 per hour
Amount earned for the week = 11400
Let overtime hours = x
Total hours worked = 40 + x
Earning for the week based on hours worked :
240(40) + 360x = 11400
9600 + 360x = 11400
360x = 1800
x = 1800 / 360
x = 5 hours
Please answer this question. I prey
Answer:
45°
Step-by-step explanation:
mLA : mLB : mLC = 1:2:1 => 1+2+1=4 (equivalent with 180°)
so, mL2 = mLC = 1/4 ×180° = 45°
Emile has calculated a one-tailed z-statistic of -1.97 and wants to see if it is significant at the 5% significance level.
What is the critical value for the 5% significance level? Answer choices are rounded to the hundredths place.
Answer:
Z = -1.65
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
What is the critical value for the 5% significance level?
One-tailed statistic, so Z with a p-value of 0.05.
Looking at the z-table, this is Z = -1.65, so this is the critical value for the 5% significance leve.
The radius of a right circular cone is increasing at a rate of 1.1 in/s while its height is decreasing at a rate of 2.6 in/s. At what rate is the volume of the cone changing when the radius is 107 in. and the height is 151 in.
Answer:
The volume of the cone is increasing at a rate of 1926 cubic inches per second.
Step-by-step explanation:
Volume of a right circular cone:
The volume of a right circular cone, with radius r and height h, is given by the following formula:
[tex]V = \frac{1}{3} \pi r^2h[/tex]
Implicit derivation:
To solve this question, we have to apply implicit derivation, derivating the variables V, r and h with regard to t. So
[tex]\frac{dV}{dt} = \frac{1}{3}\left(2rh\frac{dr}{dt} + r^2\frac{dh}{dt}\right)[/tex]
Radius is 107 in. and the height is 151 in.
This means that [tex]r = 107, h = 151[/tex]
The radius of a right circular cone is increasing at a rate of 1.1 in/s while its height is decreasing at a rate of 2.6 in/s.
This means that [tex]\frac{dr}{dt} = 1.1, \frac{dh}{dt} = -2.6[/tex]
At what rate is the volume of the cone changing when the radius is 107 in. and the height is 151 in.
This is [tex]\frac{dV}{dt}[/tex]. So
[tex]\frac{dV}{dt} = \frac{1}{3}\left(2rh\frac{dr}{dt} + r^2\frac{dh}{dt}\right)[/tex]
[tex]\frac{dV}{dt} = \frac{1}{3}(2(107)(151)(1.1) + (107)^2(-2.6))[/tex]
[tex]\frac{dV}{dt} = \frac{2(107)(151)(1.1) - (107)^2(2.6)}{3}[/tex]
[tex]\frac{dV}{dt} = 1926[/tex]
Positive, so increasing.
The volume of the cone is increasing at a rate of 1926 cubic inches per second.
20.
168
Which equation matches the graph? Click on the picture
enlarge.
126
84
42
0
0
6 12
18
24
b) y = 42x
a) y = 7x
D c) y= 6x
d) y = 2x
The price of admission to a World War I history museum is $8.29 for adults and $6.47 for children. A family of 2 adults and 4 children visits the museum. What is the total cost, in dollars, of admission?
Answer:
cost for adults=$8.29
cost for children=$6.47
cost for 2 adults and 4 children are =$(2×8.29)+(4×6.47)=$16.58+25.88=$42.46
The cylinder has a radius of 5 feet and height of 20 feet. What is the volume of the cylinder in cubic feet?
Answer:
Well the volume is 1570.8 cubed. but i don't know what it would be in your range of answers.
Step-by-step explanation:
a map shows that the top of a hill is 200m above sea level and the bottom of a lagoon is 15m below sea level. express these distancesat a distances from sea level and what is difference between the two heights
Answer:
200 m
-15 m
215 m
Step-by-step explanation:
Given :
Top of hill = 200 m above sea level ; height of hill top is positive 200m = 200 m
Bottom of lagoon = 15m *below sea level ; bottom of lagoon = - 15m
We have related the height of the two points with respect to sea level ; points above sea level are represented as positive ; points below are represented as negative.
Difference between the two heights :
Hill top - bottom of lagoon :
200 m - (-15) m
200 m + 15 m
215 m
Difference between the heights is 215 m
PLSSSS HELP ASAP !!! PLSSS WILL MARK BRAINLIEST TO WHOEVER GETS IT RIGHT
Answer:
See below.
Step-by-step explanation:
Angle 7 and Angle 4Angle 1 and Angle 5Answer:4000000
Step-by-step explanation:783
The table shows ordered pairs of the function y=8-2 x . What is the value of y when x=8 ?
The table shows ordered pairs of the function y=8-2 x . What is the value of y when x=8 ?
Solution:-The given value of x is 8.
we have to find the value of 'y' , so,
▶️ y = 8-2 x
▶️ y = 8-2 × 8
▶️ y = 8-16
▶️ y = -8
Answer:-The value of y is -8.
[tex] \\ \\ [/tex]
Tony is building a new silo to store corn as animal feed. It will be a cylinder topped with a half-sphere, and must store 21 000 t of corn. The entire silo can be filled with corn. Tony wants to minimize the surface area of the silo to reduce materials and paint costs. He has the following information:
• 1 cubic m of corn has a mass of 700 kg.
• Building costs are $8/m2, taxes included.
• Paint comes in 3.8 L cans.
Each can covers 40 sq m and costs $35,
taxes included.
• Corn costs $140 per tonne ($140/t), taxes
included.
What is the total cost to build, paint, and fill a silo with the least surface area?
Answer:
The total bill is $6900 because 69 is a man which hair is multi colour
Help please!!! I don’t understand this question
Answer:
C
Step-by-step explanation:
Let us first write an equation. Using the SOHCAHTOA rule, we should know that the tangent of an angle equals it's [tex]\frac{opposite}{adjacent}[/tex]. The opposite of our given 20° angle is 9, and the adjacent side is x.
[tex]tan(20[/tex]°[tex])=\frac{9}{x}[/tex]
[tex]0.364=\frac{9}{x} \\x=\frac{9}{0.364}\\x=24.7[/tex]
C
I hope this helps! Let me know if you have any questions :)
Determine the period of this Function.
Answer:
4p
Step-by-step explanation:
The period is basically the difference in x from one "peak" to the other "peak".
The peaks are the highest points of a sinosodial function, and the figure them out, use the formula:
[tex]|peak_1-peak_2|=period[/tex]
We know the first peak is at about x=0[tex]\pi[/tex]
We know the second peak is at about x=4[tex]\pi[/tex]
So plugging this in:
[tex]|0-4\pi |=4\pi[/tex]
So the period is [tex]4\pi[/tex]
I am assuming "p" stands for [tex]\pi[/tex], so the answer should be 4p.
There are other ways to find the period, for instance if you are given a sinusodial function in writing instead of a graph.
Here is an example:
5sin(5x+2)+3
If we want to find period, we need to find what we call "b"
b is the number in front of x, which we can identify as bx, which in this case is 5x above.
Now what do we do with this "b"?
This is the value we need to find our period.
If you know b, you can use this formula to find the period:
[tex]\frac{2\pi }{b}=p[/tex]
And when we plug in b:
[tex]\frac{2\pi }{5}[/tex]
=
1.257, which would be your period.
THis can also be reworked so that you can find b:
If the formula for period is [tex]\frac{2\pi }{b}=p[/tex], then the opposite formula would be [tex]\frac{2\pi }{ p}=b[/tex]
And when you plug the period you have in:
[tex]\frac{2\pi }{1.257}[/tex]
=
5
Anyway, your answer is 4p.
Hope this helps!
cuantos terminos tiene -3xy
Answer:
El a+b tiene 1 terminó porque para separar un término el factor es el +Step-by-step explanation: