Answer:
Yes the sample data indicate that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 51[/tex]
The sample mean is [tex]\= x = 2.03[/tex]
The sample standard deviation is [tex]\sigma = 0.82[/tex]
The population mean is [tex]\mu = 1.75[/tex]
The level of significance is [tex]\alpha = 0.01[/tex]
The null hypothesis is
[tex]H_o : \mu = 0.82[/tex]
The alternative hypothesis is
[tex]H_a : \mu >1.75[/tex]
The critical value of the the level significance [tex]\alpha[/tex] obtained from the critical value table for z-value is [tex]z_\alpha = 2.33[/tex]
Now the test statistic is mathematically evaluated as
[tex]t = \frac{\= x - \mu }{\frac{\sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 2.03 - 1.75 }{\frac{0.82}{\sqrt{51} } }[/tex]
[tex]t = 2.44[/tex]
From that calculated and obtained value we see that the critical value of the level of significance is less than the test statistics so we reject the null hypothesis
Hence there sufficient evidence to proof that the sample data indicates that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years
In a certain country the life expectancy for women in 1990 was 45 and in 2000 it was 85?years. Assuming that life expectancy between 2000 and 2100 increases by the same percentage as it did between 1900 and 2000,what will life expectancy be for women in 2100? Assuming the life expectancy between 2000 and 2100 will increase by the same percentage as it did between 1900 and 2000, the life expectancy for women will be —— years
Answer:
49145 years
Step-by-step explanation:
In a certain country the life expectancy for women in 1990 was 45 and in 2000 it was 85?years.
Assuming that life expectancy between 2000 and 2100 increases by the same percentage as it did between 1900 and 2000,what will life expectancy be for women in 2100?
In 10 years, the expectancy increased by 85/45 = 17/9
between 2000 and 2100, it will increas by 10 time 10 years, so expected expectancy is [tex]85*(\frac{85}{45})^{10} = 49145[/tex] years
The life expectancy for women will be 49145 years when It will increase by ten times between 2000 and 2100.
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
It is a relation of the form y = aˣ in mathematics, where x is the independent variable
In one country, women's life expectancy was 45 years in 1990 and 85 years in 2000.
Assuming that life expectancy grows by the same proportion between 2000 and 2100 as it did between 1900 and 2000, we have to determine the life would expectancy for women in 2100
Over a ten-year period, life expectancy rose by 85/45 = 17/9.
It will increase by ten times between 2000 and 2100, therefore the anticipated life expectancy will be
⇒ 85×(85/45)¹⁰
⇒ 85×(1.88)¹⁰
⇒ 49145 years
Hence, the life expectancy for women will be 49145 years
Learn more about exponential function here:
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The four-member math team at Pecanridge Middle School is chosen from the math club, which has three girls and five boys. How many different teams made up of two girls and two boys could be chosen?
Answer:
[tex]Total\ Selection = 30\ ways[/tex]
Step-by-step explanation:
Given
Girls = 3
Boys = 5
Required
How many ways can 2 boys and girls be chosen?
The keyword in the question is chosen;
This implies combination and will be calculated as thus;
[tex]Selection =\ ^nC_r = \frac{n!}{(n-r)!r!}[/tex]
For Boys;
n = 5 and r = 2
[tex]Selection =\ ^5C_2[/tex]
[tex]Selection = \frac{5!}{(5-2)!2!}[/tex]
[tex]Selection = \frac{5!}{3!2!}[/tex]
[tex]Selection = \frac{5 * 4 * 3!}{3!*2 * 1}[/tex]
[tex]Selection = \frac{20}{2}[/tex]
[tex]Selection = 10[/tex]
For Girls;
n = 3 and r = 2
[tex]Selection =\ ^3C_2[/tex]
[tex]Selection = \frac{3!}{(3-2)!2!}[/tex]
[tex]Selection = \frac{3!}{1!2!}[/tex]
[tex]Selection = \frac{3 * 2!}{1 *2!}[/tex]
[tex]Selection = \frac{3}{1}[/tex]
[tex]Selection = 3[/tex]
Total Selection is calculated as thus;
[tex]Total\ Selection = Boys\ Selection * Girls\ Selection[/tex]
[tex]Total\ Selection = 10 * 3[/tex]
[tex]Total\ Selection = 30\ ways[/tex]
The equation 6x2 - 132 +5 -0 has solutions of the form
NVD
M
(A) Use the quadratic formula to solve this equation and find the appropriate integer values of N.M and D. Do not worry about simplifying the VD yet in this part of the problem.
N = ]:D
M
(B) Now simplify the radical and the resulting solutions. Enter your answers as a list of integers or reduced fractions, separated with commas. Example: -5/2-3/4
Preview
Answer:
(A)
[tex]N = -b = -(-13) = 13\\\\[/tex]
[tex]D =b^2 -4ac = (-13)^2 - 4(6)(5) = 169- 120 = 49[/tex]
[tex]M = 2a = 2(6) = 12[/tex]
(B)
[tex]$ x = (\frac{5}{3} , \: \frac{1}{2}) $[/tex]
Step-by-step explanation:
The given equation is
[tex]6x^2 - 13x + 5 = 0[/tex]
The solution is of the form as given by
[tex]$x=\frac{N\pm\sqrt{D}}{M}$[/tex]
(A) Use the quadratic formula to solve this equation and find the appropriate integer values of N, M and D. Do not worry about simplifying the VD yet in this part of the problem.
The quadratic formula is given by
[tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]
The equations of N, M and D are
[tex]N = -b[/tex]
[tex]D =b^2 -4ac[/tex]
[tex]M = 2a[/tex]
The values of a, b and c are
[tex]a = 6 \\\\b = -13 \\\\c = 5[/tex]
So,
[tex]N = -b = -(-13) = 13\\\\[/tex]
[tex]D =b^2 -4ac = (-13)^2 - 4(6)(5) = 169- 120 = 49[/tex]
[tex]M = 2a = 2(6) = 12[/tex]
(B) Now simplify the radical and the resulting solutions. Enter your answers as a list of integers or reduced fractions, separated with commas. Example: -5/2-3/4
N = 13
D = 49
M = 12
[tex]$x=\frac{13\pm\sqrt{49}}{12}$[/tex]
[tex]$x=\frac{13\pm7}{12}$[/tex]
[tex]$ x=\frac{13+7}{12} $[/tex] and [tex]$ x=\frac{13-7}{12} $[/tex]
[tex]$ x=\frac{20}{12} $[/tex] and [tex]$ x=\frac{6}{12} $[/tex]
[tex]$ x=\frac{5}{3} $[/tex] and [tex]$ x=\frac{1}{2} $[/tex]
[tex]$ x = (\frac{5}{3} , \: \frac{1}{2}) $[/tex]
f(n)=4n-3 find the 15th term of the sequence defined by the explicit rule
Answer:
57
Step-by-step explanation:
f(15)=4(15)-3
f(15)=60-3
f(15)=57
Hope that helps, tell me if you need more help
Answer:
57
Step-by-step explanation:
If you plug 15 into the equation, you get f(15)=4(15)-3
60-3
57
:)
help huryyyyyyyyyyyyy
Answer: 4
Step-by-step explanation:
Because %s can be expressed as fractions over 100, because 90 is 70% of x, 70% is 70% of 100. Thus, 90/x = 70/100.
Hope it helps <3
Answer:
4
Step-by-step explanation:
90 is 70% of x.
90 = 70% × x
90 = 70/100x
Divide both sides by x.
90/x = 70/100
Three generous friends, each with some cash, redistribute their money as follows: Ami gives enough money to Jan and Toy to double the amount that each has. Jan then gives enough to Ami and Toy to double their amounts. Finally, Toy gives Ami and Jan enough to double their amounts. If Toy has $36 when they begin and $36 when they end, what is the total amount that all three friends have?
Answer:
$252
Step-by-step explanation:
This is quite a neat question, with no fixed equation. Given that each person gives the other two enough money to double their cash, if Toy had 36 dollars beginning, and 36 at the end - presumably the cash of each person, ( their starting and original ) should be the same as well. Respectively each should be a multiple of 36 dollars.
Jan's " give away " = Ami + 36, Jan - 108, Toy + 72
Toy's " give away " = Ami + 72, Jan + 36, Toy - 108
Therefore, we can conclude that Ami = 144 at the start, presuming he gave away 108 dollars, with a remaining 36. Jan, having 144 dollars ( after having his 72 dollars doubled by Ami ) gives 36 to Ami to double his amount, and 72 to double Toy's doubled amount, remaining with 36 dollars. Now Ami has 72 dollars, Jan has 36, and Toy has 144. Then, Toy double's Ami and Jan's amount, giving away 72 and 36 dollars, remaining with 36 dollars himself. Therefore, Ami has 144 dollars, Jan has 72 dollars, and Toy has 36 dollars both at the beginning and end.
144 + 72 + 36 = 252 dollars ( in total )
Answer:
answer is 252
Step-by-step explanation:
Good luck :)
Which is the simplified form of m Superscript negative 8 p Superscript 0? StartFraction 1 Over m Superscript 8 Baseline p EndFraction StartFraction 1 Over m Superscript 8 EndFraction StartFraction p over m Superscript 8 EndFraction m Superscript 8 PLS HELPP
Answer:
Correct Option is : StartFraction 1 Over m Superscript 8 EndFraction
Step-by-step explanation:
=> [tex]m^{-8} p^0[/tex]
According to law of exponents [tex]a^0 = 1[/tex]
=> [tex]m^{-8} (1)[/tex]
Using Law of exponents [tex]a^{-m} = \frac{1}{a^m}[/tex]
=> [tex]\frac{1}{m^8}[/tex]
The simplified form of [tex]m^{-8}p^0[/tex] is [tex]\frac{1}{m^8}[/tex].
The question is not well formatted the question might be as follows:
Which is the simplified form of [tex]m^{-8}p^0[/tex]?
[tex]\frac{1}{m^8p}[/tex][tex]\frac{1}{m^8}[/tex][tex]\frac{p}{m^8}[/tex]m⁸What are exponents?Exponents are numbers that say how many times a number is to be multiplied. For example, 2⁸ means 2 is multiplied 8 times.
How to solve the problem?[tex]m^{-8}p^0[/tex] = [tex]m^{-8}[/tex] since, p⁰=1.
⇒[tex]m^{-8}[/tex] = [tex]\frac{1}{m^8}[/tex] .
Hence, the simplified form of [tex]m^{-8}p^0[/tex] is [tex]\frac{1}{m^8}[/tex].
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Which point is a solution to y<=3x-4?
Answer:
(3, 1)
Step-by-step explanation:
Plug-in points and see which one works. (x, y). <= means less than or equal to.
Answer:
D. (3,1) is the correct answer
Step-by-step explanation: Just graph this question on a graph, and you will find that (3,1) is in the shaded region, which means it is part of the solution
Find the midpoint of AC.
B (0, a)
C (a, a)
A(0, 0) D (a,0)
Answer:
[tex]\huge\boxed{\bigg(\dfrac{a}{2};\ \dfrac{a}{2}\bigg)}[/tex]
Step-by-step explanation:
The formula of a midpoint:
[tex]M\bigg(\dfrac{x+1+x+2}{2};\ \dfrac{y_1+y_2}{2}\bigg)[/tex]
We have the points
[tex]A(0;\ 0)\to x_1=0;\ y_1=0\\\\C(a;\ a)\to x_2=a;\ y_2=a[/tex]
Substitute:
[tex]\dfrac{x_1+x_2}{2}=\dfrac{0+a}{2}=\dfrac{a}{2}\\\\\dfrac{y_1+y_2}{2}=\dfrac{0+a}{2}=\dfrac{a}{2}[/tex]
Answer:
The answer is (a/2,a/2)
Step-by-step explanation:
Fill in 2 then a
In conclusion (a/2,a/2)
Pls help asap What is the number of degrees in the acute angle formed by the hands of a clock at 6:44?
Answer:
264 degree angle
Step-by-step explanation:
A right triangle has legs with lengths equal to 10 inches and 9x inches. Its hypotenuse measures (x + 10) inches. What is the approximate value of the hypotenuse? 10 inches 10.25 inches 20.25 inches 81 inches
Answer:
10.25 inchesStep-by-step explanation:
Given,
Perpendicular ( p ) = 9x
Base ( b ) = 10
Hypotenuse ( h ) = x + 10
Now, let's find the value of x
Using Pythagoras theorem:
[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]
Plug the values
[tex] {(x + 10)}^{2} = {(9x)}^{2} + {(10)}^{2} [/tex]
Using [tex] {(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2} [/tex] , expand the expression
[tex] {x}^{2} + 20x + 100 = {(9x)}^{2} + {10}^{2} [/tex]
To raise a product to a power , raise each factor to that power
[tex] {x}^{2} + 20x + 100 = 81 {x}^{2} + {10}^{2} [/tex]
Evaluate the power
[tex] {x}^{2} + 20x + 100 = 81 {x}^{2} + 100[/tex]
Cancel equal terms on both sides of the equation
[tex] {x}^{2} + 20x = 81 {x}^{2} [/tex]
Move x² to R.H.S and change its sign
[tex]20x = 81 {x}^{2} - {x}^{2} [/tex]
Calculate
[tex]20x = 80 {x}^{2} [/tex]
Swap both sides of the equation and cancel both on both sides
[tex]80x = 20[/tex]
Divide both sides of the equation by 80
[tex] \frac{80x}{80} = \frac{20}{80} [/tex]
Calculate
[tex]x = \frac{20}{80} [/tex]
Reduce the numbers with 20
[tex]x = \frac{1}{4} [/tex]
The value of X is [tex] \frac{1}{4} [/tex]
Now, let's replace the value of x to find the approximate value of hypotenuse
Hypotenuse = [tex] \frac{1}{4} + 10[/tex]
Write all numerators above the common denominator
[tex] \frac{1 + 40}{4} [/tex]
Add the numbers
[tex] \frac{41}{4} [/tex]
[tex] = 10.25[/tex] inches
Hope this helps..
best regards!!
Answer:
10.25
Step-by-step explanation:
because I said so ya skoozie
the product of two consequtive integers is 72 the equation x(x+1)=72 represents the situation, where x represents the smaller integer, which equation can be factor and solve for the smaller integer?
Answer:
x² + x - 72 = 0 can be factored into (x - 8)(x + 9) = 0 to find your answer.
Step-by-step explanation:
Step 1: Distribute x
x² + x = 72
Step 2: Move 72 over
x² + x - 72 = 0
Step 3: Factor
(x - 8)(x + 9) = 0
Step 4: Find roots
x - 8 = 0
x = 8
x + 9 = 0
x = -9
Answer:
x² + x - 72 = 0 ⇒ (x - 8)(x + 9) = 0
Step-by-step explanation:
Let the first consecutive integer be x.
Let the second consecutive integer be x+1.
The product of the two consecutive integers is 72.
x(x + 1) = 72
x² + x = 72
Subtracting 72 from both sides.
x² + x - 72 = 0
Factor left side of the equation.
(x - 8)(x + 9) = 0
Set factors equal to 0.
x - 8 = 0
x = 8
x + 9 = 0
x = -9
8 and -9 are not consecutive integers.
Try 8 and 9 to check.
x = 8
x + 1 = 9
x(x+1) = 72
8(9) = 72
72 = 72
True!
The two consecutive integers are 8 and 9.
People start waiting in line for the release of the newest cell phone at 5\text{ a.m.}5 a.m.5, start text, space, a, point, m, point, end text The equation above gives the number of people, PPP, in line between the hours, hhh, of 6\text{ a.m.}6 a.m.6, start text, space, a, point, m, point, end text and 11\text{ a.m.}11 a.m.11, start text, space, a, point, m, point, end text, when the doors open. Assume that 6\text{ a.m.}6 a.m.6, start text, space, a, point, m, point, end text is when time h = 1h=1h, equals, 1. What does the 232323 mean in the equation above?
Answer:
There are 23 people in line at 6:00 A.M
Step-by-step explanation:
When you plug in h=1, we get 23 people
h corresponds with the time 6:00 am, as a result there are 23 people in line
The equation represents how many people will come as the hour increases.
23 represents the initial amount of people in line.
(got this from Khan academy too:))
f(x)=2x+1 and g(x)=3x2+4, find (f∘g)(−2) and (g∘f)(−2).
Answer:
Step-by-step explanation:
Fog=2(g)+1
2(3x+2+4)+1
2{3x+6)+1
6x+12+1
=6x+13
Fog(-2)=6(-2)+13
-12+13
=1
Gof=3(f)+2+4
=3(2x+1)+6
6x+3+6
=6x+9
Gof(-2)=6(-2)+9
-12+9
=-3
A radio transmission tower is feet tall. How long should a guy wire be if it is to be attached feet from the top and is tomake an angle of with the ground
Answer:
Length of guy wire is 590.6 ft
Step-by-step explanation:
The complete question is
A radio transmission tower is 210 feet tall. How long should a guy wire be if it is to be attached 8 feet from the top and is to make an angle of 20° with the ground. Give your answer to the nearest tenth of a foot.
height of tower = 210 ft
8 ft fro the top leaves 210 - 8 = 202 ft to the ground
This is an angle of elevation problem
the opposite is 202 ft
hypotenuse = ?
angle is 20°
using sin ∅ = opp/hyp
sin 20° = 202/hyp
0.342 = 202/hyp
hyp = 202/0.342 = 590.6 ft this is the length of the guy wire
please help answer this!!!
Answer:
49) [tex]12\,b^4[/tex]
50) [tex]200\,x^6[/tex]
Step-by-step explanation:
Use the properties of exponent to reduce this expressions:
a) [tex]3\,b\,*\,4 \,b^3=(3\,*\,4)\,(b\,*\,b^3)=12\,b^{(1+3)}=12\,b^4[/tex]
b) [tex]5\,x^2\,*\,8\,x\,5\,*\,x^3=(5\,*\,8\,*\,5)\,(x^2\,*\,x\,*\,x^3)=200\,x^{(2+1+3)}= 200\,x^6[/tex]
Hershel had 100 baseball cards that he labeled from 1-100. He started with number
one and marked every 5th card with an X, every 7th card with an O and every 10th
card with a V. What number card will be the first to have all 3 marks (XOV)?
Answer:
Hey there!
This question is basically asking for the least common multiple, or LCM of the three numbers.
If it is a multiple of 10, it has to be a multiple of 5. Thus, the only thing we need to do now, is find the LCM of 10 and 7, which is 70.
Thus, your answer is 70.
Hope this helps :)
Answer:
I think it is 70.
Step-by-step explanation:
I think that is the Lowest common Multiple of 5, 7 and 10:
10 = 2*5
7 = 7
5 = 5
So the LCM is 2 * 5 * 7 = 70.
The manager of a grocery store took a random sample of 100 customers. The avg. length of time it took the customers in the sample to check out was 3.1 minutes with a std. deviation of 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly > 3 min. At 95% confidence, it can be concluded that the mean of the population is
Answer:
Step-by-step explanation:
The data given are;
sample size n = 100
sample mean x = 3.1
standard deviation σ = 0.5
mean = 3
The value for Z can be determined by using the formula:
[tex]Z = \dfrac{x - \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]Z = \dfrac{3.1 - 3.00}{\dfrac{0.5}{\sqrt{100}}}[/tex]
[tex]Z = \dfrac{0.1}{\dfrac{0.5}{10}}}[/tex]
Z = 0.2
At 95% Confidence interval, level of significance ∝ = 0.05
From the z table ;P- value for the test statistics at ∝ = 0.05
P = 0.0228
We can see that the P-value is < ∝
Decision Rule:
Reject the null hypothesis [tex]H_o[/tex] if P-value is less than ∝
Conclusion:
At 0.05 level of significance; we conclude that the mean of the population is significantly > 3 min
Solve the quadratic equation by factoring 9x^2 -16 = 0
Answer: x= - 4/3 and x = 4/3
Step-by-step explanation:
(3x-4) times (3x+4) = 0
What is the correlation coefficient for the data in the table?
–0.57
–0.28
0.28
0.57
Answer: i believe it’s 0.28, but tbh i’m on a unit test so i can’t see what’s wrong and what’s right. good luck!
Step-by-step explanation:
Answer:
c- 0.28
Step-by-step explanation:
If f is a function f: X Y, then Y is called (a) Domain (b) Co-domain (c) Range (d) None of these
Answer:
y is the range
Step-by-step explanation:
the y is the range
x isthe domain
6x-5<2x+11. plz helpppppp
Answer:
x < 4 or x = ( -∞, 4)
Step-by-step explanation:
6x - 5 < 2x + 116x - 2x < 11 + 54x < 16 x < 16/4x < 4or
x = ( -∞, 4)
[tex]\text{Solve the inequality for x:}\\\\6x-5<2x+11\\\\\text{Subtract 2x from both sides}\\\\4x-5<11\\\\\text{Add 5 to both sides}\\\\4x<16\\\\\text{Divide both sides by 4}\\\\\boxed{x<4}[/tex]
For the functions f(x)=8 x 2 +7x and g(x)= x 2 +2x , find (f+g)(x) and (f+g)(3)
Answer:
(f+g)(x)= 9x² + 9x
(f+g)(3) = 108
Step-by-step explanation:
f(x)=8x² +7x
g(x)= x² +2x
(f+g)(x) = f(x) + g(x) = 8x² +7x +x² +2x = 9x² + 9x
(f+g)(x)= 9x² + 9x
(f+g)(3)= 9*3² + 9*3 = 108
PLEASE PLEASE PLEASE HELP TIMEDCan you prove that DE F = HGF Justify your answer. A. Yes, the triangles are congruent by SAS. B. Yes, the triangles are congruent by SSS. C. Yes, the triangles are congruent by SSA. D. No, not enough information is given.
Answer:
A. Yes, the triangles are congruent by SAS.
Step-by-step explanation:
EF = FG and DF = FH-> Given
angle EFD = angle HFG -> Vertical angles are congruent
DE F = HGF -> SAS Triangle Congruence Theorem
We can prove ∠DE F = ∠HGF by SAS congruency.
Hence option A is correct.
In the given triangle,
DE = GE
DF = FH
We know that,
SAS congruency stands for "Side-Angle-Side" congruence,
Which is a rule used in geometry to prove that two triangles are congruent or equal in size and shape.
This rule states that if two sides and the angle between them of one triangle are congruent to the corresponding two sides and angle of another triangle, then the two triangles are congruent.
Since the triangles
DE,GE and DF, FH are the corresponding sides and
DE = GE
DF = FH
Since DEF and FHG are congruent.
Therefore,
∠DE F = ∠HGF
Hence proved.
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For each of the finite geometric series given below, indicate the number of terms in the sum and find the sum. For the value of the sum, enter an expression that gives the exact value, rather than entering an approximation.
3 (0.5)^{5} + 3 (0.5)^{6} + 3 (0.5)^{7} + \cdots + 3 (0.5)^{13}
(1) Number of terms
(2) Value of Sum
Answer:
Number of term N = 9
Value of Sum = 0.186
Step-by-step explanation:
From the given information:
Number of term N = [tex]3 (0.5)^{5} + 3 (0.5)^{6} + 3 (0.5)^{7} + \cdots + 3 (0.5)^{13}[/tex]
Number of term N = [tex]3 (0.5)^{5} + 3 (0.5)^{6} + 3 (0.5)^{7} +3 (0.5)^{8}+3 (0.5)^{9} +3 (0.5)^{10} +3 (0.5)^{11}+3 (0.5)^{12}+ 3 (0.5)^{13}[/tex]
Number of term N = 9
The Value of the sum can be determined by using the expression for geometric series:
[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{a(r^m-r^{n+1})}{1-r}[/tex]
here;
m = 5
n = 9
r = 0.5
Then:
[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{3(0.5^5-0.5^{9+1})}{1-0.5}[/tex]
[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{3(0.03125-0.5^{10})}{0.5}[/tex]
[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{(0.09375-9.765625*10^{-4})}{0.5}[/tex]
[tex]\sum \limits ^n_{k=m}ar^k =0.186[/tex]
For the given the geometric series, 3·0.5⁵ + 3·0.5⁶ + 3·0.5⁷ + ...+ 3·(0.5)¹³,
the responses are;
(1) The number of terms are 9
(2) The value of the sum is approximately 0.374
How can the geometric series be evaluated?The given geometric series is presented as follows;
3·0.5⁵ + 3·0.5⁶ + 3·0.5⁷ + ...+ 3·(0.5)¹³
(1) The number of terms in the series = 13 - 4 = 9
Therefore;
The number of terms in the series = 9 terms(2) The value of the sum can be found as follows;
The common ratio, r = 0.5
The sum of the first n terms of a geometric progression is presented as follows;
[tex]S_n = \mathbf{\dfrac{a \cdot (r^n - 1)}{r - 1}}[/tex]
The sum of the first 4 terms are therefore;
[tex]S_4 = \dfrac{3 \times (0.5^4 - 1)}{0.5 - 1} = \mathbf{ 5.625}[/tex]
The sum of the first 13 terms is found as follows;
[tex]S_{13} = \dfrac{3 \times (0.5^{13} - 1)}{0.5 - 1} = \mathbf{ \dfrac{24573}{4096}}[/tex]
Which gives;
The sum of the 5th to the 13th term = S₁₃ - S₄
Therefore;
[tex]The \ sum \ of \ the \ 5th \ to \ the \ 13th \ term =\dfrac{24573}{4096} - \dfrac{45}{3} = \dfrac{1533}{4096} \approx \mathbf{0.374}[/tex]
The value of the sum of the terms of the series is approximately 0.374Learn more about geometric series here:
https://brainly.com/question/12471913
Marie is saving money for home repairs. So far, she has saved $1,558. She needs at least $2,158 for the repairs. She plans to
add $60 per week to her current savings until she can afford the repairs.
In this activity, you will algebraically model and solve an inequality based on this situation and interpret the solutions within
realistic guidelines
Part A
Question
Given the situation, which inequality models the number of additional weeks Marie needs to continue saving to afford the
home repairs?
Select the correct answer.
1,558 + 60x 22,158
60x + 1,558 5 2,158
1,558 - 60x s 2,158
2,158 - 60x 2 1,558
Answer:
Inequality: [tex]1558 + 60 x \geq 2158[/tex]
Number of Weeks: [tex]x \geq 10[/tex]
Step-by-step explanation:
Given
[tex]Initial\ Savings = \$1558[/tex]
[tex]Amount\ Needed = \$2158[/tex]
[tex]Additional\ Savings = \$60\ weekly[/tex]
Required
Represent this using an inequality
Represent the number of weeks as x;
This implies that, She'll save $60 * x in x weeks
Her total savings after x weeks would be
[tex]Initial\ Savings + 60 * x[/tex]
From the question, we understand that she needs at least 2158;
Mathematically, this can be represented as (greater than or equal to 2158)
[tex]\geq 2158[/tex]
Bringing the two expressions together;
[tex]Initial\ Savings + 60 * x \geq 2158[/tex]
Substitute 1558 for Initial Savings
[tex]1558 + 60 * x \geq 2158[/tex]
[tex]1558 + 60 x \geq 2158[/tex]
Hence, the inequality that represents the situation is [tex]1558 + 60 x \geq 2158[/tex]
Solving further for x (number of weeks)
[tex]1558 + 60 x \geq 2158[/tex]
Subtract 1558 from both sides
[tex]1558- 1558 + 60 x \geq 2158 - 1558[/tex]
[tex]60x \geq 600[/tex]
Divide both sides by 60
[tex]\frac{60x}{60} \geq \frac{600}{60}[/tex]
[tex]x \geq 10[/tex]
This means that she needs to save $60 for at least 10 weeks
Answer:
Its the first one
Step-by-step explanation:
I just did it lol
For the functions f(x)=4x+5 and g(x)=6x+4,find (f•g)(0)and (g•f)(0)
Answer:
Step-by-step explanation:
f(x)=4x+5
g(x)=6x+4,
first: (f*g)=(4x+5) (6x+4)=24x²+46x+20
next:(f*g)(0)=((g*f)=24x²+46x+20=20
Hi,
f°g means : apply first g then f . so calculate "g" and then use result as "x" in f.
g°f means : you apply first f then g
so : f°g = 4 (g (x)) +5
4 (6x+4) +5 = 24x+16+5 = 24x+21
Assume that there is a 6% rate of disk drive failure in a year. a. If all your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive? b. If copies of all your computer data are stored on independent hard disk drives, what is the probability that during a year, you can avoid catastrophe with at least one working drive? four a. With two hard disk drives, the probability that catastrophe can be avoided is . (Round to four decimal places as needed.) b. With four hard disk drives, the probability that catastrophe can be avoided is . (Round to six decimal places as needed.)
Answer: 0.9964
Step-by-step explanation:
Consider,
P (disk failure) = 0.06
q = 0.06
p = 1- q
p = 1- 0.06,
p = 0.94
Step 2
Whereas p represents the probability that a disk does not fail. (i.e. working entire year).
a)
Step 3
a)
n = 2,
let x be a random variable for number...
Continuation in the attached document
If (x+1) is the factor of polynomial p(x) = ax²+x+1, then find a.
Answer:
a = 0
Step-by-step explanation:
p(x) = ax²+x+1
Let x+1 = 0 => x = -1
Putting in the above polynomial
=> p(-1) = a(-1)^2+(-1)+1
By Remainder Theorem, Remainder will be zero
=> 0 = a(1) -1+1
=> 0 = a
OR
=> a = 0
Answer:
a = 1Step-by-step explanation:
Factors are what we can multiply to get the number.
x² + x + 1
Factor the polynomial.
x(x+1) + 1
ax² + x = x(x + 1)
ax² + x = x² + x
[tex]a=\frac{x^2 +x}{x^2 +x}[/tex]
a = 1
16. Find the equation of a parabola with a focus at (3,1) and a directrix at y = 3.
A) y = 1∕4(x – 3)^2 + 3
B) y = –1∕4 (x – 3)^2 + 3
C) y = –1∕4 (x – 3)^2 + 2
D) y = 1∕4(x – 3)^2 + 2
Answer:
C
Step-by-step explanation:
Any point (x, y) on the parabola is equidistant from the focus and the directrix.
Using the distance formula
[tex]\sqrt{(x-3)^2+(y-1)^2}[/tex] = | y - 3 | ← square both sides
(x - 3)² + (y - 1)² = (y - 3)² ← expand the y- factors
(x - 3)² + y² - 2y + 1 = y² - 6y + 9 ← subtract y² - 2y + 1 from both sides
(x - 3)² = - 4y + 8 ( subtract 8 from both sides )
(x - 3)² - 8 = - 4y ( divide both sides by - 4 )
- [tex]\frac{1}{4}[/tex] (x - 3)² + 2 = y, that is
y = - [tex]\frac{1}{4}[/tex] (x - 3)² + 2 → C
Answer:
Step-by-step explanation:
C) y = –1∕4 (x – 3)^2 + 2