The sequence is geometric with first term
a
1
=
100
and common ratio
r
=
0.5
Explanation:
a
1
=
100
,
a
2
=
50
,
a
3
=
25
,
a
4
=
25
2
,
a
5
=
25
4
...
50
100
=
0.5
,
25
50
=
0.5
,
25
2
25
=
0.5
,
25
4
25
2
=
0.5
∴
a
2
a
1
=
a
3
a
2
=
a
4
a
3
=
a
5
a
4
=
0.5
The ratio of successive term and preceeding term is constant
(
r
=
0.5
)
. Therefore the sequence is geometric whose first
term is
a
1
=
100
and common ratio is
r
=
0.5
[Ans]
There are______
Pairs of integers satisfying a÷b = -2
Answer:
There are only 1
Pairs of integers satisfying a÷b = -2
Step-by-step explanation:
Answer:
[tex]all \: positive \: integers \: in cluding \: 1[/tex]
so I dont really know how many
Step-by-step explanation:
eg
[tex] \frac{ - 2}{1} \\ \frac{ - 4}{2} \\ \frac{6}{ - 3} \\ = - 2[/tex]
they are all equal to negative 2
Insurance companies are interested in knowing the population percent of drivers who always buckle up before riding in a car. They randomly survey 387 drivers and find that 298 claim to always buckle up. Construct a 84% confidence interval for the population proportion that claim to always buckle up.
Answer:
The 84% confidence interval for the population proportion that claim to always buckle up is (0.74, 0.80).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
They randomly survey 387 drivers and find that 298 claim to always buckle up.
This means that [tex]n = 387, \pi = \frac{298}{387} = 0.77[/tex]
84% confidence level
So [tex]\alpha = 0.16[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.16}{2} = 0.92[/tex], so [tex]Z = 1.405[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.77 - 1.405\sqrt{\frac{0.77*0.23}{387}} = 0.74[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.77 + 1.405\sqrt{\frac{0.77*0.23}{387}} = 0.8[/tex]
The 84% confidence interval for the population proportion that claim to always buckle up is (0.74, 0.80).
PLS HELP ASAP! WILL GIVE U BRAINLIEST
Valid or Invalid: If a number is even, then it is a multiple of 4.
A. Invalid
B. Valid
Answer:
valid
Step-by-step explanation:
it's valid because for example here are some even numbers, 0, 2, 4, 6, 8, they're are all multiples of four.
hope that helped :)
mark me brainliest pls
A pyramid and a cone are both 10 centimeters tall and have the same
volume. What statement must be true about the two solids?
A. The vertical cross-sections of the pyramid and cone at the same
width must have the same area.
B. The cross-sections of the pyramid and cone are the same shape.
C. The area of the cross-sections of the pyramid and cone are
multiples of each other.
D. The horizontal cross-sections of the pyramid and cone at the
same height must have the same area.
Answer:
D the horizontal cross-section of the pyramid and cone at the same height must have the same area
Convert the equation into standard form 25x^2 -9y^2+200x +18y +166=0
Answer:
Step-by-step explanation:
You'd have to be really familiar with conic sections to know what to do with this. Good thing I am! ; )
Begin by grouping the x terms together and the y terms together, and getting the constant on the other side of the equals sign:
[tex]25x^2+200x-9y^2+18y=-166[/tex]
Now we need to complete the square on the x terms and the y terms. Do this by first factoring out the leading coefficient from each, the 25 from the x's and the 9 from the y's:
[tex]25(x^2+8x)-9(y^2+2y)=-166[/tex]
Now take half the linear term in each set of parenthesis, square it, and add it in to both sides, remembering the multiplier outside (the 25 and the 9). Our x linear term is 8. Half of 8 is 4, and 4 squared is 16, so we add a 16 into the parenthesis with the x's; our y linear term is 2. Half of 2 is 1 and 1 squared is 1, so we add a 1 into the parenthesis with the y's:
[tex]25(x^2+8x+16)-9(y^2+2y+1)=-166+400-9[/tex]
Note the 400 and -9 on the right side now. 25 times 16 is 400; we didn't just add in a 16, we have to multiply the scalar number into it before we know what we REALLY added in. And the -9 comes from multiplying the -9 times 1.
The reason we do this is to get the perfect square binomials on the left that we created while completing the square:
[tex]25(x+4)^2-9(y+1)^2=225[/tex]
Now, finally we will divide both sides by 225 to get this conic into standard form:
[tex]\frac{(x+4)^2}{9} -\frac{(y+1)^2}{25} =1[/tex]
This is a hyperbola with a horizontal transverse axis and a center of (-4, -1). The reason we know it's not an ellipse is because an ellipse will always have a + sign separating the x-squared from the y-squared whereas a hyperbola always has a - sign separating them. And we also know it's not a circle because the values of the leading coefficients weren't the same.
100 POINTS IF YOU GUESS RIGHT PLEASE HELP
Answer:
5 and 3Step-by-step explanation:
Let the numbers be x and y.
We have:
x + y = 8x - y = 2Sum the two and find x:
2x = 10x = 5Find y:
y = 5 - 2y = 3Let the numbers be a and b
a+b=8a-b=2Add both
2a=10a=5Put in first one
5+b=8b=3
What is the sum of the rational expressions below?
15/7x+12/7x
Answer:
27 / (7x)
Step-by-step explanation:
Since the denominators are the same, we can add the numerators
15 12
----- + ---------
7x 7x
27
----
7x
You start at (2, -1). You move down 3 units and left 3 units. Where do you end?
Answer:
(-1,-4)
Step-by-step explanation:
(2, -1)
Moving down 3 means subtract 3 from the y value
Left 3 means subtract 3 from the x value
(2-3, -1-3)
(-1,-4)
(t+5)(t+2),make t the subject of the formula
Answer:
t= 2p+5/p-1
Step-by-step explanation:
The question is not well writen
Assume p = t+5/t-2
We are to make t the subject of the formula
Cross multiply
p(t-2) = t+5
pt - 2p = t+5
pt - t = 2p+5
t(p-1) = 2p+5
t= 2p+5/p-1
Hence the value of t is 2p+5/p-1
I have 3 pictures please check them out
Point C(6, 10) is dilated and end up at the image pointC C(10.5, 17.5) . What was the scale factor that was used for the dilation?
Answer:
Step-by-step explanation:xyyxxyduxuxifg icicuddididif uicidididciifificvidid idodididix ididididix ifidididix
Can someone please help me on this work I really need help I will but you brainly
Answer:
-3 1/4 is the answer for this question
The greatest power failure in the history of Dallas, Texas lasted
13 hours. How many minutes did this power failure last?
Answer:
its 780 minutes
Step-by-step explanation:
multiply 13 by 60
What is the radius of a sphere with a volume of 62770 m, to the nearest tenth of a
meter?
Answer:
24.65
Step-by-step explanation:
The owners of an amusement park selected a random sample of 200 days and recorded the number of park patrons with annual passes who visited the park on each selected day. They computed a 90% confidence interval for the number of patrons with annual passes who visit the park daily. How would you interpret the 90% confidence interval of (35, 51)? a. There is a 90% chance that the population mean number of patrons with annual passes who are in the park on any given day is between 35 and 51. b. The method used to calculate the confidence interval has a 90% chance of producing an interval that captures the population mean number of annual pass holders in the park on any given day. c. Ten percent of the population of annual pass holders visit the park on any given day. d. There is a 90% chance that the sample percentage of park patrons with annual passes is contained in the interval 35 to 51.
Answer:
b. The method used to calculate the confidence interval has a 90% chance of producing an interval that captures the population mean number of annual pass holders in the park on any given day.
Step-by-step explanation:
The confidence interval calculated from the sample at a particular confidence level, gives a certain percentage of confidence based on the confidence level that the true mean of the population exists within the confidence interval Calculated.
For the scenario above, we can say that there is a 90% chance that the population mean number of annual pass holders in the park on a given day is within the interval (35, 51)
Interpret the results of the chi-square test.A die is rolled 180 times and the following data are obtained.Number Frequency 1 31 2 34 3 26 4 16 5 32 6 41A chi-square test was conducted to determine, at the 5% significance level, whether or not the die is loaded (i.e., that the six numbers are not equally likely).Carry out the hypothesis test.
Answer:
Step-by-step explanation:
From the given information:
Null and alternative hypothesis is:
[tex]\mathbf{H_o: \text{The die is not loaded i.e. six numbbers are equally alike}}[/tex]
[tex]\mathbf{H_a: \text{The die is loaded i.e. six numbbers are not equally alike}}[/tex]
Numbers Observed Expected (O - E) (O-E)^2 (O-E)^2/E
Frequency (O) Frequency (E)
1 31 30 1 1 0.03
2 34 30 4 16 0.53
3 26 30 -4 16 0.53
4 16 30 -14 196 6.53
5 32 30 2 4 0.13
6 41 30 11 121 4.03
Total 180 [tex]X^2= \sum (\dfrac{O-E}{E})^2=11.78[/tex]
degree of freedom = n - 1
= 6 - 1
= 5
Critical value at [tex]X^2_{0.05/2,5} =11.07[/tex]
Since the calculated [tex]X^2 \ is \ > X^2_{0.025/5}[/tex] , then we reject [tex]H_o[/tex]
Conclusion: Accept the alternative hypothesis.
The information provided gives sufficient evidence for us to conclude that the given die is loaded.
Oscar bought 12 lunches for 30$ what was the unit cost
Can somebody help me with this
Answer:
0.04997916927
Step-by-step explanation:
Answer:
30 degrees
Step-by-step explanation:
arcsin(0.5) deg
= 30
Question 20
Josh says that has the same quotient as Is this true or false?
O True
O False
is (0,0) a solution to this system
is (0,0) a solution to what system?
Lin and Claire each threw a rock into a stream. The black graph represents the height of a stone t seconds after it was tossed up by Lin and the purple graph represents the height of a stone t seconds after it was tossed up by Claire.
1) Whose stone hit the water second, and at what time?
2) How long did it take for Claire's rock to reach its maximum? What is the maximum height?
3) Who had the higher initial height? What was it?
Answer:
1) claire's stone at 1.25 seconds
2) 0.5 seconds and its max height was 9
3) lin at 8ft
Step-by-step explanation:
the intercepts tell you the first and third question and then the max height is the highest point on the graph
not sure what measurements you were supposed to use so I used seconds and feet and if that's not it then it's the same numbers just different words
Can someone explain to me the Laws of Sine and Cosine. Will mark brainliest.
Answer:
here you are
i hope it helps! :)
Step-by-step explanation:
10 points will give brainliest
Answer:
A. 9/2 × 3/8
Step-by-step explanation:
______________
What is the M.A.D. of this data set? 3,6,6,7,8,11,15,16
the answer is 8 because it was in the middle
it's 8
Combine any like terms in the expression. If there are no like terms, rewrite the expression.
5t+t–2t
Answer:
4t
Step-by-step explanation:
Note that teach term has the variable t in it. Also, note that if t is by itself, it actually means 1t. Combine the given constants:
5t + 1t - 2t
= (5t + 1t) - 2t
= (6t) - 2t
= 4t
4t is your answer.
~
what is 12.92÷10 to the power of five
than you
Answer:
0.0001292
Step-by-step explanation:
a raised to the power -m is 1/a raised to power m
Joey, Mikey, and Anna each bought an equal number of comic books. If Anna
went home with six comic books, how many did the group buy?
Answer: 6, 2, 12, 18 I NEED HELP PLEASE
Answer:
the group bought 18 comic books.
Step-by-step explanation:
It says that Anna went home with 6 comic books and there are 3 people (Joey, Mikey, and Anna). So if Anna bought 6 comic books, Joey also bought 6 books and Mikey also bought 6 books. 6 + 6 + 6 = 18
Hope this is helpful
Can someone please help?
Find the slope on the line?
Answer:
slope=0
Step-by-step explanation:
Hi there!
We're given a graph with a line and two marked points on the graph: (-1,3) and (3,3)
the formula given for slope calculated from two points is (y2-y1)/(x2-x1), where (x1,y1) and (x2,y2) are points
we have our two points: (-1,3) and (3,3) and we can label them:
x1=-1
y1=3
x2=3
y2=3
now substitute into the formula
note: Remember the formula shows SUBTRACTION, even though we have NEGATIVE numbers. When we simplify, we'll add the numbers.
slope=(3-3)/(3--1)
simplify
slope=0/4
divide
slope=0
Hope this helps!
rearrage and solve 4t-s-2t+25
Answer:
See the image below for the answer:)
Step-by-step explanation:
A sphere and a cylinder have the same radius and height. The volume of the cylinder is 18 cm
What is the volume of the sphere?
Answer:
12 cm³
Step-by-step explanation:
the volume of the sphere = 4/3 πr³
the volume of the cylinder (h=2r)= πr².2r
= 2πr³
the volume ratio of S : C =
4/3 πr³ : 2 πr³
= 4/3 : 2
= 4 : 6
= 2 : 3
so, the volume of the Sphere =
2/3 × 18 = 12 cm³
Answer:
Solution given:
radius [r]=height[h]
volume of cylinder=πr²h
18cm³=πr³
again
volume of sphere
=4/3 πr³
=4/3*18=24cm³
the volume of the sphere:24cm³