Answer:
32
Step-by-step explanation:
The pattern is multiples of 4
The 8 term will be the 8 multiple of 4
4 * 8 = 32
Answer:
32
Step-by-step explanation:
We are adding 4 each time
an = a1+d(n-1)
an = 4+4(n-1)
we want the 8th term
a8 = 4+4(8-1)
a8 = 4+4(7)
a8 = 4+28
a8 = 32
Is –8 − –95 positive or negative?
Answer:
87, which is positive
Step-by-step explanation:
-8 --95
Subtracting a negative is like adding
-8 +95
87
Rotation 90° counterclockwise around the origin of the point (-8,1)
Hello there are two questions in the link's if both were solved that would be awesome.
Answer:
[tex]\frac{x^{\frac{5}{6}} }{x^{\frac{1}{6}} } = x^{(\frac{5}{6} -\frac{1}{6}) }= x^{\frac{4}{6} }\\\sqrt{x} . \sqrt[4]{x} = x^{\frac{1}{2} } . x^{\frac{1}{4} } = x^{(\frac{1}{2} +\frac{1}{4}) } = x^{\frac{3}{4}[/tex]
Change each of the following points from rectangular coordinates to spherical coordinates and to cylindrical coordinates.
a. (4,2,−4)
b. (0,8,15)
c. (√2,1,1)
d. (−2√3,−2,3)
Answer and Step-by-step explanation: Spherical coordinate describes a location of a point in space: one distance (ρ) and two angles (Ф,θ).To transform cartesian coordinates into spherical coordinates:
[tex]\rho = \sqrt{x^{2}+y^{2}+z^{2}}[/tex]
[tex]\phi = cos^{-1}\frac{z}{\rho}[/tex]
For angle θ:
If x > 0 and y > 0: [tex]\theta = tan^{-1}\frac{y}{x}[/tex];If x < 0: [tex]\theta = \pi + tan^{-1}\frac{y}{x}[/tex];If x > 0 and y < 0: [tex]\theta = 2\pi + tan^{-1}\frac{y}{x}[/tex];Calculating:
a) (4,2,-4)
[tex]\rho = \sqrt{4^{2}+2^{2}+(-4)^{2}}[/tex] = 6
[tex]\phi = cos^{-1}(\frac{-4}{6})[/tex]
[tex]\phi = cos^{-1}(\frac{-2}{3})[/tex]
For θ, choose 1st option:
[tex]\theta = tan^{-1}(\frac{2}{4})[/tex]
[tex]\theta = tan^{-1}(\frac{1}{2})[/tex]
b) (0,8,15)
[tex]\rho = \sqrt{0^{2}+8^{2}+(15)^{2}}[/tex] = 17
[tex]\phi = cos^{-1}(\frac{15}{17})[/tex]
[tex]\theta = tan^{-1}\frac{y}{x}[/tex]
The angle θ gives a tangent that doesn't exist. Analysing table of sine, cosine and tangent: θ = [tex]\frac{\pi}{2}[/tex]
c) (√2,1,1)
[tex]\rho = \sqrt{(\sqrt{2} )^{2}+1^{2}+1^{2}}[/tex] = 2
[tex]\phi = cos^{-1}(\frac{1}{2})[/tex]
[tex]\phi[/tex] = [tex]\frac{\pi}{3}[/tex]
[tex]\theta = tan^{-1}\frac{1}{\sqrt{2} }[/tex]
d) (−2√3,−2,3)
[tex]\rho = \sqrt{(-2\sqrt{3} )^{2}+(-2)^{2}+3^{2}}[/tex] = 5
[tex]\phi = cos^{-1}(\frac{3}{5})[/tex]
Since x < 0, use 2nd option:
[tex]\theta = \pi + tan^{-1}\frac{1}{\sqrt{3} }[/tex]
[tex]\theta = \pi + \frac{\pi}{6}[/tex]
[tex]\theta = \frac{7\pi}{6}[/tex]
Cilindrical coordinate describes a 3 dimension space: 2 distances (r and z) and 1 angle (θ). To express cartesian coordinates into cilindrical:
[tex]r=\sqrt{x^{2}+y^{2}}[/tex]
Angle θ is the same as spherical coordinate;
z = z
Calculating:
a) (4,2,-4)
[tex]r=\sqrt{4^{2}+2^{2}}[/tex] = [tex]\sqrt{20}[/tex]
[tex]\theta = tan^{-1}\frac{1}{2}[/tex]
z = -4
b) (0, 8, 15)
[tex]r=\sqrt{0^{2}+8^{2}}[/tex] = 8
[tex]\theta = \frac{\pi}{2}[/tex]
z = 15
c) (√2,1,1)
[tex]r=\sqrt{(\sqrt{2} )^{2}+1^{2}}[/tex] = [tex]\sqrt{3}[/tex]
[tex]\theta = \frac{\pi}{3}[/tex]
z = 1
d) (−2√3,−2,3)
[tex]r=\sqrt{(-2\sqrt{3} )^{2}+(-2)^{2}}[/tex] = 4
[tex]\theta = \frac{7\pi}{6}[/tex]
z = 3
What is the solution to 4x + 2 = 6(-2x - 5) ?
O2
O 16
0-2
O -16
Please need help on this
4x+2=6(-2x-5)
<=>4x+2=-12x-30
<=>16x+32=0
<=>x=-2
I cant seem to get the second one right...
Rx=1 means to reflect the given point on the line of x= 1
The mapping for the reflection on line x is x = k
(-2,7) = (-2(1) - -2,7) = (4,7)
The missing value is 7
Renting a car costs $30 per day, or $600 per month. Renting daily is cheaper for a few days, but after how many days are the two options equal (after which renting monthly is cheaper)?
Answer:
20 days
Step-by-step explanation:
Renting a car costs $30 per day.
y = 30x
Renting a car costs $600 per month
y = 600
Set the two equations equal to each other.
30x = 600
(30x)/30 = (600)/30
x = 20
After 20 days, the two options have an equal cost.
A quadrilateral has vertices A(3, 5), B(2, 0), C(7, 0), and D(8, 5). Which statement about the quadrilateral is true? A. ABCD is a parallelogram with non-perpendicular adjacent sides. B. ABCD is a trapezoid with only one pair of parallel sides. C. ABCD is a rectangle with non-congruent adjacent sides. D. ABCD is a rhombus with non-perpendicular adjacent sides.
Hey There!!
The answer to this is: A quadrilateral has vertices A(3, 5), B(2, 0), C(7, 0), and D(8, 5). Which statement about the quadrilateral is true?" Line BC is parallel to line AD because their slopes is equal i.e. (0 - 0) / (7 - 2) = (5 - 5) / (8 - 3) which gives 0 / 5 = 0 / 5 giving that 0 = 0. We check whether line AB is parallel to line CD. Slope of line AB is given by (0 - 5) / (2 - 3) = -5 / -1 = 5. Slope of line CD is given by (5 - 0) / (8 - 7) = 5 / 1 = 5 We have been able to prove that the opposite sides of the quadrilateral are parallel which means that the quadrilateral is not a trapezoid. Next we check whether the length of the sides are equal. Length of line AB is given by sqrt[(0 - 5)^2 + (2 - 3)^2] = sqrt[(-5)^2 + (-1)^2] = sqrt(25 + 1) = sqrt(26) Length of line BC is given by sqrt[(0 - 0)^2 + (7 - 2)^2] = sqrt[0^2 + 5^2] = sqrt(25) = 5 Length of line CD is given by sqrt[(5 - 0)^2 + (8 - 7)^2] = sqrt[5^2 + 1^2] = sqrt(25 + 1) = sqrt(26) Length of line DA is given by sqrt[(5 - 5)^2 + (8 - 3)^2] = sqrt[0^2 + 5^2] = sqrt(25) = 5 Thus, the length of the sides of the quadrilateral are not equal but opposite sides are equal which means that the quadrilateral is not a rhombus. Finally, we check whether adjacent lines are perpendicular. Recall the for perpendicular lines, the product of their slopes is equal to -1. Slope of line AB = 5 while slope of line BC = 0. The product of their slopes = 5 x 0 = 0 which is not -1, thus the adjacent sides of the quadrilateral are not perpendicular which means that the quadrilateral is not a rectangle. Therefore, ABCD is a parallelogram with non-perpendicular adjacent sides. Thus, For (option A).
Hope It Helped!~ ♡
ItsNobody~ ☆
Answer:
A. ABCD is a parallelogram with non-perpendicular adjacent sides.
Hope this helps!
Step-by-step explanation:
During the 2014 season, the Los Angeles Dodgers won 58% of their games. Assuming that the outcomes of the baseball games are independent and that the percentage of wins this season will be the same as in 2014: What is the probability that the Dodgers will win at least one of their next seven games
Answer: 0.98
Step-by-step explanation:
given data:
probability they won a game = 58% = 0.58
since outcome of games are independent, and percentage would remain same as 2014.
probablility that Dodgers wins atleast 1 of their next 7 games
= 1 - p
= 1 - ( 0.58 )^ 7
= 1 - 0.02208
= 0.98
probabikotun that Dodgers would win one of their next seven games is 0.98
The area of a parallelogram is 60 f2.
The height is 5 ft. How long is the
base?
Answer:
12 feet
BRAINLIEST, PLEASE!
Step-by-step explanation:
Area = base x height
60 = base x 5
base = 60/5
base = 12
Describe all numbers x that are at a distance of 2 from the number 8. Express this using absolute value notation.
Answer:
The numbers that are at a distance of 2 from the number 8 can be expressed using absolute value notation as:
|x - 8| = 2
Step-by-step explanation:
The numbers that are at a distance of 2 from the number 8 are the numbers that are satisfied by the equation:
|x - 8| = 2
The equation is written in the notation of absolute value as required.
Find the least common multiple of 14 and 22.
Find the area of the triangle with vertices (0,0,0),(−4,1,−2), and (−4,2,−3).
Answer:
0.5*sqrt33
Step-by-step explanation:
A(0,0,0) B(-4,1,-2), c(-4,2,-3)
Vector AB is (-4-0,-1-0, -2-0)= (-4,-1,-2) The modul of AB is sqrt (4squared+
+(-1) squared+ (-2) squared)= sqrt (16+1+4)=sqrt21
Vector AC is (-4,2,-3) The modul of vector AC is equal to sqrt ((-4)squared+ 2squared+(-3)squared)= sqrt(16+4+9)= sqrt29
Vector BC is equal to (-4-(-4), 2-1, -3-(-2))= (0,1,-1)
The modul of BC is sqrt (1^2+(-1)^2)=sqrt2
Find the angle B
Ac^2= BC^2+AB^2-2*BC*AB*cosB
29= 2+21-2*sqrt2*sqrt21*cosB
29= 2+21-2*sqrt42*cosB
cosB= -3/ sqrt42
sinB= sqrt( 1-(-3/sqrt42)^2)=sqrt33/42= sqrt11/14
s=1/2* (sqrt2*sqrt21*sqrt11/14)=1/2*sqrt(42*11/14)= 0.5*sqrt33
Help ive been stuck on this forever
Answer:
3480
Step-by-step explanation:
It always help if you make clear how the state assesses taxes. Usually it is done the way I will do it, but it is no guarantee.
First 3000 = 3000 * 2/100 = 60.00
The next 2000 (excess over 3000) = 2000 * 3/100 = 60
The next 12000 (excess over 5000) = 12000 * 5/100 = 600
The next step would be excess over 12000 = 48000 * 5.75/100 = 2760
That's the way most taxes for federal taxes and state taxes work. What you have to know is this: does the question use the term excess anywhere? Or do your notes. If you are accustomed to the word then this is the way the question is done.
So the total taxes = 60 + 60 + 600 + 2760 = 3480
A random sample of 35 undergraduate students who completed two years of college were asked to take a basic mathematics test. The mean and standard deviation of their scores were 75.1 and 12.8, respectively. In a random sample of 50 students who only completed high school, the mean and standard deviation of the test scores were 72.1 and 14.6, respectively In order to test the equal variance assumption for two populations, Can we assume population variances are equal at the 10% significance level? (sigma subscript 1 superscript 2 space equals space sigma subscript 2 superscript 2 )
Answer:
The 90 % confidence limits are (-2.09, 8.09).
Since the calculated values do not lie in the critical region we accept our null hypothesis.
Step-by-step explanation:
The null and alternative hypothesis are given by
H0: σ₁²= σ₂² against Ha: σ₁² ≠ σ₂²
Confidence interval for the population mean difference is given by
(x`1- x`2) ± t √S²(1/n1 + 1/n2)
Where S ²= (n1-1)S₁² + S²₂(n2-1)/n1+n2-2
Critical value of t with n1+n2-2= 50+ 35-2= 83 will be -1.633
Now calculating
S ²=34* (12.8)²+ (14.6)²*49/83= 192.96
Now putting the values in the t- test
(75.1 -72.1) ± 1.633 √ 192.96(1/35 +1/50)
=3 ± 5.09
=-2.09, 8.09 is the 90 % confidence interval for the difference
The 90 % confidence limits are (-2.09, 8.09).
Since the calculated values do not lie in the critical region we accept our null hypothesis.
two identical rubber balls are dropped from different heights. Ball 1 is dropped from a height of 109 feet, and ball 2 is dropped from a height of 260 feet. Use the function f(t) -16t^2+h to determine the current height, f(t), of a ball from a height h, over given time t.
When does ball 1 reach the ground? Round to the nearest hundredth
Answer: 5.22 seconds
Step-by-step explanation:
t represents time and y represents the height.
Since we want to know when the ball hits the ground, find t when y = 0
Ball 1 starts at a height of 109 --> h = 109
0 = -16t² + 109
16t² = 109
[tex]t^2=\dfrac{109}{16}\\[/tex]
[tex]t=\sqrt{\dfrac{109}{16}}[/tex]
[tex]t=\dfrac{\sqrt{109}}{2}[/tex]
t = 5.22
=> H = 109
=> 0 = -16t² + 109
=> 16t² = 109
=> t² = 109/16
=> t = 109/2
=> t = 5.22 sec
Therefore, 5.22 second is the answer.
Find the vertex of this parabola:
y = x2 + 2x - 3
Answer:
(-1,-4)
Step-by-step explanation:
The equation of a parabola os written as: ax^2+bx+c
This parabola's equation is x^2+2x-3
● a= 1
● b= 2
● c = -3
The coordinates of the parabola are: ( (-b/2a) ; f(-b/2a) )
● -b/2a = -2/2 = -1
● f(-b/2a) = (-1)^2+2×(-1)-3=1-2-3= -4
So the vertex coordinates are (-1,-4)
Answer:
-1+2X
Step-by-step explanation:
Identify the similar triangle. Then find each measure (round to the nearest tenth).
Answer:
ZWU ~ WYU
WY = 2.5
UY= 1.5
Step-by-step explanation:
ZUW ~ WUY ~ ZWY
5/3=x+1/x
Cross multiply
5x=3x+3
2x=3
x=3/2 OR 1.5
Which of the following is equal to the rational expression below when x=-1
or -8?
11(x+8)
/(x + 1)(x+8)
Answer:
11/(x + 1) thus d: is the answer
Step-by-step explanation:
Simplify the following:
(11 (x + 8))/((x + 1) (x + 8))
(11 (x + 8))/((x + 1) (x + 8)) = (x + 8)/(x + 8)×11/(x + 1) = 11/(x + 1):
Answer: 11/(x + 1)
The U.S. Dairy Industry wants to estimate the mean yearly milk consumption. A sample of 21 people reveals the mean yearly consumption to be 74 gallons with a standard deviation of 16 gallons. Assume that the population distribution is normal. (Use t Distribution Table.)
a-1. What is the value of the population mean?
16
Unknown
74
a-2. What is the best estimate of this value?
Estimate population mean
c. For a 90% confidence interval, what is the value of t? (Round your answer to 3 decimal places.)
Value of t
d. Develop the 90% confidence interval for the population mean. (Round your answers to 3 decimal places.)
Confidence interval for the population mean is and .
e. Would it be reasonable to conclude that the population mean is 68 gallons?
a) Yes
b) No
c) It is not possible to tell.
Correct question is;
The U.S. Dairy Industry wants to estimate the mean yearly milk consumption. A sample of 21 people reveals the mean yearly consumption to be 74 gallons with a standard deviation of 16 gallons.
a. What is the value of the population mean? What is the best estimate of this value?
b. Explain why we need to use the t distribution. What assumption do you need to make?
c. For a 90 percent confidence interval, what is the value of t?
d. Develop the 90 percent confidence interval for the population mean.
e. Would it be reasonable to conclude that the population mean is 68 gallons?
Answer:
A) Best estimate = 74 gallons
B) because the population standard deviation is unknown. The assumption we will make is that the population follows the normal distribution.
C) t = 1.725
D) 90% confidence interval for the population mean is (67.9772, 80.0228) gallons
E) Yes
Step-by-step explanation:
We are given;
Sample mean; x' = 74
Sample population; n = 21
Yearly Standard deviation; s = 16
A) We are not given the population mean.
So the closest estimate to the population mean would be the sample mean which is 74.
B) We are not given the population standard deviation and as such we can't use normal distribution. So what is used when population standard deviation is not known is called t - distribution table. The assumption we will make is that the population follows the normal distribution.
C) At confidence interval of 90% and DF = n - 1 = 21 - 1 = 20
From t-tables, the t = 1.725
D) Formula for the confidence interval is;
x' ± t(s/√n) = 74 ± 1.725(16/√21) = 74 ± 6.0228 = 67.9772 or 80.0228
Thus 90% confidence interval for the population mean is (67.9772, 80.0228) gallons
E) 68 gallons lies within the range of the confidence interval, thus we can say that "Yes, it is reasonable"
Determine which is the appropriate approach for conducting a hypothesis test. Claim: The mean RDA of sodium is 2400mg. Sample data: n150, 3400, s550. The sample data appear to come from a normally distributed population.
Answer:
Use the student t distribution
Step-by-step explanation:
Here is the formula
t = (x - u) ÷(s/√N)
From the information we have in the question:
n = 150
s = 550
x = 3400
u = mean = 2400
= 3400 - 2400÷ 500/√150
= 1000/44.9
= 22.27
At 0.05 significance level, df = 149 so t tabulated will be 1.65.
We cannot use normal distribution since we do not have population standard deviationWe cannot use normal distribution since we do not have population standard deviationChisquare cannot be used since we are not testing for population varianceWe cannot use normal distribution since we do not have population standard deviationChisquare cannot be used since we are not testing for population varianceThe parametric or bootstrap method cannot be used either.Given the sequence 4, 8, 16, 32, 64, ..., find the explicit formula.
128Answer:
128
Step-by-step explanation:
vì 4+4=8
8+8=16
16+16=32
32+32=64
64+64=128
12345 are divisible by 15 with exlpin
Answer:
hfwhww45 5h wahdaw 5656 adshjdawh bh4 54
Step-by-step explanation:
5767
12345
Sum of digits = 1+2+3+4+5
= 15
Which means divisible by 3
Ends with 0 or 5 = Yes ends with 5
Therefore the number is divisible by 15
12345÷15 = 823
Divisiblity rule of 15 = Any number is divisible by 15 if the sum of the digits is divisible by 3 and the number ends with a 0 or 5.
Must click thanks and mark brainliest
If you use a 5/8 inch drill bit instead of a 3/16 that the project called for ,your hole will be too . by inches
the function y= -16t^2 + 248, models the hight y in feet of a stone t seconds after it dropped from the edge of a vertical cliff. How long will it take the stone to hit the ground?
Answer:
[tex]t \: = 3.92 \: sec[/tex]
Step-by-step explanation:
When (t =0)
Height of cliff = 248 feet = 75.5m
Using Newton's equations of motion:
[tex]s = ut + \frac{1}{2} a {t}^{2} [/tex]
75.5 = 0 * t + 4.9 * t^2
Solving further :
[tex]t \: = 3.92 \: sec[/tex]
15% of 80 is 60% of what number? There were no answer choices please help!
Answer:
80
Step-by-step explanation:
15 percent of 80 is 12
and 12 is 60 percent of 80!
hope this helps :)
what is the probability that the 2 cards you will draw will be blackjacks?
Answer:
Need more explation of the question
Step-by-step explanation:
If mowing burns average $115 over 20 minutes how many calories are you burning in one hour
Answer:
345
Step-by-step explanation:
20*3 = 60 there's 60 minutes in one hour
115*3 = 345
if k = p+2q/3 , find the value of p when k=7 and q=3
Answer:
p = 5
Step-by-step explanation:
hopefully it is clear and understandable :)
Ellen baked 115 cookies and shared them equally with her 23 classmates. How many whole cookies each can Ellen and her classmates have?
Step-by-step explanation:
Ellen - 115/23
Classmates and Ellen got = 5 each