Answer:
1. 1 * [tex]x^{3/6}[/tex] = [tex]x^{3/6}[/tex] (it will be equal to the sixth root of x cube)
2. No, the expression [tex]x^{3}[/tex] X [tex]x^{3}[/tex] X [tex]x^{3}[/tex] will be equal to [tex]x^{3 + 3 + 3 }[/tex] since the powers of numbers with the same base are added
3. B and D 1/[tex]x^{-1}[/tex] is the same as 'x'
as mentioned in the last answer, powers of numbers with same base are added. hence, option D will be [tex]x^{3/3}[/tex] which will be equal to x
Between which two whole numbers is the square root of 12
Hey there! I'm happy to help!
Let's look at all of the perfect squares (numbers with integer square roots) so that we can see where the square root of 12 lies.
√1=1
√4=2
√9=3
√16=4
√25=5
√36=6
√49=7
√64=8
√81=9
√100=100
We see that √12 would be in between √9 and √16 (3 and 4), so the square root of 12 is in between 3 and 4.
I hope that this helps! Have a wonderful day! :D
The square root of 12 lies between the whole numbers 3 and 4.
What is a square root?
The value of a number's power 1/2 is the number's square root. It is the number whose product by itself yields the original number, to put it another way.
Let's look at all of the perfect squares (numbers with integer square roots) so that we can see where the square root of 12 lies.
√1=1
√4=2
√9=3
√16=4
√25=5
√36=6
√49=7
√64=8
√81=9
√100=100
We see that √12 would be in between √9 and √16 (3 and 4), so the square root of 12 is in between 3 and 4.
Therefore, the square root of 12 lies between the whole numbers 3 and 4.
To know more about square roots follow
https://brainly.com/question/428672
#SPJ5
What is the common ratio between successive terms in the sequence?
2, 4, 8, -16, 32, 64, ...
goes by 2 then turns to a negative every 3 numbers
Step-by-step explanation:
Which of the following points does not satisfy the equation 2x2 - 5y = 20?
Which set of integers does NOT represent the lengths of the sides of a triangle?
A. (4,7,9)
B. (6,6,11)
C. (9,10,11)
D. {4,8,12)
5. The rear wheels of DeMarius' car complete 4/5 of a rotation for every full rotation of a front wheel. What is the
radius, in feet, of a rear wheel on the car? Write your answer as a simplified fraction.
Answer:
The answer to your question is 6.4 feet
Let f(x) = 7x - 4.
What is f(6)?
O A. 38
OB. 46
C. 42
D. 48
Graph the opposite of the opposite of 10 on the number line
Answer:
the opposite of 10 is -10
Step-by-step explanation:
Graph it on -10
Answer:
Just draw a solid dot in the position positive 10 on the number line
Step-by-step explanation:
Notice that the opposite of 10 is "negative 10" (-10), and the opposite of this (-10) is "positive 10" (10). So the opposite of the opposite takes you back to the original number (positive 10)
A shirt is on sale for 20% off. if the sale price is $29.90, what is the original cost of the shirt?
Answer:
$35.88
Step-by-step explanation:
Multiply 29.9 by 1.20 to get the original price
hope this helps:)
x + (x + 11) =79 solve x
Answer:
x=34
Step-by-step explanation:
x + (x + 11) =79
Combine like terms
2x+11 = 79
Subtract 11 from each side
2x+11-11 = 79-11
2x = 68
Divide by 2
2x/2 = 68/2
x = 34
Answer:
[tex]\Huge \boxed{x=34}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Step-by-step explanation:
[tex]x+x+11=79[/tex]
Combining like terms.
[tex]2x+11=79[/tex]
Subtracting 11 from both sides.
[tex]2x=68[/tex]
Dividing both sides by 2.
[tex]x=34[/tex]
[tex]\rule[225]{225}{2}[/tex]
If AABC = APQR, then
AB =
Answer:
AB = PQ
Step-by-step explanation:
ABC = PQR
The angles are equal and the segments are equal
for the angles
A = P
B = Q
C = R
For the segments
AB = PQ
BC = QR
AC = PR
Answer:
Line AB is approximately equal to Line PQ
An independent random sample is selected from an approximately normal population with an unknown standard deviation. Find the p-value for the given set of hypotheses and _t_ statistic. Also determine if the null hypothesis would be rejected at $\alpha$
The complete question is missing, so i have attached it
Answer:
A) Reject the null hypothesis
B) Reject the null hypothesis
C) Fail to reject the null hypothesis
D) Reject the null hypothesis
Step-by-step explanation:
A) We are given;
Ha: μ > μ_o (This is thus, a one-tail problem)
n = 11
T = 1.91
Using online p-value from t-score calculator as attached with a DF = n - 1 = 11 - 1 = 10, and t-value = 1.91, and significance level of 0.05, and 1 tail, we have;
The p-value is 0.042602
P-value is less than significance level, thus, we will reject the null hypothesis
B) We are given;
Ha: μ < μ_o (This is thus, a one-tail problem)
n = 17
T = -3.45
Using online p-value from t-score calculator as attached with a DF = n - 1 = 17 - 1 = 16, and t-value = 1.91, and significance level of 0.05, and 1 tail, we have;
The p-value is 0.001647
P-value is less than significance level, thus, we will reject the null hypothesis
C)We are given;
Ha: μ ≠ μ_o (This is thus, a two-tail problem)
n = 7
T = 0.83
Using online p-value from t-score calculator as attached with a DF = n - 1 = 7 - 1 = 6, and t-value = 0.83, and significance level of 0.05, and 2 tail, we have;
The p-value is 0.438308.
P-value is higher than the significance level, thus, we will fail to reject the null hypothesis.
D) We are given;
Ha: μ > μ_o (This is thus, a one-tail problem)
n = 28
T = 2.13
Using online p-value from t-score calculator as attached with a DF = n - 1 = 28 - 1 = 27, and t-value = 2.13, and significance level of 0.05, and 1 tail, we have;
The p-value is 0.021218
P-value is lower than the significance level, thus, we will reject the null hypothesis
P-value is lower than the significance level, thus, we will reject the null hypothesis.
Sam paid $3.60 for 3/4 pound of his favorite trail-mix. What is the unit price (dollars per pound)?
Answer:
So the unit price of the trail - mix is $4.80 per pound
Step-by-step explanation:
Sam paid $3.60 for 3/4 pound of his favorite trail-mix.
What it means is that said paid for 3/4 = 0.75 of a pound for $3.60
So let's determine how much he could have paid for a complete pound
$3.60= 0.75 pound
X= 1 pound
$X*0.75 pound= $3.60*1 pound
$x= ($3.60*1 pound)/0.75 pound
$x=$3.60/0.75
$x= $4.80
So the unit price of the trail - mix is $4.80 per pound
please help!! I just started college
Answer:
(r. q) (7) = [tex] \pm 220[/tex]
(q.r) (7) = [tex] \pm 220[/tex]
Step-by-step explanation:
[tex]q(x) = {x}^{2} + 6 \\ q(7) = {7}^{2} + 6 = 49 + 6 = 55\\ r(x) = \sqrt{x + 9} \\ r(7) = \sqrt{7 + 9} = \sqrt{16} = \pm 4 \\ \\ (r.q)(7) = r(7).q(7) = \pm 4 \times 55 = \pm220 \\ \\ (q.r)(7) = q(7).r(7) = 55 \times \pm 4 = \pm220 [/tex]
A teacher records the amount of time it took a random sample of students to finish a test and their scores on that test. Let x be the score and y be the amount of time. Conduct a hypothesis test of the claim that there is a linear correlation between the variables, using a 0.10 level of significance. Find the PERCENTAGE OF THE VARIANCE IN THE Y-VALUES THAT CAN BE EXPLAINED BY THEIR LINEAR RELATIONSHIP WITH THE X-VALUES.
Answer:
hello your question has a missing table attached below is the missing table
Answer : 0.55%
Step-by-step explanation:
The complete table related to the answer given above is attached below
using a 0.10 level of significance the percentage of the variance in the Y-values that shows a linear relationship with the X-values = 0.55%
The values for X^2 , y^2 and x*y is determined an entered into a table ( attached below as well )
You have 10 identical pieces of chocolate and would like to share them with your friends John, Harry, and Donald. Assuming that there are no restrictions on the number of chocolates each can have, in how many different ways can you distribute all the chocolates to the three of them
Answer:
3.3333333333333333333333 just 3.3
Step-by-step explanation:
Answer: 120 ways
Step-by-step explanation:
given data:
no of chocolate = 10pcs
to be shared among three individuals who are John, Harry and Donald.
there is no restriction to how it can be shared amongst them.
this Problem can be solved using combination as the order with which it would be shared doesn’t matter.
solution:
n = 10
r = 3
= 10C3
= n! / ( n - r )! r !
= 10! / ( 10 - 3 ! ) 3!
= 10! / ( 7! ) 3!
= 120
the chocolate can be shared amongst them in 120ways.
1. What is the number of students of Class
VIII whose marks obtained in an examination
are expressed in the following frequency distribution
Answer:
40 students
Step-by-step explanation:
and all the frequencies
there should one student per tally mark because the tally is measuring grades
Hope that helped!!! k
Answer:
[tex]\Huge \boxed{40}[/tex]
Step-by-step explanation:
Adding all the frequencies in the frequency distribution gives the total number of students.
[tex]6+10+8+9+7=40[/tex]
The number of students in class VIII whose marks obtained in an examination are 40.
Type the correct answer in each box. Round your answers to two decimal places. Find the average rate of change of f(x) = log2(3x − 6) on [3, 4], [4, 5], and [5, 6].
Answer:
[tex][3,4][/tex] : [tex]r = 1[/tex], [tex][4,5][/tex] : [tex]r = 0.59[/tex], [tex][5,6][/tex] : [tex]r = 0.42[/tex]
Step-by-step explanation:
Given a function [tex]f(x)[/tex] that is continuous on [tex][a,b][/tex], the average rate of change is:
[tex]r = \frac{f(b)-f(a)}{b-a}[/tex]
[tex]a[/tex], [tex]b[/tex] - Lower and upper bounds, dimensionless.
[tex]f(a)[/tex], [tex]f(b)[/tex] - Images of the function evaluated at lower and upper bounds, dimensionless.
Let be [tex]f(x) = \log_{2}(3\cdot x - 6)[/tex], then:
[tex][3,4][/tex]
[tex]a = 3[/tex] and [tex]b = 4[/tex]
[tex]f(3) = \log_{2}[3\cdot (3) - 6][/tex]
[tex]f(3) \approx 1.585[/tex]
[tex]f(4) = \log_{2}[3\cdot (4) - 6][/tex]
[tex]f(4) \approx 2.585[/tex]
[tex]r = \frac{2.585-1.585}{4-3}[/tex]
[tex]r = 1[/tex]
[tex][4,5][/tex]
[tex]a = 4[/tex] and [tex]b = 5[/tex]
[tex]f(4) = \log_{2}[3\cdot (4) - 6][/tex]
[tex]f(4) \approx 2.585[/tex]
[tex]f(5) = \log_{2}[3\cdot (5) - 6][/tex]
[tex]f(5) \approx 3.170[/tex]
[tex]r = \frac{3.170-2.585}{5-4}[/tex]
[tex]r = 0.59[/tex]
[tex][5,6][/tex]
[tex]a = 5[/tex] and [tex]b = 6[/tex]
[tex]f(5) = \log_{2}[3\cdot (5) - 6][/tex]
[tex]f(5) \approx 3.170[/tex]
[tex]f(6) = \log_{2}[3\cdot (6) - 6][/tex]
[tex]f(6) \approx 3.585[/tex]
[tex]r = \frac{3.585-3.170}{6-5}[/tex]
[tex]r = 0.42[/tex]
Answer:
Please mark me as brainliest :)
Step-by-step explanation:
determine the value of x using a trigonometric ratio.
Answer:
a
Step-by-step explanation:
The value of x in the triangle is given by trigonometric relations and the value is x = 8.86 units
What are trigonometric relations?
Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the triangle be represented as ABC
Now , the height of the triangle is BC = 5.5 units
Let the angle be θ = 50°
Now ,
From the trigonometric relations ,
cos θ = adjacent / hypotenuse
Substituting the values in the equation , we get
cos θ = 5.5 / x
Multiply by x on both sides of the equation , we get
x ( cos θ ) = 5.5
Divide by cos θ on both sides of the equation , we get
x = 5.5 / cos θ
when θ = 50°
x = 5.5 / cos 50°
x = 5.5 / 0.642787
x = 8.556 units
Therefore , the value of x = 8.56 units
Hence , the value of x of triangle is x = 8.56 units
To learn more about trigonometric relations click :
https://brainly.com/question/14746686
#SPJ2
If 6 oz cost $2.10 and 8 oz cost $2.80 and 16 oz cost $5.60. How much would 20 oz cost
Answer:
$7.00
Step-by-step explanation:
Since each of them are 35 cents per ounce
20 x 0.35 = 7
2x - 4 - 6(x + 1) = 5x + 6 a) 8 b) -8/9 c) 4 d) -16/9
Step-by-step explanation:
2x - 4 - 6(x + 1) = 5x + 6
2x - 4 - 6x - 6 = 5x + 6
2x - 6x - 5x = 4 + 6 + 6
-9x =16
x= -16/9
Hope this helps.. Good luck!
How many different rays can be named?
Answer:
millions
Step-by-step explanation:
the possibilities are endless
Round to the nearest whole number 90.05
Answer:
90
Step-by-step explanation:
Identify the one's place:90.05
2 . Check the number to the right of it:
90.05
If the number is greater than or equal to 5, we round up. If it's less than or equal to four, we round down.
Zero is less than four. This means we round down.
90.05 ≈ 90
Hope this helps.
An ant walked on the coordinate plane from point A( − 3,1) to point B(1,25) by the shortest path. Find y-coordinate of the point where the ant intersected y-axis.
Answer:
19
Step-by-step explanation:
The shortest path is a straight line. The slope of that line is:
m = (25 − 1) / (1 − (-3))
m = 6
The point where the ant intersects the y-axis has an x-coordinate of 0. The slope between that point, and any other point on the line, is 6.
6 = (y − 1) / (0 − (-3))
y = 19
Evaluate the limit, if it exists. Show work. lim┬(x→5)〖(x^2-3x-10)/(2x-10)〗
Hello, first of all we can notice that
[tex]5^2-3*5-10=25-15-10=0[/tex]
and
[tex]2*5-10=0[/tex]
and 0 divided by 0 is undetermined.
So, we need to factorise and simplify first.
[tex]x^2-3x-10=(x-5)(x+2)\\\\\text{Because we already known that 5 is a zero...}\\\\\text{... and the sum of the zeroes is 3 = 5 - 2 and the product is -10 = 5 * (-2).}[/tex]
For x different from 5, we can write
[tex]\dfrac{x^2-3x-10}{2x-10}=\dfrac{(x-5)(x+2)}{2(x-5)}=\dfrac{x+2}{2}[/tex]
So, the limit when x tends to 5 is
[tex]\dfrac{5+2}{2}=\boxed{\dfrac{7}{2}}[/tex]
Thank you
Which of the following pairs of functions are inverses of each
other?
Answer: C
Step-by-step explanation:
For this problem, let's find the inverse for all f(x) and see which pairs with the g(x). To find the inverse, you replace the x with y and y with x. Then you solve for y.
A. Incorrect
[tex]y=\frac{x-8}{4} +9[/tex] [replace x with y and y with x]
[tex]x=\frac{y-8}{4} +9[/tex] [subtract both sides by 9]
[tex]x-9=\frac{y-8}{4}[/tex] [multiply both sides by 4]
[tex]4(x-9)=y-8[/tex] [add both sides by 8]
[tex]4(x-9)+8=y[/tex]
This does not match g(x), therefore, they are not inverses of each other.
----------------------------------------------------------------------------------------------------------
B. Incorrect
[tex]y=4(x-12)+2[/tex] [replace x with y and y with x]
[tex]x=4(y-12)+2[/tex] [subtract both sides by 2]
[tex]x-2=4(y-12)[/tex] [divide both sides by 4]
[tex]\frac{x-2}{4} =y-12[/tex] [add both sides by 12]
[tex]\frac{x-2}{4} +12=y[/tex]
This does not match g(x), therefore, they are not inverses of each other.
----------------------------------------------------------------------------------------------------------
C. Correct
[tex]y=3(\frac{x}{2})-4[/tex] [replace x with y and y with x]
[tex]x=3(\frac{y}{2} )-4[/tex] [add both sides by 4]
[tex]x+4=3(\frac{y}{2} )[/tex] [divide both sides by 3]
[tex]\frac{x+4}{3} =\frac{y}{2}[/tex] [multiply both sides by 2]
[tex]\frac{2(x+4)}{3} =y[/tex]
This matches g(x), therefore, they are inverses of each other.
----------------------------------------------------------------------------------------------------------
D. Incorrect
[tex]y=3(\frac{2}{x} )-10[/tex] [replace x with y and y with x]
[tex]x=3(\frac{2}{y} )-10[/tex] [add both sides by 10]
[tex]x+10=3(\frac{2}{y} )[/tex] [divide both sides by 3]
[tex]\frac{x+10}{3} =\frac{2}{y}[/tex] [multiply both sides by y]
[tex](y)(\frac{x+10}{3} )=2[/tex] [multiply both sides by [tex]\frac{3}{x+10}[/tex] or divide by [tex]\frac{x+10}{3}[/tex]]
[tex]y=\frac{6}{x+10}[/tex]
This does not match g(x), therefore, they are not inverses of each other.
----------------------------------------------------------------------------------------------------------
After going through each problem, we found that the correct answer is C.
Consider the ratio of 153 per 108. Write this ratio in different forms below.
A ratio written as a reduced fraction -
A ratio written as a decimal rounded to the hundredths -
What is the answer to this?
Answer:
i) [tex]\frac{17}{12}[/tex], ii) Approximately 1.42, iii) The answer to this is given by the reduced fraction, as decimal form has an infninite periodic component.
Step-by-step explanation:
(i) A ratio written as a reduced fraction:
Given ratio is now simplified to its reduce form:
1) [tex]\frac{153}{108}[/tex] Given
2) [tex]\frac{51}{36}[/tex] Modulative property/Existence of multiplicative inverse/Definition of division/[tex]\frac{\frac{x}{y}}{\frac{w}{z}} = \frac{x\cdot z}{y\cdot w}[/tex]
3) [tex]\frac{17}{12}[/tex] Modulative property/Existence of multiplicative inverse/Definition of division/[tex]\frac{\frac{x}{y}}{\frac{w}{z}} = \frac{x\cdot z}{y\cdot w}[/tex]/Result
(ii) A ratio written as a decimal rounded to hundredths:
[tex]\frac{17}{12} \approx 1.42[/tex]
(iii) What is the answer to this?
The answer to this is given by the reduced fraction, as decimal form has an infninite periodic component.
Suppose you walk at a rate of 210ft/min. You need to walk 10,000 ft. How many more minutes will it take you to finish if you have already walked 550ft
Answer:
45 minutes
Step-by-step explanation:
Distance needed to be covered = 10,000-550= 9,450
Speed= 210ft/min
time: 9450/210= 45 mins
Which of the following expressions is the inverse of the function y = 3x + 4? (5 points)
Answer:
y = (x − 4) / 3
Step-by-step explanation:
y = 3x + 4
To find the inverse, switch x and y, then solve for y.
x = 3y + 4
x − 4 = 3y
y = (x − 4) / 3
• Check your work when you're done.
Your Assignment
Michael and his sister Mel share the job of mowing the grass in their yard. Michael mows 1/3
of the yard, and Mel mows the rest. Mel can mow 3/4 of the entire yard in an hour. How long will it take Mel to finish mowing her part of the yard?
Answer:
Approximately 53 mins
Step-by-step explanation:
Yard mowed by Michael = ⅓ of the yard
Yard mowed by Mel = 1 - ⅓ = [tex] \frac{1}{1} - \frac{1}{3} = \frac{3 - 1}{3} = \frac{2}{3} [/tex]
Rate at which Mel can mow a yard = ¾ of the yard in 1 hour
That is, it would take 1 hr to mow ¾ of the yard.
If ¾ yard requires 1 hr, then,
⅔ yard would require x hr
Thus:
x*¾ = 1*⅔
[tex] \frac{3x}{4} = \frac{2}{3} [/tex]
Cross multiply
[tex] 3(3x) = 4(2) [/tex]
[tex] 9x = 8 [/tex]
Divide both sides by 9
[tex] x = \frac{8}{9} [/tex]
It would take Mel [tex] \frac{8}{9} hr [/tex] to finish mowing her part, which is approximately 53 mins. [tex] (\frac{8}{9}*60mins = 53.3mins [/tex].
Answer:
53 min
Step-by-step explanation:
PLEASE HELP QUICKLY AS POSSIBLE THANK YOU :)
Can someone only help with b and c thanks
Answer:
b. 8.91,8.9,8.19,8.1,8.098
c. 20.005,20,19.06,2.05,1.905
Answer:
b. 8.91, 8.9, 8.19, 8.1, 8.098.
c. 20.005, 20, 19.06, 2.05, 1.905.
Step-by-step explanation: