Answer:
103
Step-by-step explanation:
[tex]\dfrac{1}{216}^{-2/3}+\dfrac{1}{256}^{-3/4}+\dfrac{1}{243}^{-1/5}= \\\\\\\sqrt[3]{216^2}+\sqrt[4]{256^3}+\sqrt[5]{243}=\\\\\\6^2+4^3+3=\\\\\\36+64+3=\\\\\\103[/tex]
Hope this helps!
simplify (6^7)^3
will give brainlist
Answer:
The answer is D.
Step-by-step explanation:
You have to apply Indices Law,
[tex] { ({a}^{m}) }^{n} \: ⇒ \: {a}^{mn} [/tex]
So for this question :
[tex] { ({6}^{7}) }^{3} [/tex]
[tex] = {6}^{7 \times 3} [/tex]
[tex] = {6}^{21} [/tex]
My son and I are stuck on this one. Can anyone give some insight to this problem? Thank you.
Answer:
I made is clear for you, now you may match each one
Step-by-step explanation:
f(1)= 11, f(n)= 3*f(n-1)
11*3= 33, 33*3= 99, 99*3= 297, ...11, 33, 99, 297...⊕ middle
f(1)= -18, f(n)= f(n-1)+21
-18+21= 3, 3+21= 24, 24+21= 45, ...-18, 3, 24, 45, ...f(1)= -18, f(n)= f(n-1) + 22
-18+22= 4, 4+22= 26, 26+22= 48, ...-18, 4, 26, 48, ...f(1)= -18, f(n)= 2*f(n-1)
-18*2= -36, -36*2= -72, -72*2= -144, ...- 18, -36, -72, -144...⊕ bottom
f(1)= -18, f(n)= 6*f(n-1)
-18*6= -108, -108*6= -648, -648*6= -3888, ...- 18, - 108, - 648, -3888, ...⊕ top
f(1)= 11, f(n)= f(n-1) + 22
11+22= 33, 33+22= 55, 55+22= 77, ...11, 33, 55, 77, ...The body temperatures of a group of healthy adults have a bell-shaped distribution with a mean of 98.19degreesF and a standard deviation of 0.61degreesF. Using the empirical rule, find each approximate percentage below. a. What is the approximate percentage of healthy adults with body temperatures within 3 standard deviations of the mean, or between 96.36degreesF and 100.02degreesF? b. What is the approximate percentage of healthy adults with body temperatures between 96.97degreesF and 99.41degreesF?
Answer:
a) From the empirical rule we know that within 3 deviations from the mean we have 99.7% of the data so then that would be the answer for this case.
b) [tex] z=\frac{96.97-98.19}{0.61}=-2[/tex]
[tex] z=\frac{99.41-98.19}{0.61}=2[/tex]
And within 2 deviations from the mean we have 95% of the values.
Step-by-step explanation:
For this case we know that the distribution of the temperatures have the following parameters:
[tex] \mu = 98.19, \sigma =0.61[/tex]
Part a
From the empirical rule we know that within 3 deviations from the mean we have 99.7% of the data so then that would be the answer for this case.
Part b
We can calculate the number of deviations from the mean with the z score with this formula:
[tex]z=\frac{X -\mu}{\sigma}[/tex]
And using this formula we got:
[tex] z=\frac{96.97-98.19}{0.61}=-2[/tex]
[tex] z=\frac{99.41-98.19}{0.61}=2[/tex]
And within 2 deviations from the mean we have 95% of the values.
Gravel is being dumped from a conveyor belt at a rate of 15 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 12 ft high? (Round your answer to two decimal places.)
Answer:
0.13 ft/min
Step-by-step explanation:
We are given that
[tex]\frac{dV}{dt}=15ft^3/min[/tex]
We have to find the increasing rate of change of height of pile when the pile is 12 ft high.
Let d be the diameter of pile
Height of pile=h
d=h
Radius of pile,r=[tex]\frac{d}{2}=\frac{h}{2}[/tex]
Volume of pile=[tex]\frac{1}{3}\pi r^2 h=\frac{1}{12}\pi h^3[/tex]
[tex]\frac{dV}{dt}=\frac{1}{4}\pi h^2\frac{dh}{dt}[/tex]
h=12 ft
Substitute the values
[tex]15=\frac{1}{4}\pi(12)^2\frac{dh}{dt}[/tex]
[tex]\frac{dh}{dt}=\frac{15\times 4}{\pi(12)^2}[/tex]
[tex]\frac{dh}{dt}=0.13ft/min[/tex]
1. In an arithmetic sequence, the first term is -2, the fourth term is 16, and the n-th term is 11,998
(a) Find the common difference d
(b) Find the value of n.
pls help...
Answer:
see explanation
Step-by-step explanation:
The n th term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
(a)
Given a₁ = - 2 and a₄ = 16, then
a₁ + 3d = 16 , that is
- 2 + 3d = 16 ( add 2 to both sides )
3d = 18 ( divide both sides by 3 )
d = 6
--------------
(b)
Given
[tex]a_{n}[/tex] = 11998 , then
a₁ + (n - 1)d = 11998 , that is
- 2 + 6(n - 1) = 11998 ( add 2 to both sides )
6(n - 1) = 12000 ( divide both sides by 6 )
n - 1 = 2000 ( add 1 to both sides )
n = 2001
------------------
Account A and Account B both have a principal of $2,000 and an annual interest rate of 5%. No additional deposits or withdrawals are made. Account A earns simple interest. Account B earns interest compounded annually. Compare the amounts in the two accounts after 20 years. Which earns more interest? How much more?
Answer:
Which earns more interest = Account B
How much more = $1,306.60
Step-by-step explanation:
Given;
Principal P = $2,000
Interest rate r = 5% = 0.05
Time t = 20 years
For account A;
Simple interest = P×r×t
Substituting the values;
Simple interest = 2,000 × 0.05 × 20 = $2000
Interest on account A = $2,000
For account B;
Compound interest
Final amount = P(1 + r)^t
Since it's compounded annually
Substituting the values;
Final amount = 2000(1+0.05)^20
Final amount = $5306.60
Interest = final amount - principal = $5306.60 -$2000
Interest = $3,306.60
Therefore, account B earns more interest.
Difference = account B interest - account A interest
Difference = $3,306.60 - $2,000
Difference = $1,306.60
At Central High School, 55% of students play a school sport. Also, 24% of the student population is in ninth grade. To ninth graders are allowed to play school sports. If two students are selected at random to receive a gift card, what is the probability that one will go to a student athlete and one will go to a freshman? Write the answer as a percent rounded to the nearest tenth of a percent.
Answer:
Probability that one of the giftcards will go to a student athlete and one will go to a freshman = 26.4%
Step-by-step explanation:
At Central High School, 55% of students play a school sport. Also, 24% of the student population is in ninth grade. No ninth graders are allowed to play school sports. If two students are selected at random to receive a gift card, what is the probability that one will go to a student athlete and one will go to a freshman? Write the answer as a percent rounded to the nearest tenth of a percent.
Solution
Probability that a student plays a school sport, that is, probability that a student is a student athlete = P(S) = 55% = 0.55
Probability that a student is in the ninth grade, that is, probability that a student is a freshman = P(F) = 24% = 0.24
It was given that no freshman is allowed to play sports, hence, it translates that the event that a student is a student athlete and the event that a student is a freshman are mutually exclusive.
P(S n F) = 0
If two students are then picked at random to receive a gift card, we require the probability that one will go to a student athlete and one will go to a freshman.
Probability that the first one goes to a student athlete = P(S) = 0.55
Probability that the second one goes to a freshman ≈ 0.24
Probability that the first one goes to a freshman = P(F) = 0.24
Probability that the second one goes to a student athlete ≈ 0.55
Probability that one will go to a student athlete and one will go to a freshman
= (0.55 × 24) + (0.24 × 0.55)
= 0.132 + 0.132
= 0.264
= 26.4% in percent to the nearest tenth.
Hope this Helps!!
Please answer this correctly
Answer:
20 total
Shelves 3 shelves /20 total=0.15=15%
Signs 2/20=0.10=10%
Benches 6/20=0.30=30%
Tablet Holders 9/20=0.45=45%
Step-by-step explanation:
Answer:
Shelves: 15%
Signs: 10%
Benches: 30%
Tablet Holders: 45%
Step-by-step explanation:
Shelves: [tex]\frac{3}{3+2+6+9} =\frac{3}{20} =\frac{15}{100} =[/tex] 15%
Signs: [tex]\frac{2}{3+2+6+9} =\frac{2}{20} =\frac{10}{100} =[/tex] 10%
Benches: [tex]\frac{6}{3+2+6+9} =\frac{6}{20} =\frac{30}{100}=[/tex] 30%
Tablet Holders: [tex]\frac{9}{3+2+6+9} =\frac{9}{20} =\frac{45}{100} =[/tex] 45%
А
What is the measure of ZDAB?
&
B
Enter your answer in the box.
D
96°
C
Next
Answer:
84°
Step-by-step explanation:
Adjacent angles in a parallelogram are supplementary:
∠A = 180° -96°
∠A = 84°
PLEASE HELP
Compare the number of x intercepts of f(x)=x^2 and g(x)= (x-4)^2. Tell me the transformations involved and how g(x) moves from the parent graph.
Answer
g(x) moves 4 spaces to the left compared to f(x),
when g(4)=0 when f(0)=0
when g(3)=1 when f(-1)=1
...
and so on
Please help me extra points for 1 math question. Please help before my time is up. Five times a number, added to -3, is 37. Find that number.
Answer:
your number should be 8
Step-by-step explanation:
5x+(-3)=37
5x-3=37
+3 +3
5x=40
÷5 ÷5
x=8
hope this helps
Answer:
The answer is 8.
5x-3=37
5x=37+3
5x=40
x=40/5
x=8
HOPE IT HELPS!!
Please answer this correctly
Answer:
10-19 ⇒ 3
50-59 ⇒ 4
Answer:
# of ties # of racks
10-19 3
50-59 4
Step-by-step explanation:
Using the Stem and Leaf plot, our data is:
11, 12, 16
21
32, 34, 36, 37, 39
41, 45
51, 52, 53, 56
# of ties # of racks
10-19 3 (11, 12, 16)
50-59 4 (51, 52, 53, 56)
Please help me with this problem
Answer:
10
-5
Step-by-step explanation:
5 - -5
Subtracting a negative is like adding
5+5 = 10
-9 - -4
-9+4
-5
Answer:
Step-by-step explanation:
5+5 = 10
-9+4 = -5
Mitch opened a retirement account that has an annual yield of 4.2% compounding annually. He is planning on retiring in 13 years. How much must he deposit into that account each year so that he can have a total of $1,000,000 by the time he retires?
Answer:
P = 4878
Step-by-step explanation:
So we'll use the formula
A = p(1+r/n)^ (nt)
A = 1000000
P is the unknown
R = 4.2
N = 13
T = 13
1000000= p ( 1+ 0.42/13)^ 169
1000000 = p (1.032)^169
1000000= p 205
P = 4878
A car company claims that its cars achieve an average gas mileage of at least 26 miles per gallon. A random sample of eight cars form this company have an average gas mileage of 25.5 miles per gallon and a standard deviation of 1 mile per gallon. At α=0.06, can the company’s claim be supported, assuming this is a normally distributed data set?
Answer:
[tex]t=\frac{25.5-26}{\frac{1}{\sqrt{8}}}=-1.414[/tex]
The degrees of freedom are given by:
[tex]df=n-1=8-1=7[/tex]
The p value for this case is given by:
[tex]p_v =P(t_{(7)}<-1.414)=0.100[/tex]
Since the p value is higher than the significance level of 0.06 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly less than 25.5 and then the claim makes sense
Step-by-step explanation:
Information given
[tex]\bar X=25.5[/tex] represent the sample mean
[tex]s=1[/tex] represent the sample standard deviation
[tex]n=8[/tex] sample size
[tex]\mu_o =26[/tex] represent the value to verify
[tex]\alpha=0.06[/tex] represent the significance level
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value
Hypothesis to est
We want to test if the true mean is at least 26 mpg, the system of hypothesis would be:
Null hypothesis:[tex]\mu \geq 25.5[/tex]
Alternative hypothesis:[tex]\mu < 25.5[/tex]
The statistic for this case is given by;
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{25.5-26}{\frac{1}{\sqrt{8}}}=-1.414[/tex]
The degrees of freedom are given by:
[tex]df=n-1=8-1=7[/tex]
The p value for this case is given by:
[tex]p_v =P(t_{(7)}<-1.414)=0.100[/tex]
Since the p value is higher than the significance level of 0.06 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly less than 25.5 and then the claim makes sense
The function s(t) represents the position of an object at time t moving along a line. Suppose s (1 )equals 62 and s (5 )equals 102. Find the average velocity of the object over the interval of time [1 comma 5 ].
Answer:
v = 10
the average velocity of the object over the interval of time [1, 5 ] is 10 units per unit time
Step-by-step explanation:
Given;
function s(t) represents the position of an object at time t moving along a line.
s(1) = 62 at t1 = 1
s(5) = 102 at t5 = 5
Velocity v = distance/time
Average velocity v over time t is;
v = ∆s/∆t
v = [s(5) - s(1)]/[t5 - t1]
Substituting the given values;
v = (102 - 62)/(5 - 1)
v = 10
the average velocity of the object over the interval of time [1, 5 ] is 10 units per unit time
Find the value of z Subscript alpha divided by 2 that corresponds to a confidence level of 89.48%.
Answer:
For this case we know that the confidence level is 89.48% or 0.8948 and the significance would be: [tex] \alpha=1-0.8948 = 0.1052[/tex] and the value of [tex]\alpha/2 =0.0526[/tex]
Now we need to find a quantile in the normal standard distribution who accumulate 0.0526 of the area on each tail of the normal standard distribution and we got:
[tex] z_{\alpha/2}= \pm 1.62015[/tex]
And we can use the following excel code for example:
"=NORM.INV(0.0526,0,1)"
Step-by-step explanation:
For this case we know that the confidence level is 89.48% or 0.8948 and the significance would be: [tex] \alpha=1-0.8948 = 0.1052[/tex] and the value of [tex]\alpha/2 =0.0526[/tex]
Now we need to find a quantile in the normal standard distribution who accumulate 0.0526 of the area on each tail of the normal standard distribution and we got:
[tex] z_{\alpha/2}= \pm 1.62015[/tex]
And we can use the following excel code for example:
"=NORM.INV(0.0526,0,1)"
Estimate and then solve the equation. X - 17 4/5=-13 1/5
Answer: 5 (estimate)
Step-by-step explanation:
x - 17 4/5 = -13 1/5
Estimate: x - 18 = -13
x - 18 + 18 = -13 + 18
x = 5
actual answer without estimating using exact numbers is 4 3/5 (so estimate is reasonable)
Please help me please I’m stuck please
[tex]answer \\ 9 \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps[/tex]
Answer:
9
Step-by-step explanation:
The ratio of 5 to 5+3 is equivalent to the ratio of 15 to 15+x. This is because when you have a triangle inside of a triangle and both of them share two of the same sides and the third sides are parallel to each other, the side ratios of the triangles are always proportionate.
[tex]\frac{5}{5+3} =\frac{15}{15+x}[/tex] Starting equation
[tex]\frac{5}{8} =\frac{15}{15+x}[/tex] Simplify
[tex]5(15+x)=8*(15)[/tex] Cross multiply
[tex]75+5x=120[/tex] Distributive Property on left and simplify on right
[tex]5x=45[/tex] Isolate the variable
[tex]x=9[/tex] Divide both sides by 5 (Division Property of Equality)
What is the next number in the sequence: 3, 8, 12, 48, 29, __
Answer:
144
Step-by-step explanation:
Answer:
116
Step-by-step explanation:
3x4=12
12x4=48
8x4=32
32-3=29
29x4=116
Hope it's clear
Can a Math expert please solve this and explain their answers. Thanks
Answer:
B152°BAStep-by-step explanation:
The measure of an arc is twice the measure of the inscribed angle that subtends that arc. A tangent is a special case where the chord that is one leg of the inscribed angle has a length of zero.
1. Short arc LJ is 2a°. Short arc LK is 2b°. Then arc JLK is 2(a+b)°, and short arc JK is ...
arc JK = 360° -2(a +b)° . . . . . matches choice B
__
2. Long arc WY is twice the measure of "inscribed" angle WYZ, so is ...
long ard WY = 2(104°) = 208°
Then short arc WY is ...
arc WXY = 360° -208° = 152°
__
3. The arc measures are double those of the corresponding inscribed angles. We can add up the arcs around the circle:
(arc AB +arc BC) = 2×70° = 140° . . . inscribed angle relation
(arc BC +arc CD) = 2×98° = 196° . . . inscribed angle relation
arc AB + arc BC +arc CD +arc DA = 360° . . . . sum around the circle
Adding the first two equations with arc DA, we have ...
(arc AB + arc BC) +(arc BC +arc CD) +arc DA = 360° +arc BC
140° +196° +80° = 360° +arc BC
416° -360° = arc BC = 56° . . . . . matches choice B
__
4. Angle C and angle A are supplementary in this inscribed quadrilateral.
angle C = 180° -98° = 82° . . . . . matches choice A
A laptop has a listed price of $875.98 before tax. If the sales tax rate is 6.5%, find the total cost of the laptop with sales tax included.
Round your answer to the nearest cent, as necessary.
please!
Answer:
$932.92
Step-by-step explanation:
6.5% = 0.065
(875.98) + (875.98)(0065)
(875.98) + (56.9387)
932.9187
$932.92
Answer:
$[tex]932.92[/tex]
Step-by-step explanation:
[tex]6.5/100=0.65[/tex]
Next, multiply the price by the sales tax.
[tex]875.98*0.65=56.94[/tex]
Then, add.
[tex]875.98+ 56.94=932.92[/tex]
$[tex]932.92[/tex] is the total cost of the laptop.
Find the missing side. Round to
the nearest tenth.
x
9
28°
x = [?]
Answer:
19.2
Step-by-step explanation:
It's right on Acellus.
The required value of x nearest to tenth is 19.17
What is hypotenuse?The longest side of the right angled triangle is called hypotenuse
By the Pythagoras theorem in the right angled triangle
h^2 = b^2 + p^2
where h = hypotenuse, b = base, p = perpendicular
How to calculate hypotenuse?Here we have given perpendicular p = 9
and an angle = 28°
Using sin for the given angle we have
sin 28° = [tex]\frac{perpendicular}{hypotenuse}[/tex]
0.46947 = [tex]\frac{9}{x}[/tex]
x = [tex]\frac{9}{0.46947}[/tex]
x = 19.17
Hence the required length of the side hypotenuse = x = 19.17
This is the conclusion to the answer.
Learn more about hypotenuse here-
https://brainly.com/question/2217700
#SPJ2
Order the numbers from least to greatest based on their absolute values.
|23|, |−37|, |−6|, |18|, |−24|, |2|
Answer:
/-37/, /-24/, /-6/, /2/, /18/, /23/
Very confused, need help quick! (see attachment) Simplify and show your work.
Answer:
27/(4x^6y^8)
Step-by-step explanation:
Target the variables first. (x^a)^b is the same as x^(a x b).
In the numerator, it is x^(2 x 3) , which is x^6, and y^(4 x 3), which is y^12.
Same principle on the bottom. the denominator is x^12 and y^20.
In the numerator, the number 4 is alone so don't do anything to it. Cube 3. The coefficient of the numerator is 4 x 3^3 . The coefficient of the denominator is 2^4. Cancel like terms. when you divide same terms' exponents, you subtract the exponent on top by the exponent on the bottom. Remember that you can only simplify LIKE terms. (x with x, y with y, number with number.)
A commuter uses a bus and a train to get to work. The train is more than 5 minutes late 1/6 of the times they use it The bus is more than 5 minutes late 3/5 of the times they use it. What is the probability that both the bus and train will be more than 5 minutes late?
Answer:
10% probability that both the bus and train will be more than 5 minutes late
Step-by-step explanation:
Independent events:
If two events, A and B, are independent, we have that:
[tex]P(A \cap B) = P(A)*P(B)[/tex]
What is the probability that both the bus and train will be more than 5 minutes late?
The bus being more than 5 minutes late is independent of the train, and vice versa. So
Event A: Bus more than 5 minutes late
Event B: Train more than 5 minutes late
The train is more than 5 minutes late 1/6 of the times they use it
This means that [tex]P(B) = \frac{1}{6}[/tex]
The bus is more than 5 minutes late 3/5 of the times they use it.
This means that [tex]P(A) = \frac{3}{5}[/tex]
Then
[tex]P(A \cap B) = \frac{3}{5}*\frac{1}{6} = \frac{3}{30} = 0.1[/tex]
10% probability that both the bus and train will be more than 5 minutes late
The sum is type answer as integer proper fraction or mixed number simplify answer
Answer:
[tex]9\dfrac{5}{6}[/tex]
Step-by-step explanation:
[tex]5\dfrac{1}{6}+4\dfrac{2}{3}=\\\\5\dfrac{1}{6}+4\dfrac{4}{6}=\\\\9\dfrac{5}{6}[/tex]
Hope this helps!
Zareen has 24 minutes to work on her math homework in each problem is taking her 2/3 of a minute on average to complete which expression can be used to determine the number of my problem she will be able to complete in the time she has
Answer:
Hey mate , here is your answer. Hope it helps you
Step-by-step explanation:
Given Zareen has 24min to work on her math homework, and each problem is taking her 2/3 of a minute
As give one problem takes
24*(2/3) minutes = 16
Hence
2/3 divided by 24
What’s the correct answer for this?
Answer:
D.
Step-by-step explanation:
Since a quadrilateral inscribed in a circle has its opposite angles adding up to 180°
So,
<MNO + <OLM = 180
82 + <OLM = 180
<OLM = 180-82
<OLM = 98°
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
its b I belive
Step-by-step explanation:
Answer:
The answer is B.
Step-by-step explanation:
In order to find (f-g)(x), you have to subtract g(x) from f(x) :
[tex]f(x) = {3}^{x} + 10[/tex]
[tex]g(x) = 2x - 4[/tex]
[tex](f - g)(x) = {3}^{x} + 10 - 2x - ( - 4)[/tex]
[tex](f - g)(x) = {3}^{x} + 10 - 2x + 4[/tex]
[tex](f - g)(x) = {3}^{x} - 2x + 14[/tex]
