Answer:
[tex]x^\frac{3}{5} = (x^3 )^\frac{1}{5}[/tex]
[tex]x^\frac{3}{5} = \sqrt[5]{x^3}[/tex]
[tex]x^\frac{3}{5} = (\sqrt[5]{x})^3[/tex]
Step-by-step explanation:
Given
[tex]x^\frac{3}{5}[/tex]
Required
The equivalent expressions
We have:
[tex]x^\frac{3}{5}[/tex]
Expand the exponent
[tex]x^\frac{3}{5} = x^{ 3 * \frac{1}{5}}[/tex]
So, we have:
[tex]x^\frac{3}{5} = (x^3 )^\frac{1}{5}[/tex] ----- this is equivalent
Express 1/5 as roots (law of indices)
[tex]x^\frac{3}{5} = \sqrt[5]{x^3}[/tex] ------ this is equivalent
The above can be rewritten as:
[tex]x^\frac{3}{5} = (\sqrt[5]{x})^3[/tex] ------ this is equivalent
Rose walks 2 2/3 km in three-fifths of an hour. If her speed remains unchanged, how many kilometres can she walk in one and three quarters of an hour? Express your answer as a mixed number in lowest terms
Answer:
Distance = 7 7/9 Km
Step-by-step explanation:
Given the following data;
Distance = 2⅔ = 8/3 Km
Time = ⅗ hour
First of all, we would find her speed;
Speed = distance/time
Speed = (8/3)/(3/5)
Speed = 8/3 * 5/3
Speed = 40/9 km/h
Next, we would find the distance covered when time = 1¾ hours
Distance = speed * time
Distance = 40/9 * 1¾
Distance = 40/9 * 7/4
Distance = 10/9 * 7
Distance = 70/9
Distance = 7 7/9 Km
F(x) = 3x+5 G(x)= 4x^2-2 H(x) = x^2-3x+1 Find f(x) +g(x) -h(x)
Answer:
Step-by-step explanation:
f(x) + g(x) = 3x + 5 + 4x^2 - 2
f(x) + g(x) = 4x^2 + 3x + 3
f(x) + g(x) - h(x) = 4x^2 + 3x + 3 - (x^2 - 3x + 1) Remove the brackets.
f(x) + g(x) - h(x) = 3x^2 +3x + 3 - x^2 + 3x - 1 Collect like terms
f(x)+g(x) - h(x) = 2x^2 + 6x + 2
Answer:
f(x)=3x^2+6x+2
Step-by-step explanation:
Bill's father is three times Bill's age. Three years ago, Bill's father was four times Bill's age.
By forming two equations, find Bill's age now.
Answer:
12 and 36
Step-by-step explanation:
Call the age of both Bill and his father is a and b, respectively
we have:
b=3a
b-3=4(a-3) ->b=4a-12 -> 3a=4a-12 ->a =12 -> b=36
Cho hai tập hợp A={1;2;3;4},B={2;4;6;8} . Tập hợp nào sau đây bằng tập hợp A ∩B ?
Answer:
A∩B ={2;4}
Step-by-step explanation:
Chúc bạn học tốt
I need the help ASAP please
Answer:
Option B
Answered by GAUTHMATH
There are 6 people named A,B,C,D,E,F. The people named A,B, and C are all over the age of 40. The people named D,E,F are all under the age of 40. How many different orders are there for the people to sit on a bench, if both ends of the bench must be occupied by someone over the age of 40?
please please help its timed -H.M
Answer:
1
General Formulas and Concepts:
Algebra I
Functions
Function NotationStep-by-step explanation:
Step 1: Define
f(-2)
Step 2: Evaluate
f(-2) is x = -2 for function f(x).
According to the table, when x = -2, f(x) = 1.
∴ f(-2) = 1
A well-known brokerage firm executive claimed that 60% of investors are currently confident of meeting their investment goals. An XYZ Investor Optimism Survey, conducted over a two week period, found that in a sample of 100 people, 69% of them said they are confident of meeting their goals. Test the claim that the proportion of people who are confident is larger than 60% at the 0.01 significance level.
The null and alternative hypothesis would be:________
a. H0:μ=0.6H0:μ=0.6
H1:μ≠0.6H1:μ≠0.6
b. H0:μ=0.6H0:μ=0.6
H1:μ<0.6H1:μ<0.6
c. H0:μ=0.6H0:μ=0.6
H1:μ>0.6H1:μ>0.6
d. H0:p=0.6H0:p=0.6
H1:p≠0.6H1:p≠0.6
e. H0:p=0.6H0:p=0.6
H1:p>0.6H1:p>0.6
f. H0:p=0.6H0:p=0.6
H1:p<0.6H1:p<0.6
The test is:________
a. two-tailed
b. left-tailed
c. right-tailed
The test statistic is:_______ (to 3 decimals)
The p-value is:_______ (to 4 decimals)
Based on this we:________
a. Fail to reject the null hypothesis
b. Reject the null hypothesis
We are testing a hypothesis. So, first we identify the null and the alternative hypothesis, then we find the test statistic, and with the test statistic, the p-value is found.
Null and alternative hypothesis:
Claim the the proportion is of 60%, thus, the null hypothesis is:
[tex]H_0: p = 0.6[/tex]
Test if the proportion is greater than 60%, thus, the alternative hypothesis is:
[tex]H_1: p > 0.6[/tex]
And the answer to the first question is given by option c.
Classification:
We are testing if the proportion is greater than a value, so it is a right-tailed test.
Test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.6 is tested at the null hypothesis:
This means that [tex]\mu = 0.6, \sigma = \sqrt{0.4*0.6}[/tex]
Survey, conducted over a two week period, found that in a sample of 100 people, 69% of them said they are confident of meeting their goals.
This means that [tex]n = 100, X = 0.69[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.69 - 0.6}{\frac{\sqrt{0.4*0.6}}{\sqrt{100}}}[/tex]
[tex]z = 1.837[/tex]
The test statistic is z = 1.837.
p-value:
The p-value of the test is the probability of finding a sample proportion above 0.69, which is 1 subtracted by the p-value of z = 1.837.
Looking at the z-table, z = 1.837 has a p-value of 0.9669.
1 - 0.9669 = 0.0331
The p-value is 0.0331.
Decision:
The p-value of the test is 0.0331 > 0.01, and thus:
a. Fail to reject the null hypothesis
For another example of a problem of a test of hypothesis, you can take a look at:
https://brainly.com/question/24166849
A tank filled with water begins draining. The number of minutes t since the water began draining from the tank is a function of the number of gallons of water in the tank, v. We will call this function f so that f(t) = v.
Required:
a. Using function notation, represent the of gallons of water in me tank 4 minutes after the water darning from the Ink.
b. Suppose that f(4) = 7, what does this mean in the context of the problem?
Answer:
[tex](a)\ f(4) = v[/tex]
(b) There are 7 gallons left in the tank after 4 minuted
Step-by-step explanation:
Given
[tex]f(t) = v[/tex]
[tex]t \to[/tex] time since water began draining
[tex]v \to[/tex] gallons in the tank
Solving (a): Notation for gallons remaining at 4 minutes
This means that [tex]t=4[/tex]
[tex]f(t) = v[/tex] becomes
[tex]f(4) = v[/tex]
Solving (b): Interpret f(4) = 7
We have:
[tex]f(t) = v[/tex]
[tex]t \to[/tex] time since water began draining
[tex]v \to[/tex] gallons in the tank
This means that:
[tex]t =4[/tex]
[tex]v =7[/tex]
It can be interpreted as:
There are 7 gallons left in the tank after 4 minuted
A researcher conducts an ANOVA analysis and reports no differences in average certification exam test scores for nurses identified as Baby Boomers, Millennials or Generation X. You would expect to see:
Answer:
"Type II error" is the right answer.
Step-by-step explanation:
A type II mistake would be that a fake null hypothesis also isn't rejected. It's also called false negatives.It happens whenever an investigator does not eliminate a truly wrong null hypothesis. Here quite a scientist determines that whenever it genuinely exists, that there's no substantial consequence.Thus the above is the right answer.
Triangle ABL is an isosceles triangle in circle A with a radius of 11, PL = 16, and ∠PAL = 93°. Find the area of the circle enclosed by line PL and arc PL. Show all work and round your answer to two decimal places.
The area bounded by a chord and arc it intercepts is known as a segment of a circle segment of a circle
The area of the circle enclosed by line PL and arc PL is approximately 37.62 square units
The reason the above value is correct is as follows:
The given parameters in the question are;
The radius of the circle, r = 11
The length of the chord PL = 16
The measure of angle ∠PAL = 93°
Required:
The area of part of the circle enclosed by chord PL and arc PL
Solution:
The shaded area of the given circle is the minor segment of the circle enclosed by line PL and arc PL
The area of a segment of a circle is given by the following formula;
Area of segment = Area of the sector - Area of the triangle
Area of segment = Area of minor sector APL - Area of triangle APL
Area of minor sector APL:
Area of a sector = (θ/360)×π·r²
Where;
r = The radius of the circle
θ = The angle of the sector of the circle
Plugging in the the values of r and θ, we get;
Area of the minor sector APL = (93°/360°) × π × 11² ≈ 98.2 square units
Area of Triangle APL:
Area of a triangle = (1/2) × Base length × Height
Therefore;
The area of ΔAPL = (1/2) × 16 × 11 × cos(93°/2) ≈ 60.58 square units
Required shaded area enclosed by line PL and arc PL:
Therefore, the area of shaded segment enclosed by line PL and arc PL is found as follows;
Area of the required segment PL ≈ (98.2 - 60.58) square units = 37.62 square units
The area of the circle enclosed by line PL and arc PL ≈ 37.62 square units
Learn more about the finding the area of a segment can be found here:
https://brainly.com/question/22599425
The area of the circle enclosed by line segment PL and circle arc PL is 37.80 square units.
The calculation of the area between line segment PL and circle arc PL is described below:
1) Calculation of the area of the circle arc.
2) Calculation of the area of the triangle.
3) Subtracting the area found in 2) from the area found in 1).
Step 1:
The area of a circle arc is determined by the following formula:
[tex]A_{ca} = \frac{\alpha\cdot \pi\cdot r^{2}}{360}[/tex] (1)
Where:
[tex]A_{ca}[/tex] - Area of the circle arc.
[tex]\alpha[/tex] - Arc angle, in sexagesimal degrees.
[tex]r[/tex] - Radius.
If we know that [tex]\alpha = 93^{\circ}[/tex] and [tex]r = 11[/tex], then the area of the circle arc is:
[tex]A_{ca} = \frac{93\cdot \pi\cdot 11^{2}}{360}[/tex]
[tex]A_{ca} \approx 98.201[/tex]
Step 2:
The area of the triangle is determined by Heron's formula:
[tex]A_{t} = \sqrt{s\cdot (s-l)\cdot (s-r)^{2}}[/tex] (2)
[tex]s = \frac{l + 2\cdot r}{2}[/tex]
Where:
[tex]A_{t}[/tex] - Area of the triangle.
[tex]r[/tex] - Radius.
[tex]l[/tex] - Length of the line segment PL.
If we know that [tex]l = 16[/tex] and [tex]r = 11[/tex], then the area of the triangle is:
[tex]s = \frac{16+2\cdot (11)}{2}[/tex]
[tex]s = 19[/tex]
[tex]A_{t} = \sqrt{19\cdot (19-16)\cdot (19-11)^{2}}[/tex]
[tex]A_{t} \approx 60.399[/tex]
Step 3:
And the area between the line segment PL and the circle arc PL is:
[tex]A_{s} = A_{ca}-A_{t}[/tex]
[tex]A_{s} = 98.201 - 60.399[/tex]
[tex]A_{s} = 37.802[/tex]
The area of the circle enclosed by line segment PL and circle arc PL is 37.80 square units.
What is 3.24 ( 4 repeating) as a fraction?
Answer:
81/25
Step-by-step explanation:
change 3.24 into faction
324 over 100 because there are two decimal points .
simplfy into the smallest fraction
the answer is 81 over 25
Find the shortest distance from A to D in the diagram
Answer:
I will choose (a) I did a problem like this last week
You are playing a game by drawing a card from a standard deck and replacing it. If the card is a face card, you win $30. If it is not a face card, you pay $2. There are 12 face cards in a deck of 52 cards. What is the expected value of playing the game
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Form a polynomial whose zeros and degree are given.
Zeros: - 2, 2, 6; degree: 3
Type a polynomial with intéger coefficients and a leading coefficient of 1 in the box below.
f(x)=(Simplify your answer.)
Answer:
[tex]f(x) = (x + 2)(x - 2)(x - 6)[/tex]
[tex]f(x) = ({x}^{2} + 4)(x - 6)[/tex]
[tex]f(x) = {x}^{3} - 6 {x}^{2} + 4x - 24[/tex]
Step-by-step explanation:
Multiply factors.
Translations _______ side lengths of the figure.
A. change
B. alter
C. preserve
D. all of these
Answer:
C. preserve
Step-by-step explanation:
When you translate something in geometry, you're simply moving it around. You don't distort it in any way. If you translate a segment, it remains a segment, and its length doesn't change. Similarly, if you translate an angle, the measure of the angle doesn't change.
Point C partitions AB into two parts so that the ratio of the length of AC to the length of CB is 1:5. What are the coordinates of point ?
Select and drag a number to each empty box to correctly complete the coordinates of point
The coordinates of point C are?
9514 1404 393
Answer:
C(-1, -4)
Step-by-step explanation:
We want ...
AC/CB = 1/5
5(C-A) = B-C . . . . multiply by 5CB
6C = B +5A . . . . . add 5A-C
C = (B +5A)/6 . . . divide by 6
C = ((4, 6) +5(-2,-6))/6 = (4-10,6-30)/6 = (-6, -24)/6
C = (-1, -4)
Keith is trying to figure out the area of his pool section in his backyard he knows that his pool is 20 feet long and 9 feet wide he also knows the sidewalk is 3 feet wide all around the floor what is the total area of the pool section of Keith’s backyard?
Answer:
The total area of the pool section of Keith's backyard is 390 square feet.
Step-by-step explanation:
Since Keith is trying to figure out the area of his pool section in his backyard, and he knows that his pool is 20 feet long and 9 feet wide, and he also knows the sidewalk is 3 feet wide all around the floor, to determine what is the total area of the pool section of Keith's backyard, the following calculation must be performed:
(20 + 3 + 3) x (9 + 3 + 3) = X
26 x 15 = X
390 = X
Therefore, the total area of the pool section of Keith's backyard is 390 square feet.
44y + 321x = 0 biết x=30000
Answer:
y= -240750/11
Step-by-step explanation:
44y + 321. 30000 = 0
44y = - 963000
y= -240750/11
The Demand function for a product is given by:
D(q) = - 0.0003q^2 - 0.04q + 23.56
where q is the number of units sold and D(q) is the corresponding price per unit, in dollars. What is the average rate of change of Demand between 40 and 175 units sold?
Answer:
The average rate of change of Demand between 40 and 175 units sold is of -0.1045.
Step-by-step explanation:
Average rate of change:
The average rate of a function f(x) in an interval [a,b] is given by:
[tex]A = \frac{f(b) - f(a)}{b - a}[/tex]
In this question:
[tex]D(q) = -0.0003q^2 - 0.04q + 23.56[/tex]
What is the average rate of change of Demand between 40 and 175 units sold?
[tex]a = 40, b = 175[/tex]. So
[tex]D(40) = -0.0003*40^2 - 0.04*40 + 23.56 = 21.48[/tex]
[tex]D(175) = -0.0003*175^2 - 0.04*175 + 23.56 = 7.3725[/tex]
So
[tex]A = \frac{f(b) - f(a)}{b - a} = \frac{7.3725 - 21.48}{175 - 40} = -0.1045[/tex]
The average rate of change of Demand between 40 and 175 units sold is of -0.1045.
Matt invests £1800 for 2 years at a simple interest rate of 10%.
How much money will he get back in interest?
Answer:
Step-by-step explanation:
P = 1800
R = 10%
T = 2 years
I = PRT
= 1800 * 10/100 * 2
= 1800 * 0.1 * 2
I = £360
The amount that will be gotten back as interest will be £360
Principal = £1800
Rate = 10%
Time = 2 years
Simple Interest will be calculated as:
= (P × R × T) / 100
= (£1800 × 10 × 2)/100
= £36000/100
= £360
Therefore, the interest is £360.
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complete the square to form a true equation;
x^2-3/4x+__ = (x-__)^2
172273-3-$=$==8399993939384888884-%"%/=%=%8%
Step-by-step explanation:
(x^2-3/4x+y^2)=(x-y)2
(x-3/4*1/2)2
(x-3/8)(x-3/8)
(x^2-3x/8-3x/8+9/64)
(x^2-6x/8+9/64)
(x-3/8)2
Identify the pair numbers
Answer:
D. 212 degrees Fahrenheit and 100 degrees Celsius.
Step-by-step explanation:
The boiling point of water in Celsius is 100.
The way to calculate Celsius to Fahrenheit:
F = (C × 9/5) + 32
So we plug in 100 for C.
F = (100 × 9/5) + 32
F = 180 + 32
F = 212
Therefore, the numbered pair is 212 degrees F and 100 degrees C.
In remodeling a house an architect finds that by adding the same amount to each dimension of a 15ft by 19ft rectangular room, the area would be increased by 98 ft^2. How
much must be added to each dimension?
Let x be the amount that is added to each dimension. After writing an equation in standard form with a > 0, a= ? b= ? and c= ?
(Simplify your answers.)
Answer:
Step-by-step explanation:
new length=15+x
width=19+x
then area=(15+x)×(19+x)=285+15x+19x+x²=x²+34x+285 ft²
original area=15×19=285 ft²
then 285+98=x²+34x+285
or
x²+34x-98=0
x²+34x+17²=98+17²
(x+17)²=98+289=387
x+17=√387=3√43
x=3√43-17 ft
Sample information: 24 out of 1000 people who were surveyed had type 2 diabetes. Use the above sample information and construct two confidence intervals (one with confidence level of 90% and the other one with confidence level of 99%) to estimate the proportion of people who have type 2 diabetes. What is the relationship between the confidence level and the size of the confidence interval? Is this significant? Why is it important to understand this concept?
Answer:
it is important because the number of people who are infected by the disease is rising
A car insurance company has determined that6% of all drivers were involved in a car accident last year. If14drivers are randomly selected, what is the probability of getting at most 3 who were involved in a car accidentlast year
Answer:
[tex]P(x \le 3) = 0.9920[/tex]
Step-by-step explanation:
Given
[tex]p = 6\%[/tex] --- proportion of drivers that had accident
[tex]n = 14[/tex] -- selected drivers
Required
[tex]P(x \le 3)[/tex]
The question is an illustration of binomial probability, and it is calculated using:
[tex]P(x ) = ^nC_x * p^x * (1 - p)^{n-x}[/tex]
So, we have:
[tex]P(x \le 3) = P(x = 0) +P(x = 1) +P(x = 2) +P(x = 3)[/tex]
[tex]P(x=0 ) = ^{14}C_0 * (6\%)^0 * (1 - 6\%)^{14-0} = 0.42052319017[/tex]
[tex]P(x=1 ) = ^{14}C_1 * (6\%)^1 * (1 - 6\%)^{14-1} = 0.37578668057[/tex]
[tex]P(x=2 ) = ^{14}C_2 * (6\%)^2 * (1 - 6\%)^{14-2} = 0.15591149513[/tex]
[tex]P(x=3 ) = ^{14}C_3 * (6\%)^3 * (1 - 6\%)^{14-3} = 0.03980719024[/tex]
So, we have:
[tex]P(x \le 3) = 0.42052319017+0.37578668057+0.15591149513+0.03980719024[/tex]
[tex]P(x \le 3) = 0.99202855611[/tex]
[tex]P(x \le 3) = 0.9920[/tex] -- approximated
A box contains 100 tickets labeled with numbers. The average of the labels is 14 and the SD of the labels is 8.2. Eighteen tickets will be drawn independently at random with replacement from the box. The chance that the absolute value of the difference between the sample sum of the labels on the tickets and 252 does not exceed 278.32 is: __________
Answer:
at most
Step-by-step explanation:
The sample drawn from the population is a relative representation not the absolute representation. The box has 100 tickets in it and sample of tickets is selected to identify difference between sample sum and 252. The at most value for the sample sum can be 278.32 and value cannot exceed beyond this.
Please help out explanation need it
Answer:
shifting to the right is just an east/west movement
not a north/south
an east west movement is on the "X" ais, a north/south is on the "Y"
axis...
so just ADD 10 units to all the "X" values
a" = (9,-3)
b"= (6,-1)
c"= (4,-4)
Step-by-step explanation:
Find the value of x and the value of y.
A. x = 4, y = 8
B.x=7, y=422
C. X= 4/3, y= 7.2
D. x= 73, y=412
Answer:
x = 7 and
y = 4[tex]\sqrt{2}[/tex]
Step-by-step explanation:
as you can see from the image we need to draw a line and when we do so we get a special right triangle with angle measures 90-45-45 and side lengths represented by a-a-a[tex]\sqrt{2}[/tex]
since the line we drew is parallel to the rectangle's length it's = 4 and so the number represented with a is also = 4
from there on we see x = 7 and y = 4[tex]\sqrt{2}[/tex]
Answer:
I can confirm, it is B! x=7 and y=4sqrt2
Step-by-step explanation:
edge
What is the more formal name used for describing the corporate-finance decision concerning which projects to invest in?
Answer:
i hope it will help you
Step-by-step explanation:
Working capital management is how companies are able to manage finances and continue operations.
