Answers
[tex]\huge\boxed{\textsf{a.)}\ 10}[/tex]
Substitute [tex]\frac{1}{2}[/tex] for [tex]x[/tex].
[tex]f\left(\frac{1}{2}\right)=5\cdot4^\frac{1}{2}[/tex]
Use [tex]a^\frac{m}{n}=\sqrt[n]{a^m}[/tex].
[tex]\begin{aligned}f\left(\frac{1}{2}\right)&=5\cdot\sqrt[2]{4^1}\\&=5\cdot\sqrt[2]{4}\\&=5\cdot2\\&=\boxed{10}\end{aligned}[/tex]
Related Questions
divided 80 by my number, and then added 13. The result was 93. What was my number?
If my number is x, then the equation is , the number is
Answers
The number is 6400.
We have given that,
divided 80 by my number, and then added 13.
What is the expression?An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Suppose the number is x
[tex]\frac{x}{80}+13=93[/tex]
Subtract 13 from both sides
[tex]\frac{x}{80}+13-13=93-13[/tex]
[tex]\frac{x}{80}=80[/tex]
Multiply both sides by 80
[tex]\\\frac{80x}{80}=80\cdot \:80[/tex]
x=6400
Therefore the number is 6400.
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7. Meghraj divided like this. 1.05 2.1 → 105 210 Do you agree with what he did? Explain your thinking.
Answers
Step-by-step explanation:
I guess that means
1.05 / 2.1
or
1.05 ÷ 2.1
both mean the same thing.
so, let's look at
1.05 / 2.1
this is the same as
105/100 / 210/100 = (105×100) / (210×100) =
= (105×100) / (210×100) × (1/100 / 1/100)
as long as we multiply numerator (top) and denominator (bottom) always with the same thing, the general fraction or division is unchanged.
(105×100) / (210×100) × (1/100 / 1/100) =
= (105 × 100/100) / (210 × 100/100) = 105 / 210
so, yes, the division of 105 / 210 is the same as 1.05 / 2.1
I need some help new topic
Answers
Answer:
1160cm squared
Step-by-step explanation:
as for me I've calculated the surface area of a closed cuboid.
this is because we are not informed whether it is open or closed.
and so my teacher told me that if you're not informed, if a cuboid is open or closed, just assume that the cuboid is closed.
and that is what I have done.
hope it helps.
in case of any questions feel free to ask.
A line has a slope of Negative three-fifths. Which ordered pairs could be points on a parallel line? Select two options. a (–8, 8) and (2, 2) b (–5, –1) and (0, 2) c (–3, 6) and (6, –9) d (–2, 1) and (3, –2) e (0, 2) and (5, 5)
Answers
Options A and D are having a slope equal to -3/5.
Given that the slope of the line is -3/5.
That is, m = -3/5
We need to find which ordered pairs could be points on a parallel line.
What is the formula to find the slope of the line?The formula for slope between two coordinates is m = (y₂ - y₁)/(x₂ - x₁).
Now,
Using (–8, 8) and (2, 2);
m = (2 - 8)/(2 - (-8))
⇒m = -6/10
⇒m = -3/5
Using (–5, –1) and (0, 2);
m = (2 - (-1))/(0 - (-5))
⇒m = 3/5
Using (–3, 6) and (6, –9);
m = (-9 - 6)/(6 - (-3))
⇒m = -15/9
⇒m = -5/3
Using (–2, 1) and (3, –2);
⇒m = (-2 - 1)/(3 - (-2))
⇒m = -3/5
Using (0, 2) and (5, 5);
m = (5 - 2)/(5 - 0)
⇒m = 3/5
We know that the condition for parallel lines slope is [tex]m_{1} =m_{2}[/tex].
Therefore, options A and D are having a slope equal to -3/5.
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Homework:Sections 4.3 and 4.4 Homework
Question 9, 4.4.9
HW Score: 53.33%, 6.4 of 12 points
Points: 0 of 1
Question content area top
Part 1
Farmer Ed has 8,000 meters of fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the river, what is the largest area that can be enclosed?
Answers
Answer:
8,000,000 m²
Step-by-step explanation:
The largest rectangular area is enclosed when half the fence is used for sides in one direction, and the other half of the fence is used for sides perpendicular.
Here, no fence is needed on the river side, so 8000/2 = 4000 meters of fence will be used parallel to the river. The other 4000 m of fence will be split between the two ends of the enclosure, so its area will be ...
4000 m × 2000 m = 8,000,000 m² . . . largest enclosed area
More formal solutionWe can let x represent the length of fence perpendicular to the river. The amount of fence available for the side parallel to the river is ...
L = 8000 -2x . . . . . the rest of the 8000 m of fence after 2 sides are used
The area is ...
A = x(8000 -2x) = 2x(4000 -x) . . . . area is product of length and width
This equation for the area describes a parabola that opens downward and has zeros at x=0 and x=4000. Its maximum will be on the line of symmetry, halfway between these zeros. The value of x that gives maximum area is ...
(0 +4000)/2 = 2000
The plot will extend 2000 meters out from the river and will have a length of ...
8000 -2(2000) = 4000 . . . meters
The maximum area is (2000 m)(4000 m) = 8,000,000 m².
GraphThe attached graph shows area as a function of the dimension perpendicular to the river.
In how many ways can four people with different heights line up single-file so that exactly two people are taller than the person behind them?
Answers
The number of ways by which exactly 2 people are taller than the person behind them is; 6.
What number of ways can they line so that exactly two people are taller than the person behind them?It follows from content that since 4 individuals with different heights are to line up, the 2 individuals who must be taller than the person behind them are represented as one entity and must be in the 1st and 2nd position or the 2nd and 3rd position.
Hence, the number of ways is; 6 upon counting the number of possible outcomes.
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The answer to this problem
Answers
Answer:
jdiddbhhuduh9ruruuehgruhrhudhheherj
Long-term assets are depreciated over time for which reason?
Answers
Step-by-step explanation:
Depreciation of Long Term Assets
As with most types of assets, long term assets needs to be depreciated over the course of their useful life. It is because a long term asset is not expected to generate a benefit for an infinite amount of time.
Answer:
Inflation
Step-by-step explanation:
The rising costs of goods and services mean that $1 in 2022 will be worth more than $1 in 2032. This is called inflation.
Let's just say you put $200,000 in a savings account in 2000. That could've purchased you a 4 bedroom house at the time.
You keep the money in the account for over 20 years. And in 2020, you want to buy a new home with the money you have saved.
However, you can only buy a 2 bedroom house, because the rising costs of the market, increased the cost, or depreciated your savings.
This is called inflation.
243 --‐ 81 --‐ 27 --‐ ___ --‐ 3 --‐ 1
Answers
A blue swimsuit costs $42 and a red swimsuit
costs 5/6 as much. How much would the two
swimsuits cost together?
Mark the $42 in the bar model. Mark what is not
known with "?". Solve.
Answers
Answer:
$77
Step-by-step explanation:
Hello!
Let's find the cost of the red swimsuit.
Red Swimsuit[tex]R = \frac56*42[/tex][tex]R = \frac{5*42}{6}[/tex][tex]R = \frac{5*7*6}{6}[/tex][tex]R = 5*7[/tex][tex]R = 35[/tex]The cost of the Red swimsuit is $35.
The cost of both swimsuits is $35 plus $42, which gives is $77.
investment of $2000 at 10% simple interest for 9 years
investment of $3000 at 3% simple interest for 20 years
investment of $2000 at 10% simple interest for 3 years
Put them in order from least interest amount to greatest interest amount
Answers
Answer:
The last investment (C) has the least interest of $600
The other two investments (A and B) have the same amount of interest of $1800.
Step-by-step explanation:
Simple Interest Formula
I = Prt
where:
I = interest earnedP = principalr = interest rate (in decimal form)t = time (in years)Investment A
P = $2000r = 10% = 0.1t = 9 yearsSubstitute the given values into the formula and solve for I:
⇒ I = 2000(0.1)(9)
⇒ I = $1800
Investment B
P = $3000r = 3% = 0.03t = 20 yearsSubstitute the given values into the formula and solve for I:
⇒ I = 3000(0.03)(20)
⇒ I = $1800
Investment C
P = $2000r = 10% = 0.1t = 3 yearsSubstitute the given values into the formula and solve for I:
⇒ I = 2000(0.1)(3)
⇒ I = $600
The last investment (C) has the least interest of $600.
The other two investments (A and B) have the same amount of interest of $1800.
URGENT!
Positive integers B and C satisfy b^2 - bC-23=0. What is the value of C.
A. 21 b. 22 c.23 d.24
Answers
The value of C based on the information given about the integer is C. 22.
How to calculate the value?From the information given,
b² + bc - 23 = 0
Let the assumed value for a = 1
b² + bc - 23 = 0
1² + (1 × c) - 23 = 0
1 + c - 23 = 0
c = 23 - 1
c = 22.
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15. Ms. Goldman is thinking of a number that is less than 20 and has three factor pairs. She says
that if she adds the factors in each factor pair the sums are 19, 11 and 9. What is her number?
Answers
Given: the number is less than 20; three-factor pairs; each factor pair individually adds up to 19, 11, and 9
Solve for her number.
Step-by-step explanation:
If you think about it for a little bit, you will eventually find that 18 + 1 = 19 and 18 × 1 = 18 which is less than 20.
Then we know 18 has 2 more factor pairs : 9 × 2 and 6 × 3 which add up to 11 and 9.
Therefore our answer is: 18
18 × 1
9 × 2
6 × 3
The trick is to pick the largest sum of one-factor pair (19 in this question) and then choose the number below it.
To decrease a number by 13%, what decimal should we multiply it by?
Answers
Answer:
0.87
Step-by-step explanation:
After decreasing new value would be : 100% - 13% = 87%
87 % = 87/100 = 0.87
True or false? in a two-column proof, the right column contains a series of
deductions.
A. True
B. False
Answers
Answer: True
Step-by-step explanation:
Answer:False
Step-by-step explanation:I took the test
She first gave a woman feeding pigeons $100. Next, she gave away half of her remaining money to a child licking an ice cream cone. She gave $50 to an old man riding a rickety bicycle. She bought a homeless woman some shoes for $20. Then she gave half of her remaining money to someone giving a sermon on a soapbox. At this point, she only had $3 left, so she handed it to another woman who lived under a bridge. How much money did the woman have in her purse before she started to give it away in dollars?
Answers
Answer:
she hd 173 i think if this is correct
Step-by-step explanation:
if she gave 100 dollars away that would add 100 and then 50 150 and another 20 dollars 170 and she has 3 left so she had 173 dollars
AND PLEASE MARK BRAINLEST
A box can be filled completely using 9 layers of 11 units cubes. What is the volume of the box?
Answers
The volume of the box is 99 unit cubes.
What is the volume of the box?A cube is a three-dimensional object that has six faces, twelve edges and eight vertices. The length, width and height of a cube usually has equal dimensions. The volume of the box is a function of the dimension of the cubes in it and the number of layers.
Volume of a box = number of layers x amount of units
9 x 11 - 99 unit cubes
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If one card is randomly selected from a well-shuffled standard deck of 52 cards, what is the probability that the card selected is not a heart?
Answers
Probability helps us to know the chances of an event occurring. The probability that the card selected is not a heart is 3/4.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
The probability of the card not being selected is a heart is,
Probability = (Number of cards without heart)/Total number of cards)
Probability = 39/52
Probability = 3/4
Hence, the probability that the card selected is not a heart is 3/4.
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Write the equation of the graph.
Number graph ranging from negative four to four on the x axis and negative two to six on the y axis. A line with a positive slope is drawn on the graph, passing through the point (two, six).
y=12x+5
y−3=−12(x+1)
y−3=12(x+1)
y+3=−12(x−1)
Answers
The line which is described as in the task content has equation; (y - 6) = 12 (x-2).
What is the equation of thee line described in the task content?From the task content, it follows that two points which can be used to evaluate the slope of the graph is positive.
Hence, the equation of the line in discuss is which passes through the points given is; (y - 6) = 12 (x-2) in which case, the positive slope number is 12.
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Which could be the graph of the function?
Answers
The graph of the function y = sin 0.5x is option A. This can be obtained by using period of the graph function.
Which is the required graph?Periodic function is a function that repeats at uniform intervals; the time interval between two waves is called the period.
A function f will be periodic with period n,f (a + n) = f (a), ∀ n > 0.
After first n the function is same that is f(a), after second function is the same, the function is repeated with an interval of n.
For example: the period of sin a is 2π for the reason that the smallest number satisfying sin (a + 2π) = sin a is 2π, for all a.Therefore the formula for period of a function is 2π/|B| when the function is y = A sin(Bx + C) and y = A cos(Bx + C).
For a function y = sin bx, period is given by,
P = 2π/b
Here function is y = sin 0.5x, therefore b = 0.5
P = 2π/0.5
=20π/5
= 4π
Period is 4π. The first graph has period 4π.
Hence the graph of the function y = sin 0.5x is option A.
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Disclaimer: The question was given incomplete on the portal. Here is the complete question.
Question: Which could be the graph of the function y = sin 0.5x?
98. A sample of 16 small bags of the same brand of candies was selected. Assume that the population distribution of bag weights is normal. The weight of each bag was then recorded. The mean weight was two ounces with a standard deviation of 0.12 ounces. The population standard deviation is known to be 0.1 ounce. a. i. x ¯ =________ ii. σ =________ iii. sx =________ b. In words, define the random variable X. c. In words, define the random variable X ¯ . d. Which distribution should you use for this problem? Explain your choice. e. Construct a 90% confidence interval for the population mean weight of the candies. i. State the confidence interval. ii. Sketch the graph. iii. Calculate the error bound. f. Construct a 98% confidence interval for the population mean weight of the candies. i. State the confidence interval. ii. Sketch the graph. iii. Calculate the error bound. g. In complete sentences, explain why the confidence interval in part f is larger than the confidence interval in part e. h. In complete sentences, give an interpretation of what the interval in part f means.
Answers
The population standard deviation is the standard deviation of the whole population denoted by sigma.
The sample mean is denoted by x bar and standard deviation by sx and it is the mean and standard deviation of the sample not the population from which the sample is chosen.
The data given in problem answers the first part.
The mean weight of the sample denoted by x bar x ¯ was two ounces with a standard deviation denoted by sx of 0.12 ounces.
The population standard deviation is denoted by σ known to be 0.1 ounce.
a. i. x ¯ =___2_____ ii. σ =___0.1_____ iii. sx =___0.12_____
e. Sub part i) 1.959 ; 2.041
Sub part iii) The error bound is 0.041
f. Sub Part i) 1.935 ; 2.065
Sub Part iii) The error bound is 0.0645
Part b)
The random variable X is any number defining the weights of the sample chosen from the population.
Part c)
The random variable X bar is the average weight of the sample obtained by adding the total weights of the sample divided by the number of the sample size.
Part d)
The normal distribution is used to solve the problem because the sample size is less than 30.
Part e
The 90 % confidence interval is calculated as ∝ = 1- 90%
∝ = 0.1
∝/2= 0.1/2= 0.05
xbar± z(∝/2) σ /√n
Putting the values
2± 1.645 (0.1)/√16
2± 0.041
or
Sub part i) 1.959 ; 2.041
Sub part iii) The error bound is 0.041
Part f
The 98 % confidence interval is calculated as ∝ = 1- 98%
∝ = 0.02
∝/2= 0.1/2= 0.01
xbar± z(∝/2) σ /√n
Putting the values
2± 2.58 (0.1)/√16
2± 0.0645
or
Sub Part i) 1.935 ; 2.065
Sub Part iii) The error bound is 0.0645
Part g
The confidence interval in part f is larger than the confidence interval in part e because we are 98 percent confident about the accuracy of the result. The interval is 0.01 for two tailed test which is very less as compared to 0.05 for 90% confidence interval.
The larger the area of the confidence interval less sure we are about the accuracy of the result hence getting a smaller value .
Part h
On the average 90 % of the 16 sample will have the true value of the mean.
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c) Describe the relationship between ∠E and ∠K. What is the measure of ∠K? (1 point)
Answers
The relationship between ∠E and ∠K is ∠E = ∠K
What is Parallel Lines ?Two lines are said to be parallel when they do not meet even at infinity and the distance between them always remains constant.
∠E = ∠G ( vertical angles) ∠H = ∠F ( vertical angles) ∠G = ∠K (corresponding angles) From equations i) and iii)
we get ∠E = ∠K and they are alternate exterior angles.
The measure of angle K can be found from the equation
∠K + ∠J = 180° (consecutive interior angles)
∠K = 180° - ∠J
∠K + ∠L = 180°
∠K = 180° - ∠L
The missing image is attached with the answer.
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The digits 0, 1, 2, 3, and 4 are to be used in a four-digit ID card. a) how many different cards are possible? b) If repetition are permitted? c) If repetition are not permitted?
Answers
Answer:
a) Varies on b and c
b) 625 combinations
c) 120 combinations
Step-by-step explanation:
a) How many different cards are possible?
Leads to (b and (c
It depends on if repetition are permitted.
↓
in a 4 digit numerical combination, you were given 5 numbers.
b) If repetition are permitted:
you can put any of the given 5 digits to the 1st, 2nd, 3rd, and 4th position.
Each digits would have 5 turns.
This means that you will have 5 x 5 x 5 x 5 If there is repetition,
which is 5⁴ is 625 possible combinations.
c) repetition are not permitted:
This would mean that you have;
5 turns for the first digit,
4 turns for the second digit,
3 turns for the third digit,
2 turns for the fourth digit.
which means you have 5 x 4 x 3 x 2 possible solutions.
5 x 4 x 3 x 2 = 120
There will be 120 possible combinations in total if there's no repetitions.
________________________________________________________
Hope this helped!
A ladder that is 20 feet in length is resting on a branch of a tree, and the base of the ladder is 12 feet from the tree on the level ground. How high up is the branch on which the ladder is resting?
Answers
Answer:
56.57 rounded to the nearest hundredths
Step-by-step explanation:
a^2 + b^2 = c^2
20^2 + x^2 = 60^2
400 to x^2 = 3600
x^2 = 3200 take the square root of each side.
x = 56.57 rounded to the nearest hundredths
State the domain and range of the following function. {(-9, 3), (5, 1), (6, 9), (-4, 7), (3, 2)}
Answers
Answer:
Step-by-step explanation:
To be able to solve equations 3 and 4 by elimination, each equation needs to be multiplied by something, Drag a red number to the red box for equation 3 and a brown number to the brown box for equation 4.
Answers
The solution to the equation 3 and 4 by elimination is x = -2 and y = -2
Simultaneous equation2x = 3y + 2. (1)
3x = 5y + 4. (2)
Rewriting the equation2x - 3y = 2. (3)
3x - 5y = 4 (4)
Multiply (3) by 3 and (4) by 26x - 9y = 6. (5)
6x - 10y = 8. (6)
subtract (5) from (6) to eliminate x-10y - (-9y) = 8 - 6
-10y + 9y = 2
-y = 2
y = -2
substitute y = -2 into (3)2x - 3y = 2. (3)
2x - 3(-2) = 2
2x + 6 = 2
2x = 2 - 6
2x = - 4
x = -4/2
x = -2
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Find the future value of $15,000 compounded continuously at 6% for 8 years.
Answers
The future value with continuous compounding is $127,420.39.
What is the future value?The formula for calculating future value when there is continuous compounding is : A x e^r x N
Where:
A= amount e = 2.7182818 N = number of years r = interest rate15,000 x (e^0.06) x 8 = $127,420.39
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FINDING THE NUMBER OF REAL AND NONREAL SOLUTIONS ( EDGE 2022 )
How many real and nonreal solutions does the equation have?
x5 – 6x + 4 = 0
Answers
By graphing the function, we can see that we have 3 real solutions and 2 non-real solutions.
How many real and nonreal solutions does the equation have?
To check this, we need to graph the equation and see how many times it intersects the x-axis.
Because the degree is 5, we know that there are 5 solutions in total.
Now if we look at the graph, we can see that it intersects the x-axis on 3 points, so there are 3 real solutions. And because there are 5 solutions in total, we conclude that the other 2 solutions are non-real.
So we have 3 real solutions and 2 non-real solutions.
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Use Stokes' Theorem to evaluate the double integral of the curl of F
F(x, y, z) = e^(xy) cos(z)i + x^2 zj + xyk,
S is the hemisphere
x = radical 49 − y^2 − z^2
oriented in the direction of the positive x-axis.
Answers
Stokes' theorem relates the surface integral of the curl of [tex]\vec F[/tex] across [tex]S[/tex] to the line integral of [tex]\vec F[/tex] along the boundary of [tex]S[/tex].
The boundary of [tex]S[/tex] is a circle with radius 7 centered at the origin in the [tex]x,y[/tex]-plane. Parameterize this path by
[tex]\vec r(t) = 7\cos(t)\,\vec\imath + 7\sin(t)\,\vec\jmath[/tex]
with [tex]0\le t\le2\pi[/tex]. Observe that [tex]z=0[/tex], so [tex]\cos(z) = 1[/tex] and the [tex]\vec\jmath[/tex]-component of [tex]\vec F[/tex] contributes nothing. The double integral then reduces to
[tex]\displaystyle \iint_S (\nabla\times\vec F)\cdot d\vec S = \int_0^{2\pi} \vec F(\vec r(t)) \cdot \frac{d\vec r}{dt} \, dt \\\\ ~~~~~~~~ = \int_0^{2\pi} \left(e^{49\cos(t)\sin(t)}\,\vec\imath + 49\cos(t)\sin(t)\,\vec\jmath\right) \cdot \left(-7\sin(t)\,\vec\imath + 7\cos(t)\,\vec\jmath\right) \, dt \\\\ ~~~~~~~~ = -7 \int_0^{2\pi} e^{49\cos(t)\sin(t)} \sin(t) \, dt[/tex]
Observe that by substituting [tex]t=u+\pi[/tex], we have
[tex]\sin(t) = \sin(u+\pi) = \sin(u)\cos(\pi) + \cos(u)\sin(\pi) = -\sin(u)[/tex]
so that the integral over [tex][\pi,2\pi][/tex] can be expressed in terms of the integral over [tex][0,\pi][/tex] as
[tex]\displaystyle \int_\pi^{2\pi} e^{49\cos(t)\sin(t)} \sin(t) \, dt = \int_0^\pi -e^{49\cos(t)\sin(t)} \sin(t) \, dt[/tex]
Then the integrals over [tex][0,\pi][/tex] and [tex][\pi,2\pi][/tex] cancel each other and integral of the curl of [tex]\vec F[/tex] is
[tex]\displaystyle -7 \int_0^{2\pi} e^{49\cos(t)\sin(t)} \sin(t) \, dt = -7 \int_0^\pi 0 \, dt = \boxed{0}[/tex]
8 squared plus 6 squared = c squared using Pythagorean theorem for right triangle
Answers
Answer:
Hypotenuse of 10
Step-by-step explanation:
The Pythagorean Theorem is [tex]a^{2} +b^{2} = c^{2}[/tex]
So let's plug in the numbers!
[tex]8^{2} +6^{2} = c^{2}[/tex]
Let's start the squaring (8*8 and 6*6)
[tex]64 + 36 = c^{2}[/tex]
Add the numbers to simplify
100 = [tex]c^{2}[/tex]
To reverse/invert a number that is squared, all you have to do is to take the square root of the number. But we have to do the same operations on both sides of the equation.
[tex]\sqrt{100} =\sqrt{c^{2} }[/tex]
We can simplify, and the square of c cancels because of the square root, leaving us with:
10 = c