Answers
First, we need to remember to rules when working with exponents:
[tex]\begin{gathered} \frac{1}{b^a}=b^{-a} \\ \text{and} \\ b^a\cdot b^c=b^{a+c} \end{gathered}[/tex]So, going back to our problem
[tex]\begin{gathered} \frac{2^{\frac{3}{4}}}{2^{\frac{1}{2}}} \\ =2^{\frac{3}{4}}\cdot2^{-\frac{1}{2}}=2^{\frac{3}{4}-\frac{1}{2}}=2^{\frac{1}{4}} \end{gathered}[/tex]And this last result is equal to
[tex]\begin{gathered} 2^{\frac{1}{4}}=\sqrt[4]{2} \\ \Rightarrow\frac{2^{\frac{3}{4}}}{2^{\frac{1}{2}}}=\sqrt[4]{2} \end{gathered}[/tex]Related Questions
find the area of a square inscribed in a circle of a radius square root 70
Answers
The area of a square inscribed in a circle of a radius square root 70 is 140 units².
What is a square inscribed in a circle?A square is inscribed in a circle if its four vertices are on the circle's circumference. When a square is inscribed in a circle, the diameter of the circle must be equivalent to the diagonal of the square
Given:
The radius of the circle = √70 units
Let the side of the square inscribed in the circle be x units.
Diagonal of the square = [tex]\sqrt{x^{2} + x^{2} }[/tex] = [tex]\sqrt{2} x[/tex]
Diameter of the circle = 2 × √70 ≅ 16.7 units
Now,
Diagonal of the square = Diameter of the circle
[tex]\sqrt{2} x = 16.7[/tex]
[tex]x = \frac{16.7}{\sqrt{2} }[/tex]
x ≅ 11.83 units
So, the Area of the square = (side)² = x²
= (11.83)²
≅ 140 units²
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What is the area of ΔABC given m∠B = 95°, a = 22 feet, and c = 17 feet?use area = 1/2 ac sin B
Answers
area = 1/2 ac sin B
1/2 ( 22) ( 17) * (sin 95)
187 sin 95
186.2884085 ft^2
3] If the p.d.f., of the random variable X is given byf(x)= K sqrt x &0 1)(c) P(|X| < 3)(d) E(2X - 2)(e) V(3X)
Answers
A manager at a shipping company will purchase boxes in the shape of a right rectangle prisms he wants the volume of each box to be exactly 98 cubic ftwhich figure shows a box with the dimensions in feet that the manager will purchase
Answers
We have that the general equation for the volume of a rectangle prism is:
[tex]V=lwh[/tex]where l represents the length of the base, w represents the width of the base and h represents the height of the prism.
Since we need that the volume be equal to 98ft³, we have that the measures for the prism are:
[tex]V=(7)(3.5)(4)=98ft³[/tex]therefore, the prism would look like this:}
Please help again please help me
Answers
Answer:
-0.5,-1/5,0.7,3/4 its correct
Answer:
-0.5, -1/5, 0.7, 3/4
Step-by-step explanation:
We can convert the fractions into decimals.
-1/5 = -0.2
3/4 = 0.75
-0.5 is the least, then -1/5, then 0.7, and lastly 3/4.
Hope this helps!
P.S, Can I get a brainliest if this is right? Thanks!
what is the daily recommended amount of vitamin A if 15% is 150 mcg?
Answers
If x is the daily amount of Vitamin A and we know that 15% of x is 150 mcg, we can calculate x as:
[tex]\begin{gathered} 15\%\cdot x=\frac{15}{100}x=0.15x=150 \\ x=\frac{150}{0.15} \\ x=1000 \end{gathered}[/tex]Answer: the recommended daily amount of Vitamin A is 1000 mcg.
Ratio
$1.25
1 slice
$10.00
8 slices
1 book
5 days
25 miles
1 gallon
Unit rate
Not a unit rate
Answers
Answer:
Step-by-step explanation:
$1.25 for 1 slice is the unit rate because a unit rate is the measure of a single unit, which in this case is 1 slice.
A hiker on the Appalachian Trail planned to increase the distance covered by 10% each day. After 7 days, the total distance traveled is 75.897 miles.Part A: How many miles did the hiker travel on the first day? Round your answer to the nearest mile and show all necessary math work. (4 points)Part B: What is the equation for Sn? Show all necessary math work. (3 points)Part C: If this pattern continues, what is the total number of miles the hiker will travel in 10 days? Round your answer to the hundredths place and show all necessary math work. (3 points)
Answers
Answer with explanation: A hiker has increased his distanced covered by 10% each day since the start, the total distance covered at the end of the 7th day is 75.897mile:
(A) The number of miles on the first day:
[tex]\begin{gathered} \text{let x be the distance covered on first day:} \\ x,1.1x,1.21x,1.331x,\ldots. \\ \text{ This is a Geomatric sequence:} \\ S_n=\frac{a(r^n-1)}{r-1} \\ a=x \\ r=\frac{1.1x}{x}=1.1 \\ r=1.1 \\ n=7 \\ S_n=\frac{x((1.1)^7-1)}{1.1-1}\Rightarrow(0) \end{gathered}[/tex]Substituting the total miles covered on the 7th day in equation(0) gives:
[tex]\begin{gathered} 75.897=\frac{x((1.1)^7-1)}{1.1-1} \\ 7.5897=0.9487171x \\ x=7.9999612107761101807904590314647 \\ x\approx7.9999mi \end{gathered}[/tex]Therefore on the first day, the hiker covered about 7.99 miles:
(B) The equation for the S:
[tex]\begin{gathered} S_n=\frac{a(r^n-1)}{r-1} \\ S_n=\frac{7.99((1.1)^n-1)}{1.1-1}\Rightarrow(1) \end{gathered}[/tex]The equation (1) gives the number of miles hiked on the nth day.
(C) miles covered on 10th day:
The number of miles covered on the 10th day is calculated using the equation(1) as follows:
[tex]\begin{gathered} S_n=\frac{7.99((1.1)^n-1)}{1.1-1}\Rightarrow n=10 \\ S_{10}=\frac{7.99((1.1)^{10}-1)}{1.1-1} \\ S_{10}=127.340mi \end{gathered}[/tex]The number of miles covered on the 10th day is 127.340miles.
About the formula used:
[tex]\begin{gathered} S_n=\frac{a-ar^n}{1-r}\Rightarrow\text{ Your formula} \\ \text{Multiply by:} \\ \frac{(-1)}{(-1)} \\ \therefore\Rightarrow \\ S_n=\frac{(-1)}{(-1)}\times\frac{(a-ar^n)}{(1-r)}=\frac{(-1)\cdot(a-ar^n)}{(-1)\cdot(1-r)}=\frac{-a+ar^n}{-1+r}=\frac{ar^n-a}{r-1} \\ S_n=\frac{ar^n-a}{r-1}=\frac{a(r^n-1)}{r-1} \\ S_n=\frac{a(r^n-1)}{r-1}\Rightarrow\text{ My formula} \end{gathered}[/tex]In conclusion, the formula used is the same as the one that was required to be used.
aIn a class of students, the following data table summarizes how many students passeda test and complete the homework due the day of the test. What is the probability thata student who passed the test did not complete the homework?Passed the test Failed the testCompleted the homework112.2Did not complete the homework3N
Answers
According to the given table, the number of students that passed the test and did not complete the homework is
[tex]3.[/tex]Also, from the table, we get that the total number of students that passed the test is
[tex]11+3=14.[/tex]Therefore, the probability that a student that passed the test did not complete the homework is:
[tex]\frac{3}{14}\text{.}[/tex]Answer:
[tex]\frac{3}{14}\text{.}[/tex]A country's education department reported that in 2015, 64.8% of students enrolled in college or a trade school within 12 months of graduating high school. In 2017, a random sample of 179 individuals who graduated from high school 12 months prior was selected. From this sample, 112 students were found to be enrolled in college or a trade school. Complete parts a through c. a. Construct a 90% confidence interval to estimate the actual proportion of students enrolled in college or a trade school within 12 months of graduating from high school in 2017.
The confidence interval has a lower limit of
and an upper limit of
(Round to three decimal places as needed.)
Answers
Answer:
Step-by-step explanation:
What is the rate of return when 25 shares of Stock A, purchased for $30/share, are sold for $825? The commission on the sale is $6. Rate of Return = [?] %
Answers
Given:
The rate of return when 25 shares of Stock
A. purchased for $30/share, are sold for $825. The commission on the sale is $6.
Required:
What is the rate of return?
Explanation:
First step is to find the shares of stock price:
Shares of stock price=25 shares×$30/share
Shares of stock price= $750
Second step is to calculate the total sold price:
Total sold price= $825+$6
Total sold price= $831
Third step is to calculate the Rate of return:
[tex]\begin{gathered} \text{ Rate if return }=\frac{831-750}{750}\times100 \\ \text{ Rate if return }=\frac{81}{750}\times100 \\ \text{ Rate of return }=10.8\% \end{gathered}[/tex]Answer:
Rate of return is 10.8%
Find the distance between the two points rounding to the nearest tenth (if necessary). (5,-8) and (-3,-1)
Answers
Answer: [tex]\sqrt{113}[/tex]
Step-by-step explanation:
You use the Pythagorean Theorem for problems like this.
1. First you figure out the distance between the points.
2. As seen in the picture, the yellow line is 7 units long and the blue line is 8 units long.
3. From here you substitute the numbers into the Pythagorean Theorem. [tex]7^{2} +8^{2} =c^2[/tex]
4. Now solve. This gives you [tex]\sqrt{113}[/tex]
Are the triangles similar! If yes state how?are the triangles similar if yes State how
Answers
Part 1
Remember that
If two triangles are similar , then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
so
Verify the proportion
38.5/14=22/8
38.5*8=14*22
308=308 -----> is true
that means
the triangles are similarPart 3
Verify the proportion
22/9=30/12=25/10
2.44=2.5=2.5 ------> is not true
that means
the triangles are not similarFor what value of x will 3x + 4 = x - 6 be a true statement?
A x = -5
В. x = -5/2
C x = -1
D x = - 1/2
Answers
Answer:
A
Step-by-step explanation:
3x + 4 = x - 6 ( subtract x from both sides )
2x + 4 = - 6 ( subtract 4 from both sides )
2x = - 10 ( divide both sides by 2 )
x = - 5
Answer:x 1= x. Examples: 41=4. 5)
Step-by-step explanation:
Which number comes first
5
1/3 -1. √3. - 12/21
6
3.4
Answers
-3.4 is the number which will come first.
What is simplifying?To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. the act of simplifying something such that it is simpler to carry out or understand, or the thing that is the product of this simplifying process: The group offers suggestions for streamlining business processes. This grossly oversimplifies what actually transpired.
Given Data
5, 1/3 -1. √3. - 12/21,6,3.4
Simplifying,
5, [tex]\frac{1}{3}[/tex] - 1, √3. -[tex]\frac{12}{21}[/tex], 6, -3.4
5, -0.6 , [tex]\sqrt{3}[/tex] , -0.5 ,6,-3.4
-3.4 is the number which will come first.
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Target's sells casual sandals for $12 and dress sandals for $22. Total sandals sales were $2,300, and customers bought twice as many casual sandals as dress sandals. How many dress sandals did customers buy? (Hint: Let D = the number of dress sandals.)
Answers
Answer:
50 dress sandals
Step-by-step explanation:
Let D = number of dress sandals and C = number of casual sandals
Customers bought twice as many casual sandals as dress sandals. In algebraic form this would be
S = 2D (number of casual sandals = 2 times number of dress sandals)
Since casual sandals sell for $12 each and dress sandals for $22 each, the total sales for S casual and D dress sandals
= 12S + 22D = 2300 (given)
Substitute S = 2D into the above equation to get
12 (2D) + 22D = 2300
24D + 22D = 2300
46D = 2300
D = 2300/46 = 0
Answer: Customers bought 50 dress sandals
Ingrid hit a golf ball. the height of the golf ball (in meters above the ground) t seconds after being hit is modeled by h(t)=-5t²+30tIngrid wants to know when the ball reached its highest point 1) rewrite the function in a different form (factored or vertex) where the awnser appears as a number in the equationh(t)=___2) How many seconds after being hit does the ball reach its highest point?____ seconds
Answers
Write the equation in vertex form to find the maximum height, as well as the time when the maximum height is reached.
The vertex form of a quadratic equation is:
[tex]y=a(x-h)+k[/tex]Where (h,k) is the vertex of the parabola, k is the maximum or minimum value and h is the value of x where that maximum or minimum is reached.
To write h in vertex form, complete the square:
[tex]\begin{gathered} h(t)=-5t^2+30t \\ =-5(t^2-6t) \\ =-5(t^2-6t+9-9) \\ =-5((t-3)^2-9) \\ =-5(t-3)^2-5(-9) \\ =-5(t-3)^2+45 \end{gathered}[/tex]We can see that in this case, the vertex is (3,45).
Therefore:
1)
[tex]h(t)=-5(t-3)^2+45[/tex]2)
The ball reaches the maximum height 3 seconds after being hit.
The average daily profit of an electronics store is $27,235. The company estimates that 15% is lost each day to returns, with a margin of error
of 13%. What is the maximum the company can expect for returned items?
O $3268.20
$3668.30
O$4425.60
O $4902.30
Answers
Using proportions, it is found that the maximum the company can expect for returned items is of:
$4,616.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using basic arithmetic operations such as multiplication or division along with the unit rates in the context of this problem.
The lost amount to returns each day is of 15% of 27235, and this amount is calculated as follows:
0.15 x 27235 = $4,085.25
(the decimal equivalent of the percentage is multiplied by the original amount to find the equivalent amount).
The margin of error is of 13%, hence this amount can still be increased by 113, that is, multiplied by 1.13, hence:
4085.25 x 1.13 = $4,616.
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Answer:
The answer is D $4902.30
Step-by-step explanation:
Amber rolls a 6-sided die. On her first roll, she gets a "4". She rolls again.(a) What is the probability that the second roll is also a "4".P(4 | 4) =(b) What is the probability that the second roll is a "1".P(1l4)
Answers
The probability of getting a 4 again means is given by the product of the probabilities to obtain 4 twice (because in this case we have independent events)
(a) P(4I4) = P(4)*P(4) = (1/6)(1/6) = 1/36
(b) P(1l4) = P(1)*P(4) = (1/6)(1/6) = 1/36
In the previous calculations we have considered that the probability for getting any number is the same and it is 1/6.
Ben has £24
He gives £16 to Rhys.
a) What fraction of the £24 does Rhys get?
Give your answer in its simplest form.
b) What fraction of the £24 does Ben have now?
Give your answer in its simplest form.
Answers
Answer:
[tex]\frac{2}{3}[/tex] and [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
(a)
fraction Rhys gets is [tex]\frac{16}{24}[/tex] = [tex]\frac{2}{3}[/tex]
(b)
Ben is left with £24 - £16 = £8
then fraction Ben has left is
[tex]\frac{8}{24}[/tex] = [tex]\frac{1}{3}[/tex]
If you could please help me with this it makes no sence to me.
Answers
Answer:
A = 7986 m²
Step-by-step explanation:
the field is in the form of a trapezium.
the area (A) of a trapezium is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the perpendicular distance between the bases b₁ and b₂
here h = 66 , b₁ = 102, b₂ = 140 , then
A = [tex]\frac{1}{2}[/tex] × 66 × (102 + 140) = 33 × 242 = 7986 m²
Answer:
7986 m²
Step-by-step explanation:
The field geometric shape is a trapezoid whose bases are 102 m and 140 m and height of 66m
The equation for the area of a trapezoid is given by
[tex]A = \dfrac{a + b}{2} h\\\\[/tex]
where a and b are the two sides and h is the height
Here a = 102, b = 140 and h = 66
Substitute these values directly into the equation for area
[tex]A = \dfrac{102 + 140}{2} \times 66\\\\A = (102 + 140) \times \dfrac{66}{2}\\\\\\102 + 140 = 242\\\\\dfrac{66}{2} = 33\\\\\\A = 242\ \times 33 = 7986\; m^2[/tex]
Bridget sold a total of $135 at her yard sale. If she sold a lamp for $35.50 more than the cost of everything else, what was the cost of the lamp and everything else.
Answers
The cost of lamp and everything else will be equal to $85.25 and $49.75 respectively.
This question can be solved by converting it into the form of linear equation. A linear equation can be expressed in the form of y = ax + b where a, b are coefficients and x, and y are independent and dependent variables. We know the total sale which is equal to $135. Let us assume the cost of everything else as x. Now, the cost of lamps is $35.50 more than cost of everything else that is equal to x + 35.50. Now, the linear equation will be written as
135 = x + (x + 35.50)
135 = 2x + 35.50
=> 2x = 99.5
=> x = $49.75 which is the cost of everything else and cost of lamp = x + 35.50 = $85.25.
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Write the equation of the line with a slope of -3 that passes through (-5,20)
Answers
SUBSTITUTE THE KNOWNS IN THE GIVEN GENERAL EQUATION BELOW AND SIMPLIFY TO GET c
[tex]y = mx + c \\ 20 = - 3( - 5) + c \\ 20 = 15 + c \\ c = 20 - 15 \\ c = 5[/tex]
Meaning
[tex]y = - 3x + 5[/tex]
IS THE EQUATION
3y=-4x+5 y=-4/3x-8 are they parallel, perpendicular or neither
Answers
the lines are parallel.......
You purchase six municipal bonds on the first of the year. The current market value price is 103. The commission charge is $5 per bond. What is the cost of the purchasing these bonds?
a.
$6210
b.
$633
c.
$648
d.
$3090
Answers
Answer:
C
Step-by-step explanation:
(103 + 5) * 6 = 648
Letter C
Explanation:
Why letter C?
You purchased 6 bonds for the price of 103 dollars the commission is 5 dollars for each, therefore we will add 103 + 5 and multiply by 6
(103 + 5) 6
(108)6
648
Or
6(103)+6(5)
618+30
648
please help me with this. I have been trying to figure it out for a long time and I need to have dinner with my family very soon.
Answers
To subtract this polynomial, we would have to open the bracket
[tex]\begin{gathered} 9x^4+8x^3-6-(5x^2-8x+6) \\ 9x^4+8x^3-5x^2+8x-6-6=9x^4+8x^3-5x^2+8x-12^{} \end{gathered}[/tex]Remember, we only add and subtact directly , Algebraic characters of the same type only
and the same power only.
a rectangular flying carpet is 1 1/2 meters wide and 2 meters long what is the area of the carpet
Answers
The area of 1 1/2 meters wide and 2 meters long carpet is 3 meters².
As per the known fact, the area of rectangular object is calculated by performing multiplication of value of two sides. These two sides are length and width. Firstly converting width from mixed fraction to fraction -
Width = (2×1 + 1)/2
Width = 3/2 meters
Area = length × width
Keep the values in formula to find the value of area of rectangular flying carpet
Area = 3/2×2
Cancelling 2 as it is common in both numerator and denominator
Area = 3 meters²
Thus, the area of rectangular flying carpet is 3 meters².
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Kathy Runde, age 66 and retired, receives a $20,000 partial distribution from her 401(k) plan. The plan does not pay out an annuity. Immediately before the distribution, her account balance is $50,000, including $10,000 in nondeductible contributions. How much of the $20,000 distribution must Kathy include in gross income?
Answers
The whole twenty thousand dollars that were distributed has to be accounted for as part of the gross revenue.
This is further explained below.
What is gross income?Generally, A person's or a household's gross income is the whole amount of money earned before any deductions or taxes are taken out of that income. This includes all wages, salaries, profits, interest payments, rentals, and other types of earnings.
Because it is treated as regular income, the amount that was withdrawn is subject to taxation at the same rate as ordinary income under the federal income tax system.
If, on the other hand, Kathy makes the decision to convert her 401(k) to a Roth 401(k), then any money she takes out of the account will not be subject to taxes.
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find the rate of change of its elevation when x=22
Answers
To find the rate of change of its elevation we can derive the position function:
[tex]y=-\frac{1}{110}x^2+127[/tex][tex]y^{\prime}=\frac{d(y)}{dx}=d(-\frac{1}{110}x^2+127)/d(x)[/tex][tex]y^{\prime}=\frac{-1}{55}x[/tex]The rate of change of its elvation when x=22 is
[tex]\frac{-1}{55}\cdot22=\frac{-22}{55}=\frac{-2}{5}=-0.4[/tex]That represents the slope of the tangent line to the function at x=22.
Elinor wanted to order an 18 inch hoagie, which cost $7.99. The sandwich shop is out of 18 inch buns. They only have 12 inch buns.
Answers
The price of 12 inch bun purchased by Elinor is $5.32.
What is defined as the method of unitary?The unitary method determines the value of a unit and afterwards the value of such a necessary number of units. The value of a unit amount is determined first in the unitary method before calculating the value of many other units. It comes in two varieties.Variation in DirectVariation in the inverseFor the given question;
Elinor wanted to have a bun.
The cost of 18 inch hoagie bun is $7.99.
As there is only 12 inch bun present, the price of 12 inch bun is calculated by unitary method.
The price can be written as;
18 inch -------> $7.99
For 1 inch bun, divide both side by 18.
18/18 inch -------> $7.99/18
1 inch -------> $7.99/18
For 12 inch, multiply each side by 12.
12 inch -------> $7.99×12/18
12 inch -------> $5.32
Thus, the price of 12 inch bun is $5.32.
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