Answers
[tex]\sqrt[n]{a^n}=a[/tex], therefore [tex]\sqrt[4]{5^4}=5[/tex].
Answer:
It is 5
Key solutions:
[tex]\left(\sqrt[n]{a}\right)^n=a[/tex]Step-by-step explanation:
Isolate the exponents and remove the square, giving you 5
[tex]\left(\sqrt[4]{5}\right)^4\\=5[/tex]
Related Questions
What is the volume of the rectangular prism?
A prism has a length of 8 inches, width of 2 inches, and height of 12 and one-half inches.
16 in.3
22 and one-half in.3
200 in.3
212 and one-half in.3
Answers
Volume is a three-dimensional scalar quantity. The volume of the rectangular prism is 200 in³.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
The volume of the rectangular prism of the length of 8 inches, the width of 2 inches, and the height of 12 1/2 inches can be written as,
The volume of the rectangular prism = 8in × 2in × 12.5in
= 200 in³
Hence, The volume of the rectangular prism is 200 in³.
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A survey of 25 randomly selected customers found the ages shown (in years). The mean is 32.64 years and the standard deviation is 9.39 years.
a) Construct a 80% confidence interval for the mean age of all customers, assuming that the assumptions and conditions for the interval have been met.
b) How large is the margin of error?
a) What is the confidence interval?
b) What is the margin of error?
The margin of error is
Answers
Answer:
See below for answers and explanations
Step-by-step explanation:
Part A
Assuming that conditions have been met for the interval, we use the formula [tex]\displaystyle CI=\bar{x}\pm t\frac{s}{\sqrt{n}}[/tex] where [tex]\bar{x}[/tex] represents the sample mean, [tex]t[/tex] represents the critical value, [tex]s[/tex] represents the sample standard deviation, and [tex]n[/tex] is the sample size.
The critical value of [tex]t[/tex] for an 80% confidence level with degrees of freedom [tex]df=n-1=25-1=24[/tex] is equivalent to [tex]t=1.317836[/tex]
Thus, we can compute the confidence interval:
[tex]\displaystyle CI=\bar{x}\pm t\frac{s}{\sqrt{n}}\\\\CI=32.64\pm1.317836\biggr(\frac{9.39}{\sqrt{25}}\biggr)\\\\CI\approx\{30.17,35.11\}[/tex]
Therefore, we are 80% confident that the true mean age of all customers is between 30.17 and 35.11 years.
Part B
The margin of error is [tex]\displaystyle t\frac{s}{\sqrt{n}}=1.317836\biggr(\frac{9.39}{\sqrt{25}}\biggr)\approx2.47[/tex]
Solve for x in the triangle. Round your answer to the nearest tenth.
X
9
64°
Answers
Answer:
x = 23.0
Step-by-step explanation:
To solve, you have to make the equation:
[tex]cos(64)=\frac{9}{x}[/tex]
Now multiply x to both sides:
[tex]cos(64)*x=9[/tex]
Next divide both sides by cos(64):
[tex]x=\frac{9}{cos(64)}[/tex]
x = 22.9675486404
Round to the tenth:
x = 23.0
Hope it helps and have a nice day!
Without calculating the cubes find 1 cube+2cube+2(4) cube+(-5)cube+(-6)cube .
Answers
Nasir is laying out a garden in the shape of a right triangle. he draws it on the coordinate grid below. The three vertices of his garden are at the points A (-3,-4), B(6, -4), and C (6,8). he wants to enclose the garden with a fence that runs along its perimeter. how many feet of fencing will Nasir needs?
Answers
Step-by-step explanation:
it is not important that the triangle is right-angled.
but the distance between each pair of points is calculated via Pythagoras
c² = a² + b²
with c being the Hypotenuse (baseline opposite of the 90° angle) = distance between the end points, and a and b are the legs (= the x and y coordinate differences of the 2 end points) of the virtual right-angled triangles between each pair of points.
so,
AB² = (6 - -3)² + (-4 - -4)² = 9² + 0² = 81
AB = 9 ft
BC² = (6 - 6)² + (8 - -4)² = 0² + 12² = 144
BC = 12 ft
and now for AC, which is because of the special case of how the main triangle is placed and oriented, the same calculation as with Pythagoras for the main right-angled triangle. but I keep showing you the point distance calculation, because this is what you will need in the future for more general triangle or other shapes calculations :
AC² = (6 - -3)² + (8 - - 4)² = 9² + 12² = 81 + 144 = 225
AC = 15 ft
so, Nasir will need
9 + 12 + 15 = 36 ft
of fencing.
n⃗ =〈−2,−1〉 and D=[−4 4 2 3].
What is D⋅n⃗ ?
Enter your answer as a vector by filling in the boxes.
Answers
The dot product of the two matrices D and n is determine as (4, - 7).
Dot product of the vector
The dot product of the two matrices is calculated as follows;
n = (-2, -1), and D = [-4 2]
[4 3]
D.n = (-2, -1). [-4 2] = (-2 x -4) + (-1 x 4) = 4
[4 3] = (-2 x 2) + (-1 x 3) = -7
D.n = (4, - 7)
Thus, the dot product of the two matrices D and n is determine as (4, - 7).
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Try This Q 1. Write the expressions for each of the following using brackets. (a) Four multiplied by the sum of nine and two. (b) Divide the difference of eighteen and six by four. (c) Forty five divided by three times the sum of three and two. 2. Write three different situations for (5+8) x 6. (One such situation is: Sohani and Reeta work for 6 days; Sohani works 5 hours a day and Reeta 8 hours a day. How many hours do both of them work in a week?) 3. Write five situations for the following where brackets would be necessary. (a) 7(8-3) (b) (7+2) (10-3)
Answers
Answer:
Step-by-step explanation:
Writing expressionsa) Sum of nine and two ⇒ 9 + 2
Four multiplied by (9+2) :
4* (9+2)
[tex]b) \dfrac{(18-6)}{4}[/tex]
[tex]c) \dfrac{45}{3*(3+2)}[/tex]
2) a) Multiply the sum of five and eight by 6
b) There 5 story books in 6 red bags and 8 art books in 6 blue bags. How many books are there?
3) a) 7*(8-3)
Multiply the difference of eight and three by 7.
Can you help me please!!
Answers
The ABEF is a parallelogram because DC is extended to point F; AB ≅ FE and FA ≅ BE.
What is parallelogram?In two-dimensional geometry, it is a plane shape having four sides, in which two pairs of sides are parallel to each other and equal in length. The sum of all angles in a parallelogram is 360°.
We have ABCD is a parallelogram.
BE is perpendicular to FC
FA is perpendicular to FC
As we know in the parallelogram ABCD:
AB ≅ DC
AD ≅ CB
As the DC is extended to F
So, AB ≅ FE
And BE is perpendicular to FC
FA is perpendicular to FC (given)
∴ FA ≅ BE
∴ ABEF is a parallelogram.
Thus, the ABEF is a parallelogram because DC is extended to point F; AB ≅ FE and FA ≅ BE.
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PLEASE HELP ME I WILL GIVE BRAINLYEST
Answers
Answer:
your answer will be 85 1/3ins
Step-by-step explanation:
16x 5 1/3 = 85.3333333333
then I took the 85 and the 1/3
and just put em together
What is the value of x? 2 3 6 7
Answers
Answer:
6
Step-by-step explanation:
Answer:
2 or A
Step-by-step explanation:
Correct on edge22
Find the hypotenuse of right angle triangle whose sides are 6.03 units and 7.96 units also find
the relative error?
Answers
Answer:
9.99 units
Step-by-step explanation:
since hyp=√b^2+h^2
=6.03^2+7.96^2
36.3609+63.3616
√99.7225
9.9861
i.e 9.99
The hypotenuse is is 9.98 units
What is Pythagoras theorem?
The square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.
Given:
Sides are 6.03 units and 7.96 units
Using Pythagoras theorem,
H²=P²+B²
H²= 7.96²+6.03²
= 63.3616+36.3609
= 99.7225
H=9.98 units.
Hence, the hypotenuse is 9.98 units.
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State your conclusion in the form of a theorem, and then prove the theorem using a two-column proof. When you write the proof, refer to the diagram you created in part A. It will be helpful to use point labels to state what is given and what you have to prove and to use those labels throughout the proof.
As part of the proof, you’ll have to construct a line segment connecting the top intersection point on one of the transversals with the lowest intersection point of the other transversal, thus forming two triangles. Take a screenshot of the construction, save it, and insert the image in the space below before you begin your written proof.
Answers
The midpoint theorem simply states that the line segment that joins the two sides of the triangle is parallel to the third side.
How to illustrate the theorem?Your information is incomplete. Therefore, an overview of the theorem will be given. It should be noted that the midpoint theorem states that the line drawn through the mid point of one side of the triangle is parallel to another side.
To find the midpoint, one can measure the distance between the two end points and divide the results by 2.
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You have a glass paperweight that is shaped like a cone. The diameter of the paperweight is 7 centimeters. The slant height is 4 centimeters. Find the surface area of the cone. Use 3.14 to approximate pi.
Answers
Step-by-step explanation:
please mark me as brainlest
Given a polynomial function f(x) = –x2 + 2x + 1 and an exponential function g(x) = 2x, what key features do f(x) and g(x) have in common?
A.)Both f(x) and g(x) decrease over the interval of [1 , ∞).
B.) Both f(x) and g(x) have the same range of (–∞, 2).
C.) Both f(x) and g(x) have the same x-intercept of (–1, 0).
D.)Both f(x) and g(x) have the same y-intercept of (0, 1).
Answers
The only key feature that these functions have in common is that they have the same y-intercept. So the correct option is D.
What do these functions have in common?
Here we have the functions:
[tex]f(x) = -x^2 + 2x + 1\\\\g(x) = 2^x[/tex]
f(x) is quadratic, and g(x) is exponential.
Notice that the exponential function has a positive base, so it is increasing. For the quadratic equation we can see a negative leading coefficient, so it opens downwards. So first and second options are false.
Also, g(x) never intersects the x-axis, so third option is false.
Finally, the y-intercepts of the given functions are:
[tex]f(0) = -0^2 + 2*0 + 1 = 1\\\\g(0) = 2^0 = 1[/tex]
So the y-intercepts are equal, meaning that the correct option is D.
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Answer:
Both f(x) and g(x) have the same y-intercept of (0, 1).
Step-by-step explanation:
I got it right on the test.
A bag contained $24.20 worth of coins. There were 20-cent and 50-cent coins only. The number of 20-cent coins was 5 fewer than the number of 50-cent coins. How many coins were there in the bag
Answers
Answer:
Their will be 2 coins in allThere were 67 coins in the bag, 36 of which were 50-cent coins and 31 of which were 20-cent coins.
Let x be the number of 50-cent coins in the bag,
And y be the number of 20-cent coins.
From the problem,
we know that y = x - 5,
Since there were 5 fewer 20-cent coins than 50-cent coins.
We can also set up an equation for the total value of the coins in the bag,
⇒ 0.5x + 0.2y = 24.20
Now we can substitute y = x - 5 into the equation,
⇒ 0.5x + 0.2(x - 5) = 24.20
Simplifying, we get,
⇒ 0.7x - 1 = 24.20
⇒ 0.7x = 25.20
⇒ x = 36
So there were 36 50-cent coins in the bag.
Using y = x - 5,
We can find that there were 31 20-cent coins.
Therefore, there were a total of 67 coins in the bag (36 + 31 = 67).
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Phyllis invested 800 dollars into two different accounts, a portion earning a yearly interest rate of
4
percent per year compounded monthly and the rest earning a rate of
6
percent per year compounded quarterly
After 12 years the investments were worth $1579.05. How much money did she invest at each rate
Answers
The amount of money that Phyllis invested at each given rate of 4 and 6 percent is = $394.57 and $591.86 respectively.
Calculation of the total capital investedThe time the investment lasted= 12 years.
Simple interest = 1579.05 - 800= $779.05
The principal capital= $800
Rate of the both capital invested;
= SI × 100/P ×T
= 779.05 × 100/800 × 12
= 77,905/9600
= 8.11%
To find the amount of money that Phyllis invested at each given rate,
Rate 1 = 4/8.11× 800
= 3200/8.11
= $394.57
Rate 2 = 6/8.11× 800
= 4800/8.11
= $591.86
The amount of money that Phyllis invested at each given rate of 4 and 6 percent is = $394.57 and $591.86 respectively.
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if for 5 pounds of beans it cost 4 dollars than how much money is needed for 50 pounds of beans
Answers
Answer:
40 dollars
Step-by-step explanation:
We can use a ratio to solve the problem
5 pounds 50 pounds
---------------- = -----------------
4 dollars x dollars
Using cross products
5 * x = 4 * 50
5x = 200
Divide by 5
5x/5 = 200/5
x = 40
40 dollars
Step-by-step explanation:
[tex]\sf 5 \: pounds \longrightarrow 4 \: dollars[/tex]
[tex]\sf 1\: pounds \longrightarrow \dfrac{4}{5} \: dollars[/tex]
[tex]\sf 50\: pounds \longrightarrow \dfrac{4}{5}×50 \: dollars[/tex]
[tex]\sf \longmapsto 40 \: dollars[/tex]
Which of the following correctly replaces the question mark in Aisha's proof?
OHL
O SSS
O SAS
O AAS
Answers
The option that correctly replaces the question mark in Aisha's proof is SAS (Option C). See it explained below.
Mathematical proofs are statements that are used to demonstrate that a mathematical expression or logic of true.
Since the portion of the question that shows the question mark is missing, we can rewrite the proof as follows:
Step 1
AB Dissects BC
AE ║ BD
Reason - It is given
Step 2
BC ≅ BE
Reason - Definition of Segment Bisector
Step 3
∠ABE ≅ ∠CBD
Step 4
∠BCD ≅ ∠BEA
Reason
Alternative Interior Angles
Step 5
ΔBCD ≅ ΔBEA
Reason
SAS Postulate
Step 6
QED
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x – y = 2 2x = 3y in elimination method
Answers
Answer:
x=6, y=4
Step-by-step explanation:
x - y = 2
2x = 3y => 2x - 3y = 0
x - y = 2 | ×(-2) => -2x + 2y = -4
2x - 3y = 0
-2x + 2y = -4
2x - 3y = 0
___________
0 - y = - 4 | ×(-1)
y = 4
Substitution in x - y = 2:
x - 4 = 2 | +4
x = 2+4 = 6
Find the area of the sector
Answers
Answer:
10:
7/4π = 5.5(1decimql place)
11:
50π = 157.1(1 decimal place)
Step-by-step explanation:
the equation is (angle/360) X πr^2
Krista got paid $43.75 for working 3.5 hours. How much did she earn per hour?
Answers
Answer:
12.5
Step-by-step explanation:
divide 43.75 by 3.5 to get your answer
Step-by-Step Explanation:
Total Earnings = $43.75
Time = 3.5 hrs
Therefore,
Earnings in 1 hr = Total Earnings/Time
= 43.75/3.5
= 12.5
Earnings in 1 hr = $12.5
√-361 what is the answer
Answers
Answer:
19i
Step-by-step explanation:
note that [tex]\sqrt{-1}[/tex] = i
[tex]\sqrt{-361}[/tex]
= [tex]\sqrt{361(-1)}[/tex]
= [tex]\sqrt{361}[/tex] × [tex]\sqrt{-1}[/tex]
= 19 × i
= 19i
he triangle on the grid will be translated two units down. On a coordinate plane, triangle A B C has points (2, 1), (0, negative 1), (2, negative 1). Which shows the triangle when it is translated two units down? On a coordinate plane, triangle A prime B prime C prime has points (0, negative 1), (0, negative 3), (2, negative 3). On a coordinate plane, triangle A prime B prime C prime has points (0, 1), (negative 2, negative 1), (0, negative 1). On a coordinate plane, triangle A prime B prime C prime has points (2, negative 1), (2, negative 3), (0, negative 3). On a coordinate plane, triangle A prime B prime C prime has points (2, negative 1), (2, negative 3), (0, negative 1).
Answers
If these coordinates are translated two units down, we will subtract 2 units from the y axis to have A(2, -1), B(0, -3) and C(2, -3)
Translation of coordinate pointTranslation is a transformation technique of changing the position of an object on the xy-plane.
Given the following coordinate of a triangle expressed as:
A(2, 1)
B(0, -1)
C(2, -1)
If these coordinates are translated two units down, we will subtract 2 units from the y axis to have:
A(2, -1)
B(0, -3)
C(2, -3)
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Beginning in the middle of summer, the average temperature for a certain year in Phoenix could approximately be modeled by the function f(x)=31cos(0.0055πx)+88, where x represents the number of days since the middle of the summer, and f(x) represents the average temperature in degrees Fahrenheit.
What was the lowest average temperature in Phoenix that year (approximately)?
A) 57∘F
B) 31∘F
C) 55∘F
D) 88∘F
Answers
By finding the minimum of the given function, we conclude that the lowest average temperature that year is 57°F.
What was the lowest average temperature in Phoenix that year?We know that the average temperature is given by the equation:
f(x)=31cos(0.0055πx)+88
And it is in Fahrenheit degrees.
To get the lowest average temperature, we just need to find the minimum of the above function.
Remember that the minimum of the cosine function is:
cos(x) = -1
Then the lowest value of the above function is:
f(x₀) = 31*(-1) + 88 = 57
From this, we conclude that the lowest average temperature that year is 57°F, so the correct option is A.
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The point at which three or more lines intersect is the point of _____ concurrency. concurrency. tangency. equality. parallelism.
Answers
The point at which three or more lines intersect is the point of concurrency.
What is the point where three line intersect?The point were three lines meet or intersect is a point of concurrency.
In other words, a point of concurrency is where three or more lines intersect in one place.
This point of concurrency is a single point shared by three or more lines.
Perpendicular bisectors, and altitudes are concurrent in every triangle.
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Answer:
concurrency
Step-by-step explanation:
Look above for more
A researcher develops a cage for a living cell in the shape of a square-based pyramid. A scale model of the cage is shown. What is the volume of the model?
A square pyramid-shaped cage with base edge labeled “20 micrometers” and height labeled “20 micrometers”.
Answers
The total volume of this squared-base pyramid based on the information provided is 2666 micrometers.
How to calculate the volume of the pyramid?The general formula to calculate the volume of a squared-based pyramid is:
base = area x height/ 3What is the volume of the model?Base area: 20 x 20 = 400
400 micrometers x 20/ 3 = 2666 micrometers.
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Find the probability that a randomly
selected point within the circle falls
in the red shaded area.
r = 4 cm
[?]%
Round to the nearest tenth of a percent.
Enter
Answers
Answer:
[tex]31.8\%[/tex]
Step-by-step explanation:
The area of the circle is [tex]A=\pi r^2=\pi(4)^2=16\pi[/tex]
The area of the triangle is [tex]A=\frac{bh}{2}=\frac{8*4}{2}=\frac{32}{2}=16[/tex]
Hence, the probability of a randomly selected point within the circle falls in the red shaded area is [tex]\frac{16}{16\pi}=\frac{1}{\pi}\approx0.318\approx31.8\%[/tex]
5. Use an inequality symbol (<, >,=, S) to compare -3 +7-10-2
A. >
B.<
C. ≤
D. =
Answers
If the question should read as the following, then I hope my answer will help; -3 +7 _ -10 - 2
Answer: A. >
Step-by-step explanation:
Given:
-3 + 7 _ -10 - 2
Simplify both sides by combining like terms:
4 _ -12
Compare, knowing that 4 is greater than -12:
4 _ -12
4 > -12
A. >
Gabrielle needs to rent a car while on vacation. The rental company charges $19.95, plus 15 cents for each mile driven. If Gabrielle only has $40 to spend on the car rental, what is the maximum number of miles she can drive?
Round your answer down to the nearest mile.
Answers
Answer:
133 miles
Step-by-step explanation:
The limited budget gives rise to an inequality that can be solved for the maximum number of miles.
__
setupThe rental cost for m miles will be the sum of the fixed charges and the product of the mileage charge and the number of miles.
cost = 19.95 +0.15m
We want this to be no greater than 40, so we have the inequality ...
40 ≥ 19.95 +0.15m
solutionThis two-step inequality can be solved in the usual way:
20.05 ≥ 0.15m . . . . . step 1, subtract 19.95 from both sides
133.667 ≥ m . . . . . . . step 2, divide by the coefficient of the variable
The maximum whole number of miles Gabrielle can drive is 133.
Wendy winholtz 8 year savings certificate pays an annual interest rate of 5.3% at the end of 5 years she cashed out the 6,000 CD and paid a penalty of 12 month simple interest. What penalty did she pay
Answers
Answer:
318
Step-by-step explanation:
The rate of 5.3% is an annual rate, and specifies the amount of interest earned in a 12-month period by the principal amount of the CD. The interest amount is found by multiplying the interest rate by the principal amount.
__
penaltyThe amount of the penalty is 5.3% of 6000:
0.053 × 6000 = 318
Wendy paid a penalty of 318 for her early withdrawal.