Answer:
[tex]\large\boxed{(4^3)^5=4^{15}}[/tex]
Step-by-step explanation:
[tex]\text{Use}\ (a^n)^m=a^{nm}\\\\(4^3)^5=4^{(3)(5)}=4^{15}[/tex]
Step-by-step explanation: Here we have the number (4^3)^5.
We can use the relationship: [tex](x^{a} )^{b} = x^{a*b}[/tex]
so our number can be written as: [tex](4^{3}) ^{5} = 4^{3*5} = 4^{15}[/tex].
But you can simplify it further!
we know that [tex]4 = 2^{2}[/tex], then [tex]4^{15} = (2^{2}) ^{15} = 2^{2*15} = 2^{30}[/tex]
Find the value of the expression given below. 2/3-1/7
Answer:
the answer is 11/21 or 0.523809524
hope this helped
Step-by-step explanation:
What is the probability of getting a vowel (a successes) for the spinner? Compute P(3 successes) for 5 spins of the spinner
Answer:
What is the probability of getting a vowel (a success) for the spinner shown?
✔ 1/3
Suppose you spin the spinner 5 times.
✔ P(3 successes) means “the probability of getting a vowel on exactly 3 of the spins.”
Step-by-step explanation:
edg 2020
Using the binomial distribution, it is found that:
The probability of a success is of 1/3.P(X = 3) = 0.1646.For each spin, there are only two possible outcomes, either it is a vowel, or it is not. The result of a spin is independent of any other spin, hence the binomial distribution is used to solve this question.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem:
The spinner has 3 regions, A, B and C, one of which is a vowel, hence p = 1/3 = 0.3333.There will be 5 spins, hence n = 5.The probability of 3 successes is given by:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{5,3}.(0.3333)^{3}.(0.6667)^{2} = 0.1646[/tex]
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FIRST PERSON TO HELP ME GETS BRANLIEST AND 100 POINTS PLUS 5-STAR RATING OH AND A THANKS
Answer:
D
the answer is D
the graph shows the amount of money Hachi earns at his job in relation to the number of hours he works.
what is Hachi's pay rent in dollars per hour? record your answer and fill in the bubbles on your answer form. Be sure to use the correct place value.
Answer:
(A) - Hachi does not earn any money if he does not work
Step-by-step explanation:
THE FIRST GUY IS WRONG TRUST ME.If you think about it the graphed point is (0,0), so it is self explanatory that he works 0 hours and OBVIOUSLY he wont earn any money if he doesnt work.
The graph shows the amount of money Hachi earns at his job in relation to the number of hours he works. Hachi does not earn any money if he does not work.
What is a function?A function is defined as a relation between the set of inputs having exactly one output each.
We can see that the graph linearly increases as the hour he worked and the money he earned will increase.
we know that the graphed point is (0,0),
He earned 10 money per hour of work.
so it is self-explanatory that he works 0 hours and obviously, he won't earn any money if he doesn't work.
Thus, Hachi does not earn any money if he does not work.
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What is the measure of the major arc?
The answer is D) 210 because arc eog is 150 and is the minor arc. A whole circle is 360 therefore 360-150=210
The measure of the major arc is found by calculating the circumference of the entire circle 2πr and then using the proportion that the angle of the major arc represents out of 360 degrees.
Explanation:The measure of the major arc in a circle depends on the angle subtended by the arc at the center of the circle. If we define the angle Θ (theta) in degrees, that subtend the arc, the length of the major arc can be found by using the circumference of the entire circle, which is 2πr (where r is the radius), and the proportion of the circle that the major arc represents. Since the entire circle is 360 degrees, if the major arc corresponds to an angle Α, which is the complement of Θ (since Α + Θ = 360 degrees for the minor and major arcs together), the major arc length will be 2πr (Α/360). To summarize, if you're given the central angle of the minor arc or can otherwise determine the central angle for the major arc, you can use this proportion to calculate the arc length.
Write an equation with integer solutions of:
x = ±6, y = 0
and
x = 0, y = ±12
A)x2 + y2 + 6 = 0
B)4x2 + y2 + 144 = 0
C)x2 + y2 − 6 = 0
D)4x2 + y2 − 1
The correct answer is:
D. 4x2 + y2 − 1
[tex]|Huntrw6|[/tex]
Answer: Option 'D' is correct.
Step-by-step explanation:
Since we have given that
x = ±6, y = 0
and x = 0 and y = ±12
And we need an equation which has above as an integer solutions.
So, it becomes,
Consider [tex]4x^2+y^2-144=0[/tex]
Put x = 0, we get
[tex]0+y^2=144\\\\y^2=144\\\\y=\sqrt{144}\\\\y=\pm 12[/tex]
Similarly,
Put y = 0,
[tex]4x^2+0=144\\\\4x^2=144\\\\x^2=\dfrac{144}{4}\\\\x^2=36\\\\\x=\pm 6[/tex]
Hence, Option 'D' is correct.
A shop sells T-shirts and shorts for the following prices: T-shirt=£3.25 Shorts=£4.99
A mother buys 3 T-shirts and a pair of shorts for her son. She pays with a £10 and a £5 note. With what coins could she be given change?
£15.00 - £14.76 = £0.24
I hope I help you..
The mother buys 3 T-shirts and a pair of shorts. The possible coins she could receive as change are £1, 50p, 20p, 2p, and 1p.
The cost of 3 T-shirts can be calculated as:
3 T-shirts= 3 x £3.25 = £9.75
The cost of a pair of shorts is £4.99
Therefore, the total cost of 3 T-shirts and a pair of shorts is £9.75 + £4.99 = £14.74
If the mother pays with a £10 note and a £5 note, she could receive coins like £1, 50p, 20p, 2p, and 1p as change.
Given a square with vertices (0,1), (1,0), (0,-1), and (-1,0), what is the perimeter of the square?
Answer:
square root 4
Step-by-step explanation:
if i worked for 7h and 45 min and got paid 93 dollors what is my dollor per hour rate
8 per hour. have a nice day
Find the surface area of the regular hexagonal pyramid. Round your answer to the nearest hundredth
Answer:A i guess i am soooooooooo sorry if i am wrong
Step-by-step explanation:
Answer:
(B) [tex]SA=79.18m^2[/tex]
Step-by-step explanation:
It is given from the figure, the side of the regular hexagonal pyramid is 3 m, slant height is 6.2 m and height is 5.6 m.
The formula for Surface area of the regular hexagonal pyramid is:
[tex]SA=\frac{pl}{2}+B[/tex]
where B is the area of the base, p is the perimeter and l is the slant height.
Now, the perimeter can be found as:
[tex]P=6{\times}3[/tex]
[tex]P=18 m[/tex]
And, the area of the base is:
[tex]B=\frac{3\sqrt{3}s^2}{2}[/tex]
Substituting the value of s in the above formula, we get
[tex]B=\frac{3\sqrt{3}(3)^2}{2}[/tex]
[tex]B=23.382m^2[/tex]
Now, substituting the values of B, and P in the formula of Surface area, we get
[tex]SA=\frac{18{\times}6.2}{2}+23.382[/tex]
[tex]SA=79.18m^2[/tex]
Thus, the Surface area of the regular hexagonal pyramid is [tex]79.18m^2[/tex].
Hence, option B is correct.
Jose left the White House and drove toward the recycling plant at an average speed of 40 km/h. Rob left some time later driving in the same direction at an average speed of 48 kn/h. After driving for five hours Rob caught up with Jose. How long did Jose drive before Rob caught up?
Answer:
6 hours
Step-by-step explanation:
6 Hours is Jose's drive time.
What is the average speed?The overall distance the object covers in a given amount of time is its average speed. A scalar value represents the average speed. It has no direction and is indicated by the magnitude.
Given
D=RT
D=40T
T=D/40 FOR JOSE.
D=48*5 FOR ROB.
D=240 Miles from the white house to the recycling plant.
240=40T
T=240/40
T=6 Hours is Jose's drive time.
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A 50ft. cable is stretched from the top of an antenna to an anchor point on the ground 15 ft. from the base of the antenna. How tall is the antenna? Round the nearest tenth.
Answer:
h = 47.70 ft
The antenna is 47.70 ft tall.
Step-by-step explanation:
The height of the antenna is approximately 47.4ft when calculated using the Pythagorean theorem: √((50ft)^2 - (15ft)^2).
Explanation:The question is asking for the height of the antenna. We can solve this problem by using the Pythagorean theorem, which states that in a right triangle the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Here, the hypotenuse is the length of the cable (50 ft), one side is the distance from the base of the antenna to the anchor point (15 ft) and the other side (which we are trying to find), is the height of the antenna.
According to the Pythagorean theorem, the height of the antenna can be calculated as follows: Height = √(Hypotenuse^2 - Base^2), which translates into Height = √((50ft)^2 - (15ft)^2). When you calculate that you get the height of the antenna as approximately 47.4 feet, rounded to the nearest tenth.
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At your construction job, you're standing on a ladder at ground level. First, you climb down 7 feet to see the basement. Then you climb up 22 feet to see the second floor. Later, you climb down 9 feet. How high above or below the ground are you?
7 feet below the ground
6 feet below the ground
9 feet above the ground
9 feet below the ground
6 feet above the ground
Final answer:
After descending 7 feet, ascending 22 feet, and descending 9 feet, the individual is 6 feet above the ground level.
Explanation:
The question involves a sequence of movements by an individual on a ladder at a construction site. To solve this, let's track each movement relative to the initial position at ground level.
The individual climbs down 7 feet to the basement, so they are now 7 feet below ground.Then they climb up 22 feet which brings them 15 feet above ground level (since they were originally 7 feet below).Finally, climbing down 9 feet from the second floor, they are now 6 feet above the ground level.Therefore, the individual is 6 feet above the ground after these movements.
The equation of a circle is (x + 3)2 + (y – 5)2 = 81. Determine the coordinates of the center of the circle and the length of the radius.
Answer:
The center of the circle is (-3 , 5) and the length of the radius is 9 units
Step-by-step explanation:
* Lets revise the standard form of the equation of the circle
- The center-radius form of the circle equation is in the format
(x – h)² + (y – k)² = r², where the center is the point (h, k) and
the radius is r.
- This form of the equation is helpful, because you can easily find
the center and the radius.
* Now lets solve the problem
- The equation is (x + 3)² + (y - 5)² = 81
- By comparing the two equations
∵ (x – h)² + (y – k)² = r² and (x + 3)² + (y - 5)² = 81
# x - h = x + 3
∴ -h = 3 ⇒ divide both sides by -1
∴ h = -3
# y - k = y - 5
∴ k = 5
# h and k are the coordinates of the center of the circle
∴ The center of the circle is (-3 , 5)
# r² = 81 ⇒ take √ for both sides
∴ r = 9
∴ The length of the radius = 9 units
* The center of the circle is (-3 , 5) and the length of the radius is 9 units
The center of the circle is at (-3, 5), and the radius of the circle is 9, determined by the given equation (x + 3)^2 + (y – 5)^2 = 81.
Explanation:The student is asking about the equation of a circle and how to determine the coordinates of the center and the length of the radius. The given equation is (x + 3)2 + (y – 5)2 = 81. The general form of a circle's equation is (x - h)2 + (y - k)2 = r2, where (h, k) is the center and r is the radius.
To find the center of the circle, we look at the values h and k in the equation, which are the opposites of the constants added to x and y, respectively. Therefore, the center is at (-3, 5). To find the radius of the circle, we take the square root of the number on the right side of the equation. The square root of 81 is 9, so the radius is 9.
Solve the equation for x by graphing
Need Help
The answer should be (B)
Answer:
B. [tex]x\approx 1.25[/tex].
Step-by-step explanation:
We have been given an equation [tex]2^x-4=-4^x+4[/tex]. We are asked to solve our given equation by graphing.
Upon graphing our given equation, we will get our required graph as shown in the attached image.
The solution for our given equation will be point, where graph intersects x-axis.
Upon looking at our given graph, we can see that it intersects x-axis at [tex]x\approx 1.25[/tex]. Therefore, option B is the correct choice.
Simplify 5x/(-3+2x+x^2)
Answer:5x/(x-1)(x+3)
Step-by-step explanation:Factor -3+2x+x^2 by using the AC method hope this helps. Branliest plz
Express 2/5% as a fraction and decimal
fraction=
decimal=
HELP ASAP!
Answer:
Fraction: 1/250
Decimal: 0.004
Step-by-step explanation:
2/5=0.4 0.4%=0.004 0.004=4/1000=2/500=1/250
Estimate the sum 7 1/4 + 2 5/8.
Answer:
10
Step-by-step explanation:
find a9 in the arithmetic sequence with a1 = -2.75 and d = 0.25
Answer:
The ninth term is -0.75.
Step-by-step explanation:
Let's write the actual formula for this arith. seq.
It will have the general form a(n) = a(1) + (n-1)d, where a(1) is the first term, n is the term counter (1, 2, 3, .... ) and d is the common difference.
Here, a(n) = -2.75 + (n - 1)(0.25)
So the ninth term of this sequence is
a(9) = -2.75 + (9 - 1)(0.25
= -2.75 + 8(0.25)
= -2.75 + 2
= -0.75
The ninth term is -0.75.
Answer:
[tex]a_9=-0.75[/tex]
Step-by-step explanation:
The given sequence has the first term, [tex]a_1=-2.75[/tex] and d=0.25
The general formula for an arithmetic sequence is given by;
[tex]a_n=a_1+d(n-1)[/tex]
Since we want to find [tex]a_9[/tex], it means n=9
We substitute the given values into the formula to obtain;
[tex]a_9=-2.75+0.25(9-1)[/tex]
[tex]a_9=-2.75+0.25(8)=-0.75[/tex]
Hence, the 9th term is
[tex]a_9=-0.75[/tex]
If a sample proportion is 0.26 which of the following is most likely the range of possible values that best describes an estimate for the population parameter
Answer: (0.15,0.37)
Step-by-step explanation:
did the quiz
The range of possible values that best describes the estimate for the population parameter is [0.16, 0.38]. Therefore, the correct answer is option D.
Given that, a sample proportion is 0.26.
In statistics, the sample proportion is an estimate for the population parameter. When given a sample proportion, the range of possible values that best describes the estimate for the population parameter is typically the 95% confidence interval for the sample proportion. The 95% confidence interval states that if the same sampling procedure is repeated on many samples, then 95% of the confidence intervals constructed this way will contain the true population parameter.
The 95% confidence interval for a sample proportion is given by [p-1.96√(pq/n), p+ 1.96√(pq/n)], where p is the sample proportion, q is the complement of the sample proportion (q = 1 − p), and n is the sample size.
In this case, the sample proportion given is 0.26, and so p = 0.26, q = 0.74, and the sample size can be assumed to be large (n ≥ 30). Substituting these values into the 95% confidence interval equation yields the range of possible values that best describes the estimate for the population parameter: [0.16, 0.38].
Therefore, the correct answer is option D.
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"Your question is incomplete, probably the complete question/missing part is:"
If a sample proportion is 0.26 which of the following is most likely the range of possible values that best describes an estimate for the population parameter?
A. (0.14, 0.36)
B. (0.17, 0.39)
C. (0.15, 0.37)
D. (0.16, 0.38)
All equilateral triangles are ________ triangles.
10pts this on is easy
Answer:
isosceles
Step-by-step explanation:
Find the volume of a rectangular prism with the following dimensions. Length: 4yd width: 5 ft height: 11ft volume =
Answer:
660 ft³
Step-by-step explanation:
The volume (V) of a rectangular prism is calculated using the formula
V = lbh ( l is length, b is breadth and h is height )
The dimensions must be in the same units, thus we need to change length into feet.
l = 4 × 3 = 12 ft ( 1 yard = 3 feet )
b = 5 ft and h = 11 ft
V = 12 × 5 × 11 = 660 ft³
Final answer:
Convert the length from yards to feet, then calculate the volume by multiplying length, width, and height to get 660 cubic feet.
Explanation:
To find the volume of a rectangular prism, you multiply the length, width, and height together. However, notice that in the problem the lengths are not all in the same units; the length is given in yards and the width and height in feet. First, we need to convert yards to feet so that all dimensions are in the same units, using the conversion factor that 1 yard is equal to 3 feet.
After converting, the length will be:
4 yd = 4 x 3 ft = 12 ft
Then you can calculate the volume:
Volume = length x width x height
= 12 ft x 5 ft x 11 ft
= 660 cubic feet
.
What is the value of x?!
Answer:
5[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Using the sine ratio in the right triangle and the exact value of
sin60° = [tex]\frac{\sqrt{3} }{2}[/tex], then
sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{10}[/tex]
Multiply both sides by 10
10 × sin60° = x
10 ×[tex]\frac{\sqrt{3} }{2}[/tex], hence
x = 5[tex]\sqrt{3}[/tex]
I don't know how to do this practice problem :/
Could someone explain? I was told in class that the answer is yes but don't quite understand why
First of all, we know that Emily travels 3/4 of a mile in 4 minutes and 30 seconds (i.e. 9/2 of a minute). So, her current velocity is
[tex]v = \dfrac{\frac{3}{4}}{\frac{9}{2}} =\dfrac{3}{4}\cdot\dfrac{2}{9} = \dfrac{1}{6}[/tex] of a mile per minute.
At this speed, it takes
[tex]t = \dfrac{s}{v} = \dfrac{3.42}{\frac{1}{6}} = 3.42\cdot 6 = 20.52[/tex]
minutes to travel 3.42 miles.
Since she left at 8.25, she will arrive at about 8.46, so she's on time for school.
Please help. Brainliest to first answer.
I think they are complementary angles but i am not sure
Answer:
They form a linear pair.
Step-by-step explanation:
Because both are not 180 so that marks out the last checkbox and the second. Plus, they both don't add up to 90 so it checks off the first.
In 2011, it was estimated that the number of U.S households which had dogs as pets was 4.33 x 10^7 and the average number of dogs per household was 1.6 based on the infomation, approximately how many dogs were household pets in the US in 2011 in Scientific notation
A. 2.71 x 10^7
B. 3.70 x 10^8
C. 5.33 x 10^8
D. 6.93 X 10^7
The right answer is
D. 6.93 X 10^7
Find the arc length of a partial circle
Answer is...
23.55
See attached photo
Find the missing term. The roots of x2 − ( ) + 34 are 5 ± 3i.
Answer:
the required equation is:
[tex]x^2 -10 +34[/tex]
Step-by-step explanation:
The equation given is:
[tex]x^2 -()+34[/tex]
Comparing it with standard quadratic equation
[tex]a^2 +bx+c[/tex]
a= 1,
b=?
C= 34
We can find the value of b using Vieta's formulas :
That states that if roots x₁ and x₂ are given then,
x₁ + x₂ = -b/a
We are given roots: 5 ± 3i i.e, x₁= 5 + 3i and x₂= 5 - 3i
solving
5 + 3i + 5 - 3i = -b/1
10 = -b
Since the given equation already gives b as -b so, -b= 10 => b=10
Putting value of b in the missing place the required equation will be:
[tex]x^2 -10 +34[/tex]
To find the missing term in a quadratic equation given complex roots, use the properties of conjugate roots to determine the term.
Since the roots are in the form of a complex number, they are conjugates of each other, which helps in finding the missing term.
Given roots: 5 ± 3i
Using the sum and product of roots formula
Sum: (5 + 3i) + (5 - 3i) = 10. Product: (5 + 3i)*(5 - 3i) = 34
Construct the equation: x2 - (10x) + 34 = 0
Combine the like terms to create an equivalent expression: r+(−5r)
Answer:
-4r
Step-by-step explanation:
Since r and -5r both have the same variable, we can combine them
r-5r = -4r
r+(−5r) = -4r
Answer:
Step-by-step explanation:
-4r
Emma is 9 and one fourths Year’s old. How many months old is Emma?
She is 4 years an d3 months old
Answer:
111 months
Step-by-step explanation:
First, look at how many whole years old Emma is. Emma is 9 whole years old. 1 year consists of 12 months. So, multiply 9 [years] by 12 [months] to get 108. The number 108 is how many months are in 9 years. However, Emma is 9 months and 1/4 years old.
To find out how many months 1/4 of a year is, multiply 1/4 [year] by 12 [months] . 12 is the same as 12/1, so multiply the numerators and denominators of 1/4 and 12/1
1 x 12 = 12
4 x 1 = 4
12/4 = 3
Therefore, 1/4 year is 3 months. Now, add 108 months and 3 months to get 111 months. Therefore, Emma is 111 months old.
I hope this helps! :)