The expression that is equivalent to the given expression is 125y⁵.
The given expression is:
[tex]\frac{5y^{3} }{(5y)^{-2} }[/tex]
What are some important power rules applicable to the given problem?Some important power rules applicable to this problem are:
1)[tex](ab)^m=a^mb^m[/tex]
2)[tex]\frac{1}{a^{-n} } =a^n[/tex]
So, [tex]\frac{5y^{3} }{(5y)^{-2} } =\frac{5y^{3} }{5^{-2} y^{-2} }[/tex].....by power rule (1)
[tex]=(\frac{5}{5^{-2} } )(\frac{y^3}{y^{-2} })[/tex]
[tex]=5^3y^5[/tex].....by power rule(2)
[tex]=125y^5[/tex]
Hence, the expression that is equivalent to the given expression is 125y⁵.
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nidarians include all of the following EXCEPT:
A. snails
B. jellyfish
C. sea anemone
Please help with algebra
In how many ways could you choose 3 side dishes from a menu that offers 5 vegetable side dishes
and 3 starches if you want at least one vegetable and one starch?
Using the Fundamental Counting Theorem, it is found that there are 90 ways to choose the three side dishes.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
In this problem:
For the vegetable, there are 5 options, hence [tex]n_1 = 5[/tex].For the starch, there are 3 options, hence [tex]n_2 = 3[/tex].The remaining dish is free, which means that there are 5 + 3 - 2 = 6 options, hence [tex]n_3 = 6[/tex].Then:
N = 5 x 3 x 6 = 90.
There are 90 ways to choose the three side dishes.
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State the quadrant in which lies if secθ > 0
and cscθ < 0.
A) Quadrant I
B) Quadrant II
C) Quadrant III
D) Quadrant IV
Answer:
D
Step-by-step explanation:
secΘ > 0 in 1st and 4th quadrants
cscΘ < 0 in 2nd and 4th quadrants
then
secΘ > 0 and cscΘ < 0 in the 4th quadrant
Jenni is eating a package of gummy bears. There are 4 red, 2 yellow and 3 green gummy bears left. What is the probability that she'll eat two yellows without looking in the bag.
Answer:
1/45
Step-by-step explanation:
Total = 10
Probaility of getting yellow: 2/10
Probbaility of getting yellow again: 1/9
2/10 * 1/9= 2/90 or 1/45
can i have help? (picture included)
Which statement about standard error is false?
O A. It is a measure of the variability of a statistic.
O B. It can be calculated using either the population or sample
standard deviation.
O C. It can be calculated as a
n
O D. It is an estimate of the standard deviation of a sampling
distribution.
Answer:
I'm pretty sure it's C.
Step-by-step explanation:
A segment 150 units long is divided into 3 parts in the ratio 2:3:5. How long is the shortest part?
3x-6y=-12
x-2y=-8
Is it:
Inconsistent
Not enough information
Coincident
Consistent Independent
Answer:
(a) Inconsistent
Step-by-step explanation:
Two linear equations can be compared by putting both of them in standard form. Here, that means removing a common factor from the coefficients of the first equation.
3x -6y = -12 . . . . given first equation
x -2y = -4 . . . . . . divide by 3
Compare this to the second equation:
x -2y = -8
The constants (-4, -8) are different, so there are no values of x and y that can satisfy both equations. The equations are described as inconsistent.
Answer:
InconsistentStep-by-step explanation:
Equation 1
3x - 6y = -12Divide throughout by 3 to simpliest formx - 2y = -4Equation 2
x - 2y = -8On comparison, it is seen that the slopes are same, but the y-intercepts are different.
This means this has no solution, or the graph is inconsistent.
2(4y-9)=14 solve for y
Answer:
y = 4
Step-by-step explanation:
2(4y - 9) = 14
8y - 18 = 14
8y = 32
y = 4
Answer:
y = 4
Step-by-step explanation:
Simplifying
2[4y + -9] = 14
Reorder the terms:
2[-9 + 4y] = 14
[-9 * 2 + 4y * 2] = 14
[-18 + 8y] = 14
Solving
-18 + 8y = 14
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '18' to each side of the equation.
-18 + 18 + 8y = 14 + 18
Combine like terms: -18 + 18 = 0
0 + 8y = 14 + 18
8y = 14 + 18
Combine like terms: 14 + 18 = 32
8y = 32
Divide each side by '8'.
y = 4
This graph plots the number of wins last year and this year for a sample of professional football teams.
Based on the line of best fit, which is the BEST prediction for wins this year for a team that won 4 games last year?
A. 2
B. 4
C. 5
D. 7
Answer:
C.5, Because when you you add the line of best fit on the graph it goes through the 5 point right over 4 wins won last year.
If (x - 3) 2 = 5, then
need help asap pleaseeeee
Answer:
x = 3 ± [tex]\sqrt{5}[/tex]
Step-by-step explanation:
(x - 3)² = 5 ( take square root of both sides )
x - 3 = ± [tex]\sqrt{5}[/tex] ( add 3 to both sides )
x = 3 ± [tex]\sqrt{5}[/tex]
Answer:
×=5.5
Step-by-step explanation:
exact form would be 11/5
and mixed form is 5 1/2
win a brainliest for free by answering questions
Answer: 1.2
Step-by-step explanation:
helpppp please please
Answer:
the answer is 51.315
Step-by-step explanation:
hope i was able to help you out
Which of the following are possible side lengths for a triangle
Answer:
B
Step-by-step explanation:
The two smallest sides of a triangle must be greater than the third, larger one.
A: 6 + 2 > 9
8 > 9
False
B: 5 + 7 > 8
12 > 8
True
C: 2 + 4 > 6
6 > 6
False
I DONT UNDERSTAND Julio bought a backpack for 39$ and 2 belts for 17$ each the sales tax is 6%. How much did Julio spend for all items including tax??
A-$59.64 C-$77.38
B-$63.00 D-$89.01
Answer: C
Steps:
39+17+17=73
73x0.06=4.38
4.38+73=77.38
Add the sales tax to price without tax
Answer:
C. $77.38
Step-by-step explanation:
Items + tax = total
Items × .06 = tax
OR
Items × 1.06 = total
39 + 17 + 17 = 73
73 × .06 = 4.38
73 + 4.38 = 77.38
OR
73 × 1.06 = 77.38
Use x = 2 to identify the value of each expression.
Exponent Value of expression
25
32
82
16
64
Answer:
25/2 = 12.5 32/2= 16 82/2= 41 16/2=8 64/2= 32
Step-by-step explanation:
If corect please give branlieist
Region R is bounded by the curves y = 4x^2 and y = 4. A solid has base R, and cross sections perpendicular to the y-axis are semicircles with the diameter lying in R. The volume of this solid is
A. pi/4
B. pi/2
C. pi
D. 2pi
Each cross section has a diameter equal the horizontal distance between the two "halves" of the parabola. We have
y = 4x² ⇒ x = ±√y/2
so the diameter for some given y would be √y/2 - (-√y/2) = √y.
The volume of a cross section with thickness ∆y is then
π/2 (√y/2)² ∆y = π/8 y ∆y
The total volume of the solid would then be
[tex]\displaystyle \int_0^4 \frac\pi8 y \, dy = \frac\pi8 \times \frac12 y^2 \bigg|_{y=0}^{y=4} = \boxed{\pi}[/tex]
Four racers are racing on a track.
Raheem covers 26% of the track, Lila covers 38 of the track, Khalid covers 0. 3 of the track, and Juanita covers 0. 24 of the track.
List the people in order by the distance on the track each person covers from least to greatest
answer this for 25 points and brainliest
Answer:
B
Step-by-step explanation:
For percentage, you take the percent symbol and move it two spaces to the left and make it a decimal, hence the .32 and then you multiply it by the integer you want to find the percent of, 130.
Answer:
0.32 x 130
Step-by-step explanation:
A percentage is out of 100;
32% = 32/100
32/100 = 0.32
32% of 130 is a multiplication problem (of : multiplication).
0.32 x 130 = 41.6
What is the measure of ∠E, rounded to the nearest degree?
28°
36°
54°
80°
Answer:
```30.
<30`
<98
<`36ok this is your answer....
Christopher determines the system of s(x) and t(x) has only one solution.Which system is Christopher solving?
Christopher is solving a system of equations that has one solution and can be seen in Option C.
What is a system of equations?A system of equations is more than one equation that can be solved together to get a unique solution. In this situation, the power of the equation must be in one degree.
A quadratic equation is an algebraic equation whose power is raised to the second degree.
However, if their power is not in one degree, they are regarded as a quadratic equation and it usually produces two solutions.
From the given options, we can see that only option c is not a quadratic equation, Hence, it is the right answer.
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Hello, I need help with sample dpace
Answer:1/2 problability for both odd and same for evens.1/8 chance of spinning a 3 .25% chance of a 4 or 6.one eight of a chance of spinning a 7 or 1.part 2. a is false because the chance of spinning and odd is 50% and their is 3 numbers less than 4 .4 numbers would be a 50% chance to buts its not.b is true because he has a chance of spinning any number i think.c is true because there are 4 odd numers and 2 and 4 is half of 4
Step-by-step explanation:
Triangle DEF contains right angle E. If angle D measures 50° and its opposite side measures 7.6 units, what is the measure of side DE? Round your answer to the nearest hundredth. 4.89 units 5.34 units 6.38 units 9.06 units
Answer:
It is 6.38 units!
Step-by-step explanation:
I took the test and it was correct.
The measure of the side length DE is 6.38 units after applying the tan ratio in the right-angle triangle option (C) 6.38 units is correct.
What is a right-angle triangle?It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
We have a right-angle triangle given:
Triangle DEF contains right angle E. If angle D measures 50° and its opposite side measures 7.6 units,
After drawing the triangle:
Applying the tan ratio in the right-angle triangle:
tan50 = EF/DE
tan50 = 7.6/DE
DE = 7.6/tan50
DE = 6.377 ≈ 6.38 units
Thus, the measure of the side length DE is 6.38 units after applying the tan ratio in the right-angle triangle option (C) 6.38 units is correct.
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The resting heart rate for a pig is about 100 beats per
minute.
A pig's resting heart rate is about 75 beats per minute
higher than an elephant's resting heart rate.
What is an elephants resting heart rate? Choose the correct equation and
answer.
O A. X+75 = 100
x = 25 beats per minute
O B. X+175 = 100
x= 75 beats per minute
O C. x+100 = 75
x = 175 beats per minute
O D. x+75 = 100
x= 175 beats per minute
Answer:
a
Step-by-step explanation:
pigs are 75 bpm more than elephants
so elephants are x + 75
and pigs are 100 bpm
so this means your answer is a
I need help in this problem
Answer:
Step-by-step explanation:
4x + 9y = 5
-4x + 7y = 11
Isolate y for 4x + 9y = 5
9y = 5-4x
y = (5-4x) / 9
Now plug it in this equation: -4x + 7y = 11
-4x + 7[(5-4x)/9] = 11
now just solve it.
-4x + (35 - 28x / 9) = 11
multiply both sides by 9
-36x + 35 - 28x = 99
-64x = 64
divide both sides by -64
x = 1
Solve this quadratic equation using the quadratic formula.
2x 2 - 2x = 1
[tex]x_{1} = \frac{1+\sqrt{3}}{2}[/tex] or [tex]x_{1} = \frac{1-\sqrt{3}}{2}[/tex]
The point (-1,4)is translated five units right and three units down.which rule describes the translation
Answer:
(x, y ) → (x + 5, y - 3 )
Step-by-step explanation:
5 units right means add 5 to the x- coordinate
3 units down means subtract 3 from the y- coordinate
the translation rule is
(x, y ) → (x + 5, y - 3 )
find x and y intercepts y=(2x+10)(x-2)
Step-by-step explanation:
[tex]y = (2x + 10)(x - 2)[/tex]
[tex]y = 2x(x - 2) + 10(x - 2)[/tex]
[tex]y = 2x ^{2} - 4x + 10x - 20[/tex]
[tex]y = 2x ^{2} + 6x - 20[/tex]
[tex]to \: find \: x \: intercept \: y = 0[/tex]
[tex]0 = 2x ^{2} + 6x - 20[/tex]
[tex]x = 2 \: or \: - 5[/tex]
[tex]to \: find \: y \: intercept \: x = 0[/tex]
[tex]y = 2(0)^{2} + 6(0) - 20[/tex]
[tex]y = - 20[/tex]
Answer:
y = -20
x- 2, -5
Step-by-step explanation:
Estimate the perimeter and the area of the shaded figure.
A shaded composite figure is shown on a grid. The figure is made up of an isosceles triangle and an isosceles trapezoid. The triangle has a base of 6 units and height of 3 units. The trapezoid has a shorter base of 4 units, longer base of 6 units, and height of 3 units. The longer base of the trapezoid is aligned with the base of the triangle.
perimeter: about
units
area: about
square units
The shapes in the composite figures are a triangle and a trapezoid
The area of the figure is about 24 square units
The area of the figureThe dimensions of the figure are given as:
Triangle
Base = 6 unitsHeight = 3 unitsTrapezoid
Shorter base = 4 unitsLonger base = 6 unitsHeight = 3 unitsThe longer base of the trapezoid and the base of the triangle are aligned.
So, the area is:
Area = Area of triangle + Area of trapezoid
This gives
Area = 0.5 * base * height + 0.5 * (sum of bases) * height
So, we have:
Area = 0.5 * 6 * 3 + 0.5 * (4 + 6) * 3
Evaluate
Area = 24
The figure is needed to determine the perimeter
Hence, the area of the figure is about 24 square units
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Answer:
47.3
Step-by-step explanation:
yes
i forgot how to do this
help
Answer:
62.8 inStep-by-step explanation:
C=2πr
r=10in
C=2*π*10
C=20*3.14
62.8 in
If you flip, slide, and then spin the preimage of a shape in the coordinate plane, what sequence of transformations have you performed?
A. reflection, rotation, rotation
B. reflection, translation, reflection
C. reflection, translation, translation
D. reflection, translation, rotation
Answer:
D
-by-step explanation:
all other is incorrect