Select the equivalent expression.
(3^4 / 7^3)^3 =?
Answers
The equivalent expression is (3⁴/7³)³ = 3¹²/7⁹
Define Power Rule for Exponents
The Power Rule for Exponents: (aⁿ)ˣ= aⁿ*ˣ .
To raise a number with an exponent to a power, multiply the exponent times the power.
Negative Exponent Rule: x⁻ⁿ = 1/xⁿ.
Given expression is,
(3⁴/7³)³
We need to find equivalent expression,
⇒ (3⁴/7³)³
first, split up exponent 3 to both Numerator and denominator as ,
⇒ (3⁴)³ / (7³)³
Now, power of a power can be done as product as,
⇒ 3¹² / 7⁹
Hence,the equivalent expression is (3⁴/7³)³ = 3¹²/7⁹
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Related Questions
What is the x coordinate of the inflection point for the graph of h(x) = 5x³ + 8x² – 3x + 7? (Do not include "x=" in your answer.)
Answers
the x-coordinate of the inflection point for the graph of h(x) = 5x³ + 8x² – 3x + 7 is -4/15.
To find the x-coordinate of the inflection point for the graph of h(x) = 5x³ + 8x² – 3x + 7, we need to determine where the concavity changes.
The concavity changes when the second derivative of h(x) changes sign. Let's first find the second derivative of h(x):
h'(x) = 30x² + 16x - 3 (first derivative of h(x))
h''(x) = 60x + 16 (second derivative of h(x))
To find the x-coordinate of the inflection point, we set h''(x) = 0 and solve for x:
60x + 16 = 0
60x = -16
x = -16/60
x = -4/15
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Find a plane through the point (−1,8,6) and orthogonal to the line:
x(t)=−8+8t
y(t)=−1+7t
z(t)=−2−6t
Answers
A line is orthogonal to a plane if and only if it is parallel to a normal vector of the plane.
Therefore, the direction vector of the line should be perpendicular to the normal vector of the plane.
To find the normal vector of the plane, we need two more points on the plane, but we don't have them.
However, we can use the point given to get an equation for the plane and then find the normal vector of the plane using that equation.
Let's assume the equation of the plane is Ax + By + Cz = D, then by using the point (-1, 8, 6) on the plane, we have:-
A + 8B + 6C = D
We also know that the plane is perpendicular to the line, which means that the direction vector of the line is orthogonal to the normal vector of the plane.
Therefore, -8A + 7B - 6C = 0 or 8A - 7B + 6C = 0
We have two equations with three variables.
We can set A=1, and then solve for B and C in terms of
D:8B + 6C = D + 1 ------ (1)
-7B + 6C = D - 8 ------- (2)
Adding equation (1) and (2), we get:
B = D - 7
Then, substituting back into equation (1),
we get:
6C - 8(D - 7) = D + 16C - 8D + 56 = D + 16C = D - 56
Finally,
substituting B = D - 7 and C = (D-56)/6 into the equation of the plane we get:
A x - (D-7)y + (D-56)z = D
or
A x - (D-7)y + (D-56)z - D = 0
Therefore, the normal vector of the plane is
N = [A, -(D-7), (D-56)].
Since the plane contains the point (-1, 8, 6), we have:-
A + 8(D-7) + 6(D-56) = D
or
-7A + 50D = 334
Equations of a plane passing through the point (-1, 8, 6) and orthogonal to the line are as follows:
A x - (D-7)y + (D-56)z = D
or
A x - y + z - 63 = 0.
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Callie has 3,264 beads. She wants to divide the beads evenly to make 32 necklaces. How many beads will be
used for each necklace?
Answers
Answer:
102 beads will be used for each necklace.
Step-by-step explanation:
3,264/32=102
2. pvalue
3.critical value
4.test value
5.make a desision
Noise Levels in Hospitals In a hospital study, it was found that the standard deviation of the sound levels from 30 areas designated as "casualty doors" was 6.4 dBA and the standard deviation of 28 areas designated as operating theaters was 4.1 dBA. At a 0.10, can you substantiate the claim that there is a difference in the standard deviations? Use a, for the standard deviation of the sound levels from areas designated as "casualty doors." Part 1 of 5 (a) State the hypotheses and identify the claim. H_0: sigma_1^ = sigma_2^ _____
H_1: sigma_1^ ≠ sigma_2^ _____
This hypothesis test is a___test.
Answers
The hypotheses for the test are H₀: σ₁² = σ₂² and H₁: σ₁² ≠ σ₂². This is a two-tailed test to assess if there is a difference in the standard deviations of sound levels between the areas designated as "casualty doors" and operating theaters. The claim being investigated is whether or not there is a difference in the standard deviations.
The hypotheses for the test are:
H₀: σ₁² = σ₂² (There is no difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)
H₁: σ₁² ≠ σ₂² (There is a difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)
This hypothesis test is a two-tailed test because the alternative hypothesis is not specifying a direction of difference.
To substantiate the claim that there is a difference in the standard deviations, we will conduct a two-sample F-test at a significance level of 0.10, comparing the variances of the two groups.
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The number of loaves of bread purchased and the total cost of the bread in dollars can be modeled by the equation c = 3.5b. Which table of values matches the equation and includes only viable solutions?
A 2-column table with 4 rows. The first column is labeled loaves (b) with entries negative 2, 0, 2, 4. The second column is labeled cost (c) with entries negative 7, 0, 7, 14.
A 2-column table with 4 rows. The first column is labeled loaves (b) with entries 0, 0.5, 1, 1.5. The second column is labeled cost (c) with entries 0, 1.75, 3.5, 5.25.
A 2-column table with 4 rows. The first column is labeled loaves (b) with entries 0, 3, 6, 9. The second column is labeled cost (c) with entries 0, 10.5, 21, 31.5.
Answers
The table for the function c{b} is -
{b} : 1 2 3 4
c{b} : 3.5 7.0 10.5 14
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that the number of loaves of bread purchased and the total cost of the bread in dollars can be modeled by the equation c = 3.5b.
We can write the table for the function c{b} as -
b c{b}
1 3.5
2 7.0
3 10.5
4 14
Therefore, the table for the function c{b} is -
{b} : 1 2 3 4
c{b} : 3.5 7.0 10.5 14
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Automatic Transmissions, Inc., has the following estimates for its new gear assembly project: price = $940 per unit; variable cost = $340 per unit; fixed costs = $3.4 million; quantity = 53,000 units. Suppose the company believes all of its estimates are accurate only to within ±15 percent. What values should the company use for the four variables given here when it performs its best-case scenario analysis? What about the worst-case scenario?
Answers
In the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units.
In the best-case scenario analysis for Automatic Transmissions, Inc.'s new gear assembly project, the company assumes the upper limit of the ±15 percent range for its estimates. For the price per unit, they take a 15 percent increase, resulting in a value of $1081. Similarly, the variable cost per unit is increased by 15 percent to $391. The fixed costs are also adjusted upwards by 15 percent, reaching $3.91 million. Finally, the quantity is decreased by 15 percent, leading to a value of 45,050 units.
On the other hand, in the worst-case scenario analysis, the company assumes the lower limit of the ±15 percent range for its estimates. The price per unit is decreased by 15 percent, resulting in $799. The variable cost per unit is decreased to $289. The fixed costs are adjusted downwards to $2.89 million. Lastly, the quantity is increased by 15 percent to 60,950 units.
Therefore, in the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units
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6. Find the missing angle.
Answers
Step-by-step explanation:
one triangle has total 180°. so, 180° - 45° - 30° = 105°
Answer : 105°
PLS HELP ME!!! which matrix represents the system of equations below {8x-9y+13z=11
{-8x-5y+5z=15
{3x+4y-8z=-10
Answers
Answer:
The answer is below
Step-by-step explanation:
The system of equations:
8x-9y+13z=11
-8x-5y+5z=15
3x+4y-8z=-10
The equations can be represented in matrix form as:
AX = B
X = A⁻¹B
Therefore:
\(\left[\begin{array}{ccc}8&-9&13\\-8&-5&5\\3&4&-8\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{c}11\\15\\-10\end{array}\right]\\\\\\\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{ccc}8&-9&13\\-8&-5&5\\3&4&-8\end{array}\right] ^{-1}\left[\begin{array}{c}11\\15\\-10\end{array}\right]\\\)
\(\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{ccc}\frac{1}{19} &-\frac{1}{19}&\frac{1}{19}\\-\frac{49}{380}&-\frac{103}{380}&-\frac{36}{95} \\-\frac{17}{380}&-\frac{69}{380}&-\frac{28}{95} \end{array}\right] \left[\begin{array}{c}11\\15\\-10\end{array}\right]\\\\\\\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{c}-0.74\\-1.69\\0.13\end{array}\right] \\\)
√3 is a polynomial of degree ________.
Answers
Step-by-step explanation:
Therefore, the degree of polynomial √3 is zero.
\(\sf\huge\underline\color{pink}{༄Answer:}\)
\(\tt{\sqrt{3}}\) is a polynomial of degree 0
\(\sf\huge\underline\color{pinl}{༄Note:}\)
The expression is constant, which means it can be rewritten with a factor of x^0. The degree is the largest exponent on the variable.\(\color{pink}{==========================}\)
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What is the solution to the following equation? -32-8x=-7x+8(8x-4)
Answers
the answer to your question is x=0
X=0
−32−8x=−7x+8(8x−4)
−8x−32=−7x+8(8x−4)
−8x−32=−7x+64x−32
−8x−32=57−32
−8−32+32=57−32+32
−8=57
Find the value of x, y, and z in the rhombus
below.
(-x+6)°
(5z+1)°
(2y-5)°
79°
Answers
Answer:
Step-by-step explanation:
value of x is 9 y is 3.4 z is 6.78
Which number is a rational number, but not an integer
A. -10/2
B. 36/4
C. -11/2
D. 3
Answers
Answer: the answer the D. 3
hi who know how to do this question?can someone help me solve
Answers
Answer:
Below
Step-by-step explanation:
f(1) - 2 = a(1) + b
- 2 = a + b (1)
f(5) 10 = a (5) + b
10 = 5a + b (2)
Multiply first underlined equation by -5 to get
10 = -5a - 5b add this to the second equation (this will eliminate 'a')
20 = - 4 b so b = -5
then the first equation becomes - 2 = a + (-5)
which shows a = 3
so your function is just f(x) = 3x -5
what is the perimeter of a rectangle with a length of (x^2+x) and a width of (2x^2+3x)
Answers
Answer:
Perimeter = 6x² + 8x
Step-by-step explanation:
Perimeter = 2(length + width)
perimeter = 2((x²+x)+(2x²+3x))
perimeter = 2(x²+2x² + x+3x)
perimeter = 2(3x² + 4x)
perimeter = 2*3x² + 2*4x
perimeter = 6x² + 8x
1. Find the value of x in the parallelogram.
Ox=37
Ox=53
Ox = 127
Ox = 307
xº
53°
Answers
Answer:
its 53 they equal the same length if you looking of the answer with a x then maybe its 0x=53
hope this works
A tabletop in the shape of a trapezoid has an area of 5,700 square centimeters. its longer base measures 135 centimeters, and the shorter base is 105 centimeters. what is the height? the height of the tabletop is centimeters.
Answers
Answer:
47.5 cm
Step-by-step explanation:
You want the height of a trapezoid with bases of lengths 135 cm and 105 cm, and an area of 5700 cm².
AreaThe formula for the area of a trapezoid is ...
A = 1/2(b1 +b2)h
Filling in the given values, we have ...
5700 = 1/2(135 +105)h
5700 = 120h
h = 5700/120 = 47.5
The height of the tabletop is 47.5 cm.
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Which of the following correctly names an angle of the triangle below? A. AB B. AABC C. C D. B
Answers
Answer:
Based on the information provided, none of the given options correctly names an angle of the triangle. The options provided do not correspond to the standard way of naming angles in a triangle.
In triangle ABC, the angles are typically named using capital letters at the vertices of the triangle. For example:
Angle A refers to the angle formed at vertex A.
Angle B refers to the angle formed at vertex B.
Angle C refers to the angle formed at vertex C.
Therefore, none of the given options (A, AABC, C, B) correctly name an angle of the triangle.
Step-by-step explanation:
Based on the information provided, none of the given options correctly names an angle of the triangle. The options provided do not correspond to the standard way of naming angles in a triangle.
In triangle ABC, the angles are typically named using capital letters at the vertices of the triangle. For example:
Angle A refers to the angle formed at vertex A.
Angle B refers to the angle formed at vertex B.
Angle C refers to the angle formed at vertex C.
Therefore, none of the given options (A, AABC, C, B) correctly name an angle of the triangle.
The baker made a batch of chocolate chip, oatmeal raisin, and sugar cookies. if p(chocolate chip) = 18%, interpret the likelihood of randomly selecting a chocolate chip cookie from the batch. a. likely b. unlikely c. equally likely and unlikely d. this value is not possible to represent probability of a chance event.
Answers
Answer: Either Likely or This value is not possible to represent probability of a chance event.
Step-by-step explanation:
So, if P = Chocolate Chip cookies, it is 68%, its more then a 50/50 percentage so most kids would **probably** choose Chocolate Chip cookies so it could be likely.
Hope this helps!
Determine if segments JK and LM are parallel, perpendicular, or neither.
J(-10, -7) K(-4, 1) L(-1, 1) M(-6, -2)
Answers
Answer:
perpendicular
Step-by-step explanation:
the lines meet together
the art teacher is sending home a total of 3,150 projects before winter break if each of her 150 students had the same number of projects how many did each student do?
Answers
Answer:
21 projects each
Step-by-step explanation:
3150 ÷150
7. Drag the fractions in order from least to greatest value.7/4, 4/8, 7/8, 3/4
Answers
7/4 can be expressed as
\(\frac{7}{4}=\frac{7}{4}\cdot\frac{2}{2}=\frac{7\cdot2}{4\cdot2}=\frac{14}{8}\)3/4 can be expressed as
\(\frac{3}{4}=\frac{3}{4}\cdot\frac{2}{2}=\frac{3\cdot2}{4\cdot2}=\frac{6}{8}\)Then, the fractions to compare are:
14/8, 4/8, 7/8, 6/8
We can order them only considering the numerators. from least to greatest value the ordered list is:
4/8, 6/8, 7/8, 14/8
or
4/8, 3/4, 7/8, 7/4
Select all of the answers that apply. Z-scores are useful because ________________________. Group of answer choices the standard deviation is a natural ruler for comparing values to the mean ZZZZZzzzzzzzzzzz WAKE UP you're almost done. they are applicable to both symmetric and skewed distributions it is a standardized way of saying how unusual an observation is
Answers
The correct answers are: 1. Z-scores are useful because they provide a standardized way of indicating how unusual an observation is. 2. The standard deviation is a natural ruler for comparing values to the mean. 3. Z-scores and the standard deviation are applicable to both symmetric and skewed distributions.
These answers accurately describe the benefits of using Z-scores and the standard deviation in statistical analysis. Z-scores allow us to determine how many standard deviations away from the mean a particular observation is, providing a measure of how unusual or extreme that observation is compared to the rest of the data set.
The standard deviation serves as a measure of dispersion, representing the average amount by which data points vary from the mean. It provides a useful reference point for comparing individual values to the mean. Additionally, both Z-scores and the standard deviation can be applied to distributions with varying shapes, including both symmetric and skewed distributions.
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Select all of the answers that apply. Z-scores are useful because it is a standardized way of saying how unusual an observation is ZZZZZzzzzzzzzzzz <snore snore> WAKE UP you're almost done. the standard deviation is a natural ruler for comparing values to the mean they are applicable to both symmetric and skewed distributions.
The price of a skirt was increased from $40 to $64. By what percentage was the price of the skirt
Increased?
Answers
Answer: 11 percent
Step-by-step explanation:
Answer:
24%
Step-by-step explanation:
After school Andy spends 15 minutes on science homework 20 minutes on math homework 15 minutes on literature homework what was the ratio of the number of minutes she spends on on math homework to the total she spends on homework each night
Answers
The ratio of the number of minutes she spends on on math homework to the total she spends on homework each night is 2:5.
What is ratio?
When b does not equal 0, an ordered pair of numbers a and b, represented as a / b, is said to be a ratio. Two ratios are set to be equal in an equation called a proportion. You might express the ratio as 1: 3 for instance, if there is 1 boy and 3 girls (for every one boy there are 3 girls)
Here Andy spends 15 minutes on science homework 20 minutes on math homework 15 minutes on literature homework then,
Total time is ,
Science home work time+ Math home work time+ Literature home work time
=> 15+20+15 = 50 mins.
Now the ratio to the number of minutes she spends on on math homework to the total she spends on homework each night then
=> 20 : 50
=> 2 : 5.
Hence the ratio of the number of minutes she spends on on math homework to the total she spends on homework each night is 2:5.
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A publisher reports that 54T% of their readers own a laptop. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 110110 found that 50P% of the readers owned a laptop. Is there sufficient evidence at the 0.100.10 level to support the executive's claim
Answers
There is not sufficient evidence at the 0.10 level to support the marketing executive's claim that the percentage of readers owning a laptop is different from the reported percentage of 54T%.
To test whether the sample proportion of 50P% is significantly different from the reported proportion of 54T%, we can use a one-sample z-test.
The null hypothesis is that the true proportion is equal to 54T%, and the alternative hypothesis is that the true proportion is different from 54T%.
The test statistic is calculated as:
z = (p - p₀) / √(p₀(1-p₀)/n)
where p is the sample proportion, p₀ is the hypothesized proportion, and n is the sample size.
Plugging in the values, we get:
z = (0.50 - 0.54) / √(0.54(1-0.54)/110) ≈ -1.38
The critical value for a two-tailed test at the 0.10 level with a sample size of 110 is ±1.645. Since the calculated test statistic (-1.38) does not exceed the critical value (-1.645), we fail to reject the null hypothesis.
Therefore, there is not sufficient evidence at the 0.10 level to support the marketing executive's claim that the percentage of readers owning a laptop is different from the reported percentage of 54T%.
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Isaaq put 2b + 3 dollars in the bank in the first week. The following week he doubled the first week’s savings and put that amount in the bank. The next week he doubled what was in the bank and put that amount in the bank. If he now has $477 in the bank, how much did he put in the bank the first week? Please add an numerical explanation
Answers
Answer:
The answer is $159
Step-by-step explanation:
2b + 3 - Day 1
4b + 6 - Day 2
6b + 9 - Day 3
477=6b+9
-9 -9
468=6b
78=b
(2x78) + 3 = 159
The answer is $159
How long is the diagonal of a 9inch by 40 inch rectangle
Answers
Answer:
The Answer is 360
Step-by-step explanation:
cause u got to multiple
Answer:
around 29.7
Step-by-step explanation:
We can make a rectangle two tringles
Using a^2 + b^2 = c^2 we can find the diagonal
40^2 + 9^2 = c^2
800 + 81 = c^2
sqrt 881 is 29.6816442
we can round this to around 29.7
I NEED HELP ON THIS ASAp!
Answers
A graph of each inequality is shown in the grid below.
A shape which the solution region represent is a rectangle.
How to graph the solution to this system of inequalities?In order to to graph the solution to the given system of inequalities on a coordinate plane, we would use an online graphing calculator to plot the given system of inequalities and then take note of the point of intersection;
0.4r ≤ 120 .....equation 1.
r ≥ 4(360/5) .....equation 2.
By evaluating the given system of inequalities, we have;
r ≤ 120/0.4
r ≤ 300
r ≥ 4(360/5)
r ≥ 4(72)
r ≥ 288
By combining the system of inequalities, we have:
288 ≤ r ≤ 300
Based on the graph (see attachment), we can logically deduce that the solution to the given system of inequalities is the shaded region between the solid line, and the point of intersection of the lines on the graph representing each.
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Colin buys a tv for £800.
It depreciates at a rate of 1% per year.
How much will it be worth in 2 years?
Give your answer to the nearest penny where appropriate.
Answers
explanation: 1% of 800 = 8
in 2 years it will be 2%
2% = 16
800-16=784
Find the value of x and EF. A and B are midpoints.
Answers
Answer:
x = 5.5
EF = 14
Step-by-step explanation:
We can use ratios to solve
AG 7
----------- = -----------------
EG 2x+3
We know that EG is 2 times AG since A is the midpoint
AG 7
----------- = -----------------
2 AG 2x+3
Canceling like terms
1 7
----------- = -----------------
2 2x+3
Using cross products
1 (2x+3) = 2*7
2x+3 = 14
Subtract 3 from each side
2x+3-3 = 14-3
2x =11
Divide by 2
x = 11/2
x = 5.5
EF = 2x+3 = 2*5.5+3 = 14