When raising a power inside parentheses to another power, multiply the numbers:
(6^4)^2 = 6^(4x2) = 6^8
Simplified = 6^8
6^8 = 1679616
Answer:
[tex] \boxed{ \purple{ {6}^{8} }}[/tex]Step-by-step explanation:
[tex] \mathsf{ ( { {6}^{4}) }^{2} }[/tex]
It is the example of Power to power law of indices.
Multiply the exponents
⇒[tex] \mathsf{ {6}^{4 \times 2} }[/tex]
Multiply the numbers
⇒[tex] \mathsf{ {6}^{8} }[/tex]
-------------------------------------------------------
[tex] \mathsf{\orange{ \underline{ power \: to \: power \: law \: of \: indices}}}[/tex]
If [tex] \mathsf{ ({x}^{a} )^{b}} [/tex] is an algebraic term then [tex] \mathsf{( {x}^{a} ) ^{b} = {x}^{a \times b} }[/tex]
i.e When an algebraic term in the index form is raised to another index , the base is raised to the power of two indices.
Hope I helped!
Best regards!!
All human blood can be "ABO-typed" as O, A, B, or AB, but the distribution of the types varies a bit among groups of people. Here are the distributions of blood types for a randomly chosen person in China and in the United States:The probability O A B ABChinese 0.35 0.27 0.26 0.12American 0.45 0.4 0.11 0.04Suppose we randomly select an American and a Chinese, independently of each other, apply multiplication and addition probability rules, compute:a. Pr(They both have type O)b. Pr( they both have the same blood type)c. Pr( at least one person has type O)
Answer:
a. Pr(They both have type O)
= Pr(They both have type O)
= 0.35 x 0.45
= 0.1575 = 15.75%
b. Pr( they both have the same blood type)
= Pr( they both have the same blood type)
= 2/8
= 0.25 = 25%
c. Pr( at least one person has type O)
= Pr (at least one person has type O)
= 1 - 0.3575
= 0.6425 = 64.25%
Step-by-step explanation:
a) Data:
O A B AB
Chinese 0.35 0.27 0.26 0.12
American 0.45 0.4 0.11 0.04
b) Calculations:
i. Pr(They both have type O)
= Probability of Chinese with O multiplied by Probability of American with O
= 0.35 * 0.45
= 0.1575 = 15.75%
ii. Pr( they both have the same blood type)
= Probability of two out of 8 outcomes
= 2/8
= 0.25 = 25%
iii. Pr( at least one person has type O)
= Probability of (1 – p(none) )
The probability of none = p(none O blood type)
= p(none)
for Chinese = (0.27 + 0.26 + 0.12) * for American ( 0.4 + 0.11 + 0.04)
= 0.65 * 0.55 = 0.3575
Pr (at least one person has type O) = 1 - 0.3575
= 0.6425
The function g(x) = x2 is transformed to obtain function h:
h(x) = g(x) – 5.
Which statement describes how the graph of his different from the graph of g?
A.
The graph of h is the graph of g horizontally shifted right 5 units.
B.
The graph of h is the graph of g vertically shifted up 5 units.
C.
The graph of h is the graph of g vertically shifted down 5 units.
OD.
The graph of h is the graph of ghorizontally shifted left 5 units.
Answer:
Option C
The graph of g is vertically shifted 5 units down
The diameter of a large lawn ornament in the shape of a sphere is 16 inches. What is the approximate volume of the ornament? Use 3.14 for Pi. Round to the nearest tenth of a cubic inch. Recall the formula V = four-thirds pi r cubed.
Answer:
Sphere Volume = 4/3 * PI * radius^3
Sphere Volume = 4/3 * PI * 8^3
Sphere Volume = 4/3 * PI * 512
Sphere Volume = 2,144.7 cubic inches
Step-by-step explanation:
if given the diameter how can you find the radius
Answer:
Divide the diameter by 2.
Step-by-step explanation:
The radius of any circle is always the end to the center.
The diameter is a point of the circle to the opposite side.
This means that the diameter is twice the size of the radius, so to find the radius from the diameter, divide the diameter by 2.
Hope this helped!
Answer:
Divide the diameter by 2. d/2=r
Step-by-step explanation:
If a diameter has been given instead of a radius, you can find the radius by dividing the diameter by 2, for example.
If the diameter was 10, the radius would 10/2=5.
According the the U.S. Department of Education, full-time graduate students receive an average salary of $15,000 with a standard deviation of $1,200. The dean of graduate studies at a large state university in PA claims that his graduate students earn more than this. He surveys 100 randomly selected students and finds their average salary is $16,000. Use a significance level of 0.05 to test if there is evidence that the dean's claim is correct. What are the hypotheses
Answer:
Step-by-step explanation:
Given that :
population Mean = 15000
standard deviation= 1200
sample size n = 100
sample mean = 16000
The null and the alternative hypothesis can be computed as follows:
[tex]\mathtt{H_o : \mu = 15000 }\\ \\ \mathtt{H_1 : \mu > 15000}[/tex]
Using the standard normal z statistics
[tex]z = \dfrac{\overline X - \mu}{\dfrac{\sigma }{\sqrt{n}}}[/tex]
[tex]z = \dfrac{16000 -15000}{\dfrac{1200 }{\sqrt{100}}}[/tex]
[tex]z = \dfrac{1000}{\dfrac{1200 }{10}}[/tex]
[tex]z = \dfrac{1000\times 10}{1200}[/tex]
z = 8.333
degree of freedom = n - 1 = 100 - 1 = 99
level of significance ∝ = 0.05
P - value from the z score = 0.00003
Decision Rule: since the p value is lesser than the level of significance, we reject the null hypothesis
Conclusion: There is sufficient evidence that the Dean claim for his graduate students earn more than average salary of $15,000
Dean's Claim of Average Salary = 16000, ie greater than 15000 : is correct
Null Hypothesis [ H0 ] : Average Salary = 15000
Alternate Hypothesis [ H1 ] : Average Salary > 15000
Hypothesis is tested using t statistic.
t = ( x - u ) / ( s / √ n ) ; where -
x = sample mean , u = population mean , s = standard deviation, n = sample size
t = ( 16000 - 15000 ) / ( 1200 / √100 )
= 1000 / 120
t {Calculated} = 8.33,
Degrees of Freedom = n - 1 = 100 = 1 = 99
Tabulated t 0.05 (one tail) , at degrees of freedom 99 = 1.664
As Calculated t value 8.33 > Tabulated t value 1.664 , So we reject the Null Hypothesis in favour of Alternate Hypothesis.
So, conclusion : Average Salary > 15000
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Question (2)
ASAP Please help.
Construct the "Square root spiral". Take a large sheet of paper and construct the "Square root spiral" in the following fashion.
Start with a point O and draw a line segment [tex]\rm{P_{1} P_{2}}[/tex] perpendicular to [tex]\rm{OP_{1}}[/tex] of unit length. Now draw a line segment [tex]\rm{P_{2} P_{3}}[/tex] perpendicular to [tex]\rm{OP_{2}}[/tex] . Then draw a line segment [tex]\rm{P_{3} P_{4}}[/tex] perpendicular to [tex]\rm{OP_{3}}[/tex]. Continuing in this matter, you get line segment of unit length perpendicular to [tex]\rm{OP_{n-1}}[/tex]. In this manner, you will have created the points [tex]\rm{P_{2}, P_{3},...... P_{n}....}[/tex], and joined them to create a beautiful spiral depicting [tex]\rm{\sqrt{2}, \sqrt{3}, \sqrt{4},...}[/tex]
Answer:
The "square root spiral," donned the "Spiral of Theodorus" was created by Theodorus to visualize a set of 17 isosceles triangles where [tex]n[/tex] is equal to a value between one and seventeen.
The central angle is attached to a central point, and the side opposite of the central angle is always equal to 1.The hypotenuse of the triangle is equivalent to [tex]\sqrt{n+1}[/tex]. The hypotenuse becomes a leg for the next triangle.I have attached an image of the Square Root spiral below.
Sienna is solving the quadratic equation by completing the square. 3x2 + 9x – 4 = 0 3x2 + 9x = 4 A(x2 + 3x) = 4 What is the value of A? –4 –3 3 4
Answer:
I am going to show you the first steps to complete squares for the given equation: 1) Starting equation: 3x^2 + 9x -4 = 0 2) Add 4 to both sides => 3x^2 + 9x - 4 + 4 = 4 => 3x^2 + 9x = 4 3) Extract common factor 3 in the left side => 3 (x^2 + 3x). Now, compare with a(x^2 + 3x) and you get a = 3. Answer: a = 3.
Answer:
its c
Step-by-step explanation:
find the unknown angles .......... please answer number wise .................................... please help!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
x=
a.60
b.25
c.45
d.30
e.53
f.is a right angle so 90
g.15
h.is a right angle so 90.we have to divide it so it's 45.equal to both sides.
Step-by-step explanation:
by looking at the angles we know
first one is 180.so simply just subtract from the number given.like that we do..
as you can see H ,there the symbol means both sides are equal so the amount will be same.
Please help solve for the median !!
Answer:
Median = 14
Step-by-step explanation:
2, 5, 14, 15, 21, 18, 15, 9, 2
First, order the numbers:
2, 2, 5, 9, 14, 15, 15, 18, 21
Then, cancel out the numbers, starting the first and last number, going outwards in. If there is 1 number left, it is your median. If there are 2 left, add the 2 numbers together and divide them by two:
2, 2, 5, 9, 14, 15, 15, 18, 21
2, 5, 9, 14, 15, 15, 18
5, 9, 14, 15, 15
9, 14, 15
14
The median is 14.
Please tell me if I was wrong! I hope this helps you!
Answer: The median is 14
Step-by-step explanation: The median is the number that is halfway into the data set. To find the median, the data should be arranged in order from least to greatest. For this example. 2,2,5,9,14,15,15,18,21. Find the number that is halfway. which is 14
A mechanic ground 6 valves in 25 minutes. At that rate,
how long will it take to grind 45 valves of the same kind?
Answer:
3hours and 12.5 minutes
Step-by-step explanation:
45/6=7.5x25=187.5/60=3hours and 12.5 minutes
Find a • b. a = 5i + 7j, b = -4i + 3j
Answer:
[tex]a \cdot b = 1[/tex]
Step-by-step explanation:
[tex] a = 5i + 7j [/tex]
[tex] b = -4i + 3j [/tex]
[tex] a = a_xi + a_yj [/tex]
[tex]b = b_xi + b_yj[/tex]
[tex] a \cdot b = a_xb_x + a_yb_y [/tex]
[tex] a \cdot b = (5)(-4) + (7)(3) [/tex]
[tex] a \cdot b = -20 + 21 [/tex]
[tex]a \cdot b = 1[/tex]
Answer:
[tex]\boxed{-20i^2 -13ij+21j^2}[/tex]
Step-by-step explanation:
[tex]\sf Plug \ in \ the \ values.[/tex]
[tex](5i+7j) \cdot (-4i+3j)[/tex]
[tex]\sf Expand \ brackets.[/tex]
[tex]5i(-4i+3j)+7j(-4i+3j)[/tex]
[tex]-20i^2 +15ij+-28ij +21j^2[/tex]
[tex]\sf Combine \ like \ terms.[/tex]
[tex]-20i^2 -13ij+21j^2[/tex]
I need some help with this please :)
Answer:18 ft
Step-by-step explanation: Perimeter=2(L+B)
Perimeter=2(7 + 2)
2×9=18
Answer:
18feet.
Step-by-step explanation:
To find the perimemter of a rectangle, you just add all the sides.
A rectangle has 4 sides in total, where 2 are equal, and the other 2 are als equal.
So, you just add 7+2+7+2, which gives 18.
This is why, the perimeter of this rectangle is 18feet.
Hope this helped, have a nice day!
Which statements are true about triangle QRS?
Select
three options.
Answer:
The side opposite <Q is RS
The hypothenuse is QR
The side adjacent to <Q is QS
Step-by-step explanation:
Side RS is directly opposite <Q. The first statement provided in the options is correct.
The side that is opposite to <R is QS. The second statement in the options is not correct.
The longer leg of a right triangle is always the hypotenuse. Side QR in ∆QRS is the hypotenuse. The third statement given in the options is correct.
The side adjacent to <R is not SQ. RS is the side adjacent to <R. The fourth statement in the given options is not correct.
Side QS is adjacent to <Q. The fifth option is correct.
Answer:
A, C, E
Step-by-step explanation:
on edge! hope this helps!!~ （‐＾▽＾‐）
the principal p is borrowed at a simple interest rate r for a period of time t. find the loan's future value g P = 700, r = 8.25, t = 3 months
Answer:
Hey there!
Simple interest formula: I=PRT
I=700(8.25)(0.25)
I=1443.75
Hope this helps :)
Answer:
Step-by-step explanation:
I = PRT
I = 700(0.0825)(1/4) = 14.44
Because the interest is usually in percentage and it's impossible to have 825% as your interest rate. So the actual interest rate has to be 0.0825.
The formula above calculated the interest, if you want the total, you will need to add 700 to that number.
[img id="5156824"][/img]Here's a small quick example of the formula that should help.
A bike wheel. A bike wheel is 26 inches in diameter. What is the bike wheel's diameter in millimeters (1 inch = 25.4 millimeters)?
Answer:
The answer is 660.4 millimetersStep-by-step explanation:
Diameter = 26 inches
From the question
1 inch = 25.4 mm
To find it's equivalent in millimeters multiply 26 inches by 25.4 millimeters and divide by 1 inch
so we have 26 inches as
[tex] \frac{26 \: inches \times 25.4mm}{1 \: inch} [/tex]
Simplify
We have
26 × 25.4 mm
We have the final answer as
660.4 millimetersHope this helps you
Answer: B.) 26 inches (25.4 millimeters/ 1 inch)
Step-by-step explanation: i hope this helps :)
renea is going to the lake to visit some freinds if the lake is 60 miles away and renae is driving at 40 miles per hour the entire time how long will it take her to get to the lake
Answer:
1.5 hours
Step-by-step explanation:
Set up a proportion:
[tex]\frac{40 miles}{1 hour}[/tex] = [tex]\frac{60 miles}{x}[/tex]
Cross multiply:
40x = 60
x = 1.5
= 1.5 hours
The equation below is written in words. x plus ten equals two. What's the value of x?
Answer:
x+10 =2
x = -8
Step-by-step explanation:
plus means add
x+10 =2
Subtract 10 from each side
x+10-10 =2-10
x = -8
Use the Pythagorean theorem to find the length of the hypotenuse in the triangle shown below.4,3
Answer:
5
Step-by-step explanation:
a^2 + b^2 = c^2
4^2 + 3^2 = c^2
16 + 9 = c^2
25 = c^2
c = 5
Answer:
5Step-by-step explanation:
[tex]Hypotenuse = ?\\Opposite = 4\\Adjacent = 3\\\\Pythagoras \: Theorem ;\\\\Hypotenuse^2 =Opposite^2+Adjacent ^2\\\\Hypotenuse^2 = 4^2 +3^2\\\\Hypotenuse^2 = 16+9\\\\Hypotenuse^2 = 25\\\\\sqrt{Hypotenuse^2}=\sqrt{25} \\Hypotenuse = 5[/tex]
What is the correct answer and how can this be solved?
Answer:
A. 0,2,0,2
Step-by-step explanation:
Firstly, Insert 1-4 into [tex]u^n=1+(-1)^n[/tex]
[tex]u^1=1+(-1)^1\\1+(-1)1=0\\\\\\\\u^2=1+(-1)^2\\\\1+1=2\\\\\\u^3=1+(-1)^3\\\\1+(-1)^3=0\\\\\\\\u^4=1+(-1)^4\\\\1+(-1)^4=2\\[/tex]
Simple explanation, for the first number.
-1+1=0
For the second number we are saying, -1*-1=1
and then 1+1=2
For the third number we are saying, -1*-1*-1=-1
-1+1=0
For the fourth number we are saying, -1*-1*-1*-1=1
1+1=2
A baseball player has a batting average of 0.26. What is the probability that he has exactly 2 hits in his next 7 at bats
Answer:
The probability is [tex]P(2) = 0.426[/tex]
Step-by-step explanation:
From the question we are told that
The probability of success is [tex]p = 0.26[/tex]
The number of hits is n = 7
Generally this probability follows a binomial distribution given there can only be two outcome i.e the probability of success and the probability of failure
The probability of failure is [tex]q = 1- p[/tex]
substituting values
[tex]q = 1 - 0.26[/tex]
[tex]q = 0.74[/tex]
Now the probability of exactly 2 hits in his next 7 at bats is mathematically evaluated as
[tex]P(2) = \left n} \atop {}} \right. C_2 *p^{2} * q^{n- 2}[/tex]
substituting values
[tex]P(2) = \left 7} \atop {}} \right. C_2 *p^{2} * q^{7- 2}[/tex]
Here [tex]\left 7} \atop {}} \right. C_2[/tex] means 7 combination 2 and using a calculator(reference calculator soup website) to compute, the value obtained is
[tex]\left 7} \atop {}} \right. C_2 =21[/tex]
So
[tex]P(2) = 21 *(0.26)^{2} * (0.74)^{5}[/tex]
[tex]P(2) = 0.426[/tex]
When comparing more than two treatment means, why should you use an analysis of variance instead of using several t tests?
Answer:
Because it increases the risk of Type 1 error
Step-by-step explanation:
ANOVA is the analysis of the variance .
When comparing more than two treatment means we use ANOVA because a t test increases the risk of type 1 error .
For example if we wish to compare 4 population means there will be 4C2 = 6 separate pairs and to test the null hypothesis that all four population means are equal would require six two sample t test. Similarly to test 10 population mean would require 45 separate two sample t test.
This has two disadvantages .
First the procedure is too lengthy and tediuos.
Second the overall level of significance greatly increases as the number of t- tests increases.
The analysis of the variance compares two different estimates of variance using the F distributionto determine whether the population means are equal.
Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim (x, y, z)→(7, 0, 2) e−xysin π z 4
Answer:
The limit of the function is 0Step-by-step explanation:
Given the limit of the function [tex]\lim_{(x,y,z) \to (7,0,2)} e^{-xy}sin\dfrac{\pi z}{4} }[/tex]
First step is to substitute the given values of x, y and z into the function given as shown;
[tex]\lim_{(x,y,z) \to (7,0,2)} e^{-xy}sin\dfrac{\pi z}{4} }\\\\= e^{-(7)(0)}sin\dfrac{\pi (2)}{4} }\\\\\\= e^{-0}sin\dfrac{\pi}{2} }\\\\\\= 1*sin\frac{\pi}{2} \\\\= 1*sin90^0\\\\= 1* 0\\\\= 0[/tex]
The limit therefore exist since the limit of the function at the given point gave us a finite value which is zero.
Subtract 750 -389 plzzz help
Find the length of AC¯¯¯¯¯¯¯¯ A. 211.63 B. 44.98 C. 9.35 D. 207
Answer:
Step-by-step explanation:
tanθ= opp / adj
tan(12) = AC/44
now
AC = tan(12)/44
AC = ...
use calculator to find the value
I just broke mine
PLEASE HELP !! (1/5) - 50 POINTS - no wrong answers please. A) y = 6x - [tex]\frac{11}{8}[/tex] B) y = -6x - 2 C) y = [tex]\frac{3}{2}[/tex] x - [tex]\frac{1}{8}[/tex] D) y = -3x + 9
Answer:
C) 3/2x-1/8
Step-by-step explanation:
We can see that it has a generally positive slope, which rules out B and D.
Plugging in a few numbers for x, we can quickly see that 6 is too high of a slope. (If we plug in 6 for x, the y value would be almost 35, not 10). This rules out A.
While it doesn’t fit perfectly, C is by far the closest.
what is the radius for a circle whose equation is x2 + y2 = 64
Answer:
radius of 8Step-by-step explanation:
step one :
Given that the equation of the circle is described as
[tex]x^2 + y^2 = 64[/tex]
To correctly identify the center of the circle we have to place the equation in the standard form.
the standard equation for a circle is
[tex](x-h)^2+(x-k)^2= r^2[/tex]
step two :
let us re-write the given equation so that we can compare it with the general equation of circle
[tex](x-0)^2+(x-0)^2= 8^2[/tex]
step three:
From this above equation in step two we can see that the circle has a radius of 8
Can someone do this assuming that it is infinite and as well as assuming it's not infinite? Thanks!
Answer:
see below
Step-by-step explanation:
4,7,12,19
We are adding 3,5,7,9..... each time
The sequence is not arithmetic because we are not adding a constant. It is not geometric since we are not multiplying by a constant term each time
There is no common difference or common ratio.
The explicit formula is
an =n^2 +3
The recursive formula is
(n+1)^2 +3 - (n^2 +3)
n^2 +2n+1+3 - ( n^2+3)
2n+1
a sub(n+1) = a sub( n) + 2n+1
The 10th term
an = n^2 +3
Let n=10
an = 10^2+3
= 100+3
= 103
summation
see image
since the numbers are increasing and greater than 1 the sum does not exist
A health insurer has determined that the "reasonable and customary" fee for a certain medical procedure is $1200. They suspect that the average fee charged by one particular clinic for this procedure is higher than $1200.
Explain in context the conclusion of the test if H0 is rejected.
Answer:
For the null hypothesis to be rejected , then the conclusion of the test is that the absolute values of the z-statistic and/or the t-test statistic is greater than the critical value
Step-by-step explanation:
Here, we want to explain the conclusion of the test given that the null hypothesis is rejected.
Mathematically, the null hypothesis is as expressed as below;
H0: μ = 1,200
The alternative hypothesis H1 would be;
H1: μ > 1,200
Now, before we can reject or accept the null hypothesis, we will need a sample size and thus calculate the test statistics and the z statistics
For us to reject the null hypothesis, one of two things, or two things must have occurred.
The absolute value of the z statistic |z| or the test statistic |t| must be greater than the critical value.
If this happens, then we can make a rejection of the null hypothesis
Does coordinate x or coordinate y represent a greater number?
Answer:
Y
Step-by-step explanation:
You see that (x,3) and (2,7) are on the exact same x-value, which is 2. Y, on the other hand, is on the same y-value as (4,3), so it's going to be 4. 4 > 2, so your answer is y.
Y represents the greater number.
We see that (x,3) and (2,7) are on the exact same x-value, which is 2. Y, on the other hand, is on the same y-value as (4,3), so it's going to be 4. 4 > 2, so your answer is y.
What is an example of a coordinate?A set of values that display an actual role. On graphs it is also a pair of numbers: the first variety indicates the gap along, and the second variety indicates the distance up or down. As an example, the factor (12,5) is 12 units long, and five units up.
Learn more about coordinate here: https://brainly.com/question/11337174
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Which of the following classifications of polygons could be a valid description? an equilateral scalene triangle an obtuse scalene triangle a square trapezoid a rectangular kite
Answer:
B. An obtuse scalene triangle
Step-by-step explanation:
Polygons are plane figures bounded by three or more straight sides. Examples are: trigon, quadragon, hexagon, nonagon etc. They are named with respect to their number of sides.
An obtuse triangle has one of its angles greater than [tex]90^{0}[/tex] but less than [tex]180^{0}[/tex]. While a scalene triangles has non of its sides to be equal in length.
The valid description of the classes of polygons is: an obtuse scalene triangle. Which implies that the triangle has one of its angles to be obtuse, and non of its sides equal.
