True
Step-by-step explanation:
[tex]P(t) = I^2(t)R[/tex]
Taking the derivative of P(t) with respect to time,
[tex]\dfrac{dP(t)}{dt} = 2I(t)\dfrac{dI(t)}{dt}R[/tex]
[tex]\:\:\:\:\:\:\:\:= 2(1)(-0.5)(500) = -500[/tex]
Simplify.
Rewrite the expression in the form 6^n6
n
6, start superscript, n, end superscript.
\dfrac{6^{4}}{6}=
6
6
4
Answer:
6^3
6 to the third power
or 3x3x3
Step-by-step explanation:
The solution of the expression 6⁻⁴.6⁶ will be 6².
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that the expression is 6⁻⁴.6⁶. The expression will be solved as below:-
6⁻⁴.6⁶ = 6⁻⁴⁺⁶
Use the exponent property when the bases are the same then the powers will be added.
6⁻⁴.6⁶ = 6²
Therefore, the solution of the expression 6⁻⁴.6⁶ will be 6².
The complete question is to simplify the expression 6⁻⁴.6⁶.
To know more about an expression follow
https://brainly.com/question/8844911
#SPJ2
(3k + 5)(2k2 – 5k – 3)
A random sample of 20 individuals who graduated from college five years ago were asked to report the total amount of debt (in $) they had when they graduated from college and the total value of their current investments (in $) resulting in the data set below.
Debt Invested
16472 37226
19048 33930
4033 66292
22575 24887
12020 44976
4731 59924
4571 59901
Which statement best describes the relationship between these two variables?
a. As college debt decreases current investment decreases.
b. College debt is not associated with current investment.
c. As college debt increases current investment decreases.
d. As college debt increases current investment increases.
Answer:
The answer is "Option c".
Step-by-step explanation:
Please find the complete question and its solution in the attached file.
what is the graph of this function?
Answer:
You MADE IT EASY
Step-by-step explanation:
[tex] {y - 5 \times 9}^{2} \: times \: sevem \\ n \: equals \sec(x + {}^{2} ) [/tex]
You want to put a 5 inch thick layer of topsoil for a new 23 ft by 27 ft garden. The dirt store sells by the cubic yard. How many cubic yards will you need to order?
Answer:
9.5833333333 yd³
9 7/12 yd³
Step-by-step explanation:
23 * 27 * 5/12 = 258.75 ft³
1 yd³ = 3ft * 3ft * 3ft
1 yd³ = 27 ft³
258.75 ft³ * 1 yd³/27 ft³ = 9.5833333333 yd³
9.5833333333 yd³
9 7/12 yd³
Lindsay is checking out books at the library, and she is primarily interested in mysteries and nonfiction. She has narrowed her selection down to ten mysteries and twelve Nonfiction books. If she randomly chooses four books fro her selections, what’s the probability that they will all be nonfiction?
twelve nonfiction books. If she randomly chooses four books
answer to 4 decimal places, if necessary.
Answer
Answer:
0.0677 = 6.77% probability that they will all be nonfiction
Step-by-step explanation:
The books are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
10 + 12 = 22 books.
She chooses 4 books, which means that [tex]n = 4[/tex]
12 nonfiction, which meas that [tex]k = 12[/tex]
What’s the probability that they will all be nonfiction?
This is P(X = 4). So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 4) = h(4,22,4,12) = \frac{C_{12,4}*C_{10,0}}{C_{22,4}} = 0.0677[/tex]
0.0677 = 6.77% probability that they will all be nonfiction
A salesman receives a salary of RM 2000 per month. He wis receive a commission of RM 800 for each car he sells. If he sells n cars in a particular month,
a. Find his monthly salary when n = 18.
b. Express his salary in terms of n.
Answer:
a) month salary = RM(18×800+2000)
= RM 16400
b) his salary = RM(800n+2000)
Hope it helps
Need answers asap!!!!!!!!!!!!!!
Answer:
The answer is
x equal -243
Answer:
-243 is yr correct answer.
Step-by-step explanation:
(-3)^-5=1/x1/(-3)^5=1/x1/-243=1/xx= -243hope it helps
stay safe healthy and happy...Find m angle NML; m angle QML=115^ and m angle NMQ=28^
Answer:
We're provided - m ∠ QML = 115° , m ∠ NMQ = 28° and we're asked to find out m ∠ NML. Set up an equation and solve for m ∠ NML.[tex] \large{ \tt{❀ \: m \: \angle \: NML= m \: \angle \:QML + m \: \angle \: NMQ}}[/tex]
[tex] \large{ \tt{⤇m \: \angle \:NML= 115 \degree + 28 \degree }}[/tex]
[tex] \boxed{ \large{ \tt{⤇ \: m \: \angle \:NML = 143 \degree }}}[/tex]
Hence , Our final answer is 143° . Hope I helped! Let me know if you have any questions regarding my answer and also notify me , if you need any other help! :)▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁
Lauren flips a coin, spins the spinner, and rolls a standard number cube. Find the probability that the coin will
show heads, the spinner will land on green, and the cube will show an even number.
Lauren will get 2/25 because the coin only lands on heads or tail
Here is the setup for a non-traditional casino game: You draw a card from a well shuffled full deck and if the card is a king you win $100. The game costs $2 to play and you decide to play the game until you win the $100. Each time you draw a card you pay $2, and if the card is not a king, the card is put back in the deck, and the deck is reshuffled. How much money should you expect to spend on this game?
Answer:
$26
4/52 = 1/13.. the king will appear one in 13 tries... 13 tries is $26
Step-by-step explanation:
You should expect to spend $26 to win $100 playing this game.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
To calculate the expected cost of playing this game until you win $100, we need to determine the probability of drawing a king on any given turn, as well as the number of times you are expected to play the game before you win.
So,
The probability of drawing a king on any given turn is 4/52, or 1/13 since there are 4 kings in a standard deck of 52 cards.
To determine the number of times you are expected to play the game before you win, we can use the geometric distribution, which models the number of trials it takes to achieve success in a sequence of independent trials, where the probability of success remains constant across trials.
The probability of winning on any given trial is 1/13, and the probability of losing is 12/13.
The expected number of trials until the first success (drawing a king) is:
= 1 / (1/13) = 13
This means that on average, you can expect to play the game 13 times before drawing a king and winning the $100 prize.
Now,
Since each game costs $2 to play, the total cost of playing the game 13 times is:
13 x $2 = $26
Therefore,
You should expect to spend $26 to win $100 playing this game.
Learn more about probability here:
https://brainly.com/question/14099682
#SPJ2
A regular hexagon has sides of 5 feet. What is the area of the hexagon? 12.5 ft 2 37.5 ft 2 25 ft 2 50 ft 2
Answer: [tex]37.5\sqrt{3}[/tex]
This value is exact. We can write this as 37.5*sqrt(3)
This approximates to roughly 64.9519
The units for the area are in square feet.
==========================================
Explanation:
Split the regular hexagon into 6 identical equilateral triangles.
Each equilateral triangle has side length x = 5 ft.
The exact area of one of the equilateral triangles is
A = 0.25*sqrt(3)*x^2
A = 0.25*sqrt(3)*5^2
A = 0.25*sqrt(3)*25
A = 0.25*25*sqrt(3)
A = 6.25*sqrt(3)
Multiply this by 6 to get the exact area of the regular hexagon.
6*A = 6*6.25*sqrt(3) = 37.5*sqrt(3) which is the exact area in terms of radicals or square roots.
If your teacher meant to say choice B is 37.5*sqrt(3), then that would be the final answer. If your teacher only said 37.5 without the sqrt(3) term, then there's a typo.
How do I solve this. Y=f(x)+a moves the function
Answer:
up
Step-by-step explanation:
for linear functions, adding a constant will increase the y value by two and shift the line up two units on the graph.
Answer: It moves the function 'a' units up if a > 0. Or it moves the function |a| units down if a < 0.
Explanation:
Consider an example like y = f(x)+2. This shifts the f(x) curve 2 units up because we're adding 2 to each y or f(x) output. A point like (5,7) shifts up to (5,9).
As another example, y = f(x)-5 moves the curve 5 units down.
In the first example, we had a > 0 which moved the function 'a' units up (a = 2 in that case). The second example had a = -5 which means a < 0, so that's why we shifted |a| = |-5| = 5 units down.
How do I solve this?
Answer:
Step-by-step explanation:
4x+3y=13
5x-4y=-7
The sum of two six-digit numbers is a seven-digit number
Answer
500,000 + 500,000 = 1,000,000
Step-by-step explanation:
Jessica purchases a kayak in Florida, where the state sales taxes are 6%. She paid $72 in sales tax. What was the retail price of the kayak?
Answer:
72 is 6% of 1200.
Step-by-step explanation:
Multiply 72 by 100.
72*100
Then divide the number by 6
(72*100)/6
You should get 1200.
Determine the degree of the polynomial:
7m^6n^5
9514 1404 393
Answer:
11
Step-by-step explanation:
The degree of the given monomial is the sum of the exponents of the variables.
m has degree 6
n has degree 5
The degree of the monomial is 6+5 = 11.
Find the values of x and y
Answer:
d
Step-by-step explanation:
Answer:
x=5, y=52
Step-by-step explanation:
Hi there!
1) Determine y
Because length AB is equal to length BC (making this an isosceles triangle), angle y is equal to 52 degrees.
y = 52
2) Determine x
The sum of the interior angles of a triangle will always be 180 degrees. Knowing this, we can construct the following equation and solve for x:
[tex]180=52+52+(14x+6)[/tex]
Open up the parentheses
[tex]180=52+52+14x+6\\180=104+14x+6\\180=110+14x[/tex]
Subtract 110 from both sides to isolate 14x
[tex]180-110=110+14x-110\\70=14x[/tex]
Divide both sides by 14 to isolate x
[tex]\frac{70}{14} =\frac{14x}{14} \\5=x[/tex]
Therefore, the value of x is 5.
I hope this helps!
Help. Does anyone know the answer. Pls help!
Answer:
Step-by-step explanation:
the first and last choices look good
Find the slope of the line y= -3x+7
Answer:
If you had a line of x = 7, (or any time you have an equation where x equals a number) then you would have a vertical line. In every vertical line, the slope is undefined. In equations of lines that are in the format of y = mx + b, the slope is represented by the "m".Answer:
-3
Explanation:
The given equation is in slope-intercept form. The format of slope-intercept is y = mx + b, where m is the slope and b is the y-intercept.
The slope is the coefficient of x.
In the equation y = -3x + 7, the slope is -3, because -3 is the coefficient of x.
Hence, the slope is -3.find the measure of angle BAC
Answer:
a= 26
Step-by-step explanation:
180-130=50
total angle in triangle =180
4a+a+50=180
then proceed like norma algebra
Help Me ASAP this is the last day of Summer School
Answer:
22.2222%
Step-by-step explanation:
total amout of owners all around is 90 and Dal. Owners is 20 so divide 20 by 90.
Step-by-step explanation:
[tex]percentage= \frac{20}{25 + 20 + 15 + 30} \times 100 \\ = \frac{2}{9} \times 100\% \\ = 22.2\%[/tex]
Find the intercepts for the graph of the equation.
-3x + y = 6
Answer:
y = 9
Step-by-step explanation:
Given the following angles, what ray is the common side of CFD and ZDFE?
Answer:
B. Ray FD
Step-by-step explanation:
A common side of two angles is the side shared by the two angles. It is part of the sides that forms both angles.
The common side of <CFD and <DFE is therefore ray FD. Ray FD is part of the sides that forms <CFD and also <DFE.
Answer:
B. Ray FD
Step-by-step explanation:
A common side of two angles is the side shared by the two angles. It is part of the sides that forms both angles.
The common side of <CFD and <DFE is therefore ray FD. Ray FD is part of the sides that forms <CFD and also <DFE.
Here are the test scores for 8 students in Mr. M's class. 87, 55, 96, 38, 83, 64, 44, 81. What is the percentage of these test scores that are less than 84?
Answer:
75%
Step-by-step explanation:
Given that the score of 8 students in Mr. M's class are 87, 55, 96, 38, 83, 64, 44, 81, the scores less than 84 are 55, 38, 83, 64, 44, 81.
These means that 6 student had scores less that 84 of the 8 students hence the percentage of these test scores that are less than 84
= 6/8 * 100%
= 75%
This means that 75% of the students had scores less than 84
Please answer & number. Thank you! <33
Answer:
2）=2
4）=3
5）=5
8）=-1
Step-by-step explanation:
just divide the number by the number with variable
The categories of a categorical variable are given along with the observed counts from a sample. The expected counts from a null hypothesis are given in parentheses. Compute the x-test statistic, and use the x-distribution to find the p-value of the test. Category Observed (Expected) A 25 (20) B 35(40) C 50(60) D 90(80) Round your answer for the chi-square statistic to two decimal places, and your answer for the p-value to four decimal places. chi-square statistic = p-value = i
Answer:
χ² = 4.80
Pvalue = 0.1874
Step-by-step explanation:
Given :
Category Observed (Expected)
A 25 (20)
B 35(40)
C 50(60)
D 90(80)
The Chisquare statistic (χ²) is given by :
χ² = Σ(observed - Expected)² / Expected
χ² = (25-20)²/20 + (35-40)/40 + (50-60)²/60 + (90-80)²/80
χ² = 1.25 + 0.625 + 1.67 + 1.25
χ² = 4.795
χ² = 4.80 (2 decimal places)
Using the Chisquare Pvalue calculator :
df = n - 1 = 4 - 1 = 3
Pvalue = 0.1874
What is the following product?(2square root 7 +3square root 6)(5square root2+4square root3)
Answer:
[tex]10\sqrt{14} + 8\sqrt{21} + 30 \sqrt{3} +36\sqrt{2}\\\\[/tex]
Step-by-step explanation:
[tex]( 2 \sqrt7 + 3 \sqrt6)(5\sqrt2 + 4\sqrt3)\\\\= 2\sqrt7(5\sqrt2 + 4\sqrt3) + 3\sqrt6 ( 5\sqrt2 + 4\sqrt3)\\\\=10\sqrt{7 \times 2} + 8\sqrt{7 \times 3} + 15\sqrt{6 \times 2} + 12\sqrt{ 6\times 3}\\\\=10\sqrt{14} + 8\sqrt{21} + 15 \sqrt{12} +12\sqrt{18}\\\\= 10\sqrt{14} + 8\sqrt{21} + 15 \sqrt{4 \times 3 } +12\sqrt{9 \times 2}\\\\= 10\sqrt{14} + 8\sqrt{21} + 15 \sqrt{2^2 \times 3} +12\sqrt{3^2 \times 2}\\\\= 10\sqrt{14} + 8\sqrt{21} + 30 \sqrt{3} +36\sqrt{2}\\\\[/tex]
Find the distance between the points (-5, -4) and (3, 1).
On a coordinate plane, points are at (3, 1), (negative 5, negative 4).
Step-by-step explanation:
it will help u
When 50% of a number is added to the number, the results is 165
Answer:
this would look like
0.5x+x=165
1.5x=165
x=110
Hope This Helps!!!
