Answer:
24 ways
Step-by-step explanation:
There are 4!=24 ways to make distinct codes with the given distinct digits. So the probability of guessing it the first time is 1/24.
The probability that you guess the code correctly on the first try will be 1/24.
What is the probability?Probability is synonymous with possibility. It is concerned with the occurrence of a random event.
Probability can only have a value between 0 and 1. Its simple notion is that something is very likely to occur. It is the proportion of favorable events to the total number of events.
If the code is arranged then the total number of ways possible is;
⇒4!
⇒4×3×2×1
⇒24
Possible outcome = 1
Total outcome = 24
Probability = Possible outcome/total outcome
Probability = 1/24
Hence the probability that you guess the code correctly on the first try will be 1/24.
To learn more about probability, refer to the link: https://brainly.com/question/795909.
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Evaluate the limit, if it exists.
lim (h - > 0) ((-7 + h)^2 - 49) / h
Expand everything in the limit:
[tex]\displaystyle\lim_{h\to0}\frac{(-7+h)^2-49}h=\lim_{h\to0}\frac{(49-14h+h^2)-49}h=\lim_{h\to0}\frac{h^2-14h}h[/tex]
We have [tex]h[/tex] approaching 0, and in particular [tex]h\neq0[/tex], so we can cancel a factor in the numerator and denominator:
[tex]\displaystyle\lim_{h\to0}\frac{h^2-14h}h=\lim_{h\to0}(h-14)=\boxed{-14}[/tex]
Alternatively, if you already know about derivatives, consider the function [tex]f(x)=x^2[/tex], whose derivative is [tex]f'(x)=2x[/tex].
Using the limit definition, we have
[tex]f'(x)=\displaystyle\lim_{h\to0}\frac{f(x+h)-f(x)}h=\lim_{h\to0}\frac{(x+h)^2-x^2}h[/tex]
which is exactly the original limit with [tex]x=-7[/tex]. The derivative is [tex]2x[/tex], so the value of the limit is, again, -14.
What is the solution to this system of linear equations? y − 4x = 7 2y + 4x = 2
━━━━━━━☆☆━━━━━━━
▹ Answer
(-1, 3)
▹ Step-by-Step Explanation
y - 4x = 7
2y + 4x = 2
Substitute
y - (2 - 2y) = 7
Solve
y = 3
Substitute
4x = 2 - 2 * 3
Solve
x = -1
Final Answer
(x, y) = (-1, 3)
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Answer:
D: (-1,3)
Edg 2020
Simply the expression 3.4-1/2(0.75)
Answer:
3.025
Step-by-step explanation:
3.4-1/2(0.75)
3.4-0.375
3.025
Can somebody please help me with this question?
Answer:
A = x² + 9x + 8
Step-by-step explanation:
Area of Parallelogram Formula: A = bh
We are given b = x + 8 and h = x + 1, so simply plug it in:
A = (x + 8)(x + 1)
A = x² + x + 8x + 8
A = x² + 9x + 8
━━━━━━━☆☆━━━━━━━
▹ Answer
A = x² + 9x + 8
▹ Step-by-Step Explanation
A = bh
A = (x + 8) * (x + 1)
A = x² + 9x + 8
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Determine the inverse of this function.
f(x) = 3 cos(2x – 3) + 1
Answer:
a) [tex]f^{-1} (x) = \frac{1}{2} Cos^{-1} (\frac{x-1}{3} ) +\frac{3}{2}[/tex]
The inverse of given function
[tex]f^{-1} (x) = \frac{1}{2} Cos^{-1} (\frac{x-1}{3} ) +\frac{3}{2}[/tex]
Step-by-step explanation:
Step(i):-
Given function f(x) = 3 cos (2 x -3) + 1
Let y = f(x) = 3 cos (2 x -3) + 1
y = 3 cos (2 x -3) + 1
⇒ y - 1 = 3 cos (2 x -3)
⇒ [tex]cos ( 2 x - 3 ) =\frac{y -1}{3}[/tex]
⇒[tex]cos ^{-1} ( cos (2 x - 3)) = Cos^{-1} (\frac{y-1}{3} )[/tex]
We know that inverse trigonometric equations
cos⁻¹(cosθ) = θ
[tex]2 x - 3 = Cos^{-1} (\frac{y-1}{3} )[/tex]
[tex]2 x = Cos^{-1} (\frac{y-1}{3} ) +3[/tex]
[tex]x = \frac{1}{2} Cos^{-1} (\frac{y-1}{3} ) +\frac{3}{2}[/tex]
Step(ii):-
we know that y= f(x)
The inverse of the given function
[tex]x = f^{-1} (y)[/tex]
[tex]f^{-1} (y) = \frac{1}{2} Cos^{-1} (\frac{y-1}{3} ) +\frac{3}{2}[/tex]
The inverse of given function in terms of 'x'
[tex]f^{-1} (x) = \frac{1}{2} Cos^{-1} (\frac{x-1}{3} ) +\frac{3}{2}[/tex]
conclusion:-
The inverse of given function
[tex]f^{-1} (x) = \frac{1}{2} Cos^{-1} (\frac{x-1}{3} ) +\frac{3}{2}[/tex]
First person to solve correctly gets brainliest please answer quickly, I'm on a time limit lol A DVD is on sale for $1.05 off. This is a 15% discount from the original price. Use an equation to find the original price. Answer choices: $16.05 $15.75 $10.50 $7.00
Divide the amount off the price by the percentage off:
1.05 / 0.15 = 7
The original price is $7.00
Orchid wants to retile her bathroom floor, which has an area of 40 square feet. She is deciding between two types of custom tiles. The square tile is One-half foot by One-half foot and costs $0.45 per tile. The rectangular tile is 2 feet by One-fourth foot and costs $0.80 per tile.
Which tile should Orchid choose to minimize costs? Explain.
She should choose the square tiles because the total cost will be $8 less.
She should choose the rectangular tiles because the total cost will be $8 less.
She should choose the square tiles because the total cost will be $14 less.
She should choose the rectangular tiles because the total cost will be $14 less.
Your answer is the second option, she should choose the rectangular tiles because the total cost will be $8 less.
To find this answer we need to first find the total cost for using square tiles, and the cost for using rectangular tiles, and compare them. We can do this by finding the area of each tile individually, calculating how many tiles we would need, and multiplying this by the cost for one tile:
Square tiles:
The area of one square tile is 1/2 × 1/2 = 1/4 ft. Therefore we need 40 ÷ 1/4 = 160 tiles. If each tile costs $0.45, this means the total cost will be $0.45 × 160 = $72
Rectangular tiles:
The area of one rectangular tile is 2 × 1/4 = 2/4 = 1/2 ft. Thus we need 40 ÷ 1/2 = 80 tiles. Each tile costs $0.80, so the total cost will be 80 × $0.80 = $64.
This shows us that the rectangular tiles will be cheaper by $8.
I hope this helps! Let me know if you have any questions :)
Answer:
B
Step-by-step explanation:
E2020 : )
Use the Integral Test to determine whether the series is convergent or divergent.
n =1 summation [infinity] n / n2 + 8 n = 1
Evaluate the following integral.
1 integral [infinity] x/x2 + 8 dx
We have
[tex]\displaystyle \sum_{n=1}^\infty \frac{n}{n^2+8} < \int_1^\infty \frac{x}{x^2+8}\,\mathrm dx[/tex]
For the integral, substitute y = x ² + 8 and dy = 2x dx. Then
[tex]\displaystyle \int_1^\infty \frac{x}{x^2+8}\,\mathrm dx = \frac12 \int_9^\infty \frac{\mathrm dy}y = \frac12 \ln(y)\bigg|_{y=9}^{y\to\infty} = \infty[/tex]
The integral diverges, so the sum also diverges by the integral test.
4. A rectangle-shaped picture frame has a length of 4b cm and an area of 12ab² square cm. Find the width. *
Answer:
3ab
Step-by-step explanation:
area = length * width
width = area/length
width = (12ab^2)/(4b)
width = 3ab
what is u over 4-4= -20
u/4 - 4 = -20
Add 4 to both sides:
u/4 = -16
Multiply both sides by 4:
u = -64
Answer:
u=-64
Step-by-step explanation:
u/4 -4 = -20
First add 4 to both sides.
u/4=-16
Now multiply both sides by 4
u=-64
Dairy cows at large commercial farms often receive injections of bST (Bovine Somatotropin), a hormone used to spur milk production. Bauman et al. (Journal of Dairy Science, 1989) reported that 12 cows given bST produced an average of 28.0 kg/d of milk. Assume that the standart deviation of milk production is 2.25 kg/d.
Requried:
a. Find a 99% confidence interval for the true mean milk production.
b. If the farms want the confidence interval to be no wider than ± 1.25 kg/d, what level of confidence would they need to use?
Answer:
a) 26.33 kg/d and 29.67 kg/d
b) 94.5%
Step-by-step explanation:
a. Find a 99% confidence interval for the true mean milk production.
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.575*\frac{2.25}{\sqrt{12}} = 1.67[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 28 - 1.67 = 26.33 kg/d
The upper end of the interval is the sample mean added to M. So it is 28 + 1.67 = 29.67 kg/d
The 99% confidence interval for the true mean milk production is between 26.33 kg/d and 29.67 kg/d
b. If the farms want the confidence interval to be no wider than ± 1.25 kg/d, what level of confidence would they need to use?
We need to find z initially, when M = 1.25.
[tex]M = z*\frac{2.25}{\sqrt{12}} = 1.67[/tex]
[tex]1.25 = z*\frac{2.25}{\sqrt{12}} = 1.67[/tex]
[tex]2.25z = 1.25\sqrt{12}[/tex]
[tex]z = \frac{1.25\sqrt{12}}{2.25}[/tex]
[tex]z = 1.92[/tex]
When [tex]z = 1.92[/tex], it has a pvalue of 0.9725.
1 - 2*(1 - 0.9725) = 0.945
So we should use a confidence level of 94.5%.
Simplify: |2-5|-(12 ÷4-1)^2
The value of the expression when simplified is -13
How to determine the valueIt is important to note:
PEDMAS is a mathematical acronym that representing;
P for ParenthesesE for exponentsD for divisionM for multiplicationA for additionS for subtractionAlso, we should note that absolute value of a number is the non-negative value of that number. It s the value of a number irrespective of its direction from zero.
It is denoted with the symbol '| |'
Given the expression;
|2-5|-(12 ÷4-1)^2
Solve the bracket
|-3| - (12 /3)^2
Solve further
|-3| - 4^2
Find the absolute value
3 - 4^2
Find the square
3 - 16
-13
The value is - 13
Thus, the value of the expression when simplified is -13
Learn more about PEDMAS here:
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The operation manager at a tire manufacturing company believes that the mean mileage of a tire is 44,111 miles, with a variance of 5,943,844. What is the probability that the sample mean would be less than 44,257 miles in a sample of 80 tires if the manager is correct? Round your answer to four decimal places.
Answer:
[tex] z=\frac{44257-44111}{\frac{2438}{\sqrt{80}}}= 0.536[/tex]
And if we use the normal standard table we got this:
[tex] P(z<0.536) =0.7040[/tex]
Step-by-step explanation:
For this case we have the following info :
[tex]\mu = 44111[/tex] represent the true mean
[tex]\sigma= \sqrt{5943844}= 2438[/tex] represent the deviation
n= 80 represent the sample size
And we want to find the follwing probability:
[tex] P(\bar X< 44257)[/tex]
For this case since the sample size is larger than 30 we can apply the central limit theorem and we can use the z score formula given by:
[tex] z=\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
The distribution for the sample mean would be:
[tex]\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})[/tex]
And if we find the z score for this case we got:
[tex] z=\frac{44257-44111}{\frac{2438}{\sqrt{80}}}= 0.536[/tex]
And if we use the normal standard table we got this:
[tex] P(z<0.536) =0.7040[/tex]
Which expression is equivalent to 3m + 1 - m? 2 + m - 1 + m 1 + m 3m - 1 3m
Answer:
2m + 1
Step-by-step explanation:
Simply combine like terms. m terms go with m terms and constants go with constants.
Answer:
2m + 1
Step-by-step explanation:
3m + 1 - m =
= 3m - m + 1
= 2m + 1
x + 4y = 23
-3x = 12y + 1
is it no solution?
Answer: Yes
Step-by-step explanation:
First multiply the first equation by three to get 3x+12y=69
Then subtract 12y from both sides of the second equation
Then add the first system and the second like this:
[tex]3x+12y=69\\-3x-12y=1\\--------\\0+0=70\\0=70[/tex]
Because 0≠70, the system has no solutions
Factor completely 5x(x + 3) + 6(x + 3). (1 point)
Answer:
The answer is ( 5x + 6 ) ( x + 3 )Step-by-step explanation:
5x(x + 3) + 6(x + 3)
The final answer is
( 5x + 6 ) ( x + 3 )
Hope this helps you
Not sure how to solve this
Answer:
Step-by-step explanation:
x-y=3
-y=3-x
y=x-3
when x=3 y=0
when x=1 y=-2
when x=2 y=-1
The endpoints of line segment CD are C (1, -9) and D (7, 5 ). Find the coordinates of the midpoint M.
Answer:
(4, -2)
Step-by-step explanation:
To find the midpoint of two points you have to take the average of those two points. So, I can do (1+8)/2, which is 4, to find the midpoint of the x coordinates. I can then do (-9+5)/2, which is -2 to find the midpoint of the y coordinates.
A frequency table for the 60 best batting averages from a baseball league is
shown below. Which of the following histograms best represents the data in
the table?
The correct answer is Graph B
Explanation:
The purpose of histograms is to display visually the frequency of a variable. Additionally, a higher bar represents a higher frequency.
According to this, the correct histogram is graph B because in this the frequencies for each batting average are displayed correctly. For example, the highest bar is related to the average 0.330-0.339, which has the highest frequency (28), this is followed in height by the bar that represents a frequency of 24 and is related to the average 0.340-0.349.
At the same time, the averages 0.320-0.329 and 0.360-0.369 that have a frequency of 2 are represented through the shortest bars, while the average 0.350-0.359 with a frequency of 4 is related to a bar with exactly the double of heigh than those with a frequency of 2.
Answer:
graph B
Step-by-step explanation:
what happened to your screen
algebraic expression Monica asked her friends to buy a charity raffle ticket for $3. All but 4 of her friends bought a ticket, and she raised $18. How many friends did Monica ask?
plz explain me not answer
Answer:
Step-by-step explanation:
Let x represent the number of friends that Monica asked to a charity raffle ticket. If all but 4 of her friends bought a ticket, it means that only 4 of her friends did not buy the charity raffle ticket. Thus, the number of her friends that bought the charity raffle ticket is
x - 4
If each ticket costs $3 and the total amount that was raised is $18, then algebraic expression representing the number of friends that Monica asked is
3(x - 4) = 18
3x - 12 = 18
3x = 18 + 12 = 30
x = 30/3 = 10
Monica asked 10 friends
The Pythagorean Theorem states that for any given right triangle, a2 + b2 = c2. Using the Pythagorean Theorem, what should be the relationship between the areas of the three squares?
Answer:
The relationship between the areas of the three squares is that square A plus square B equals the area of square C.
The sum of the square of a and b is equal to the area of square of c
Data;
abcPythagorean TheoremThis theorem is used to calculated a missing side from a right angle triangle when we have the value of at least two sides.
Given that
[tex]c^2 = a^2 + b^2[/tex]
This indicates a relationship such that the sum of square of two sides is equal to the area of the square of one side. I.e the area of the square of c is equal to the sum of the square of both a and b.
Learn more on Pythagoras Theorem here;
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A series of rigid motions maps ΔUVW onto ΔRST. Based on this information, which of the following is a true statement? Question 12 options: A) ΔUVW is half the area of ΔRST. B) The corresponding pairs of angles of ΔUVW and ΔRST are congruent, but the corresponding sides aren't. C) ΔUVW and ΔRST are congruent. D) There isn't enough information to make a statement about ΔUVW and ΔRST.
Answer: C) ΔUVW and ΔRST are congruent
Step-by-step explanation:
Rigid motions move a geometric figure but do not change the size and shape of the figure. It produces congruent images.There are four kinds of rigid transformation.
1) translation 2) reflection 3) rotation 4) glide reflection.
If a series of rigid motions maps ΔUVW onto ΔRST.
Then, ΔUVW and ΔRST must be congruent. (No change in size or shape)
hence, the correct statement is C) ΔUVW and ΔRST are congruent.
Answer:
C) ΔUVW and ΔRST are congruent
Step-by-step explanation:
find the value of x. m<2= x + 119
Answer: x = -10
Step-by-step explanation:
see image
A) congruent sides implies congruent angles A = 64°
B) Use the Triangle Sum Theorem: 64° + 64° + B = 180° --> B = 52°
C) B and C are complimentary angles: 52° + C = 90° --> C = 38°
D) Use the Triangle Sum Theorem knowing that congruent sides implies congruent angles: 38° + 2D = 180° --> D = 71°
∠2) D and ∠2 are supplementary angles: 71° + ∠2 = 180° --> ∠2 = 109°
Solve for x:
109° = x + 119
-10 = x
Answer:
x = -10
Step-by-step explanation:
Find the measure of angle m∠2
The triangles are isosceles triangles, the base angles are equal.
The other base angle is also 64°.
Using Triangle Sum Theorem.
64 + 64 + y = 180
y = 52
The top angle is 52°.
The whole angle is 90°.
90 - 52 = 38
The second triangle has base angles equal.
Using Triangle Sum Theorem.
38 + z + z = 180
z = 71
The two base angles are 71°.
Angles on a straight line add up to 180°.
71 + m∠2 = 180
m∠2 = 109
The measure of m∠2 is 109°
Find the value of x
m∠2 = x + 119
109 = x + 119
x = 109 - 119
x = -10
What number is 408% of 568?
Answer:
2317.44
Step-by-step explanation:
Solution for What is 408 percent of 568:
408 percent *568 =
(408:100)*568 =
(408*568):100 =
231744:100 = 2317.44
Answer:
2317.44
Step-by-step explanation:
In how many different ways can each of the letters in the following words be arranged? Show your work and solutions. 25. LEARN
Answer:
120 waysStep-by-step explanation:
This problem bothers on permutation
Given the letters LEARN
The total alphabets are 5 in numbers
Since there are no repeating letters, and there are 5 total letters, there are 5!=5*4*3*2*1= 120 ways to arrange them
What is the quadratic regression equation that fits these data
Answer:
Rounded to two decimals the regression curve is:
[tex]y=-0.70\,x^2+2.37\,x+11.96[/tex]
Step-by-step explanation:
The objective of this problem is to have you use a calculator and enter the data in to separate lists: one containing the x-values, and the other the correspondent y-values (following the same order).
Once the data is entered, you need to access the regression tool and request a quadratic form of regression.
You should get and image and resulting function as shown in the attached image.
Answer:
Rounded to two decimals the regression curve is:
Step-by-step explanation:
Patty buys a new car and gets it appraised every few years. After owning the car for 3 years, its value is $15,000. After owning the car for 5 years, its value is $9,000. What is the constant of proportionality in this inverse variation?
Answer: 45,000.
Step-by-step explanation:
The equation of inverse variation is given by:-
[tex]k=xy[/tex]
, where k is the constant of proportionality.
Given: After owning the car for 3 years, its value is $15,000. After owning the car for 5 years, its value is $9,000.
Here,
[tex]x_1=3,\ y_1=15000\\\\x_2=5,\ y_2=9000[/tex]
Then, [tex]k=x_1y_1=3\times15000=45,000[/tex]
or [tex]k=x_2y_2=5\times9000=45,000[/tex] [answer is same in both cases.]
Hence, the constant of proportionality in this inverse variation is 45,000.
help whats the answer !!!
Answer:
[tex]\angle n=69^o[/tex]
which agrees with answer C in your list of possible options.
Step-by-step explanation:
Notice that you have a triangle defined by the three intersecting lines, and for which you know the internal angles, since you can use supplementary angle properties as well as the property of addition of all internal angles of a triangle. Please see attached image.
Notice that the angles noted in green are those that were obtained via supplementary angle calculation, while the angle noted on orange was obtained using the addition of all internal angles of a triangle.
[tex]180^o-131^o=49^o\\180^o-160^o=20^o\\180^o-49^o-20^o=111^o[/tex]
[tex]\angle n[/tex] can then be obtained based on supplementary angles as well;
[tex]\angle n=180^o-111^o=69^o[/tex]
Adam has $15$ of a certain type of rare coin and is interested in knowing how much this collection is worth. He discovers that $5$ of these coins are worth $12$ dollars in total. Assuming that the value of each coin is the same, how many dollars is his entire collection worth?
Answer:
$36 is the correct answer.
Step-by-step explanation:
Given that:
Adam has $15 of a certain type of rare coin.
$5 of this type of rare coins are equivalent to $12.
To find:
The total worth of $15 of rare coins = ?
If value of each coin is same.
Solution:
We are given that value of each coin is same.
So, We can simply use unitary method to find out the total worth of $15 of rare coins.
i.e. we first find out what is the worth of $1 of rare coins and then we find the worth of total required quantity.
Given that
$5 of rare coins are worthy of = $12
$1 of rare coins are worthy of = [tex]\frac{12}{5}[/tex]
$15 of rare coins are worthy of =
[tex]\\\dfrac{12}{5}\times 15\\\Rightarrow \dfrac{12\times 15}{5}\\\Rightarrow 12\times 3\\\Rightarrow \$36[/tex]
[tex]\therefore[/tex] $15 of rare coins are worth of $36.
confused on question in screenshot.
Answer:
The right answer is the second option, 9,747.
Step-by-step explanation:
[tex]EG^2 = DG*FG \\ EG^2 = 5*14 \\ EG = \sqrt{70}[/tex]
Now let's find DE (Pythagorean theorem).
[tex]DE^2 = DG^2+EG^2\\ DE = \sqrt{25+70} \\ DE = \sqrt{95}[/tex]
[tex]\sqrt{95} =9,7467... = 9,747[/tex]