Answers
Related Questions
A bicycle lock has a four-digit code. The possible digits, 0 through 9, cannot be repeated. What is the probability that the lock code will begin with the number 5? . What is the probability that the lock code will not contain the number 0? .
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The first digit is any of {0, 1, 2...,9}, that is 10 possibilities
the second digit is any of the remaining 9, after having picked one.
and so on...
so in total there are 10*9*8*7 = 5040 codes.
a. What is the probability that the lock code will begin with 5?
Lets fix the first number as 5. Then there are 9 possibilities for the second digit, 8 for the third on and 7 for the last digit.
Thus, there are 1*9*8*7=504 codes which start with 5.
so
P(first digit is five)=[tex] \frac{n(first -digit- is- 5)}{n(all-codes)}= \frac{1*9*8*7 }{10*9*8*7 }= \frac{1}{10}=0.1 [/tex]
b. What is the probability that the lock code will not contain the number 0?
from the set {0, 1, 2...., } we exclude 0, and we are left with {1, 2, ...9}
from which we can form in total 9*8*7*6 codes which do not contain 0.
P(codes without 0)=n(codes without 0)/n(all codes)=(9*8*7*6)/(10*9*8*7)=6/10=0.6
Answer:
0.1 ; 0.6
The probability that the lock code will begin with the number 5 is:
0.1The probability that the lock code will not contain the number 0 is:
0.6What is Probability?This refers to the use of permutations to find the possible occurrence of events.
The total number of elements is 10
Hence, the total codes is 5040.
P(five)= n(first number)/n(all codes)= 1/10= 0.1
Next,
P(codes without zero)= n(codes without zero)/n(all codes)
(9*8*7*6)/(10*9*8*7)=6/10=0.6
=0.6
Read more about probability here:
https://brainly.com/question/24756209
$15 represents 20% of the spending money Arie is saving for camp this summer. What is the total amount of money she hopes to take to camp?
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0.20x = 15
x = 15 / 0.20
x = 75 <==
Answer: $75
Step-by-step explanation: i got it right on my quiz
In pentagon ABCDE, angle A= 87, angle B=125, angle C= 63, angle D=169. Find angle E
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m<E = 540 - (87+125+63+169)
m<E = 540 - 444
m<E = 96
answer
m<E = 96
Using the given points, determine the slope.
(0, 32) and (100, 212)
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To find the slope of two given points, subtract the y values, and subtract the x values, or..
[tex] \frac{(y2 - y1)}{(x2 - x1)} [/tex]
[tex] \frac{(212 - 32)}{(100 - 0)} [/tex]
[tex] \frac{180}{100} [/tex]
The answer is 9/5 or 1.8.
Hope this helps! :)
The slope is the change in y divided by the change in x.
or
The slope is the ratio of rise to run.
so:slope = (212-32) / (100-0) = 9/5 = 1.8
Rewrite using standard notation: 2.43 × 104
A: 24,300
B: 2,430
C: 2.43
D: 0.000243
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What is the simplified form of the expression?
5(14 - 2)2 ÷ 2
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[tex] \frac{5(14 - 2)^2}{2} = \frac{5(12)^2}{2}=\frac{5*144}{2}=5*72=360[/tex]
12 times 5 and get 60
2 divided by 2 is 1
so i broke it down for you, you should figure it out from here hope i helped
In rectangle JKLM, angle JML is 3x - 15. Find the value of x.
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Right angles measure up to 90 degrees.
JML is also a right angle which means 3x - 15 is equal to 90
3x - 15 = 90
3x = 105
x = 35
Joey has a full 40 coins consisting of only quarters and nickels if the total value is $5.00 how many of each does joey have.
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0.25q + 0.05n = 5
0.25(40 - n) + 0.05n = 5
10 - 0.25n + 0.05n = 5
-0.25n + 0.05n = 5 - 10
- 0.20n = -5
n = -5 / -0.20
n = 25 <=== 25 nickels
q + n = 40
q + 25 = 40
q = 40 - 25
q = 15 <== 15 quarters
q=number of quarters
40 coins total so
n+q=40
total value is 500 cents
5n+25q=500
divide both sides by 5
n+5q=100
so we gots
n+q=40
n+5q=100
elimination
multily first equation by -1 and add to 2nd equation
-n-q=-40
n+5q=100 +
0n+4q=60
4q=60
divide both sides by 4
q=15
sub back
n+q=40
n+15=40
minus 15 both sides
n=25
25 nickles and 15 quarters
Choose the correct simplification of (5x3 − 5x − 8) + (2x3 + 4x + 2).
Answers
7x^3-x-6
Answer:
7x^3+x+6
Step-by-step explanation:
Its answer choice A on a test.
#27 how do I find x?
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E to F is 6 F to G is x
and overall distance from e to g is 1.6x
so:
6+x = 1.6x
subtract x from each side
6 = 0.6x
now divide both sides by .6
x = 6/0.6 = 10
x = 10
The following is an arithmetic sequence.
-3, 3, -3, 3
true false
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A(n)=a1 + d*(n-1)
So it should increase all the time linearly or decrease...
Answer: False
A country population in 1993 was 94 million. In 1999 it was 99 million. Estimate the population in 2005 using the expoetential growth formula. Round your answer to the nearest million
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The formula is
P=Ae^rt
P 99 million
A 94 million
E constant
R rate of growth?
T time 1,999−1,993=6 years
Solve the formula for r
R=[log (p/A)÷log (e)]÷t
R=(log(99÷93)÷log(e))÷6
R=0.01
the population in 2005
P=Ae^rt
T time 2,005−1,993=12 years
P=93×e^(0.01×12)
P=105 million
Find the surface area of the figure below. Leave answer in terms of π.
A. 1060π in2
B. 1160π in2
C. 1260π in2
D. 1000π in2
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Use SA=2πrh+2πr^2.
Plug in the numbers A=2π*10*40+2*π*10^2.
and you get 3141.59.
divide by Pi and you get 1000
2Pi *r*h + Pi*r^2 = 2Pi*10*40 + 10^2 *Pi
= 800Pi + 100Pi = 900Pi
Cone:
Height = SQRT(26^2 - 10^2) = 24
=2Pi*r*h/3 = 160Pi
Total Surface Area is 1060Pi
The word that best describes two acute angles of a right triangle is:
inductive.
supplementary.
vertical.
complementary.
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So, the angle is the fourth choice, complementary.
Aunt Mary is 6 times as old as Jane. If Aunt Mary is 72 years old, how old is Jane?
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6x =Aunt Mary's age
6x = 72
x = 72/6
x = 12 years [Jane]
Because if Mary is 6 times older than just divide her age by 6. Which is 12.
And you can check like this:
-Jane is 12
-Mary is 6 times that
-so Mary is 72
Zeus Industries bought a computer for $2740. It is expected to depreciate at a rate of 24% per year. What will the value of the computer be in 3 years?
Round to the nearest penny. Do not type the "$" sign in your answer
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A=p (1-r)^t
A ?
P 2740
R 0.24
T 3years
A=2,740×(1−0.24)^(3)
A=2,740×(0.76)^(3)
A=1,202.8 round your answer to get
A=1203
Find the equation of the linear function which passes through the points (-1, 3) and (4, -2). give your answer in y = mx + b form.
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Hello : let
A(-1,3) B(4,-2)
the slope is : (YB - YA)/(XB -XA)
(-2-3)/(4+1) = -1
an equation is : y=ax+b a is a slope
y = -x +b
the line through
point B(4,-2) : -2 = -1(4)+b
b = 2
the equation is : y =-x+2
Does anyone know how to do this problem? Thanks.
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NEED AN ANSWER ASAP
Figure ABCD is a rectangle with point A (−2, 5). What rule would rotate the figure 90° clockwise?
A. (x,y)→(y,−x)
B. (x,y)→(y,x)
C. (x,y)→(−y,x)
D. (x,y)→(−y,−x)
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Answer:
A. [tex](x,y)\rightarrow (y,-x)[/tex]
Step-by-step explanation:
We have been given that figure ABCD is a rectangle with point A (−2, 5). We are asked to choose the rule that would rotate the figure 90° clockwise.
We know that rule of rotating a figure 90 degrees clockwise is: [tex](x,y)\rightarrow (y,-x)[/tex]
Upon looking at our given choices we can see that option A is the correct choice.
After rotating our given point 90 degree clockwise, the coordinates of point A would be:
[tex](-2,5)\rightarrow (5,--2)=(5,2)[/tex]
The survey of study habits and attitudes (ssha) is a psychological test that measures the motivation, attitude, and study habits of college students. scores range from 0 to 200 and follow (approximately) a normal distribution with mean 115 and standard deviation 25. you suspect that incoming freshmen at your school have a mean μ which is different from 115 because they are often excited yet anxious about entering college. to test your suspicion, you decide to test the hypotheses h0: μ = 115 versus ha: μ ≠ 115. you give the ssha to 25 incoming freshmen and find their mean score to be 116.2. what is the value of the test statistic?
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Final answer:
The value of the test statistic in this scenario is 0.24, calculated using the z-score formula based on the provided sample mean, population mean, standard deviation, and sample size.
Explanation:
The value of the test statistic for a hypothesis testing can be calculated using the formula for the z-score, which is (sample mean - population mean) / (standard deviation / √sample size). In this case, given that the sample mean is 116.2, the population mean is 115, the standard deviation is 25, and the sample size is 25 students, the test statistic can be calculated as follows:
(116.2 - 115) / (25 / √25)
This computation yields a z-score of:
(1.2) / (25 / 5)
(1.2) / 5 = 0.24.
Therefore, the value of the test statistic is 0.24.
Find the area of a regular hexagon with a perimeter of 42 feet. Round to the nearest tenth if necessary. Select one: a. 128.1 units2 b. 256.2 units2 c. 42.7 units2 d. 21.35 units2
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Each triangle has base 42/6 = 7 feet
Height of each triangle 7 * sqrt3/2 = 3.5 sqrt3
Area of 1 triangle = 3.5^2 sqrt3
area of hexagon = 6 * 3.5^2 sqrt3 = 73.5 sqrt3 or 127.3 sq feet to nearest tenth
What is the solution to this system of linear equations?
x + y = 4
x − y = 6
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x = 5 when y = -1.
Answer:
x = 5 and y = -1
Step-by-step explanation:
[tex]x + y = 4[/tex]
[tex]x - y = 6[/tex]
To solve for x and y , we use elimination method
In the given equations, the co efficient of y are same with different coefficient
So we add both equations
[tex]x + y = 4[/tex]
[tex]x - y = 6[/tex]
--------------------------------
[tex]2x=10[/tex]
Divide both sides by 2
x= 5
now we plug in x value in first equation
[tex]5 + y = 4[/tex]
Subtract 5 on both sides
y= -1
If two tangent segments to a circle share a common endpoint outside a circle, then the two segments are
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If two tangent segments to a circle share a common endpoint outside a circle, then the two segments are congruent. This is according to the intersection of two tangent theorem. The theorem states that given a circle, if X is any point within outside the circle and if Y and Z are points such that XY and XZ are tangents to the circle, then XY is equal to XZ.
Final answer:
Two tangent segments to a circle that share a common endpoint outside the circle are congruent, meaning they have the same length. This is a fundamental concept in circle geometry, illustrating the unique properties of tangents and their interactions with circles.
Explanation:
If two tangent segments to a circle share a common endpoint outside a circle, then the two segments are congruent. This means the lengths of the two tangent segments from the common external point to their respective points of tangency on the circle are equal. This concept is important in the study of circle geometry, as it helps in understanding relationships between tangents and circles.
A tangent to a circle is a line that touches the circle at exactly one point, ensuring it does not cross the circle at that touchpoint. This property of tangents being congruent when they share an external point is proven using the properties of right triangles and the fact that tangents from a point outside the circle to the circle are perpendicular to the radius at the point of tangency.
An example of this concept in action is if you draw two tangents from a single point outside of the circle to any two points on the circle's boundary, the segments of these tangents from the external point to the points of tangency will have the same length.
a basketball player has already scored 56 points in a game the team record for point a in a game is 72 which equation would allow you to find out how many more points the player needs to tie the record
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Answer: The player needs 16 more points to tie the record.
Step-by-step explanation:
Let the number of points the player needs to tie the record be 'x'.
Number of points that a basketball player has already scored = 56
Number of points a team need for record in a game = 72
According to question, it becomes,
[tex]x+56=72\\\\x=72-56\\\\x=16[/tex]
Hence, the player needs 16 more points to tie the record.
A person is standing exactly 36 ft from a telephone pole. There is a 30 degree angle of elevation from the ground to the top of the pole. What is the height of the pole?
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[tex]tanA = \frac{BC}{AB} \ \ \to \ \\BC = AB * tanA = 36 * \frac{ \sqrt{3} }{3} =12 \sqrt{3} \approx 20.78 \ ft. [/tex]
By using the tangent function in trigonometry, we find that the height of the telephone pole is approximately 20.78 feet. This was calculated using the given angle of elevation and the distance from the pole.
To find the height of the telephone pole, we can use trigonometry, specifically the tangent function. The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side.
Given:
Distance from the person to the base of the pole (adjacent side) = 36 ftAngle of elevation from the ground to the top of the pole = 30 degreesWe know that:
tan(30°) = opposite / adjacent
So,
tan(30°) = height / 36 ft
From a trigonometric table or calculator, tan(30°) ≈ 0.5774.
We can set up the equation as:
0.5774 = height / 36 ft
Solving for the height of the pole:
height = 0.5774 * 36 ftheight ≈ 20.78 ftTherefore, the height of the pole is approximately 20.78 feet.
If 7 is added to twice a number and this sum is multiplied by 5 â, the result is the same as if the number is multiplied by 6 and 11 is added to the product. what is theâ number?
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(2x+7)*5 = 6x+11
10x+35 = 6x+11
4x+35 =11
4x=-24
x=-6
the number is -6
If a and b are positive numbers such that 2b=3a, what's the value of ((a+b)/b)? I know you can plug in numbers for this, but i'm interested in solving this algebraically. Thanks.
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In two or more complete sentences describe how to determine the appropriate model for the set of data, (0,2), (2,3), (5,4), (10,5).
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Once you plot the data points, make a trendline. You are given with options. If you want a linear function, then you will have a linear model with a function equation of y = 0.2907x + 2.2643. It has a correlation coefficient of 0.9595. That's a strong correlation already. The R² value tells how good your model fits the data points. If you want to increase the R², a better model would be a quadratic function with the equation, y = -0.0209x²+0.506x+2.0232. As you can see the R² increase even more to 0.9992.
Angle bisectors TX and UY triangle TUV meet at point I. Find all possible values of angleV if angleTIU = 109. As your answer, enter the number of degrees in angleV. If you find more than one possibility, list the possible values in increasing order, separated by commas.
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let m(VTI)= m(ITU)=a and let m(VUI)= m(IUT)=b
Then, in triangle TUV:
2a+2b+c=180°
2(a+b)+c=180°
c=180°-2(a+b)
In triangle TUI:
a+b+109°=180°
a+b=180°-109°=71°
substitute in c=180°-2(a+b):
c=180°-2(a+b)=180°-2*71°=180°-142°=38°
10 POINTS AND BRAINLIST ANSWER TO FIRST CORRECT ANSWER
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