Answer:
1716
Step-by-step explanation:
The first choice would be 1 of 13
The second choice would be 1 of 12 (it can't be the same as the first number since they don't repeat)
The third choice would be 1 of 11 (again, can't use the same number more than once)
That gives you 13*12*11=1716
The number of ways we can choose three different numbers in order for a unique code for this case is 2730.
What is combination?In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter.
here, we have,
We can use combinations for this case,
Total number of distinguishable things is m.
Out of those m things, k things are to be chosen such that their order doesn't matter.
This can be done in total of mCk ways.
If the order matters, then each of those choice of k distinct items would be permuted k! times.
So, total number of choices in that case would be:
mPk = m! / (m - k)!
This is called permutation of k items chosen out of m items (all distinct).
Given that:
The considered lock as a 3 number code
There are 15 numbers available.
None of the number can repeat.
In a lock, the order of the way numbers are arranged matters.
Because of no repetition allowed, we can simulate this situation as:
The number of ways we can choose 3 numbers out of 15 numbers with order = The number of different ways we can choose three different numbers in order for a unique code.
And we have:
The number of ways we can choose 3 numbers out of 15 numbers with order = 15P3 = 2730
Thus, the number of ways we can choose three different numbers in order for a unique code for this case is 2730
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Sean asked 10 of his classmates the amount of their weekly allowance. He recorded the information in this table. $15 $15 $22 $14 $12$24 $16 $25 $15 $15 Match the measures with their values. 13 12 22 15 7 third quartile interquartile range first quartile range
The interquartile range = Third quartile - First quartile = 22 - 15 = 7
The range = 25 - 12 = 13
What is the Interquartile Range (IQR) and Range ofa Data?Range = largest data value - the least data value
Interquartile range = Q3 - Q1
Given the following weekly allowance of Sean's classmates as, 15, 15, 22, 14, 12, 24, 16, 25, 15, 15:
Third quartile (Q3) = 22
First quartile (Q1) = 15
Interquartile range = 22 - 15 = 7
Range = 25 - 12 = 13
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Jose is starting a word-processing business out of his home. He plans to charge $15 per hour. He anticipates his monthly expenses to be $490 for equipment rental, $45 for materials, and $65 for phone usage. What is the minimum number of hours he must work in a month to make a profit of at least $600?
Answer:
80
Step-by-step explanation:
profit = revenue - expenses
revenue = $15 per hour = $15 * number of hours (n) = $15 * n
expenses = $490 + $45 + $65 = $600
we want profit to be 600 or more
15 * n - 600 = profit
profit ≥ 600
15 * n - 600 ≥ 600
add 600 to both sides to isolate the variable and its coefficient
15 * n ≥ 1200
divide both sides by 15 to isolate the variable
n ≥ 80
Jose must therefore work 80 or more hours, for a minimum of 80
What is the length of the missing leg? If necessary, round to the nearest tenth
Answer: 48
Step-by-step explanation:
Which statement about the function is true? the domain of the function is all real numbers less than or equal to −2. the domain of the function is all real numbers less than or equal to 9. the range of the function is all real numbers less than or equal to −2. the range of the function is all real numbers less than or equal to 9.
The statement which is true about the function is the range of the function is all real numbers less than or equal to 9.
What is domain and range of function?
The Domain of a function is the set of all the possible input values which are valid for that function.
Range of a function is the set of all the possible output values which are valid for that function.
The function shown in the graph can be given as,
[tex]f(x)=-x^2-4x+5[/tex]
The one coordinate point of this equation is -2, 9, which is shown in the graph. At the value of x as -2, the value of f(x) is 9,
[tex]f(-2)=-(-2)^2-4(-2)+5\\f(-2)=-4+8+5\\f(-2)=9[/tex]
Here, the input value is -2 and the output value is 9. The domain for this function is all real number, but the range of this function is (-∞,9).
Hence, the statement which is true about the function is the range of the function is all real numbers less than or equal to 9.
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Answer:
its literally D bro on edge
Step-by-step explanation:
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
PLEASE HELP 20 POINTS!
Answer:
Step-by-step explanation:
Which of the following is a geometric series? 0.1 0.3 0.5 0.7 1 3 9 27 19 17 15 13 0.4 0.9 1.5 2.2
Geometric series have the same ratio. The series which is a geometric series is 1, 3, 9, 27.
What is a geometric series?A series of numbers is a geometric series if the quotient of any two consecutive numbers is the same.
A series of numbers is a geometric series if the quotient of any two consecutive numbers is the same.
A.) 0.1 0.3 0.5 0.7
To check if the series is geometric series, find the quotient.
[tex]r_1=\dfrac{0.3}{0.1} = 3\\\\r_2 = \dfrac{0.5}{0.3} = 1.66[/tex]
Since the ratio is different this is not a geometric series.
B.) 1 3 9 27
To check if the series is geometric series, find the quotient.
[tex]r_1=\dfrac{3}{1} = 3\\\\r_2 = \dfrac{9}{3} = 3[/tex]
Since the ratio is the same this is a geometric series.
C.) 19 17 15 13
To check if the series is geometric series, find the quotient.
[tex]r_1=\dfrac{17}{19} = 0.8947\\\\r_2 = \dfrac{15}{17} = 0.8823[/tex]
Since the ratio is different this is not a geometric series.
D.) 0.4 0.9 1.5 2.2
To check if the series is geometric series, find the quotient.
[tex]r_1=\dfrac{0.4}{0.9} = 0.4444\\\\r_2 = \dfrac{0.9}{1.5} = 0.6[/tex]
Since the ratio is different this is not a geometric series.
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Answer:
its b 1 + 3 + 9 + 27
Step-by-step explanation:
Julia had 164 apples. She gave her friend 30 apples.
Answer:
134
Step-by-step explanation:
164 minus 30 equals 134. Julia has 134 apples left after giving her friend 30 of them.
Answer:
if your asking how much she has in all it would be 134
Step-by-step explanation:
Because
164
30-
____
134
1. Find two numbers that...
a. multiply to -40 and add to -6.
b. multiply to -40 and add to 6.
c. multiply to -36 and add to 9.
d. multiply to -36 and add to -5.
If you get stuck, try listing all the factors of the first number.
Answer:
a. +34 b. +46 c. +45 d. +31
Step-by-step explanation: use a number line
what is the slope of a line
(a) where the line crosses at the y-axis
(b) the amount the line rises on the y-axis over the amount it moves horizontally on the x-axis
(c) where the line crosses at the x-axis
(d) where the line begins
Answer:
the answer is (b), because
Step-by-step explanation:
rise over run
Answer:
B
because I
saw someone else say it was b
Step-by-step explanation:
I'm smart
△ACE, B is the midpoint of AC and D is the midpoint of EC.
Answer:
See below
Step-by-step explanation:
[tex]1.\:\:\overline{BD}||\overline{AE}[/tex]
(By Midsegment theorem)
[tex]2.\:\:m\angle 1=48\degree\implies m\angle 4=48\degree [/tex]
([tex]\angle 1\: \&\:\angle 4[/tex] are alternate angles)
[tex]3.\:\:m\angle 3=25\degree\implies m\angle 2=25\degree [/tex]
([tex]\angle 2\: \&\:\angle 3[/tex] are vertical angles)
[tex]4.\:\:\overline {AE}=17\: cm\implies BD = 8.5\: cm [/tex]
(By midsegment theorem: [tex]BD=\frac{1}{2}AE[/tex]
[tex]5.\:\: BD=\frac{1}{2}AE\\\\\implies (3x+10)=\frac{1}{2}\times (12x+2)\\\\\implies 2(3x +10) = 12x+2\\\\\implies 6x +20= 12x+2\\\\\implies 6x - 12x = 2-20\\\\\implies -6x =-18\\\\\implies x =\frac{-18}{-6}\\\\\implies x = 3\\\\\implies \overline{BD}= (3\times 3 + 10)\\\\=(9+10)\\\\\implies \overline{BD}= (9 + 10)\\\\\implies \huge{\purple{\overline{BD}=19}}[/tex]
Translate the point A (-3,4) right 5 up 1
Answer:
(2,5)
Step-by-step explanation:
-3+5=2 and 4+1=5
The diameter of a circle is 14 ft. Find the circumference to the nearest tent
h
circumference = πd
= 3.14 × 14
43.98 ft
hope it helps...!!!
Answer:
44
Step-by-step explanation:
We are given that the diameter is 14 ft.
The radius is half the diameter, so the radius is 7 ft.
Now, the formula for circumference is: 2πr
So: 2 * π * (7) = 43.98
Round: 43.98 >> 44.0
33. At 6 p.m, the temperature at the
North Pole was -19°F. By
midnight
the temperature had dropped
18°, What was the temperature
at
midnight?
A. 1°F
C.-37°F
B.-1°F
D.37°F
Answer:
C.
Step-by-step explanation:
Since you are subtracting a positive from a negative, your absolute value will get greater. With negative numbers, the less they become in value, the higher their absolute value will get. So, since we are subtracting a positive from a negative, we add them together. However, we need to add them as if they were both positive signs.
Once you do this:
19
+18
You should get 37. Since -19 has a greater absolute value than 18, you keep the negative sign and apply it to 37, getting you -37.
Find the missing length of the triangle.
a= in.
Answer:
9 in.
Step-by-step explanation:
a^2 + 5.6^2 = 10.6^2
a^2 + 31.36 = 112.36
Subtract 31.36 from both sides
a^2 = 81
Squart Root both sides
a = 9 inches
Answer:
a = 11.9883 in
Step-by-step explanation:
Sides:
a = 5.6 in
b = 11.9883 in
c = 10.6 in
Angles:
A = 27.8476 °
B = 90 °
C = 62.1524 °
Other:
P = 28.1883 in
s = 14.0942 in
K = 29.68 in2
r = 2.10584 in
R = 5.99416 in
SAS is Side, Angle, Side
Given the size of 2 sides (c and a) and the size of the angle B that is in between those 2 sides, you can calculate the sizes of the remaining 1 side and 2 angles. Use The Law of Cosines to solve the remaining side.
Law of Cosines
If a, b and c are the lengths of the legs of a triangle opposite to the angles A, B and C respectively; then the law of cosines states:
a^2 = c^2 + b^2 - 2bc cos A, solving for cos A, cos A = ( b^2 + c^2 - a^2 ) / 2bc
b^2 = a^2 + c^2 - 2ca cos B, solving for cos B, cos B = ( c^2 + a^2 - b^2 ) / 2ca
c^2 = b^2 + a^2 - 2ab cos C, solving for cos C, cos C = ( a^2 + b^2 - c^2 ) / 2ab
Solving, for example, for an angle, A = cos^-1 [ ( b^2 + c^2 - a^2 ) / 2bc ]
Find the measure of <1
Please answer ASAP!!!!
This is for my Iready and I’m super confused the story problem reads ""Lola rode her bike for 7/10 of an hour on Saturday and 3/5 of an hour on Sunday. How much longer did she ride her bike on Saturday than Sunday?
Which is the equation of a hyperbola with directrices at x = ±2 and foci at (6, 0) and (−6, 0)? x squared over 12 minus y squared over 24 equals 1 x squared over 12 minus y squared over 48 equals 1 y squared over 12 minus x squared over 24 equals 1 y squared over 48 minus x squared over 12 equals 1
The equation of a hyperbola with directrices at x = ±2 and foci at (6, 0) and (−6, 0) is y squared over 48 minus x squared over 12 equals 1.
What is the equation of hyperbola?The equation of the hyperbola is the equation which is used to represent the hyperbola in the algebraic equation form, with the value of center point in the coordinate plane and foci.
The standard form of the equation of the hyperbola can be given as,
[tex]\dfrac{(y-k)^2}{b^2}-\dfrac{(x-h)^2}{a^2}=r^2[/tex]
Here (h,k) is the center of the hyperbola, (b) is the transverse axis, and (a) is the conjugate axis.
The foci of the hyperbola is,
[tex](h,k\pm c)[/tex]
The directrix is,
[tex]y=k\pm \dfrac{a^2}{c}[/tex]
A hyperbola is given with directrices at x = ±2 and foci at (6, 0) and (−6, 0). Thus, the directrix is,
[tex]y=k\pm \dfrac{a^2}{c}\\\pm 2=k\pm \dfrac{a^2}{c}\\\dfrac{a^2}{6}=2\\a^2=12\\[/tex]
It is known that,
[tex]a^2+b^2=c^2\\[/tex]
Put the value of a and c,
[tex](12)+b^2=6^2\\b^2=36-12\\b^2=24[/tex]
The value of center is (0,0). Thus, the equation of hyperbola is,
[tex]\dfrac{(y-0)^2}{24^2}-\dfrac{(x-0)^2}{12^2}=1\\\dfrac{y^2}{24^2}-\dfrac{x^2}{12^2}=1[/tex]
Thus, the equation of a hyperbola with directrices at x = ±2 and foci at (6, 0) and (−6, 0) is y squared over 48 minus x squared over 12 equals 1.
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The area of a parallelogram is given by the formula A=bh. The area of the parallelogram is 85 sq. Units. Find it’s base and height.
Answer:
the height is 5 and the base is 17.
Step-by-step explanation:
X + 1 is the height and 4x + 1 is the base, so we can substitute this into an equation:
( x + 1 ) (4x + 1) = 85
{apply the distributive law}
4x² + x + 4x + 1 =
4x² + 5x + 1 = 85
Take 85 to the other side by -85 each side:
4x² + 5x + 1 - 85 = 85 - 85
4x² + 5x - 84 = 0
{Now we have a quadratic equation}
The roots are either -5.25 or 4. X must be 4 since it must be positive as it is a side length.
Substitute x into the base and height to get the answers.
X + 1 = 4 + 1 = 5
4x + 1 = 16 + 1 = 17
Therefore the height is 5 and the base is 17.
For what value of x does 3 superscript 2 x baseline = 9 superscript 3 x minus 4?
Equations are expressions separated by equal sign. The value of x that make the expression equal is 2
Equation and expressionsGiven the equation expressed as:
3^2x = 9^3x - 4
This can be further simplified as:
3^2x = 3^2(3x-4)
2x = 2(3x - 4)
x = 3x - 4
x - 3x = -4
-2x = -4
x = 2
Hence the value of x that make the expression equal is 2
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Answer: its 2
Step-by-step explanation: just took test on chrome 2022, and got 100%
How many cups of flour would be needed to make all of the cookie recipes that use 2 3/4 cups of flour?
help pls!!!! ASAPPPPPP
Answer:eht sistep 2 and step 4 is the correct answer
Step-by-step explanation:
The table shows the number of men and women who have entered a grocery store. Outcome: Man Woman Frequency: 25 20 What is the experimental probability that the next person to enter the store will be a woman? 3/4, 1/2, 3/7, 4/7
Answer:
1 because I don't know how to do this stuff yet
Drag each pair of rates to the correct location on the table.
Identify the pairs of rates as equivalent or not equivalent
hand
18/3 and 9/1
20/5 and 3/1
36/6 and 6/1
32/4 and 8/1
35/7 and 5/1
100/10 and 5/1
1/8 is in it 3/2 if that is it
I’m very confused please help:)
Answer:
b=20°, c=160°
Step-by-step explanation:
b=20° [vertically opposite angle]
c+b=180° [angle at same line ]
c=180° - 20°
c = 160°
Abby used the law of cosines for trianglekmn to solve for k. k2 = 312 532 – 2(31)(53)cos(37°) triangle k n m is shown. the length of k n is 53, the length of n m is k, and the length of k m is n. law of cosines: a2 = b2 c2 – 2bccos(a) what additional information did abby know that is not shown in the diagram? manglek = 37° and n = 31 manglek = 37° and k = 31 manglen = 37° and n = 31 manglen = 37° and k = 31
Answer:
(A) mK = 37° and n = 31.
Step-by-step explanation:
The following are A of ed.
If you spin the spinner 36 times, what is the best prediction possible for the number of times it will not land on yellow?
The best prediction for the number of times it will not land on yellow would be 29 times.
We have,
Assuming the spinner has an equal probability of landing on each color, The probability of it not landing on yellow is 4/5.
So,
If you spin the spinner 36 times, the expected number of times it will not land on yellow is:
= (4/5) x 36
= 28.8
Since you can't have a fraction of a spin,
= 28
Thus,
The best prediction for the number of times it will not land on yellow would be 29 times.
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A circle is centered at (7,8). The point (11,8) is located on the lip of the circle. Write the equation for this circle.
The center of the circle is (7,8) and the equation of the given circle is (x- 7)^2 + (y - 8)^2 = 16
How to determine the equation of the circle?The given parameters are:
Center (a,b) = (7,8)
Point (x,y) = (11,8)
Calculate the radius (r) using:
[tex]r = \sqrt{(x- a)^2 + (y - b)^2}[/tex]
So, we have:
[tex]r= \sqrt{(11- 7)^2 + (8 - 8)^2}[/tex]
Evaluate the expression
[tex]r = 4[/tex]
The circle equation is then calculated using:
[tex](x- a)^2 + (y - b)^2 =r^2[/tex]
So, we have:
[tex](x- 7)^2 + (y - 8)^2 = 4^2[/tex]
Evaluate the exponent
[tex](x- 7)^2 + (y - 8)^2 = 16[/tex]
Hence, the equation of the given circle is (x- 7)^2 + (y - 8)^2 = 16
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Is 10/12 greater less or equal to 3/8 also it's the same question for 1/7 4/11 and 2/6 5/8
Answer:
10/12 is greater and for the second one, 4/11 is greater and 5/8 is greater
FIND THE SLOPE OF A LINE THAT PASSES THROUGH THE POINT (-3-3) AND (-4-4)
Answer:
m=1
Step-by-step explanation:
y2-y1/x2-x1
-4+3/-4+3
-1/-1
1
only question 5 parts a and b PLEASE HELP!!
Answer:
slope = 3/2
the plant grows 3 centimeters every 2 weeks
Step-by-step explanation: