There are total 56 combination of your locker contains 3 non-repeating digits from the numbers 0-9.
Combinations are mathematical operations that count all possible arrangements of a set of components when the order in which they are selected is irrelevant. Components for combos can be selected in any hierarchy.
Moreover, there are two other kinds of combinations (the specific sequence is not relevant at this time): It's acceptable to repeat phrases like "coins in your pocket" (5,5,5,10,10) In the same way, lottery numbers (2,14,15,27,30,33)
Combinations are mathematical operations that count all possible arrangements of a set of components when the order in which they are selected is irrelevant. Components for combos can be selected in any hierarchy.
Permutations and combinations are compatible.
As the first digit is fixed i.e. 9,
So, there are 2 non-repeating digits left,
Using permutations,
we are left with 8 × 7 = 56 ways.
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Calculate the volume of a prism with:
L = 9 in
W = 1 ¹⁄ ³ in.
H = 4 ²⁄ ³ in.
Select one:
A.
56 in³
B.
52 in³
C.
54 in³
Answer:
The volume of the prism is 54 in³.
This can be calculated by multiplying the length by the width by the height.
Which comes out to 9 in x 1 ¹⁄ ³ in x 4 ²⁄ ³ in = 54 in³.
Holly opened a savings account at a local bank. She deposited $1,300.00 into the account 6 years ago. If the account earns an annual simple interest rate of 6.8%, how much interest has she earned?
Answer:
Interest = $530.4
Step-by-step explanation:
We know:
Interest = Principal x Rate x Time
First, put in the numbers:
Interest = $1,300 x 6.8% x 6 years
Interest = $1,300 x [tex]\frac{6.8}{100}[/tex] x 6 years
Interest = $13 x 6.8 x 6 years
Interest = $88.4 x 6
Interest = $530.4
find the equation of the line using the point-slope formula. write the final equation using the slope-intercept form. (1,2) with a slope of -5/6
Answer: The point-slope formula is given by:
y - y1 = m(x - x1)
where m is the slope of the line and (x1, y1) is a point on the line.
We have a point (1,2) and a slope of -5/6. Substituting these values into the point-slope formula, we get:
y - 2 = (-5/6)(x - 1)
Expanding and rearranging this equation gives:
y - 2 = (-5/6)x + (5/6)
y = (-5/6)x + (5/6) + 2
y = (-5/6)x + (17/6)
This is the equation of the line in slope-intercept form, y = mx + b, where m is the slope (-5/6) and b is the y-intercept (17/6).
Step-by-step explanation:
Problem 7
Remember that base five numbers are in a 1- 5 dots-and-boxes system. What are the place values in the
15 system? Fill in the blanks:
-
25 5 1
1. Draw a dots-and-boxes picture of the number 424five-
2. Draw a dots-and-boxes picture of the number 11 five
3. Use the dots and boxes method to find
424five 11five-
Rewritethedivisionsentence424_\text{five} \div
Answer:
sorrrrrry
Step-by-step explanation:
sorrrrrrŕreeeeeeey
Select the correct answer. Consider functions f and g. The picture shows a one-to-one function diagram. x has values of 1, 2, 3, and 4, and g of x has values of minus 1, minus 2, minus 4, and minus 8. Every x value has a relation in g of x. What is the value of x when (f o g)(x)= -8? A. -4 B. 0 C. 3 D. 4
A ladder 17 feet long is leaning against a wall. The bottom of the ladder is 8 feet from base of the wall. How far up the wall is the top of the ladder?
Round to the nearest tenth if necessary.
ANSWER IN FEET!!!
The top of the ladder is 15 feet up the wall.
What is right-angle triangle?
If one of the triangle's angles is 90 degrees, the triangle is said to be right-angled. The combined angles of the other two are 90 degrees. The triangle's base and perpendicular sides both include the right angle. The longest side of the three sides, known as the hypotenuse, is the third side.
Given that the height of the ladder is 17 feet. The distance between the base of the ladder and the wall is 8 feet.
It forms a right-angle triangle.
The hypotenuse of the triangle is 17 feet and the base is 8 feet.
Apply Pythagorean theorem:
Altitude² = Hypotenouse² - Base²
Altitude² = 17² - 8²
Altitude² = 289 - 64
Altitude² = 225
Take square root on both sides:
Altitude = ± 15
Since height can't be a negative number, Altitude = 15 feet.
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Classifying a Parallelagram
The values are, ∠BCA = 65°, ∠B = 72°, x = 3
Define the term parallelogram?A quadrilateral with two sets of parallel sides is referred to as a parallelogram. As a result, a parallelogram's opposite sides are parallel and congruent in length, and its opposite angles are similarly congruent.
Given that the diagram ABCD is a parallelogram,
So, BC = AD (parallel sides are equal)
2x = 6
x = 3
BC ║ AD and AC is a transversal line,
then, ∠BCA = ∠DAC (alternate interior angle)
∠BCA = 65°
Opposite angles are equal for parallelogram then,
∠B = ∠D
∠B = 72°
Therefore, the values are, ∠BCA = 65°, ∠B = 72°, x = 3
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Ayudaaaaa no sé cuando vaya a venir a revisar estoooolo
huh um intentaría ayudar pero no tiene mucho sentido lo siento
What is the outlier in the set of data below:
12, 8, 15, 45, 7, 13
a
7
b
8
c
15
d
45
Answer:
D
Step-by-step explanation:
60 people plan to attend the dance and each person will eat 2 slices of cake. If each cake contains 8 slices, how many cakes should you order?
Answer: 15 Cakes
Step-by-step explanation:
2 slices per person, and 8 slices in 1 cake means that 4 people can share 1 cake.
So, you would do the amount of people (60) divided by the number of people that can eat 1 cake (4) to end up with ordering 15 cakes
6. The table below displays the distances driven during each 1-hour interval of a 4 hour trip.
A. 235mi
B. 240mi
C. 245mi
D. 250mi
The total distance for the 4 hour trip can be calculated by adding the distances for each hour interval. 55.23 + 64 3/4 + 52 3/10 + 67.89 = 250 mi.
What is distance?Distance is the measurement of how far apart two points are in space. It is an important concept in mathematics, science, engineering, and many other disciplines. Distance can be measured in terms of length, time, speed, and direction. Distance is often measured in units such as meters, kilometers, feet, and miles, but it can also be measured using other units such as light years. Distance is a concept that can be used to describe the physical relationship between two objects, the location of an object relative to another object, the length of a journey, or the amount of time it takes to travel between two points.
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Select the values that make the inequality y/8 ≤ 2. true. Then write an equivalent inequality, in terms of y. (Numbers written in order from least to greatest going across.)
y/8 ≤ 2 is equivalent to y ≤ 16.
What is inequality?Inequality in math is a statement that two expressions or values are not equal. This can be expressed using symbols such as >, <, ≥, or ≤. Inequality problems are used to solve for a variable that is not necessarily equal to a given value. An example of an inequality problem is finding the value of a variable in the equation x > 5. The solution to this problem is all real numbers greater than 5.
This is happening because when we divide both sides of the inequality y/8 by 8, we are essentially dividing both sides of the inequality by the same number. This preserves the order of the numbers and the inequality sign. So, dividing both sides by 8 results in y ≤ 16, which is the same as y/8 ≤ 2.
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Consider the functions f and g.
Which statement is true about these functions ?
The correct statement regarding the average rate of change of the functions f(x) and g(x) on the interval [-2,2] is given as follows:
Over the interval [-2,2], the function f is increasing at a faster rate than function g is decreasing.
How to obtain the average rate of change?The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function. Hence we must identify the change in the output, the change in the input, and then divide then to obtain the average rate of change.
For the function f(x), the numeric values at x = -2 and x = 2 are given as follows:
f(-2) = (-2)³ + 5(-2)² - (-2) = 14.f(2) = (2)³ + 5(2)² - 2 = 26.Hence the rate is of:
(26 - 14)/(2 - (-2)) = 12/4 = 3. -> positive rate -> increasing.
For function g(x), the rate is given as follows:
(-16 - 4)/4 = -5.
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Match the vocabulary terms to the correct definitions.piecewise function
A piecewise function is a function that has different definitions, based on the interval of the input values of the function.
What is a piecewise function?A piecewise function is a mathematical function that is defined by different rules over different intervals or subdomains of its domain. These different rules can take on different forms or expressions, allowing the function to behave differently on different parts of its domain.
Hence one example of a piecewise function is the absolute value function, which is defined as follows, depending on the signal of the input:
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Find the equation of a line that passes through the point (-3,-1) and has a gradient of 2.
Leave your answer in the form
y=mx+c
-1=2(-3)+c
-1=-6+c
-1+6=c
c=5
therefore...
y=2x+5
Step-by-step explanation:
In
help me graph this pls
The frisbee would spend 2.62 seconds in air before touching ground.
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators such as addition, subtraction, exponent, multiplication and division.
Let h represent the height of the frisbee after t seconds.
h = -16t² + 40t + 5
The time the Frisbee is in air is at h = 0, hence:
-16t² + 40t + 5 = 0
t = 2.62 seconds
The frisbee would spend 2.62 seconds in air
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a) Note that given the above function the height of the Frisbee each second it is in the air are:
t=1; h=29 feett=2; h = 21 feett =3; h = -19b) The frisbee lasts t [tex]\approx[/tex] 2.6 (s) in the air.
What is the justification for the above response?Recall that the function given is -16t² + 40t + 5
t=0; and h = 5
a)
Where t is 1
h = -16t² + 40t + 5
h= -16(1)² + 40(1) + 5
h= -16 + 40 + 5
h= 24 + 5
h= 29, thus, where = 1, h = 29
Using a similar sequence above, where t is
t=2; h = 21 feet; and where
t =3; h = -19
b) in this case, we must set h(t) = 0
⇒ -16t² + 40t + 5 = 0
To solve for t in the equation -16t² + 40t + 5 = 0, we can use the quadratic formula:
t = (-b ± √(b² - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation.
In this case, a = -16, b = 40, and c = 5, so substituting these values into the quadratic formula, we get:
t = (-40 ± √(40² - 4(-16)(5))) / 2(-16)
Simplifying:
t = (-40 ± √(1600 + 320)) / (-32)
t = (-40 ± √(1920)) / (-32)
t = (-40 ± 8 √(30)) / (-32)
t = (5/4) ± (√(30)/4)
Thus we have:
t = (5/4) + (√(30)/4) or t = (5/4) - (√(30)/4)
t₁ = 1.25 + (5.477225575051661134569697828008/4) or
t₂ = 1.25 - (5.477225575051661134569697828008/4)
t₁ = 1.25 + 1.369306393762915283642424457002
t₁ [tex]\approx[/tex] 2.6
t₂ = 1.25 - 1.369306393762915283642424457002
t₂ [tex]\approx[/tex] -0.119
Thus the Frisbee lasts approximatley 2.6 seconds in the air.
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What percent of the customers purchased fewer than 6 flowers
Finding the percentage of consumers who bought fewer than six flowers requires figuring out what proportion of the data is below six. [tex]40[/tex] % of customers purchased fewer than 6 flowers.
What is the parameter for calculating percent?Based on the box plot, we can see that the minimum value is 2, and the maximum value is 12. The box plot also shows that the median (50th percentile) is between 6 and 8.
To find the percent of customers who purchased fewer than 6 flowers, we need to determine what percent of the data is below 6.
From the box plot, we can see that the lower quartile (25th percentile) is at 2, and the upper quartile (75th percentile) is at 10.
Therefore, the interquartile range (IQR) is [tex]10 - 2 = 8.[/tex]
To find the percentage of customers who purchased fewer than 6 flowers, we need to find the percentile rank of 6.
Percentile rank = ((value below target) / (total values)) x 100
Percentile rank of [tex]6 = ((2 / 5) \times 100) = 40[/tex]%
Therefore, [tex]40[/tex] % of customers purchased fewer than 6 flowers.
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The given question is incomplete. the complete question is given below.
Rodrigo works at a flower shop. He recorded how many flowers each customer purchased
yesterday. This box plot shows the results.
Flowers purchased
++
2
6
8
10
12
What percent of the customers purchased fewer than 6 flowers?
%
How many 2-digit numbers contain the digit 7 only once
Answer:
18
Step-by-step explanation:
Counting:
07 17 27 37 47 57 67 70 71 72 73 74 75 76 78 79 87 97
notice we can ALSO use variation with no repetition equation with n=9 (numbers from 0 to 10) and p=1 (two digits) but the value can be in the first position or the second position
[tex]\frac{9!}{(9-8)!}[/tex] + [tex]\frac{9!}{(9-8)!}[/tex][tex]=9+9=18[/tex]
Brian is at the grand opening celebration of a supermarket. He spins a wheel with 10 equal-sized slices, as shown below. The wheel has 3 black slices, 3 grey slices, and 4 white slices. When the wheel is spun, the arrow stops on a slice at random. If the arrow stops on the border of two slices, the wheel is spun again. (a) If the arrow stops on a black slice, then Brian wins a gift card. Find the odds against Brian winning a gift card.
The probability against Brian winning a gift card are approximately 3.118 to 1.
What is probability?Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event happening is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in various fields, such as statistics, finance, science, engineering, and gaming, to make predictions and decisions based on uncertain events.
In the given question,
The probability of the arrow stopping on a black slice is 3/10. Therefore, the probability of the arrow stopping on a non-black slice is 7/10.
If the arrow stops on the border of two slices, the wheel is spun again, so Brian has another chance to win. The probability of the arrow stopping on a non-black slice is 7/10, so the probability of the arrow stopping on a black slice on the second spin is 3/7.
To find the odds against Brian winning a gift card, we first find the probability of him not winning a gift card on either spin:
P(not winning) = P(non-black on first spin) + P(black on first spin and non-black on second spin)
P(not winning) = (7/10) + (3/10) × (4/7)
P(not winning) = 0.7571
The probability of not winning is 0.7571, so the odds against winning are:
Odds against winning = P(not winning) / P(winning)
Odds against winning = 0.7571 / 0.2429
Odds against winning = 3.118
Therefore, the odds against Brian winning a gift card are approximately 3.118 to 1.
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What is the ratio of the amount spent on staff salaries to the total budget for the youth programs?
1:10
1:8
1:5
1:4
1:2
Answer:1:2
Step-by-step explanation:
Gasoline costs $0.83/liter and has a density of 900 g/liter. What is the cost of 48.5 kg of gasoline? Round to the nearest cent.
By simplification, the cost of 48.5 kg of gasoline is approximately $0.04.
What is density?
Density is a physical property of matter that describes how much mass is present in a given volume of a substance. It is defined as the amount of mass per unit volume and is usually expressed in kilograms per cubic meter (kg/m³) or grams per cubic centimeter (g/cm³). The formula for density is:
Density = Mass / Volume
First, we need to find the volume of 48.5 kg of gasoline using its density:
Volume = Mass / Density = 48.5 kg / 900 g/L = 0.05389 L
Next, we can find the cost of this volume of gasoline:
Cost = Volume x Price per liter = 0.05389 L x $0.83/L = $0.0448
Rounding this to the nearest cent, we get:
Cost = $0.04
Therefore, the cost of 48.5 kg of gasoline is approximately $0.04.
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6.) Information collected from a random sample of 29 visitors to a civic art fair indicates an average amount of money spent per person (Symbol) of $38.75, with a sample standard deviation (s) of $6.33. Based on that information, develop a 99% confidence interval to provide an estimate of the mean expenditure per person for the entire population of visitors.
We can be 99% confident that the true mean expenditure per person for the entire population of visitors falls between $35.72 and $41.78.
What is the mean expenditure?Mean expenditure per person for the entire population of visitors refers to the average amount of money spent by each person who visited a particular place, calculated across the entire population of visitors. To calculate the mean expenditure per person, you would add up the total amount of money spent by all visitors and divide that by the total number of visitors.
To develop a 99% confidence interval (CI) to provide an estimate of the mean expenditure per person for the entire population of visitors, we can use the following formula:
CI = X ± Zα/2 * (s/√n)
Where:
X = sample mean = $38.75
s = sample standard deviation = $6.33
n = sample size = 29
Zα/2 = critical value from the standard normal distribution for a 99% confidence level, which is 2.576
Plugging in the values, we get:
CI = 38.75 ± 2.576 * (6.33/√29)
CI = 38.75 ± 2.576 * 1.176
CI = 38.75 ± 3.031
CI = [35.72, 41.78]
Therefore, we can be 99% confident that the true mean expenditure per person for the entire population of visitors falls between $35.72 and $41.78.
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classifying parallelograms
The values are, ∠Q = 96°, x = 1, ∠QTR = 47°
Define the term parallelogram?A quadrilateral with two sets of parallel sides is referred to as a parallelogram. As a result, a parallelogram's opposite sides are parallel and congruent in length, and its opposite angles are similarly congruent.
Given that the diagram QRST is a parallelogram then the parallel sides and angles are equal.
So, ∠Q = ∠S (Equal angles)
∠Q = 96°
and, QT = RS (Equal parallel sides)
6x = 6
x = 1
Co-interior angle of figure, RS║QT and ST is a transversal line,
So, ∠RST + ∠STQ = 180°
96° + 37° + ∠QTR = 180° (here ∠STQ = 37° + ∠QTR)
∠QTR = 180° - 133°
∠QTR = 47°
Therefore, The values are, ∠Q = 96°, x = 1, ∠QTR = 47°
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Is y= |x| + 4 a relation or function
Answer: probably a function
Step-by-step explanation:
In triangle ABC, let the angle bisectors be BY and Cz. Given AB = 8, $AY = 6, and CY = 3, find BZ and BC.
Therefore , the solution of the given problem of triangle comes out to be BZ = (8/9) * BC = 40/9 as a result.
Exactly what is a triangle?Due to its two or more extra sections, a trapezoid is a polygon. Its shape is a simple rectangle. Only the three edges A, B, but instead C distinguish a triangle from a regular triangle. Euclidean geometry produces a singular area rather than a cube when the borders are not perfectly collinear. Triangular shapes are defined as having three sides and three angles. Angles are formed by the meeting of a quadrilateral's 3 sides.
Here,
Let D represent the intersection of the angle bisector BY and the side AC, and let E represent the intersection of the angle bisector CZ and the side AB.
=>BC² = AB² + AC² - 2AB * AC * cos(BAC)
However, since BY and CZ are angle bisectors, we can calculate BAC as follows:
=> BC² = 8² + 9² - 2(8)(9)cos[(180° - (ABC + ACB))/2]
If we simplify, we get:
=> BC² = 145 - 144cos[(ABC + ACB)/2]
Using the angle bisector theory once more, we have the following:
=> AD/DC = 8/BC
=> DC = BC(AD/8)
Simplifying and substituting into the Law of Cosines equation yields:
=> BC² = 145 - 144cos[(ABC + ACB)/2]
=> 145 - 144cos[(180° - BAC)/2]
=> 145 - 144cos(B/2)
in which B Equals ABC.
We can now replace the value of BZ that we discovered earlier with:
=> BZ = (8/9) * BC
and solve for BC:
=> BC² = 145 - 144cos(B/2)
=> (9/8)² * (145 - 144cos(B/2)) + (8/9)² * BZ²
Simplifying and substituting BZ results in:
BC² = 25
Since BC is a length, we obtain: by taking the positive square root.
=> BC = 5
=> BZ = (8/9) * BC = 40/9 as a result.
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Employees at a computer store are paid a base salary of $2,000 a month plus an 8% commission on sales over $7,000 for the month. How much must an employee sell a month to make a total of $4,000 for the month?
The employee must sell $32,000 worth of merchandise in the month to make a total of $4,000.
How to calculate the employee must sell a month to make a total of $4,000 for the monthLet's first find out how much commission an employee would earn if they sold $x in a month,
where x is the amount of sales over $7,000.
The commission earned would be 8% of x, or 0.08x.
To earn a total of $4,000 for the month, the employee would need to earn a base salary of $2,000 plus an additional $2,000 in commission.
So we can set up the following equation:
0.08x + 2000 = 4000
Subtracting 2000 from both sides, we get:
0.08x = 2000
Dividing both sides by 0.08, we get:
x = 25000
Therefore, the employee must sell $25,000 in a month to make a total of $4,000 for the month. Note that this is the amount of sales over $7,000, so the total sales for the month would be $25,000 + $7,000 = $32,000.
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The national history museum has collected 45 dinosaurs. George has collected 3/5 of this amount. How many dinosaurs has george collected?
(g3 math)
the total number of dinosaurs: George has collected 27 dinosaurs.
What is multiplication?Multiplication is a mathematical operation that involves combining two or more numbers to find their total or product. It is a way to represent repeated addition. For example, 3 times 4 can be written as 3 x 4, which means adding 3 to itself 4 times to get a total of 12. Multiplication is denoted by the symbol "x" or "·" or "*", and the numbers being multiplied are called factors or multiplicands, while the result is called the product. Multiplication can be done using different methods, such as memorization of multiplication tables, or using algorithms like long multiplication or lattice multiplication. Multiplication is a fundamental operation in mathematics, and it is used in many areas of science, engineering, and economics.
Given by the question.
To find out how many dinosaurs George has collected, we can start by calculating 3/5 of the total number of dinosaurs:
3/5 x 45 = 27
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Use the quadratic formula to find the exact solutions of x2 − 5x − 2 = 0. x equals negative b plus or minus the square root of b squared minus 4 times a times c, all over 2 times a x equals 5 plus or minus the square root of 33, all over 2 x equals negative 5 plus or minus the square root of 33, all over 2 x equals 5 plus or minus the square root of 17, all over 2 x equals negative 5 plus or minus the square root of 17, all over 2
Answer: The correct solution using the quadratic formula is:
x = (-(-5) ± sqrt((-5)^2 - 4(1)(-2))) / (2(1))
Simplifying:
x = (5 ± sqrt(33)) / 2
Therefore, the exact solutions of x^2 - 5x - 2 = 0 are:
x = (5 + sqrt(33)) / 2 or x = (5 - sqrt(33)) / 2
So the final answers are:
x = 2.79 or x = 2.21 (rounded to two decimal places)
Your welcome (:
Answer:
C
Step-by-step explanation:
It was right for me
question is in the picture . please help me
Answer:
C m∠A + m∠B = 180°
Step-by-step explanation:
Because angle A and angle B are inscribed angles on the diameter they are half of 180° which is 90°
When both of these angles are added they equal 180°
What fraction does each person get if 8 friends share 5 apples equally?
Answer:
.625
Step-by-step explanation: calculator