The number of possible choices for a 4-digit PIN where the digits can't repeat is 5040, coming from the product of the choices per position: 10 choices for the first digit, 9 for the second, 8 for the third, and 7 for the fourth.
Explanation:The subject of this question is combinatorics, a branch of mathematics that focuses on the counting and arrangement of objects. We want to find out the number of possible choices for a 4-digit PIN, where the same digit can't repeat. In this situation, at the first position, we have 10 choices (from 0 to 9). However, once we pick one number, it can't be repeated, so in the second, third and fourth positions, we have 9, 8, and 7 choices respectively.
So, we multiply the choices together to come up with 5040 (10*9*8*7) possible choices for a 4-digit PIN where the same digit can't be repeated. This method of counting is generally known as the multiplication principle in combinatorics.
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A parallelogram has an area of 108 square centimeters. If the base measures 18 centimeters, what is the height?
The height of the parallelogram is 6cm.
What is Area?Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. The area of a plane figure is the area that its perimeter encloses. The quantity of unit squares that cover a closed figure's surface is its area.
We have,
Area of parallelogram = 108 square cm
Base = 18 cm
So, Area of parallelogram
108 = base x height
108 = 18 x height
Height= 108/ 18
Height = 6 cm
Thus, the height is 6 cm.
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In Mark's class, there are 15 students with brown hair, 3 students with blonde hair, and 5 students with black hair. What is the ratio of students with brown hair to students with black hair?
Answer: 3 : 1
Step-by-step explanation:
We know that the ratio of A to B is given by :-
[tex]\dfrac{A}{B}[/tex] or A : B .
Given : Number of students having brown hair = 15
Number of students having black hair = 5
Then , the ratio of students with brown hair to students with black hair will be :-
[tex]=\dfrac{\text{No. of students with brown hair}}{\text{No. of students with black hair}}\\\\=\dfrac{15}{5}=\dfrac{3}{1}[/tex]
Hence, the ratio of students with brown hair to students with black hair = 3 : 1.
Answer:
3 to 1
Step-by-step explanation:
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Find the missing measures for the rectangle.
l = _?_
w = 2 cm
A = _?_
P = 25 cm
12.5 cm; 21 cm2
10.5 cm; 21 cm2
12.5 cm; 25 cm2
10.5 cm; 25 cm2
Which expression is equivalent to to the equivalent -1/2(-3/2x+6x+1)-3x
Answer:
Step-by-step explanation:
Bonjour
Which expression is equivalent to the equivalent -1/2(-3/2x+6x+1)-3x
= 3/4 x - 3x - 1/2 - 3x
= 3/4 x - 24/4 x - 1/2
= -21/4 x - 1/2
Melinda needs 6 gallons of punch for her party. the grocery only sells quarts of punch. how many quarts will she need?
Chen can jump rope 60 times a minute at that rate how many jumps can he make in 9 minutes
A rock is dropped into a water well and it travels approximately 16t2 in t seconds. If the splash is heard 3.5 seconds later and the speed of sound is 1087 feet/second, what is the height of the well?
Which expression is equivalent to −1/4x + 1/2 ?
−1/4 (−x + 1/2)
1/4 (−x + 1/2)
−1/4 (x + 2)
1/4 (−x +2)
A letter grade of a B+ average in a regular class counts for how many points?
Answer:
3.33
Step-by-step explanation:
Jason and Donny painted a room and received $300. To complete the painting job Jason spent 4 hours and 25 minutes and Donny spent 2 hours and 15 minutes. If they split the $300 in proportion to the time each spent painting, how much did Donny receive?
Donny spent 2.25 hours painting, while Jason spent 4.4167 hours. The total time spent was 6.6667 hours, and Donny's percentage of this time was approximately 33.75%. Therefore, Donny received $101.25 of the $300 payment.
To determine how much Donny received from the $300 for the painting job, we first need to calculate the total amount of time Jason and Donny spent painting, then divide the total earnings based on the proportion of time spent. Jason spent 4 hours and 25 minutes, which is equivalent to 4.4167 hours (4 hours and 25 minutes / 60 minutes). Donny spent 2 hours and 15 minutes, which is equivalent to 2.25 hours (2 hours and 15 minutes / 60 minutes).
The total time spent on the painting job is the sum of Jason's time and Donny's time, which is 4.4167 + 2.25 = 6.6667 hours. The proportion of time Donny spent is 2.25 hours / 6.6667 total hours, which equals approximately 0.3375 (or 33.75%).
Therefore, Donny's share of the $300 is 0.3375 * $300, which equals $101.25. As a result, Donny received $101.25 for his part of the painting job.
please help me find the simple interest.
A prism with a volume of 360yd^3 is scaled down to a volume of 45yd^3. What is the scale factor? Enter your answer, as a decimal or a fraction in simplest form, in the box.
Sketch the region bounded by the curves y=3x3, x+y=4, and y=0. Find the coordinates of the centroid.
To sketch the region, find the intersection points and use them to form a triangle. The centroid is found by taking the average of the x and y values of the vertices.
Explanation:To sketch the region bounded by the curves y=3x^3, x+y=4, and y=0, we first need to find the x-coordinates of the points where the curves intersect. Setting the equations equal to each other, we get 3x^3 + x = 4. Solving for x, we find x = 1. The region bounded by the curves is a triangle with the vertices (0,0), (1,0), and (1,3).
To find the coordinates of the centroid, we first find the x-coordinate by taking the average of the x-values of the vertices: (0 + 1 + 1)/3 = 2/3. Next, we find the y-coordinate by taking the average of the y-values of the vertices: (0 + 0 + 3)/3 = 1. So, the coordinates of the centroid are (2/3, 1).
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if a circle has a radius of 12 inches what is the arc length inside the interior angle 90 degrees
Ferdinand wrote a check for $96 to pay his monthly cable bill, but when balancing his checkbook, he accidentally recorded it as a credit rather than as a debit. How will his check register compare to his monthly bank statement when he receives it?
Answer:
$192 is over in his check-register.
Step-by-step explanation:
Ferdinand wrote a check to pay his monthly cable bill = $96.00
He accidentally recorded it as a credit in his check register rather than as a debit.
When he receives his bank statement he found his bank statement balance is less than his check register, he should compare it by debiting twice of the cable bill from balance of his check register.
96 × 2 = $192
Ferdinand would compare his check register to his monthly bank statement by subtracting $192 form his balance of check register.
if cos28 = x/4, find x(3sf)
The value of x when cos(28°) = x/4 is found by solving the equation, leading to x = 3.53 to three significant figures. This involves basic trigonometry and arithmetic operations.
Explanation:If cos(28°) = x/4, we are asked to find the value of x to three significant figures. This type of problem involves trigonometry, a branch of mathematics that deals with the relationships between the sides and angles of triangles. To solve for x, we use the equation given and manipulate it to isolate x.
Given that cos(28°) = x/4, we can find x by multiplying both sides of the equation by 4:
x = 4 * cos(28°)Using a calculator, cos(28°) approximately equals 0.8829. Therefore, x is equal to 4 * 0.8829, which simplifies to:
x = 3.5316To three significant figures, x = 3.53.
Use the graph of f(x) below to estimate the value of f '(3):
Based on the graph of f(x), the value of f '(3) is approximately 3.
Based on the graph of f(x) below, the value of f '(3) is approximately 3.
graph of f(x) with a tangent line drawn at x=3 and the slope of the tangent line labeled as 3.
To estimate the value of f '(3), we can approximate the slope of the tangent line to the graph at x=3. The slope of the tangent line represents the instantaneous rate of change of the function at that point, which is equal to the derivative of the function at that point.
To approximate the slope of the tangent line, we can choose two points on the line and use the rise-over-run formula. In this case, we can choose the points (2,2) and (4,4), which are two points on the tangent line that are close to x=3. The slope of the tangent line is then:
(4-2)/(4-2) = 2/2 = 1
Therefore, we can estimate that the value of f '(3) is approximately 1.
Note that this is just an estimate, since we are approximating the slope of the tangent line. If we were to calculate the exact derivative of f(x) at x=3, we might get a slightly different answer. However, this estimate is close enough for most practical purposes.
There are 30 dogs at the park. 5/6 of the dogs are large. Which method is a way to find the number of large dogs at the park?
Answer:
Divide 30 by 6 and then multiply the quotient by 5.
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For what value of x is the square of the binomial x+1 twenty greater than the square of the binomial x–3?
A rectangular prism has a length of 20 in a width of 2 in and a height of 3 1/4 in the prism is filled with cubes that have edge lengths of 1/4 in how many cubes are needed ro fill the rectangular prism
Find the zeros of f(x) = 4x 2 + 5x - 21.
The required zeros of the given polynomial equation are x = 7/4 and x = -3.
Zeros of an equation is defined as the value of the independent variable where the equation or function gives zero.
here,
Given expression,
f(x) = 4x² + 5x - 21.
Putting the above expression equal to zero,
4x² + 5x - 21 = 0
Factorizing the above equaiton gives,
(x - 7/4)(x + 3) = 0
Now,
x = 7/4 and x = -3
Thus, the required zeros of the given polynomial equation is x = 7/4 and x = -3.
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The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces. refer to exhibit 6-5. what is the probability that a randomly selected item will weigh more than 10 ounces?
A box of fruit has three times as many nectarines as grapefruit. Together there are 36 pieces of
fruit. How many pieces of each type of fruit are there?
write an equation to repsent this problem
Final answer:
The problem involves forming and solving a linear equation to determine the number of nectarines and grapefruits in a box, where the total count is 36 and the nectarines are three times as many as the grapefruits. By setting up the relationship as 'n = 3g' and 'n + g = 36', we can solve for 'g' and 'n' to find that there are 9 grapefruits and 27 nectarines.
Explanation:
The student's question involves solving a linear equation to find the number of nectarines and grapefruits in a box when given a specific ratio and total. Let's denote the number of grapefruits as 'g' and the number of nectarines as 'n'. According to the problem, there are three times as many nectarines as grapefruit, so we can write this relationship as 'n = 3g'. Also, we know that the total number of fruit is 36, which gives us another equation: 'n + g = 36'.
Now we have a system of two equations:
n = 3gn + g = 36To find the values of 'g' and 'n', we can substitute the first equation into the second one, resulting in '3g + g = 36', which simplifies to '4g = 36'. Dividing both sides by 4 gives us 'g = 9'. Having found the number of grapefruits, we can now determine the number of nectarines by multiplying the number of grapefruits by 3, thus 'n = 3 times 9 = 27'.
So, there are 9 grapefruits and 27 nectarines in the box.
∠1 and ∠2 are a linear pair. m∠1 = x - 29, and m∠2 = x + 61. Find the measure of each angle.
Describe a real- world situation in which there is an additive or multiplicative relationship between two quantities . Make a table that includes at least three pairs of values. Then write an equation that models the relationship between the quantities
Final answer:
An example of a real-world situation with an additive relationship between two quantities is the distance traveled by a car and the time it takes. The equation that models this relationship is Distance = Time x Speed.
Explanation:
An example of a real-world situation with an additive relationship between two quantities is the distance traveled by a car and the time it takes. Let's say that the car travels at a constant speed of 60 miles per hour. We can create a table with three pairs of values:
Time (hours), Distance (miles)
1 60,
2 120,
3 180
In this case, the equation that models the relationship between the time and distance is Distance = Time x Speed. Since the car travels at a constant speed of 60 miles per hour, the equation can be simplified to Distance = 60 x Time.
Draw a number line and mark all described points.
x2=4
Question solved! please dont answer
if (-4,-2) and (2,6) are opposite points on a circle, what is the equation of the circle?
What is 48% of $430.00?
(calculate the percent or value)
I need answers!
On Monday 21 dvd's were checked out at the library. This is 3 less than half the amount of books check out that day. How many books were checked out?
Find two consecutive whole numbers that the square root of 17 lies between.
The square root of 17 is between the integers 4 and 5
In order to know which two whole numbers the square root of 31 fall ib between, we need to get a perfect square that is less than 31 and also greater than 31
The two perfect numbers are 16 and 325
Taking the square root of these numbers;
√16 = √4 *4 = 4
√25 = √5 * 5 = 5
This shows that the square root of 17 is between the integers 5 and 6
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