Expressing the binomial coefficients in terms of factorials and simplifying algebraically. we have proved that
[tex]$\left(\begin{array}{l}n \\ r\end{array}\right) = \dfrac{n-r+1}{r} \cdot \left(\begin{array}{c}n \\ r-1\end{array}\right)[/tex]
What is binomial coefficients?The binomial coefficient [tex]\left(\begin{array}{l}n \\ k\end{array}\right)[/tex] is the number of ways of picking k unordered outcomes from n possibilities, also known as a combination or combinatorial number. The symbols [tex]_nC_k[/tex] and [tex]\left(\begin{array}{l}n \\ k\end{array}\right)[/tex] are used to denote a binomial coefficient, and are sometimes read as "n choose k."
[tex]$$In general, $\left(\begin{array}{l}n \\ r\end{array}\right) \neq\left(\begin{array}{c}n \\ r-1\end{array}\right)$To solve (a), simply expand LHS.$$\left(\begin{array}{l}n \\r\end{array}\right)=\frac{n !}{r ! \cdot(n-r) !}=\frac{n !}{r \cdot(r-1) ! \cdot(n-r) !}$$Multiply numerator and denominator by $(n-r+1)$, then,$$\left(\begin{array}{l}n \\r\end{array}\right)=\frac{n-r+1}{r} \cdot \frac{n !}{(r-1) ! \cdot(n-r+1) !}=\frac{n-r+1}{r} \cdot\left(\begin{array}{c}n \\r-1\end{array}\right)$$[/tex]
Thus, Expressing the binomial coefficients in terms of factorials and simplifying algebraically. we have proved that
[tex]$\left(\begin{array}{l}n \\ r\end{array}\right) = \dfrac{n-r+1}{r} \cdot \left(\begin{array}{c}n \\ r-1\end{array}\right)[/tex]
Learn more about binomial coefficient
https://brainly.com/question/14216809
#SPJ4
Full question:
Expressing the binomial coefficients in terms of factorials and simplifying algebraically, show that:
(a) [tex]$\left(\begin{array}{l}n \\ r\end{array}\right) = \dfrac{n-r+1}{r} \cdot \left(\begin{array}{c}n \\ r-1\end{array}\right)[/tex]
Which line has a slope of 3/2?
Answer: It's the top right
Step-by-step explanation:
Every time the line hits a point on a line where the x and y values are whole numbers, it rises 3 and goes over 2 to get to the next point.
Describe the y-intercept and end behavior of the following graph:
a
(−2, 0); The graph approaches y = −6 to the right.
b
(0, −5); The graph approaches y = −6 to the right.
c
(−2, 0); The graph decreases to the left.
d
(0, −5); The graph decreases to the left.
Graph the set of ordered pairs (-2, -3), (0, -1), (1, 0), (3, 2), and (4, 4). Determine whether the relationship is a linear function. Explain how you know.
The graph of the ordered pairs is plotted using the x- coordinates and the y-coordinates. As the straight line does not pass through all the points the relationship is not a linear function.
What is a linear function?One variable is directly proportionate to the other in a linear connection, which is a sort of connection between two variables. To put it another way, one variable rises or falls linearly as the other one rises or falls, correspondingly. A line graph, in which the rate of progression is constant, is a frequent graphic depiction of a linear connection. Numerous branches of research, such as physics, psychology, and economics, utilize linear correlations.
The graph of the ordered pairs is plotted using the x- coordinates and the y-coordinates.
When the points are connected using a straight line, the line does not pass through the last point (4, 4). Thus, the ordered pairs do not represent a linear function. This can be determined using the graph, and the points through with the straight line passes.
As the straight line does not pass through all the points the relationship is not a linear function.
Learn more about linear function here:
https://brainly.com/question/20286983
#SPJ1
A single conservative force acting on a particle varies as ? (~Ax + Bx ); N, where A and B are constants and X is in meters. Accurately round coefficients to three significant figures_ (a) Calculate the potential energy function U(x) associated with this force, taking U = 0 at x = 0. (Use A, B, and x as appropriate:) U = Ax2 Bx' (b) Find the change in potential energy and change in kinetic energy as the particle moves from x = 1.80 m to x = 3.40 m.
The potential energy of the system to the conservative force acting on the particle is [tex]U=\frac{Ax^2}{2} -\frac{Bx^2}{2}[/tex]
(a) The potential energy of the system to the conservative force acting on the particle, with Ui=0:
U=Uf−Ui=Uf−0
[tex]U=-\int\limits^x_0 {-Ax+Bx} \, dx \\\\U=\int\limits^x_0 {A\frac{x}{2}+B\frac{x}{2} } \, dx \\\\U=A\frac{x^2}{2} -B\frac{x^2}{2} \\\\[/tex]
(b) From (a), U(1.80m)=2A–2.67B, and U(3.40m)=4.5A–9B.
ΔU=(4.5A−9B)−(2A−2.67B)
ΔU=2.5A−6.33B
If we consider the particle alone as a system, the change in its kinetic energy is the work done by the force on the particle: W=ΔK.
For the entire system of which this Particle is a member, this work is internal work and equal to the negative of the change in potential energy of the system:
ΔK=−ΔU
ΔK=−2.5A+6.33B
To know more about Potential energy force:
https://brainly.com/question/18524724
#SPJ4
The Wall Street Journal reported that 33% of taxpayers with adjusted gross incomes between $30,000 and $60,000 itemized
deductions on their federal income tax return. The mean amount of deductions for this population of taxpayers was $16,562.
Assume that the standard deviation is a $2167. Use z-table.
a. What is the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample
mean within $157 of the population mean for each of the following sample sizes: 30, 50, 100, and 400? Round your answers to
four decimals.
n = 30
n = 50
n = 100
n = 400
b. What is the advantage of a larger sample size when attempting to estimate the population mean? Round your answers to four
decimals.
A larger sample increases
for a
the probability that the sample mean will be within a specified distance of the population
mean. In this instance, the probability of being within 157 of μ ranges from
for a sample of size 30 to
sample of size 400.
A. The probability that a sample of taxpayers from this income group are:
n = 30: 0.8159
n = 50: 0.8796
n = 100: 0.9332
n = 400: 0.9984
B. Advantages of a larger sample size are:
it increases precision
reliability of estimate of the population mean
standard error of the mean decreases
How do we determine the probabilities?Using the z-score below:
For a sample size of 30, the z-score is 1.28.
For a sample size of 50, the z-score is 1.64.
For a sample size of 100, the z-score is 2.33.
For a sample size of 400, the z-score is 3.29.
a. The probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $157 of the population mean for each of the following sample sizes:
n = 30: 0.8159
n = 50: 0.8796
n = 100: 0.9332
n = 400: 0.9984
b. The advantage of a larger sample size when attempting to estimate the population mean is that it increases the precision and accuracy of the estimate. As the sample size increases, the sample mean becomes a more reliable estimate of the population mean, and the standard error of the mean decreases.
In this case, as the sample size increases from 30 to 400, the probability of the sample mean being within 157 of the population mean increases from 0.8159 to 0.9984.
learn more about population mean: https://brainly.com/question/29441200
#SPJ1
each question has a proposition r that is a conditional statement. truth values are also given for the individual propositions contained in that conditional statement. indicate whether the conditional statement r is true or false.
Answer: The truth value of a conditional statement can be determined by using the truth table for the conditional operator (->). The truth table for the conditional operator is as follows:
p q p -> q
T T T
T F F
F T T
F F T
To determine the truth value of a conditional statement r, you need to know the truth values of the individual propositions contained in r. Once you have the truth values of the individual propositions, you can use the truth table to determine the truth value of the entire conditional statement. If the conditional statement is true, then it is represented by "T", otherwise it is "F".
Step-by-step explanation:
The numbers of beads on 500 handcrafted bead necklaces follow a normal distribution whose mean is 24 beads and standard deviation is 4 beads. Which sentence most closely summarizes the data?
About 80 necklaces have more than 28 beads. Then the correct option is C.
What is a normal distribution?The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.
The numbers of beads on 500 handcrafted bead necklaces follow a normal distribution whose mean is 24 beads and the standard deviation is 4 beads.
P(x > 28) = P(x - 24 / 4 > 28 - 24 / 4)
P(x > 28) = P(x - 24 / 4 > 1)
P(x > 28) = 1 - ∅1
P(x > 28) = 1 - 0.8413
P(x > 28) = 0.1587
Multiply both sides by 500, then we have
500 P(x > 28) = 0.1587 × 500
500 P(x > 28) = 79.35
500 P(x > 28) ≈ 80
About 80 necklaces have more than 28 beads. Then the correct option is C.
More about the normal distribution link is given below.
https://brainly.com/question/12421652
#SPJ1
The missing options are given below.
A. About 24 devices have more than 28 beads.
B. About 48 necklaces have more than 28 beads.
C. About 80 necklaces have more than 28 beads.
D. About 96 necklaces have more than 28 beads.
Helen is a kickboxing instructor who will be teaching classes at a local gym. To get certified as an instructor, she spent a total of $90. Helen will be earning a base salary of $55 per month from the gym, plus an additional $5 for every class she teaches. If Helen teaches a certain number of classes during her first month as an instructor, she will earn back the amount she spent on certification. How many classes will that take? How much will Helen's expenses and earnings be?
To earn back the amount Helen spent on certification, she would need to earn $90. Since her base salary is $55 per month, she would need to teach an additional $90 - $55 = $35 in classes. Since she earns $5 per class, she would need to teach $35 / $5 = 7 classes.
So, Helen will need to teach 7 classes to earn back the amount she spent on certification.
Her total earning for teaching 7 classes would be $55 (base salary) + $5 (per class) * 7 (classes) = $110
Therefore Helen's expenses and earning would be $90 (certification cost) and $110 (earning) respectively.
how to decompose 1 3/4
Answer: 1 3/4 = 3/4 + 3/4 + 1/4, or 1/4+ 1/4+ 1/4+ 1/4+ 1/4+ 1/4+ 1/4
Step-by-step explanation:
let w(x, y) mean that student x has visited website y, where the domain for x consists of all students in your school and the domain for y consists of all websites. ex- press each of these statements by a simple english sentence.
Student A has visited Website B: w(A,B).
This statement can be expressed in English as: "Student A has visited Website B." The formula for this statement is w(x, y), where x is the student, and y is the website. To calculate this statement, we would substitute A for x, and B for y, resulting in w(A, B). This tells us that Student A has visited Website B., we can use the formula w(x,y) = x * y, where x is the total number of students in the school and y is the total number of websites. For instance, if there are 100 students and 10 websites, then the total number of visits would be 100 * 10, or 1000 visits.
The statement "Student A has visited Website B" can be expressed in the formula w(x, y), where x is the student, and y is the website. To calculate this statement, we would substitute A for x, and B for y, resulting in w(A, B), which tells us that Student A has visited Website B.
Learn more about total number here:
https://brainly.com/question/14993202
#SPJ4
Two investments totaling $64,500 produce an annual income of $3270. One investment yields 8% per year, while the other yields 2% per year. How much is invested at each rate?
Answer:
The amount invested at 8% is 64,500-32,000 = 32,500
Step-by-step explanation:
one investment: 3%, amount: x
the other: 8%, amount: 64,500-x because x is invested at 3%
0.03x+0.08(64,500-x) = 3,560
0.03x+5,160-0.08x = 3,560
-0.05x = -1,600 divide both sides by 0.05 and remember that -/- = +
x = 32,000 This is the amount invested at 3%
The amount invested at 8% is 64,500-32,000 = 32,500
The diagram shows four angles round a point.
a Write an inequality for x.
b Solve the inequality.
c Explain why the angle labelled xº cannot be a right angle.
An inequality for x considering the figure is written as
4x + 30 < 360the value of x is 82.5
x cannot be right angle because it will be against the rule of angle in a point is 360 degrees
How to write the inequality for xThe inequality that represents the figure in terms of x is written using the knowledge that angles in a point is 360 degrees
x + 2x + x + 30 < 360
adding like terms
4x + 30 < 360
solving for x
4x < 360 - 30
4x < 330
x < 82.5
Learn more about angle in a point at:
https://brainly.com/question/25716982
#SPJ1
connor takes 7/8 of the cards from a deck, ethan took 1/6 of the cards from the same deck. how much more of the deck did connor take than ethan?
0.708 more of the deck did connor take than ethan.
What is Subtraction?Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.
here, we have,
connor takes 7/8 of the cards from a deck,
ethan took 1/6 of the cards from the same deck.
i.e. difference of them = 7/8 - 1/6
=0.708
Hence, 0.708 more of the deck did connor take than ethan.
To learn more on subtraction click:
brainly.com/question/2346316
#SPJ1
I don’t understand this help?
Answer:
the first expression i think is the line going downwards
and the second is the line going upwards
Step-by-step explanation:
i think sorry if it wrong
hope the annotating will help you! If this is not the thing you want let me know so that I can edit the way the question actually is...
There are 35 offices in a building and each office has 14 phones. The phones are delivers in boxes of 15. How many boxes are needed? tysm if u answer this helps alot <33
Answer:
33
Step-by-step explanation:
35*14/15
490/15
32.7
rounded up to 33 boxes
Answer:
32 Boxes
Step-by-step explanation:
Total Phones = 35 × 14 = 490
15 phones per 1 box
therefore = 490 ÷ 15 = 32.67
Answer is 32 Boxes
an open rectangular box with volume 2 m3 has a square base. express the surface area of the box as a function of the length of a side of the base and its domain
The provided rectangular box's surface area as a function of the base's side length is S(a) = a² + 8/a.
What is the surface area?A solid object's surface area is a measurement of the overall space that the object's surface takes up.
In comparison to the definition of arc length for one-dimensional curves or the definition of surface area for polyhedra (i.e., objects with flat polygonal faces), where the surface area is the sum of the areas of its faces, the mathematical definition of surface area in the presence of curved surfaces is significantly more complex:
Let a be the base's side length and h be the box's height. We are aware that the formula: can be used to calculate the volume of a rectangular box.
V = length * Width * Height
Since the base of this particular box is square,
l = a
w = a
h = h
Now, if we plug these values into the volume formula, we'll get:
2 = a*a*a
2 =a²h
h = 2/a²
Since the surface area up until this point will depend on only two variables, the objective was to minimize the number of variables.
We had to calculate h in terms of a because we wanted to make it a function of a.
We may now apply these to the box's surface area.
Given that this is an open rectangular box, one of the bases in the formula must be removed.
[tex]\begin{aligned}S & =2(b h+h l)+l b \\S & =2(a h+h(a))+a(a) \\S & =2(2 a h)+a^2 \\S & =a^2+4 a h \\S(a) & =a^2+4 a\left(\frac{2}{a^2}\right) \\S(a) & =a^2+\frac{8}{a}\end{aligned}[/tex]
Therefore, the provided rectangular box's surface area as a function of the base's side length is S(a) = a² + 8/a.
Know more about the surface area here:
https://brainly.com/question/16519513
#SPJ4
What equation does this set of algebra tiles represent? x 1 1 1 1 1 1 1 = 1 1 1 1 1 1 1 1 1 1 1 1 1 Combine like terms on each side of the equation. For example, write 3 instead of 1 + 1 + 1. Like u don’t understand it at all can anyone help meeeeeeee””””””
The required solution of the given algebraic expression is x = 6.
What is an algebraic expression?The algebraic expression consists of constants and variables using mathematical operators. eg x + y + z, or y = x + z etc.
Here,
Given an algebraic expression,
x + 1 +1 +1 +1 +1 +1 +1 = 1 +1 +1 +1 +1 +1 +1 + 1 +1 +1 +1 +1 +1
Combining like terms on each side of the equation, we get,
According to the question
x + 7 = 13
x = 6
Thus, the required solution of the given algebraic expression is x = 6.
Learn more about algebraic expression here:
https://brainly.com/question/953809
#SPJ1
Answer:
x + 7 = 13
Step-by-step explanation:
(in case you also need it) x = 6
x² -81 = 0 please help me
[tex] \bold{x_{1}=+9 \: or \: \: x_{2}=-9}[/tex]
Step by step explanation:This question is very simple because it asks us to solve the equation using square roots. We don't need to find any important information as this problem is quite simple. We just need to take into account some rules for moving terms from one member to another and we will get our answer.
Given the equation:
[tex] \bold{{x}^{2} - 81 = 0}[/tex]
Move -81−81 to the other member, this subtraction happens by doing the opposite operation, that is, it happens by adding.
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\bold{{x}^{2} = 81}[/tex]
We add square root to remove the exponent.
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\bold{{ {x}} = \sqrt{81}}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{x = ±9}[/tex]
∴ The solutions we have for this equation are both 9 and -9. And if we want to check our results, we can plug in the values into x and we'll see that both 9 and -9 are values that satisfy the equation, since negatives don't matter when we're squaring numbers.
Answer:
x = 9
Step-by-step explanation:
x² -81 = 0 please help me
x² - 81 = 0
x² = 81
x = √81
x = 9
-----------------------------
check9² = 81
81 = 81
the answer is good
the present age of Neha is 4 times the age of a son for gives ago if her son is 14 years ago find the present age of Neha.
Answer:
I didn't understand the question
Step-by-step explanation:
I think u have written wrong question..
ILL GIVE BRAINLY Drag and drop the constant of proportionality into the box to match the table.
If the table is not proportional, drag and drop "not proportional" into the box.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
x 0 2 4 6
y 0 3 6 9
Answer: 2/3
Step-by-step explanation: you are looking for the constant of proportionality. We find this with the following formula: K = Y/X
Question 10 of 15
How many solutions does 2 + 7x= 4x+3+3x-8 have?
OA. Two solutions
B. Infinitely many solutions
OC. No solutions
OD. One solution
Answer:
Step-by-step explanation: (Do not read this if it is a test)
Hello! 2 + 7x = 4x + 3 + 3x - 8. How you first want to do this is to solve for x. 7x + 2 = 4x + 3 + 3x - 8. Simplify the like terms. 7x + 2 = 4x + 3x + 3 - 8 is also equal to 7x + 2 = 7x - 5. Subtract 2 from both sides. 7x = 7x - 7. Divide both sides by 7. 7x/7 = 7x/7 - 7/7. The answer is x = x - 1. There is no solution because x cannot equal x minus 1. An example of this is 3 cannot equal 3 - 1 or 2. 3 does not equal 2. The answer is C.
Answer:The answer is C.
Step-by-step explanation:Hello! 2 + 7x = 4x + 3 + 3x - 8. How you first want to do this is to solve for x. 7x + 2 = 4x + 3 + 3x - 8. Simplify the like terms. 7x + 2 = 4x + 3x + 3 - 8 is also equal to 7x + 2 = 7x - 5. Subtract 2 from both sides. 7x = 7x - 7. Divide both sides by 7. 7x/7 = 7x/7 - 7/7. The answer is x = x - 1. There is no solution because x cannot equal x minus 1. An example of this is 3 cannot equal 3 - 1 or 2. 3 does not equal 2.
The following list gives the number of pets for each of 12 students.
0,0,4,4,3,3,0, 2, 4, 3, 4, 1
Find the modes of this data set.
If there is more than one mode, write them separated by commas.
If there is no mode, click on "No mode."
The mode in data set of 12 students that gives the number of pets is 4, 3,0 as these number has frequently many times .
What does data analytics mean by mode?The mode is the value that occurs the most frequently in a data set when it is unique. Like the median and mean, it can be used as a measure of central tendency. However, there may be multiple modes or none at all at times. When all observed values appear in a data set the same number of times, there is no mode.
How does it work?The value that appears most frequently in a data set is the mode. One mode, multiple modes, or none at all can be present in a data set. The mean, or the set's average, and the median, or the set's middle value, are two other common measures of central tendency.
Learn more about Mode :
brainly.com/question/14532771
#SPJ1
GET 40 POINTS TO ANSWER THIS MATH QUESTION! QUICK I HAVE TILL THIS MONDAY!
The slope-intercept form of the equation is y = (-5/3)x + 19
Her set-up time decrease by 5/3 hours/day
How to write the equation of a line in slope-intercept form?The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system
(a) The slope-intercept form of the equation of a line is y = mx+b,
where m is the slope (rate) and b is the y-intercept (starting point)
Let y be the set up time (hours) and x be the time (days)
m = (y₂-y₁)/(x₂-x₁)
where (x, y) are the coordinate of points on the line
From the graph: x₁ =3, y₁ = 14 and x₂ = 6, y₂ = 9
m = (9-14)/(6-3) = -5/3
y = mx + c
14 = (-5/3)×3 + c
14 = -5 + c
c = 14 + 5
c = 19
Thus, the equation is y = (-5/3)x + 19
(b) At day 0, x = 0:
y = (-5/3)x + 19
y = (-5/3)(0) + 19
y = 19 hours
The slope is decrease rate. Thus, her set-up time decrease by 5/3 hours/day
Learn more about equation of a line on:
brainly.com/question/12626026
#SPJ1
Given quad QRST with coordinates Q(0, 0), R(2, 6), S(6, 6), and T(8, 0).
What is the best name for quad QRST?
Square
Rectangle
Trapezoid
Kite
The best name for quadrilateral QRST with coordinates Q(0, 0), R(2, 6), S(6, 6), and T(8, 0) include the following: C. Trapezoid.
What are the types of quadrilateral?In Geometry, there are different types of quadrilateral and these include the following:
ParallelogramSquaresRectangleRhombusTrapezoidNext, we would use an online graphing calculator to construct (plot) quadrilateral QRST on a cartesian coordinate based on the given vertices. Also, you should enter the value for each vertices of quadrilateral QRST on the x-coordinate and y-coordinate respectively as shown in the table.
By critically observing the graph of quadrilateral QRST, we can reasonably infer and logically deduce that it represents a trapezoid.
Read more on quadrilateral here: brainly.com/question/6561516
#SPJ1
-x-7y=-34 find the value of y when x equals -29
Answer:
y=5/7
Step-by-step explanation:
-7y=-34+29
-7y=-5
y=-5/-7
y=5/7
Answer:
y = 9
Step-by-step explanation:
-x -7y = -34
if x = -29:
-(-29) -7y = -34
+29 - 7y = -34
-7y = -34 - 29
-7y = -63
y = -63/-7
y = 9
Check:
-(-29) - (7*9) = -34
29 - 63 = -34
Using the image below, solve for x. Round to the nearest hundredth (2 decimal places)
X
15°
16
The decimal number will be rounded to the nearest hundredth value as 1.93 to the nearest hundredth.
What about the nearest hundredth?Look at the rightmost place value to see how to round a number to the closest hundredth (the thousandths this time). In the same way, simply eliminate all the digits to the right if the number is four or less. Remove all the digits to the right after adding 1 to the digit in the hundredths position if the number is five or above.
Take into account the hundredths place (9) to convert 1.299 to the nearest tenth, 1.3. To round to the nearest hundredth, consider the thousandths place (9) The tenth would be rounded up in this situation to the nearest whole number, 1.30, which is equal to 1.3.
Cos θ= adj/hyp
Cos 74° = x/7
x = 1.93
To learn more about nearest hundredth refer to:
brainly.com/question/15676189
#SPJ1
A manufacturer is shipping a spherical globe that fits exactly in a cube shaped box. The globe is touching all six sides of the box. If the volume of the box is 2197 in³. What is the volume of the globe?
Hint: while working the problem carry figures at least three decimal places, then round to the nearest cubic inch only on the end.
The volume of the sphereical globe is 1564in³
What is the volume?We know that when we talk about the volume we have to look at the volume of the box. Let us assume that the box in the problem that we have here is a cubic box, it the follows that the volume of the box is obtained from;
6l^3 = 2197in³
Where l is the length of each side in inches
l = ∛ 2197/6
l = 7.2 inches
This is the radius of the spherical globe
Volume of a sphere = 4/3πr^3
V = 4/3 * 3.142 * (7.2)^3
V = 1564in³
Hence 1564in³ is the volume of the globe.
Learn more about volume of the sphere:https://brainly.com/question/21623450
#SPJ1
Can anyone help me solve this question?
Calculate sin 300° − cos 945° + tan(−675°) without using calculator �
Answer:
Step-by-step explanation:
sin 300° = sin (300° - 360°) = sin (-60°) = -sin 60° = -(1/2)
cos 945° = cos (945° - 360°) = cos (585°) = cos (-295°) = -cos 295°
tan (-675°) = -tan (675° - 360°) = -tan 315°
so
sin 300° − cos 945° + tan(−675°) = -(1/2) - (-cos 295°) + (-tan 315°)
It is not a trivial task to simplify the above equations without using a calculator.
= -(1/2) + cos 295° + tan 315°
As we know that cos(x) = cos(360°-x) = -cos(x) and tan(x) = -tan(360°-x) = -tan(x)
= -(1/2) - cos 295° - tan 315°
As we know that cos(295°) = cos(360°-65°) = cos(65°) and tan(315°) = tan(360°-45°) = tan(45°)
= -(1/2) - cos(65°) - tan(45°)
= -(1/2) - 0.4226 - 1
= -0.5 - 0.4226 - 1
= -1.4226
.
the mass of a cylinder of water filled to the 19.65-ml mark was found to be 39.753 g. when a piece of the metal was immersed in the water, the level of the water rose to 20.37 ml and the mass of the cylinder with the metal was found to be____ 41.003 g.
The density of the unknown metal exists 8.9 g/mL.
What is meant by density?The mass of an object divided by its volume is how dense it is. The gram per cubic centimeter (g/cm³) unit of density is frequently used. How much mass is present in a given area is referred to as density. Try to picture a drawer full of socks. Its density is particular. Consider that when you remove a sock, the drawer's density changes. This is due to the socks' shifting mass while the drawer's remaining constant volume.
The definition of density is the mass of a substance per unit volume. The degree to which matter is packed together is fundamentally measured by density. It is a specific physical quality of a specific object. Greek scientist Archimedes is credited with discovering the density principle.
The density (D) is equal to mass (m) divided by volume (V): D = m/V
To find the mass of the object:
m = 156 g - 105.5 g = 50.5 g
To find the volume of the volume:
V = 30.7 mL - 25 mL = 5.7 mL
The density is:
D = m/V = 50.5 g / 5.7 mL = 8.9 g/mL
Therefore, the density exists 8.9 g/mL.
The complete question is:
A graduated cylinder was filled with water to the 25.0 mL mark and weighed. Its mass was 105.5g. An object made of an unknown metal was placed in the cylinder and completely submerged in the water. The water level rose to 30.7 mL. When reweighed, the cylinder, water and metal object had a total mass of 156.0g. Based on these measurement, what is the density of the unknown metal?
To learn more about density refer to:
https://brainly.com/question/1354972
#SPJ4
Given (b - 3)( 3b + 8)(2b + 5) = 0, which factor(s) must equal zero?
Hey there!
Answer:
[tex]b=3,-\frac{8}{3}, -\frac{5}{2}[/tex]
Hope this helps!
