Answer: 7 handshakes in all.
Step-by-step explanation:
If you and another person have one shake and there are 14 total people in the cabin that means that there will be 7 handshakes in all.
(3xy2x2y−3)2(9xy−3x3y2)−1.
Answer:
-18x square y -+36xy square + 54 xy - 1
Step-by-step explanation:
collect the terms, calculate the product, collect the terms, then distribute
Can someone help explain how i would solve this using the pascals triangle? Like how to convert it into (x + 4)^3 = ax^b+cx^d+ex^f+g
Pascal's triangle is a way of organizing the coefficients in the binomial expansion, [tex](a+b)^n[/tex]:
n = 0 => 1
n = 1 => 1 1
n = 2 => 1 2 1
n = 3 => 1 3 3 1
n = 4 => 1 4 6 4 1
and so on, where each row starts and ends with a 1, and the numbers in the middle are obtained by adding together the two numbers directly above and to the left. These coefficients are then mulitplied by descending powers of a and descending powers of b (or vice versa, because the pattern is symmetric), starting with 0 and going up to n.
In this case, we have
[tex](x+4)^3=1\cdot x^3\cdot4^0+3\cdot x^2\cdot4^1+3\cdot x^1\cdot4^2+1\cdot x^0\cdot4^3[/tex]
Notice how the powers of x and 4 always sum to n = 3.
Simplifying, we get
[tex](x+4)^3=x^3+12x^2+48x+64[/tex]
so that
a = 1
b = 3
c = 12
d = 2
e = 48
f = 1
g = 64
The expression 0.09x+(x−30) models the final price of a bicycle with an instant rebate in a state that charges a sales tax. The tax is on the original price. Which expression represents the amount of tax that is paid on the bicycle?
A. x−30
B. 0.09x
C. 1.09x
D. 0.09x−30
Answer:
B. 0.09x
Step-by-step explanation:
x is the initial price.
0.09x is the 9% sales tax.
-30 is the instant rebate.
A man walks along a straight path at a speed of 3 ft/s. A searchlight is located on the ground 4 ft from the path and is kept focused on the man. At what rate is the searchlight rotating when the man is 3 ft from the point on the path closest to the searchlight
Answer: 0.48 rad/sec
Step-by-step explanation:
dx/dt = 3ft
to find d∅/dt when x = 3
Using the right angled triangle
ΔABC
Now perpendicular (BC) = X FT
Base ( AC) 4 ft
so Hypotenuse(AB) = √ (BC² + AC²) = √ ( x² + 4²) = √ ( x² + 16)
and x/4 = tan∅ ; x = 4tan∅
now we differentiate each side
dx/dt = d/dt(4tan∅) = d/d∅(4tan∅) d∅/dt
⇒ dx/dt = (4sec²∅) d∅/dt = ( 1/4 cos²∅) dx/dt
⇒ d∅/dt = cos²∅/4 × 3 = 3/4 cos²∅
now when x = 3, the length of the beam is
{from our initial equation (AB) = √ (BC² + AC²)}
AB = √(3² + 4²) = √(9 + 16) = 5ft
therefore cos∅ = 4/5
so we substitute in (d∅/dt = ( 1/4 cos²∅) dx/dt)
d∅/dt = 1/4 ( 4/5)² × 3
d∅/dt = 12/15 = 0.48 rad/sec
find the first principle f(x)=1/x
Answer:
see explanation
Step-by-step explanation:
Assuming you require the derivative of f(x) from first principles, then
f' (x) = [tex]lim_{h>0}[/tex] [tex]\frac{f(x+h)-f(x)}{h}[/tex]
= [tex]lim_{h>0}[/tex] [tex]\frac{\frac{1}{(x+h)}-\frac{1}{x} }{h}[/tex]
= [tex]lim_{h>0}[/tex] [tex]\frac{\frac{x-(x+h)}{x(x+h)} }{h}[/tex]
= [tex]lim_{h>0}[/tex] [tex]\frac{\frac{x-x-h}{x(x+h)} }{h}[/tex]
= [tex]lim_{h>0}[/tex] [tex]\frac{-h}{hx(x+h)}[/tex] ← cancel h on numerator/ denominator
= - [tex]\frac{1}{x^2}[/tex]
Use the number line below, where RS=7y+2, ST=5y+7, and RT=14y−3. a. What is the value of y? b. Find RS, ST, and RT.
Answer:
j
Step-by-step explanation:
Points P, Q, and R are shown on the number line. What is the distance between point P and point R?
Answer:
5
Step-by-step explanation:
2.75-(-2.25)=
2.75+2.25=
5
Is a − b equal to b − a?
Answer:
a is a 1 and then you subtraction the b is equal 0
Two adjacent sides of a parallelogram are 6mm and 10mm respectively, and they form an angle measuring 60. Find the area of the parallelogram.
Answer:
51.96 mm² approximately
Step-by-step explanation:
the first thing you should know is that the area of a rectangle is base*height sin of (
the included angle i.e
Arectangle= bh sin90° since all angles of a rectangle are equal then the included angle is 90°
Arectangle= bh sin90° since sin90 is 1 we simply use the equation bh because multiplying bh by one is bh. bearing this in mind , the area of the parallelogram can be calculated as:
Aparallelogram= bh sin of sin of the included angle
Aparallelogram= bh sin of sin of the included angle Aparallelogram=6mm*10mm sin 60°
Aparallelogram= bh sin of sin of the included angle Aparallelogram=6mm*10mm sin 60°Aparallelogram=60mm² * 0.866
Aparallelogram= bh sin of sin of the included angle Aparallelogram=6mm*10mm sin 60°Aparallelogram=60mm² * 0.866Aparallelogram=51.96 mm² approximately
Alex buys a car for $19500 and later sells it at a profit of 5%. At what price did he sell the car?
Answer:
$20,475
Step-by-step explanation:
you multiply 19,500 by 0.05 (19500*0.05) to get $20,475
Hope this helps :)
f (x) = √2X-6
What is f(5)?
Answer:
f(5) = 2
Step-by-step explanation:
Given:
Function f(x) = [tex]\sqrt{2x - 6}[/tex]For x=5 :
f(5) = [tex]\sqrt{2*5 - 6}[/tex] = [tex]\sqrt{4}[/tex] = 2can someone PLEASE help me with these two ill mark them as brainliest!!!!!
Answer:
20
Step-by-step explanation:
A=1/2bh
A=1/2(8×5)
A=1/2(40)
A=20
The CEO of a large corporation asks his Human Resource (HR) director to study absenteeism among its executive-level managers at its head office during the year. A random sample of 30 executive level managers reveals the following: Absenteeism: Sample mean = 7.3 days, Sample standard deviation=6.2 days 18 mid-level managers out of the 30 randomly selected mid-level managers, cite stress as a cause of absence. (a) Construct a 90% confidence intervalestimate for the mean number of absences for mid- level managers during the year.(b) Construct a 98% confidence intervalestimate for the population proportion of mid-level managers who cite stress as a cause of absence. (c) What sample size is needed to have 95% confidence in estimating the population mean absenteeism to within 1.5 days if the population standard deviation is estimated to be 8 days? (d) How many mid-level managers need to be selected to have 99% confidence in estimating population proportion of mid-level managers who cite stress as a cause of absence to within +0.075 if no previous estimate is available?
Answer:
Following are the answer to this question:
Step-by-step explanation:
Given:
n = 30 is the sample size.
The mean [tex]\bar X[/tex] = 7.3 days.
The standard deviation = 6.2 days.
df = n-1
[tex]= 30-1 \\ =29[/tex]
The importance level is [tex]\alpha[/tex] = 0.10
The table value is calculated with a function excel 2010:
[tex]= tinv (\ probility, \ freedom \ level) \\= tinv (0.10,29) \\ =1.699127\\ = t_{al(2x-1)}= 1.699127[/tex]
The method for calculating the trust interval of 90 percent for the true population means is:
Formula:
[tex]\bar X - t_{al 2,x-1} \frac{S}{\sqrt{n}} \leq \mu \leq \bar X+ t_{al 2,x-1} \frac{S}{\sqrt{n}}[/tex]
[tex]=\bar X - t_{0.5, 29} \frac{6.2}{\sqrt{30}} \leq \mu \leq \bar X+ t_{0.5, 29} \frac{6.2}{\sqrt{30}}\\\\=7.3 -1.699127 \frac{6.2}{\sqrt{30}}\leq \mu \leq7.3 +1.699127 \frac{6.2}{\sqrt{30}}\\\\=7.3 -1.699127 (1.13196)\leq \mu \leq7.3 +1.699127 (1.13196) \\\\=5.37 \leq \mu \leq 9.22 \\[/tex]
It can rest assured that the true people needs that middle managers are unavailable from 5,37 to 9,23 during the years.
If you were to open an account that will pay you 3.5% interest with a deposit of $150 so find the following ending amount for each period at the end of 2 years
Answer:
FV= $160.68
Step-by-step explanation:
Giving the following information:
Initial investment= $150
Interest rate= 3.5% compounded annually
Number of periods= 2
To calculate the future value, we need to use the following formula:
FV= PV*(1+i)^n
PV= present value
i= interest rate
n= number of periods
FV= 150*(1.035^2)
FV= $160.68
A spherical bowl of radius r cm is a quarter full when 6 liters of water is poured into it.calculate correct to three significant figures, the diameter of the bowl.
Answer:
The bowl's diameter is 35.8 cm
Step-by-step explanation:
Recall that 1 liter = 1000 cubic cm ad have in mind that in order to get a diameter in cm, we would need to write the volume of the bowl in cubic cm.
if 6 liters is 1/4 of the bowl, then 4 times 6 liters must fill the bowl. That is: the volume of the sphere is 24 liters.
24 liters in cubic cm is: 24000 cubic cm
now, we need to use the formula for the volume of a sphere of radius R:
[tex]Vol=\frac{4}{3} \pi\,R^3\\24000=\frac{4}{3} \pi\,R^3\\R^3=\frac{24000\,(3)}{4\,\pi} \\R=\sqrt[3]{\frac{24000\,(3)}{4\,\pi} } \\R\approx 17.894\,\,cm[/tex]
therefore, the diameter of the bowl is twice this radius value:
[tex]Diameter\approx 17.894\,* 2=35.788\,\,cm[/tex]
this value rounded to 3 significant figures is: 35.8 cm
Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n.
x3 sin(x) dx, n = 8
1) The Trapezoidal Rule
2) The Midpoint Rule
3) Simpson's Rule
Answer:
-1392.09-1744.43-1636.41Step-by-step explanation:
using the given integral
calculate: Δx = (12-0) / 8 = 3/2
Xo = 0, f(x) = [tex]x^3sin(x)[/tex]
X1 = 3/2 , X2 = 3, X3 = 9/2, X4 = 6, X5 = 15/2, X6 = 9, X7 = 21/2, X8 = 12
Inputting the given values into the Trapezoid rule, midpoint rule and Simpson's rule to approximate the given integral with the specified value of n = 8
Manolo has a toy in the shape of a triangle pyramid If x=6" y=8" and z=10", what is the volume of the toy
Answer:480
Step-by-step explanation:
To find volume u need to multiply height * width * length
iven h (t) = t squared + t + 12 andk (t) = StartRoot t minus 1 EndRoot, evaluate (k compose h) (10)
Answer:
11Step-by-step explanation:
Given h(t) = t²+t+ 12 and k(t) = √t-1, we are to find k(k.h)(10)
k{h(t)} = k{ t²+t+ 12}
Since k(t)= √t-1, we will replace the variable t in the function with t²+t+ 12
k(h(t)) = √{(t²+t+ 12)-1}
k(h(t)) = √t²+t+12-1
k(h(t)) = √t²+t+11
Substituting t = 10 into the resulting function;
k(h(10)) = √(10)²+(10)+11
k(h(10)) = √100+10+11
k(h(10)) = √121
k(h(10))= 11
hence the value of (k compose h) (10) is 11
one third divided by eight
Answer:
1/24
Step-by-step explanation:
1/3÷ 8
Copy dot flip
1/3 * 1/8
1/24
Answer:
1/24
Step-by-step explanation:
Divide. Give the quotient and remainder.
746+21
Answer:
well you put a plus sign, but im letting you know I did the division.
Step-by-step explanation:
The answer is 35 remainder 11.
Hope this helped
solve for n+4 + n/6=16
Answer:
n = 10.286 aprox.
Step-by-step explanation:
n+4 + n/6 = 16
n/6 = 16 - 4 - n
n = 6(12-n)
n = 6*12 + 6*-n
n = 72 - 6n
n + 6n = 72
7n = 72
n = 72/7
n = 10.286 aprox.
verify:
10.286 + 4 + (10.286/6) = 16
14.286 + 1.714 = 16
Mark this question Select the following statement that describes non-overlapping events.
A. Jon needs to roll an even number to win. When it's his turn, he rolls a two.
B. Jon wants a face card so he can have a winning hand, and he receives the eight of clubs.
C. Receiving the King of Hearts fulfills Jon's need of getting both a face card and a heart.
D. To win, Jon needs a red card. He receives a Queen of Diamonds.
Answer:
B. Jon wants a face card so he can have a winning hand, and he receives the eight of clubs.
Step-by-step explanation:
non overlapping events are mutually exclusive events meaning that they do not occur together, one occurs and the other doesn't and vice versa. From the example, Jon wants a face card but got eight of clubs, he cannot have a face card and eight of clubs together, one occurs while the other is absent. So if Jon got a face card, he would not have eight of clubs
Jon wants a face card so he can have a winning hand, and he receives the eight of clubs.
Given,
Statements .
Here,
Non overlapping events are mutually exclusive events meaning that they do not occur together, one occurs and the other doesn't and vice versa.
For instance,
Jon wants a face card but got eight of clubs, he cannot have a face card and eight of clubs together, one occurs while the other is absent.
So if Jon got a face card, he would not have eight of clubs .
Thus option B is correct statement .
Know more about mutually exclusive events,
https://brainly.com/question/28565577
#SPJ6
100POINTS!!!!!!!!!!!!!!! Use the table to answer the questions. The values in the table form a(n) ______ sequence. The term values are shown in the ______ row, and the term numbers are shown in the ______ row. This sequence is associated with a(n) ______ function. The domain of the function is the set of time values: __________.
Answer:
arithmeticbottomtoplinear≥ 0Step-by-step explanation:
We observe that the values in the top row are sequential, and that the values in the bottom row have a common difference of 32. That means the sequence is an arithmetic sequence.
__
The values in the table form an arithmetic sequence. The term values are shown in the bottom row, and the term numbers are shown in the top row. This sequence is associated with a linear function. The domain of the function is the set of time values: greater than or equal to zero.
__
Comment on the function
This function seems to be the linear function ...
distance = 32×time - 16
It seems a little odd that the distance associated with time zero is negative. We usually think of distance as a positive value, whereas displacement can be a signed value.
As a rule, time is measured as positive from some reference point (the start of motion, for example). Here, we have no reason to believe that the function is intended to be defined for negative time values.
Answer:
arithmetic
bottom
top
linear
≥ 0
Step-by-step explanation:
carol had 3/4 yard of ribbon .she wanted decorate two picture frames if she uses half the ribbon on each frame how many feet will she use for one frame
Answer:
1.125 feet
Step-by-step explanation:
1 yard = 3 feet
3/4 yard = 2.25 feet
2.25 feet / 2 = 1.125 feet per frame
i hope this helps!
-TheBusinessMan
Evaluate n/6+2when n=12
An instructor of a biology class believes the average final exam score for his biology class was more than 75. Suppose a sample of 25 was taken and the sample mean he observed was 78.48 and a standard deviation of 5 points. What is the value of the test statistic?Report your answer to 2 decimal places.
Answer:
The value for the test statistics = 3.48
Step-by-step explanation:
Given that:
population mean [tex]\mu[/tex] = 75
sample size n = 25
sample mean [tex]\overline x[/tex]= 78.48
standard deviation = 5
The value for the test statistics can be computed by using the formula:
[tex]z = \dfrac{\overline x- \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \dfrac{78.48- 75}{\dfrac{5}{\sqrt{25}}}[/tex]
[tex]z = \dfrac{3.48}{\dfrac{5}{5}}[/tex]
z = 3.48
The value for the test statistics = 3.48
Simplify the expression below.
Answer:
c or b
Step-by-step explanation:
What is 1000 words in 5 minutes rate as a unit rate.
Answer:
200 words per minute
Step-by-step explanation:
1000:5
1000/5 reduced will give you your unit rate.
200 words/minute
If 1000 words were read in 5 minutes, each minute would be 1000 divided by 5 which is 200.
Select all the correct answers.
Which expressions are equivalent to the given expression.
y^-8y^3x^0x^-2
Answer:
[tex]x^{-2}y^{-5}[/tex]
Step-by-step explanation:
The options are not given; however, the question can still be solved
Given
[tex]y^{-8}y^3x^0x^-2[/tex]
Required
Simplify
Start by rewriting the expression
[tex]y^{-8} * y^3 * x^0 * x^{-2}[/tex]
Apply the following laws of indices: [tex]a^x * a^y = a^{x+y}[/tex]
This gives:
[tex]y^{-8+3} * x^{0-2}[/tex]
Evaluate the exponents
[tex]y^{-5} * x^{-2}[/tex]
[tex]x^{-2}y^{-5}[/tex]
Hence, [tex]x^{-2}y^{-5}[/tex] is equivalent to [tex]y^{-8}y^3x^0x^-2[/tex]
Answer:
The answer is- (Drumroll)
Step-by-step explanation:
The answers are [tex]x^-2y^-5[/tex], and [tex]1/x^2y^5[/tex]
To draw a gragh for y = 2x +5, a person can draw a point at x of 0 and y of _, a second point by going over 1 and ip _, and then draw a line through the points.
Answer: A person can draw a point of x of 0 and y of 5, a second point by going over 1 and up 2, and then draw a line through the points.
Step-by-step explanation:
if x is equal to 0 then y will equal to 5 which in this case will represent the y intercept. And after plotting the point (0,5) you can use the slope and move over or left by 1 and move up by 2 to find the next point.