Answer:
we need at least 17 - card deck
Step-by-step explanation:
From the information given :
We can attempt to solve the question by using pigeonhole principle;
"The pigeonhole principle posits that if more than n pigeons are placed into n pigeonholes some pigeonhole must contain more than one pigeon"
Thus; the minimum number of pigeon; let say at least n pigeons sit on at least one same hole among m hole can be represented by the formula:
m( n - 1 ) + 1
where ;
pigeons are synonymous to card
pigeonholes are synonymous to suits
So; m = 4 ; n = 5
∴ 4 (5 -1 ) + 1 ⇒ 4 (4) + 1
= 16 + 1
= 17
Hence; we need at least 17 - card deck
Suppose you want to have $0.5 million saved by the time you reach the age of 30 years and suppose that you are 20 years old now. If you can earn 5% on your funds, how much would you have to invest today to reach your goal?
Answer:
$306,956,6268
Step-by-step explanation:
Future value, FV = Present value PV [1 + rate]^t
PV = FV/[1 + rate]^t
PV = 500,000/[1.05]^10
PV = $306,956,6268
The water works commission needs to know the mean household usage of water by the residents of a small town in gallons per day. They would like the estimate to have a maximum error of 0.12 gallons. A previous study found that for an average family the variance is 5.29 gallons and the mean is 17 gallons per day. If they are using a 85% level of confidence, how large of a sample is required to estimate the mean usage of water
Answer:
[tex]n=(\frac{1.440(2.3)}{0.12})^2 =761.76 \approx 762[/tex]
So the answer for this case would be n=762 rounded up to the nearest integer
Step-by-step explanation:
Information given
[tex]\bar X = 17[/tex] represent the mean
[tex]\mu[/tex] population mean (variable of interest)
[tex]\sigma= \sqrt{5.29}= 2.3[/tex] represent the standard deviation
Solution to the problem
The margin of error is given by this formula:
[tex] ME=z_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (a)
And on this case we have that ME =0.12 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex] (b)
The confidence level is 85%, the significance level would be [tex] \alpha=1-0.85 = 0.15[/tex] and [tex]\alpha/2 =0.075[/tex] the critical value for this case would be [tex]z_{\alpha/2}=1.440[/tex], replacing into formula (b) we got:
[tex]n=(\frac{1.440(2.3)}{0.12})^2 =761.76 \approx 762[/tex]
So the answer for this case would be n=762 rounded up to the nearest integer
Farhan has three pieces of rope with lengths of 140cm, 168cm and 210cm. He wishes to cut all the three pieces of ropes into smaller pieces of equal length and that there is no leftover rope. (i) What is the greatest possible length of each of the smaller pieces of rope? How many smaller pieces of rope can he get altogether?
give correct answer
Answer:
The greatest possible length is 14 cm.
The total number of smaller pieces is 37.
Step-by-step explanation:
The greatest common factor of these three numbers is 14.
Total number of smaller pieces = 10+12+15 = 37
Best Regards!
The radius of a circle is 4 miles. What is the length of a 45° arc?
45°
r=4 mi
Give the exact answer in simplest form.
Answer:
2π miles
Step-by-step explanation:
2πr is the formula for the circumference of a circle.
Using that formula, the circumference for this circle is 8π.
Since the circle's full angle is 360°, we can use a ratio to find out how long the 45° arc is.
° : length
360 : 8π
9 : 0.4π
45 : 2π
The 45° is 2π mi long.
The Environmental Protection Agency must visit nine factories for complaints of air pollution. In how many ways can a representative visit five of these to investigate this week? Since the representative's travel to visit the factories includes air travel, rental cars, etc., then the order of the visits will make a difference to the travel costs.
Answer:
The number of ways is [tex]\left 9}\atop } \right. P _5 = 15120[/tex]
Step-by-step explanation:
From the question we are told that
The number of factories visited is [tex]n = 9[/tex]
The number of factories to be visited by a representative r = 5
The number of way to visit the 5 factories is mathematically represented as
[tex]\left 9}\atop } \right. P _5 = \frac{9!}{(9-5)!}[/tex]
Where P represents permutation
=> [tex]\left 9}\atop } \right. P _5 = \frac{9 \ !}{4\ !}[/tex]
=> [tex]\left 9}\atop } \right. P _5 = \frac{9 *8*7 * 6 * 5 * 4!}{4\ !}[/tex]
=> [tex]\left 9}\atop } \right. P _5 = 15120[/tex]
The equation f(x) is given as x2_4=0. Considering the initial approximation at
x0=6 then the value of x1 is given as
Select one:
O A. 10/3
O B. 7/3
O C. 13/3
O D. 4/3
Answer:
The value of [tex]x_{1}[/tex] is given by [tex]\frac{10}{3}[/tex]. Hence, the answer is A.
Step-by-step explanation:
This exercise represents a case where the Newton-Raphson method is used, whose formula is used for differentiable function of the form [tex]f(x) = 0[/tex]. The expression is now described:
[tex]x_{n+1} = x_{n} - \frac{f(x_{n})}{f'(x_{n})}}[/tex]
Where:
[tex]x_{n}[/tex] - Current approximation.
[tex]x_{n+1}[/tex] - New approximation.
[tex]f(x_{n})[/tex] - Function evaluated in current approximation.
[tex]f'(x_{n})[/tex] - First derivative of the function evaluated in current approximation.
If [tex]f(x) = x^{2} - 4[/tex], then [tex]f'(x) = 2\cdot x[/tex]. Now, given that [tex]x_{0} = 6[/tex], the function and first derivative evaluated in [tex]x_{o}[/tex] are:
[tex]f(x_{o}) = 6^{2} - 4[/tex]
[tex]f(x_{o}) = 32[/tex]
[tex]f'(x_{o})= 2 \cdot 6[/tex]
[tex]f'(x_{o}) = 12[/tex]
[tex]x_{1} = x_{o} - \frac{f(x_{o})}{f'(x_{o})}[/tex]
[tex]x_{1} = 6 - \frac{32}{12}[/tex]
[tex]x_{1} = 6 - \frac{8}{3}[/tex]
[tex]x_{1} = \frac{18-8}{3}[/tex]
[tex]x_{1} = \frac{10}{3}[/tex]
The value of [tex]x_{1}[/tex] is given by [tex]\frac{10}{3}[/tex]. Hence, the answer is A.
a triangle has a base length of 15.4 cm. the area of the triangle is 65.45 cm.
Answer:
8.5 cm
Step-by-step explanation: The formula for the area of a triangle is base times height divided by 2. To find the original number before dividing by 2 you have to multiply 65.45 times 2, which is 130.9. The length is 15.4 and the original number before dividing by 2 is 130.9 to find the height divide 130.9 by 15.4 which is 8.5. If you plug in the value height is 8.5 cm , length is 15.4 and multiply it and divide it by 2 you will get 65.45.
Please answer this correctly
Answer:
50%
OR
1/2
Step-by-step explanation:
The box and whisker plot shows the time spent from 4 to 6 hours is Quartile 1 to 3 which makes it 50%.
Find the equation for the line containing the points (-2,-5) and (6,3)
Answer:
y = x - 3
Step-by-step explanation:
Do rise/run to find the slope
8/8 = 1
y = x + b
Plug in a point to find the y-intercept
-5 = -2 + b
-3 = b
The equation will be y = x - 3
Please answer this correctly without making mistakes I want genius,expert or ace people to answer this correctly
Answer:
It would decrease by 9.
Step-by-step explanation:
52 is the original mean or the initial mean.
43 is the final mean.
52-43 = 9
So 9 is the difference.
Hope this helped!
how to solve this? please help me
Answer:
tangent: y = 2x -2normal: y = -1/2x +3Step-by-step explanation:
Differentiating implicitly, you have ...
-y²·dx +(4-x)(2y)dy = 3x²·dx
So, the slope is ...
dy/dx = (3x² +y²)/(2y(4 -x))
At (x, y) = (2, 2), the slope of the curve is ...
dy/dx = (3·2² +2²)/(2·2(4 -2)) = 16/8 = 2
In point-slope form, the equation of the tangent line is then ...
y = m(x -h) +k
y = 2(x -2) +2
y = 2x -2 . . . . equation of tangent line
__
The normal to the curve is perpendicular to the tangent at the same point. The slope of the perpendicular line is the negative reciprocal of the tangent's slope, so is -1/2.
y = (-1/2)(x -2) +2
y = -1/2x +3 . . . equation of normal line
What is the common difference between successive terms in the sequence?
0.36, 0.26, 0.16, 0.06, –0.04, –0.14, ...
–0.1
–0.01
0.01
0.1
Answer:
0.1
Step-by-step explanation:
0.36-0.26=0.1
hope u understand
Answer:
A
Step-by-step explanation:
How long dose it take to travel 84 miles at an average speed of 30 mph? Give your answer in hours and minutes
Answer:
2 hours and 48 minutes
Step-by-step explanation:
Time = Distance/Speed
= 84/30
= 2.8 hours
To convert 2.8 hours into hours and minutes, 2.8*60 = 168 minutes. Therefore the time taken to travel 84miles is 2 hours and 48 minutes
Answer:
In hours:
Time = 2.8 hours
In minutes:
Time = 168 minutes
Step-by-step explanation:
Given:
Distance = 84 miles
Speed = 30 mph
Required:
Time = ?
Formula:
Speed = Distance/Time
Solution:
Time = Distance/Speed
Time = 84/30
In hours:
Time = 2.8 hours
In minutes:
Time = 168 minutes
What is the measure of AC?
Enter your answer in the box.
Answer:
21
Step-by-step explanation:
Since angle ABC is an inscribed angle, its measure is half that of arc AC. Therefore:
[tex]2(3x-1.5)=3x+9 \\\\6x-3=3x+9 \\\\3x-3=9 \\\\3x=12 \\\\x=4 \\\\AC=3(4)+9=12+9=21[/tex]
Hope this helps!
Use the Inscribed Angle theorem to get the measure of AC. The intercepted arc AC is, 21°.
What is the Inscribed Angle theorem?We know that, Inscribed Angle Theorem stated that the measure of an inscribed angle is half the measure of the intercepted arc.
Given that,
The inscribed angle is, (3x - 1.5)
And the Intercepted arc AC is, (3x + 9)
So, We get;
(3x - 1.5) = 1/2 (3x + 9)
2 (3x - 1.5) = (3x + 9)
6x - 3 = 3x + 9
3x = 9 + 3
3x = 12
x = 4
Thus, The Intercepted arc AC is,
(3x + 9) = 3×4 + 9
= 21°
Learn more about the Inscribed Angle theorem visit:
brainly.com/question/5436956
#SPJ2
15. Simplify sin(90° - O) cos 0 - sin(180° +0) sin e.
Answer: cos²(θ) + sin(θ)sin(e)
Step-by-step explanation:
sin (90° - θ)cos(Ф) - sin(180° + θ) sin(e)
Note the following identities:
sin (90° - θ) = cos(x)
sin (180° + θ) = -sin(x)
Substitute those identities into the expression:
cos(x)cos(x) - -sin(x)sin(e)
= cos²(x) + sin(x)sin(e)
Can someone please help me with this problem?
Answer: -13
Step-by-step explanation:
c-2y
= -5-2(4)
= -5 - 8
= -13
Answer:
-13
Step-by-step explanation:
[tex]c=-5\\y=4\\c-2y=\\-5-(4*2)=\\-5-8=\\-13[/tex]
The expression is equal to -13 when [tex]c=-5[/tex] and [tex]y=4[/tex].
A list of numbers begins iwth the number 6. Each number on the list is 10 more than -2 times the previous terms. what is the fourth number
Answer:
The fourth term is -18
Step-by-step explanation:
an = -2(an-1) +10
This is the recursive formula
a1 = 6
a2 = -2(a1) +10 = -2(6) +10 = -12+10 = -2
a3 = -2(a2) +10 = -2(-2) +10 = 4+10 = 14
a4 = -2(a3) +10 = -2(14) +10 = -28+10 = -18
problem decoded dude
follow meh
Need help ASAP Thankyou!!!
Answer:
216
Step-by-step explanation:
To find the volume of the pyramid we have to do length * width * height / 3
The length is 9yd
The width is 8yd
The height is 9yd
So 9 * 9 * 8 = 648
648 / 3 = 216
The function f(x) is given by the set of ordered pairs.
{(8,3), (0, 4), (1, 5), (2, -1), (-6, 10)}
Which is true regarding the function?
f(-3) = 8
f(3) = 5
f(8) = 0
f(-6) = 10
Answer: f(-6) = 10.
Step-by-step explanation: This above equation is the only one that contains both coordinates of one of the ordered pairs in the correct order, so it is the answer.
Let f(x)= x^3 −6x^2+11x−5 and g(x)=4x^3−8x^2−x+12. Find (f−g)(x). Then evaluate the difference when x=−3 x=−3 .
Answer: (f-g)(x)= -138
Step-by-step explanation:
plsssssssssssssssssssssssssssssss help
Answer:
X=166°Solution,
<ABE+<ABC=180
<ABE=180-97
<ABE=83°
<ABC=<ACB=83°
<ABC+<ACB+<CAB=180
<CAB=180-83-83
<CAB=14
<DAC+<CAB=180
<DAC+14=180
<DAC=180-14
<DAC(X)=166°
Hope this helps...
Good luck on your assignment...
3 squared times 3 squared simplified
Answer:
3^4
Step-by-step explanation:
3^2*3^2
3*3*3*3
3^4
Carlos is almost old enough to go to school! Based on where he lives, there are 666 elementary schools, 333 middle schools, and 222 high schools that he has the option of attending.
Answer:
There are 36 education paths available to Carlos based on the schools around where he lives.
Step-by-step explanation:
Complete Question
Carlos is almost old enough to go to school. Based on where he lives, there are 6 elementary schools, 3 middle schools, and 2 high schools that he has the option of attending. How many different education paths are available to Carlos? Assume he will attend only one of each type of school.
Solution
We can use mathematics or manually writing out the possible combinations of elementary, middle and high school that Carlos can attend.
Using Mathematics
There are 6 elementary schools, meaning Carlos can make his choice in 6 ways.
There are 3 middle schools, meaning Carlos can make his choice in 3 ways.
Together with the elementary school choice, Carlos can make these two choices in 6 × 3 ways.
There are 2 high schools, Carlos can make his choice in 2 ways.
Combined with the elementary and middle school choices, Carlos can make his choices in 6×3×2 ways = 36 ways.
Manually
If we name the 6 elementary schools letters A, B, C, D, E and F.
Name the 3 middle schools letters a, b and c.
Name the 2 high schools numbers 1 and 2.
The different combinations of the 3 choices include
Aa1, Aa2, Ab1, Ab2, Ac1, Ac2
Ba1, Ba2, Bb1, Bb2, Bc1, Bc2
Ca1, Ca2, Cb1, Cb2, Cc1, Cc2
Da1, Da2, Db1, Db2, Dc1, Dc2
Ea1, Ea2, Eb1, Eb2, Ec1, Ec2
Fa1, Fa2, Fb1, Fb2, Fc1, Fc2
Evident now that there are 36 ways in which the 3 stages of schools can be combined. There are 36 education paths available to Carlos based on the schools around where he lives assuming that he will attend only one of each type of school.
Hope this Helps!!!
Answer:
36 education paths
Step-by-step explanation:
Hope this helps!
Which expression is equivalent to Left-bracket log 9 + one-half log x + log (x cubed + 4) Right-bracket minus log 6? log StartFraction 3 StartRoot x EndRoot (x cubed + 4) Over 2 EndFraction log StartFraction 3 StartRoot x EndRoot (3 x + 4) Over 2 EndFraction log StartFraction StartRoot 9 x (x cubed + 4) EndRoot Over 6 EndFraction StartFraction StartRoot log 9 x ( x cubed + 4) EndRoot Over 6 EndFraction
Answer:
[tex]\log{\dfrac{3\sqrt{x}(x^3+4)}{2}}[/tex]
Step-by-step explanation:
[tex]\log{9}+\dfrac{1}{2}\log{x}+\log{(x^3+4)}-\log{6}=\log{\left(\dfrac{9x^{\frac{1}{2}}(x^3+4)}{6}\right)}\\\\=\boxed{\log{\dfrac{3\sqrt{x}(x^3+4)}{2}}}\qquad\text{matches choice A}[/tex]
__
The applicable rules of logarithms are ...
log(ab) = log(a) +log(b)
log(a/b) = log(a) -log(b)
log(a^b) = b·log(a)
Answer:
A
Step-by-step explanation:
Just did it on edge2020
what is the recursiveformula for this geometric sequence? 4,-12,36,108
Answer:
a[1] = 4
a[n] = -3·a[n-1]
Step-by-step explanation:
The sequence given is not a geometric sequence, since the ratios of terms are -3, -3, 3 -- not a constant.
If we assume that the last given term is supposed to be -108, then the common ratio is -3 and each term is -3 times the previous one. That is expressed in a recursive formula as ...
a[1] = 4 . . . . . . . . . . . first term is 4
a[n] = -3·a[n-1] . . . . . each successive term is -3 times the previous one
Which best explains whether 9 is a solution to the inequality x greater-than 9? It is not a solution because 9 is not greater than 9. It is not a solution because 9 is not less than 9. It is a solution because 9 is greater than 9. It is a solution because 9 is less than 9.
Answer:
"It is not a solution because 9 is not greater than 9."
Step-by-step explanation:
[tex]x>9\\[/tex]
If x is 9, then the inequality would be untrue because x must be GREATER than 9 not equal or greater.
Answer:
It is not a solution because 9 is not greater than 9.
Step-by-step explanation:
i took the test and got it right hope it helps :)
Ken runs 12 miles in a marathon. Every 3.5 miles, he stopes to take a drink. How many times does he stop during the marathon ?
Answer:
Brainleist!
Step-by-step explanation:
12/3.5
3.42857142857
round down so its 3!
I need help pleaseee!
Step-by-step explanation:
we can use o as the center of the circle
OB=13
EB=12
OE=?
OE^2 +EB^2=OB^2
OE^2+12^2=13^2
OE^2=169-144
OE=
√25
OE=5
OC=OE+EC
EC =13-5
EC=8
multiply and remove all perfect square roots. Assume y is positive. √12
Answer:
2√3
Step-by-step explanation:
Step 1: Find perfect square roots
√4 x √3
Step 2: Convert
2 x √3
Step 3: Answer
2√3
A rectangle is 4.2 centimetres wide and each diagonal is 8.6 centimetres long. What is the measure of the angle between a diagonal and the shorter side of the rectangle, to the nearest tenth of a degree?
Answer:
[tex] 60.8^\circ [/tex]
Step-by-step explanation:
First, let's check side lengths.
Using the Pythagorean theorem we can find the length of the other side of the rectangle.
a^2 + b^2 = c^2
4.2^2 + b^2 = 8.6^2
b^2 = 56.32
b = 7.5
The other side of the rectangle measures 7.5 cm, so now we know that 4.2 cm is indeed the shorter side of the rectangle.
For the angle in question, the 4.2 cm side is the adjacent leg.
The diagonal of 8.6 cm is the hypotenuse.
The trig ratio that relates the adjacent leg to the hypotenuse is the cosine.
[tex] \cos \alpha = \dfrac{adj}{hyp} [/tex]
[tex] \cos \alpha = \dfrac{4.2~cm}{8.6~cm} [/tex]
[tex] \alpha = \cos^{-1} \dfrac{4.2~cm}{8.6~cm} [/tex]
[tex] \alpha = 60.8^\circ [/tex]