Answer:
63
Step-by-step explanation:
A composite number is an integer which can be found by mulitplying 2 smaller integers, 7 and 9 in this case
PLEASE HELP!!! You want to distribute 7 candies to 4 kids. If every kid must receive at least one candy, in how many ways can you do this?
Answer:
1140 ways.
Step-by-step explanation:
The applicable formula is: (n +r - 1)C(r-1), where n is the number of identical items (the candies), and r is the possible number of recipients (the kids).
The 17 identical candies, can be distributed among the 4 children in :
=(17 + 4 - 1)C(4–1) = 20C3 ways.
= 20!/((20–3)!*3!) ways.
= 20*19*18*17!/(17!*(3*2*1)) = 20*19*18/6 ways
= 20*19*3 ways.
=1140 ways.
5(2x - 3) = 5
What does x equal?
Answer:
x=2
Step-by-step explanation:
5(2x - 3) = 5
Divide by 5
5/5(2x - 3) = 5/5
2x-3 = 1
Add 3 to each side
2x-3 +3 = 1+3
2x = 4
Divide by 2
2x/2 = 4/2
x =2
Answer:
x = 2
Step-by-step explain:
5(2x-3) = 5
Divide both sides by 5
2x-3 = 1
Add 3 to both sides
2x = 4
Divide both sides by 2
x = 2
Today, the waves are crashing onto the beach every 4.8 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 4.8 seconds. 61% of the time a person will wait at least how long before the wave crashes in?
Answer:
61% of the time a person will wait at least 1.872 seconds before the wave crashes in.
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The probability that we find a value X lower than x is given by the following formula.
[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]
Uniform distribution from 0 to 4.8 seconds.
This means that [tex]a = 0, b = 4.8[/tex]
61% of the time a person will wait at least how long before the wave crashes in?
This is the 100 - 61 = 39% percentile, which is x for which [tex]P(X \leq x) = 0.39[/tex]. So
[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]
[tex]0.39 = \frac{x - 0}{4.8 - 0}[/tex]
[tex]x = 4.8*0.39[/tex]
[tex]x = 1.872[/tex]
61% of the time a person will wait at least 1.872 seconds before the wave crashes in.
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
n = 130
x = 69; 90% confidence
a. 0.463 < p < 0.599
b. 0.458 < p < 0.604
c. 0.461 < p < 0.601
d. 0.459 < p < 0.603
Answer:
d. 0.459 < p < 0.603
Step-by-step explanation:
We have to calculate a 90% confidence interval for the proportion.
The sample proportion is p=0.531.
[tex]p=X/n=69/130=0.531[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.531*0.469}{130}}\\\\\\ \sigma_p=\sqrt{0.001916}=0.044[/tex]
The critical z-value for a 90% confidence interval is z=1.645.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=1.645 \cdot 0.044=0.072[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z \cdot \sigma_p = 0.531-0.072=0.459\\\\UL=p+z \cdot \sigma_p = 0.531+0.072=0.603[/tex]
The 90% confidence interval for the population proportion is (0.459, 0.603).
A random sample of 13 items is drawn from a population whose standard deviation is unknown. The sample mean is x¯ = 950 and the sample standard deviation is s = 10. Use Appendix D to find the values of Student’s t.
1. Construct an interval estimate of mu with 99% confidence. (Round your answers to 3 decimal places.)
The 99% confidence interval is from_____ to ______ .
2. Construct an interval estimate of mu with 99% confidence, assuming that s = 20. (Round your answers to 3 decimal places.)
The 99% confidence interval is from_____ to ______ .
3. Construct an interval estimate of mu with 99% confidence, assuming that s = 40. (Round your answers to 3 decimal places.)
The 99% confidence interval is from_____ to ______ .
Answer:
1. The 99% confidence interval is from 941.527 to 958.473
2. The 99% confidence interval is from 933.054 to 966.946
3. The 99% confidence interval is from 916.108 to 983.892
Step-by-step explanation:
The confidence interval is given by
[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\[/tex]
Where [tex]\bar{x}[/tex] is the sample mean and Margin of error is given by
[tex]$ MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $ \\\\[/tex]
Where n is the sample size,
s is the sample standard deviation,
[tex]t_{\alpha/2[/tex] is the t-score corresponding to some confidence level
The t-score corresponding to 99% confidence level is
Significance level = α = 1 - 0.99 = 0.01/2 = 0.005
Degree of freedom = n - 1 = 13 - 1 = 12
From the t-table at α = 0.005 and DoF = 12
t-score = 3.055
1. 99% Confidence Interval when s = 10
The margin of error is
[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{10}{\sqrt{13} } \\\\MoE = 3.055\cdot 2.7735\\\\MoE = 8.473\\\\[/tex]
So the required 99% confidence interval is
[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 8.473\\\\\text {confidence interval} = 950 - 8.473, \: 950 + 8.473\\\\\text {confidence interval} = (941.527, \: 958.473)\\\\[/tex]
The 99% confidence interval is from 941.527 to 958.473
2. 99% Confidence Interval when s = 20
The margin of error is
[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{20}{\sqrt{13} } \\\\MoE = 3.055\cdot 5.547\\\\MoE = 16.946\\\\[/tex]
So the required 99% confidence interval is
[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 16.946\\\\\text {confidence interval} = 950 - 16.946, \: 950 + 16.946\\\\\text {confidence interval} = (933.054, \: 966.946)\\\\[/tex]
The 99% confidence interval is from 933.054 to 966.946
3. 99% Confidence Interval when s = 40
The margin of error is
[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{40}{\sqrt{13} } \\\\MoE = 3.055\cdot 11.094\\\\MoE = 33.892\\\\[/tex]
So the required 99% confidence interval is
[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 33.892\\\\\text {confidence interval} = 950 - 33.892, \: 950 + 33.892\\\\\text {confidence interval} = (916.108, \: 983.892)\\\\[/tex]
The 99% confidence interval is from 916.108 to 983.892
As the sample standard deviation increases, the range of confidence interval also increases.
Find the values of a and b in the rhombus. Solve for the value of c, if c=a+b.
Answer:
a = 5
b = 1.3
c = 6.3
Step-by-step explanation:
To find the values of a, b and C respectively, let's find a first by recalling that the diagonals of a rhombus are perpendicular to each other.
Therefore, the angle given as (14a + 20) = 90°
Solve for a
14a + 20 = 90
14a = 90 - 20
14a = 70
a = 70/14
a = 5
==>To find b, also recall that all sides of a rhombus are equal.
Therefore 3b + 4 = 13b - 9
Solve for b
4 + 9 = 13b - 3b
13 = 10b
13/10 = b
b = 1.3
==>Find value of c
c = a + b
c = 5 + 1.3
c = 6.3
What is the measure of angle S?
480
56°
930
101°
Answer:
m∠s = 93°
Step-by-step explanation:
We know that any quadrilateral's sum of angles adds up to 360°. In that case,
360 - (56 + 132 + 79) = m∠s
m∠s = 93°
Answer:
S° = 93 °
Step-by-step explanation:
[tex]The- diagram- is- a- trapezoid (quadrilateral)\\Sum- of- angles-in a- quadrilateral = 360\\ 132\° + 56\° + 79\° + x\° = 360\° \\267\° + x\° = 360\° \\x = 360 \° - 267 \° \\x\° = 93\°[/tex]
Using the diagram below, solve the right triangle. Round angle measures to the
nearest degree and segment lengths to the nearest tenth.
Answer:
m∠A = 17 degrees m∠B = 73 degrees m∠C = 90 (given) a = 12 (given) b = 40 c = 42 (given)
Step-by-step explanation:
Use sin to solve m∠A
sin x = 12/42 Simplify
sin x = 0.2857 Use the negative sin to solve for x
sin^-1 x = 17 degrees
Add together all of the angle measures to solve for m∠B
17 + 90 + x = 180 Add
107 + x = 180
-107 -107
x = 73 degrees
Use Pythagorean Theorem to solve for b
12^2 + x^2 = 42^2 Simplify
144 + x^2 = 1764
-144 -144
x^2 = 1620 Take the square root of both sides
x = 40
Diane's bank is offering 5% interest, compounded monthly. If Diane invests $10,500 and wants $20,000 when she withdrawals, how long should she keep her money in for? Round to the nearest tenth of a year.
Answer:
The time period is 13 years.
Step-by-step explanation:
Interest rate (r )= 5% or 5%/12 = 0.42% per months
The investment amount (Present value) = $10500
Final expected amount (future value) = $20000
Since we have given the initial amount and final amount. Therefore we have to calculate the time period for which the initial amount is kept in the bank.
Use the below formula to find the time period.
Future value = present value (1 + r )^n
20000 = 10500(1+0.0042)^n
1.9047619 = (1+0.0042)^n
1.9047619 = 1.0042^n
n = 153.74 months.
Time in years = 153.74 / 12 = 12.8 years or 13 years (round off)
I NEED HELP PLEASE, THANKS! :)
Answer:
Option B
Step-by-step explanation:
Again, another great question! Here we are given the following system of equations, bound by quadrant 1 -
[tex]\begin{bmatrix}2x+7y\le \:70\\ 8x+4y\le \:136\end{bmatrix}[/tex]
Convert this to slope - intercept form -
[tex]\begin{bmatrix}y\le \frac{70-2x}{7}\\ y\le \:2\left(-x+17\right)\end{bmatrix}[/tex]
Now the graphed solution of this intersects at a shaded region with which there are 3 important point that lie on the border. They are the following -
( 0, 10 ),
( 15, 9 ),
( 17, 0 )
When these point are plugged into the main function f ( x, y ) = 2x + 6y, the point ( 15, 9 ) results in the greatest solution of 84. Thus, it is our maximum point -
Option B
Julie has three boxes of pens. The diagram shows expressions for the number of pens in each box. Look at these equations.
Equals B +12
B equals C +4
Write an equation to show the relationship between a + c
Answer:
a=c+16here,
a=b+12
b=a-12----> equation (i)
b= c+4
putting the value of b from the equation (I)
a-12=c+4
a=c+4+12
a=c+16
hope this helps...
Good luck on your assignment...
The value of a + c is 16.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
a=b+12
So, b=a-12 ---- equation (i)
and, b= c+4
Substitute the value of b from the equation (I)
a-12=c+4
a=c+4+12
a=c+16
Hence, the value of a+ c is 16.
Learn more about Algebra here:
https://brainly.com/question/24875240
#SPJ2
Could someone explain how to find square roots please?
Answer: graphing calculator!
Step-by-step explanation: if you’re looking for the square root of a # that isn’t a perfect square (ie. sqrt4, sqrt 36) then you have to use a calculator for that. however the idea behind square roots is just a # multiplied by itself to give the original #. just ask yourself “what can i multiply by itself to get the original number”. hope that helped !
Answer:
By multiplying the number by its power 2.
E.g= 4^2
In this activity, you will use equations to represent this proportional relationship: Olivia is making bead bracelets for her friends. She can make 3 bracelets in 15 minutes.
Part A
Find the constant of proportionality in terms of minutes per bracelet.
Part B
What does the proportionality constant represent in this situation?
Part C
Write an equation to represent the proportional relationship. Use the constant of proportionality you found in part A. Be sure to assign a variable for each quantity.
Part D
Now find the constant of proportionality in terms of number of bracelets per minute.
Part E
What does the proportionality constant represent in this situation?
Part F
Write an equation to represent the proportional relationship. Use the constant of proportionality you found in part D. Be sure to assign a variable for each quantity.
Part G
How are the constants of proportionality you found in parts A and D related?
Part H
Are the two equations you developed in parts C and F equivalent? Explain.
Answer:
Step-by-step explanation:
A) The constant of proportionality in terms of minutes per bracelet is
15/3 = 5 minutes per bracelet
B) The constant of proportionality represents man hour rate
C) let k = constant of proportionality, t = time in minutes and b = number of bracelets produced. Therefore,
t = kb
D) the constant of proportionality in terms of number of bracelets per minute is
3/15 = 1/5
E) The constant of proportionality represents production rate
F) let k = constant of proportionality, t = time in minutes and b = number of bracelets produced. Therefore,
b = kt
G) The constants of proportionality are reciprocals
H) Two equations are equivalent if they have the same solution. They are not equivalent. By inputting the different values of k, the solutions will always be the same. Therefore, they are equivalent.
Answer:the sample answers, change them up so you dont get in trouble
A To find the constant of proportionality in minutes per bracelet, divide the total time by the number of bracelets:
constant of proportionality=15 MINUTES/3 BRACELETS=5 minutes per bracelet.
B The proportionality constant of 5 minutes per bracelet means it takes Olivia 5 minutes to make 1 bracelet.
C Here’s one way to set up the equation:
time = constant of proportionality × number of bracelets
Let m be time in minutes and let b be the number of bracelets. Substitute the variables (m and b) and the value of the proportionality constant (5 minutes per bracelet) into the equation: m = 5b.
thats all ik srry
Step-by-step explanation:
what does r equal? 1/13r=-8/15
Answer:
[tex]\boxed{\sf \ \ \ -\dfrac{15}{104} \ \ \ }[/tex]
Step-by-step explanation:
hello,
first of all let's assume that r is different from 0 as this is not allowed to divide by 0
[tex]\dfrac{1}{13r}=\dfrac{-8}{15}[/tex]
multiply by 13r it comes
[tex]\dfrac{13r}{13r}=1=\dfrac{-8*13r}{15}[/tex]
now multiply by 15
[tex]-8*13r=15\\<=> r = \dfrac{-15}{8*13}=-\dfrac{15}{104}[/tex]
hope this helps
Answer:[tex]r=-\frac{104}{15}[/tex] or -6.93333....
Step-by-step explanation:
[tex]\mathrm{Multiply\:both\:sides\:by\:}13[/tex]
[tex]13\cdot \frac{1}{13}r=13\left(-\frac{8}{15}\right)[/tex] =-104/15
simplify
[tex]r=-\frac{104}{15}[/tex]
MARK BRAINLIEST PLEASE
Please answer this correctly
Answer:
1/9
Step-by-step explanation:
first, u need 9 ---> 1/3
then u need 8 ---> 1/3 also
Multiply them and get...1/9
Help me plzzzzz!!!!
Answer:124
Step-by-step explanation:
2x + 8 + x - 2 = 180
Add like terms
3x + 6 = 180
Subtract the 6 from both sides
3x + 6 - 6 = 180 - 6
3x = 174
Divide by 3
x = 58
Now we have to find the measure of angle ACD
2(58) + 8 = 124
Please answer this correctly
Answer:
50%
Step-by-step explanation:
Even numbers on a 6-sided die are 2, 4, and 6.
3 numbers out of 6 are even.
3/6 = 1/2
0.5 = 50%
Quadrilaterals WXYZ and BADC are congruent. In addition, WX ≅ DC and XY ≅ BC.
If AD = 4 cm and AB = 6 cm, what is the perimeter of WXYZ?
18 cm
20 cm
22 cm
24 cm
Answer: 20 cm
If quadrilaterals WXYZ and BADC are congruent, then their corresponding sides are congruent.
Given that
WX≅DC,
XY≅BC,
you can state that
YZ≅AB,
WZ≅AD.
If AD = 4 cm and AB = 6 cm, then WZ = 4 cm and YZ = 6 cm. Opposite rectangle sides are congruent, then XY = 4 cm and WX = 6 cm.
The perimeter of WXYZ is
P = WX + XY + YZ + WZ = 6 + 4 + 6 + 4 = 20 cm.
Find the value of x that makes A||B
Answer:
For lines A and B to be parallel, the Same Side Interior angles must be supplementary which means:
2x + 10 + 4x + 80 = 180
6x + 90 = 180
6x = 90
x = 15°
3. A plane travels at a constant speed. It takes 6 hours to travel 3,360 miles. (20 points)
a. What is the plane's speed in miles per hour?
b. At this rate, how many miles can it travel in 10 hours?
Answer:
a. The plane's speed in mph is 560
b. At this rate, the plane can travel 5,600 miles in 10 hours.
Step-by-step explanation:
In order to find the planes speed in mph, some simple arithmetic must be done and you should divide 3,360 by 6. Now that you have determined that 3,360/6 equals 560, you know that in order to figure out how many miles the plane can travel in 10 hours, all you must do is multiply 560 by 10 which equals 5,600.
Answer:
A. 560B. 5,600Step-by-step explanation:
A. = 3,360 / 6 = 560B. = 560 x 10 = 5,600How do you solve 36 times [tex]\sqrt{3}[/tex]
Answer:
62.3538
Step-by-step explanation:
There is nothing to solve. If you need a decimal value, you can use a calculator or table of square roots.
A surveyor is trying to find the height of a hill. He/she takes a ‘sight’ on the top of the hill and find that the angle of elevation is 40°. He/she move a distance of 150 metres on level ground directly away from the hill and takes a second ‘sight’. From this point, the angle of elevation is 22°. Find the height of the hill, correct to 1 d.p.
Answer:
The height of the hill is 116.9 meters.
Step-by-step explanation:
The diagram depicting this problem is drawn and attached below.
From Triangle ABC
[tex]\tan 22^\circ=\dfrac{h}{150+x}\\\\h=\tan 22^\circ(150+x)[/tex]
From Triangle XBC
[tex]\tan 40^\circ =\dfrac{h}{x}\\\\h=x\tan 40^\circ[/tex]
Therefore:
[tex]h=\tan 22^\circ(150+x)=x\tan 40^\circ\\150\tan 22^\circ+x\tan 22^\circ=x\tan 40^\circ\\x\tan 40^\circ-x\tan 22^\circ=150\tan 22^\circ\\x(\tan 40^\circ-\tan 22^\circ)=150\tan 22^\circ\\x=\dfrac{150\tan 22^\circ}{\tan 40^\circ-\tan 22^\circ} \\\\x=139.30[/tex]
Therefore, the height of the hill
[tex]h=139.3\times \tan 40^\circ\\=116.9$ meters( correct to 1 d.p.)[/tex]
The height of the hill is 116.9 meters.
[tex]\frac{5x-11}{2x^2+x-6}[/tex] You need to work for your points now!
Answer:
[tex]\frac{5x-11}{\left(2x-3\right)\left(x+2\right)}[/tex]
Step-by-step explanation:
[tex]\frac{5x-11}{2x^2+x-6}[/tex]
Factor the denominator.
[tex]\frac{5x-11}{\left(2x-3\right)\left(x+2\right)}[/tex]
The fraction cannot be simplified further.
Answer:
[tex] \frac{5x - 11}{(x + 2)(2x - 3)} [/tex]solution,
[tex] \frac{5x - 11}{2 {x}^{2} + x - 6} \\ = \frac{5x - 11}{2 {x}^{2} + (4 - 3)x - 6} \\ = \frac{5x - 11}{2 {x}^{2} + 4x - 3x - 6 } \\ = \frac{5x - 11}{2x(x + 2) - 3(x + 2)} \\ = \frac{5x - 11}{(x + 2)(2x - 3)} [/tex]
Hope this helps..
Calculate
(14x5x4) / (28 x 2)
Answer:
5
Step-by-step explanation:
(14 × 5 × 4) ÷ (28 × 2)
Solve brackets.
280 ÷ 56
Divide.
= 5
A ship traveled at an average rate of 25 miles per hour going west. It then traveled at an average rate of 19 miles per hour heading north. If the ship traveled a total of 145 miles in 7 hours, how many miles were traveled heading west?
Answer:
50 miles
Step-by-step explanation:
hello,
let's note x the number of miles travelled heading west,
it takes 1 hour to travel 25 miles
so it takes x/25 hours to travel x miles
we know that in total it travels 7 hours so it will travel 7-x/25 hours heading North, then heading North it takes 1 hour to travel 19 miles
so in 7-x/25 hours it travels 19(7-x/25) miles
we can write, as the total distance is 145 miles
[tex]x+19(7-\dfrac{x}{25})=145\\<=> 25x+3325-19x=3625\\<=> 6x=300\\<=> x = 50[/tex]
we can verify
50 miles heading West takes 2 hours
in 5 hours it travels 19*5 = 95 miles
the total is 145 miles
so this is correct
hope this helps
What tool is used to draw circles
Answer:
Pair of compasses.
Step-by-step explanation:
These are used to inscribe circles/arcs.
Compasses are used in maths, navigation,e.t.c.
Hope it helps.
Two identical decks of 52 cards are mixed together, yielding a stack of 104 cards. How many different ways are there to order this stack of 104 cards?
Answer:
here the order will be 104! =[tex]1.029e^{166}[/tex]
Step-by-step explanation:
since the cards are to arranged in no particular order that is why we used combination to find the result.
Combination can simply be explained as the method of selecting items from a collection of items where the order of the selections does not matter.
A triangle with side lengths of 4 , 5 , 6 , what are the measures of it angles to the nearest degree ?
Answer:
41°, 56°, 83°
Step-by-step explanation:
We can find the largest angle from the law of cosines:
c² = a² +b² -2ab·cos(C)
C = arccos((a² +b² -c²)/(2ab))
C = arccos((4² +5² -6²)/(2(4)(5))) = arccos(5/40) ≈ 82.8192°
Then the second-largest angle can be found the same way:
B = arccos((4² +6² -5²)/(2·4·6)) = arccos(27/48) ≈ 55.7711°
Of course the third angle is the difference between the sum of these and 180°:
A = 180° -82.8192° -55.7711° = 41.4096°
Rounded to the nearest degree, ...
the angles of the triangle are 41°, 56°, 83°.
The mean of 100 numerical observations is 51.82 what is the value of all 100 numbers
Answer: 5182
To get the value of all 100 numbers you would need to multiply.
Step-by-step explanation:
51.82x100= 5182
Do class limits and class marks make sense for qualitative data classes? Explain
your answer.
NEED QUICKLY
Answer: NO, class limits and class marks are not meaningful to qualitative data.
Step-by-step explanation: Qualitative data are non-numerical data. They are collected mostly through observation. They include; sex, name and soon.
Class limits and class marks are groupings used in numerical data (quantitative data). They are not relevant and are meaningless to qualitative data classes as these data class are non- numerical.