9514 1404 393
Answer:
7 quarters, 14 dimes, 7 nickels total $3.50$0.80 will remainStep-by-step explanation:
a) 1/4 of 28 = 28/4 = 7 coins are quarters.
2/3 of (28 -7) = (2/3)(21) = 14 coins are dimes
The remaining 28 -7 -14 = 7 coins are nickels
__
b) The amount of money in coins is ...
7×$0.25 +14×$0.10 +7×$0.05 = $3.50 . . . in coins
__
c) 2 packs of cards at $1.35 each will cost 2×$1.35 = $2.70. After the purchase, the remaining money would be ...
$3.50 -2.70 = $0.80 . . . remaining
PLEASE HELPPO The top shelf of a bookcase holds 6 fiction and 4 nonfiction books. On the bottom shelf are 3 fiction and 5 nonfiction books.
Choosing which 2 books describes a pair of dependent events?
Answer:
Two consecutive events are dependent if the outcome of the second event depends on the outcome of the first event.
Now, suppose that all the books have the same probability of being drawn, let's look at a single shelf.
we take a book from the first shelf, let's ignore the type of book for now.
Now, if we want to get a second book from that shelf, the probability of getting a fiction book is equal to the quotient between the number of fiction books on the shelf and the total number of shelf.
Now we can see that, if the first book drawn was a fiction book, now there are 5 fiction books and 9 books in total, so:
p = 5/9
if the first book was a non-fiction book, now there are 6 fiction books in the shelf and 9 books in total, so the probability in this case is:
q = 6/9
So you can see that the outcome of the second draw depends on the outcome of the first one (only in the case where we take two books from the same shelf)
Then the pair of dependent events is:
A: because in both cases we choose a book from the same shelf
D: because in both cases we choose a book from the top shelf.
!!!HELPPP PLEASE ASAP!!! I don’t know how to solve this problem nor where to start? Can some please help me out and explain how you got the answer please. Thank you for your time.
Step-by-step explanation:
a)
0.00000000007
b)
0.00000001
PLEASE HELP ME IM HAVING TROUBLE WITH IT
Answer:
True
False
Step-by-step explanation:
BC are on the same line so, the new [tex]B^{1}[/tex][tex]C^{1}[/tex] will also be on the same. Just a different line than the original. The both move the same distance when dilated.
CD and the new [tex]C^{1}[/tex][tex]D^{1}[/tex] cannot be the same length. The dilation will increase their length by 1[tex]\frac{2}{3}[/tex]
A certain drug carn be used to reduce the acid produced by the body and heal damage to the esophagus due to acid reflux. The manufacturer of the drug claims that more than 94% of patients taking the drug are healed within B weeks. In clinical trials, 228 of 240 patients suffering from acid reflux disease were healed after 8 weeks. Test the manufacturer's claim at the a=0.05 level of significance. Click here to view the standard nomal distribution table (page 1). Cick here to view the standard nomal distribution table (page 2). Because rea (1-Po) =| satistied. (Pound to one decimal place as needed.) V 10, the sample size is 5% of the population size, and the sample the requirements for testing the hypothesis
According to the manufacturer's claim, we build an hypothesis test, find the test statistic and the p-value relative to this test statistic, reaching a conclusion that:
The p-value of the test is 0.2578 > 0.05, which means that there is not sufficient evidence to conclude that more than 94% of patients taking the drug are healed within B weeks.
The manufacturer of the drug claims that more than 94% of patients taking the drug are healed within 8 weeks.
At the null hypothesis, we test if the proportion is of at most 0.94, that is:
[tex]H_0: p \leq 0.94[/tex]
At the alternative hypothesis, we test if the proportion is of more than 0.94, so:
[tex]H_1: p > 0.94[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, is the value tested at the null hypothesis, is the standard deviation and n is the size of the sample.
0.94 is tested at the null hypothesis:
This means that [tex]\mu = 0.94, \sigma = \sqrt{0.94*0.06}[/tex]
In clinical trials, 228 of 240 patients suffering from acid reflux disease were healed after 8 weeks.
This means that [tex]n = 240, X = \frac{228}{240} = 0.95[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.95 - 0.94}{\frac{\sqrt{0.94*0.06}}{\sqrt{240}}}[/tex]
[tex]z = 0.65[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample proportion above 0.95, which is 1 subtracted by the p-value of Z = 0.65.
Looking at the z-table, Z = 0.65 has a p-value of 0.7422.
1 - 0.7422 = 0.2578.
The p-value of the test is 0.2578 > 0.05, which means that there is not sufficient evidence to conclude that more than 94% of patients taking the drug are healed within B weeks.
A similar example can be found at https://brainly.com/question/24166849
Solve the equation for x: 6-(4x-2)/5=x
Suppose a + bi and c + di are complex numbers with b not equaling 0.
(a) Calculate (a + bi) + (c + di) and (a + bi)(c + di).
(b) Show that if both the sum and product are real numbers, then either the complex numbers are real numbers or conjugates.
9514 1404 393
Answer:
(a) sum: (a+c) +(b+d)i
product: (ac -bd) +(bc +ad)i
(b) (b+d)=0 and (bc+ad)=0 ⇒ a=c, d=-b or b=d=0
Step-by-step explanation:
(a) Combining like terms the sum is ...
(a +bi) +(c +di) = (a+c) +(b+d)i . . . . sum
And the product is ...
(a+bi)(c+di) = ac +(ad+bc)i +bd·i²
Since i = √-1, i² = -1 and the product can be written as ...
(a+bi)(c+di) = (ac-bd) +(ad+bc)i . . . . product
__
(b) If both the sum and product are real numbers, then we have ...
b +d = 0
ad +bc = 0
The first equation tells us d = -b. Substituting that into the second equation, we get ...
a(-b) +b(c) = 0
b(c -a) = 0
The zero product rule tells us this will be true if and only if b = 0 or c = a.
if b = 0, then d = 0 and both numbers are real.
if c = a, then c+di = a-bi and the numbers are conjugates.
Hence, if both the sum and product are real, both are real numbers or they are conjugates.
Figure out the pattern, and write the next number.
2,6,21,88
I am need help and an explanation on how to read these graphs.
Answer:
A is the answer
Step-by-step explanation:
A
plz mark it brainlist
MFP15017010 2021 Question 2 2.1 Calculate the following 2- and 3-digit numbers using strategic doubling: 34 2.1.2 340 2.13 277 214 00 (10) 2.15 500
Answer:
plz check ur school solution down.
Step-by-step explanation:
A. Given that K = {x: x ≤ -2}, Y = { x: 1 < x < 6} and z = {x: x < 3}
where x is an integer, find
i. K n (Y u Z)
ii. (K n Y) u (K n Z)
III. What property of operations on sets is shown by your answers in i and ii?
Since x is an integer, we have
K = {…, -6, -5, -4, -3, -2}
Y = {2, 3, 4, 5}
Z = {…, -1, 0, 1, 2, 3}
Then
(i)
Y U Z = {…, -1, 0, 1, 2, 3, 4, 5}
==> K ∩ (Y U Z) = {…, -6, -5, -4, -3, -2} = K
(ii)
K ∩ Y = { } (empty set)
K ∩ Z = {…, -6, -5, -4, -3, -2} = K
==> (K ∩ Y) U (K ∩ Z) = { } U K = K
(iii) This is a demonstration of the distributive property. That is, the intersection distributes over a union:
K ∩ (Y U Z) = (K ∩ Y) U (K ∩ Z)
y=5/3x + 3 in ordered pairs
Answer:
(3,8) ; (-3,-2) ; (6,13)
Step-by-step explanation:
A linear equation in Slope Intercept Form is given to us and we need to write the ordered pairs for x and y . The given equation is ,
[tex]\rm\implies y =\dfrac{5}{3}x + 3 [/tex]
For finding the ordered pairs , substitute different values of x to get different values of y.
Put x = 3 :-
[tex]\rm\implies y =\dfrac{5}{3}\times 3 + 3 [/tex]
[tex]\rm\implies y = 5+ 3 [/tex]
[tex]\rm\implies y =8[/tex]
Put x = -3 :-
[tex]\rm\implies y =\dfrac{5}{3}\times -3 + 3 [/tex]
[tex]\rm\implies y = -5+ 3 [/tex]
[tex]\rm\implies y =-2[/tex]
Put x =6 :-
[tex]\rm\implies y =\dfrac{5}{3}\times 6 + 3 [/tex]
[tex]\rm\implies y = 10+ 3 [/tex]
[tex]\rm\implies y =13[/tex]
Therefore ,
[tex]\small\implies\boxed{\rm\blue{ Odered \ Pairs \ = (3,8) ; (-3,-2) ; (6,13) }}[/tex]
Area: Change in Dimensions
A rectangle FGHJ has a width of 3 inches and a length of 7 inches.
Step-by-step explanation:
this is not complicated at all. first and second graders can do a-c (come on, you know how to calculate the area of a rectangle) and with some imagination also d and e.
this is meant for you to actually do it so that you get a feeling for these things.
I will therefore leave the pure calculation to you.
and I will give you some help for the conceptual/ theoretical part.
the area of a rectangle is, of course, length × width (or height some on the view you have on an object).
let's just call them l and w.
so the regular area is
Ar = l×w
now one dimension (or example and for the width, but it does not matter, it is the same for the length) is doubled.
it simply means the new width is twice the old width.
so the area with a double width is
A2w = l×(2×w) = 2×(l×w)
so, that means also the area is doubled compared to the regular area.
now, both dimensions are doubled.
A2w2l = (2×l)×(2×w) = 4×(l×w)
so, the area grew 4 times a large as the regular area.
what is the rule here ?
let's triple the dimensions.
A3w3l = (3×l)×(3×w) = 9×(l×w)
as you can easily see : the new area grows with the square of the scaling factor, when we change both dimensions equally.
the reason is simple - as our little equations show, we have to multiply in the scaling factor of every dimension in play.
therefore, the new area grows with the product of the scaling factors of the involved dimensions. if both scaling factors are the same, then the area grows therefore by the square of the common factor.
and this principle applies to every shape, where the area is constructed out of 2 dimensions. any other additional multiplication factors don't matter for this, because this is all one big multiplication of several factors, and if you multiply one of these factors by an additional factor, the whole result changes by that factor.
In this problem, x = c1 cos t + c2 sin t is a two-parameter family of solutions of the second-order DE x'' + x = 0. Find a solution of the second-order IVP consisting of this differential equation and the given initial conditions. x(π/4) = 2 2 , x'(π/4) = 0
Differentiate the given solution:
[tex]x=C_1\cos(t)+C_2\sin(t) \implies x'=-C_1\sin(t)+C_2\cos(t)[/tex]
Now, given that x (π/4) = √2/2 … (I'm assuming there are symbols missing somewhere) … you have
[tex]\dfrac{\sqrt2}2=C_1\cos\left(\dfrac\pi4\right)+C_2\sin\left(\dfrac\pi4\right)[/tex]
[tex]\implies\dfrac1{\sqrt2} = \dfrac{C_1}{\sqrt2}+\dfrac{C_2}{\sqrt2}[/tex]
[tex]\implies C_1+C_2=1[/tex]
Similarly, given that x' (p/4) = 0, you have
[tex]0=-C_1\sin\left(\dfrac\pi4\right)+C_2\cos\left(\dfrac\pi4\right)[/tex]
[tex]\implies 0=-\dfrac{C_1}{\sqrt2}+\dfrac{C_2}{\sqrt2}[/tex]
[tex]\implies C_1=C_2[/tex]
From this result, it follows that
[tex]C_1+C_2=2C_1=1 \implies C_1=C_2=\dfrac12[/tex]
So the particular solution to the DE that satisfies the given conditions is
[tex]\boxed{x=\dfrac12\cos(t)+\dfrac12\sin(t)}[/tex]
Resolve into factors. px + qx + py + qy (algebra).
Answer:
(p+q)(x+y)
HOPE IT HELPS YOU.....
Step-by-step explanation:
we want to factor the following expression
[tex] \displaystyle px + qx + py + qy[/tex]
to do so group px's and qy's
[tex] \displaystyle px + py + qx + qy[/tex]
factor out p:
[tex] \displaystyle p(x + y ) + qx + qy[/tex]
factor out "q":
[tex] \displaystyle p(x + y ) + q(x + y)[/tex]
group:
[tex]\boxed{ \displaystyle( p+ q)(x + y)}[/tex]
If Tevin has 2 times as many dimes as nickels and they have a combined value of 100 cents, how many of each coin does he have?
dimes____
nickels____
Answer:
dimes- 8
nickels- 4
Step-by-step explanation:
dime=10 cents
nickels=5 cents
5 x 4 = 20
10 x 8 = 80
80 + 20 = 100
... please give brainliest ...
Find the area of the shaded regions.
QUICKLY PLEASE
Answer:
the answer is 270° on this
Answer:
84.78
Step-by-step explanation:
Area of a circle is pi(radius)^2
In this case it would be (pi(radius)^2)270/360 since it's 3/4 of a circle.
So we replace the values and solve:
3.14(36)(270/360)= 84.78 square centimeters.
HELP HELP HELP HELP PLEASE
Answer:
It is indeed 63
Step-by-step explanation:
The easy way to go about this is to recognize that if the triangles are similar, the ratio between the similar sides will be the same.
Notice:
4/5 = 36/45
So:
4/7 should = 36/x
If:
4/7 = 36/x
4x/7 = 36
4x = 36*7
x=36*7/4
x=63
A sales firm receives an average of three calls per hour on its toll-free number. For any given hour, find the probability that it will receive at least three calls. Use the Poisson distribution.
Answer:
At most 3 calls: 64.7%
At least 3 calls: 57.7%
5 or more calls: 18.5%
Step-by-step explanation:
Si una vara 2,15 mts de longitud da una sombra de 6,45 mts
Answer:
he casted 4.3. away
Step-by-step explanation:
An article in Fire Technology, 2014 (50.3) studied the effectiveness of sprinklers in fire control by the number of sprinklers that activate correctly. The researchers estimate the probability of a sprinkler to activate correctly to be 0.7. Suppose that you are an inspector hired to write a safety report for a large ballroom with 10 sprinklers. Assume the sprinklers activate correctly or not independently.
Required:
a. What is the probability that all of the sprinklers will operate correctly in a fire?
b. What is the probability that at least 7 of the sprinklers will operate correctly in a fire?
Answer:
a) 0.0282 = 2.82% probability that all of the sprinklers will operate correctly in a fire
b) 0.6496 = 64.96% probability that at least 7 of the sprinklers will operate correctly in a fire.
Step-by-step explanation:
For each sprinkler, there are only two possible outcomes. Either they will operate correctly, or they will not. The sprinklers activate correctly or not independently, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The researchers estimate the probability of a sprinkler to activate correctly to be 0.7.
This means that [tex]p = 0.7[/tex]
10 sprinklers.
This means that [tex]n = 10[/tex]
a. What is the probability that all of the sprinklers will operate correctly in a fire?
This is [tex]P(X = 10)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 10) = C_{10,10}.(0.7)^{10}.(0.3)^{0} = 0.0282[/tex]
0.0282 = 2.82% probability that all of the sprinklers will operate correctly in a fire.
b. What is the probability that at least 7 of the sprinklers will operate correctly in a fire?
This is:
[tex]P(X \geq 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 7) = C_{10,7}.(0.7)^{7}.(0.3)^{3} = 0.2668[/tex]
[tex]P(X = 8) = C_{10,8}.(0.7)^{8}.(0.3)^{2} = 0.2335[/tex]
[tex]P(X = 9) = C_{10,9}.(0.7)^{9}.(0.3)^{1}= 0.1211[/tex]
[tex]P(X = 10) = C_{10,10}.(0.7)^{10}.(0.3)^{0} = 0.0282[/tex]
Then
[tex]P(X \geq 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.2668 + 0.2335 + 0.1211 + 0.0282 = 0.6496[/tex]
0.6496 = 64.96% probability that at least 7 of the sprinklers will operate correctly in a fire.
If POR ~ ASTU, what is the scale factor of APQR to ASTU?
A. 1/5
B. 1/4
C. 5
D. 4
Answer:
[tex]k = \frac{1}{5}[/tex]
Step-by-step explanation:
Given
The attached triangles
Required
The scale factor
From the attachment, we have:
[tex]TU = 4[/tex]
[tex]QR = 20[/tex]
So, the scale factor from PQR to STU is:
[tex]k = \frac{TU}{QR}[/tex]
[tex]k = \frac{4}{20}[/tex]
[tex]k = \frac{1}{5}[/tex]
find all the missing measurement
Answer:
find all the missing measurementFind Y. round to the nearest tenth.
9514 1404 393
Answer:
32.7°
Step-by-step explanation:
Solve the given equation for C, then fill in the given values and evaluate.
C = arccos((a² +b² -c²)/(2ab))
Y = arccos((50² +90² -55²)/(2·50·90)) = arccos(7575/9000) ≈ 32.7°
__
Y is angle A in the attached triangle solver.
Convert 0.181818 … to a fraction by writing the repeating decimal as an infinite geometric series. Show all of your work (please)
0.181818… = 18 (0.010101…)
… = 18 (0.01 + 0.0001 + 0.000001 + …)
… = 18 (1/100 + 1/100² + 1/100³ + …)
… = 18 (1 + 1/100 + 1/100² + 1/100³ + …) - 18
Then you have
[tex]0.181818\ldots = \displaystyle18\sum_{k=0}^\infty\frac1{100^k} - 18 = \frac{18}{1-\frac1{100}} - 18 = \boxed{\frac2{11}}[/tex]
an experiment consists of tossing a coin five times and observing and the sequence of heads and tails. find pr
Answer:
[tex]P(TTTTT) = \frac{1}{32}[/tex]
Step-by-step explanation:
Given
[tex]n = 5[/tex] --- toss
See comment for complete question
Required
[tex]P(TTTTT)[/tex]
First, we calculate the number of possible outcomes
A coin has 2 faces; Since the coin is to be tossed 5 times;
[tex]Outcome = 2^5[/tex]
[tex]Outcome = 32[/tex]
There is only one outcome of TTTTT;
So:
[tex]P(TTTTT) = \frac{1}{32}[/tex]
Which one correct answer??
What is the question of it ?
Use all the six numerals 4, 5, 6, 7, 8 and 9 to form two 3-digit even numbers whose sum is smallest, and what is the sum?
Step-by-step explanation:
this Is hard to find.............
Answer:
The numbers should be even, it means the unit digits are 4, 6 or 8.
The numbers should be minimal, it means the hundred's digits are 4 and 5.
With this we have possible numbers:
4x6 and 5y8, here 6 and 8 could be exchanged.The options are:
496 and 578 or476 and 598 or498 and 576 or478 and 596The sum of the two numbers is:
1074Please help!
Solve for x
9514 1404 393
Answer:
x = 1
Step-by-step explanation:
The product of lengths to the two circle intercepts are the same for each secant.
7(7+9) = (8x)(8x+6x)
112 = 112x² . . . simplify
1 = x² . . . . . . divide by 112
x = 1 . . . . . . . take the square root (segment lengths are positive)
The figure below consists of a rectangle and a
semicircle. Find the perimeter of the figure. Use π =
3.14.
Step 1: Find the perimeter of the rectangle
The rectangle has two lengths and one width that we need to add together. The width of the rectangle is equal to 2 times the radius (or the diameter) of the circle, which is 16.
25 + 25 + 16 = 66
Step 2: Find the perimeter of the semicircle
The perimeter of a semicircle is equal to half of the circumference.
C = pi x diameter
1/2 (3.14) x (16) = 25.12
Step 3: Find the perimeter of the figure
All that's left to do is add the two perimeters together.
66 + 25.12 = 91.12 m
Hope this helps!
In a sample of 56 bags of fertilizer, the average weight was found to be 17.2lb with a standard deviation of 0.7. Give a point estimate for the population standard deviation of the weight of the bags of fertilizer.
Answer:
???????????????????????