Jessica has 28 coins. One fourth of them are quarters. Two thirds of the rest of the coins are dimes. The remaining ones are nickels. How many quarters, dimes, and nickels does he have? How much money does he have in coins? If he wants to buy 2 packs of cards, with each pack $1.35, how much money would he have left?

Answer:

???????????????????????

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.

Answer:

plz check ur school solution down.

Step-by-step explanation:

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.

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)

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]

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]

Step-by-step explanation:

a)

0.00000000007

b)

0.00000001

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.

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]

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]

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.

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]

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.

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

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.

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

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]

Answer:

At most 3 calls: 64.7%

At least 3 calls: 57.7%

5 or more calls: 18.5%

Step-by-step explanation:

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 ...

What is the question of it ?

Answer:

Answer:

A is the answer

Step-by-step explanation:

A

plz mark it brainlist

Answer:

he casted 4.3. away

Step-by-step explanation:

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:

The options are:

The sum of the two numbers is:

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]

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)

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!