Think about Digit's game of spinning the spinner.

He wants to know the probability of the following events happening on two separate spins.

A: spinning praline wafer

B: spinning oven-baked apple & lavender calzone

Which formula should Digit use to find the probability?

P(A∩B)=P(A)⋅P(B|A)
P(A∪B)=P(A)+P(B)
P(A∪B)=P(A)+P(B)−P(A∩B)
P(A∩B)=P(A)⋅P(B)

Answer:

y = 3x

Step-by-step explanation:

In this case, the ratio between sugar and water is 0.5 : 1.5 or 1 : 3.

That means that you need three cups of water for every cup of sugar.

In order to put this into an equation, the slope would be 3/1 or simply 3, and the y-intercept is 0. Even if you used the 0.5 : 1.5 ratio, the slope would be the same since 1.5 / 0.5 = 3.

Answer: (0,2)

The y-int is 2

Answer:

the y-intercept is 2

Answer:

Step-by-step explanation:

5

Answer:

800

Step-by-step explanation:

Answer:

The answer is 15. Each one is 5 pieces and there are 3 of them. so 5 x 3 = 15

Step-by-step explanation:

Answer:

15 pieces

Step-by-step explanation:

3*5= 15

Answer:

y=6x+1

Step-by-step explanation:

y=mx+b

You replace m with 6 and b with 1.

Answer:

m=6,b=1

Step-by-step explanation:

bc find the value of b using formal for the equation of the line , hope this helped ^^

Answer:

270,650 is the answer

Step-by-step explanation:

Answer:

21.6

Step-by-step explanation:

Do  0.18 (18%) times 120

Answer:

21.60

Step-by-step explanation:

18% of 120 is 21.60, so we would tip her hairdresser that much :)

160-120= 40

She lost 40 pounds

25% of 160 is 40

Percentage=160 x 25/100 =40

So she lost %25 of her weight (good job lol)

Answer:

I think its A

Step-by-step explanation:

...

Answer:

the answer is D I hope it helps you

Answer:

a

Step-by-step explanation:

Answer:

The answer is A

Step-by-step explanation:

If you put in a calculator 4/5 and then 64/80 you get the same decimal meaning that they have the same ratio.

Answer:

T = -22/r + 39

(a) y = [130 − 130e^(-0.015t)] / 3

(b) 22.9

Step-by-step explanation:

d²T/dr² + 2/r dT/dr = 0

If S = dT/dr, then:

dS/dr + 2/r S = 0

dS/dr = -2/r S

dS / S = -2/r dr

ln S = -2 ln r + C

S = e^(-2 ln r + C)

S = Ce^(-2 ln r)

S = C [e^(ln r)]^-2

S = C / r²

dT/dr = C / r²

dT = C dr / r²

T = -C / r + D

When r=1, T=17.

17 = -C + D

When r=2, T=28.

28 = -C/2 + D

Solving:

11 = C/2

C = 22

D = 39

T = -22/r + 39

We can check our answer by finding dT/dr and d²T/dr².

dT/dr = 22/r²

d²T/dr² = -44/r³

Plug into the original equation:

d²T/dr² + 2/r dT/dr = 0

-44/r³ + 2/r (22/r²) = 0

0 = 0

The total flow into the tank is 15 L/min, and the total flow out is 15 L/min, so the volume is constant at 1000 L.  The amount of salt added to the tank is:

(0.05 kg/L) (5 L/min) + (0.04 kg/L) (10 L/min) = 0.65 kg/min

If y is the amount of salt in the tank at time t, and y/1000 is the concentration in the tank at time t, then the amount of salt removed from the tank is:

(y/1000 kg/L) (15 L/min) = 0.015y kg/min

The change in salt over time equals the amount of salt in minus the amount of salt out.

dy/dt = 0.65 − 0.015y

-200 dy/dt = 3y − 130

dy / (3y − 130) = -0.005 dt

3 dy / (3y − 130) = -0.015 dt

ln(3y − 130) = -0.015t + C

3y − 130 = Ce^(-0.015t)

3y = 130 + Ce^(-0.015t)

y = [130 + Ce^(-0.015t)] / 3

At t=0, y=0:

0 = (130 + C) / 3

C = -130

y = [130 − 130e^(-0.015t)] / 3

At t=50:

y = [130 − 130e^(-0.75)] / 3

y ≈ 22.9

Answer:

94.2%

Step-by-step explanation:

Most of the materials is converted into product.

Assuming the amount of material discharged = the amount of product discharged.

The percentage of material discharged is

(895/950)×100 = 94.2%

Answer:

$1.50

Step-by-step explanation:

The constant of proportionality will be the cost for 1 ticket. This means you can find it by dividing the amount for 5 tickets.

7.5=5 tickets

divide both sides by 5

1.5= 1 ticket

one ticket costs $1.50, or the constant of proportionality

Answer:

1.50 would be your answer

Step-by-step explanation:

Ride Tickets x $1.50 = Cost

Hope this helpss!!

Answer:

x plus 4 times 5

Step-by-step explanation:

Answer:

5x + 20

Step-by-step explanation:

5 (x + 4)

which is 5x + 20

.

Answer:

(−7,−8)

Step-by-step explanation:

Answer:

2.5%

Step-by-step explanation:

Since the mean is 53.2, a fuel consumption of 43.6 mpg is 53.2−43.6=9.6 mpg less than the mean, which is 2 standard deviations.

By the Empirical Rule, we know that about 95% of the data lies within 2 standard deviations of the mean. Therefore, 100%−95%=5% of the data lie more than 2 standard deviations away from the mean.

Since the distribution of hybrid vehicle fuel consumptions is symmetric, about half of the remaining 5% will lie to either extreme. So about 2.5% of fuel consumptions are less than 43.6 mpg.

The normal distribution is a symmetric probability distribution about the mean. The percentage of hybrid vehicle fuel consumption that is less than 43.6 mpg is 2.5%.

The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.

Given that the mean is 53.2, while the standard deviation is 4.8 mpg. Therefore, Accoding to the emperical rule, we can write the values as,

μ+3σ = 67.6

μ+2σ = 62.8

μ+σ = 58

μ = 53.2

μ-σ = 48.4

μ-2σ = 43.6

μ-3σ = 38.8

Therefore, The percentage of hybrid vehicle fuel consumption that is less than 43.6 mpg is,

Percentage = (0.15 + 2.35)% = 2.5%

Hence, The percentage of hybrid vehicle fuel consumption that is less than 43.6 mpg is 2.5%.

Learn more about Normal Distribution:

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Answer:

None of the choices are correct.

Step-by-step explanation:

To divide a fraction by another fraction, multiply the first fraction by the reciprocal of the second fraction.

2/5 divided by 1/4 = 2/5 times 4/1 = 2/5 times 4

Correct answer: Multiply 2/5 by 4

Answer: None of the answers are correct.

Answer:

None

Step-by-step explanation:

Answer:

8.2

Step-by-step explanation:

1. Since AD is equal to DB, we will need to set 3x-11 equal to 5x-29. When you solve the equation you will get 9 for x.

2. Plug the 9 in for x in DB (you could plug it in for AD instead if you want since DB and AD are equal to each other). You should get 16.

3. Take a look at the smaller triangle DBP which is part of triangle ABC. We will need to use the Pythagorean Theorem. Square the legs of the triangle and set it equal to the hypotenuse squared. One of the legs, DP, is unknown so we will just have it as x. The other leg is DB, which is 16.

* PB is the hypotenuse and has a value of 18. Remember that P is the circumcenter, which means it is equidistant to each vertex and each angle bisector is equal to each other. As a result PC is equal to PB which happens to be 18.

You should have it something like this:

16^2 + x^2 = 18^2

Now do all the squaring and stuff and you should eventually get x^2 = 68

4. Square root x^2 = 68 and you will get a long decimal. You will need to round it to the tenths place.

5. After rounding you will finally get 8.2

The measurement of DP is 8.2 units.

The circumcenter of a triangle is defined as the point where the perpendicular bisectors of the sides of that particular triangle intersect.

Given that, P is the circumcenter △ ABC, and AD = 3x - 11, DB =5x - 29,

PC = 18

Since, DP bisects AB, so, AB = DP

3x-11 = 5x-29

x = 9

DB = 5*9 - 29 = 16

Since, P is the circumcenter, then PB = PC = PA = 18

Using Pythagoras theorem in Δ BPD

PB² = DB² + DP²

DP² = PB² - DB²

DP² = 18² - 16²

DP² = 324 - 256

DP² = 68

DP = 8.2

Hence, The measurement of DP is 8.2 units.

For more references on circumcenter of a triangle, click;

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Answer:

A

Step-by-step explanation:

Answer:

24 1/4 lbs

Step-by-step explanation:

She starts off with 32 1/2 lbs.

She then gives 8 1/4 to her friend.

To find how much she has left, we subtract 8 1/4 from 32 1/2.

To make this easier, lets make them both have a common denominator:

32 2/4 - 8 1/4 = 24 1/4

I hope this helped, please mark Brainliest, thank you so much!

Answer:

gcf is 20 lcm is 40

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

Recall that circumference is given by:

[tex]C=2\pi r[/tex]

We know that the circumference is 8π inches. Thus, we can substitute 8π for C:

[tex]8\pi =2\pi r[/tex]

To solve for r, the radius, we can divide both sides by 2π. Hence:

[tex]\displaystyle r = \frac{8\pi}{2\pi}=4[/tex]

Therefore, the radius is four inches.

Our answer is A.

Answer:

7/60 hour or 7 minutes b) 8 or 8 4/7 depending if you consider a fraction of a task is yes or no

Step-by-step explanation:

Answer:

y = 4x + 9

week 21

Step-by-step explanation:

first I did 37-9 and got 28 I divide that by 7 ( seven weeks) and got 4 so I know the slope is 4.

so to find how many weeks till 93 I did; 93 = 4x + 9. We have to get x by its self so I minus 9 by both sides and got 84 = 4x. So now we divid both sides by 4 to get x by its self and we end up with 21 = x

Answer: A) [tex]y=13e^{-0.1359t}[/tex]

              B) H = 5.10

              C) Yes

Step-by-step explanation: Exponential Decay function is a model that describes the reducing of an amount by a constant rate over time. Generally, it is written in the form: [tex]y(t)=Ce^{rt}[/tex]

A) C is initial quantity, in this case, the initial concentration of DDT. To determine r, using the data given:

[tex]y(t)=Ce^{rt}[/tex]

[tex]2.22=13e^{13r}[/tex]

[tex]e^{13r}=0.1708[/tex]

Using a natural logarithm property called power rule:

[tex]13r=ln(0.1708)[/tex]

[tex]r=\frac{ln(0.1708)}{13}[/tex]

[tex]r=-0.1359[/tex]

The decay function for concentration of DDT through the years is [tex]y(t)=13e^{-0.1359t}[/tex]

B) The value of H is calculated by [tex]y=C(0.5)^{\frac{t}{H} }[/tex]

[tex]2.22=13(0.5)^{\frac{13}{H} }[/tex]

[tex](0.5)^{\frac{13}{H} }=0.1708[/tex]

Again, using power rule for logarithm:

[tex]\frac{13}{H} log(0.5)=log(0.1708)[/tex]

[tex]\frac{13}{H} =\frac{log(0.1708)}{log(0.5)}[/tex]

[tex]\frac{13}{H} =2.55[/tex]

H = 5.10

Constant H in the half-life formula is H=5.10

C) Using model [tex]y(t)=13e^{-0.1359t}[/tex] to determine concentration of DDT in 1995:

[tex]y(24)=13e^{-0.1359.24}[/tex]

y(24) = 0.5

By 1995, the concentration of DDT is 0.5 ppm, so using this model is possible to reduce such amount and more of DDT.

Answer: yo if you look up math equation calculator and type that equation in it would solve the problem step by stem.

Step-by-step explanation: i hope this helps :D

Answer:

Number 6 is 3, Iḿ pretty sure if not sorry I tried my best

Step-by-step explanation:

Answer:

n=0.6

Step-by-step explanation:

We want to get n alone so we can divide each side by 0.09.

So then n= 0.054/0.09.

n=0.6

Hope this helps! If you have any questions on how I got my answer feel free to ask. Stay safe!

Complete question is;

Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other two vertices above the x-axis and lying on the parabola. (Round your answers to the nearest hundredth.) y = 6 - x²

Answer:

height = 4 and base = 2√2

Step-by-step explanation:

Area of a rectangle is given by;

A = base(b) × height(h)

To start off, we will first have to consider half of the rectangle.

Due to the fact that it is bounded by a parabola which is symmetric over the y-axis, it means that the rectangle will have the same area on the right and left hand sides.

So if we maximize the area of the first quadrant, it means that we are also maximizing the area of the entire rectangle.

Now, since we are dealing with the base and other 2 vertices on the x-axis, it means that the base(b) of this half rectangle will be x.

The height of this rectangle is the y coordinate of the corner that is directly above the x coordinate, which is also on the rectangle.

Therefore, the coordinates of the upper corner will be (x, y), or (x, 6 - x²). Thus our half base is x and full height is 6 - x². Area will be;

A = x(6 - x²)

A = 6x - x³

We will maximize this area by finding the derivative and equating to zero.

Thus;

A' = 6 - 3x²

At A' = 0,we have;

6 - 3x² = 0

3x² = 6

x² = 6/3

x² = 2

x = √2

Thus, from y = 6 - x², we have;

y = 6 - (√2)²

y = 6 - 2

y = 4

Since x is half base, it means our full width is 2x = 2 × √2 = 2√2

So, height = 4 and base = 2√2