Tabetha spends $1.79 on a 20 oz bottle of Mountain Dew. How much did she pay per ounce?

Answer:

a) 0.30567

b) 0.69433

Step-by-step explanation:

We solve using z score formula

z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.

,a.Find the probability that the student earned between 80 and 90 points.

For 80 students

z = 80 - 78/10

= 0.2

P-value from Z-Table:

P(x = 80) = 0.57926

For 90 students

z = 90 - 78/10

= 1.2

P-value from Z-Table:

P(x = 90) = 0.88493

The probability that the student earned between 80 and 90 points.

P(x = 90) - P(x = 80)

= 0.88493 - 0.57926

= 0.30567

b.Find the probability that the student earned either less than 80 points or more than 90 points.

For less than80 students

z = 80 - 78/10

= 0.2

P-value from Z-Table:

P(x < 80) = 0.57926

For 90 students

z = 90 - 78/10

= 1.2

P-value from Z-Table:

P(x<90) = 0.88493

P(x>90) = 1 - P(x<90) = 0.11507

The probability that the student earned either less than 80 points or more than 90 points.

= 0.57926 + 0.11507

= 0.69433

Answer:

I never learned that sorry ‍♀️

Answer:

y=-2x

Step-by-step explanation:

rise over run. Points to points

you do down 2 to get to another point and you go over 1.

rear makes the slope -2x

Answer:

12 ( or 24, depending on what the question is asking)

Step-by-step explanation:

The lowest common multiple of 12 and 2 is 12.

If Charlotte doesn't write anymore pages after writing the original twelve, and Barry writes 2 pages six times, they both write the same number of pages. So, the smallest number of pages is 12

However, if the question is asking for the smallest total number of pages, then the answer is 24 since they both write 12 pages each.

Answer:

Answer: 1. x = 10, y = 6 2. x = 12, y = 3 3. x = 5, y = 2.5 4. x = 1, y = 14 5. x = 0.6, y = 7 6. x = 11, y = 1

Step-by-step explanation:

Answer:

38 students

Step-by-step explanation:

100+(16x6)=196

800-196=631

4.50+12=16.5

63/116.5=38.24

Answer:

100+4.50(s)+12(s)+96 less than or equal to 800

[tex] \leqslant [/tex]

s=students

Step-by-step explanation:

they can spend up to 800 dollars OR LESS. They have a charge of 100 dollars for the bus, plus a charge of 4.50 per student for lunches, plus a charge of 12 dollars per student for admissions plus 16 dollars times 6 (96) for the chaperones. All of this gives us our inequality above.

I really hope this helps!

PS: the reason why the adults don't get their own variable is because it says to define the variable not variable(s). You also cannot group the adults with the students because the student costs and the adult costs are two totally seperate and different amounts. if you just used variable p for people it wouldn't work because you wouldn't know how many adults were required to pay adult admission.

Answer:

She should add 6 cups.

Answer 6

Step-by-step explanation: 4 divided by 2/3

Answer:

do you have the graph?

Step-by-step explanation:

Answer:

0.621%

Step-by-step explanation:

First of all let's find the z-score which is given by the formula;

z = (x' - μ)/σ

We are given;

Mean; μ = 80 g

Standard deviation; σ = 2 g

Test score; x' = 85 g

Thus;

z = (85 - 80)/2

z = 5/2

z = 2.5

From the z-distribution table attached, at z = 2.5, the probability is:

P(z > 2.5) = 1 - 0.99379 = 0.00621 or 0.621%

Answer:

10.16°

Step-by-step explanation:

To solve for this question, we use Sine rule

Sin θ = Opposite/Hypotenuse

θ =??

Opposite = Height of the truck = 3 feet

Hypotenuse = length of the ramp = 17 feet

Hence

Sin θ = 3/17

Sin θ = 0.1764705882

θ = arcsin(0.1764705882)

θ = 10.16424862°

Approximately

10.16°

The angle the ramp makes with the ground is 10.16°

The angle that the ramp makes with the ground is 10.2 degrees

The set-up will give a right triangle.

Given the following parameters:

To get the angle of elevation, we will use the SOH CAH TOA identity as shown:

Sin theta = opp/hyp

Sin theta = 3/17

theta = arcsin(3/17)

theta = 10.2 degrees

Hence the angle that the ramp makes with the ground is 10.2 degrees

Learn more on trigonometry here: https://brainly.com/question/24349828

Answer:

68.6433≤x≤82.3568

Explanation

confidence interval formula is expressed as

CI = xbar ± z × S/√n

xbar is the mean

z is the z score at 90% = 1.645

s is the Standard deviation

N is the sample size = 5

xbar = 60+75+80+70+ 90/5

xbar = 375/5

xbar = 75

Get standard deviation

SD =√\sum(x-xbar)²/N

SD = √(60-75)²+(75-75)²+(80-75)²+(70-75)²+(90-75)²/5

SD = √15²+0²+5²+5²+15²/5

SD = √225+50+225/5

SD = √500/5

SD =√100

SD = 10

Substitute the derived values into the formula

CI = 75±1.645 × 10/√5

CI = 75 ± (1.645×4.4721)

CI = 75±7.3568

CI = (75-7.3568, 75+7.3568)

CI = (67.6433, 82.3568)

Hence the 90% confidence interval of the student is:

68.6433≤x≤82.3568

The first question shows how the value of x is bigger than the value of -3 while the second question shows how the value of x is smaller than the value of -3.

Hope this helps!

Answer:

  40

Step-by-step explanation:

2³ + 4×8

8 + 32 = 40

PEMDAS:

  Handle the exponents, multiply, then add.

Answer:

X = -10

Step-by-step explanation:

Combine like terms

2x + 34 = 14

minus 34.

2x = -20

divide by 2

x = -10

Answer:

x=-10???

Step-by-step explanation:

I just combined like terms and got it from there.

Answer: 1 student scored above an 85%.

Step-by-step explanation:

Let X = percentage score in test (normally distributed).

Given: Sample size = 15 , mean score : [tex]\mu[/tex]= 74.8% = 0.748 ,standard deviation :  [tex]\sigma=7.57[/tex]

Now, The probability that student scores above 85%:

[tex]P(X>85)=P(\dfrac{X-\mu}{\sigma}>\dfrac{85-74.8}{7.57})\\\\=P(Z>1.347)\\\\=1-P(Z<1.347)\\\\=1-0.9110= 0.089[/tex]

Probability that student scores above 85% = 0.089

Number of students scored above an 85% = 0.089 x 15 = 1.335 ≈ 1

hence, 1 student scored above an 85%.

Answer:

=11/14

Step-by-step explanation:

Step-by-step explanation:

Number of blue marbles n(blue)=4

Number of red marbles n(red)=3

number of yellow marbles n(yellow)= 2

number of green marbles n(green)=5

total number of marbles n(S)=4+3+2+5=14

P(red)=n(red)/n(S)

P(red)=3/14

We have to determine the probability that the card picked is not red which means the card can be blue or yellow or green.

P(not red)=1-P(red)

               =1-3/14

                =11/14

Answer:

11/14

Step-by-step explanation:

These are all the marbles that are there:

4 blue

3 red

2 yellow

5 green

If you want to figure out the probability of a marble not being red, you can either find the probability that the marble is blue, yellow, or green or you could subtract the probability that the marble is red from 1 (same thing either way)

There are 14 marbles and 11 of them are not red, so the the probability that a marble drawn will not be red is 11/14.

Answer:

5

Step-by-step explanation:

90-45 = 45

45 x 1/9 = 5

45 x 1/9 is the same thing as saying 45/9, FYI

Answer:

5

Step-by-step explanation:

sub 45 into x

h(x) = h(45)

h(45) = 1/9(90-45)

= 1/9(45)

= 5

^^

Answer:

P(A ∪ C) = 0.35

Step-by-step explanation:

Given:

25% speak Arabic

20% speak Chinese

10% speak both languages

Find:

Probability that the student can speak Chinese or Arabic P(A U C)

Computation:

P(A ∪ C) = P(A) + P(C) - P(A ∩ C)

P(A ∪ C) = 0.25 + 0.2 - 0.1

P(A ∪ C) = 0.35

Answer:

Kindly check explanation

Step-by-step explanation:

Given that:

Variable cost = $20

Fixed cost = $30000

selling price = $49

Number of CD's produced = x

Cost (C) as a function of number of CD's produced :

Fixed cost + (variable cost * Number produced)

C = $30000 + ($20 * x)

C = $30000 + 20x

Revenue :

Selling price per CD * number of CDs produced

$49 * x

R = 49x

PROFIT:

REVENUE - COST

$30000 + 20x - 49x

30000 - 29x

Number of CD's which must be produced to break even:

Break even quantity = Fixed costs / (Sales price per unit – Variable cost per unit)

Break even quantity = 30000 / (49 - 20)

= 30000 / 29

= 1034.48

= 1034

Answer:

12

Step-by-step explanation:

It seems like the one that's most likely

Answer:

The interest rates implied by the combinations of present and future values are:

Present Value   Years   Future Value   Interest Rate

$310                     12             496                 3.994%

 138                      5              194                 7.049%

210                      8              210                  -0.000%

Step-by-step explanation:

a) Data and Calculations:

Present Value   Years   Future Value    Interest Rate

$310                     12             496                 3.994  %

 138                      5              194                  7.049%

210                      8              210                  -0.000%

b) You will need an annual return rate of 3.994% to reach the future value of $496.00.

FV (Future Value) $496.00

PV (Present Value) $310.00

N (Number of Periods) 12.000

I/Y (Interest Rate) 3.994%

PMT (Periodic Payment) $0.00

Starting Investment $310.00

Total Principal $310.00

Total Interest $186.00

c) You will need an annual return rate of 7.049% to reach the future value of $194.00.

FV (Future Value) $194.00

PV (Present Value) $138.00

N (Number of Periods) 5.000

I/Y (Interest Rate) 7.049%

PMT (Periodic Payment) $0.00

Starting Investment $138.00

Total Principal $138.00

Total Interest $56.00

d) You will need an annual return rate of -0.000% to reach the future value of $210.00.

FV (Future Value) $210.00

PV (Present Value) $210.00

N (Number of Periods) 8.000

I/Y (Interest Rate) -0.000%

PMT (Periodic Payment) $0.00

Starting Investment $210.00

Total Principal $210.00

Total Interest $-0.00

Answer:

[tex]y=15e^{e^{- \frac{t}{100}}}kg[/tex]

Step-by-step explanation:

Let y(t) represent the amount of salt in the tank after t minutes. Therefore:

[tex]\frac{dy}{dt}=rate\ in-rate\ out[/tex]

Pure water is entering at a rate of 10 L/min, therefore rate in = 0

The tank contains 1000 L of brine (salt water) with 15 kg of dissolved salt, and a mixed solution leaving at 10 L/min hence;

[tex]rate\ out = \frac{y(t)\ kg}{1000\ L}*10\ L/min= \frac{y(t)\ kg}{100\ min}\\\\Therefore:\\\\\frac{dy}{dt}=0- \frac{y(t)}{100} \\\\\frac{dy}{dt}=- \frac{y(t)}{100}\\\\\frac{dy}{y}=- \frac{1}{100}dt\\\\\int\limits{\frac{dy}{y}} =\int\limits- \frac{1}{100}dt\\\\lny=- \frac{t}{100}+C\\\\Taking\ exponetial\ of\ both\ sides:\\\\y=e^{- \frac{t}{100}+C}\\\\y=e^C.e^{- \frac{t}{100}}\\\\y=Ae^{- \frac{t}{100}}(A=e^C)\\\\at\ y=15kg, t=0\\\\15=Ae^{e^{- \frac{0}{100}}}\\\\A=15\\\\[/tex]

[tex]y=15e^{e^{- \frac{t}{100}}}kg[/tex]

Answer:

[tex]\displaystyle 5[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Calculus

Limits

Limit Rule [Variable Direct Substitution]:                                                             [tex]\displaystyle \lim_{x \to c} x = c[/tex]

Derivatives

Derivative Notation

Instantons Rate of Change

Step-by-step explanation:

Step 1: Define

Identify

f(x) = 2x² + x - 1

x = 1

Step 2: Find Change

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Derivatives

Book: College Calculus 10e

Answer:

P (x= 0) =  0.00384

P (x= 1) =   0.000009133

P (x= 2) = 0.00009399

P (x= 3) =  0.0061

P (x= 4) = 0.00281

P (x= 5) =  0.00975

P (x= 6) = 0.0264

P (x= 7) = 0.05772

P (x= 8) =  0.0202

P (x= 9) = 0.14550

P (x= 10) =  0.1733

P (x= 11) =  0.17077

P (x= 12) =  0.138751

P (x= 13) =  0.0925

P (x= 14) = 0.0501

P (x= 15) = 0.0217

P (x= 16) =  0.00735

P (x= 17) =  0.00187

P (x= 18) =  0.000259

P (x= 19) = 2 0.0000385

P (x= 20) =0.000000208

Step-by-step explanation:

This is a binomila probability distribution as the success and failure are same and number of trials is fixed.

Here p =0.52 and q= 1-0.52= 0.48

n= 20 Now the probability distribution of X = 0,1,2,--------20

Applying the binomial distribution we can find the probability  distribution of X taking the different values as

P (x= 0) = 20c0 (0.52)^0 (0.48)^20= 0.00384

P (x= 1) = 20c1 (0.52)^1 (0.48)^19=  0.000009133

P (x= 2) = 20c2 (0.52)^2 (0.48)^18=  0.00009399

P (x= 3) = 20c3 (0.52)^3 (0.48)^17= 0.0061

P (x= 4) = 20c4 (0.52)^4 (0.48)^16= 0.00281

P (x= 5) = 20c5 (0.52)^5 (0.48)^15= 0.00975

P (x= 6) = 20c6 (0.52)^6 (0.48)^14= 0.0264

P (x= 7) = 20c7 (0.52)^7 (0.48)^13= 0.05772

P (x= 8) = 20c8 (0.52)^8 (0.48)^12= 0.0202

P (x= 9) = 20c9 (0.52)^9 (0.48)^11= 0.14550

P (x= 10) = 20c10 (0.52)^10 (0.48)^10= 0.1733

P (x= 11) = 20c11 (0.52)^11 (0.48)^9= 0.17077

P (x= 12) = 20c12 (0.52)^12 (0.48)^8= 0.138751

P (x= 13) = 20c13 (0.52)^13 (0.48)^7= 0.0925

P (x= 14) = 20c14 (0.52)^14 (0.48)^6= 0.0501

P (x= 15) = 20c15 (0.52)^15 (0.48)^5= 0.0217

P (x= 16) = 20c16 (0.52)^16 (0.48)^4= 0.00735

P (x= 17) = 20c17 (0.52)^17 (0.48)^3= 0.00187

P (x= 18) = 20c18 (0.52)^18 (0.48)^2= 0.000259

P (x= 19) = 20c19 (0.52)^19 (0.48)^1= 0.0000385

P (x= 20) = 20c20 (0.52)^20 (0.48)^0= 0.000000208

Answer: -12

Step-by-step explanation:

If the equation is multiplying all the numbers, the equation would be -2x2y, which is making the new equation is -2(-3)2(-1). Multiply the numbers 6x-2, which is -12

Answer:

the simplest form of 1/9 is: 1/9

Step-by-step explanation:

1. A number that will divide evenly into both the numerator and denominator so it can be reduced. No such number exists for 1 and 9.

2. The numerator must be greater than the denominator, an improper fraction, so it can be converted to a mixed number. 1 is not greater than 9.

Answer:

I think it goes like this: 10^-99, 10^-17, 10^-5, 10^5, 10^14, 10^30

Step-by-step explanation: