Suppose that you are holding your toy submarine under the water. You release it and it begins to ascend. The graph models the depth of the submarine as a function of time. What is the domain and range of the function in the graph?

Answer:

40.1% probability that he will miss at least one of them

Step-by-step explanation:

For each target, there are only two possible outcomes. Either he hits it, or he does not. The probability of hitting a target is independent of other targets. So we use the binomial probability distribution 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.

0.95 probaiblity of hitting a target

This means that [tex]p = 0.95[/tex]

10 targets

This means that [tex]n = 10[/tex]

What is the probability that he will miss at least one of them?

Either he hits all the targets, or he misses at least one of them. The sum of the probabilities of these events is decimal 1. So

[tex]P(X = 10) + P(X < 10) = 1[/tex]

We want P(X < 10). So

[tex]P(X < 10) = 1 - P(X = 10)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 10) = C_{10,10}.(0.95)^{10}.(0.05)^{0} = 0.5987[/tex]

[tex]P(X < 10) = 1 - P(X = 10) = 1 - 0.5987 = 0.401[/tex]

40.1% probability that he will miss at least one of them

Answer:

i) [tex] 3y^2 -4y +1=0[/tex]

We can divide both sides of the equation by 3 and we got:

[tex] y^2 -\frac{4}{3}y +\frac{1}{3}=0[/tex]

Now we can complete the square and we got:

[tex] (y^2 -\frac{4}{3}y +\frac{4}{9}) +(\frac{1}{3} -\frac{4}{9})=0[/tex]

[tex] (y- \frac{2}{3})^2 =\frac{1}{9}[/tex]

We take square root on both sides and we got:

[tex] y-\frac{2}{3}= \pm \frac{1}{3}[/tex]

And the solutions for y are:

[tex] y_1 = \frac{1}{3} +\frac{2}{3}=1[/tex]

[tex] y_1 = -\frac{1}{3} +\frac{2}{3}=\frac{1}{3}[/tex]

ii) [tex] y =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]

And with [tex] a = 3, b=-4 and c =1[/tex] we got:

[tex] y =\frac{4 \pm \sqrt{(-4)^2 -4(3)(1)}}{2*3}[/tex]

And we got:

[tex] y_1 = 1 , y_2 =\frac{1}{3}[/tex]

Step-by-step explanation:

Part i

For this case we have the following function given:

[tex] 3y^2 -4y +1=0[/tex]

We can divide both sides of the equation by 3 and we got:

[tex] y^2 -\frac{4}{3}y +\frac{1}{3}=0[/tex]

Now we can complete the square and we got:

[tex] (y^2 -\frac{4}{3}y +\frac{4}{9}) +(\frac{1}{3} -\frac{4}{9})=0[/tex]

[tex] (y- \frac{2}{3})^2 =\frac{1}{9}[/tex]

We take square root on both sides and we got:

[tex] y-\frac{2}{3}= \pm \frac{1}{3}[/tex]

And the solutions for y are:

[tex] y_1 = \frac{1}{3} +\frac{2}{3}=1[/tex]

[tex] y_1 = -\frac{1}{3} +\frac{2}{3}=\frac{1}{3}[/tex]

Part ii

We can use the quadratic formula:

[tex] y =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]

And with [tex] a = 3, b=-4 and c =1[/tex] we got:

[tex] y =\frac{4 \pm \sqrt{(-4)^2 -4(3)(1)}}{2*3}[/tex]

And we got:

[tex] y_1 = 1 , y_2 =\frac{1}{3}[/tex]

Answer:

the answer is 8x^2+49x+294+1759/x-6

Answer:

g(x)=3x^2

Step-by-step explanation:

Answer:

8n-25=15+3n

Step-by-step explanation:

We can do this by working backwards and making suitable substitutions.

If n=8

Multiply both sides of the equation by 5

5n=8*5

5n=40

Now, we can rewrite the two sides of the equation as follows

Thus:

5n=40 is equivalent to:

8n-3n=25+15

Add 3n to both sides

8n-3n+3n=25+15+3n

8n=25+15+3n

Subtract 25 from both sides

8n-25=25-25+15+3n

We have:

8n-25=15+3n

Solving this equation will have a solution of n=8.

Answer:

≈103.67cm

Step-by-step explanation:

Shape: Circle

Solved for circumference

Diameter: 33cm

Formula: C=πd

Answer: ≈103.67cm

Hope this helps.

Answer:

C = 33 pi

Step-by-step explanation:

The circumference of a circle is given by

C = pi *d

C = 33 pi

We can approximate pi by 3.14

C = 33*3.14 =103.62

or by using the pi button

C =103.6725576

Answer:

Without any multiple choice options i would have to guess square feet.

Step-by-step explanation:

Answer and Step-by-step explanation:

The matching of the vocabulary word with its corresponding example is shown below:-

a. Data - The list of answers that the 85 Americans give.

Data refers the information that is to be collected.

b. Variable - The answer "Strongly Agree" or "Agree" or "Disagree" or "Strongly disagree".

Variable refers the changes of the expression according to the context.

c. Parameter - The proportion of all Americans who strongly agree that prisoners with life sentences who has Alzheimer's should be released.

A parameter is a quantity that affects a mathematical object's production or behavior, but is considered constant

d. Statistics - The proportion of 85 Americans surveyed who strongly agree that prisoners with life sentences who has Alzheimer's should be released.

Statistics is a field of mathematics involved in data collection, organisation and analysis.

e. Sample - The 85 Americans who participated in the survey.

A sample is the result of an experiment on randomly.

f. Population - All Americans

Population refers to the number of the public.

Answer:

a. Data - The list of answers that the 85 Americans give.

Data refers the information that is to be collected.

b. Variable - The answer "Strongly Agree" or "Agree" or "Disagree" or "Strongly disagree".

Variable refers the changes of the expression according to the context.

c. Parameter - The proportion of all Americans who strongly agree that prisoners with life sentences who has Alzheimer's should be released.

A parameter is a quantity that affects a mathematical object's production or behavior, but is considered constant

d. Statistics - The proportion of 85 Americans surveyed who strongly agree that prisoners with life sentences who has Alzheimer's should be released.

Statistics is a field of mathematics involved in data collection, organisation and analysis.

e. Sample - The 85 Americans who participated in the survey.

A sample is the result of an experiment on randomly.

f. Population - All Americans

Population refers to the number of the public.

Step-by-step explanation:

Answer:

[tex]t=\frac{2.8-3}{\frac{1.2}{\sqrt{64}}}=-1.33[/tex]      

The degrees of freedom are given by:

[tex]df=n-1=64-1=63[/tex]  

The p value for this case would be given by:

[tex]p_v =P(t_{63}<-1.33)=0.0942[/tex]  

If we use a significance level lower than 9% we have enough evidence to FAIL to reject the null hypothesis that the true mean is greater or equal than 3 but if we use a significance level higher than 9% the conclusion is oppossite we reject the null hypothesis

Step-by-step explanation:

Information given  

[tex]\bar X=2.8[/tex] represent the sample mean

[tex]s=1.2[/tex] represent the standard deviation

[tex]n=64[/tex] sample size      

[tex]\mu_o =3[/tex] represent the value to verify

[tex]\alpha[/tex] represent the significance level

t would represent the statistic (variable of interest)      

[tex]p_v[/tex] represent the p value

Hypothesis to verify

We want to check if the true mean for this case is less than 3 minutes, the system of hypothesis would be:      

Null hypothesis:[tex]\mu \geq 3[/tex]      

Alternative hypothesis:[tex]\mu < 3[/tex]      

The statistic for this case is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)      

Replacing we got:

[tex]t=\frac{2.8-3}{\frac{1.2}{\sqrt{64}}}=-1.33[/tex]      

The degrees of freedom are given by:

[tex]df=n-1=64-1=63[/tex]  

The p value for this case would be given by:

[tex]p_v =P(t_{63}<-1.33)=0.0942[/tex]  

If we use a significance level lower than 9% we have enough evidence to FAIL to reject the null hypothesis that the true mean is greater or equal than 3 but if we use a significance level higher than 9% the conclusion is oppossite we reject the null hypothesis

Answer:

B

Step-by-step explanation:

JK = LM (equidistant from centre)

3x+19=6x+7

19-7=6x-3x

12 = 3x

Dividing both sides by 3

x = 4

JK = 3(4)+19

JK = 12+19

JK = 31

Answer:

31

Step-by-step explanation:

JK = LM (since they are equidistant from centre)

3x + 19 = 6x + 7

- 3x = - 12

x = 4

JK = 3 * (4) + 19

= 12 + 19

= 31

Hope this helps!

SEE BELOW FOR THE CORRECT FORMAT OF THE QUESTION

Answer:

(a) [tex]\mathbf{C_{(t)} =\dfrac{I}{F} [ 1- e \dfrac{-Ft}{v}+ C_oe \dfrac{-Ft}{v} ]}[/tex]

(b) [tex]\mathbf{\lim_{t \to \infty} C_t = \dfrac{I}{F}[1-0+ 0 ] \ = \dfrac{I}{F}}[/tex]

(c) T = 6.02619 years

(d) T = 431.593 years

Step-by-step explanation:

(a)

[tex]\dfrac{dC}{dt} = -\dfrac{F}{v}C + \dfrac{I}{v} \\ \\ \\ \dfrac{dC}{dt} + \dfrac{F}{v}C = \dfrac{I}{v}[/tex]

By integrating the factor of this linear differential equation ; we have :

[tex]= e \int\limits \dfrac{F}{v}t \\ \\ \\ = e \dfrac{Ft}{v}[/tex]

[tex]C* e \frac{Ft}{v}= \int\limits \dfrac{I}{v}*e \dfrac{Ft}{v} dt[/tex]

[tex]C* e \frac{Ft}{v}= \dfrac{I}{v}* \dfrac{e \frac{Ft}{v} }{F/v}+ K[/tex]

[tex]C* e \frac{Ft}{v}= \dfrac{I}{v}* \dfrac{V}{F} e \dfrac{Ft}{v} + K[/tex]

[tex]Ce \dfrac{Ft}{v} = \dfrac{I}{F} \ * \ e \dfrac{Ft}{v} + k \ \ \ \ (at \ t = 0 \ ; C = C_o)[/tex]

[tex]C_o = \dfrac{I}{F} e^o + K[/tex]

[tex]K = C_o - \dfrac{I}{F}[/tex]

[tex]C_{(t)} = [ \dfrac{I}{F}e \dfrac{Ft}{v}+ C_o - \dfrac{I}{F}] e\dfrac{-Ft}{v}[/tex]

[tex]C_{(t)} =\dfrac{I}{F} [ e \dfrac{Ft}{v} * e \dfrac{-Ft}{v}+ C_oe \dfrac{-Ft}{v} - 1* e \dfrac{-Ft}{v}][/tex]

[tex]\mathbf{C_{(t)} =\dfrac{I}{F} [ 1- e \dfrac{-Ft}{v}+ C_oe \dfrac{-Ft}{v} ]}[/tex]

(b)

[tex]\lim_{t \to \infty} C_t = \dfrac{I}{F}[1-e^{- \infty} + C_o e^{- \infty} ][/tex]

since  [tex](e^{- \infty} = 0)[/tex]

[tex]\mathbf{\lim_{t \to \infty} C_t = \dfrac{I}{F}[1-0+ 0 ] \ = \dfrac{I}{F}}[/tex]

(c)

V = 458 km³   and F = 175 km³  , I = 0

[tex]\dfrac{dC}{dt} = - \dfrac{-175}{458}C[/tex]

[tex]= \int\limits \ \dfrac{dC}{C} = - \dfrac{175}{458}\int\limits dt[/tex]

[tex]In (C_{(t)}) = - \dfrac{175}{458} t + K[/tex]

[tex]C_{(t)} = e \dfrac{-175}{458}t + K[/tex]

Let at time t = 0 [tex]C_{(t)}} = C_o \to C_o = e^{0+k} = e^K[/tex]

[tex]C_{(t)} = e \dfrac{-175}{458}t[/tex]

Now at time t = T ; [tex]C_{9t)} = \dfrac{C_o}{10}[/tex]

[tex]\dfrac{C_o}{10} = C_o e \dfrac{-175}{458}T \to \dfrac{1}{10} = e \dfrac{-175}{458}T[/tex]

[tex]In ( \dfrac{1}{10}) = \dfrac{-175}{459}T[/tex]

[tex]- In (10) = \dfrac{175}{458}T[/tex]

[tex]T = \dfrac{458}{175} In (10)[/tex]

T = 6.02619 years

(d) V = 12221 km³

F = 65.2 km³/ year

[tex]\mathbf{T = \dfrac{v}{F}In (10)}[/tex]

[tex]T = \dfrac{12221}{65.2}In (10)[/tex]

T = 431.593 years

Answer:

Domain: [10, ∞)

Step-by-step explanation:

Domain is the set of x-values that can be inputted into function f(x).

Step 1: Write equation

f(x) = √(x - 10)

We know that if we get negatives under the square root, we would get imaginary numbers.

Our domain to include all x-values would have to be bigger than 10:

f(10) = √(10 - 10) = √0 = 0

If the number is smaller than 10, we get: f(9) = √(9 - 10) = √-1 = i

Therefore, our real numbers domain would be [10, ∞) or x ≥ 10.

Answer:

The translation corresponds to : [tex]g(x)=\sqrt[3]{x-4}[/tex]

which is the first option in your list of possible answers

Step-by-step explanation:

Notice that this new function's graph responds to a horizontal translation to the right of the original graph of [tex]f(x)=\sqrt[3]{x}[/tex]. Notice that the crossing of the x-axis, which for f(x) is at the origin (0, 0), has now moved to the point (4,0), which means a translation to the right in exactly 4 units.

Recall that horizontal translations are performed by subtracting from the independent variable  (x) , the number of units you move (in this case 4)

Therefore the new function should look like:

[tex]g(x)=\sqrt[3]{x-4}[/tex]

The answer is A.

did the test

Answer:

5/4   5 ft

Step-by-step explanation:

We are going from 12 to 15

We need to multiply by

15 = k *12

Divide each side by 12

15/12 = k

5/4 = k

The scale factor is 5/4

1 in = 4 ft

Multiply the 4 ft by the scale factor

1 in = 4 * 5/4 = 5 ft

1 in = 5 ft

Answer:

Raphael saw a square patio that was 12-feet long on each side. He wants to build a patio that will be 15-feet long on each side.

The change in the scale factor is  

✔ 4/5

.

The change of scale means that 1 inch represented  4 feet, but now 1 inch represents  

✔ 5

feet.

Step-by-step explanation:

Meters measures length, hectares measures area.

1 hectare = 10,000 m²

Answer Meters measures length, hectares measures area.

1 hectare = 10,000 m²

Step-by-step explanation:

Answer:

8 units

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh where b is the base and h is the height

16 = 1/2 (4)*x

16 = 2x

Divide each side by 2

16/2 = 2x/2

8 =x

Answer:

  6%

Step-by-step explanation:

Out of 100 rolls, there were 6 instances of 3. The experimental probability of rolling a 3 is ...

  6/100 = 6%

Step-by-step explanation:

-3(7 + 5) + 9(2)

-3(12) + 18

-36 + 18

= - 18

In my opinion this should be the answer

Answer:

14

Step-by-step explanation:

Your welcome!

Answer:

= 140800 cubic (ft/meters/yards/cm/inches)

Step-by-step explanation:

For Cone

radius (r) = 80

height (h) = 21

Volume Of Cone

= π r² h/3

= 22/7 x 80 x 80 x 21/3

= 22 x 80 x 80

= 22 x 6400

= 11 x 12800

= 140800 cubic (ft/meters/yards/cm/inches)

Answer: 39 minutes 51 seconds

Step-by-step explanation:

Nt=N0 * 2^n

N0=Initial population

n=number of times bacteria divide

700=320*2^n

log2(700/320)=1.129283017=n

45/1.129283017=39.84829252 minutes

0.84829252*60=50.89755135≈51seconds

so the answer is

39minutes and 51seconds

Answer:

2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

[tex]\dfrac{1}{5} $ square foot.[/tex]

Step-by-step explanation:

Area of the Poster =1 sq.ft.

The collage will cover a part of the poster that is [tex]\dfrac{1}{3} ft.$ wide and \dfrac{3}{5} ft.$ long.[/tex]

Area of the Photo Collage Section

=Length X Width

[tex]=\dfrac{1}{3} X \dfrac{3}{5} \\\\=\dfrac{1}{5} $ square foot.[/tex]

[tex]\text{Therefore, the photo collage will cover }\dfrac{1}{5} $ of a square foot.[/tex]

Answer:

x = 40

Step-by-step explanation:

The angles are vertical angles.  We know that vertical angles are equal

120 = 3x

Divide each side by 3

120/3 = 3x/3

40 =x

Answer:

40

Step-by-step explanation:

I forgot what you would call this, but basically 3x = 120. both of the angles are the same. So divide both sides of the equation by 3. 3x/3 = 120/3 and your answer is 40.

It's a bad explanation but I hope it helps!

Answer:

82 1/3

Step-by-step explanation:

89 - 6 2/3

Borrow 1 from the 89 in the form of 3/3

88 + 3/3 - 6 2/3

88 3/3 - 6 2/3

Subtract the whole numbers

88-6 =82

Subtract the fractions

3/3 - 2/3 = 1/3

82 1/3

9514 1404 393

Answer:

  B, D

Step-by-step explanation:

The volume is the product of the dimensions. For dimensions 9 ft, 9 ft, 10 ft, the volume is found by multiplying (9 ft) × (9 ft) × (10 ft) = 810 ft³.

To fill the volume with boxes of volume 1 ft³ would require 810 boxes.

Answer:

[tex] \boxed{D. \: 40\degree} [/tex]

Step-by-step explanation:

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°

So,

[tex] = > 2y \degree + (y + 10)\degree + 50\degree = 180\degree \\ \\ = > 2y\degree + y\degree + 10\degree + 50\degree = 180\degree \\ \\ = > 3y\degree + 60\degree = 180\degree \\ \\ = > 3y\degree = 180\degree - 60\degree \\ \\ = > 3y\degree = 120\degree \\ \\ = > y = \frac{120\degree}{3\degree} \\ \\ = > y = 40\degree [/tex]

Answer:

0.7881 = 78.81% probability that the percent of 18 to 34 year olds who check social media before getting out of bed in the morning is, at most, 32.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

[tex]\mu = 28, \sigma = 5[/tex]

Find the probability that the percent of 18 to 34 year olds who check social media before getting out of bed in the morning is, at most, 32.

This is the pvalue of Z when X = 32. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{32 - 28}{5}[/tex]

[tex]Z = 0.8[/tex]

[tex]Z = 0.8[/tex] has a pvalue of 0.7881

0.7881 = 78.81% probability that the percent of 18 to 34 year olds who check social media before getting out of bed in the morning is, at most, 32.

Answer:

The standard cost of Bramble's product is $69.5 per unit.

Step-by-step explanation:

We can calculate the standard cost per unit of Bramble's product as the sum of the material cost, direct labor cost and overhead cost.

Each unit of product uses 2 pounds of materials, that cost $6 per pound. So the material cost is:

[tex]MC=2\,lb/u\cdot6\,\$/lb=12\,\$/u[/tex]

Each unit needs 2.5 direct labor hours, and they have a cost of $11 per hour, so the direct labor cost is:

[tex]LC=2.5\,h/u\cdot11\,\$/h=27.5\,\$/u[/tex]

The overhead costs are calculated in this case as $12 per direct labor hour. As 2.5 labor hours are needed per unit, we have:

[tex]OC=2.5\,h/u\cdot 12\,\$/h=30\,\$/u[/tex]

The standard cost is then:

[tex]C=MC+LC+OC=12+27.5+30=69.5\,\$/u[/tex]