Questions 16-17. Suppose a tortoise is 1000 feet from the ocean. Each day the tortoise travels three-fifths of the remaining distance to the ocean. Use this information to: Construct a model that represents the remaining distance that the tortoise must travel to reach the ocean.

Answer:  m∠BAC =36.87°

It is given, but maybe difficult to see.

Step-by-step explanation: If you had to calculate it yourself, you need a scientific calculator or a conversion chart. You could figure the sine by dividing the  length of the opposite side, 6 by the length of the hypotenuse, 10. you get sine=0.6  

Then use the calculator or chart to get the angle.

input sin^-1 (0.06)

Answer:

p > α

0.7038 > 0.05

Also since F < F critical

0.475 < 3.238

We failed to reject H₀

We do not have significant evidence at the given significance level to show that there is a difference among the four chemical agents on the strength of a particular type of  cloth.

Step-by-step explanation:

We are given that a chemist wishes to test the effect of four chemical agents on the strength of a particular type of  cloth.

Since we are given data for four independent chemical agents to determine the effect on the strength of a particular type of cloth, therefore, a one-way analysis of variance may be used for the given problem.

ANOVA:

The one-way analysis of variance (ANOVA) may be used to find out whether there is any significant difference between the means of two or more independent categories of data.

Set up hypotheses:

Null hypotheses = H₀: μ₁ = μ₂ = μ₃ = μ₄

Alternate hypotheses = H₁: μ₁ ≠ μ₂ ≠ μ₃ ≠ μ₄

Set up decision rule:

We Reject H₀ if p ≤ α

OR

We Reject H₀ if F > F critical

ANOVA in Excel:

Step 1:

In the data tab, select data analysis

Step 2:

Select "Anova single factor" from the analysis tools

Step 3:

Select the destination of input data in the "input range"

Step 4:

Select "rows" for the option "Group By"

Step 5:

Tick the option "labels in first row"

Step 6:

Set alpha = 0.05

Step 7:

Select the destination of output data in the "output options"

Conclusion:

Please refer to the attached results.

The p-value is found to be

p = 0.7038

The F value is found to be

F = 0.475

The F critical value is found to be

F critical = 3.238

Since p > α

0.7038 > 0.05

We failed to reject H₀

Also since F < F critical

0.475 < 3.238

We failed to reject H₀

We do not have significant evidence at the given significance level to show that there is a difference among the four chemical agents on the strength of a particular type of cloth.

Answer:

The null hypothesis is rejected.

There is enough evidence to support the claim that the true average strength for the 1078 grade exceeds that for the 1064 grade by more than 10 kg/mm^2.

Test statistic t=-40.91

P-value = 0

Step-by-step explanation:

This is a hypothesis test for the difference between populations means.

The claim is that the true average strength for the 1078 grade exceeds that for the 1064 grade by more than 10 kg/mm^2.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu_1-\mu_2=-10\\\\H_a:\mu_1-\mu_2< -10[/tex]

The significance level is 0.05.

The sample 1 (AISI 1064), of size n1=126 has a mean of 102.8 and a standard deviation of 1.2.

The sample 2 (AISI 1078), of size n2=126 has a mean of 121.3 and a standard deviation of 2.

The difference between sample means is Md=-18.5.

[tex]M_d=M_1-M_2=102.8-121.3=-18.5[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{1.2^2}{126}+\dfrac{2^2}{126}}\\\\\\s_{M_d}=\sqrt{0.011+0.032}=\sqrt{0.043}=0.2078[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{-18.5-(-10)}{0.2078}=\dfrac{-8.5}{0.2078}=-40.91[/tex]

The degrees of freedom for this test are:

[tex]df=n_1+n_2-2=126+126-2=250[/tex]

This test is a left-tailed test, with 250 degrees of freedom and t=-40.91, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t<-40.91)=0[/tex]

As the P-value (0) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the true average strength for the 1078 grade exceeds that for the 1064 grade by more than 10 kg/mm^2.

Answer:

Prime number

Step-by-step explanation:

A prime number has 2 factors.

A composite number has more than 2 factors.

47 has the factors 1 and 47.

47 is a prime number.

Answer:

47 is prime.

Step-by-step explanation:

Its factors are 1 and 47.

If a number has only 2 factors, then it's prime.

Answer:

z = 1.476

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.86}{2} = 0.07[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.07 = 0.93[/tex], so [tex]z = 1.476[/tex]

The answer is z = 1.476

Answer:

The two equations that can be used to find each of their ages are [tex]x=4 \times y[/tex] and [tex]x+y=60[/tex] .

Step-by-step explanation:

We are given that Mrs. Lang is 4 times as old as her daughter Jill. The sum of their ages is 60 years.

Let the age of Mrs. Lang be 'x years' and the age of her daughter Jill be 'y years'.

Now, according to the question;

                                     [tex]x=4 \times y[/tex]   ----------------- [equation 1]

                                 [tex]x+y=60[/tex]

                                [tex]4y + y = 60[/tex]     {using equation 1}

                                  [tex]5y=60[/tex]

                                   [tex]y=\frac{60}{5}[/tex]

                                   y = 12 years

Now, putting the value of y in equation 1 we get;

                               [tex]x=4 \times y[/tex]

                               [tex]x= 4 \times 12[/tex] = 48 years

Hence, the age of Mrs. Lang is 48 years and her daughter Jill is 12 years old.

Answer:

Mrs. Lang is 48 and her daughter is 12 years old.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

area of top on triangle=1/2×4×3=6m²

area of four top triangles=6×4=24 m²

area of bottom square=4×4=16 m²

area of four side rectangles=4×(4×5)=80 m²

Total area= 24+16+80=120m²

Answer:

An object balances itself when a perpendicular line drawn through its Centre of Gravity (CG), passes through its base.

See the picture of a popular toy given below. The horse, the rider and the ball are all joined together as one single unit. This entire unit is balanced on the thin black rod shown. At which of the indicated positions, could the Centre of Gravity (CG) of the horse, rider and ball unit be?

July 10 book Science up55 down8

AA BB

CC DD

Step-by-step explanation:

Answer:

x = 5 and y = -4

Step-by-step explanation:

y = - 3x + 11 ______(1)

5x + y = 21______(2)

Substitute (1) into (2).

5x + (-3x + 11) = 21

5x - 3x + 11 = 21

2x = 21-11

2x = 10

x = 10/2

x = 5

Now substitute x = 5 into (1).

y = -3(5) + 11

y = -15 + 11

y = -4

Hence, x = 5 and y = -4

Answer:

Minimum 8 at x=0, Maximum value: 24 at x=4

Step-by-step explanation:

Retrieving data from the original question:

[tex]f(x)=x^{2}+8\:over\:[-1,4][/tex]

1) Calculating the first derivative

[tex]f'(x)=2x[/tex]

2) Now, let's work to find the critical points

Set this

[tex]2x=0\\x=0[/tex]    

0, belongs to the interval. Plug it in the original function

[tex]f(0)=(0)^2+8\\f(0)=8[/tex]

3)  Making a table x, f(x) then compare

x|  f(x)

-1 | f(-1)=9  

0 | f(0)=8   Minimum

4 | f(4)=24 Maximum

4) The absolute maximum value is 24 at x=4 and the absolute minimum value is 8 at x=0.    

Answer:

probability of chosing a student that has a cat and a dog is 9/25

Step-by-step explanation:

And yes the Venn diagram is wrong because you forgot to subtract 9 from 15 and 16

This makes it

[ 3 ( 6 ( 9 ) 7 ) ]

3 + 6 + 9 + 7 = 25

Answer:

3

Step-by-step explanation:

minus the variable, 4-1 is 3.

Answer:

Q9 X=42.5

Step-by-step explanation:

let unknown angle be x

cos x=45/61

X=cos^-1 45/61

X=42.463...

X=42.5 (1 decimal place)

Answer:

A) A = {RRR, LLL, SSS}

B) B = {LRS. LSR, RLS, RSL, SLR, SRL}

C) C = {RRL, RRS, RSR, RLR, LRR, SRR}

D) D = {RRL, RRS, RSR, RLR, LRR, SRR. LLR, LLS, LSL, LRL, RLL, SLL, SSL, SSR, SLS, SRS, LSS, RSS}

E) D' ={RRR, LLL, SSS, LRS. LSR, RLS, RSL, SLR, SRL}

F) C ∪ D = {RRL, RRS, RSR, RLR, LRR, SRR. LLR, LLS, LSL, LRL, RLL, SLL, SSL, SSR, SLS, SRS, LSS, RSS}

G) C ∩ D = {RRL, RRS, RSR, RLR, LRR, SRR}

Step-by-step explanation:

A) All vehicles must go right, left or straight ahead (three possibilities):

A = {RRR, LLL, SSS}

B) One vehicle must go right, one must go left, and the remaining one must go straight ahead (six possibilities):

B = {LRS. LSR, RLS, RSL, SLR, SRL}

C) There are three ways that exactly two vehicles go right (1 and 3, 2 and 3, 1 and 2), there are then two options for the remaining vehicle (left and straight) for a total of six possibilities:

C = {RRL, RRS, RSR, RLR, LRR, SRR}

D) Follow the same reasoning from the previous item, but multiply the number of possibilities by 3 (for each direction in which both cars can go: right, left or straight):

D = {RRL, RRS, RSR, RLR, LRR, SRR. LLR, LLS, LSL, LRL, RLL, SLL, SSL, SSR, SLS, SRS, LSS, RSS}

E) D' is the set containing all possibilities not present in set D. D' is comprised by the possibilities of all vehicles going in the same direction, or each vehicle in a different direction:

D' ={RRR, LLL, SSS, LRS. LSR, RLS, RSL, SLR, SRL}

F) The outcomes in C ∪ D is the union of elements from set C and D (neglecting repeated values), which happens to be all values in set D.

C ∪ D = {RRL, RRS, RSR, RLR, LRR, SRR. LLR, LLS, LSL, LRL, RLL, SLL, SSL, SSR, SLS, SRS, LSS, RSS}

G) The outcomes in C ∩ D is the list of values present in both sets C and D, which happens to be all values in set C:

C ∩ D = {RRL, RRS, RSR, RLR, LRR, SRR}

The slope greater than one would be the last image, because for every step in x, you get more than one y step.

The slope between 1 and 0 would be the second image

And the slope less than 0 would be the third image

━━━━━━━☆☆━━━━━━━

▹ Answer

15.75

▹ Step-by-Step Explanation

3 ÷ 4 = .75

15 + .75 = 15.75

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

The horizontal asymptote of the function f(x) = (x-2)/(x-3)² is at y = 0 which is the x-axis.

An asymptote is a line that is approached by a curve but never touches it. In other words, an asymptote is a line where the graph of a function converges.

Because a horizontal asymptote is a horizontal line, its equation is of the form y = k. The horizontal asymptote of a rational function is at y = 0, which is the x-axis if the degree of the numerator is smaller than the degree of the denominator.

Here, the function is f(x) = (x-2)/(x-3)². Here the degree of the numerator of this rational function is 1 and the degree of the denominator is 2. Since 1<2, the horizontal asymptote is at y = 0 which is the x-axis.

The horizontal asymptote of the function f(x) = (x-2)/(x-3)² is at y = 0 which is the x-axis.

Learn more about horizontal asymptotes here -

https://brainly.com/question/14357352

#SPJ2

Answer:

c

Step-by-step explanation:

Answer:

[tex]Area=7\,\pi\,\sqrt{\frac{53}{4}}\,\,\frac{25}{2}[/tex]

Step-by-step explanation:

Let's use the integral formula for the surface area of revolution of the function y(x) around the x-axis, which is:

[tex]Area=\int\limits^b_a {2\,\pi\,y\,\sqrt{1+(\frac{dy}{dx} )^2} } \, dx[/tex]

and which in our case, we can obtain the following:

[tex]y=\frac{7}{2} \,x\\\frac{dy}{dx} =\frac{7}{2} \\(\frac{dy}{dx})^2=\frac{49}{4} \\\sqrt{1+(\frac{dy}{dx})^2} =\sqrt{1+\frac{49}{4} } =\sqrt{\frac{53}{4} }[/tex]

Recall as well that [tex]0\leq x\leq 5[/tex], which gives us the limits of integration:

[tex]Area=\int\limits^b_a {2\,\pi\,y\,\sqrt{1+(\frac{dy}{dx} )^2} } \, dx\\Area=\int\limits^5_0 {2\,\pi\,(\frac{7}{2}\,x) \,\sqrt{\frac{53}{4} } } \, dx\\Area=7\,\pi\,\sqrt{\frac{53}{4}}\,\, \int\limits^5_0 {x} \, dx \\Area=7\,\pi\,\sqrt{\frac{53}{4}}\,\,\frac{x^2}{2} |\limits^5_0\\Area=7\,\pi\,\sqrt{\frac{53}{4}}\,\,\frac{25}{2}[/tex]

If we compare it with the geometry formula:

Lateral surface of cone = [tex]\frac{1}{2} \,\,(Base_{circ})\,\,(slant\,height)= \frac{1}{2} (2\,\pi\,\frac{7}{2} 5)\.(\sqrt{5^2+(\frac{35}{2})^2 } =\frac{7}{2} \,\pi\,25\.\,\sqrt{\frac{53}{4} }[/tex]

which is exactly the expression we calculated with the integral.

Answer:

Fail to reject the null hypothesis because the p-value =0.10 is more than the significance level α=0.05.

Step-by-step explanation:

The significant level for this case study is 5% - 0.05. If the results gotten is less than the significance level, we reject the null hypothesis, but if greater, we fail to reject the null hypothesis.

In this case study, the p-value is 0.10 which is a lot higher than 0.05, thus we will fail to reject the null hypothesis because the p-value =0.10 is more than the significance level α=0.05.

Answer:

84%

Step-by-step explanation:

The probability of Thomas bumping into her at school is 80%, so the probability of not bumping into her is 100% - 80% = 20%.

If he doesn't bump into her (20% chance), he will call her, and the probability of asking her in this case is 60%, so the final probability of asking her in this case is:

[tex]P_1 = 20\% * 60\% = 12\%[/tex]

If he bumps into her (80% chance), the probability of asking her is 90%, so the final probability of asking her in this case is:

[tex]P_2 = 80\% * 90\% = 72\%[/tex]

To find the probability of Thomas inviting Madeline to the party, we just have to sum the probabilities we found above:

[tex]P = P_1 + P_2[/tex]

[tex]P = 12\% + 72\% = 84\%[/tex]

Answer:

Total distance= 15.055 unit

Step-by-step explanation:

Distance between the first journey i.e from her office to the supermarket is calculated as follows given the coordinates.

(-5,-7) and (4,-6)

The distance between those tow points

Is

= √((4-(-5))² +( (-6)-(-7))²)

= √(9²+1²)

= √ 81+1

= √ 82

= 9.055

Noe the distance between the second journey traveled i.e from the supermarket to her house is calculated as follows given the coordinates.

(4,-6) and (-2,-6)

Distance= √((4--2)² +( -6--6)12

Distance = √(4+2)² + 0

Distance = √ 6²

Distance = 6

Total distance= 9.055 + 6

Total distance= 15.055

Answer:

z = -17.67 + i3.43

Step-by-step explanation:

Let us apply the formula z = r(cos Ф + i sin Ф), given 18(cos169° + isin169°) -

z = 18( cos169 + isin169 ),

z = r(cos Ф + i sin Ф)

Now we can solve this question in the form z = a + bi, in this case where a = 18 cos169, and b = 18 sin169. This is as a = r cos Ф and b = r sin Ф -

sin169 is positive, while cos169 is negative, thus -

a = -17.6692893021...,

b = 3.43456191678...

Rectangular Form, z = -17.67 + i3.43

Hope that helps!

Answer:

[tex] P(X\geq 20)= P(X=20)+P(X=21)+P(X=22)+P(X=23)+P(X=24)+P(X=25)[/tex]

And replacing using the mass function we got:

[tex]P(X=20)=(25C20)(0.85)^{20} (1-0.85)^{25-20}=0.156[/tex]  

[tex]P(X=21)=(25C21)(0.85)^{21} (1-0.85)^{25-21}=0.211[/tex]  

[tex]P(X=22)=(25C22)(0.85)^{22} (1-0.85)^{25-22}=0.217[/tex]  

[tex]P(X=23)=(25C23)(0.85)^{23} (1-0.85)^{25-23}=0.161[/tex]  

[tex]P(X=24)=(25C24)(0.85)^{24} (1-0.85)^{25-24}=0.0759[/tex]  

[tex]P(X=25)=(25C25)(0.85)^{25} (1-0.85)^{25-25}=0.0172[/tex]  

And adding the values we got:

[tex] P(X\geq 20) = 0.8381[/tex]

Step-by-step explanation:

Let X the random variable of interest, on this case we now that:  

[tex]X \sim Binom(n=25, p=0.85)[/tex]  

The probability mass function for the Binomial distribution is given as:  

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

Where (nCx) means combinatory and it's given by this formula:  

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]  

We want to find the following probability:

[tex] P(X\geq 20)= P(X=20)+P(X=21)+P(X=22)+P(X=23)+P(X=24)+P(X=25)[/tex]

And replacing using the mass function we got:

[tex]P(X=20)=(25C20)(0.85)^{20} (1-0.85)^{25-20}=0.156[/tex]  

[tex]P(X=21)=(25C21)(0.85)^{21} (1-0.85)^{25-21}=0.211[/tex]  

[tex]P(X=22)=(25C22)(0.85)^{22} (1-0.85)^{25-22}=0.217[/tex]  

[tex]P(X=23)=(25C23)(0.85)^{23} (1-0.85)^{25-23}=0.161[/tex]  

[tex]P(X=24)=(25C24)(0.85)^{24} (1-0.85)^{25-24}=0.0759[/tex]  

[tex]P(X=25)=(25C25)(0.85)^{25} (1-0.85)^{25-25}=0.0172[/tex]  

And adding the values we got:

[tex] P(X\geq 20) = 0.8381[/tex]

Answer:

all squares are quadrilaterals

Answer:

D

Step-by-step explanation:

Parallel lines are those that have the same slope, or coefficient of x.

Here, let's calculate the slope of the given line. Slope is the difference in the y-coordinates divided by the difference in the x-coordinates, so given the two coordinates (12, 6) and (0, -4):

slope = m = (-4 - 6) / (0 - 12) = -10 / (-12) = 10/12 = 5/6

So the slope is 5/6. That means the equation we want should also have a slope of 5/6. Already, we can eliminate A, B, and C, leaving D as our answer. But, let's check.

The equation of a line can be written as [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1,y_1)[/tex] is the coordinates of a given point.

Here, our slope is 5/6 and our given point is (12, -2). So plug these in:

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y-(-2)=(5/6)(x-12)[/tex]

[tex]y+2=\frac{5}{6} x-10[/tex]

[tex]y=\frac{5}{6} x-12[/tex]

This matches D, so we know that it's the correct answer.

~ an aesthetics lover

The answer is D I just took the test

Answer:

[tex]P(X<0.4375)=P(\frac{X-\mu}{\sigma}<\frac{0.4375-\mu}{\sigma})=P(Z<\frac{0.4375-0.635}{0.082})=P(z<-2.41)[/tex]

And we can find this probability using the z table and we got:

[tex]P(z<-2.41)=0.0080[/tex]

Step-by-step explanation:

Let X the random variable that represent the thickness of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(0.635,0.082)[/tex]  

Where [tex]\mu=0.635[/tex] and [tex]\sigma=0.032[/tex]

We are interested on this probability

[tex]P(X<0.4375)[/tex]

And the best way to solve this problem is using the normal standard distribution and the z score given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

If we apply this formula to our probability we got this:

[tex]P(X<0.4375)=P(\frac{X-\mu}{\sigma}<\frac{0.4375-\mu}{\sigma})=P(Z<\frac{0.4375-0.635}{0.082})=P(z<-2.41)[/tex]

And we can find this probability using the z table and we got:

[tex]P(z<-2.41)=0.0080[/tex]

Answer:  x = 4

4x - 6=10

4x = 10 + 6

4x = 16

[tex]x = \frac{16}{4}[/tex]

x = 4  ←  the missing value

Therefore the the solution is (4,-6) of the equation 4x+y=10 .

Hope this helped You!

Answer:

Step-by-step explanation:

The fire department property is 2 units in height. 2 units from the line y=3 can be on the line y=5, or on the line y=1.

There are no answer choices with y=5, so the appropriate choices are those with C and D having the x-coordinates of B and A, respectively, and y=1.

  C(1, 1), D(4, 1)

Answer:

a = 4 /b

or ab = 4

Step-by-step explanation:

An inverse relation is given by

a = k/b where k is the constant

Rewriting

ab = k

12 * 1/3 = k

4 = k

a = 4 /b

or ab = 4

Answer:

The expected number of the people at the reception whose favorite snack will be chips is 1152

Step-by-step explanation:

Given

The data in the above table and

Reception = 3600

Required

Predict the number of the people at the reception whose favorite snack will be chips.

The first step is to determine the total number of samples;

[tex]Total = Brownies + Cookies + Chips + Other[/tex]

[tex]Total = 32 + 22 + 56 + 65[/tex]

[tex]Total = 175[/tex]

The next step is to determine the fraction of people whose favorite is chips

[tex]Fraction = \frac{Chips}{Total}[/tex]

[tex]Fraction = \frac{56}{175}[/tex]

The product of the above fraction and the expected number of people in the reception is the solution to this question;

[tex]Expected\ Number = \frac{56}{175} * 3600[/tex]

[tex]Expected\ Number = \frac{56* 3600}{175}[/tex]

[tex]Expected\ Number = \frac{201600}{175}[/tex]

[tex]Expected\ Number = 1152[/tex]

Hence, the expected number of the people at the reception whose favorite snack will be chips is 1152