What percent of the area underneath
this normal curve is shaded?

Answer:

Step-by-step explanation:

From the given information;

let the hypotenuse be a , the opposite which is the north direction be b and the west direction which is the adjacent be c

SO, using the Pythagoras theorem

a² = c² + 177²

By taking the differentiation of both sides with respect to time t , we have

[tex]2a \dfrac{da}{dt} = 2c \dfrac{dc}{dt} + 0[/tex]

[tex]\dfrac{da}{dt} = \dfrac{c}{a} \dfrac{dc}{dt}[/tex]

At c = 71 miles,[tex]a = \sqrt{ (71)^2 +(177)^2}[/tex]

[tex]a = \sqrt{ 5041+31329}[/tex]

[tex]a = \sqrt{ 36370}[/tex]

a = 190.71

SImilarly, [tex]\dfrac{dc}{dt} = \ 31 miles \ / hr[/tex]

Thus, the rate of change of the distance between Morristown and the van when the van has been travelling for 71 miles can be calculate as:

[tex]\dfrac{da}{dt} = \dfrac{c}{a} \dfrac{dc}{dt}[/tex]

[tex]\dfrac{da}{dt} = \dfrac{71}{190.71} \times 31[/tex]

[tex]\dfrac{da}{dt} = 0.37229 \times 31[/tex]

[tex]\mathbf{\dfrac{da}{dt} = 11.54}[/tex]  to the nearest hundredth.

Answer:

The width is  [tex]w = 282.8[/tex]

Step-by-step explanation:

From the question we are told that

  The sample size is n =  50

  The  population standard deviation is  [tex]\sigma = \$ 1000[/tex]

   The sample size is  [tex]\= x = \$ 15,000[/tex]

Given that the confidence level is  90%  then the level of significance can be mathematically represented as

             [tex]\alpha = 100 - 90[/tex]  

             [tex]\alpha = 10 \%[/tex]  

              [tex]\alpha = 0.10[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the  normal distribution table, the value is  

             [tex]Z_{\frac{0.10 }{2} } = 1.645[/tex]

Generally the margin of error is mathematically represented as

               [tex]E = Z_{\frac{0.10}{2} } * \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

                 [tex]E = 1.645 * \frac{1000 }{\sqrt{50 }}[/tex]

=>                [tex]E = 141.42[/tex]

  The width of the 90%  confidence level is mathematically represented as

                      [tex]w = 2 * E[/tex]

substituting values

                       [tex]w = 2 * 141.42[/tex]

                       [tex]w = 282.8[/tex]

Answer:

45

62x

______

  90

2700+

_________

2790

Step-by-step explanation:

Answer:

The answer is below

Step-by-step explanation:

The box contains 5 red and 4 white balls.

A) The probability that at least 1 ball was​ red = P(both are red) + P(first is red and second is white) + P(first is white second is red)

Given that the first ball was (Upper A )Replaced before the second draw:

P(both are red) = P(red) × P(red) = 5/9 × 5/9 = 25/81

P(first is red and second is white) = P(red) × P(white) = 5/9 × 4/9 = 20/81

P(first is white and second is red) = P(white) × P(red) = 4/9 × 5/9 = 20/81

The probability that at least 1 ball was​ red = 25/81 + 20/81 + 20/81 = 65/81

B) The probability that at least 1 ball was​ red = P(both are red) + P(first is red and second is white) + P(first is white second is red)

Given that the first ball was not Replaced before the second draw:

P(both are red) = P(red) × P(red) = 5/9 × 4/8 = 20/72 (since it was not replaced after the first draw the number of red ball remaining would be 4 and the total ball remaining would be 8)

P(first is red second is white) = P(red) × P(white) = 5/9 × 4/8 = 20/72

P(first is white and second is red) = P(white) × P(red) = 4/9 × 5/8 = 20/72

The probability that at least 1 ball was​ red = 20/72 + 20/72 + 20/72 = 60/72

Answer:

Any point N on line r maps to itself.

Step-by-step explanation:

Reflection is one of the examples of solid transformation in which a given point, segment, or figure is flipped over a reference point or line to produce its image. The distance of the object to the reference point or line is the same as the distance of its image to the point or line. And both have the same size, but different orientation.

The option that does not fully define a reflection is; any point N on line r maps to itself, because no image of point N is produced after the operation.

Answer:

C. This matches Heng's definition, but is not a reflection, because MM'MM

′

M, M, prime is not perpendicular to line rrr.

Step-by-step explanation:

Answer:

E(x)  [tex]= \frac{n+1}{2}[/tex]

Var(x) [tex]= \frac{1}{4} [ n - 1 ][/tex]

Step-by-step explanation:

Hint x = 1 + x1 + ......... Xn-1

[tex]X_{i} = \left \{ {{1} if the ith adjacent pair of magnets repel each other \atop {0} if ith adjacent pair of magnets join} \right.[/tex]

attached below is the detailed solutioN

usually like poles of magnets repel each other and unlike poles of magnets attract each other forming a block

Answer:

See answer and graph below

Step-by-step explanation:

∬Ry2x2+y2dA

=∫Ry.2x.2+y.2dA

=A(2y+4Ryx)+c

=∫Ry.2x.2+y.2dA

Integral of a constant ∫pdx=px

=(2x+2.2Ryx)A

=A(2y+4Ryx)

=A(2y+4Ryx)+c

The graph of y=A(2y+4Ryx)+c assuming A=1 and c=2

The evaluation of the double integral is [tex]\mathbf{ \dfrac{105}{2}\pi }[/tex]

The double integral [tex]\mathbf{\int \int _R\ \dfrac{y^2}{x^2+y^2} \ dA}[/tex], where R is the region that lies between

the circles [tex]\mathbf{x^2 +y^2 = 16 \ and \ x^2 + y^2 = 121}[/tex].

Let consider x = rcosθ and y = rsinθ because x² + y² = r²;

Now, the double integral can be written in polar coordinates as:

[tex]\mathbf{\implies \int \int _R\ \dfrac{y^2}{x^2+y^2} \ dxdy}[/tex]

[tex]\mathbf{\implies \int \int _R\ \dfrac{r^2 \ sin^2 \theta}{r^2} \ rdrd\theta}[/tex]

[tex]\mathbf{\implies \int \int _R\ \ sin^2 \theta \ r \ drd\theta}[/tex]

Thus, the integral becomes:

[tex]\mathbf{=\int^{2 \pi}_{0} sin^2 \theta d\theta \int ^{11}_{4} rdr }[/tex]

∴

[tex]\mathbf{=\int^{2 \pi}_{0} \dfrac{1-cos 2 \theta }{2} \ \theta \ d\theta\dfrac{r}{2} \Big|^{11}_{4}dr }[/tex]  

[tex]\mathbf{\implies \dfrac{1}{2} \Big[\theta - \dfrac{sin \ 2 \theta}{2}\Big]^{2 \pi}_{0} \ \times\Big[ \dfrac{11^2-4^2}{2}\Big]}[/tex]

[tex]\mathbf{\implies \dfrac{\pi}{2} \times\Big[ 121-16\Big]}[/tex]

[tex]\mathbf{\implies \dfrac{105}{2}\pi }[/tex]

Learn more about double integral here:

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Answer: Transitive property.

Step-by-step explanation:

First, for the equality we have:

Reflexive:

  For all real numbers x, x = x.

Symmetric:  

 For all real numbers x, y

 if x= y, then y = x.

Transitive:

 For reals x, y and z.

 if x = y, and y = z, then x = z.

Now, let's talk about inequalities.

first, the reflexive property will say that:

x > x.

This has no sense, so this property does not work for inequalities.

Now, the reflexive.

If x > y, then y > x.

Again, this has no sense, if x is larger than y, then we can never have that y is larger than x. This property does not work for inequalities.

Not, the transitive property.

if x > y, and y > z, then x > z.

This is true.

x is bigger than y, and y is bigger than z, then x should also be bigger than z.

x > y > z.

And this also works for the inverse case:

x < y and y < z, then x < z.

So the correct option is transitive property.

Answer: B. 25

Step-by-step explanation:

Given: Total books = 625

Number of books can fit in one box = 25

Now, the number of boxes she need to move all of the books = (Total books) ÷ (Number of books can fit in one box )

= 625÷25

= 25

hence, she requires 25 boxes in order to move all of the books.

So, correct option is B. 25.

Answer: 1023.75 (a)

Step-by-step explanation:

The sequence is a Geometric progression with the common ratio of ¹/₂ and first term of 512.

a = 512, r = ¹/₂. To determine the ratio, just divide the second term by the first term.

Now to calculate the sum, we consider two formula here and select the one that is most appropriate,

(1)  a( rⁿ - 1 )/r - 1, when r is greater than 1

(2) a( 1 - rⁿ )/1 - rⁿ, when r is less than 1.

In this question, formula 2 shall be appropriate because r is less than 1.

so,

S₁₂      =  512( 1 - 0.5¹² )/1 - 0.5

             512( 1 - 2.44 ₓ 10⁻⁴ )/0.5

          = 512( 0,9998 )/0.5

          = 511.875/0.5

          = 1023.75

The answer is a

Step-by-step explanation:

I(S) = aS / (S + c)

As S approaches infinity, S becomes much larger than c.  So S + c is approximately equal to just S.

lim(S→∞) I(S)

= lim(S→∞) aS / (S + c)

= lim(S→∞) aS / S

= lim(S→∞) a

= a

As S approaches infinity, I(S) approaches a.

Step-by-step explanation:

For a left-hand limit, we start at the left side and move right, and see where the function goes as we get close to the x value.

For a right-hand limit, we start at the right side and move left, and see where the function goes as we get close to the x value.

If the two limits are equal, then the limit exists.  Otherwise, it doesn't.

1.  As we approach x = 2 from the left, f(x) approaches -2.

lim(x→2⁻) f(x) = -2

As we approach x = 2 from the right, f(x) approaches 1.

lim(x→2⁺) f(x) = 1

The limits are not the same, so the limit does not exist.

lim(x→2) f(x) = DNE

2. As we approach x = 2 from the left, f(x) approaches 4.

lim(x→2⁻) f(x) = 4

As we approach x = 2 from the right, f(x) approaches 2.

lim(x→2⁺) f(x) = 2

The limits are not the same, so the limit does not exist.

lim(x→2) f(x) = DNE

3. As we approach x = 2 from the left, f(x) approaches 2.

lim(x→2⁻) f(x) = 2

As we approach x = 2 from the right, f(x) approaches 2.

lim(x→2⁺) f(x) = 2

The limits are equal, so the limit exists.

lim(x→2) f(x) = 2

4. As we approach x = 2 from the left, f(x) approaches 2.

lim(x→2⁻) f(x) = 2

As we approach x = 2 from the right, f(x) approaches infinity.

lim(x→2⁺) f(x) = ∞

The limits are not the same, so the limit does not exist.

lim(x→2) f(x) = DNE

Answer:

simply convert first feets into miles

Given is 5280 feets=1 miles

63756 /5280=12.075 miles

70 minutes  = 1.16666= 1.17 hrs

rate is 12.075 miles/1.17 hrs

Step-by-step explanation:

Answer:

15x+6u−3

Step-by-step explanation:

This means -3 times -5x, -3 times -2u, and -3 times 1.

Do this and you have, 15x+6u-3.

Answer:

-35

Step-by-step explanation:

7*5*(-1)

The solution to the expression 7 * -5 is -35

From the question, we have the following parameters that can be used in our computation:

7 * -5

Evaluate all the products in the expression

so, we have the following representation

7 * -5 = -35/1

Evaluate all the quotients in the expression

so, we have the following representation

7 * -5 = -35

Lastly, we have

7 * -5 = -35

Hence, the solution is -35

Read more about expressions at

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Answer:

total amount paid = 32.5 + 28.9 + 24.95 = 86.35

20% of the total amount paid = 0.2 * 86.35 = 17.27

you tip 17.25$

Answer:

-7/6

Step-by-step explanation:

-2/3 x 7/4 = -14/12 = -7/6

Answer: -7/6

Step-by-step explanation: (-2/3) ÷ (4/7) can be rewritten as (-2/3) · (7/4).

Remember that dividing by a fraction is the same thing

as multiplying by the reciprocal of the fraction.

Before multiplying however, notice that we

can cross-cancel the 2 and 4 to 1 and 2.

So multiplying across the numerators and denominator and

remembering our negative in the first fraction, we have -7/6.

Answer:

The median would be 7.0.

Step-by-step explanation:

The median of a set of numbers means it is the middle number. since this set has 7 numbers you would need to find the number that is in the middle of the set. This would be the 4th number since it is in the middle. 7.0 is your answer.

Answer:

The answer is in the photo below. The interval is (-pi, pi) and the function is y = tanx.

Answer:

19x

Step-by-step explanation:

product means multiply

19*x

19x

Answer:

The answer is C.

Step-by-step explanation:

if a number and a variable are next to each other, it is assumed they will be multiplied.

*a clearer picture containing the graph is shown in the attachment

Answer:

20% of the class earned a D

Step-by-step Explanation:

Step 1: Determine the total number of students represented on the graph:

9 students => D

5 students => C

14 students => B

17 students => A

Total number of students = 45

Step 2: Express each category of students who scored a particular grade as a fraction and as percentage.

9 students => D => [tex] \frac{9}{45} = \frac{1}{5} [/tex] => as percentage, we have [tex] \frac{1}{5} * 100 = 20 percent [/tex]

5 students => C => [tex] \frac{5}{45} = \frac{1}{9} [/tex] => as percentage, we have [tex] \frac{1}{9} * 100 = 11.1 percent [/tex]

14 students => B => [tex] \frac{14}{45} [/tex] => as percentage, we have [tex] \frac{14}{45} * 100 = 31.1 percent [/tex]

17 students => A => [tex] \frac{17}{45} [/tex] => as percentage, we have [tex] \frac{17}{45} * 100 = 37.8 percent [/tex]

Step 3: Check each statement to see if they are true or not based on the calculations above.

Statement 1: "⅕ of the students earned a C."

This is NOT TRUE From our calculation, ⅑ of the students earned a C.

Statement 2: "3% more students earned an A than a B." This is also NOT TRUE.

37.8% earned A, while 31.1% earned a B. Thus, about 6.7% more students earned an A than a B.

Statement 3: "20% of the class earned a D".  This is TRUE.

Check calculation in step 2.

Statement 4: "¼ of the class earned a B". This is NOT TRUE.

¼ is 25% of the class. Those who earned a B account for 31.1% not 25% (¼ of the class).

The correct statement is: "20% of the class earned a D"

Answer:

30,455

Step-by-step explanation:

Exponential decay

y = a(1 - b)^x

y = final amount

a = initial amount

b = rate of decay

x = time

We are looking for the rate of decay, b.

900 = 450000(1 - b)^30

1 = 500(1 - b)^30

(1 - b)^30 = 0.002

1 - b = 0.002^(1/30)

1 - b = 0.81289

b = 0.1871

The equation for our case is

y = 450000(1 - 0.1871)^x

We are looking for the amount in 13 hours, so x = 13.

y = 450000(1 - 0.1871)^13

y = 30,455

Answer:

a.  k = -0.01014 s⁻¹

b.  [tex]\mathbf{\dfrac{dy}{dt} = - \dfrac{In(\dfrac{3}{2})}{40}(y-60)}[/tex]

c.  [tex]\mathbf{y(t) = 60+ \dfrac{60 \sqrt{3}}{\sqrt{2}} \ e^{\dfrac{-In(\dfrac{3}{2})\ t}{40}}}[/tex]

d.  y(t) = 130.485°F

Step-by-step explanation:

A hot metal bar is submerged in a large reservoir of water whose temperature is 60°F. The temperature of the bar 20 s after submersion is 120°F. After 1 min submerged, the temperature has cooled to 100°F.

(Let y be measured in degrees Fahrenheit, and t be measured in seconds.)

We are to determine :

a.  Determine the cooling constant k. k = s−1

By applying the new law of cooling

[tex]\dfrac{dT}{dt} = k \Delta T[/tex]

[tex]\dfrac{dT}{dt} = k(T_1-T_2)[/tex]

[tex]\dfrac{dT}{dt} = k (T - 60)[/tex]

Taking the integral.

[tex]\int \dfrac{dT}{T-60} = \int kdt[/tex]

㏑ (T -60) = kt + C

T - 60 = [tex]e^{kt+C}[/tex]

[tex]T = 60+ C_1 e^{kt} ---- (1)[/tex]

After 20 seconds, the temperature of the bar submersion is 120°F

T(20) = 120

From equation (1) ,replace t = 20s and T = 120

[tex]120 = 60 + C_1 e^{20 \ k}[/tex]

[tex]120 - 60 = C_1 e^{20 \ k}[/tex]

[tex]60 = C_1 e^{20 \ k} --- (2)[/tex]

After 1 min i.e 60 sec , the temperature  = 100

T(60) = 100

From equation (1) ; replace t = 60 s and T = 100

[tex]100 = 60 + c_1 e^{60 \ t}[/tex]

[tex]100 - 60 =c_1 e^{60 \ t}[/tex]

[tex]40 =c_1 e^{60 \ t} --- (3)[/tex]

Dividing equation (2) by (3) , we have:

[tex]\dfrac{60}{40} = \dfrac{C_1e^{20 \ k } }{C_1 e^{60 \ k}}[/tex]

[tex]\dfrac{3}{2} = e^{-40 \ k}[/tex]

[tex]-40 \ k = In (\dfrac{3}{2})[/tex]

- 40 k = 0.4054651

[tex]k = - \dfrac{0.4054651}{ 40}[/tex]

k = -0.01014 s⁻¹

b. What is the differential equation satisfied by the temperature y(t)?

Recall that :

[tex]\dfrac{dT}{dt} = k \Delta T[/tex]

[tex]\dfrac{dT}{dt} = \dfrac{- In (\dfrac{3}{2})}{40}(T-60)[/tex]

Since y is the temperature of the body , then :

[tex]\mathbf{\dfrac{dy}{dt} = - \dfrac{In(\dfrac{3}{2})}{40}(y-60)}[/tex]

(c) What is the formula for y(t)?

From equation (1) ;

where;

[tex]T = 60+ C_1 e^{kt} ---- (1)[/tex]

Let y be measured in degrees Fahrenheit

[tex]y(t) = 60 + C_1 e^{-\dfrac{In (\dfrac{3}{2})}{40}t}[/tex]

From equation (2)

[tex]C_1 = \dfrac{60}{e^{20 \times \dfrac{-In(\dfrac{3}{2})}{40}}}[/tex]

[tex]C_1 = \dfrac{60}{e^{-\dfrac{1}{2} {In(\dfrac{3}{2})}}}[/tex]

[tex]C_1 = \dfrac{60}{e^ {In(\dfrac{3}{2})^{-1/2}}}}[/tex]

[tex]C_1 = \dfrac{60}{\sqrt{\dfrac{2}{3}}}[/tex]

[tex]C_1 = \dfrac{60 \times \sqrt{3}}{\sqrt{2}}}[/tex]

[tex]\mathbf{y(t) = 60+ \dfrac{60 \sqrt{3}}{\sqrt{2}} \ e^{\dfrac{-In(\dfrac{3}{2})\ t}{40}}}[/tex]

(d) Determine the temperature of the bar at the moment it is submerged.

At the moment it is submerged t = 0

[tex]\mathbf{y(0) = 60+ \dfrac{60 \sqrt{3}}{\sqrt{2}} \ e^{\dfrac{-In(\dfrac{3}{2})\ 0}{40}}}[/tex]

[tex]\mathbf{y(t) = 60+ \dfrac{60 \sqrt{3}}{\sqrt{2}} }[/tex]

y(t) = 60 + 70.485

y(t) = 130.485°F

Answer: 35 scoops total!

Step-by-step explanation: FIrst, you would add the number of scoops in total which is 3+1+1=5 scoops.

Now you would do 7*5=35

Therefore, Theo uses 35 scoops in all. I hope this helps you!

Answer:

(-3,-3)

B=(6-9,6+3)

Answer:

Step-by-step explanation:

I answered this already a few minutes ago.

Answer:

yes you can

Step-by-step explanation:

you can write algebraic expressions and use variables for the unknown

We have

[tex]2+\dfrac54+\dfrac{11}{16}+\dfrac{23}{64}+\cdots=\displaystyle\sum_{n=0}^\infty\frac{3\cdot2^n-1}{4^n}[/tex]

(notice that each denominator is a power of 4, and each numerator is one less than some multiple of 3, in particular 3 times some power of 2)

Recall for [tex]|x|<1[/tex], we have

[tex]\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n[/tex]

So we have

[tex]\displaystyle\sum_{n=0}^\infty\frac{3\cdot2^n-1}4=3\sum_{n=0}^\infty\left(\frac12\right)^n-\sum_{n=0}^\infty\left(\frac14\right)^n=\frac3{1-\frac12}-\frac1{1-\frac14}=\boxed{\frac{14}3}[/tex]

Answer:

For the null hypothesis to be rejected , then the conclusion of the test is that the absolute values of the z-statistic and/or the t-test statistic is greater than the critical value

Step-by-step explanation:

Here, we want to explain the conclusion of the test given that the null hypothesis is rejected.

Mathematically, the null hypothesis is as expressed as below;

H0: μ = 1,200

The alternative hypothesis H1 would be;

H1: μ > 1,200

Now, before we can reject or accept the null hypothesis, we will need a sample size and thus calculate the test statistics and the z statistics

For us to reject the null hypothesis, one of two things, or two things must have occurred.

The absolute value of the z statistic |z| or the test statistic |t| must be greater than the critical value.

If this happens, then we can make a rejection of the null hypothesis

Answer:

9 hours

Step-by-step explanation:

Since the group of men remains the same, number of hours is proportional to number of radios.

1300/26 = 450/h

h = 26 * 450 / 1300 = 9 hours