part 7: please assist me with these problems​

Answer:

Step-by-step explanation:

42/14 = 57/x

42x = 57*14

42x = 798

x = 19 months

Answer: Actually its 18 months they calculated wrong

Answer:

851- 473 = 373

(751)-378 = 373

[tex]y=\dfrac{sin(x^2)}{x^3}[/tex]

Apply the quotient rule:

[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{x^3\frac{\mathrm d\sin(x^2)}{\mathrm dx}-\sin(x^2)\frac{\mathrm dx^3}{\mathrm dx}}{(x^3)^2}[/tex]

Chain and power rules:

[tex]\dfrac{\mathrm d\sin(x^2)}{\mathrm dx}=\cos(x^2)\dfrac{\mathrm dx^2}{\mathrm dx}=2x\cos(x^2)[/tex]

Power rule:

[tex]\dfrac{\mathrm dx^3}{\mathrm dx}=3x^2[/tex]

Putting everything together, we have

[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{x^3(2x\cos(x^2))-\sin(x^2)(2x\cos(x^2))}{(x^3)^2}[/tex]

[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2x^3\cos(x^2)-2x\sin(x^2)\cos(x^2)}{x^6}[/tex]

[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2x^2\cos(x^2)-\sin(2x^2)}{x^5}[/tex]

When [tex]x=\sqrt{\frac\pi2}[/tex], we have

[tex]\cos\left(\left(\sqrt{\dfrac\pi2}\right)^2\right)=\cos\left(\dfrac\pi2\right)=0[/tex]

[tex]\sin\left(2\left(\sqrt{\dfrac\pi2}\right)^2\right)=\sin(\pi)=0[/tex]

so the derivative is 0.

Answer:

equal and equivalent sets

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]Circumference = 2\pi r\\\\2 \pi \times 40 ft = 80\pi ft = 253.3274123 ft\\\\= 253.3274123 ft \times 12 \: \frac{inches }{feet} \\\\ = 3015.928947 in\\\\\\10 min = 10 min \times 60 \: sec / min = 600 sec\\\\4 \: revolutions / 10 min = 4 \times 3015.928947\: in / 600 sec \\\\ = 5.0 in/sec[/tex]

The linear velocity of the Ferris wheel is 20.1 inches per secnod.

Suppose the body revolves θ angle in t time then the angular velocity of the body is

ω= θ/t

Suppose the rotating body covers 's' distance in 't' which is actually 'rθ' distance in 't' time because, s=rθ.

Then the linear velocity of the rotating body is

v=s/t=r(θ/t)=r ω

i.e. v=r ω.

The speed of the Ferris wheel is given by 4 revs in 10 minutes. That means 4(2π) radians in 10 minutes.

Hence, the angular velocity of the Ferris Wheel is

ω= 8π/(10×60) rad/s= π/(75) rad/s

Hence, the linear velocity of the Ferris Wheel is

v=r ω= 40 Feet ( π/(75) rad/s)

= (12×40π)/(75) inch/s

= 20.1062 inch/s

≈20.1 inch/s (rounded to the nearest tenth)

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Complete question is;

Use technology and a t-test to test the claim about the population mean μ at the given level of significance α using the given sample statistics. Assume the population is normally distributed.

Claim: μ > 71; α = 0.05

Sample statistics:

¯x = 73.9, s = 3.7, n = 25

A) What are the null and alternative hypotheses?

Choose the correct answer below.

A. H0:μ = 71 ; HA:μ ≠ 71

B. H0:μ ≤ 71; HA:μ > 71

C. H0: μ ≥ 71; HA: μ < 71

D. H0: μ ≠ 71; HA: μ = 71

B) What is the value of the standardized test statistic? The standardized test statistic is (Round to two decimal places as needed.)

C) What is the P-value of the test statistic? P-value = Round to three decimal places as needed.)

D) Decide whether to reject or fail to reject the null hypothesis.

Answer:

A) Option B - Alternative hypothesis: HA: μ > 71

Null hypothesis: H0: μ ≤ 71

B) t = -7.54

C) p-value = 0.000

D) we reject the null hypothesis

Step-by-step explanation:

A) We are told that the claim is: μ > 71. Thus, due to the sign, the alternative hypothesis would be the claim. So;

Alternative hypothesis: HA: μ > 71

Null hypothesis: H0: μ ≤ 71

B)Formula for standardized test statistic with a t-test is;

t = (¯x - μ)/√(s/n)

Plugging in the relevant values, we have;

t = (71 - 73.9)/√(3.7/25)

t = -7.54

C) From online p-value from t-score calculator attached using t = -7.54, n = 25, significance level = 0.05, DF = 25 - 1 = 24 and a one - tailed test, we have;

p-value = 0.00001 ≈ 0.000

D) The p-value of 0.000 is less than the significance value of 0.05,thus we will reject the null hypothesis

Answer:

The Stem plot is displayed below.

Step-by-step explanation:

A Stem Plot is a chart for demonstrating the distribution of numeric variables .

It is used to analyze the shape of the distribution.

The data provided is as follows:

S = {46, 65, 55, 43, 51, 48, 57, 30, 43, 49, 32, 56}

The Stem plot is displayed as follows:

3 | 0  2

4 | 3  3  6  8  9

5 | 1  5  6  7

6 | 5

Answer:

1. 5 times

2. 1/5

Step-by-step explanation:

I can explain later if you want, but you seem like you're in a rush so I'll do it later :)

Answer:

Estimated cost per capsule = 4.288 (penny)

Step-by-step explanation:

Given:

Cost of 1000 capsule = $42.88

Number of capsules = 1000

Find:

Estimated cost per capsule

Computation:

1 dollar = 100 penny

So,

$42.88 = 4288 penny

Estimated cost per capsule = 4288 / 1000

Estimated cost per capsule = 4.288 (penny)

Answer: TRUE

Step-by-step explanation:

you can't never change an irrational number into rational number

2 × √3 = 2√3 ⇔ still an irrational number

Answer:

False

Step-by-step explanation:

 The product of two irrational number 2 is irrational. False. Counterexample: (√2) ∙ (−√2) = 2. (c) The sum of a rational number and an irrational number is irrational.

Answer:

Step-by-step explanation:

s = πrl + πr²

First move πr² to the left side of the equation

We have

πrl = s - πr²

Divide both sides by πr to make l stand alone

That's

We have the final answer as

Hope this helps you

Answer:

[tex]3.126666666666...=3.12\overline{6}[/tex]

Step-by-step explanation:

If the decimal number is repeating, then bar notation is used. A symbol called "bar" is used to express that type of numbers. it is placed at the top of the number that is repeating.

We have a number i.e. 3.126666666666...

We need express it in bar notation.

In this problem, 6 is repeating. It means "bar" is placed over 6.

So,

[tex]3.126666666666...=3.12\overline{6}[/tex]

It is the bar notation of 3.126666666666...

Answer:

1) 12

2) c=-25

3) x = -16 2/3

Step-by-step explanation:

1) ..........................

2) ..........................

3) ..........................

Answer:

[tex]\mathbf{X_E (2) = 1}[/tex]

[tex]\mathbf{X_E (-2) = 0 }[/tex]  

[tex]\mathbf{\{ x \in Z: X_E(x) = 1\} = E}[/tex]

Step-by-step explanation:

Let E be the set of all even positive integers in the universe Z of integers,

i.e

E = {2,4,6,8,10 ....∞}

[tex]X_E : Z \to R[/tex] be the characteristic function of E.

∴

[tex]X_E(x) = \left \{ {{1 \ if \ x \ \ is \ an \ element \ of \ E} \atop {0 \ if \ x \ \ is \ not \ an \ element \ of \ E}} \right.[/tex]

For XE(2)

[tex]\mathbf{X_E (2) = 1}[/tex]  since x is an element of E (i.e the set of all even numbers)

For XE(-2)

[tex]\mathbf{X_E (-2) = 0 }[/tex]   since  - 2 is less than 0 , and -2 is not an element of E

For { x ∈ Z: XE(x) = 1}

This can be read as:

x which is and element of Z such that X is also an element of x which is equal to 1.

∴

[tex]\{ x \in Z: X_E(x) = 1\} = \{ x \in Z | x \in E\} \\ \\ \mathbf{\{ x \in Z: X_E(x) = 1\} = E}[/tex]

E = {2,4,6,8,10 ....∞}

Answer:

A:{(-9/7,-17/7)}

Step-by-step explanation:

3x - 2y - 1 = 0    ⇒  3x - 2y = 1

y = 5x + 4

then:

3x - 2(5x+4) = 1

3x - 2*5x - 2*4 = 1

3x - 10x - 8 = 1

-7x = 1 + 8

7x = 9

x = -9/7

y = 5x + 4

y = 5(-9/7) + 4

y = -45/7 + 4

y = -45/7 + 28/7

y = -17/7

Answer:

A:{(-9/7, -17/7)}

Answer:

a)$15.95

b) 8kg

Step-by-step explanation:

a)Approach this question by finding how much does it cost for 1g

So,

$2.1/50=$0.042per gram

then, multiple 380 to get the cost of sweets for 380 g

$0.042/gram*380gram=$15.96(Note: the gram cancel out each other)

Which is $15.95 as the question requested

b)This question stated that 3/4 of the metal has 15 kg

So, in order to find the total mass of metal we invert the 3/4 fraction

e.g 4/3*15=20kg

now we have the total mass we can find the mass for 2/5 of the metal

2/5*20kg=8kg

Answer: A = 58

Step-by-step explanation: The sketched region enclosed by the curves and the approximating rectangle are shown in the attachment.

From the sketches, the area will be integrated with respect to y.

To calculate the integral, first determine the limits, which will be the points where both curves meet.

In respect to y:

[tex]2x+y^{2} = 48[/tex]

[tex]2x= 48- y^{2}[/tex]

[tex]x= 24 - \frac{y^{2}}{2}[/tex]

Finding limits:

[tex]y= 24 - \frac{y^{2}}{2}[/tex]

[tex]24 - \frac{y^{2}}{2}-y=0[/tex]

Multiply by 2 to facilitate calculations:

[tex]48 - y^{2}-2y=0[/tex]

Resolving quadratic equation:

[tex]y=\frac{-2+\sqrt{2^{2}+192} }{2}[/tex]

y = 6 and y = -8

Then, integral to calculate area will be with limits -8<y<6:

[tex]A = \int {24-\frac{y^{2}}{2}-y } \, dy[/tex]

[tex]A = 24y - \frac{y^{3}}{6}-\frac{y^{2}}{2}[/tex]

[tex]A = 24.6 - \frac{6^{3}}{6}-\frac{6^{2}}{2}-[24.(-8) - \frac{(-8)^{3}}{6}-\frac{(-8)^{2}}{2}][/tex]

A = 58

The area of the enclosed region is 58 square units.

Answer:

9 miles

Step-by-step explanation:

Hour = 6 miles

Half an hour = 3

6 + 3 = 9

Answer: The answer is 209.40625

The fractional equivalent of 33505 divided by 160 is 6701/32 .

Given,

33505/160

Now,

To get the fractional equivalent of 33505/160,

Divide numerator and denominator by the common factor .

So divide numerator and denominator by 5.

33505/5 = 6701

160/5 = 32

Now the simplified fraction is 6701/32.

Know more about fractions,

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*see attachment for the data set given

Answer:

[tex] Q_1 = 2.5 [/tex]

[tex] Q_2 = 5.5 [/tex]

[tex] Q_3 = 8 [/tex]

The box plot is shown in the attachment below.

Step-by-step Explanation:

a. To find Q1, Q2 (median), and Q3, first order the data from the least to the largest. We would have:

0, 1, 1,1, 2, 2, 2, 3, 4, 5, 5, 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9

Q2 which is also the median, is the middle value that divides the data set into two equal parts. In the data set given, Q2 is the data value between the 14th and 15th data value. The average of the 14th and the 15th data value would give us Q2.

0, 1, 1,1, 2, 2, 2, 3, 4, 5, 5, 5, 5, [5,Q2, 6], 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9

They are 5 and 6. Average = [tex] \frac{5+6}{2} = 5.5 [/tex]

Q1 is the middle value of the lower part of the data set from Q2 down to your left.

0, 1, 1,1, 2, 2, [2, Q1, 3,] 4, 5, 5, 5, 5, 5, Q2, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9

Q1 = average of the 7th and 8th value = [tex] \frac{2+3}{2} = 2.5 [/tex]

Q3 = [tex] \frac{8+8}{2} = 8 [/tex]

0, 1, 1,1, 2, 2, 2, 3, 4, 5, 5, 5, 5, 5,Q2, 6, 6, 7, 7, 7, 8, [8, Q3, 8], 8, 9, 9, 9, 9, 9.

Answer:

Divide by 3

Step-by-step explanation:

Answer:

Sub. 10

Answer:

0.87

Step-by-step explanation:

Answer:

hello attached below is the required table that is missing and the completed table as well

A) mean deviation = 0.1645

B) 2/3

Step-by-step explanation:

From the table we calculated the midpoint value (x) and c.f

N = 27

median class = 2.35 to 2.45

median = l + [ (N/2) - cf / F ] * H

             = 2.35  + [ (13.5 - 13) / 6 ] *0.1 = 2.3583

hence mean deviation by median

= summation of  fi |xi -M| / summation of fi

= 4.4417 / 27 = 0.1645

B ) probability of getting an odd number or prime number or both

the probability of an odd number = 1/2

also the probability of an even number = 1/2

while the probability of getting neither of them = 1/3

hence the probability of getting odd or prime or both

= 1/2 + 1/2 - 1/3 = 2/3

Answer:

Step-by-step explanation:

The question is incomplete. Here is the complete question.

Find the average rate of change of the area of a circle with respect to its radius r as r changes from 3 to each of the following.

(i)    3 to 4

(ii)    3 to 3.5

(iii)    3 to 3.1

(b) Find the instantaneous rate of change when r = 3.  A'(3)

Area of a circle A(r)= πr²

The average rate of change of the area of a circle with respect to its radius

ΔA(r)/Δr = πr₂²-πr₁²/r₂-r₁

ΔA(r)/Δr = π(r₂²-r₁²)/r₂-r₁

i) If the radius changes from 3 to 4

ΔA(r)/Δr = π(r₂²-r₁²)/r₂-r₁

ΔA(r)/Δr = π(4²-3²)/4-3

ΔA(r)/Δr = π(16-9)/1

ΔA(r)/Δr = 7π

Hence, average rate of the area of a circle when the radius changes from 3 to 4 is 7π

ii) If the radius changes from 3 to 3.1

ΔA(r)/Δr = π(r₂²-r₁²)/r₂-r₁

ΔA(r)/Δr = π(3.5²-3²)/3.5-3

ΔA(r)/Δr = π(12.25-9)/0.5

ΔA(r)/Δr = 3.25π/0.5

ΔA(r)/Δr = 6.5π

Hence, average rate of the area of a circle when the radius changes from 3 to 3.5 is 6.5π

iii) If the radius changes from 3 to 3.1

ΔA(r)/Δr = π(r₂²-r₁²)/r₂-r₁

ΔA(r)/Δr = π(3.1²-3²)/3.1-3

ΔA(r)/Δr = π(9.61-9)/0.1

ΔA(r)/Δr = 0.61π/0.1

ΔA(r)/Δr = 6.1π

Hence, average rate of the area of a circle when the radius changes from 3 to 3.1 is 6.1π

iv) Instantaneous rate of change A'(r) = 2πr

When r = 3;

A'(3) = 2π(3)

A'(3) = 6π

Hence, the instantaneous rate of change when r = 3 is 6π

Answer:A number decreased by 4 is the same as 12.5

Step-by-step explanation:

Answer:

x +13.

where

x is number of people

Step-by-step explanation:

Let the number of people be x

given that number of people increased by 13

increased by 13 means that we whatever is the initial number of people, new number of people is 13 more than that.

thus, new number of people = x +13

to  translate the number of people increased by 13 into an algebraic expression

we add 13 to number of people which can be represented by  x +13.

Answer: a. 0.6759    b. 0.3752    c. 0.1480

Step-by-step explanation:

Given : The long-distance calls made by the employees of a company are normally distributed with a mean of 6.3 minutes and a standard deviation of 2.2 minutes

i.e. [tex]\mu = 6.3[/tex] minutes

[tex]\sigma=2.2[/tex] minutes

Let x be the long-distance call length.

a. The probability that a call lasts between 5 and 10 minutes will be :-

[tex]P(5<X<10)=P(\dfrac{5-6.3}{2.2}<\dfrac{X-\mu}{\sigma}>\dfrac{10-6.3}{2.2})\\\\=P(-0.59<Z<1.68)\ \ \ \ [z=\dfrac{X-\mu}{\sigma}]\\\\=P(z<1.68)-(1-P(z<0.59))\\\\=0.9535-(1-0.7224)\ \ \ \ [\text{by z-table}]\\\\=0.6759[/tex]

b. The probability that a call lasts more than 7 minutes. :

[tex]P(X>7)=P(\dfrac{X-\mu}{\sigma}>\dfrac{7-6.3}{2.2})\\\\=P(Z>0.318)\ \ \ \ [z=\dfrac{X-\mu}{\sigma}]\\\\=1-P(Z<0.318)\\\\=1-0.6248\ \ \ \ [\text{by z-table}]\\\\=0.3752[/tex]

c. The probability that a call lasts more than 4 minutes. :

[tex]P(X<4)=P(\dfrac{X-\mu}{\sigma}<\dfrac{4-6.3}{2.2})\\\\=P(Z<-1.045)\ \ \ \ [z=\dfrac{X-\mu}{\sigma}]\\\\=1-P(Z<1.045)\\\\=1-0.8520 \ \ \ [\text{by z-table}]\\\\=0.1480[/tex]

Answer:52-12=$40

1/8*40 = 5 hours.

Step-by-step explanation:

Answer:

Least number of bus require for trip = 5 buses (Approx)

Step-by-step explanation:

Given:

Total number of classes = 9

Number of student in each class = 25

Number of teacher = 4

Number of chaperones = Double of teacher

Bus hold = 45 people

Find:

Least number of bus require for trip

Computation:

Total number of student = 9 × 25

Total number of student = 225

Number of chaperones = 4 × 2

Number of chaperones = 8

Total people = 225 + 8 + 4

Total people = 237

Least number of bus require for trip = Total people / Bus hold

Least number of bus require for trip = 237 / 45

Least number of bus require for trip = 5.266

Least number of bus require for trip = 5 buses (Approx)

Answer:

Least number of bus require for trip = 5 buses

Step-by-step explanation:

Hello, please consider the following.

f is differentiable so g is differentiable and we we can compute the derivative of g.

[tex]\text{derivative of } u^2\text{ is } 2uu'\\\\\text{derivative of } f(f(x^3)+x)\text{ is } (3x^2f'(x^3)+1)f'(f(x^3)+x)\\\\\text{So, }\\\\g'(x)=2f(f(x^3)+x)(3x^2f'(x^3)+1)f'(f(x^3)+x)\\\\\text{ We replace x par 1}\\\\g'(1)=2f(f(1)+1)(3f'(1)+1)f'(f(1)+1)\\\\g'(1)=2f(2)(3f'(1)+1)f'(2)\\\\\text{ We can put f'(2) in one part of the equation}\\\\f'(2)=\dfrac{2f(2)(3f'(1)+1)}{g'(1)}=\dfrac{2*5*(3*(-3)+1)}{2}\\\\=5*(-9+1)\\\\=5*(-8)\\\\=\boxed{-40}[/tex]

Thank you.

Answer

[0,-3] should be the right answer

The line should intersect at y axis i.e x=0

Then put the value of x as zero in the equation to find the value of y.

3*0-4y=12

-4y=12

y=12/-4=-3

y=-3 ..

HOPE THIS HELPS YOU