Help Please???? Question is above, it has to do with repeating decimal converting to a fraction

Help Please???? Question Is Above, It Has To Do With Repeating Decimal Converting To A Fraction

Answers

Answer 1
For number 3.it would be 87/200 and 4. Would be 713/500

Related Questions

ASAP! GIVING BRAINLIEST! Please read the question THEN answer correctly! No guessing. Show your work or give an explaination.

Answers

Answer:

A

Step-by-step explanation:

The form for a parabola with vertex form is y=(x-h)^2+k, where h is the x coordinate and k is the y. Therefore, since the x coordinate of the graph is -2, the answer is A. Hope this helps!

Answer:

its A

hop this helps

PLEASEEEE HELPP MEEE WITHHH NUMBERSSS 9 AND 10

PLEASEEE HELPPP MEEEEE!!!!!!!!

Answers

Answer:

9: 89°

Step-by-step explanation:

Inside of a triangle is 180, so 180-39-52=89

I'm sorry I can't answer 10 for you

The scale for a drawing is 1 centimeter to 5 meters. If the actual object is 35 meters, the drawing is _____ centimeters long.

30
175
7
40

Answers

Answer:

7

Step-by-step explanation:

Answer:

the answer is 7

Step-by-step explanation:

An importer of electronic goods is considering packaging a new, easy-to-read instruction booklet with DVD players. It wants to package this booklet only if it helps customers more than the current booklet. Previous tests found that only 30% of customers were able to program their DVD player. An experiment with the new booklet found that 16 out of 60 customers were able to program their DVD player. a. State the null and the alternative hypot

Answers

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached image below to see the step by step explanation to the question above.

What’s the correct answer for this?

Answers

Answer:

Step-by-step explanation:

C-Spec, Inc., is attempting to determine whether an existing machine is capable of milling an engine part that has a key specification of {eq}4 \pm 0.003 {/eq} inches. After a trial run on this machine, C-Spec has determined that the machine has a sample mean of 4.001 inches with a standard deviation of 0.002 inch.
a. Calculate the {eq}C_{pk} {/eq} for this machine
b. Should C-Spec use this machine to produce this part? Why?

Answers

Answer:

Step-by-step explanation:

Given that :

sample mean = 4.001 inches

sample standard deviation = 0.002 inch

a.

[tex]C_{pk} = min [\dfrac{(USL- \bar X)}{(3*std \ dev)} \ ; \ \dfrac{ (\bar X- LSL)}{(3*std \ dev)}][/tex]

specification = [tex]4 \pm 0.003[/tex]

Upper specification limit USL = 4 + 0.003  = 4.003

Lower specification limit LSL =  4 - 0.003 = 3.997

[tex]\dfrac{ (\bar X- LSL)}{(3*std \ dev)} = \dfrac{ (4.001-3.997)}{(3*0.002)}[/tex]  [tex]= 0.667[/tex]

[tex]\dfrac{(USL- \bar X)}{(3*std \ dev)} =\dfrac{(4.003-4.001)}{(3*0.002)}[/tex][tex]= 0.333[/tex]

Thus ;

[tex]C_{pk} =[/tex][tex]min (0.333 , 0.667)[/tex]  = 0.333

[tex]C_{pk}[/tex]  is a measure of closeness to one's target and the consistency around the average performance.

b) No, C - spec should not use this machine to produce this part because [tex]C_{pk}[/tex] <  1.33 which typical means that the part is not fully capable of hitting the target specification on a consistent basis .

tbe ages of jerry mile and rawl total 80 years jerry is twice as old as mile and mile is three times as old as rawl how old is jerry????​

Answers

Answer:

rawl- 8 years old

mile- 24 years old

jerry- years old

Step-by-step explanation:

Please answer this correctly without making mistakes

Answers

Answer:

g=56

Step-by-step explanation:

In similar shapes, corresponding sides are always in the same ratio.

For example,

if the sides in triangle 1 were a and b, and triangle 2 had side lengths c and d, c and a had the same ratios, and b and d had the same ratios

and triangle 1 was similar to triangle 2, the ratio between the sides of the triangles would be

a/c, which is also equal to b/d

What that means is that in this situation, 8/5=g/35.

8/5=g/35

Cross multiply.

(8)*(35)=g*(5)

280=5g

g=56

As quality control manager at a raisin manufacturing and packaging plant, you want to ensure that all the boxes of raisins you sell are comparable, with 30 raisins in each box (assume the population average number of raisins per box is 30). In the plant, raisins are poured into boxes until the box reaches its sale weight. To determine whether a similar number of raisins are poured into each box, you randomly sample 36 boxes about to leave the plant and count the number of raisins in each. In this sample, you find the mean number of raisins in each box to be 28.05, with a standard deviation of 3.87.
1. Perform a two-tailed, single sample t test (p<.05) to determine whether the average number of raisins per box differs from the expected 30.
2. What type of statistical analysis should be run to address this question?3. What are the assumptions of your chosen statistical test?4. Identify the null and alternative/research hypotheses in both words and symbols.

Answers

Answer:

Step-by-step explanation:

The population average number of raisins per box is 30.

The type of statistical analysis to be run here is the inferential statistical analysis and its assumptions include normality, linearity and equality of variance.

Null hypothesis: Average number of raisins per box is 30: u = 30

Alternative hypothesis: Average number of raisins per box is not 30: u ≠ 30

To perform a two tailed single sample test, we have

z statistic = (the sample mean - hypothesized mean) / (SD/√n)

sample mean = 28.05, SD = 3.87 hypothesized mean = 30 n = 36

Thus, we have 28.05 - 30 / (3.87/√36)

= -1.95 / (3.87/6)

= -1.95 / 0.645

= -3.023

we say this is a left tailed test and use the negative z table

where -3.02 = 0.0013

To determine whether the average number of raisins per box differs from the expected 30.

Using p < 0.05, since the observed value 0.0013 is less than 0.05, we conclude the the average number of raisins per box differs from the expected 30.

Write what the expressions below best represent within the context of the word problem.

Mark had 3 times as many quarters as nickels. He had $1.60 in all. How many nickels and how many quarters did Mark

have?

x represents

3x represents

TURN IT IN

NEXT QUESTION

ASK FOR HELP

Answers

Answer:

2 nickels

6 quarters

Step-by-step explanation:

Let quarters be 3x and nickels be $x

if Mark had 3 times as many quarters as nickels, and if he had $1.60 in all, than

( 0.25)3x + 0.05x=1.6

0.75x+ 0.05x=1.6

0.8x=1.6

x=1.6/0.8

x=2 nickels

and 3 (2)=6 quarters

Answer:

There are 4 quarters and 12 nickels.

Step-by-step explanation:

A quarter is equal to $0.25.

A nickel is equal to $0.05.

Let the number of nickels be y.

Let the number of quarters be x.

Mark had 3 times as many quarters as nickels. This means that:

y = 3x

3x represents the number of nickels.

We are told that he had $1.60 in all. This means that:

0.25x + 0.05y = 1.60

=> 0.25x + 0.05 * 3x = 1.60

0.25x + 0.15x = 1.60

0.40x = 1.60

=> x = 1.6 / 0.4 = 4

Therefore:

y = 3 * 4 = 12

There are 4 quarters and 12 nickels.

Job has to pay $9.00 admission for the skating rink and $2 per to rent rollerblades how many hours can he skate for $19

Answers

Answer:

5 hours

Step-by-step explanation:

Here we can create an equation to solve for the number of hours (x) this man can skate for.

Since he has to pay a $9 flat fee, that will be a constant value or our y-intercept in this case.

Our equation will be y = 2x + 9

Since we know his budget is $19, we can set our equation equal to 19, or replace y in this case.

So now we have 19 = 2x +9

Now we need to subtract 9 from both sides to get 10 = 2x

Then we need to divide both sides by 2 to get 5 = x

So this man can skate for 5 hours considering his budget

And object Weighs a quarter of a kilogram . I add one half of a kilogram to the object. I take 200g off. I double the mass of the object. I add one tone the object and then half it what is the mass of object

Answers

If the final weight is halved then the mass of the object will be 500,550 grams

Measurement of an object

1 kg of an object = 1000 grams

If an object weighs a quarter of a kilogram, then

New weight = 1/4(1000) = 250 grams

If  I add one-half of a kilogram to the object, then the new weight will be 750grams

If I take 200grams off, the new weight will be 550 grams

If the mass is doubled, then the new weight will be 2(550) which is 1100grams

If 1 tonne is added, then the new mass will be 1000000 + 1100)grams.

If the final weight is halved then the mass of the object will be 500,550 grams

Learn more on measurement here: https://brainly.com/question/13893070

The owner of a small deli is trying to decide whether to discontinue selling magazines. He suspects that only 10% of his customers buy a magazine and he thinks that he might be able to use the display space to sell something more profitable. Before making a final decision, he decides that for one day he will keep track of the number of customers that buy a magazine. Assuming his suspicion that 10% of his customers buy a magazine is correct, what is the probability that exactly 5 out of the first 13 customers buy a magazine?

Answers

Answer:

0.55% probability that exactly 5 out of the first 13 customers buy a magazine

Step-by-step explanation:

For each customer, there are only two possible outcomes. Either they buy a magazine, or they do not. The probability of a customer buying a magazine is independent of other customers. 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.

10% of his customers buy a magazine

This means that [tex]P = 0.1[/tex]

What is the probability that exactly 5 out of the first 13 customers buy a magazine?

This is P(X = 5) when n = 13. So

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

[tex]P(X = 5) = C_{13,5}.(0.1)^{5}.(0.9)^{8} = 0.0055[/tex]

0.55% probability that exactly 5 out of the first 13 customers buy a magazine

Answer:

[tex] P(X=5) = (13C5) (0.1)^5 (1-0.1)^{13-5}= 0.00554[/tex]

So then  he probability that exactly 5 out of the first 13 customers buy a magazine is 0.0554

Step-by-step explanation:

Let X the random variable of interest "number of customers that buy a magazine", on this case we can model the variable of interest with this distribution:

[tex]X \sim Binom(n=13, p=0.1)[/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 this probability:

[tex] P(X=5)[/tex]

And using the probability mass function we got:

[tex] P(X=5) = (13C5) (0.1)^5 (1-0.1)^{13-5}= 0.00554[/tex]

So then  he probability that exactly 5 out of the first 13 customers buy a magazine is 0.0554

At the bank, Mr Smith changes a £5 note for 20p pieces.
How many 20p pieces does he-get?

Answers

Answer:

erm

Step-by-step explanation:

25

In a science fair​ project, Emily conducted an experiment in which she tested professional touch therapists to see if they could sense her energy field. She flipped a coin to select either her right hand or her left​ hand, and then she asked the therapists to identify the selected hand by placing their hand just under​ Emily's hand without seeing it and without touching it. Among 329 ​trials, the touch therapists were correct 154 times.
a. Given that Emily used a coin toss to select either her right hand or her left hand, what proportion of correct responses would be expected if the touch therapists made random guesses?
b. Using Emily's sample results, what is the best point estimate of the therapists' success rate?
c. Using Emilys sample results, construct a 90% confidence interval estimate of the proportion of correct responses made by touch therapists.

Answers

Answer:

a) [tex] p = 0.5[/tex]

b) [tex] \hat p= \frac{X}{n}= \frac{154}{329}= 0.468[/tex]

c) [tex]0.468 - 1.64 \sqrt{\frac{0.468(1-0.468)}{329}}=0.423[/tex]

[tex]0.468 + 1.64 \sqrt{\frac{0.468(1-0.468)}{329}}=0.513[/tex]

And the 90% confidence interval for the true proportion is given by (0.527;0.593).

Step-by-step explanation:

Part a

For this case we don't have any prior info given so then the probability assumed for this case is:

[tex] p = 0.5[/tex]

Part b

For this case the proportion of success is given by:

[tex] \hat p= \frac{X}{n}= \frac{154}{329}= 0.468[/tex]

Part c

The confidence interval for the true proportion would be given by this formula

[tex]\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

For the 90% confidence interval the value of and , and the critical value would be given by:

[tex]z_{\alpha/2}=1.64[/tex]

The confidence interval is given by:

[tex]0.468 - 1.64 \sqrt{\frac{0.468(1-0.468)}{329}}=0.423[/tex]

[tex]0.468 + 1.64 \sqrt{\frac{0.468(1-0.468)}{329}}=0.513[/tex]

And the 90% confidence interval for the true proportion is given by (0.527;0.593).

A movie theater has a seating capacity of 253. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 1828 on a sold out night, how many children, students, and adults attended?

children attended=
adults attended=
students attended=

Answers

Answer:

children attended= 114

adults attended= 57

students attended= 82

Step-by-step explanation:

children attended= c

adults attended=  a

students attended=  s

c+s+a = 253

5c + 7s + 12a = 1828

c=2a

2a + s + a =253

5*2a + 7s + 12a = 1828

3a + s = 253

22a + 7s = 1828

s = 253 - 3a

22a + 7(253 - 3a) = 1828

22a - 21a + 7*253 = 1828

a = 1828 - 7*253

a = 57

s = 253 - 3a = 253 - 3*57 = 82

s = 82

c=2a=2*57= 114

c=114

Which inequality is true if p=3.4

3p<10.2

13.6<3.9p

5p>17.1

8.5>2.5

Answers

Answer:

None of the inequalities are correct if p = 3.4

Step-by-step explanation:

Mathematical inequality is an order relation proposition existing between two algebraic expressions connected through the signs: unequal than ≠, greater than>, less than <, less than or equal to ≤, as well as greater than or equal to ≥, resulting in both expressions of different values. That is, an inequality is a relationship that exists between two quantities or expressions and, which indicates that they have different values.

To check an inequality, you must replace the inequality variable with the value of the solution.  In this case, being p=3.4, you must do it with each of the inequalities, as shown below:

A. 3p<10.2 ⇒ 3*3.4<10.2 ⇒ 10.2 <10.2  

This inequality is not true, because 10.2 is not less than 10.2, but they are equal.

B. 13.6<3.9p ⇒ 13.6<3.9*3.4 ⇒ 13.6<13.26  

This inequality is not true, because 13.6 is greater than 13.26 and not less as the inequality shows.

C. 5p>17.1 ⇒ 5*3.4 >17.1 ⇒ 17 > 17.1  

This inequality is not true, because 17 is less than 17.1 and not greater as the inequality shows.

D. 8.5> 2.5p ⇒ 8.5 >2.5*3.4 ⇒ 8.5 > 8.5

This inequality is not true, because 8.5 is not less than 8.5. These values ​​are the same.

None of the inequalities are correct if p = 3.4

The correct answer is C. By substituting the greatest number in each set for p, you can quickly tell which sets make the inequality false.

Which two sentences contain incorrect punctuation?

One question that society finds problematic to answer is what energy sources will people utilize when the earth is drained of natural resources such as coal or oil.

Upon discovering the errors in the film —the abusive remarks—the movie release was immediately postponed and was sent back to the editors for correction.

Maintaining hygiene is a good way to keep illnesses at bay; this can be done by washing hands, brushing teeth, and bathing regularly.

The American writer and philosopher, Henry David Thoreau comments that by simplifying one's life, "the laws of the universe will appear less complex."

The adrenaline produced in our body during a confrontation leads to two possible responses by the person run away to safety, or stand one's ground and fight.

Reset

Answers

Answer:

D). The American writer and philosopher, Henry David Thoreau comments that by simplifying one's life, "the laws of the universe will appear less complex."

E). The adrenaline produced in our body during a confrontation leads to two possible responses by the person run away to safety, or stand one's ground and fight.

Explanation:

Punctuation marks are elucidated as the signs and symbols that function to enhance the readability of the sentences and indicate the grammatical construction of the readers. It assists them in understanding the meaning of the sentence more clearly and comprehensively.

In the given sentences, the last two sentence are incorrectly punctuated as they both wrongly employ comma(,) in it. Option D inappropriately punctuates comma(,) in the complex sentence while the last option falsely puts comma before conjunction 'or.' Thus, options D and E are the correct answers.

What is the solution to the equation?

t+55=466

t+55



Answers

Answer:

t=411

Step-by-step explanation:

t+55=466

466-55

Subtract the numbers

t=411

Pythagorean Theorem Word
Problems
You start driving north for 32 miles, turn
right, and drive east for another 24 miles,
At the end of driving, what is your straight
line distance from your starting point?​

Answers

Answer:

40 miles

Step-by-step explanation:

In the attached diagram, Point A is the starting point and C is the end point. We want to determine the distance from A to C.

The path driven forms a right triangle in which AC is the hypotenuse.

We therefore use the Pythagorean Theorem to solve for the AC.

Pythagorean Theorem: [tex]Hypotenuse^2=Opposite^2+Adjacent^2[/tex]

[tex]|AC|^2=32^2+24^2\\|AC|^2=1600\\|AC|=\sqrt{1600}\\ |AC|=40$ miles[/tex]

The  straight  line distance from the starting point is 40 miles.

Paj is filling a 9-cubic-inch flower pot with soil from small bags. Each bag of soil contains 2 2/3
cubic inches of soil. Exactly how many bags of soil are needed for Paj to fill the flower pot?

Answers

Answer:

3.375 bags of soil are needed for Paj to fill the flower pot

Step-by-step explanation:

This question can be solved using a rule of three.

One bag contains 2 + (2/3) = (8/3) cubic inches of soil. How many bags are needed to fill 9 cubic inches of soil?

1 bag - (8/3) cubic inches

x bags - 9 cubic inches

[tex]\frac{8x}{3} = 9[/tex]

[tex]8x = 27[/tex]

[tex]x = \frac{27}{8}[/tex]

[tex]x = 3.375[/tex]

3.375 bags of soil are needed for Paj to fill the flower pot

Paj needs 3.375 bags of soil to fill the bag.

Each bag contains 2²/₃ inch³ of soil and they need to fill up a 9 inch³ pot of soil.

First convert the mixed fraction to an improper one:

2²/₃ = 8/3

The number of bags needed is:

= Volume of pot / Quantity of soil in each bag

= 9 ÷ 8/3

= 9 x 3/8

= 3.375 bags of soil

Paj therefore needs 3.375 bags of soil to fill the pot

Find out more at https://brainly.com/question/17205287.

Please help. I will make brainlest award for the correct answers

Answers

Step-by-step explanation:

HOPE THIS HELP YOU !!! :)))

John borrowed $150,500 to start up his business. He borrowed the money at a 7.75% simple
interest rate for 2 years. How much does John have to pay back at the end of two years

Answers

Answer:

John have to pay back $23,327.50 at the end of two years

Step-by-step explanation:

Simple Interest (I) = (PRT) ÷ 100

where P = Principal, R = Rate, T= Time

I = ($150500 × 7.75 × 2) ÷ 100

I = ($2332750) ÷ 100

I = $23,327.50

what is the area of this circle?

Answers

Answer:

113.1

Step-by-step explanation:

d= 2r

r = 6

area = [tex]\pi r^{2}[/tex] = 36 x [tex]\pi[/tex] = 113.09

The drama club is selling short-sleeved shirts for $5 each, and long-sleeved shirts for $10 each. They hope to sell all of the shirts they ordered, to earn a total of $1,750. After the first week of the fundraiser, they sold StartFraction one-third EndFraction of the short-sleeved shirts and StartFraction one-half EndFraction of the long-sleeved shirts, for a total of 100 shirts. How many short-sleeved shirts were ordered?


How many long-sleeved shirts were ordered?

Answers

Answer:

150 short-sleeved shirts100 long-sleeved shirts

Step-by-step explanation:

Let S and L represent the numbers of short- and long-sleeved shirts ordered.

The expected earnings were ...

  5S +10L = 1750

The number sold was ...

  (1/3)S + (1/2)L = 100

We can multiply the first equation by 1/5 and the second equation by 6 to put the equations into standard form:

S +2L = 3502S +3L = 600

Subtracting the second equation from twice the first gives ...

  2(S +2L) -(2S +3L) = 2(350) -(600)

  L = 100 . . . . . . simplify

  2S +3(100) = 600

  S = 150

150 short-sleeved and 100 long-sleeved shirts were ordered.

Answer:

b

Step-by-step explanation:

i did it on edge

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Science

ULUSULUI

Sixth grade

FF.21 Relate volume andsurface area HVU

The surface area of this cube is 54 square meters. What is the volume?

cubic meters

Submit pls help

Answers

Answer:

27 cubic meters

Step-by-step explanation:

The surface area of this cube is 54 square meters.

Given a cube of side length s,

Surface Area [tex]=6s^2[/tex]

Therefore:

[tex]6s^2=54\\s^2=54/6\\s^2=9\\s=\sqrt{9}\\ s=3$ meters[/tex]

Volume of a Cube of side length s [tex]=s^3[/tex]

Volume of the cube [tex]=3^3[/tex]

=27 cubic meters

The volume of the cube is 27 cubic meters.

Which game isn’t fair for two players to play?

Answers

Answer:

cube game

Step-by-step explanation:

one of them wins every time

A number cube is rolled. Player 1 gets a point for any number that is 3 or higher, and player 2 gets a point for any number less than 3

If a number cube is rolled and Player 1 gets a point for any number that is 3 or higher and Player 2 gets a point for any number less than 3 it wouldn't be fair to Player 2 because Player 1 has a higher chance of getting points because he/she has more opportunities.

I hope this is correct

Find the value of m.
C
1190

A
B
A 61
B 30°
C 45
D 41°​

Answers

Answer:

b

Step-by-step explanation:

please help :( please help :( please help :( please help :( please help :( please help :( please help :( please help :(​

Answers

Answer:

(1) 23.55mm³

(2) 340.17in³

Step-by-step explanation:

Volume of a cone is: [tex]V=\frac{1}{3} \pi r^2h[/tex]

'r' - radius

'h' - height

Cone 1:

The height of Cone 1 is 10 mm. The Diameter of Cone 1 is 3mm.

Radius is half the Diameter.

[tex]3/2=1.5[/tex]

The radius is 1.5 mm.

[tex]\text {Using 3.14 as pi: }\\V=(1/3)3.14*1.5^2*10\\V=(1/3)3.14*2.25*10\\V=(1/3)70.65\\\boxed{V=23.55}[/tex]

The volume of Cone 1 should be about 23.55mm³.

Cone 2:

The height of Cone 2 is 13 in. The Radius of Cone 2 is 5 in.

Using 3.14 as pi:

[tex]V=(1/3)3.14*5^2*13\\V=(1/3)3.14*25*13\\V=(1/3)1020.5\\\boxed {V=340.166666667}[/tex]

340.166666667 ≈ 340.17

The volume of Cone 2 should be about 340.17in³.

For the given functions, (a) express dw/dt as a function of t, both by using the chain rule and by expressing w in terms of t and differentiating directly with respect to to Then (b) evaluate dw/dt at the given value of t. w = 7y e^x - Inz,x = ln(t^2 + 1), y = tan^-1t,z=e^t;t = 1
(a) dw/dt =?

Answers

By the chain rule,

[tex]\dfrac{\mathrm dw}{\mathrm dt}=\dfrac{\partial w}{\partial x}\dfrac{\mathrm dx}{\mathrm dt}+\dfrac{\partial w}{\partial y}\dfrac{\mathrm dy}{\mathrm dt}+\dfrac{\partial w}{\partial z}\dfrac{\mathrm dz}{\mathrm dt}[/tex]

We have

[tex]w=7ye^x-\ln z\implies\begin{cases}\dfrac{\partial w}{\partial x}=7ye^x\\\\\dfrac{\partial w}{\partial y}=7e^x\\\\\dfrac{\partial w}{\partial z}=-\dfrac1z\end{cases}[/tex]

and

[tex]\begin{cases}x=\ln(t^2+1)\\y=\tan^{-1}t\\z=e^t\end{cases}\implies\begin{cases}\dfrac{\mathrm dx}{\mathrm dt}=\dfrac{2t}{t^2+1}\\\\\dfrac{\mathrm dy}{\mathrm dt}=\dfrac1{t^2+1}\\\\\dfrac{\mathrm dz}{\mathrm dt}=e^t\end{cases}[/tex]

Putting everything together, we get

[tex]\dfrac{\mathrm dw}{\mathrm dt}=\dfrac{14ye^xt}{t^2+1}+\dfrac{7e^x}{t^2+1}-\dfrac{e^t}z[/tex]

[tex]x=\ln(t^2+1)[/tex], so [tex]e^x=e^{\ln(t^2+1)}=t^2+1[/tex], and [tex]z=e^t[/tex], so [tex]\frac{e^t}z=1[/tex].

[tex]\dfrac{\mathrm dw}{\mathrm dt}=14yt+7-1[/tex]

[tex]\dfrac{\mathrm dw}{\mathrm dt}=14t\tan^{-1}t+6[/tex]

Then when [tex]t=1[/tex], the derivative has a value of [tex]\frac{7\pi}2+6[/tex].

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