You begin with $90 in your savings account and your friend begins with $35 in her savings account. You deposite $10 in savings each week, and your friend deposites $15 in savings each week

Answer:Area of shaded region is 454.97

Step-by-step explanation:

The formula for determining the area of a circle is expressed as

Area of circle = πr^2

Where

r represents the radius of the circle.

π is a constant whose value is 3.14

From the information given,

r = 14

Area of the circle = 3.14 × 14^2 = 615.44

The shaded area is a sector

Area of a sector is expressed as

Area = #/360 × πr^2

Where

# = 94 = central angle

Area of sector = 94/360 × 3.14 × 14

= 160.68

Area of shaded region would be

615.44 - 160.68

= 454.97

Answer:

454.97 unit^2.

Step-by-step explanation:

The area of the whole circle = pi r^2

= 14^2 pi.

As there are 360 degrees in a circle the area  of the shaded region , by proportion = [ (360 - 94) / 360  ] * 14^2 pi

= 454.972 unit^2.

Answer:

Hence Nell's mom Chocolate milk is more Chocolaty.

Step-by-step explanation:

Given:

Chocolate syrup used by Nell's mom  = 30 ml

Amount of milk used = 2 ounces.

We will first find Amount of chocolate syrup used in 1 ounce of milk.

Now In 2 ounces of milk = 30 ml of chocolate syrup.

So in 1 ounce of milk = Amount of Chocolate syrup used for 1 ounce milk.

By using Unitary method we get;

Amount of Chocolate syrup used for 1 ounce milk= [tex]\frac{30}{2}=15\ ml[/tex]

Hence For every 1  ounce of milk Nell's mom uses 15 ml of chocolate syrup.

Also Given:

Chocolate syrup used by Nell's dad  = 65 ml

Amount of milk used = 5 ounces.

We will first find Amount of chocolate syrup used in 1 ounce of milk.

Now In 5 ounces of milk = 65 ml of chocolate syrup.

So in 1 ounce of milk = Amount of Chocolate syrup used for 1 ounce milk.

By using Unitary method we get;

Amount of Chocolate syrup used for 1 ounce milk= [tex]\frac{65}{5}=13\ ml[/tex]

Hence For every 1  ounce of milk Nell's dad uses 13 ml of chocolate syrup.

Since The amount of chocolate syrup used by Nell's mom is more than Nell's dad.

Hence Nell's mom Chocolate milk is more Chocolaty.

Answer:

They are both the same

Step-by-step explanation:

Answer: 38.41 minutes

Step-by-step explanation:

The standard error for the difference in means is given by :-

[tex]SE.=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma^2_2}{n_2}}[/tex]

where , [tex]\sigma_1[/tex] = Standard deviation for sample 1.

[tex]n_1[/tex]= Size of sample 1.

[tex]\sigma_2[/tex] = Standard deviation for sample 2.

[tex]n_2[/tex]= Size of sample 2.

Let the sample of Latino name is first and non -Latino is second.

As per given , we have

[tex]\sigma_1=82[/tex]

[tex]n_1=9[/tex]

[tex]\sigma_2=101[/tex]

[tex]n_2=14[/tex]

The standard error for the difference in means will be :

[tex]SE.=\sqrt{\dfrac{(82)^2}{9}+\dfrac{(101)^2}{14}}[/tex]

[tex]SE.=\sqrt{\dfrac{6724}{9}+\dfrac{10201}{14}}[/tex]

[tex]SE.=\sqrt{747.111111111+728.642857143}[/tex]

[tex]SE.=\sqrt{1475.75396825}=38.4155433158\approx38.41[/tex]

Hence, the standard error for the difference in means =38.41 minutes

Answer:

Explanation:

A geometric progression is a sequence of terms in which the consecutive terms have a constant ratio; thus, each term is equal to the previous one multiplied by a constant value:

[tex]First\ term=a_1\\\\ Second\ term=a_2=a_1\times r\\\\ Third\ term=a_3=a_2\times r=a_1\times r^2\\\\n_{th}\ term=a_n=a_{n-1}\times r=a_1\times r^{n-1}[/tex]

A infinite geometric progression may have a finite sum. When the absolute value of the ratio is less than 1, the sum of the infinite geometric progression has a finite value equal to:

Thus, the information given translates to:

[tex]a_1=5\\ \\ S_{\infty}=20=\frac{5}{1-r}[/tex]

Now you can solve for the constant ratio, r:

[tex]1-r=\frac{5}{20}\\ \\ r=1-\frac{5}{20}\\ \\ r=\frac{15}{20}\\  \\ r=3/4[/tex]

The common ratio of the infinite geometric progression with the first term of 5 and a sum of 20 is 0.75.

The question pertains to finding the common ratio of an infinite geometric progression (GP) when given the first term and the sum of all its terms. The first term is known as 5, and the sum of the infinite GP is 20. To find the common ratio, we use the formula for the sum of an infinite GP, which is S = a / (1 - r), where S is the sum, a is the first term, and r is the common ratio.

Plugging in the given values, we have:

20 = 5 / (1 - r)

We can solve for r by multiplying both sides by (1 - r) and then simplifying:

20(1 - r) = 5

20 - 20r = 5

15 = 20r

r = 0.75

Thus, the common ratio of the infinite GP with a first term of 5 and a sum of 20 is 0.75.

Answer:

2. a. [tex]\displaystyle \frac{p}{r}[/tex]

1. [tex]\displaystyle 15,35842773 ≈ c[/tex]

Step-by-step explanation:

2. Extended Information on Trigonometric Ratios

[tex]\displaystyle \frac{OPPOSITE}{HYPOTENUSE} = sin\:θ \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:θ \\ \frac{OPPOSITE}{ADJACENT} = tan\:θ \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:θ \\ \frac{HYPOTENUSE}{OPPOSITE} = csc\:θ \\ \frac{ADJACENT}{OPPOSITE} = cot\:θ[/tex]

__________________________________________________________

1. We have to determine which trigonometric ratio[s] to use, depending on what is given to us, and in this case, we will be using the secant [or cosine] ratio:

[tex]\displaystyle sec\:43° = \frac{21}{c} → \frac{21}{sec\:43°} ≈ c → 15,35842773 ≈ c \\ \\ OR \\ \\ cos\:43° = \frac{c}{21} → 21cos\:43° ≈ c → 15,35842773 ≈ c[/tex]

ONCE AGAIN...

Extended Information on Trigonometric Ratios

[tex]\displaystyle \frac{OPPOSITE}{HYPOTENUSE} = sin\:θ \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:θ \\ \frac{OPPOSITE}{ADJACENT} = tan\:θ \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:θ \\ \frac{HYPOTENUSE}{OPPOSITE} = csc\:θ \\ \frac{ADJACENT}{OPPOSITE} = cot\:θ[/tex]

I am joyous to assist you anytime.

Answer:

15.36.

p/r.

Step-by-step explanation:

cos 43 = c/21

c = 21 cos 43

c = 15.36.

Tan P = opposite side / adjacent side

=  p/r.

Tom has 29 points in the video game whereas mitch has 79 points.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given, Tom and Mitch are engaged in video game gaming. Tom has eight more points than Mitch does, but not by much. Let points of mitch be y and points of tom be x.

Based on the given conditions, formulate y = 3x -8

Rearrange unknown terms to the left side of the equation: 3x = 79 + 8

Calculate the sum or difference: 3x = 87

Divide both sides of the equation by the coefficient of the variable: x = 87/3

Cross out the common factor: x = 29

Therefore, Tom has 29 points in the video game.

Learn more about linear equations here:

https://brainly.com/question/11897796

#SPJ5

By solving the equation 3T - 8 = 79, we find that Tom has 29 points.

The student is asking a mathematical word problem that involves forming and solving an equation. To find how many points Tom has, we need to work with the information given: Mitch has eight less than triple the points that Tom has, and Mitch has 79 points.

Let's define Tom's points as 'T'. The problem tells us that Mitch's points are eight less than triple Tom's points, which can be written as the equation: 3T - 8 = 79.

Now we solve for 'T':

Tom has 29 points.

Answer:

a) Monetary values corresponding to the two events are:

-In case of surviving the year = -166$

-In case of a death in the year = 89834$

b) Expected value of the purchasing the insurance is -85 $

c) Yes, insurance company can make a profit with this policy.

Step-by-step explanation:

a) The man need to pay 166$ first to enroll the insurance policy. If he survives within a year, he will lose 166$. Otherwise, if he dies within a year he will profit 89834$.

b) Expected value of the purchasing the insurance as following:

-In case of surviving the year:

Value: -166$

Probability: 0,9991

-In case of death in a year

Value: 89834$

Probability: 0,0009

Expected value is E(x) = -166×0,9991 + 89834×0,0009 = -85 $

c) Lets consider that 10000 different 31 year old man enrolled to this insurance policy. According to probability of death, 9 out of 10000 man expected to be dead within the year. Therefore, company need to pay 9*90000 = 810000$ to their costumers. But, company will collect 10000*166=1660000$ from their costumers in the beginning of the year

So, it is expected that company is going to profit 1660000-810000=850000$ per year.

The monetary values corresponding to surviving or not surviving for a 31-year-old male are $166 and $90,000 respectively. The expected value for the male purchasing the policy is $83.75. The insurance company can expect to make a profit from many such policies.

a. From the perspective of the 31-year-old male, the monetary value of surviving the year is $166 (the cost of the insurance). The monetary value of not surviving is $90,000 (the death benefit).

b. To find the expected value, we multiply the probability of each outcome by its corresponding monetary value and sum them. The expected value is calculated as: (0.9991 * $166) + (0.0009 * (-$90,000)) = $164.75 + (-$81) = $83.75.

c. The insurance company can expect to make a profit from many such policies. This is because the expected value for the 31-year-old male is positive ($83.75), meaning that on average the insurance company will earn more in premiums than it pays out in benefits.

https://brainly.com/question/32117953

#SPJ3

Answer:

Part 1: N(x) = 50,000 - 300(x-19)

Part 2: R(x) =-300x² + 55700x

Step-by-step explanation:

Given,

The original price of each ticket = $ 19,

The original attendance = 50,000

Part 1 :

∵ For the each​ $1 increase in the ticket​ price, attendance decreases by 300.

Let x represents the price of each ticket after increment,

Thus, if price increment = (x-19) dollars,

New attendance, N(x) = 50,000 - 300(x-19)

Part 2 :

Since, revenue = price of each ticket × attendance

Thus, the revenue from the football​ game,

R(x) = x(50,000 - 300(x-19))

R(x) = 50000x - 300x²+ 5700x

⇒ R(x) =-300x² + 55700x

Answer:

The store must sell 35 bikes to break even.

Step-by-step explanation:

115-65 = 50. 1750 divided by 50 = 35.

Answer:you must sell 35 bikes each month to break even

Step-by-step explanation:

The point at which you break even is the point when there is neither profit nor loss. It mean that

Revenue - cost = 0

Revenue = cost

The cost of operating the bicycle per month is ​$1750

The store pays an average of ​$65 per bike. Let x represent the number of bikes that the store gets in a month. The total cost of x bikes would be

1750 + 65x

The average selling price of each bicycle is ​$115. Total revenue from x bikes would be

115 × x = 115x

Therefore, to break even,

1750 + 65x = 115x

115x - 65x = 1750

50x = 1750

x = 1750/50 = 35

Answer: Averages less than 2litres per day

Step-by-step explanation:

The normal range of urine excreted per day is between 1 to 2 litres, but the kidney must produce a minimum urine volume of 500mL per day, to get rid of body waste, anything below that is abnormal, and not good for the body

Final answer:

For a 229-pound individual, they should receive approximately 11947 mg of the drug every 6 hours.

Explanation:

The student is asking how to calculate the appropriate dosage of a medication based on a person's weight. Specifically, the problem is determining how many milligrams of a drug should be administered every 6 hours when the dosage calls for 460 mg per kg per day and the person weighs 229 pounds.

First, we convert the person's weight from pounds to kilograms, knowing that 1 pound is approximately 0.453592 kg. So, 229 pounds is equal to 229 × 0.453592 kg = 103.890648 kg.

Next, we calculate the daily dosage in milligrams using the provided dosage requirement of 460 mg per kg per day:

103.890648 kg × 460 mg/kg = 47789.09808 mg per day.

Since the medication is divided into four doses, we divide the daily total by 4 to find the amount per dose:

47789.09808 mg ÷ 4 = 11947.27452 mg per dose.

Therefore, the individual should receive approximately 11947 mg of the drug every 6 hours.

Answer:

It takes 16 days to quadruple its population.

Step-by-step explanation:

The population of the virus can be represented by the following exponential function.

[tex]A(t) = A_{0}e^{rt}[/tex]

In which A(t) is the population after t days, [tex]A_{0}[/tex] is the initial population and r is the growth rate.

In this problem, we have that:

[tex]A(8) = 2A_{0}[/tex]

So, we use this to find the value of r.

[tex]A(t) = A_{0}e^{rt}[/tex]

[tex]2A_{0} = A_{0}e^{8r}[/tex]

[tex]e^{8r} = 2[/tex]

Applying ln to both sides

[tex]8r = 0.6931[/tex]

[tex]r = 0.0867[/tex]

How long will it take to quadruple its population?

This is t when [tex]A(t) = 4A_{0}[/tex]

[tex]A(t) = A_{0}e^{rt}[/tex]

[tex]4A_{0} = A_{0}e^{0.0867t}[/tex]

[tex]e^{0.0867t} = 4[/tex]

Again we apply ln to both sides.

[tex]0.0867t = 1.39[/tex]

[tex]t = 16[/tex]

It takes 16 days to quadruple its population.

The number of days it takes to quadruple it's population is; 16days

According to the question;

Therefore;

8days = 2A.

We are required to determine how long it will take to quadruple it's population;

Let no. of days required = x days.

By cross multiplication; we have;

By dividing through by 2A; we have;

Read more:

https://brainly.com/question/20875637

Set up an equation for each customer:

4C + 5S = 22.50

7C + 6S = 35.25

Multipyy the first equation by -1.75 to make the 4C the inverse of 7c:

4C + 5S = 22.50 x -1.75 = -7C - 8.75S = -39.375

Now add the two equations to eliminate the C variable:

7C +6S = 35.25 + -7C - 8.75S = -39.375

= -2.75S = -4.125

Divide both sides by -2.75 to solve for S:

S = -4.125 / -2.75

S = 1.50

The price of a soda is $1.50

Now replace S in an equation with 1.50 and solve for C:

4C + 5(1.50) = 22.50

Simplify:

4C + 7.50 = 22.50

Subtract 7.50 from both sides:

4C = 15

Divide both sides by 4:

C = 15/4

C = 3.75

The sandwich costs $3.75

Soda = $1.50

Sandwich = $3.75

Answer: the cost of a chicken sandwich is $3.75

the cost of a large soda is $1.5

Step-by-step explanation:

Let x represent the cost of a chicken sandwich.

Let y represent the cost of a large soda.

A costumer walked into a restaurant and purchased 4 chicken sandwiches and 5 large sodas for $22.50. This means that

4x + 5y = 22.5 - - - - - - - -1

The customer behind him bought 7 chicken sandwiches and 6 large sodas for $35.25. This means that

7x + 6y = 35.25 - - - - - - - - - -2

Multiplying equation 1 by 7 and equation 2 by 4, it becomes

28x + 35y = 157.5

28x + 24y = 141

Subtracting

11y = 16.5

y = 16.5/11 = 1.5

Substituting y = 1.5 into equation 1, it becomes

4x + 5 × 1.5 = 22.5

4x + 7.5 = 22.5

4x = 22.5 - 7.5 = 15

x = 15/4 = 3.75

Answer:

12 units

Step-by-step explanation:

A-------6--------B-------?--------C

Midpoint is center that divides the line segment into two equal halves.

∴    AB = BC

If line AB measures 6 units in length, then, line BC will measure 6 units in length.

     AB = BC = 6 units

     AC = AB + BC

     AC = 6 units + 6 units

     AC = 12 units

OR

We can say If B is the midpoint of AC, then AC is twice as long as AB.

     AC = 2AB

     AC = 2 × 6 units

     AC = 12 units        

Therefore, the length of line AC is 12 units.  

Answer:

Step-by-step explanation:

Given that the profit the company makes on each customer visit is $0.75 per DVD minus $0.05 "fixed costs."

i.e. Profit

= P(x) = 0.75 x - 0.05  where x is the no of dvds sold

E(x) = [tex]E(0.75x-0.05)\\= E(0.75x) -E(0.05)\\= 0.75E(x) -0.05[/tex]

(using linear transformation rules for mean)

VarP(x) = [tex]Var(0.75 x - 0.05)\\= Var(0.75x)\\= 0.75^2 Var(x)[/tex]

Hence std dev P(X) = 0.75 std dev (x)

Answer:

The probability the number of heads will be even is 0.4922.

Step-by-step explanation:

Consider the provided information.

It is given that coin flip seven times.

Thus, the total number of possible outcomes are: [tex]2^7[/tex]

We want heads will be even.

Even numbers are 2, 4, 6.....

Thus, the possible case are: 2 heads, 4 heads or 6 heads.

The required probability is:

[tex](^7C_2+^7C_4+^7C_6)\times\frac{1}{2^7}=\left(\frac{7!}{2!5!}+\frac{7!}{4!3!}+\frac{7!}{6!1!}\right)\frac{1}{128}\approx 0.4922[/tex]

Hence, the probability the number of heads will be even is 0.4922.

Answer:

B) -3/2

Step-by-step explanation:

If [x/2]=0 then x/2 is a number such that the least integer greater than or equal to x/2 is 0. We can rewrite this as the inequality x/2≤0. Then, the value of x in C, D and E is wrong because they are positive numbers, then x/2 would be a positive number which contradicts this inequality.

Now, 0 is the least integer that satisfies this inequality, therefore we cannot have that x/2≤-1 since -1 is an integer and -1<0. Then x/2>-1. This discards A as wrong, because for x=-2, x/2=-1, contrary to x/2>-1.

Thus B is the right answer. To verify, if x=-3/2, then x/2=-3/4 and we have that -1<-3/4≤0 as required.

Answer: it will take 14 years

Step-by-step explanation:

A savings account is started with an initial deposit of $600. This means that the principal P is

P = 600

It was compounded annually. This means that it was compounded once in a year. Therefore,

n = 1

The rate at which the principal was compounded is 2.1%. So

r = 2.1/100 = 0.021

The duration of time that for which the money stayed in the account is t years. So

Time = t

The formula for compound interest is expressed as

A = P(1+r/n)^nt

Where

A = total amount in the account at the end of t years. Therefore,

a) the equation to represent the amount of money in the account as a function of time in years would be

A = 600 (1+0.021/1)^1×t

A = 600 (1.021)^t

b) the amount of time it takes for the account balance to reach $800 would be

800 = 600 (1.021)^t

Dividing both sides of the equation by 600, it becomes

1.33 = (1.021)^t

t = 14

The overall width of the path and garden is 12 feet.

The area of the entire garden and path is 12 x 12 = 144 square feet.

The path is 1 foot wide, so the garden would be 12 - 2 = 20 feet wide.

The area of the garden only would be 10 x 10 = 100 square feet.

The area of the path only = 144 - 100 = 44 square feet.

1 bag covers 9 square feet:

44 / 9 = 4.88

You would need 5 bags.

Number of dimes are 18 and number of quarters are 31

Solution:

Let "d" be the number of dimes

Let "q" be the number of quarters

value of 1 dime = $ 0.10

value of 1 quarter = $ 0.25

A collection of dimes and quarters is worth $9.55

value of 1 dime x number of dimes + value of 1 dime x number of quarters = 9.55

0.10d + 0.25q = 9.55 ---------- eqn 1

If the quarters were dimes and the dimes were quarters, the total value would be 7.60

quarters were dimes means , q = d

dimes were quarters means d = q

0.25d + 0.10q = 7.60 ----- eqn 2

Let us solve eqn 1 and eqn 2 to find "d" and "q"

Multiply eqn 1 by 2.5

0.25d + 0.625q = 23.875 ---- eqn 3

Subtract eqn 2 from eqn 3

0.25d + 0.625q = 23.875

0.25d + 0.10q = 7.60

( - ) ----------------------

0.525q = 16.275

q = 31

Substitute q = 31 in eqn 1

0.10d + 0.25q = 9.55

0.10d + 0.25(31) = 9.55

0.10d + 7.75 = 9.55

0.10d = 1.8

d = 18

Thus dimes are 18 and number of quarters are 31

Answer:

i needed the answer to this too!! have a good life

Answer:

  14.5 m

Step-by-step explanation:

Let x represent the length of the diagonal. Then the length of the rectangle is (x-3) and its width is (x-8). The area is the product of these, so is ...

  (x -3)(x -8) = 74

  x^2 -11x +24 = 74 . . . . eliminate parentheses

  x^2 -11x = 50 . . . . . . . .subtract 24

  x^2 -11x +30.25 = 80.25 . . . . add 30.25 to complete the square

  (x -5.5)^2 = 80.25 . . . . . . write as square

  x - 5.5 = √80.25 ≈ 8.958 . . . . take the square root

  x = 8.958 + 5.5 = 14.458 . . . . .add 5.5

The length of the diagonal is about 14.5 meters.

Answer:

Step-by-step explanation:

The diagram of the rectangle, ABCD is shown in the attached photo. The diagonal of the rectangle forms a triangle, ABC

Applying Pythagoras theorem,

d^2 = (d - 8)^2 + (d - 3 )^2

d^2 = d^2 - 16d + 64 + d^2 - 6d + 9

d^2 = 2d^2 - 22d + 73

d^2 - 22d + 73 = 0

d^2 = 22d - 73 - - - - - - 1

If the area is 74 m^2, it means that

(d- 8)(d- 3) = 74

d^2 - 11d + 24 = 74

d^2 = 74 - 24 + 11d

d^2 = 50 + 11d - - - - - - - -2

Equating equation 1 and 2, it becomes

22d - 73 = 50 + 11d

22d - 11d = 50 + 73

11d = 123

d = 123/11 = 11.182

diagonal = 11.2 m to the nearest tenth.

Answer:

35

Step-by-step explanation:

Use the combination formula:

[tex]C(n,r)=\frac{n!}{r!(n-r)!}[/tex]

Substitute known values:

[tex]C(7,3)=\frac{7!}{3!(7-3)!}=35[/tex]

We don't use the permutation formula since the order of the drawn marbles does not matter.

Answer: 35

Step-by-step explanation:  

He can choose 3 marbles from 7 distinct marbles in (7/3) ways

C(7/3) = 7!/(3!-(7-3)!)

= 7*6*5*4/4*3*2

= 35

Answer:

9

Step-by-step explanation:

Answer:

B. $337.50

Step-by-step explanation:

1.5% of $22,500 is 337.5

Answer:

B. $337.50

Step-by-step explanation:

Answer:

option C

Step-by-step explanation:

[tex]\dfrac{3}{5}[/tex] class left [tex]\dfrac{2}{5}[/tex] of the class left.

now,

[tex]\dfrac{1}{3}[/tex] of stayed did not want to go so,  [tex]\dfrac{2}{3}[/tex] of the student wanted to go.

[tex]\dfrac{1}{2}[/tex] of the stayed student join the trip.

number of student that stayed and wanted to go are

     =[tex]\dfrac{2}{5}\times \dfrac{2}{3}\times \dfrac{1}{2}[/tex]

     =[tex]\dfrac{2}{15}[/tex]

fraction of class on the field trip

= [tex]\dfrac{3}{5}+\dfrac{2}{15}[/tex]

= [tex]\dfrac{11}{15}[/tex]

Hence, the correct answer is option C

Answer:

The real roots are

[tex]x=\frac{(-3+\sqrt{37})}{4}[/tex] and [tex]x=\frac{(-3-\sqrt{37})}{4}[/tex]

The sum of the squares of these roots is [tex]\frac{-3}{2}[/tex]

Step-by-step explanation:

The given quadratic equation is [tex]8x^2+12x-14[/tex] has two real roots.

To find the roots .

[tex]8x^2+12x-14=0[/tex]

Dividing the above equation by 2

[tex]\frac{1}{2}(8x^2+12x-14)=\frac{0}{2}[/tex]

[tex]4x^2+6x-7=0[/tex]

For quadratic equation [tex]ax^2+bx+c=0[/tex] the solution is [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Where a and b are coefficents of [tex]x^2[/tex] and x respectively, c is a constant.

For given quadratic equation

a=4, b=6, c=-7

[tex]x=\frac{-6\pm\sqrt{6^2-4(4)(-7)}}{2(4)}[/tex]

[tex]=\frac{-6\pm\sqrt{36+112}}{8}[/tex]

[tex]=\frac{-6\pm\sqrt{148}}{8}[/tex]

[tex]=\frac{-6\pm\sqrt{37\times 4}}{8}[/tex]

[tex]=\frac{-6\pm\sqrt{37}\times\sqrt{4}}{8}[/tex]

[tex]=\frac{-6\pm\sqrt{37}\times 2}{8}[/tex]

[tex]=2\frac{(-3\pm\sqrt{37})}{8}[/tex]

[tex]=\frac{-3\pm\sqrt{37}}{4}[/tex]

[tex]x=\frac{(-3\pm\sqrt{37})}{4}[/tex]

The real roots are

[tex]x=\frac{(-3+\sqrt{37})}{4}[/tex] and [tex]x=\frac{(-3-\sqrt{37})}{4}[/tex]

Now to find the sum of the squares of these roots

[tex]\left[\frac{-3+\sqrt{37}}{4}+\frac{(-3-\sqrt{37})}{4}\right]^2=\frac{-3+\sqrt{37}-3-\sqrt{37}}{4}[/tex]

[tex]=\frac{-6}{4}[/tex]

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

[tex]\left[\frac{-3+\sqrt{37}}{4}+\frac{(-3-\sqrt{37})}{4}\right]^2=\frac{-3}{2}[/tex]

Therefore the sum of the squares of these roots is [tex]\frac{-3}{2}[/tex]

The value of w in the given figure of parallelogram is, w = 37 degrees.

We can see that the diagonals of the parallelogram divided it into four number of parallelogram.

We know that the sum of all interior angles of a triangle is 180 degrees according to Angle Sum Property of Triangle.

So, from the given figure we can see that in a triangle the interior angles are w, 2w and 69 degrees.

According to Angle Sum Property,

w + 2w + 69 = 180

3w = 180 - 69 = 111

w = 111/3 = 37

Hence the value of w in the given parallelogram is 37 degrees.

To know more about Angle Sum Property here

https://brainly.com/question/8492819

#SPJ2

Answer:

  20%

Step-by-step explanation:

If there are 4 adults, 2 are female, and 1 of those has 1 child. Then the population is 4 adults and 1 child. The children make up 1/5 = 20% of the population.

Answer

20%

Step-by-step explanation:

Aops Question

Answer:

Independent variable : Anaerobic Exercise

Step-by-step explanation:

The dependent variable is known as the variable of interest or "Y" and usually the independent variables are expressed by "X".

The independent variable is the "variable that is changed or controlled in a scientific experiment to test the effects on the dependent variable"

For this case our independent variable would be the  anerobic exercise, since we want to se the effect of the exercise on the weigth loss, so then our dependent variable would be th weigth loss.

And for this case we can check the hypothesis with a paired t-test if we use the same individuals.

A paired t-test is used to compare two population means where you have two samples in which observations in one sample can be paired with observations in the other sample. For example if we have Before-and-after observations we can use it.

The independent variable in Susan's experimental research on weight loss is the introduction of aerobic exercise. How much weight loss is achieved can have multiple contributing factors, including individual differences. Incorporating moderate to vigorous physical activity is crucial for weight control and may need to be adjusted based on individual needs.

The independent variable in Susan's experimental research is the type of exercise performed by the subjects — specifically, the aerobic exercise. This is because the independent variable is the factor that the researcher manipulates to determine if it causes a change in another variable. In this case, the independent variable is the introduction of aerobic exercise compared to just walking. Susan's goal is to measure the effects of aerobic exercise on weight loss among the participants over a period of 3 months.

Variations in weight loss outcomes in a workout program can be attributed to individual differences such as metabolism, diet, genetics, lifestyle, and adherence to the exercise regimen. For effective weight control, research suggests a combination of aerobic activity and muscle-strengthening exercises. Susan can compare her findings to these variables to gain insight into the weight loss effects of aerobic exercise.

For those looking to use physical activity for weight loss and control, it might make sense to increase either the intensity or the minutes per week of physical activity, depending on their individual circumstances. Incorporating moderate to vigorous aerobic activity combined with a reduction in caloric intake can help meet weight-control goals for many adults.

Answer:

The term exponential is often used.

Step-by-step explanation:

The term exponential is used to represent changes in population over time.  The idea of (positive) exponential is that the higher the number, the higher the growth. You can relate this with a population, because the higher the population, the more opportunities for it to multiply, thus, the higher it grows.

Usually the way to meassure the population of an species after certain number of years x, you use an exponential function of the form

[tex] f(x) = K_0 * a^x [/tex]

For certain constants K₀ and a. K₀ is the initial population at the start of the experiment and a number of exponential growth. Essentially, the population of the species is multiplied by a during each year.

For example, if K₀ = 1000 and a = 2, then the population at the start of the experiment is 1000. After the first year is 1000*2 = 2000 and after the second year it is 2000*2 = 4000. Note that, not only the population grow during the years, but also the amount that the population increases also grow: in the first year it grows 1000, and between the first and second year it grows 2000.