g(x) = x - 6

Domain of g:

Answer:

A = 35 cm²

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × width

by counting the squares on the sides

length = 7 cm and width = 5 cm , then

A = 7 × 5 = 35 cm²

The proposed skyscraper is 172.8 m tall

From the question, we are to determine the how tall the proposed skyscraper is in meters

From the given information,

The scale of the model is

1 in : 7.2 m

and

The model is 2 ft tall

First, convert 2 ft to inches

NOTE: 1 foot = 12 inches

∴ 2 feet = 2 × 12 inches

= 24 inches

Now,

If 1 inch represents 7.2 m

Then,

24 inches will represent 24 × 7.2 m

24 × 7.2 m = 172.8 m

Hence, the proposed skyscraper is 172.8 m tall

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If you mean

\(\displaystyle \lim_{x\to0^+} \frac{(1+\sin(7x))^8}x\)

then the limit doesn't exist, since 1 + sin(7x) approaches 1 while the denominator approaches 0.

However, if instead you mean

\(\displaystyle \lim_{x\to0^+}(1+\sin(7x))^{8/x}\)

rewrite the limand as

\((1+\sin(7x))^{8/x} = \exp\left(\ln(1+\sin(7x))^{8/x}\right) \\\\ = \exp\left(\dfrac{8\ln(1+\sin(7x))}x\right) \\\\ =\exp\left(\dfrac{\ln(1+\sin(7x))}x\right)^8\)

The exponential function is continuous at 0, so we can pass the limit through it:

\(\displaystyle\lim_{x\to0^+}\exp\left(\dfrac{\ln(1+\sin(7x))}x\right)^8 = \exp\left(\lim_{x\to0^+}\dfrac{\ln(1+\sin(7x))}x\right)^8\)

The remaining limit takes the indeterminate form 0/0, since ln(1 + sin(7x)) approaches ln(1) = 0, and so does x in the denominator. Apply L'Hopital's rule:

\(\displaystyle\exp\left(\lim_{x\to0^+}\dfrac{7\cos(7x)}{1+\sin(7x)}\right)^8 = \exp\left(7\right)^8 = \left(e^7\right)^8 = \boxed{e^{56}}\)

Answer:

the bigger pack is better

Answer:I believe it is -4

Step-by-step explanation:

Answer:

-3z-5t+3g

Step-by-step explanation:

-7(3z+5t-3g)

= -7×3z +( -7×5t)( -7×-3g)

= -21z-35t+21g

divide all elements by 7

= -21÷7 -35÷7+21÷7

= -3z-5t+3g

Not all intersecting lines are perpendicular.

Perpendicular lines require a 90-degree angle of intersection, creating the formation of right angles.

Nonetheless, unlike perpendicular lines that necessitate exactly 90 degrees of intersections, other types of driven lines can be at varying angles beside these.

As such, it is critical to highlight that in general intersecting lines come with different angles of intersection, and only those featuring exact 90-degree angle of intersection become normal cases of intersecting lines, becoming one among many subtypes existing today.

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Answer:

  4 +7x

Step-by-step explanation:

You want the additive inverse of -4-7x.

The additive inverse of an expression is the value that gives zero when added to the expression. It is the expression multiplied by -1.

  -1 · (-4 -7x) = 4 +7x

The additive inverse is 4 +7x.

__

Additional comment

  (-4 -7x) + (4 +7x) = 0

Answer:

12

Step-by-step explanation:

x = number of $1 bills

y = number of $5 bills

z = number of $10 bills

We know that:

x + y + z = 25 (total amount of bills)

x + 5y + 10z = 100 (total amount of money)

y = 4z (Given)

Substitute the third equation into the first one.

x + 4z + z = 25

x = 25 - 5z

Put this into the second equation.

(25 - 5z) + 5 (4z) + 10z = 100

Simplify and solve.

25 - 5z + 20z + 10z = 100

25z + 25 = 100

25z = 75

z = 3

Substitute this into y = 4z

y = 4 * 3

y = 12

So, there are 12 $5 bills.

Answer:

12 $5 bills

Step-by-step explanation:

Represent the number of each kind of bill by x, y and z:  there are x $1 bills, y $5 bills and z $10 bills.

According to the problem statement,

x + y + z = 25 and y = 4z (or z = y/4).  Also, the values of the bills add up to $100:

($1)x + ($5)y + ($10)z = $100.  Eliminate z by typing y/4 in its place:

x + y + (y/4) = 25 and

x  + 5y + 10(y/4) = 100

Doing this has reduced the number of variables to two:  x and y.  Combining like terms in both equations, we get:

1x + (5/4)y = 25 and

1x +  (30/4)y       =100

Subtracting the 1st equation from the 2nd, we get:

(25/4)y = 75, or

(4/25)(25/4)y = (4/25)(75) , or y = 12.

If y = 12, z = 12/4, or 3.

Then x + 12 + 3 = 25 coins in all; therefore, x = 15 = 25, and x = 10

There are 10-$1 bills, 12-$5 bills and 3-$10 bills.

Answer:

x =  ±2

Step-by-step explanation:

3x^2-4=8

Add 4 to each side

3x^2-4+4=8+4

3x^2 = 12

Divide by 3

3x^2 /3 = 12/3

x^2 = 4

Take the square root of each side

sqrt(x^2) = ±sqrt(4)

x =  ±2

Answer:

\(x=\± 2\)

Step-by-step explanation:

\(3x^2-4=8\)

\(3x^2-4+4=8+4\)

\(3x^2=12\)

\(\displaystyle \frac{3x^2}{3}=\frac{12}{3}\)

\(x^2=4\)

\(x=\± \sqrt{4}\)

\(x=\± 2\)

Answer:

b

Step-by-step explanation:

A crotchet is one, a tied crotchet is 2-3, the quavers are 4 +

There are 4 cups of brown sugar are required for every 12 cups of white sugar.

A recipe calls for 2 cups of brown sugar for every 6 cups of white sugar. We can set up a proportion to find the relationship between the two quantities:

2 cups brown sugar / 6 cups white sugar = x cups brown sugar / 12 cups white sugar

To find the number of cups of brown sugar required for 12 cups of white sugar, we can cross-multiply and then solve for x:

2 cups brown sugar × 12 cups white sugar = 6 cups white sugar × x cups brown sugar

24 cups brown sugar = 6x cups brown sugar

x = 24/6

x = 4

So, 4 cups of brown sugar are required for every 12 cups of white sugar.

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Answer: f(x)=2^x+5

Step-by-step explanation:

math

Answer:

The correct option is (a) 0.9780.

Step-by-step explanation:

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

 \(\mu_{\hat p}=p\)

The standard deviation of this sampling distribution of sample proportion is:

 \(\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}\)

As the sample selected is quite large, i.e. n = 110 > 30, the central limit theorem can be applied to approximate the sampling distribution of sample proportion by a Normal distribution.

The mean and standard deviation are:

\(\mu_{\hat p}=p=0.70\\\\\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.70(1-0.70)}{110}}=0.044\)

Compute the probability that the sample proportion of students living in the dormitories falls in between 0.60 and 0.80 as follows:

\(P(0.60<\hat p<0.80)=P(\frac{0.60-0.70}{0.044}<\frac{\hat p-\mu_{\hat p}}{\sigma_{\hat p}}<\frac{0.80-0.70}{0.044})\)

                              \(=P(-2.27<Z<2.27)\\\\=P(Z<2.27)-P(Z<-2.27)\\\\=0.98840-0.01160\\\\=0.9768\\\\\approx0.9780\)

*Use a z-table.

Thus, the probability that the sample proportion of students living in the dormitories falls in between 0.60 and 0.80 is approximately equal to 0.9780.

The correct option is (a).

Answer:

perpendicular lines

Step-by-step explanation:

Answer:

  y = x^2 +2x +1

Step-by-step explanation:

Let's see how this works.

Two of the given points have the same y-value, so the axis of symmetry is located halfway between. If we translate the desired curve down 1 unit, those symmetrical values become zeros, and our function will look like ...

  f(x) = ax(x +2)

We want this to go through the third point, also translated down by 1 unit, so we have ...

  3 = a(1)(1+2) = 3a

That is, a=1, so f(x) = x(x+2) and translating that up 1 unit gives our desired function:

  y = x(x+2) +1

  y = x^2 +2x +1

_____

Using the quadratic regression function of a graphing calculator gives the same result.

_____

Comment on the solution approach

For arbitrary points, one would generally substitute them into the formula for  the function you want:

  y = ax^2 +bx +c

to get three equations in the parameters a, b, and c. These equations would be solved to find the desired coefficients. As noted elsewhere, one of the given points for this problem is the y-intercept (0, 1), so right away we know c = 1. ("c" is the y-intercept.)

That leaves two remaining equations in two unknowns (using the other two points).

Using the point (-2, 1), the equation is ...

  1 = a(-2)^2 +b(-2) +1   ⇒   4a - 2b = 0   ⇒   2a -b = 0

Using the point (1, 4), the equation is ...

  4 = a(1^2) +b(1) +1   ⇒   a +b = 3

Adding these gives 3a = 3, or a=1. Then substitution gives b=2, so the final equation is ...

  y = x^2 +2x +1

Answer:

36 square inches.

Step-by-step explanation:

volume is given by 1 by 3, into base into height is based. His height and volume and area of the base is given by area of the ashe area of the base is given by 3 into 60 by 5. As given in the question on solving it, we get it equals to 36 square inches.

Answer:

y < 13x – 15

Step-by-step explanation:

13x – y < 15

–y < –13x +15

divide both sides by (–)

–(–y) < –(–13)x –(15)

y < 13x – 15

Answer:

Step-by-step explanation:

\(\sf 14=-6+2\left(2x+4\right)\)

\(\sf -6+2\left(2x+4\right)=14\)

\(\sf -6+2\left(2x+4\right)+6=14+\)

\(\sf 2\left(2x+4\right)=2\)

\(\sf \frac{2\left(2x+4\right)}{2}=\frac{20}{2}\)

\(\sf 2x+4=10\)

\(\sf 2x+4-4=10-4\)

\(\sf 2x=6\)

\(\sf \frac{2x}{2}=\frac{6}{2}\)

\(\sf x=3\)

The length of the side of triangle is found.

Part a: b = 4 in; c = 4√2 in

part b: a = √3/21 in; c = 42 /√3 in

Part a:

tan 45 = 4/b

b = 4 in

sin 45 = 4/c

c = 4/(1/√2)

c = 4√2 in

Part b:

tan 60 = 21/a

a = √3/21 in

sin 60 = 21 / c

c = 21 / (√3 /2)

c = 42 /√3 in

Thus, the length of the side of triangle is found.

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A share of stock is quoted at 25 1/4. If you have 30 shares of stock that were purchased at 20 1/4 and you sell them at 25 1/4, what is your profit or loss?A share of stock is traded on the stock market, and the stock price is determined by the supply and demand of the stock.

The stock market is a market where stocks are traded. Stocks can be bought and sold on the stock market, and the price of a share of stock is determined by supply and demand.Suppose you purchased 30 shares of stock at 20 1/4 dollars per share.

The total cost of the 30 shares is calculated as follows:20 1/4 dollars/share × 30 shares = $607.50.The share of stock is now priced at 25 1/4 dollars per share.

The total revenue you would earn if you sold all of your shares at this price is calculated as follows

:25 1/4 dollars/share × 30 shares = $757.50.

The profit or loss on the stock transaction is calculated as follows:

Profit or loss = Total revenue - Total cost= $757.50 - $607.50= $150.

If the stock is sold at 25 1/4 dollars per share, the profit is 150 dollars.

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Answer:

159 bagels left

Step-by-step explanation:

add the 32 and 37 then subtract the answer from 32 and 37 from 228 and your answer is 159

Since the final result is 1, which is the same as the result obtained in step 5, we can conclude that the calculation is correct.

Division is a mathematical operation used to distribute a quantity or value into equal parts. It is the opposite of multiplication. In division, a number called the dividend is divided by another number called the divisor, and the result is called the quotient. The dividend is the total quantity or value that is being divided into parts, while the divisor is the number of equal parts the dividend is being divided into. For example, in the expression 12 ÷ 4, the number 12 is the dividend and the number 4 is the divisor. The process of division involves finding out how many times the divisor can be subtracted from the dividend without resulting in a negative number. The result of division can be expressed as a whole number or a decimal, depending on the numbers being divided.

Here,

The process you are describing is known as "casting out nines" or "the rule of nines" and it is a method for verifying calculations carried out by hand. The basic idea is that if the sum of the digits of a number is divisible by 9, then the number itself is also divisible by 9.

Here is an example of how to use the rule of nines to verify the calculation 58 x 16 = 928:

Add the digits of 58: 5 + 8 = 13

Since 13 is not divisible by 9, add its digits again: 1 + 3 = 4

Add the digits of 16: 1 + 6 = 7

Add the digits of 928: 9 + 2 + 8 = 19

Since 19 is not divisible by 9, add its digits again: 1 + 9 = 10, then 1 + 0 = 1

Multiply the two numbers obtained at the top and bottom: 4 x 7 = 28

Add the digits of the product: 2 + 8 = 10, then 1 + 0 = 1

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What is the central conflict (usually internal)? State the opposing forces as specifically as possible (? vs. ?). Remember, the central conflict is usually the beginning key trait vs. the ending key trait or some opposing trait. ( The Story of an Hour by Kate Chopin )

The probability that all 4 people spend more than an hour a day using the Internet is 0.053 or 5.3%.

The given problem is an example of a binomial probability distribution, where there are only two outcomes - success and failure. Here, success means spending more than an hour a day using the internet, and failure means spending an hour or less a day.

The probability of success is p = 0.48, and the probability of failure is q = 1 - p = 0.52.

To find the probability that all 4 people spend more than an hour a day using the Internet, we need to use the formula for the binomial probability distribution:

P(X = k) = (n choose k) * \(p^{k }* q^{(n-k)\)

Here, n = 4 (the number of people selected), and k = 4 (the number of people who spend more than an hour a day using the Internet).

Plugging in the values, we get:

P(X = 4) = (4 choose 4) * 0.48⁴ * 0.52⁴⁻⁴ = 0.053

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You would need to save approximately $56.62 each month to achieve your savings goal of $3,000.00 over four years.

To calculate the monthly savings required to reach a savings goal of $3,000.00 over four years with a 10% annual interest rate,  we can use the PMT (Payment) function.

The PMT function helps us determine the fixed payment amount needed to achieve a specific future value within a given time frame.

Let's break down the given information:

Present Value (PV): $0.00 (initial account balance)

Future Value (FV): $3,000.00 (savings goal)

Interest Rate (rate): 10% per year (annual interest rate)

Number of Periods (nper): 4 years (48 months)

Using the PMT function, we need to plug in the values and solve for the monthly payment (savings amount).

The formula for the PMT function is:

PMT(rate, nper, pv, [fv], [type])

Where:

rate = Interest rate per period

nper = Total number of periods

pv = Present value (initial account balance)

fv = Future value (savings goal)

type = (Optional) Indicates whether the payment is made at the beginning (1) or end (0) of the period.

We'll assume 0 for monthly savings.

Let's calculate the monthly savings using the PMT function:

PMT(10%/12, 4*12, 0, -3000, 0)

Here, we divide the annual interest rate by 12 to get the monthly interest rate (10%/12), multiply the number of years by 12 to get the total number of months (4*12), set the initial account balance (pv) as $0, set the future value (fv) as -$3,000 (negative because it's an outgoing payment), and assume the savings are made at the end of each month (type = 0).

Using a financial calculator or spreadsheet software, the monthly savings required to reach the goal of $3,000.00 over four years with a 10% annual interest rate is approximately $56.62.

Therefore, you would need to save approximately $56.62 each month to achieve your savings goal of $3,000.00 over four year.

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Question : you want to reach $3,000.00 in savings over four years. Your account will earn 10% interest per yea Initially your account has a zero balance. How much must you save each month to achieve this goal? Use the PMT() function. Look it up in the e-book if you do not know how to use it. TIP: This is monthly so do not forget to adjust the interest rate and number of payment.

Answer:

a) 52

B)6

Step-by-step explanation:

B) -5+11=6

It's not that hard, you shall know negative signs rules

The measure of the angles are:: x = 20. so, angles are, 20°, 40°, 120°.

Here, we have,

we know that,

The sum of the angles in a triangle add to 180

x+2x+6x = 180

Combine like terms

9x= 180

Divide by 9

9x/9 = 180/9

x = 20.

Hence, The measure of the angles are:: x = 20. so, angles are, 20°, 40°, 120°.

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complete question:

The sum of the angle measures in a triangle is 180°. The angles of a certain triangle measure x°, 2x°, and 6x°. Solve for x.