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The factorization of 9t² - u² is (3t + u)(3t - u).

To factorize the expression 9t² - u² completely, we need to identify any patterns or common factors that can be extracted. In this case, we have a difference of squares, which is a special pattern that can be factored using a specific formula.

The difference of squares formula states that for any two terms, a² - b², we can factorize it as (a + b)(a - b).

Applying this formula to our expression 9t² - u², we can rewrite it as (3t)² - u². Now we can clearly see that a = 3t and b = u.

Using the difference of squares formula, we can factorize 9t² - u² as follows:

9t² - u² = (3t + u)(3t - u)

Therefore, the expression 9t² - u² is completely factorized as (3t + u)(3t - u).

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Answer of the statements is describe below.

Given that,

For general :

cost of admission  = $15

cost of per taco = $4

For VIP :

cost of admission  = $36

cost of per taco = $1.50

Therefore,

Since price of taco in VIP is less than General admission

Then Deric should choose VIP if he plan to buy 6 tacos.

The amount Deric have to spent = $55

As Deric wants to eat many tacos so he should go for VIP in which price of taco in VIP is less than General admission so he can buy more taco.

Since price of each taco in general admission = $4

Then he can buy 55/4  = 13.74 tacos in general admission

And  price of each taco in VIP = $1.5

Then he can buy 55/1.5 = 36.66 tacos in VIP

Since price of tacos in VIP is cheaper then he can buy

37 tacos nearly.

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Answer:

3

Step-by-step explanation:

The square root of 9 is 3

Answer:

Option B

Step-by-step explanation:
\(6^{2} = 36\)

\(\sqrt{81} = 9\)

Substitute the above two values in each of the four expressions and solve using BODMAS and Distributive Law:

A. \((36 + 2) - 8(9)\)

  = \((18) -(72)\)

  = \(18 - 72\)

  = \(-54\) ≠ \(-18\)

C. \((36 + 2 - 8)(9)\)

   = \((30)(9)\)

   = \(270\) ≠ \(-18\)

D. \(36 + 2 - [(8)(9)]\)

   = \(36 + 2 - 72\)

   = \(-34\) ≠ \(-18\)

B. \(36 + (2-8)(9)\)

 = \(36 + (-6)(9)\)

= \(36 -54\)

= \(-18\) ≡ \(-18\)

∴Option B

Answer:

3 to 1

Step-by-step explanation:

it says cookies first so there a 3 cookies and 1 icecream.

The mean for the given set of data exists at -1 1/3.

Mean exists an arithmetic average of the data set and it can be estimated by dividing a totality of all the data points by the digit of data points in the data set. It exists a point in a data set that exists as the average of all the data points we keep in a set.

Mean = (Sum of terms) / (Number of elements)

To find the mean, we must add all of the numbers and then divide them by the number of values you were given.

-4 + -3 + -1 + -1 + 0 + 1 = -8

There exist a total 6 number of elements in the set of data.

Mean = (Sum of terms) / (Number of elements)

Mean = (-4 + -3 + -1 + -1 + 0 + 1) / 6

-4 + -3 + -1 + -1 + 0 + 1 = -8

Mean = -8 / 6

= -4/3 = -1 1/3

The mean for the given set of data exists at -1 1/3.

Therefore, the correct answer is option a) -1 1/3.

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The difference quotient of f(x) is \(\frac{-\frac{1}{h}+ 5}{5x+ h -12}\) .

According to the given question.

We have a function

f(x) = -1/(5x -12)

As we know that, the difference quotient is a measure of the average rate of change of the function over and interval.

The difference quotient formula of the function y = f(x) is

[f(x + h) - f(x)]/h

Where,

f(x + h) is obtained by replacing x by x + h in f(x)

f(x) is a actual function.

Therefore, the difference quotient formual for the given function f(x)

= [f(x + h) - f(x)]/h

= \(\frac{\frac{-1}{5(x+h)-12} -\frac{-1}{5x-12} }{h}\)

= \(\frac{\frac{-1}{5x + 5h -12}+\frac{1}{5x-12} }{h}\)

= \(\frac{\frac{-1+5h}{5x + 5h-12} }{h}\)

= \(\frac{-1+5h}{(5x +h-12)(h)}\)

= \(\frac{-1+5h}{5xh + h^{2} -12h}\)

= \(\frac{h(-\frac{1}{h}+5) }{h(5x+h-12)}\)

= \(\frac{-\frac{1}{h}+ 5}{5x+ h -12}\)

Hence, the difference quotient of f(x) is \(\frac{-\frac{1}{h}+ 5}{5x+ h -12}\) .

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Answer:

she needs to save 150 a month

Step-by-step explanation:

1500 - 300 = 1200

1200 / 8 = 150

Answer: 150 dollars a month

Step-by-step explanation: 1500 - 300 = 1200

1200/8 = 150

Answer:

Step-by-step explanation:

Answer:

ion kno gang ask a teacher

The required slope of the tangent line to f(x) = 6 sin(x) at x = π/6 is 3 √3.

The value of the steepness or the direction of a line in a coordinate plane is known as the slope of a line, often known as the gradient. Given the equation of a line or the coordinates of points situated on the straight line, slope can be determined using a variety of techniques.

The formula for slope between two points (x₁, y₁) and (x₂, y₂) is,

m = (y₂ - y₁)/(x₂ - x₁)

The slope is also denoted by tan θ.

The given equation of line,

f(x) = 6 sin(x)

To find the slope of the given line, differentiate with respect to x,

f'(x) = tan θ = d/dx(6 sin(x))

                  = 6 d/dx(sin(x))

                  = 6 cos x

At x = π/6, the slope of line,

f'(π/6) = 6 cos(π/6)

          = 6 (√3 / 2)

          = 3 √3

The slope of the tangent line to f(x) = 6 sin(x) is 3 √3.

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Answer: Area = pie multiplied by radius multiplied by radius (pie × square of radius)

Step-by-step explanation: If you are given diameter, radius will be half of the diameter.

Simply multiply 3.14 by radius squared

Answer:

400 J

Step-by-step explanation:

Kinetic energy = ½ mv²

mass = 50 kg

velocity = 4 m/s

Kinetic energy = ½×50×(4)²

= ½×50×16

= 50×8

= 400 J

Option Four

\(mass(m) = 50kg \\ velocity(v) = 4ms {}^{ - 1} \\ kinetic \: energy = \frac{1}{2} mv {}^{2} \\ = \frac{1}{2} \times 50 \times (4) {}^{2} \\ = 400\)

the perimeter and area is the hypotenuse multiplied

The number of periods is approximately 26.98.

To calculate the number of periods it takes to double your money at 5.25 percent interest, you can use the formula for compound interest:

Future value = Present value * (1 + interest rate) ^ number of periods

In this case, the future value is twice the present value, so the equation becomes:

2 = 1 * (1 + 0.0525) ^ number of periods

To solve for the number of periods, you can take the logarithm of both sides:

log(2) = log((1 + 0.0525) ^ number of periods)

Using the logarithmic properties, you can bring the exponent down:

log(2) = number of periods * log(1 + 0.0525)

Finally, you can solve for the number of periods:

number of periods = log(2) / log(1 + 0.0525)

Using a calculator, the number of periods is approximately 13.27.

To calculate the number of periods it takes to quadruple your money at 5.25 percent interest, you can follow the same steps as above, but change the future value to four times the present value:

4 = 1 * (1 + 0.0525) ^ number of periods

Solving for the number of periods using logarithms:

number of periods = log(4) / log(1 + 0.0525)

Using a calculator, the number of periods is approximately 26.98.

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Answer:

The answer is x=294 (B)

Step-by-step explanation:

Remember, all interior angles of a hexagon add to 720.

So add all the  given numbers first.

92+100+94+140+x= 720

426+x=720

-426 from both sides

x= 294

I know this is a week later since you posted the question, sorry.

Answer:

  3/8 cubic units

Step-by-step explanation:

The volume of a rectangular prism is given by the formula ...

  V = LWH

Using the given dimensions, we find the volume to be ...

  V = (1/2)(1)(3/4) = 3/8 . . . . cubic units

Answer:

Step-by-step explanation:

for 2 1/2 h at the speed of 60 miles/h

60+60+30=150 miles

for 30 min he drove 20 miles

150+20=170 miles

The critical value of the test statistic t for a one-tailed (upper tail) hypothesis test with a sample size of 26 and a significance level of 0.01 is 2.479. This value is used to determine whether the sample data provides enough evidence to reject the null hypothesis in favor of the alternative hypothesis.

If the calculated test statistic is greater than 2.479, it falls into the critical region, and we reject the null hypothesis. Conversely, if the calculated test statistic is less than 2.479, it does not fall into the critical region, and we fail to reject the null hypothesis. The critical value is determined based on the desired level of significance and the degrees of freedom, which in this case is 26 - 1 = 25. For a one-tailed test with a significance level of 0.01, we need to find the t-value that corresponds to the 0.99 percentile of the t-distribution with 25 degrees of freedom. By consulting the t-distribution table or using statistical software, we find that the critical value is 2.479. This means that the calculated test statistic must be greater than 2.479 for us to reject the null hypothesis in favor of the alternative hypothesis at the 0.01 significance level in the upper tail of the distribution.

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Answer:

l = 194999.45

Step-by-step explanation:

I'm going to assume that you meant 3.14 by 3,14.

336,765 = 3.14 × 0.55 × (l + 0.55)

336,765 ÷ (3.14 × 0.55) = l + 0.55

(336,765 ÷ (3.14 × 0.55)) - 0.55 = l

l = 194999.45

Answer:

C

Step-by-step explanation:

The quotient of d minus 16 and 3 means that d - 16 is in the numerator and 3 is in the denominator. This equation is equal to 4, so the answer is:

(d - 16) / 3 = 4

I hope this helped and please mark me as brainliest!

The sandbox's 3/4ths fraction is full, the volume of sand can be found by multiplying the volume of the entire sandbox (0.33 ft³) by 3/4, which gives us 0.2475 ft³ of sand.

The area given (64 cm²) is the base of the sandbox, we can find the height of the sandbox in cm using the formula for the area of a rectangle: A = l × w.

Since the area is 64 cm², and we know that the sandbox has a rectangular base, we can assume the length and width are equal and each measure 8 cm.

Next, we need to convert the height of the sandbox from cm to feet. One foot is equal to 30.48 cm, so the sandbox is 0.33 feet tall (approximately). Since the sandbox is 3/4ths full, the volume of sand can be found by multiplying the volume of the entire sandbox (0.33 ft³) by 3/4, which gives us 0.2475 ft³ of sand.

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The sandbox was a foot tall, but the sand only was only filled up 3/4ths of the way with an area of 64 cm². How many cubic feet of sand are there in the box?

The admissions clerk at Tops Hospital is responsible for entering patient registration information into a computerized system, which creates an admission log as well as daily census summaries. The computerized system likely includes fields for various patient details, such as their name, date of birth, address, contact information, insurance details, reason for admission, attending physician, admission date, and other relevant information.

By accurately inputting this data into the system, the admissions clerk helps maintain an up-to-date record of all patients admitted to the hospital. This information is crucial for managing patient care, tracking occupancy levels, coordinating with medical staff, billing and insurance purposes, and overall hospital administration.

It is essential for the admissions clerk to be diligent and accurate in data entry to ensure that the information is reliable and accessible for various hospital departments and personnel. Mistakes or inaccuracies in data entry can lead to issues in patient care, billing disputes, or other administrative problems.

In conclusion, the admissions clerk's role in entering patient registration information into the computerized system plays a crucial part in maintaining accurate records and facilitating smooth hospital operations.

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Step-by-step explanation:

\( - 4x + 3(2x - 5) = 31 \\ - 4x + 6x - 15 = 31 \\ 2x - 15 = 31 \\ 2x = 31 + 15 \\ 2x = 46 \\ x = 46 \div 2 \\ x = 23\)

The correct option is c. 33%.

The job rate of industry’s percent increase from 2003 to 2013 is 33%.

The percentage increase would be the change between the final and initial values given as a percentage. We need the initial value and the enhanced (new) value to calculate the percentage.

In other words, % growth is a measurement of percent change that indicates the amount by which a quantity increases in magnitude, strength, or value.

If the % rise is negative, we might conclude that there is corresponding proportion reduction. Let's look at the percentage growth calculation now.

Now, according to the question;

Total Number of years = 10 years

Total number of new jobs created = 2.65 thousand x 10

                                                         = 26.5 thousand

                                                         = 26,500

Number of jobs in 2013 = 78,900 + 26,500

                                       = 105,400

Percentage increase = (105,400 - 78,900)/78,900 x 100

                                   = 26,500/78,900 x 100

                                   = 0.3359 x 100

                                    = 33.59%

Percentage increase = 33% (approx)

Therefore, the percentage increases in the job between 2003 and 2013 is 33%.

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Answer:

C

Step-by-step explanation:

We have the following response after answering the given question: To interest the nearest penny, the balance in the account after 12 years is thus $17,821.76.

To calculate simple interest, divide the principal by the interest rate, the duration, and other variables. The marketing formula is simple return = capital + interest + hours. The easiest way to calculate interest is with this approach. The most popular method for calculating interest is as a percentage of the principal amount. For instance, if he borrows $100 from a friend and agrees to pay it back at 5% interest, he will only pay his portion of the 100% interest. $100 (0.05) = $5. Interest must be paid when you borrow money and must be added to any loans you make. The yearly percentage of the loan amount is frequently used to calculate interest. This percentage represents the loan's interest rate.

Continuously compounded interest is calculated as follows:

\(V = Pe^(rt) (rt)\)

where: V = the investment's final value

P is the original investment's principle.

r equals the yearly interest rate (as a decimal)

t is the duration of the investment, in years.

P = $8290, r = 0.06 (6% as a decimal), and t = 12 years in this example.

So, \(V = 8290e^(0.06*12) = $17,821.76\)

To the nearest penny, the balance in the account after 12 years is thus $17,821.76.

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Answer:

15

Step-by-step explanation:

To find the rate of change, find the slope

Slope= \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

        \(=\frac{35-20}{2-1}\\\\=\frac{15}{1}\\\\=15\)

Answer:

470 potatoes or toes

Answer:

X= 470

Step-by-step explanation:

You Just subtract 520 - 50

Hope this helps ^o^

Answer:

B

Step-by-step explanation:

Based on the given information, option 4 seems to be the most likely candidate to be positive for the entire interval [-3, -2]. Correct option is 4.

To determine which function is positive for the entire interval [-3, -2], we need to look for the part of the curve that lies above the x-axis within this interval.

The curve has a minimum value of (0, -3) and crosses the x-axis at (-3, 0) and (3, 0), which means it goes below the x-axis in the interval [-3, -2]. So, this option is not positive for the entire interval.

The curve has a minimum value of (2, -3) and crosses the x-axis at (-1, 0) and (5, 0). Since it crosses the x-axis at -1 which is outside the interval [-3, -2], this option is not positive for the entire interval.

The curve has a minimum value of (2, 4) and a maximum value of (0.5, 6). Since the minimum value is above the x-axis, this option is not positive for the entire interval.

The curve has a minimum value of (-1.75, -3.9) and a maximum value of (0, 2). It also crosses the x-axis at (-2.2, 0), (-0.75, 0), and (0.75, 0). Since the minimum value is above the x-axis, and all the points where it crosses the x-axis are outside the interval [-3, -2], this option could potentially be positive for the entire interval.

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