select all of the following expressions that are equivalent to 9 1/2
(1) 3 1/2 * 3 1/2 (2) sqrt[6]{27} (3) 27 1/3 * 3 1/2 (4) 81 1/2 * 81 1/2 (5) 729 1/6 (6) 81 1/3 * 81 1/3 (7) 81 1/4 * 81 1/4

Answer:

(x-3) times (x+1)

Answer:

Yes, -3 is a solution to the inequality.

Step-by-step explanation:

Plug -3 into the inequality.

3 - 4x ≤ 15

3 - 4(-3) ≤ 15

3 + 12 ≤ 15

15 ≤ 15

The resulting inequality is true, so -3 is a solution.

Answer:560

Step-by-step explanation:

Answer:

he value of the integral ∫ y tan(x) dx is y sin(x) + C.

Step-by-step explanation:

Property 8 of integrals states that if we have an integral of the form ∫ f(x) g'(x) dx, it can be rewritten as ∫ f(x) dg(x), where g(x) is an antiderivative of g'(x).

In this case, we have the integral ∫ y tan(x) dx. By applying Property 8, we can rewrite it as ∫ y d(sin(x)).

Now, integrating with respect to y while treating sin(x) as a constant, we get:

∫ y d(sin(x)) = y sin(x) + C,

where C is the constant of integration.

So, using Property 8, the value of the integral ∫ y tan(x) dx is y sin(x) + C.

Use dot products to express y as a linear combination of the vectors in S.

To represent y as a linear combination of the vectors in S using dot products, we calculate the dot product of y with each vector in S and divide it by the squared length of the corresponding vector. The coefficients obtained from the dot products form the linear combination. The steps for each exercise are as follows:

Let S = {7, 20} and y = {-1, 0, 9}.

Dot product with the first vector: (-1)⋅7 = -7

Dot product with the second vector: 0⋅20 = 0

y = (-7/149)⋅7 + (0/400)⋅20 = (-7/149)⋅7

Let S = {3, 1, 2, 0, 9} and y = {5, 5, -1}.

Dot product with the first vector: 5⋅3 = 15

Dot product with the second vector: 5⋅1 = 5

Dot product with the third vector: -1⋅2 = -2

Dot product with the fourth vector: 0⋅0 = 0

Dot product with the fifth vector: 9⋅9 = 81

y = (15/19)⋅3 + (5/26)⋅1 + (-2/14)⋅2 + (0/5)⋅0 + (81/186)⋅9

Let S = {-1, 0} and y = {1, 0}.

Dot product with the first vector: 1⋅(-1) = -1

Dot product with the second vector: 0⋅0 = 0

y = (-1/1)⋅(-1) + (0/1)⋅0 = -1

Let S = {5, 5, -1, -1} and y = {2, 1}.

Dot product with the first vector: 2⋅5 = 10

Dot product with the second vector: 1⋅5 = 5

Dot product with the third vector: 2⋅(-1) = -2

Dot product with the fourth vector: 1⋅(-1) = -1

y = (10/50)⋅5 + (5/50)⋅5 + (-2/2)⋅(-1) + (-1/2)⋅(-1)

Let S = {A, B} and v = {p}.

Dot product with the first vector: p⋅A

Dot product with the second vector: p⋅B

y = (dot product with A)⋅A + (dot product with B)⋅B

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Answer: \(y=5.666667\)   or   \(y=5 \frac{6}{9}\) in fraction

Step-by-step explanation:

1. Simplify  -9.8-y+2.8y  to  -9.8+1.8y

0.4=-9.8+1.8y0.4=−9.8+1.8y

2. Regroup terms

0.4=1.8y-9.8

3. Add 9.8 to both sides.

0.4+9.8=1.8y

4. Simplify  0.4+9.8  to  10.2

10.2=1.8y

5. Divide both sides by 1.8

\(\frac{10.2}{1.8} =y\\\)

6. Simplify \(\frac{10.2}{1.8\\}\) to 5.666667

5.666667 = \(y\)

7. Switch sides.

\(y=5.666667\)

Hope this helps and can you please mark me brainliest because I just need 1 more brainliest to become expert:)

Answer:

\(y=\frac{17}{3}\\\\y =5\frac{2}{3}\)

Step-by-step explanation:

\(0.4 = -9.8 -y + 2.8y\\\\Switch\:sides\\\\-9.8-y+2.8y=0.4\\\\\mathrm{Add\:similar\:elements:}\:-y+2.8y=1.8y\\\\-9.8+1.8y=0.4\\\\\mathrm{Multiply\:both\:sides\:by\:}10\\\\-9.8\times\:10+1.8y\times\:10=0.4\times\:10\\\\Refine\\\\-98+18y=4\\\\\mathrm{Add\:}98\mathrm{\:to\:both\:sides}\\\\-98+18y+98=4+98\\\\Simplify\\\\18y=102\\\\\mathrm{Divide\:both\:sides\:by\:}18\\\\\frac{18y}{18}=\frac{102}{18}\\\\Simplify\\\\y=\frac{17}{3}\\\\y =5\frac{2}{3}\)

The rate of change, in square inches per second, of the area of the region at the instant when R is 44 inches and r is 33 inches is

8363 square inches

The rate of change is the derivative, the rate of change is calculated by differentiation the area

formula for area of concentric circle is given by

Area A = π(R^2 - r^2) =

R = radius of the inner circle

r = radius of the outer circle

δA/δt = δA/δRδr * δRδr/δt

δA/δt = π * (2RδR/δt - 2rδr/δt)

δA/δt = π * 2(R * δR/δt - r * δr/δt)

where R = 44 and δR/δt = 22

r = 33 and δr/δt = -11

= 2π(44 * 22 - 33 * -11)

= 2π (968 - -363)

=  2π (1331)

= 2662π

= 8362.9196 square inches

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we remove the parenthesis and add the number that have the same exponent

The correct answer is 5! × 2! × 4! ways = 5760 ways.

Given that Professor Chang has nine different language books lined up on a bookshelf: two Arabic, three German, and four Spanish. The problem requires us to find out how many ways there are to arrange the nine books on the shelf while keeping the Arabic books together and keeping the Spanish books together.

The number of ways that the nine books can be arranged on the shelf keeping the Arabic books together and keeping the Spanish books together is as follows:

First, we group the Arabic books and the Spanish books. The Arabic books consist of two books, and the Spanish books consist of four books. These two groups will be treated as a single book, so there are 5 books on the shelf instead of 6.

The 5 books can be arranged among each other in 5! ways. The Arabic books can be arranged among each other in 2! ways and the Spanish books can be arranged among each other in 4! ways.

Therefore, the total number of ways to arrange the nine books on the shelf while keeping the Arabic books together and keeping the Spanish books together is 5! × 2! × 4! = 5760 ways.

Hence, the correct answer is 5! × 2! × 4! ways = 5760 ways.

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Answer:

The annual interest rate is 0.018, or 1.8%.

Step-by-step explanation:

Let r be the annual interest rate, t be the number of years the money was in the account, and I be the amount of interest earned. Since the interest is simple interest, the amount of interest earned is given by the formula I = Prt, where P is the principal, or initial amount deposited. In this case, we know that P = $3000, t = 3.5 years, and I = $262.50. Substituting these values into the formula, we get:

262.50 = 3000r * 3.5

r = 0.018

Thus, the annual interest rate is 0.018, or 1.8%.

Therefore, it will take approximately 13.7 years for the population to double.

a. To determine the growth rate, you need to calculate the percentage increase in population. The formula for growth rate is:

Growth Rate = (New Value - Old Value) / Old Value * 100

Using the given values, we have:

Growth Rate = (1577 - 1500) / 1500 * 100
Growth Rate = 77 / 1500 * 100
Growth Rate ≈ 5.13%

b. To write a general equation for the population, you can use the formula:

p(t) = p(0) * (1 + r/100)^t

where p(t) is the population at time t, p(0) is the initial population, r is the growth rate, and t is the number of years.

c. To estimate the population in 2010, we need to find the population at time t = 2010 - 2000 = 10 years. Using the general equation from part b, and substituting the given values:

p(10) = 1500 * (1 + 5.13/100)^10
p(10) ≈ 1500 * (1.0513)^10
p(10) ≈ 1500 * 1.6436
p(10) ≈ 2465.4

Therefore, the estimated population in 2010 is approximately 2465.

d. To find out how many years it will take for the population to double, we need to solve the equation:

2 * p(0) = p(0) * (1 + r/100)^t

Simplifying the equation, we have:

2 = (1 + r/100)^t

Taking the logarithm of both sides, we get:

log(2) = t * log(1 + r/100)

Finally, solving for t, we have:

t = log(2) / log(1 + r/100)

Substituting the growth rate from part a, we have:

t = log(2) / log(1 + 5.13/100)
t ≈ log(2) / log(1.0513)
t ≈ 13.7 years

Therefore, it will take approximately 13.7 years for the population to double.

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The conclusion in the argument is "the good, according to Plato, is that which furthers a person's real interests." which it is the correct answer.

In a well-structured argument, the conclusion is what the argument aims to prove.

The conclusion can be located at the beginning or end of the argument, and it should always be precise, clear, and understandable.

The conclusion in the argument above is that "the good, according to Plato, is that which furthers a person's real interests."

The argument tries to explain that the good in Plato's philosophical teachings is a thing that advances a person's genuine interests.

The statement "it follows that" is the premise that links the argument with the conclusion.

The premise and the conclusion have a relationship of cause and effect, and this implies that the argument's conclusion is "the good, according to Plato, is that which furthers a person's real interests."

Therefore, the right option is: the good, according to Plato, is that which furthers a person's real interests.

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The inequalities that the represents the graph is;  y < 1 and y  ≥ x

The general form of the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Now, when the line is horizontal line is parallel to the x - axis, the equation is y equal to the number that the line crosses.

Now, Inequalities that use < or > symbols are plotted with a dashed line to show that the line is not included in the region. Thus, the horizontal line has the inequality; y = 1 But since the shading is below, then we have; y < 1

Now, the solid line shows that the symbol used is ≤ or ≥.

In this case, the x-values and the corresponding y-values are the same and as such we have; y = x

However, since the shading is above, then we have;

y  ≥ x

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The square root of the decimal number is √0.0016 = 0.04

Here we can find the square root of the decimal number:

N = 0.0016

Notice that we can write this number as:

0.0016 = 16*10⁻⁴

Now we can take the square root of that, so we will get:

√(16*10⁻⁴)

We can distribute the square root to get:

√16*√10⁻⁴

These two are easy, we will get:

√16*√10⁻⁴ = 4*10⁻² = 0.04

That is the square root.

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Answer:

the answer is b

Step-by-step explanation:

hope I'm right

Answer:

D. –x^4 + 6x^3 + 7x^2 – 4x – 4

Step-by-step explanation:

When writing in standard form you have to put the monomials from greatest to least according to their exponent.

\(-x^4+6x^3+7x^2-4x-4\)

The first number is \(-x^4\) because 4 is the greatest exponent we see, then comes \(+6x^3\) which is next because it has the second greatest exponent. And so on and so on.

The breadth of the rectangle is 6 cm.

To find the breadth, we can use the formula for the perimeter of a rectangle:

Perimeter = 2 × (length + breadth)

Substituting the given values, we get:

18 cm = 2 × (3 cm + breadth)

Simplifying the right side of the equation, we get:

18 cm = 6 cm + 2 × breadth

Subtracting 6 cm from both sides of the equation, we get:

12 cm = 2 × breadth

Dividing both sides by 2, we get:

breadth = 6 cm

Therefore, the breadth of the rectangle is 6 cm.

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She can see the horizon till 2.604 meters when the person is standing at a height of 5.76 meters above sea level.

Given that,

If a person can see d kilometers into the distance from her eye level, which is h meters above sea level, then d=3.57 √h. Let's say the person is standing at a height of 5.76 meters above sea level.

We have to find she can see the horizon, but how far.

The SI unit of length is the meter. In addition to meters, length can also be expressed in other units like centimeters, inches, feet, and yards.

So,

d=h

3.57 √h= 5.76 meters

Divide both sides by 3.57

√h= 5.76 meter/ 3.57

√h=1.614

Squaring on both sides.

h=2.604

Therefore, She can see the horizon till 2.604 meters when the person is standing at a height of 5.76 meters above sea level.

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During the winter season, a family sets up a hot chocolate stand near a local ice skating rink. They sell cups of hot chocolate for $1.50 each and typically sell 50 cups per day.

However, due to changes in weather conditions and customer preferences, the family decides to conduct a market experiment by varying the price of hot chocolate to assess the impact on sales volume. The experiment involves increasing the price to $2.00 per cup and monitoring the resulting sales.

By increasing the price of hot chocolate from $1.50 to $2.00 per cup, the family aims to observe how the change in price affects the demand for their product. The experiment helps them understand the price elasticity of demand, which measures the responsiveness of quantity demanded to changes in price. If the increase in price leads to a significant decrease in sales volume, it suggests that the demand for hot chocolate is elastic, meaning consumers are sensitive to price changes. Conversely, if sales remain relatively stable despite the price increase, it indicates that the demand is inelastic, indicating that consumers are less sensitive to price changes. The family can analyze the results of this experiment to make informed pricing decisions and optimize their profitability during the winter season.

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Answer:

See below for answers and explanations

Step-by-step explanation:

Part A

10x - 12x - 3 does not equal -5x. Looks like what she did wrong was treating -3 as -3x and got her incorrect result that way

Part B

10x - 12x - 3 = (10-12)x - 3 = -2x - 3

The exercise heart rate of the 50-year-old athlete can be calculated using the maximal heart rate method. The maximal heart rate is estimated by subtracting the person's age from 220.

To calculate the exercise heart rate using the maximal heart rate method, we first need to determine the maximal heart rate. This can be estimated by subtracting the person's age from 220. In this case, the athlete is 50 years old, so the maximal heart rate would be 220 - 50 = 170 beats per minute.

Next, we need to find the exercise heart rate at 70% of the maximal heart rate. This can be done by multiplying the maximal heart rate by 0.7.

Therefore, the exercise heart rate for the 50-year-old athlete training at 70% of his maximal heart rate is 119 beats per minute. This means that during his training, his heart should be beating at approximately 119 beats per minute.

In summary, the main answer is that the exercise heart rate for the 50-year-old athlete is 119 beats per minute when training at 70% of his maximal heart rate.

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The name of every month ends in the letter y is the given statement. February is a counterexample to this statement. This is because February does not end with the letter 'y'. So the right  option is (c) February.

What is a counterexample?

In mathematics, a counterexample is an example that opposes or disproves a statement, proposition, or theorem. It is a scenario, an instance, or an example that goes against the given statement.

Therefore, a counterexample demonstrates that the given statement is false or invalid.In this case, the statement is: "The name of every month ends in the letter y." We have to find which of the months listed does not end in "y."February is the only month in the options listed that does not end in the letter "y."

Thus, it is a counterexample to the given statement. Therefore, the correct option is C, February.

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Answer:

what will be the price of the next model= 59,748

Step-by-step explanation:

7748 is 14.9% of 52000

Solution:

What is 14.9% of 52000?

Y is 14.9% of 52000

Equation: Y = P% * X

Solving our equation for Y

Y = P% * X

Y = 14.9% * 52000

Converting percent to decimal:

p = 14.9%/100 = 0.149

Y = 0.149 * 52000

Y = 7748

To find the price for the next model

7748 + 52000

=> 59,748

Check the picture below.

The surface area of the prism shown in the figure is equal to 480 square inches. (Right choice: B)

In this problem we need to determine the surface area of a prism, that is, the sum of the areas of the five faces of the prism. There are three rectangles and two right triangles as faces of the prism, whose area formulas are described below:

Rectangle

A = w · l

Triangle

A = 0.5 · w · l

Where:

Now we proceed to determine the areas of all faces of the prism:

A = (8 in) · (9 in) + 2 · 0.5 · (15 in) · (8 in) + (9 in) · (15 in) + (17 in) · (9 in)

A = 480 in²

The prism shown in the figure has a surface area of 480 square inches.

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Answer: The ratio would be 73.6

Answer:

Step-by-step explanation:

I hope this is what you need

you could do 5.74+5 or you could do 10+ .74

or you could do 5.70+5.4

Answer:

(x+1)+(3x+1)+(2x+4)=180 (sum od all sode of a triangle is 180)

x+1+3x+1+2x+4=180

6x+6=180

6x=180-6

x=174/6

x=66

Answer:

x = 4

Step-by-step explanation:

Using Pythagoras' identity on the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

(3x + 1)² = (x + 1)² + (2x + 4)² ← expand all factors using FOIL

9x² + 6x + 1 = x² + 2x + 1 + 4x² + 16x + 16 , simplify right side

9x² + 6x + 1 = 5x² + 18x + 17 ( subtract 5x² + 18x + 17 from both sides )

4x² - 12x - 16 = 0 ( divide through by 4 )

x² - 3x - 4 = 0 ← in standard form

(x - 4)(x + 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

x + 1 = 0 ⇒ x = - 1

However, x > 0 thus x = 4

Answer:

its 30

Step-by-step explanation:

Answer: C

Step-by-step explanation:

The pair of angles created on the inner side of the parallel lines intersected by a transversal but on opposing sides of the transversal is known as an alternative interior angle. The correct option is C.

When two parallel lines are intersected by a transversal, the pair of angles created on the inner side of the parallel lines but on opposing sides of the transversal is known as an alternative interior angle. These angles are always equal in measure.

The best statements BEST that proves ∠XWY ≌ ∠ZYW is that If two parallel lines are cut by a transversal, then alternate interior angles are congruent.

Hence, the correct option is C.

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