identify the inequality graphed on the number line. responses ax2 2 > 10x 2 2 > 10 b2x 2 < 102x 2 < 10 c2x 2 > 102x 2 > 10 dx2 2 < 10

Answer: -15=x

Step-by-step explanation: subtract 10 on each side then divide -5 on both sides to isolate the variable

-5x=+10-85

5x=-75

x=-75/5=> x= -15

Recall the formula for compound interest

Using the formula, rearrange the equation and solve in terms of time t

Substitute the given values and we get

A = $2700, P = $1100, n = 12 (12 months in a year), r = 0.045 (from 4.5%)

Rounding the answer to the nearest tenth, the time it takes is 20 years.

Answer:

X=2

Step-by-step explanation:

(a) The doubling time of the population is approximately 13.86 years., (b) It takes approximately 23.10 years for the population to triple in size, (c) It takes approximately 27.72 years for the population to quadruple in size.

To calculate the doubling time of the population, we need to find the time it takes for the population to double from its initial value. In this case, the initial population is 9 million.

(a) Doubling Time:

Let's set up an equation to find the doubling time. We know that when the population doubles, it will be 2 times the initial population.

2P(0) = P(t)

Substituting P(t) = 9e^(0.05t), we have:

2 * 9 = 9e^(0.05t)

Dividing both sides by 9:

2 = e^(0.05t)

To solve for t, we take the natural logarithm (ln) of both sides:

ln(2) = 0.05t

Now, we can isolate t by dividing both sides by 0.05:

t = ln(2) / 0.05

Using a calculator, we find:

t ≈ 13.86

Therefore, the doubling time of the population is approximately 13.86 years.

(b) Time to Triple the Population:

Similar to the doubling time, we need to find the time it takes for the population to triple from its initial value.

3P(0) = P(t)

3 * 9 = 9e^(0.05t)

Dividing both sides by 9:

3 = e^(0.05t)

Taking the natural logarithm of both sides:

ln(3) = 0.05t

Isolating t:

t = ln(3) / 0.05

Using a calculator, we find:

t ≈ 23.10

Therefore, it takes approximately 23.10 years for the population to triple in size.

(c) Time to Quadruple the Population:

Similarly, we need to find the time it takes for the population to quadruple from its initial value.

4P(0) = P(t)

4 * 9 = 9e^(0.05t)

Dividing both sides by 9:

4 = e^(0.05t)

Taking the natural logarithm of both sides:

ln(4) = 0.05t

Isolating t:

t = ln(4) / 0.05

Using a calculator, we find:

t ≈ 27.72

Therefore, it takes approximately 27.72 years for the population to quadruple in size.

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Answer:

18.445

Step-by-step explanation:

Multiply

9514 1404 393

Answer:

  1.6n -4p +3

Step-by-step explanation:

Distributing the minus sign changes the signs of all the terms inside parentheses.

  -(4p-3) = -4p +3

When that is added to 1.6n, the entire expression is ...

  1.6n -4p +3

To solve this exercise we must take into account the given table

Since x is the number of people in the car, the probability that the car has only one passenger is:

If we want to make the probability that a car has less than 4 people, we have to add the probabilities from 1 to 3

Chebyshev's theorem states that for any distribution, the proportion of observations in any sample or population that lie within k standard deviations of the mean is at least 1 - 1/k². This means that the farther away an observation is from the mean, the less likely it is to occur.

Therefore, Chebyshev's theorem provides a measure of how spread out a distribution is. In contrast, the formula for the coefficient of variation is the standard deviation of the observations divided by their mean. It is a measure of the relative variability of a distribution. When this value is small, it indicates that the distribution is less spread out. In other words, the observations are closer to the mean. Finally, the statement that approximately 68% of all observations fall within one standard deviation of the mean is known as the empirical rule. This rule only applies to distributions that are bell-shaped and symmetrical.

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Answer:

\((4+4n)+(7+2a) = 11+4n+2a\)

Step-by-step explanation:

Answer:

34 unit squared

Step-by-step explanation:

4*12 then divide 2

4*5 then divide by 2

add two values together and get 34

Answer:

24

Step-by-step explanation:

A=bh x (1/2)

base times height divided by two

Answer:

\(6x+5\)

Step-by-step explanation:

Given that:

Perimeter of the trapezoid = \(15x+11\)

Shorter base = \(3x+4\)

One leg = \(2x+3\)

Second base = \(4x-1\)

To find:

The length of fourth Side = ?

Solution:

Let us have a look at the perimeter of a trapezoid.

Perimeter = Sum of all the sides

Let the fourth side = \(y\)

Using the formula and putting the given values:

\(15x+11=3x+4+2x+3+4x-1+y\\\Rightarrow 15x+11=9x+6+y\\\Rightarrow y = 15x-9x+11-6\\\Rightarrow y =6x+5\)

Fourth side is: \(6x+5\)

The value of equation A is 29/4 or 7 1/4.

An equation is a mathematical statement that shows the equality between two expressions using an equal sign. Equations are used to solve problems and model real-world situations in a variety of fields, including physics, engineering, and economics.

To solve the equation:

\((1/2 x 3) + (3/4 x 6) + (1 x 3) + (1 1/4 x 1)\)

We need to simplify the fractions first:

\((1/2 x 3) = 3/2\\(3/4 x 6) = 9/2\\(1 1/4 x 1) = 5/4\)

Now, substituting the values, we have:

\(3/2 + 9/2 + 3 + 5/4\)

To add these fractions, we need to find a common denominator. The least common multiple of 2, 4, and 4 is 4. So, we can convert the fractions as follows:

\(3/2 = 6/4\\9/2 = 18/4\\5/4 = 5/4\)

Now, adding the fractions, we get:

\(6/4 + 18/4 + 3(4/4) + 5/4 = 29/4\)

Therefore, the value of A is 29/4 or 7 1/4.

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There are 100 integers 'a' satisfying the congruence relation $a(a-1)^{-1} \equiv 4a^{-1} \pmod{20}$, where $0 \leq a < 100$.

To determine the number of integers 'a' satisfying the congruence relation:

$a(a-1)^{-1} \equiv 4a^{-1} \pmod{20}$

First, we can rewrite the congruence as:

$a(a-1)^{-1} - 4a^{-1} \equiv 0 \pmod{20}$

Multiplying both sides by $(a-1)a^{-1}$ (which is the inverse of $(a-1)$ modulo 20) yields:

$a - 4(a-1) \equiv 0 \pmod{20}$

Simplifying further, we have:

$a - 4a + 4 \equiv 0 \pmod{20}$

$-3a + 4 \equiv 0 \pmod{20}$

To solve this congruence relation, we can consider the values of 'a' from 0 to 99 and check how many satisfy the congruence.

For $a = 0$:

$-3(0) + 4 \equiv 4 \pmod{20}$

For $a = 1$:

$-3(1) + 4 \equiv 1 \pmod{20}$

For $a = 2$:

$-3(2) + 4 \equiv -2 \pmod{20}$

Continuing this process for each value of 'a' from 0 to 99, we can determine how many satisfy the congruence relation. However, in this case, we can observe a pattern that repeats every 20 values.

For $a = 0, 20, 40, 60, 80$:

$-3a + 4 \equiv 4 \pmod{20}$

For $a = 1, 21, 41, 61, 81$:

$-3a + 4 \equiv 1 \pmod{20}$

For $a = 2, 22, 42, 62, 82$:

$-3a + 4 \equiv -2 \pmod{20}$

And so on...

Thus, the congruence relation is satisfied for the same number of integers in each set of 20 consecutive integers. Hence, there are 5 sets of 20 integers that satisfy the congruence relation. Therefore, the total number of integers 'a' satisfying the congruence is 5 * 20 = 100.

Therefore, there are 100 integers 'a' satisfying the congruence relation $a(a-1)^{-1} \equiv 4a^{-1} \pmod{20}$, where $0 \leq a < 100$.

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Let us assume Gary sat at the left edge of the table. Imagine looking at the friends from behind so they are facing the table.

It is assumed that Bill is sitting on the right of Gary.

Next we put Tom on the right of Bill and Mike on the right of Tom.

Gary is at the edge of the table and Howard is sitting in the third seat from Bill, so Howard is sitting towards the right of Mike.

Gary is sitting in the third seat from Mike this means that Tom is sitting at the right of Bill.

So, from the left the seating arrangement is Gary, Bill, Tom Mike and Howard.

Hence, Bill is sitting on the other side of Tom.

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Answer:

Bill

Step-by-step explanation:

Answer:

\(52 \leqslant h \leqslant 60\)

Step-by-step explanation:

Add and subtract 4 to and from 56

Here's the explanation :

we know,

\( \boxed{\sin( \theta) = \frac{opposite \: \: side}{hypotenuse} }\)

so,

\( \sin(k) = \dfrac{11}{61} \)

hence, option b. is correct

To evaluate which of a set of curves fits the data best, you can use the option "c. R2", also known as the coefficient of determination.

R2 is a statistical measure that helps determine the proportion of variance in the dependent variable explained by the independent variable(s) in the regression model. It ranges from 0 to 1, with higher values indicating a better fit of the curve to the data.

To evaluate which of a set of curves fits the data best, we can use the R2 (coefficient of determination) metric. R2 is a statistical measure that represents the proportion of the variance in the dependent variable that is explained by the independent variable(s) in a regression model.

                                         A higher R2 value indicates a better fit of the curve to the data. APE (absolute percentage error), MAPE (mean absolute percentage error), and NPV (net present value) are not appropriate metrics for evaluating the fit of a curve to data. APE and MAPE are typically used to measure forecasting accuracy, while NPV is a financial metric used to determine the present value of future cash flows.

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The triangle with sides of length 5 cm 3 cm and 4 cm is a right angled triangle because (3, 4, 5) is a Pythagorean triple.

We know that if non zero real numbers a, b, c follows Pythagoras theorem  c² = a² + b², the numbers a, b, c is called as a Pythagorean triple.

And these numbers are nothing but the sides of right triangle.

Here we have been given the triangle with sides of length 5 cm 3 cm and 4 cm

Assume that p = 5 cm, q = 3 cm and r = 4 cm

p² = 25

q² = 9

and r² = 16

Consider q² + r² = 16 + 9

q² + r² = 25

q² + r² = r²

Since given numbers follows Pythagoras theorem, (3, 4, 5) is a  Pythagorean triple.

And p = 5 cm, q = 3 cm and r = 4 cm are the lengths of sides of right triangle.

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Answer:

$835 (Answer c)

Step-by-step explanation:

Write out the Cost function:  C(n) = $65 + ($11/person)n

Then the total cost for 70 people would be C(70) = $65 + ($11/person)(70 people)

C(70) = $65 + $770 = $835 (Answer c)

Answer:

43,000: 4.3×10^4

0.0072: 7.2×10^-3

0.0000901: 9.01×10^-5

Step-by-step explanation:

scientific notation: a×10^b, where should be 0<a<10

Step 1. Count the zeros

Step 2. Look at the number left, and determine whether or not it fits in the range of [a]. If not, we divide or multiply 10 to get it fit

------------------------

43,000: 4.3×10^4 (since 43 does not fit, we divide by 10 to get it fit)

0.0072: 7.2×10^-3 (since 0.72 does not fit, we multiply 10 to get it fit)

0.0000901: 9.01×10^-5 (since 0.901 does not fit, we multiply 10 to get it fit)

Hope this helps!! :)

Please let me know if you have any question

Step-by-step explanation:

3 of the 4 options aren't prisms

A is a cuboid

B is a cube

C is a prism

D is a pyramid

Answer:

The answer is D.

I hope this helps.

Have nice day/night!!!!(wherever you are)

The solution to the given differential equation 2xy(dy/dx) = y², with the initial condition y(2) = 3, is y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\).

To solve the given differential equation

2xy(dy/dx) = y²

We will use separation of variables and integrate to find the solution.

Start with the given equation

2xy(dy/dx) = y²

Divide both sides by y²:

(2x/y) dy = dx

Integrate both sides:

∫(2x/y) dy = ∫dx

Integrating the left side requires a substitution. Let u = y², then du = 2y dy:

∫(2x/u) du = ∫dx

2∫(x/u) du = ∫dx

2 ln|u| = x + C

Replacing u with y²:

2 ln|y²| = x + C

Using the properties of logarithms:

ln|y⁴| = x + C

Exponentiating both sides:

|y⁴| = \(e^{x + C}\)

Since the absolute value is taken, we can remove it and incorporate the constant of integration

y⁴ = \(e^{x + C}\)

Simplifying, let A = \(e^C:\)

y^4 = A * eˣ

Taking the fourth root of both sides:

y = (A * eˣ\()^{1/4}\)

Now we can incorporate the initial condition y(2) = 3

3 = (A * e²\()^{1/4}\)

Cubing both sides:

27 = A * e²

Solving for A:

A = 27 / e²

Finally, substituting A back into the solution

y = ((27 / e²) * eˣ\()^{1/4}\)

Simplifying further

y = (27 *  e⁽ˣ⁻²⁾\()^{1/4}\)

Therefore, the solution to the given differential equation with the initial condition y(2) = 3 is

y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\)

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Answer: 1 km

Step-by-step explanation: For this question, you need to first convert the 20 minutes into hours. You know that an hour is 60 minutes, so dividing 20 by 60 leaves you with 1/3 of an hour. The question says that she can go 3 km/h in her wheelchair, so 3 x 1/3 = 1 km.

Answer:

the price of each kind of ticket is $22 and $3 respectively

Step-by-step explanation:

Let us assume the adult be x

And, the children be y

Now the equations would be

x + y = $25

x = $25 - y ............(1)

45x + 60y = $1,170

3x + 4y = $78........(ii)

Now put the x value in the equation 2

3($25 - y) + 4y = $78

$75 - 3y + 4y = $78

y = $3

x = $25 - y

= $25 - $3

= $22

hence, the price of each kind of ticket is $22 and $3 respectively

(a) Chloe's budget constraint can be written as:

Pₓx + Pᵧy = I

where Pₓ is the price of books, Pᵧ is the price of video games, and I is Chloe's income.

(b) The Marginal Rate of Substitution (MRS) at an arbitrary bundle (x, y) can be calculated by taking the partial derivative of the utility function U(x, y) = xy² with respect to x and dividing it by the partial derivative of U(x, y) with respect to y. Mathematically, it is given by:

MRS = (∂U/∂x) / (∂U/∂y) = (y²) / (2xy) = y / (2x)

(c) To find Chloe's demand for books and video games for any possible values of Pₓ, Pᵧ, and I, we need to maximize her utility subject to the budget constraint. We can set up the following optimization problem:

Maximize U(x, y) = xy²

subject to the budget constraint Pₓx + Pᵧy = I

Solving this problem will give us the demand equations for books and video games, which represent Chloe's optimal choices given the prices and her income.

(d) The expenditure on books (Eₓ) can be calculated by multiplying the demand for books (x) by the price of books (Pₓ). Similarly, the expenditure on video games (Eᵧ) can be calculated by multiplying the demand for video games (y) by the price of video games (Pᵧ). Therefore:

Eₓ = Px * x

Eᵧ = Pᵧ * y

(e) If Chloe's utility function is U(x, y) = (x + 5)y² and her income (I) is $15, the price of books (Pₓ) is $3, and the price of video games (Pᵧ) is $5, we can use the optimization problem to find her demand for books and video games. By maximizing U(x, y) subject to the budget constraint, we can find the values of x and y that yield the highest utility.

(f) Continuing from the previous question, if Chloe's utility function is U(x, y) = (x + 5)y² and her income (I) is $15, the price of books (Pₓ) is $5, and the price of video games (Pᵧ) is $5, we can again use the optimization problem to find her demand for books and video games. By maximizing U(x, y) subject to the budget constraint, we can determine the values of x and y that maximize her utility given the prices and income.

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The 15 and 9 units side lengths of the parallelogram ABCD, and the 36° measure of the acute interior angle, A indicates the values of the ratios are;

1. AB:BC = 5:3

2. AB:CD = 1:1

3. m∠A : m∠C= 1 : 4

4. m∠B:m∠C = 4:1

5. AD: Perimeter ABCD = 3:16

A ratio is a representation of the number of times one quantity is contained in another quantity.

The shape of the quadrilateral ABCD in the question = A parallelogram

Length of AB = 15

Length of BC = 9

Measure of angle m∠A = 36°

Therefore;

1. AB:BC = 15:9 = 5:3

2. AB ≅ CD (Opposite sides of a parallelogram are congruent)

AB = CD (Definition of congruency)

AB = 15, therefore, CD = 15 transitive property

AB:CD = 15:15 = 1:1

3. ∠A ≅ ∠C (Opposite interior angles of a parallelogram are congruent)

Therefore; m∠A = m∠C = 36°

∠A and ∠D are supplementary angles (Same side interior angles formed between parallel lines)

Therefore; ∠A + ∠D = 180°

36° + ∠D = 180°

∠D = 180° - 36° = 144°

∠D = 144°

m∠A : m∠C = 36°:144° =1:4

m∠A : m∠C = 1:4

4. ∠B = ∠D = 144° (properties of a parallelogram)

m∠B : m∠C = 144° : 36° = 4:1

5. AD ≅ BC (opposite sides of a parallelogram)

AD = BC = 9 (definition of congruency)

The perimeter of the parallelogram ABCD = AB + BC + CD + DA

Therefore;

Perimeter of parallelogram ABCD = 15 + 9 + 15 + 9 = 48

AD:Perimeter of the ABCD  = 9 : 48  = 3 : 16

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Answer:

The remaining dimensions of the triangle are \(A \approx 31.7368^{\circ}\), \(C \approx 18.2632^{\circ}\) and \(a \approx 45.3201\).

Step-by-step explanation:

As angle B is an obtuse angle, Angle C can be obtained by means of the Law of Sine:

\(\frac{b}{\sin B}=\frac{c}{\sin C}\)

\(\sin C = \frac{b}{c}\cdot \sin B\)

\(C = \sin^{-1}\left(\frac{b}{c}\cdot \sin B \right)\)

Where:

\(b\), \(c\) - Measures of triangle sides, dimensionless.

\(B\), \(C\) - Measures of angles, measured in degrees.

If \(b = 27\), \(c = 66\) and \(B =130^{\circ}\), then:

\(C = \sin^{-1}\left(\frac{27}{66}\cdot \sin 130^{\circ} \right)\)

\(C \approx 18.2632^{\circ}\)

Given that sum of internal angles in triangles equals to 180º, the angle A is now determined:

\(A = 180^{\circ}-B-C\)

\(A = 180^{\circ}-130^{\circ}-18.2632^{\circ}\)

\(A \approx 31.7368^{\circ}\)

Lastly, the length of the side \(a\) is calculated by Law of Cosine:

\(a = \sqrt{b^{2}+c^{2}-2\cdot b\cdot c\cdot \cos A}\)

\(a =\sqrt{27^{2}+66^{2}-2\cdot (27)\cdot (66)\cdot \cos 31.7368^{\circ}}\)

\(a \approx 45.3201\)

The remaining dimensions of the triangle are \(A \approx 31.7368^{\circ}\), \(C \approx 18.2632^{\circ}\) and \(a \approx 45.3201\).

Answer:

10%

Step-by-step explanation:

Answer:

2 1/5+6 4/5 =  9

6 5/12 -2 1/12 = 4 1/3

11 8/9+4 1/3 =16  2/9

7 1/6-5 3/4 = 1  5/12

11/18+ 6 1/10 = 6 64/90

15 1/3- 2 5/8 = 12  17/24

Step-by-step explanation:

Using the technique of mixed numbers to add the fractions

2 1/5+6 4/5

=2+6 + 1/5+4/5     add the whole numbers separately and then the fractions

=8 5/5= 9

6 5/12 -2 1/12

=6-2 + 5-1/12

=4 4/12

= 4 1/3

11 8/9+4 1/3

=11+4 +8/9+1/3     adding the whole numbers separately

=15 + 8+3/9

= 15+11/9             adding the fractions separately

= 15+1+2/9

= 16+2/9

=16  2/9

7 1/6-5 3/4

= 7-5 +1/6 -3/4   subtracting the whole numbers separately

= 2+ 2-9/12   subtracting the fractions separately

= 2-7/12  

= 24-7/12

= 17/12

=1  5/12

11/18+ 6 1/10

= 11/18 + 61/10

= 110 +1098/180

= 1208/180

= 6 128/180

= 6 64/90

15 1/3- 2 5/8

=15- 2 + 1/3- 5/8

=13 + 8- 15/24

= 13 + -7/24

= 312-7/24

= 12 17/24

The value of the double integral is 0.

We are given the double integral:

\(\int \int x^2 2y\) da,

where d is bounded by y=x and y=x³.

To evaluate this integral, we first need to find the limits of integration for x and y.

Since d is bounded by y=x and y=x³, the limits of integration for y are from y=x to y=x³.

For a fixed value of y, the limits of integration for x are from\(x=y^(^1^/^3^)\)to \(x=y^(^1^/^2^)\), since \(y^(^1^/^3^)\) is the smaller x-value on the curve y=x³ and \(y^(^1^/^2^)\) is the larger x-value on the curve y=x.

Therefore, the integral becomes:

∫ from \(x=y^(^1^/^3^)\) to \(x=y^(^1^/^2^)\) ∫ from y=x to y=x³ x² 2y dy dx

Integrating with respect to y first, we get:

∫ from \(x=y^(^1^/^3^)\) to \(x=y^(^1^/^2^) [(y^4^/^2^) - (y^2^/^2^)] x^2 dx\)

Simplifying, we get:

∫ from \(x=y^(1^/^3^) to x=y^(^1^/^2^) [(y^4^/^2^) - (y^2^/^2^)] x^2 dx\)

\(= (1/10) [y^(^5^/^2^) - y^(^7^/^2^)] [y^(^4^/^3^) - y^(^1^/^2^)]\)

\(= (1/10) [(y^3)^(^5^/^6^) - (y^3)^(^7^/^6^)] [(y)^(^4^/^3^) - (y)^(^1^/^2^)]\)

\(= (1/10) [y^(^5^/^3^) - y^(^7^/^3^)] [(y)^(^4^/^3^) - (y)^(^1^/^2^)]\)

Integrating this expression with respect to x, we get:

\(= (1/30) [y^(^5^/^3^) - y^(^7^/^3^)] [(y^2)^(^4^/^3^) - (y^2)^(^1^/^2^)]\)

\(= (1/30) [y^(^5^/^3^) - y^(^7^/^3^)] [(y^(^8^/^3^) - y)^(^1^/^2^)]\)

Now we can evaluate the integral by plugging in the limits of integration for y:

\(= (1/30) [(y^(^5^/^3^) - y^(^7^/^3^))] [(y^(^8^/^3^) - y)^(^1^/^2^)]\) evaluated from y = 0 to y = 1

\(= (1/30) [(1 - 1/1)] [(1 - 0)^(^1^/^2^)] - (1/30) [(0 - 0)] [(0 - 0)^(^1^/^2^)]\)

= 0

Therefore, the value of the double integral is 0.

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