Donnie's height increased by 9 is 74 . Use the variable d to represent Donnie's height.

Therefore , the solution of the given problem of equation comes out to be False.

In order to demonstrate consistency between two opposing statements, variable words are frequently used in sophisticated algorithms. Equations are academic phrases that are used to demonstrate the equality of different academic figures. Consider expression the details as y + 7 offers. In this case, elevating produces b + 7 when partnered with building y + 7.

Here,

False.

The order of operations we use to solve two-step equations is the same order we use to solve every other mathematical statement,

which is commonly recalled by the acronym PEMDAS. (parentheses, exponents, multiplication and division from left to right, and addition and subtraction from left to right).

The fundamental distinction is that we are carrying out the operations against the equation's representation. For instance, consider the following equation:

=> 2x + 5 = 11

To get the following result, we would first subtract 5 from both sides, then divide by 2.

=> x = 3

In order to "undo" the operations that were carried out on the variable in the original equation, we are utilising the same series of operations as usual, but in reverse order.

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I would have labeled the points as

(x1,y1) = (11,12)

(x2,y2) = (15,16)

then used the formula

m = (y2-y1)/(x2-x1)

However, your idea works as well. I don't see any errors with your steps. Nice work.

To evaluate the function at the indicated value of x:

To evaluate the function f(x) = 500e^(0.04x) at x = 26, follow these steps:

1. Replace x with 26 in the function: f(26) = 500e^(0.04 * 26)

2. Multiply 0.04 by 26: f(26) = 500e^(1.04)

3. Calculate the exponential value: e^(1.04) ≈ 2.832

4. Multiply 500 by the calculated exponential value: f(26) = 500 * 2.832

5. Round the result to three decimal places: f(26) ≈ 1416.000

So, when evaluating the function f(x) = 500e^(0.04x) at x = 26, f(26) ≈ 1416.000.

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The end behavior of the function is as x approaches positive infinity, the function approaches y = 0 from below, and as x approaches negative infinity, the function approaches y = 0 from above. The vertical asymptote at x = 2 does not affect the end behavior of the graph. It only affects the behavior of the function near x = 2.

a) The end behavior of a function describes what happens to the function as the input values approach positive infinity and negative infinity. To determine the end behavior, we look at the leading term of the function.

In this case, since there is a horizontal asymptote at y = 0, the function approaches the x-axis as the input values become very large in magnitude (either positive or negative). This means that the end behavior of the function is as follows:
- As x approaches positive infinity, the function approaches y = 0 from below.
- As x approaches negative infinity, the function approaches y = 0 from above.

b) The vertical asymptote at x = 2 does not affect the end behavior of the graph. Vertical asymptotes indicate where the function is undefined and where the graph has a "break" or a "hole". They do not determine the behavior of the function as the input values become very large in magnitude.

Therefore, even though there is a vertical asymptote at x = 2, the end behavior of the function is still determined by the horizontal asymptote at y = 0. The vertical asymptote only affects the behavior of the function near x = 2.

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Answer:

6 people

Step-by-step explanation:

The algebraic expression is (x² - 4x - 21)/4(x - 7) , we need to find the simplified value of it . Therefore , the simplified form is (x + 3)/4 .

What is simplification?

Rules are typically rewritten to achieve this simplicity. Systems for computer algebra use them in a methodical way. Associative operations, such as addition and multiplication, can be challenging. It is common practice to approach associativity by assuming that addition and multiplication can have any number of operands, such that the symbol for a + b + c is "+." (a, b, c). It follows that a + (b + c) and (a + b) + c are both condensed to "+"(a, b, c), which is shown as a + b + c.

In the question ,it is given that ,

the algebraic expression is (x² - 4x - 21)/4(x - 7) ,

we need to find the simplified value of it .

we first simplify the

numerator

that is x² - 4x - 21 ,

By using the split the

middle term method ,

we get ,

= x² - 7x  3x - 21

= x(x - 7)  3(x - 7)

= (x  3)(x - 7)

Writing the simplified numerator in the expression ,

we get ,

= (x  3)(x - 7)/4(x - 7)

cancelling out the common term (x-7) , we get

= (x  3)/4

Therefore , the simplified form is (x + 3)/4  . It is important to take into account different classes of rewriting rules. The easiest are formulas like E E 0 or sin(0) 0 that always make the expression smaller.

Complete question

What is the simplified form of the expression  

(x² - 4x - 21)/4(x - 7) ?

(a) (x+3)/4

(b) (x-3)/4

(c) (x+3)/(x-7)

       (d) (x-3)/(x-7)

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Answer:

c=7.17

Step-by-step explanation:

23=6c-20

43=6c

7.17=c

Answer:

7.16

I think this is correct

Answer: m angle3 = 3x - 7 = 3(14) - 7 = 37 degrees

Step-by-step explanation:

Since angles 3 and 9 are complementary, their measures add up to 90 degrees. So, we can set up the equation:

m angle3 + m angle9 = 90

We can substitute in the given values for the measures of each angle:

(3x - 7) + (4x - 1) = 90

Solving for x:

7x - 8 = 90

7x = 98

x = 14

Answer:

40

Step-by-step explanation:

50% is half and half of 40 is 20

Answer: 40

Step-by-step explanation:

50%=1/2

20+20=40

Therefore making half of 40 is 20.

The margin of error for the 95% confidence interval used to estimate the population proportion is 0.0680. So, the correct answer is option d.

Calculate the sample proportion:

The formula (p) = x/n, where x is the sample size (163) and n is the number of successes (96), yields the sample proportion.

Therefore, the sample proportion is 96/163 = 0.5896.

Calculate the standard error:

The formula SE(p) yields the sample proportion's standard error = √[p(1-p)/n], where n is the sample size, and p is the sample proportion.

Consequently, the sample proportion's standard error is as follows:

SE(p) = √[0.5896(1-0.5896)/163] = 0.037

Calculate the margin of error:

The margin of error is given by the formula ME = z × SE(p), where SE(p) is the standard error of the sample proportion and z is the z-score corresponding to the desired level of confidence.

The z-score for a 95% confidence interval is 1.96.

As a result, the error margin is:

ME = 1.96 × 0.037 = 0.0680

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Answer:

im not 100% sure but its "c"

Answer:

C C C C C

Step-by-step explanation:

Answer:

The statement is True

Step-by-step explanation:

You can substitute the 2y for z, which makes 3x=z

The result of subtracting 7x - 9 from 2x² - 11 is 2x² - 7x - 2.

To subtract the expression 7x - 9 from 2x² - 11, we need to distribute the negative sign to every term within the expression 7x - 9, and then combine like terms.

First, let's distribute the negative sign:

2x² - 11 - (7x - 9)

Now, distribute the negative sign to each term within the parentheses:

2x² - 11 - 7x + 9

Next, let's combine like terms:

2x² - 7x - 2

Therefore, the result of subtracting 7x - 9 from 2x² - 11 is 2x² - 7x - 2.

In this expression, the highest power of x is 2, which means it is a quadratic expression. The coefficient of x² is 2, and the coefficient of x is -7. The constant term is -2.

This quadratic expression can be further simplified or factored if needed, but the subtraction process is complete with the result 2x² - 7x - 2.

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use pythagorean theorem : a²+b²=c²

Answer:

4.082 radians

Step-by-step explanation:

Here we want to convert 234° into radians.

To do it, we use the fact that pi radians is equal to 180°

Then we can write two equations:

x radians = 234°

3.14 radians  = 180°

Where we want to find the value of x, which is the equivalent in radians to 234°.

Now we can take the quotient of these two equations to get:

( x radians)/(3.14 radians) = (234°/180°)

Solving this for x, we get:

x radians = (234°/180°)*(3.14 radians) = 4.082 radians.

The margin of error of the 99% confidence interval is given as follows:

0.0549 = 5.49%.

A confidence interval of proportions has the bounds given by the rule presented as follows:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.99}{2} = 0.995\), so the critical value is z = 2.575.

The margin of error is given as follows:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

The parameters for this problem are given as follows:

\(n = 143, \pi = \frac{10}{143} = 0.0699\)

Hence the margin of error is of:

M = 2.575 x sqrt(0.0699 x 0.9301/143)

M = 0.0549 = 5.49%.

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Answer:

3

Step-by-step explanation:

159-12=147-12=... keep going until you get to

15-12=3

The integral of \(e^{-2\ln(x)}dx\) simplifies to \(-\frac{1}{x} + C\), where \(C\) is the constant of integration.

The integral of \(e^{-2\ln(x)}dx\) can be simplified and evaluated as follows:

First, we can rewrite the expression using the properties of logarithms. Recall that \(\ln(x)\) is the natural logarithm of \(x\) and can be expressed as \(\ln(x) = \log_e(x)\). Using the logarithmic identity \(\ln(a^b) = b\ln(a)\), we can rewrite the expression as \(e^{-2\ln(x)} = e^{\ln(x^{-2})} = \frac{1}{x^2}\).

Now, the integral becomes \(\int \frac{1}{x^2}dx\). To solve this integral, we can use the power rule for integration. The power rule states that \(\int x^n dx = \frac{1}{n+1}x^{n+1} + C\), where \(C\) is the constant of integration.

Applying the power rule to the integral \(\int \frac{1}{x^2}dx\), we have \(\int \frac{1}{x^2}dx = \frac{1}{-2+1}x^{-2+1} + C = -\frac{1}{x} + C\).

Therefore, the integral of \(e^{-2\ln(x)}dx\) simplifies to \(-\frac{1}{x} + C\), where \(C\) is the constant of integration.

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400

Explanation:

1/3 of 600 is 200. That represents the boys.

Subtract 200 from 600, you get 400. That represents everybody else in the sample size (in this case, girls).

Answer:

10 feet

Step-by-step explanation:

It becomes a right-angled triangle with height of 8feet and base of 6feet.

Using Pythagoras theorem:

a² = b² + c²

a² = 8² + 6²

a² = 64 + 36

a² = 100

a = √100

a = 10

Answer:

the answer is 5

Step-by-step explanation:

Answer:

0.27272727272 is the reciproval of 3 2/3

The probability of bachelor's degree holding resident aged 40 or over is 0.118.

Given:

There are 576 residents with a bachelor's degree who are aged 40 and over.

The total number of residents with a bachelor's degree is 4,879.

Therefore, the probability that resident with bachelor's degree is aged 40 or over is:

= Number of residents aged 40 or over with a bachelor's degree / Total number of residents with abachelor's degree

= 576 / 4,879

= 0.118057

= 0.118.

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Statement : 2(x+10)=7x-15

Reason : Original equation

Statement : 2x+20=7x-15

Reason : Distribute 2 through the parentheses

Statement : 20=5x-15

Reason : Move the variable to the right-hand side and change its sign and then subtract the like terms

Statement : 35=5x

Reason : Move the constant to the left-hand side and change its sign and subtract the like terms

Statement : 7=x

Reason : Divide both sides of the equation by 5

Statement : x=7

Reason : Change the sides of the equation

Therefore, a 2 by 4 by 1.5-inch juice box holds approximately 34 square inches of cardboard.

An inch is a unit of measurement commonly used to express length or distance in the United States, Canada, and the United Kingdom. It is defined as exactly 2.54 centimeters, or 1/12th of a foot. The symbol for inch is "in" or double prime ("). The inch is often used to measure small distance.

To determine the amount of cardboard used by a juice box, we need to calculate the surface area of the box.

A 2 x 4 x 1.5 inch juice box has six sides, each with a different surface area. The formula for calculating the surface area of a rectangular box is:

\(Surface Area = 2lw + 2lh + 2wh\)

where l, w, and h are the length, width, and height of the box.

For the juice box in question, we have:

\(l = 4 inches\\w = 2 inches\)

\(h = 1.5 inches\)

So, the surface area of the juice box is:

\(Surface Area = 2(4 x 2) + 2(4 x 1.5) + 2(2 x 1.5)\)

\(= 16 + 12 + 6\)

\(= 34 square inches\)

Therefore, a 2 by 4 by 1.5-inch juice box holds approximately 34 square inches of cardboard.

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The estimated cost of the new 3000-ft2 heat exchange system for the plant retrofit can be calculated using the power-sizing exponent and the price index. Based on the given information, the rough estimate for the cost of the new heat exchanger system is approximately $108,984.

To estimate the cost of the new heat exchange system, we need to consider the price index and the power-sizing exponent. The price index provides a measure of the change in prices over time. In this case, the price index 7 years ago was 1360, and the current price index is 1478.

To calculate the cost estimate, we can use the following formula:

Cost estimate = (Cost of previous heat exchanger) × (Current price index / Previous price index) × (New size / Previous size) ^ power-sizing exponent

Using the given information, the cost of the previous heat exchanger was $75,000, the previous size was 1200 ft2, and the new size is 3000 ft2.

Plugging in these values into the formula, we get:

Cost estimate = ($75,000) × (1478 / 1360) × (3000 / 1200) ^ 0.55

Simplifying the calculation, we find:

Cost estimate ≈ $108,984

Therefore, a rough estimate for the cost of the new 3000-ft2 heat exchanger system for the plant retrofit is approximately $108,984. It's important to note that this is just an estimate and the actual cost may vary based on specific factors and market conditions.

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Answer:

45 pages a day

450(pages)/10(days)

=45 pages a day

In this problem, we have i.i.d. random variables X1, X2, ..., Xn with a specific density function. We are interested in estimating the parameter a using the method of moments. The method of moments involves equating the sample moments with the theoretical moments to obtain an estimate for the parameter.

The maximum likelihood estimation (MLE) of a satisfies a certain equation. The asymptotic variance of the MLE can be determined, and a sufficient statistic for a can be found.

(i) To estimate the parameter a using the method of moments, we equate the sample moments with the theoretical moments. Since we know that E(X) = 1/2 and Var(X) = 1/4(2a + 1), we can set the sample mean and sample variance equal to their respective theoretical values and solve for a.

(ii) The maximum likelihood estimation (MLE) of a can be found by maximizing the likelihood function based on the observed data. In this case, the MLE of a satisfies an equation obtained by taking the derivative of the log-likelihood function with respect to a and setting it equal to zero.

(iii) The asymptotic variance of the MLE in (ii) can be determined using the Fisher information. The Fisher information quantifies the amount of information that the data provides about the parameter. In this case, it involves taking the second derivative of the log-likelihood function with respect to a and evaluating it at the MLE.

(iv) To find a sufficient statistic for a in (i), we need to determine a statistic that captures all the information in the data regarding the parameter a. In this case, a sufficient statistic can be found using the factorization theorem or by considering the joint density function of the random variables. The specific form of the sufficient statistic will depend on the given density function and the parameter a.

Overall, these steps provide a framework for estimating the parameter a, determining the MLE, calculating the asymptotic variance, and finding a sufficient statistic based on the given i.i.d. random variables and their density function.

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Answer:

9 + 4(1) \(\neq \\\) 17

Step-by-step explanation:

to satisfy inequality

9 + 4(1) < 17

13 < 17

The option D is correct that is at about 0.5 seconds and about 7.5 seconds the firework will be at height 64 feet.

What is a quadratic equation ?

A quadratic equation is an equation which contains a single variable of degree 2 and its general form is ax² + bx + c = 0.

The height of firework is represented by a quadratic equation which is 16t² + 128t.

Let's find out that at what time the rocket will be at height of 64 feet.

So,

16t² + 128t = 64 feet

or

16t² + 128t - 64 = 0

or

t² + 8t - 4 = 0

We know that quadratic equation is in form ax² + bx + c = 0.

Using the quadratic formula to find value of t :

\(t=\frac{-b\pm\sqrt{b^2-4ac}}{2a}.\)

t = [ -8 ± √(8² - (4 × 1 × - 4))] / ( 2 × 1 )

t = [ - 8 ± 8.94 ] / 2

t = -4 ± 4.47

So , the value of t can be either -4 + 4.47 or -4 - 4.47 which is equal to 0.47 or - 8.47 seconds. Time can't be negative , so t = 0.47 or 0.5 seconds.

Therefore , the option D is correct that is at about 0.5 seconds and about 7.5 seconds the firework will be at height 64 feet.

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