Edward plans to put $75 into a savings account. He can place his money into an account represented by b(x) = 7x + 75, or into another account represented by c(x) = 75(1.06)x. Which account has the highest value in 2 years? Which account has the highest in 12 years?

Answer:

7.14

Step-by-step explanation:

The area of rectangle is 25, the smaller and larger values are 5 and 5.

The area of Rectangle is length times of width.

Area = A = xy

A = x.√49-x²

Derivate with respect to x

A'=x/2√49-x² .(-2x)+√49-x²

A'=-2x²+49/√49-x²

Derivate value equate with zero

A'=0

-2x²+49/√49-x²=0

-2x²+49=0

-2x²=-49

x²=49/2

x=7/√2 =4.95=5

Now y=√49-x²

Put x value in y

y=√49-4.95²

=√49-24.5=√24.5=5

Hence the area of rectangle is 25, the smaller and larger values are 5 and 5.

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Answer:

The answer is \(y=\frac{1}{6} x\).

Step-by-step explanation:

According to the table, when you insert 6, it should give 1 as the area covered. The equation can be found by the slope formula, the change in y over the change in x. Which is in one increase in y, leads to 6 increase in x.

In that case, the equation holds. The same thing, when you put 12 to x. Gives you 2 as the area covered.

The z-score of 0.3162 is less than 2.33, we fail to reject the null hypothesis. There is not enough evidence to conclude that the valve performs above the specifications.

The null hypothesis is that the valve produces a mean pressure of 5.5 pounds/square inch. The alternative hypothesis is that the valve produces a mean pressure greater than 5.5 pounds/square inch.
The decision rule for rejecting the null hypothesis at a significance level of 0.01 is to reject it if the test statistic (z-score) is greater than 2.33.
To calculate the z-score, we use the formula:
z = (sample mean - hypothesized mean) / (standard deviation / sqrt(sample size))
z = (5.6 - 5.5) / (0.8 / sqrt(18))
z = 0.3162
Since the z-score of 0.3162 is less than 2.33, we fail to reject the null hypothesis. There is not enough evidence to conclude that the valve performs above the specifications.

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The expression II i! represents the factorial of an integer i. Among the given options, the correct representation of II i! is (4).

The factorial of an integer i, denoted as i!, is the product of all positive integers from 1 to i. In the given options, we need to find the equivalent representation of II i!. Option (4) states II i!, which means we need to multiply the factorial of each integer from 1 to i. In this case, i = 4. So, (4) represents the multiplication of 1!, 2!, 3!, and 4!.

On the other hand, the other options do not represent the factorial of i. Option (1) represents the multiplication of individual numbers without the factorial notation. Option (2) and (3) represent the multiplication of specific numbers without considering the factorial notation. Option (5) represents the multiplication of specific numbers without considering the factorial notation and includes additional numbers not present in the factorial calculation. Option (6) represents a combination of factorial notation and specific numbers.

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Answer:

1i = 1

4 + i = 4 + 1 = 5

Step-by-step explanation:

hope it's helpful

The pH of the solution prepared by dissolving 4.00 g of NaOH in enough water to produce 500.0 mL of solution is approximately 13.302.

To calculate the pH of a solution prepared by dissolving NaOH in water, we need to determine the concentration of hydroxide ions (OH-) in the solution. Here's how we can do that:

Convert the mass of NaOH to moles:

Given mass of NaOH = 4.00 g

Molar mass of NaOH = 22.99 g/mol (sodium) + 16.00 g/mol (oxygen) + 1.01 g/mol (hydrogen)

Molar mass of NaOH = 39.99 g/mol

Moles of NaOH = 4.00 g / 39.99 g/mol ≈ 0.100 mol

Determine the volume of the solution:

Given volume of solution = 500.0 mL = 0.500 L

Calculate the concentration of hydroxide ions (OH-):

Concentration of OH- = moles of NaOH / volume of solution

Concentration of OH- = 0.100 mol / 0.500 L = 0.200 M

Calculate the pOH of the solution:

pOH = -log10[OH-]

pOH = -log10(0.200) ≈ 0.698

Calculate the pH of the solution:

pH = 14 - pOH

pH = 14 - 0.698 ≈ 13.302

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Answer:

hope this answer helps you dear...take care and may u have a great day ahead!

The answers that describe the quadrilateral DEFG area rectangle and parallelogram.

The correct answer choice is option A and B.

A quadrilateral is a parallelogram, which has opposite sides that are congruent and parallel.

Quadrilateral DEFG

if line DE || FG,

line EF // GD,

DF = EG and

diagonals DF and EG are perpendicular,

then, the quadrilateral is a parallelogram

Hence, the quadrilateral DEFG is a rectangle and parallelogram.

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Answer:

y=-8x-2

Step-by-step explanation:

Answer:x − x^{2} − 1.

Step-by-step explanation:

.

To find the function r(t) given its derivative r′(t) and an initial condition, we need to integrate r′(t) and apply the initial condition.

Step 1: Integrate r′(t) component-wise:
For the i-component: ∫(te^(-t^2)) dt
For the j-component: ∫(-e^(-t)) dt
For the k-component: ∫(1) dt

Step 2: Find the antiderivatives for each component:
For the i-component: -(1/2)e^(-t^2) + C1
For the j-component: e^(-t) + C2
For the k-component: t + C3

Step 3: Combine the antiderivatives to obtain the general solution for r(t):
r(t) = [-(1/2)e^(-t^2) + C1]i + [e^(-t) + C2]j + [t + C3]k

Step 4: Apply the initial condition r(0):
r(0) = [-(1/2)e^(0) + C1]i + [e^(0) + C2]j + [0 + C3]k
Given r(0), we can determine the constants C1, C2, and C3.

Without the provided value for r(0), I can't find the specific constants, but you can use the general solution r(t) and plug in r(0) to find the exact function for r(t).

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The smallest value of |S| that guarantees the existence of two distinct subsets of S whose elements sum to the same value is 289.

Let S be a set of 1-digit or 2-digit numbers. We want to find the smallest value of |S|, the cardinality of S, such that there exist two distinct subsets of S whose elements sum to the same value.

Consider the largest possible sum of two elements in S. If the largest possible sum is less than or equal to 100, then every subset of S must have a sum less than or equal to 200, since at most two elements can be selected from S to form a sum greater than 100. Therefore, if |S| > 200, then by the Pigeonhole Principle, there must be two distinct subsets of S whose elements sum to the same value.

On the other hand, if the largest possible sum of two elements in S is greater than 100, then we can consider the set S' obtained by removing all elements of S greater than 100. Since S' consists of only 1-digit and 2-digit numbers, the largest possible sum of two elements in S' is 99 + 99 = 198. Therefore, if |S'| > 198, then by the Pigeonhole Principle, there must be two distinct subsets of S' whose elements sum to the same value.

But note that |S'| is at most the number of 1-digit and 2-digit numbers, which is 90 (10 1-digit numbers and 90 2-digit numbers). Therefore, if |S| > 90 + 198 = 288, then by the Pigeonhole Principle, there must be two distinct subsets of S whose elements sum to the same value.

Thus, the smallest value of |S| that guarantees the existence of two distinct subsets of S whose elements sum to the same value is 289.

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Answer:

\(\frac{(8+2)^2}{2} = 50\)

\(10+5^2-3 * 2^2 = 23\)

Step-by-step explanation:

\(\frac{(8+2)^2}{2}\)

\(\frac{10^2}{2}\)

\(\frac{100}{2}\)

50

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

\(10+5^2-3 * 2^2\)

\(10+25-3 * 4\)

\(10+25-12\)

\(35-12\)

23

Given the function f(n) defined as the remainder when dividing n by 9, where n is a natural number and B is the set {0, 1, 2, 3, 4, 5, 6, 7, 8}, we can evaluate the function for specific values of n.

a) To evaluate f(5), we divide 5 by 9 and find the remainder. Since 5 is less than 9, the remainder is 5. Therefore, f(5) = 5.
b) For f(78), we divide 78 by 9. The quotient is 8 with a remainder of 6. Hence, f(78) = 6.
c) Evaluating f(126), we divide 126 by 9. The quotient is 14 and the remainder is 0. Therefore, f(126) = 0.

d) Lastly, considering f(4343), we divide 4343 by 9. The quotient is 482 with a remainder of 7. Thus, f(4343) = 7. For the given function f(n) defined as the remainder when dividing n by 9, we evaluated its values for different inputs. f(5) equals 5, f(78) equals 6, f(126) equals 0, and f(4343) equals 7. These results are obtained by dividing the respective numbers by 9 and considering the remainder as the output of the function for each input value.

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The best definition of the test statistic is the number of standard errors above or below the expected outcome that our sample z-score corresponds to. In other words, the test statistic measures how far our sample mean deviates from the expected population mean in terms of standard deviation units.

The test statistic is a crucial element in hypothesis testing as it helps us determine the probability of obtaining our sample mean by chance. We use the test statistic to calculate the p-value, which is the probability of obtaining a result as extreme as our sample mean under the null hypothesis.

The boundary value corresponding to the p-value is determined by the level of significance we choose for our test. If our p-value is less than the level of significance (usually 0.05), we reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis.

In summary, the test statistic is a measure of how far our sample mean deviates from the expected population mean in standard deviation units. It is used to calculate the p-value and determine the level of significance for our hypothesis test.
The best definition of the test statistic among the given terms is: the number of standard errors above or below the expected outcome that our sample represents. A test statistic is a value calculated from sample data that is used to determine whether to reject or fail to reject a null hypothesis in hypothesis testing. It measures how far the sample statistic is from the hypothesized population parameter, considering the sample's variability.

In simpler terms, the test statistic helps us understand how likely our sample results are, given the null hypothesis. It does this by comparing the sample's outcome to what we would expect under the null hypothesis, considering the variability within the sample. By calculating the test statistic, we can then determine the corresponding p-value, which represents the probability of obtaining the observed results or more extreme results, assuming the null hypothesis is true.

In summary, the test statistic quantifies the difference between the sample outcome and the expected outcome under the null hypothesis, expressed in terms of the number of standard errors. It helps us make decisions about the null hypothesis based on the calculated p-value.

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Answer:

-82

Step-by-step explanation:

84/21=4

-25x4=-100

-3x-6=18

-100+18=-82

The volume of the cylinder depends on its radius and height. The volume of the cylinder is 49806.05 ft3.

The volume of the cylinder is defined as the three-dimensional space occupied by a cylinder.

Given that the height h of the cylinder is 22 1/4 ft. The diameter d of the cylinder is 2 2/5 times its height.

h = 22 1\4 ft = 89/4 ft

The diameter of the cylinder is calculated as given below.

\(d = \dfrac {12}{5} \times h\)

\(d = \dfrac {12}{5} \times \dfrac {89}{4}\)

\(d = 53.4 \;\rm ft\)

The radius of the cylinder is given below.

\(r = \dfrac {d}{2}\)

\(r = \dfrac { 53.4}{2}\)

\(r = 26.7 \;\rm ft\)

The volume of the cylinder is calculated as given below.

\(V = \pi r^2 h\)

\(V = 3.14 \times (26.7)^2 \times \dfrac {89}{4}\)

\(V = 49806.05 \;\rm ft^3\)

Hence we can conclude that the volume of the cylinder is 49806.05 ft3.

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Answer:

Step-by-step explanation: substitute 0 in for x for the y intercept

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Answer: 19

Step-by-step explanation: it says you already found X so you substitute it into angle m2

ANSWER

9.5

EXPLANATION

To find the distance between home and work, we have to use the formula:

We have that home is at point (3, -3) and work is at point (0, 6).

Therefore:

(x1, y1) = (3, -3)

(x2, y2) = (0, 6)

Therefore, we have that:

The answer is 9.5

Answer:

The first x is 9

The second x is -5

Step-by-step explanation:

Answer:

Try a,d,b,a

Step-by-step explanation:

The requried width of the model of the classroom made by Daylan is 11 feet.

The scale factor is defined as the ratio of the modified change in length to the original length.

Here,
To find the model width, we can use the scale provided by Daylan, which is 1/2. This means that 1 unit on the model represents 2 units in the real world.

Let's use "w" to represent the model width. According to the scale, we know that:

1 unit on the model = 2 units in the real world

So, we can set up a proportion,

1 unit on the model / 2 units in the real world = w / 22 ft

To solve for w, we can cross-multiply,

1 unit on the model * 22 ft = 2 units in the real world * w

22/2 = w/1

11 = w

Therefore, the model width is 11 feet.

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the value of cot(8) is 24/7.

To find cot(8) using the given values sin(7/24) and cos(8/25), we can use the ratio identity cot(x) = cos(x) / sin(x).

Step 1: Substitute the given values into the ratio identity:

cot(8) = cos(8/25) / sin(7/24)

Step 2: Simplify further by evaluating the cosine and sine values using the given information:

cos(8/25) = 25/25 = 1

sin(7/24) = 7/24

Step 3: Substitute the values into the ratio identity:

cot(8) = 1 / (7/24)

Step 4: To divide by a fraction, we can multiply by its reciprocal:

cot(8) = 1 * (24/7)

Step 5: Simplify the expression:

cot(8) = 24/7

Therefore, using the given values, the value of cot(8) is 24/7.

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Answer: x-6, x+3, x-3

Step-by-step explanation;

Split the equation into two.

x2(x-6)-9(x-6)

(x-6) is seen as one of the tiles. Now work on x2-9

x2-9 is a difference of squares meaning the last two are (x+3) and (x-3).

The required number of touchdowns are 8, number of extra- point kicks are 8 and number of field goals are 4 can be obtained from the system of equations.

The orange team scores 44 points and the blue team scores 24 points.

The touchdowns are worth 6 points.

The extra- point kicks are worth 1 point.

The field goals are worth 3 points.

Let the number of touchdowns, extra- point kicks and field goals be x, y and z respectively.

According to the question, the numbers of touchdowns was equal to the number of extra-point kicks.

That is, x= y

Also according to the question, there are twice as many touchdowns as field goals.

That is, x= 2z

From the above two equations we can say that,

x= y= 2z

⇒y= 2z

We can state the total score by the two teams by the following equations as,

6x+ 1y+ 3z = 44+24

⇒ 6(2z)+ 1(2z)+ 3(z) = 68

⇒ 17z = 68

⇒ z= 68/17

⇒ z= 4

Hence, x= 2z = 2(4) = 8

and y= x= 8

Hence the number of touchdowns, extra- point kicks and field goals are 8, 8 and 4 respectively.

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