What is equivalent of square root of 200 in simplest form

Answer: 2/90 = 1/45

Step-by-step explanation:

The maximum amount of monthly rent payment he could pay would be $755 per month.

Mika has the option of buying a condominium for a monthly payment of $675 or renting it with an option to buy it at the end of 3 years.

If he buys it now, he must pay $7,100 for closing costs. If he rents it, he must pay one month’s rent and a $750 security deposit for move-in costs.

Mika decides to rent instead of buying because it is the cheapest option over the first 3 years. He would still need to pay his first month’s rent on top of these move-in costs.

The maximum amount of monthly rent payment Mika could pay would be $755 per month.

Here's how to determine it: In the case of renting, Mika pays $750 for the security deposit, $675 for the first month’s rent, and $675 for the remaining 35 months of the lease.

So the total cost of renting the condominium for 3 years will be:750 + 675 + (675 × 35) = 24,375 To determine the maximum monthly rental payment that Mika could pay, we must divide the total rental cost by the total number of rental months: 24,375 ÷ 36 = 676.25 Since we are looking for the maximum amount of monthly rent payment, we can round up to the nearest dollar: $677.

Therefore, the maximum amount of monthly rent payment he could pay would be $755 per month.

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Answer:

c

Step-by-step explanation:

it's a property of powers, when the base is the same (-5) , you need to

sum the powers when both terms are multiplyng

subtract the powers when both terms are dividing (numerator power minus denominator power, in that order)

The statement is saying that if k is an element of the set obtained by combining the elements of n and the singleton set {n}, then k must either already belong to n or be equal to n.

The statement "It's obvious that k ∈ n ∪ {n} if and only if k ∈ n or k = n" expresses a relationship between the elements of a set n and the element n itself, along with another element k. In simpler terms, it states that if k belongs to the set obtained by taking the union of n and {n}, then k must either belong to n or be equal to n.

To understand this statement, let's break it down:

- The symbol "∈" denotes membership, indicating that an element belongs to a set.

- The symbol "∪" represents the union of two sets, which combines all the elements from both sets without duplication.

This is essentially highlighting the fact that when you take the union of a set with another set containing a single element (in this case, the set {n}), the resulting set will contain all the elements of the original set along with the additional element.

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To solve for x and y in the system of equations:

y = 3x^2 + 6x + 4

y = -3x^2 + 4

We can set the two expressions equal to each other:

3x^2 + 6x + 4 = -3x^2 + 4

Combining like terms, we get:

6x^2 + 6x = 0

Factor out 6x:

6x(x + 1) = 0

This gives us two possible solutions:

x = 0 or x = -1

To find the corresponding y-values, we plug in each value of x into either of the equations. We'll use the first equation:

y = 3x^2 + 6x + 4

If x = 0, we get:

y = 3(0)^2 + 6(0) + 4

y = 4

So one solution is (0, 4).

If x = -1, we get:

y = 3(-1)^2 + 6(-1) + 4

y = 1

So the other solution is (-1, 1).

Therefore, the solutions are (0, 4) and (-1, 1).

Answer:

Step-by-step explanation:

Surface area of a cone = surface area of a circle = pi r^2

250 = pi r^2

[tex]r = \sqrt{ \frac{250}{2} } = 5 \sqrt{5} \: cm[/tex]

Because the height (h) of the cone is double the length of its radius

Then

h = 2r

[tex]h \: = 2 \times 5 \sqrt{5} = 10 \sqrt{5} = 22.36 \: cm[/tex]

Answer:

f(10) = 3(10) - 5 = 30 - 5 = 25

f(-10) = 3(-10) - 5 = -30 - 5 = -35

Step-by-step explanation:

you shuld us student demos brow it wold grafe that for you easyly

To identify the correct weight to the nearest 1/8 pound, you need to have a weight measurement that is divisible by 1/8 pound. If you have a weight that is not divisible by 1/8 pound, then you need to round it to the nearest 1/8 pound.

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By following this rounding method, you can determine the correct weight to the nearest 1/8 pound based on the specific weight measurement provided.

To identify the correct weight to the nearest 1/8 pound, we need a specific weight or measurement to work with.

Once we have that information, we can apply the rounding method.

When rounding to the nearest 1/8 pound, we look at the digit immediately after the 1/8 pound mark, which is 0.125 pounds.

If this digit is 4 or less, we round down, and if it is 5 or greater, we round up.

For example, let's say we have a weight of 15.6 pounds. The digit after the 1/8 pound mark is 6, which is greater than 4.

Therefore, we round up, and the weight to the nearest 1/8 pound is 15.75 pounds.

On the other hand, if we have a weight of 12.3 pounds, the digit after the 1/8 pound mark is 3, which is less than 4.

Thus, we round down, and the weight to the nearest 1/8 pound is 12.25 pounds.

Similarly, if the weight is 22.7 pounds, the digit in the thousandth place is 7. Since 7 is greater than 4, we round up.

The 1/8 pound measurement is 0.125 pounds, so rounding up gives us 22.875 pounds.

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The domain of the square root function is x greater-than-or-equal-to 0, since the function is defined for all non-negative x-values or x-values greater than or equal to zero.

The domain of the square root function graphed below can be determined by looking at the x-values of the points on the graph.

From the given information, we can see that the curve starts at (0, -1) and goes through (1, -2) and (4, -3).

The x-values of these points are 0, 1, and 4.

Since the square root function is defined for any non-negative x-values or x-values more than or equal to zero, its domain is x greater-than-or-equal-to 0.

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To complete the sequence "7444> →→19-", we need to find the missing terms that fit the pattern established by the given numbers. Let's analyze the sequence and identify any discernible pattern or rule.

Looking at the sequence, we can observe that each number is decreasing by a certain value. In this case, the first number is 7444, and the second number is 19, indicating a decrease of 7425. Now, we need to continue this pattern.

To find the third missing term, we subtract 7425 from 19, resulting in -7406. Therefore, the third missing term is -7406

To find the fourth missing term, we subtract 7425 from -7406, resulting in -14831. Therefore, the fourth missing term is -14831.

To find the fifth missing term, we subtract 7425 from -14831, resulting in -22256. Therefore, the fifth missing term is -22256.

Therefore, the completed sequence is:

7444> →→19- → -7406 → -14831 → -22256

Each term in the sequence is obtained by subtracting 7425 from the previous term.

It's important to note that this solution assumes a linear pattern in which the same subtraction value is applied to each term. However, without additional context or information about the sequence, there could be alternative patterns or interpretations.

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The statement that is true about the function is:

A function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given:

The minimum value of the curve = (1.9, -5.7),

The maximum value = (0, 2)

The point the function crosses the x-axis (the x-intercept) = (-0.7, 0), (0.76, 0), and (2.5, 0)

The point the function crosses the y-axis (the y-intercept) = (0, 2)

The given points can be plotted using MS Excel, from which we have:

F(x) is less than 0 over the interval from x = -∞, to x = -0.7, and the interval from x = 0.76 to x = 2.5.

Hence, the correct option is A.

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The total cost of 24 copper hearts is approximately $13.08.

To find the total cost of 24 copper hearts, we need to calculate the total amount of copper used and then multiply it by the cost per pound of copper.

Given:

- Each heart uses 0.75 in³ of copper.

- There is 0.323 pound of copper per cubic inch.

- The cost of copper is $2.25 per pound.

First, we calculate the total amount of copper used by multiplying the copper volume per heart by the number of hearts:

Total copper used = 0.75 in³/heart * 24 hearts = 18 in³.

Next, we convert the copper volume to pounds by multiplying it by the copper density:

Total copper in pounds = 18 in³ * 0.323 lb/in³ = 5.814 lb.

Finally, we find the total cost by multiplying the total copper weight by the cost per pound:

Total cost = 5.814 lb * $2.25/lb = $13.0825.

Therefore, the total cost of 24 copper hearts is approximately $13.08.

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The 95% confidence interval for the effectiveness of the blood-pressure drug is given as follows:

[tex]22.6 < \mu < 24.4[/tex]

The mean, the standard deviation and the sample size for this problem, which are the three parameters, are given as follows:

[tex]\overline{x} = 23.5, \sigma = 12.2, n = 775[/tex]

Looking at the z-table, the critical value for a 95% confidence interval is given as follows:

z = 1.96.

The lower bound of the interval is then given as follows:

[tex]23.5 - 1.96 \times \frac{12.2}{\sqrt{775}} = 22.6[/tex]

The upper bound of the interval is then given as follows:

[tex]23.5 + 1.96 \times \frac{12.2}{\sqrt{775}} = 24.4[/tex]

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The value of 4 Superscript negative 4 is negative StartFraction 1 Over 4 Superscript negative 4 EndFraction.

In the given table, Tasha observed a pattern in the powers of 4. When the exponent decreases by 1, the previous value is divided by 4. Using this pattern, she determined the values for 4 squared, 4 Superscript 1, 4 Superscript 0, 4 Superscript negative 1, and 4 Superscript negative 2.

To find the value of 4 Superscript negative 3, she divided the previous value (StartFraction 1 Over 16 EndFraction) by 4, resulting in StartFraction 1 Over 64 EndFraction.

Similarly, for 4 Superscript negative 4, she divided the previous value (StartFraction 1 Over 64 EndFraction) by 4, yielding StartFraction 1 Over 256 EndFraction.

Finally, to rewrite the value for 4 Superscript negative 4, she expressed it as negative StartFraction 1 Over 4 Superscript negative 4 EndFraction.

Therefore, the value of 4 Superscript negative 4 is negative StartFraction 1 Over 4 Superscript negative 4 EndFraction, which simplifies to StartFraction 1 Over 256 EndFraction

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Answer:

[tex]\textsf{25)} \quad y=6\cdot 2^x[/tex]

[tex]\textsf{26)}\quad y=3\cdot 7^x[/tex]

Step-by-step explanation:

The general form of an exponential function is:

[tex]\boxed{y=ab^x+c}[/tex]

where:

As the asymptote is y = 0 for both equations, the general function to use is:

[tex]\boxed{y=ab^x}[/tex]

To write the equation of an exponential function that passes through the given pairs of points, substitute both points into the exponential function and solve to find the values of a and b.

[tex]\hrulefill[/tex]

Given points:

Substitute point (0, 6) into the formula and solve for a:

[tex]\begin{aligned}y&=ab^x\\\implies 6&=ab^0\\6&=a(1)\\a&=6\end{aligned}[/tex]

Substitute the found value of a and the point (3, 48) into the formula and solve for b:

[tex]\begin{aligned}y&=ab^x\\\implies48&=6b^3\\8&=b^3\\b&=\sqrt[3]{8}\\b&=2\end{aligned}[/tex]

Therefore, the exponential equation with asymptote y = 0 that passes through points (0, 6) and (3, 48) is:

[tex]\boxed{y=6\cdot 2^x}[/tex]

[tex]\hrulefill[/tex]

Given points:

Substitute point (1, 21) into the formula, and point (2, 147) into the formula, to create two equations:

[tex]21=ab^1 \implies ab=21[/tex]

[tex]147=ab^2 \implies ab^2=147[/tex]

Divide the second equation by the first equation to eliminate a and solve for b:

[tex]\dfrac{ab^2}{ab}=\dfrac{147}{21}[/tex]

 [tex]\dfrac{b^2}{b}=7[/tex]

   [tex]b=7[/tex]

Substitute the found value of b into the first equation and solve for a:

[tex]\begin{aligned}ab&=21\\7a&=21\\a&=3\end{aligned}[/tex]

Substitute the found values of a and b into the formula to write an exponential equation with asymptote y = 0 that passes through points (1, 21) and (2, 147):

[tex]\boxed{y=3\cdot 7^x}[/tex]

The values into the slope-intercept form, we have y = -5x - 6

The slope-intercept form of a linear equation is given by:

y = mx + b

where 'm' represents the slope of the line, and 'b' represents the y-intercept.

In this case, the y-intercept is (0, -6), which means that the line crosses the y-axis at the point (0, -6).

The slope is given as -5.

Therefore, substituting the values into the slope-intercept form, we have:

y = -5x - 6

This equation represents the line with a y-intercept of (0, -6) and a slope of -5.

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The number of minutes Hakeem was 1 blocks from his house is one minutes

The distance between the store and the bank is 3 blocks.

y axis: the position of Hakeem

Hakeem left his house and drove to the store, the store is 3 blocks away from house .

since he stopped and went inside the store , a flat line is shown in the graph from 8 minutes to 11 minutes , which means that he stopped at the store for 3 minutes .

next he starts moving and stop at the bank whose position is 6 blocks away from home .

Therefore, it can be concluded that it takes Hakeem 1 minutes to cover each block.

Complete question:

Hakeem left his house and drove to the store. He stopped and went inside. From there, he drove in the same direction until he got to the bank. He stopped and went inside the bank. Then he drove home. The graph below shows the number of blocks away from home Hakeem is x minutes after he left his house, until he got back home , How many blocks is it from the store to the bank ?

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The transformation from the function f(x) to g(x) is:

The graph was shrunk vertically by a factor of ¹/₉ and then moved downwards by 2 units

Multiplying the outside of a function would lead to multiplying the y-values.

Multiplying a function by a number greater than 1 means that the graph is stretched vertically.

Multiplying the function by a number between 0 and 1 makes the graph shrink vertically.

Thus, since we have f(x) = x transformed to g(x) = ¹/₉x - 2, then it means that the graph was shrunk vertically by a factor of ¹/₉.

Now, when we shift, move, or translate vertically, shifting upwards by "c" units means we add c to the function.
Moving downwards by c units means we subtract c from the function.

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Answer:

835.66m^2 (to 2d.p)

Step-by-step explanation:

Firstly split the shape up so you get a rectangle and 2 circles.
Find the area of the circle:
formulae = πr^2
14/2=7
7^2=49
49π*2 (as there is two circles)= 98
98π=307.876
Find the circumference of the circle
formulae = dπ
14π=43.98
43.98 is the height of the rectangle
43.98*12=527.79 (rounded to 1d.p)
Area of rectangle is 527.79
Area of two circles is 307.876
Add them together = 835.66m^2 (to 2d.p)

Answer:

836cm^2

Step-by-step explanation:

For the sides, do 14/2 to find the radius (r) which is 7.

7^2 x pi = 153.9380400259 (formula for area of a circle is pi x r^2)

Multiply this by 2 to account for both sides of the cylinder.

For the cross-section of the cylinder, do 2 x pi x the radius (7) x 12 (the length, or l) which gets you 527.787565803085.

527.787565803085 + (153.9380400259 x 2) = 835.663645854885, rounded to 836 centimetres squared.

Hope this helps :D

Answer:

9

Step-by-step explanation:

[tex]\frac{3^4}{3^2}=3^{4-2}=3^2=9[/tex]

Answer:

  (d)  5/8 in

Step-by-step explanation:

You want the measure indicated by the compass points in the figure.

The largest mark between the end of the ruler and the mark labeled 1 is at the 1/2 inch point. The compass is to the right of that.

The mark halfway between the 1/2 inch mark and the 1 inch mark is 3/4 inches. The compass is to the left of that.

The mark halfway between 1/2 inch and 3/4 inch is 5/8 inch. The compass seems to be nearer this mark than it is to the 1/2 inch mark.

The measure of the distance between compass points is about 5/8 inch.

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The measure of x in the circle is 21 degrees

From the question, we have the following parameters that can be used in our computation:

The circle

The measure of x can be calculated using the fact that the angle in a semicircle is 90 degrees

So, we have

4x + 6 = 90

Using the above as a guide, we have the following:

4x = 84

Evaluate

x = 21

Hence, the value of x is 21

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Test for Proportion Hypothesis Conclusion: There is not sufficient evidence to conclude that more than 1.6% of this drug's users experience flulike symptoms as a side effect at the 0.05 level of significance.

To determine if there is sufficient evidence to conclude that more than 1.6% of this drug's users experience flulike symptoms as a side effect, we can perform a hypothesis test.

Let's define the null and alternative hypotheses:

Null hypothesis (H₀): The proportion of this drug's users experiencing flulike symptoms is 1.6% or less.

Alternative hypothesis (H₁): The proportion of this drug's users experiencing flulike symptoms is greater than 1.6%.

We can use the normal approximation to the binomial distribution since the sample size is large (846 patients) and the expected number of successes (flulike symptoms) is greater than 5.

First, let's calculate the expected number of patients experiencing flulike symptoms if the proportion is 1.6%:

Expected number = (proportion) * sample size = 0.016 * 846 = 13.536

Now, let's calculate the test statistic (Z-score):

Z = (observed number of successes - expected number of successes) / sqrt(expected number of successes * (1 - proportion))

Z = (17 - 13.536) / sqrt(13.536 * (1 - 0.016))

Z = 3.464 / sqrt(13.536 * 0.984) ≈ 3.464 / sqrt(13.316)

Z ≈ 3.464 / 3.648 ≈ 0.950

The test statistic (Z) is approximately 0.950.

Next, we need to find the p-value associated with this test statistic. Since the alternative hypothesis is one-tailed (we're testing if the proportion is greater than 1.6%), we'll find the p-value corresponding to the area to the right of the observed test statistic.

Using a standard normal distribution table or a calculator, we find that the area to the right of Z = 0.950 is approximately 0.1711.

Therefore, the p-value is approximately 0.1711.

Finally, let's compare the p-value with the significance level (α = 0.05). Since the p-value (0.1711) is greater than the significance level (0.05), we do not have sufficient evidence to conclude that more than 1.6% of this drug's users experience flulike symptoms as a side effect at the 0.05 level of significance.

In summary:

Test statistic (Z) ≈ 0.950

P-value ≈ 0.1711

Test for Proportion Hypothesis Conclusion: There is not sufficient evidence to conclude that more than 1.6% of this drug's users experience flulike symptoms as a side effect at the 0.05 level of significance.

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Given statement solution is :- a) T = [tex]A^−1[/tex] b) T - 1.

For suitable values of s = -2 and t = 1, T = [tex]A^−1[/tex] and T - 1.

To show that for suitable values of s and t, T = [tex]A^−1[/tex], and T - 1, let's assume a matrix A and its inverse [tex]A^−1[/tex]. We'll find suitable values of s and t such that T = [tex]A^−1[/tex] and T - 1.

Consider the equation T = [tex]A^−1[/tex]. If T is the inverse of A, then we have A * [tex]A^−1[/tex] = I, where I is the identity matrix. Let's construct a specific matrix A and solve for [tex]A^−1[/tex] to find T.

Let's take the following matrix A:

A = [[1, 2],

[3, 4]]

To find the inverse of A, we can use the formula:

[tex]A^−1[/tex] = (1 / det(A)) * adj(A)

where det(A) represents the determinant of A, and adj(A) is the adjugate of A.

The determinant of A is calculated as follows:

det(A) = 1 * 4 - 2 * 3 = -2

Now, let's find the adjugate of A by interchanging the elements of the main diagonal and changing the sign of the other elements:

adj(A) = [[4, -2],

[-3, 1]]

Finally, we can compute [tex]A^−1[/tex] by multiplying the adjugate by the reciprocal of the determinant:

[tex]A^−1[/tex] = (1 / -2) * [[4, -2],

[-3, 1]]

= [[-2, 1],

[3/2, -1/2]]

Therefore, we have found the inverse of A. We can set T =[tex]A^−1[/tex]:

T = [[-2, 1],

[3/2, -1/2]]

Now, let's show that T - 1 using suitable values of s and t. To do that, we'll assume T - 1 = [tex]A^−1[/tex] and solve for s and t.

Let's set T - 1 =[tex]A^−1:[/tex]

T - 1 = [[-2, 1],

[3/2, -1/2]]

We can rewrite T - 1 as:

T - 1 = [[s, t],

[u, v]]

Comparing the corresponding elements, we have:

s = -2

t = 1

u = 3/2

v = -1/2

Therefore, for s = -2 and t = 1, we have T - 1 = [tex]A^−1.[/tex]

In conclusion, we have shown that for suitable values of s = -2 and t = 1, T = [tex]A^−1[/tex] and T - 1.

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Answer:

-4 < x < 1/2

Step-by-step explanation:

Given the inequality:

[tex]\displaystyle{\dfrac{x+4}{2x-1} < 0}[/tex]

Where x can not equal 1/2 since it will result the undefined expression. Furthermore, by solving a rational inequality (fractional inequality) is different from solving a linear inequality.

If we assume that for the expression on the left side is always positive, we can say that:

[tex]\displaystyle{\dfrac{x+4}{2x-1} < 0}[/tex]

However, the expression can remain negative. If a denominator remains somewhat negative and you multiply both sides by the denominator, you'll end up from < to >, basically swap in inequality sign.

Thus. If we let x > 1/2, the interval where the expression is always positive, we can solve the inequality as:

[tex]\displaystyle{\dfrac{x+4}{2x-1} \cdot \left(2x-1\right) < 0 \cdot \left(2x-1\right)}\\\\\displaystyle{x+4 < 0}\\\\\displaystyle{x < -4}[/tex]

However, this inequality is false so we can say that there's no region where this expression is less than 0 at x > 1/2.

Now let's say that at x < 1/2, the expression will start to remain in negative (although there is an interval that the expression is positive at x < 1/2 but majority negative.) Therefore, let's say:

[tex]\displaystyle{-\dfrac{x+4}{2x-1} < 0}\\\\\displaystyle{\dfrac{x+4}{2x-1} > 0}[/tex]

When we solve for the inequality, we should have x + 4 > 0 which results in x > -4. When union x > -4 with x < 1/2, it fits perfectly. Thus, the solution is:

[tex]\displaystyle{-4 < x < \dfrac{1}{2}}[/tex]

a) The mean of the data-set is of 2 hours.

b) The mean absolute deviation of the data-set means that the measures vary by an average amount of 0.93 hours from the mean.

The dot plot gives a dot to each measure for each time that it appears, hence it says the same thing as a table, in a different format.

The sum of the fifteen observations in this problem is given as follows:

0 x 1 + 1 x 5 + 2 x 3 + 3 x 5 + 4 x 1 = 30.

The mean of the data-set is given as the sum of all the observations divided by the number of values, hence:

30/15 = 2.

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