The volume of the triangular prism below is 120 cubic units. Solve for X and for the surface area.

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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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 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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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 given statement "There is no tax jump from 0.33E − 15,207.50 to 0.35E − 21,346.50" is false.

The tax jump from 0.33E − 15,207.50 to 0.35E − 21,346.50 is not zero. Let us look at how this is not true.

Firstly, 0.33E − 15,207.50 and 0.35E − 21,346.50 are both amounts of tax that need to be paid. E here stands for exponential notation of the number 10.

For example, 0.33E − 15,207.50 = 0.33 x 10 ^ -15,207.50.

This means that 0.33E − 15,207.50 is 0.33 multiplied by 10 raised to the power of -15,207.50.

Similarly, 0.35E − 21,346.50 = 0.35 x 10 ^ -21,346.50 which means 0.35E − 21,346.50 is 0.35 multiplied by 10 raised to the power of -21,346.50.

It is important to note that the power of E in 0.35E − 21,346.50 is higher than that of 0.33E − 15,207.50. This means that the second tax amount is lower than the first.

However, the tax jump from 0.33E − 15,207.50 to 0.35E − 21,346.50 is still not zero. A tax jump is the difference in the amount of tax paid between two different amounts.

Therefore, the difference between the two taxes is:

= 0.35 x 10 ^ -21,346.50 - 0.33 x 10 ^ -15,207.50

= 0.002E-2134650 - 0.0033E-1520750

= 0.00000167 - 0.000033 = -0.00003133

The tax jump is equal to 0.00003133 which is not zero.

Therefore, the given statement is false.

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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)

Answer:

a rectangle, because it has 2 pairs of parallel sides

Step-by-step explanation:

A parallelogram is a two-dimensional figure with two sets of parallel lines and equal opposite-interior angles. A hexagon has too many sides to qualify, trapezoids only have one set of parallel lines, and quadrilaterals can have anywhere from 0 to 2 sets of parallel sides. Because of this, these three other options are eliminated

A rectangle is always a parallelogram because, by definition, a parallelogram is a four-sided plane rectilinear figure with opposite sides parallel which fits the description of a rectangle.

The correct answer to which shape is always a parallelogram is a rectangle, because it has 2 pairs of parallel sides. By definition, a parallelogram is a four-sided plane rectilinear figure with opposite sides parallel. This means that a quadrilateral with two sets of parallel sides is a parallelogram, which fits the description of a rectangle. Other options like hexagon and trapezoid do not always adhere to this definition and hence can't be considered as a parallelogram.

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The amount of money in your account after 4 years would be $541.22.

We might utilize the accompanying recipe to work out how much money will be in your ledger following four years with a 2% yearly funding cost:

A = P(1 + r)ᵗ

Where:

A is the final amount.

P is the principal amount(initial deposit).

r means the interest rate (in decimal structure).

t is the number of years

Given:

P = $500

r = 2% = 0.02 (expressed as a decimal)

t = four years

Associating these qualities to the situation:

A = $500(1 + 0.02)⁴

Making the condition:

A = $500(1.02)⁴

A = $500(1.082432)

A ≈ $541.22

Subsequently, following four years, the cash in your ledger would be around $541.22.

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A tessellation is a pattern made by repeating geometric shapes without any gaps or overlaps. These shapes, called tiles or polygons, fit together perfectly to cover a plane or a surface. Tessellations can be found in various forms of art, architecture, and design. They are used to create visually appealing patterns and decorations, as well as to explore mathematical concepts.

Tessellations are utilized in various practical applications, such as tiling floors, walls, and pavements, designing mosaics and quilts, and creating computer graphics and textile patterns. They are also studied in mathematics to understand concepts like symmetry, geometry, and transformations.

For polygons to tessellate, certain conditions must be met at their vertices. At each vertex, the angles formed by the polygons must add up to a whole number of degrees, typically 360 degrees. In other words, the sum of the interior angles of each polygon meeting at a vertex must be a multiple of 360 degrees.

This ensures that the polygons can fit together seamlessly without leaving any gaps or overlaps. Examples of polygons that tessellate include equilateral triangles, squares, and hexagons, as their angles add up to 360 degrees at each vertex.

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Step-by-step explanation:

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

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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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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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:

  (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.

<95141404393>

There are infinitely many solutions for a and b that satisfy the given conditions, as long as they satisfy the above equations.

To solve this problem, we need to use the concepts of tangent and normal lines to a circle.

First, we find the equation of the given circle[tex]x^2+y^2-2x=5/3[/tex]. Completing the square, we get [tex](x-1)^2+y^2=8/3[/tex].

To find the tangent line to this circle that is also normal to the circle [tex]x^2+y^2+2x-4y+1=0[/tex], we need to first find the point of intersection between the two circles.

By solving the simultaneous equations of the two circles we obtain the point of intersection [tex](-1/2, y=\sqrt(11/12))[/tex].

We then find the gradient of the tangent at this point by differentiating the equation of the circle x^2+y^2-2x=5/3. At the point (-1/2, √(11/12)), the gradient of the tangent is m = 1/√(33/4).

Since the tangent line is also normal to the circle x^2+y^2+2x-4y+1=0, its gradient is the negative reciprocal of the gradient of the tangent at the point of intersection, which is m'= -√(33/4).

Using the point-gradient form of a straight line, we can then write the equation of the tangent line as y-√(11/12) = (-√(33/4))(x+1/2).

To find the values of a and b that satisfy this equation of the tangent line and also the equation ax+by+c=0, we substitute the expression for y in terms of x into the second equation:

a(x)-b(√(33/4))(x+1/2)+c= 0 (ax-b(√33/4)x)+(-b(√33/4)/2+a)+c=0

We now compare the coefficients of x and constants in each equation

ax-b(√33/4)x = 0 -b(√33/4)/2+a+c = 0

We now have a system of two equations in two unknowns (a and b). Solving this system of equations we get a = (b√33/4) - 2c and plugging this into the second equation we get b = c/√(33/4).

Therefore, there are infinitely many solutions for a and b that satisfy the given conditions, as long as they satisfy the above equations.

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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 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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Answer:

169

Step-by-step explanation:

360-[36+160]-36

360-160-72

169

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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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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From the first equation you can get that -2x = 36 + 2t; and after adding those equations to each other we get that y - 2x = 3 - 2t + 36 + 2t = 39; y = 2x + 39.

The answer is 2x + 39.

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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Answer:

B, No solution

Step-by-step explanation:

If two lines are graphed, the point they intersect is the solution. However, if the slope is the same, they will never intersect

In the first and second equation, the slopes are both 3 so they will never intersect.

The variance of the data-set in this problem is given as follows:

σ² = 366.3.

The variance of a data-set is calculated as the sum of the differences squared between each observation and the mean, divided by the number of values.

The mean for this problem is given as follows:

205.

Hence the sum of the differences squared is given as follows:

SS = (198 - 205)² + (190 - 205)² + (245 - 205)² + (211 - 205)² + (193 - 205)² + (193 - 205)²

SS = 2198.

There are six values, hence the variance is given as follows:

σ² = 2198/6

σ² = 366.3

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Answer:

Let's denote the amount of the short-term note as x and the amount of the long-term note as y. We know that:

1. The total amount of the property is $145,000, so x + y = $145,000.

2. The total annual interest is $11,650, which is the sum of the interest from the short-term note (9% of x) and the long-term note (7% of y). So, 0.09x + 0.07y = $11,650.

We now have a system of two equations that we can solve to find the values of x and y.

Let's solve this system of equations:

1. Multiply the first equation by 0.07: 0.07x + 0.07y = $10,150.

2. Subtract this from the second equation: 0.02x = $1,500.

3. Solve for x: x = $1,500 / 0.02 = $75,000.

Substitute x = $75,000 into the first equation to find y:

$75,000 + y = $145,000

y = $145,000 - $75,000 = $70,000.

So, the short-term note is $75,000, and the long-term note is $70,000.

The equation of the line perpendicular to  y = 2 / 3 x - 4 and passes through (6, -2) is y = - 3 / 2x + 7.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

The slopes of perpendicular lines are negative reciprocals of one another.

Therefore, the slope of the line perpendicular to y = 2 / 3 x - 4 is - 3 / 2.

Hence, let's find the line as its passes through (6, -2).

Therefore,

y = - 3 / 2 x + b

-2 = - 3 / 2(6) + b

-2  = -9 + b

b = -2 + 9

b = 7

Therefore, the equation of the line is y = - 3 / 2x + 7.

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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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The yield to maturity for the ABC Inc. bonds is 4.95%.

The yield to maturity (YTM) represents the effective interest rate that an investor would earn if they hold the bond until its maturity date.

To calculate the YTM for the ABC Inc. bonds, we need to find the interest rate that equates the present value of the bond's cash flows (coupon payments and par value) to its current price.

Given that the bond has a $1,000 par value and an 8.40% coupon rate, it pays a coupon of $42 (8.40% × $1,000 / 2) semi-annually for 18 years, totaling 36 coupon payments. At maturity, the bond will also repay the par value of $1,000.

To calculate the YTM, we can use a financial calculator or a spreadsheet software. By inputting the cash flows and solving for the interest rate, we find that the YTM is approximately 4.95% (rounding to two decimal points).

Therefore, the yield to maturity for the ABC Inc. bonds is 4.95%.

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