a) The particle is farthest to the left at t = 0.
b) The speed of the particle is decreasing at t = π.
c) The value of k is 2π.
a) To find the time at which the particle is farthest to the left, we need to determine when the particle's position is at its minimum on the x-axis. The position function x(t) = [tex]e^t^2 cos(t^2)[/tex] represents the particle's position at time t.
To find the minimum, we can take the derivative of x(t) with respect to t and set it equal to zero. Let's differentiate x(t) to find the velocity function v(t):
v(t) = [tex](1/2)e^t^2 (cos(t^2) - sin(t^2))[/tex]
Next, we solve the equation v(t) = 0 to find the critical points:
0 = [tex](1/2)e^t^2 (cos(t^2) - sin(t^2))[/tex]
Since [tex]e^t^2[/tex] is always positive, the critical points occur when cos([tex]t^2[/tex]) - sin([tex]t^2[/tex]) = 0. By solving this equation, we find that it is true for t = 0 and t = π/2.
Now, to determine which critical point corresponds to the particle being farthest to the left, we evaluate the positions at t = 0 and t = π/2:
x(0) = [tex]e^0^2 cos(0^2)[/tex]= 1 * 1 = 1
x(π/2) = e(π/[tex]2)^2[/tex] cos((π/[tex]2)^2[/tex]) = [tex]e^{(\pi ^{2/4)[/tex] * 0 = 0
The particle is farthest to the left when x(0) = 1. Therefore, the particle is farthest to the left at t = 0.
b) To determine if the speed of the particle is increasing or decreasing at t = π, we need to analyze the velocity function v(t).
Let's calculate the derivative of v(t) with respect to t to find the acceleration function a(t):
a(t) = [tex]d(v(t))/dt[/tex] = [tex]d^2x(t)/dt^2[/tex] = [tex]e^t^2 * (-2t^2[/tex] - 2) * [tex]sin(t^2)[/tex]
To determine if the speed is increasing or decreasing, we need to evaluate a(t) at t = π. Plugging in t = π into the acceleration function, we have:
a(π) = [tex]e^\pi ^2 * (-2\pi ^2[/tex] - 2) * si[tex]n(\pi ^2[/tex]) = [tex]e^\pi ^2 * (-2\pi ^2[/tex] - 2) * 0 = 0
Since the acceleration at t = π is zero, the speed of the particle is neither increasing nor decreasing at that time.
c) The total distance traveled by the particle can be calculated by integrating the absolute value of the velocity function v(t) with respect to t over the interval [0, 2π]. The expression given is:
∫ v(t) dt from 0 to k − ∫ v(t) dt from 0 to 2π
To find the value of k, we can evaluate the integral on the right side:
∫ v(t) dt from 0 to 2π = ∫ [(1/[tex]2)e^t^2[/tex] (co[tex]s(t^2[/tex]) - [tex]sin(t^2[/tex]))] dt from 0 to 2π
Evaluating this integral gives us the total distance traveled by the particle over the interval [0, 2π]. Since k represents a different upper limit, the integral from
0 to k will give us the distance traveled up to the time t = k.
To find the value of k, we need to find the total distance traveled. Since the integral from 0 to 2π represents the total distance, we have k = 2π.
Therefore, the value of k is 2π.
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PLSSS HELP 13 POINTS
The equation of the line perpendicular to y = 2 / 3 x - 4 and passes through (6, -2) is y = - 3 / 2x + 7.
How to represent equation in slope intercept form?The equation of a line can be represented in slope intercept form as follows:
y = mx + b
where
m = slope of the lineb = y-interceptThe 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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graph h(x)=(x-1)^2-9
The graph of h(x) = (x-1)^2 - 9 is a U-shaped parabola that opens upwards, with the vertex at (1, -9), and it extends indefinitely in both directions.
The function h(x) = (x-1)^2 - 9 represents a quadratic equation. Let's analyze the different components of the equation to understand the behavior of the graph.
The term (x-1)^2 represents a quadratic term. It indicates that the graph will have a parabolic shape. The coefficient in front of the quadratic term (1) implies that the parabola opens upwards.
The constant term -9 shifts the graph downward by 9 units. This means the vertex of the parabola will be at the point (1, -9).
Based on this information, we can draw the following conclusions:
The graph will be a U-shaped curve with the vertex at (1, -9).
The vertex represents the minimum point of the parabola since it opens upward.
The parabola will be symmetric with respect to the vertical line x = 1 since the coefficient of the quadratic term is positive.
The graph will extend indefinitely in both directions.
To accurately plot the graph, you can choose several x-values, substitute them into the equation to find the corresponding y-values, and then plot the points on the graph. Alternatively, you can use graphing software or calculators that can plot the graph of the equation for you.
Remember to label the axes and indicate the vertex at (1, -9) to provide a complete representation of the graph of h(x) = (x-1)^2 - 9.
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here is a number machine
input - x5 - -2 - output
whats the output when the input is 8
The output when the input is 8 in the given number machine is 1.
The given number machine input is - x5 - -2 - output. Now, we have to find the output when the input is 8. Let's understand how we can solve this problem.
What is a number machine? The numbering machine is an imaginary box or machine that takes in a number and does a specific task on it to produce an output.
This concept is usually taught to children in primary grades. It is a fun way to introduce basic mathematical operations such as addition, subtraction, multiplication, and division.
The machine we are dealing with here subtracts the input by 5 and then subtracts 2 from the result to get the output. We can write this as output = (input - 5) - 2 Now we have to find out what the output would be when the input is 8. We can substitute 8 into the formula to get: output = (8 - 5) - 2 Simplifying this, we get: output = 3 - 2output = 1
Therefore, the output when the input is 8 in the given number machine is 1.
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As he heads to the store, after how many minutes was Hakeem 1 blocks from his house?
The number of minutes Hakeem was 1 blocks from his house is one minutes
How many minutes was Hakeem 1 blocks from his house?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 dot plot shown represents the number of hours fifteen friends spent at the park last week.
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.
What is the dot plot?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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Mika wants to buy a condominium. He has the choice of buying it now or renting it with the option to buy at the end of 3 years. If he buys now, he could put $0 down, but he must pay closing costs of $7,100. His monthly mortgage payment will be $675.
Mika decides to rent instead of buy because it is the cheapest option over the first 3 years. His move-in costs are one month's rent and a $750 security deposit, and he would still need to pay his first month's rent on top of these move-in costs. To the nearest dollar, what is the maximum amount of monthly rent payment he could pay?
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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360-[6*6+4(5*2*2*2)-6*2)]
Answer:
169
Step-by-step explanation:
360-[36+160]-36
360-160-72
169
Find the variance of the data. 198, 190, 245, 211, 193, 193
bar x=205
Variance(o2)=?
Round to the nearest tenth.
The variance of the data-set in this problem is given as follows:
σ² = 366.3.
How to obtain the variance of the data-set?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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Which shape is always a parallelogram?
a hexagon, because it has 3 pairs of parallel sides
a rectangle, because it has 2 pairs of parallel sides
a trapezoid, because it has 1 pair of parallel sides
a quadrilateral, because it has 4 sides
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.
Explanation: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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What is a tessellation, how are tessellations used, and what must happen at vertices in order for polygons to tessellate?
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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True or false: There is no tax jump from 0.33E − 15,207.50 to 0.35E − 21,346.50.
true
false
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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Solve y = 3x2 + 6x + 4
y = −3x2 + 4
show ALL work and solutions
Ill give brainliest
please no wrong answers this time
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).
Question 2 of 10
How many solutions does the system of equations below have?
y=3x+4
y+6= 3x
OA. Exactly 1 solution
B. No solution
OC. More than 1 solution
OD. At least 1 solution
SUBMIT
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.
if the line ax+by+c=0 touches the circle x2+y2-2x=5/3 and is normal to the circle x2+y2+2x-4y+1=0 then find the the value of (a,b)?
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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Identify the correct measure of the distance between the compass points, to the nearest
1/8 inch.
Answer:
(d) 5/8 in
Step-by-step explanation:
You want the measure indicated by the compass points in the figure.
Ruler marksThe 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>
The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 23.5 for a sample of size 775 and standard deviation 12.2. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 95% confidence level). Enter your answer as a tri-linear inequality accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).
The 95% confidence interval for the effectiveness of the blood-pressure drug is given as follows:
[tex]22.6 < \mu < 24.4[/tex]
How to obtain the confidence interval?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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A triangular truss is shown in the figure. Find angle theta
Answer:
40.45°
Step-by-step explanation:
You want the angle opposite the side of length 13 ft in a triangle with the other sides being 16 ft and 20 ft.
Law of cosinesThe law of cosines tells you ...
c² = a² +b² -2ab·cos(C)
Then angle C is ...
C = arccos((a² +b² -c²)/(2ab))
In the given triangle, this is ...
C = arccos((16² +20² -13²)/(2·16·20)) = arccos(487/640) ≈ 40.453°
The measure of angle θ is about 40.45°.
<95141404393>
Answer:
Step-by-step explanation:
Simplify the expression so there is only one positive power for the base, -5.
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)
PLEASE ANSWER AND FILL IN THE BOX if needed
There is no solution in the system
How to determine the solution to the systemFrom the question, we have the following parameters that can be used in our computation:
The augmented matrix
In the augmented matrix, we have
Rows = 2
Columns = 4
This means that
there are 2 equations in the system and there are 3 variables
The general rule is that
The number of variables must be equal to or less than the number of equations
Hence, there is no solution in the system
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In a clinical trial, 17 out of 846 patients taking a prescription drug daily complained of flulike symptoms. Suppose that it is known that 1.6% of patients taking competing drugs complain of flulike symptoms. Is there sufficient evidence to conclude that more than 1.6% of this drug's users experience flulike symptoms as a side effect at the a= 0.05 level of significance?
Please help me solve
FIND THE TEST STATISTIC,
Z=
Find the P-Value
P=
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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Eliminate the parameter t to find a simplified Cartesian equation of the form y=mx+b for
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.
which equation represents the slope intercept form of the line when the y intercept is (0,-6) and the slope is -5
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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Find the value of x . Please Help Urgent!!
Answer:
x = 13
Step-by-step explanation:
Since [tex]\angle M\cong \angle Y[/tex], then we set the angles equal to each other:
[tex]m\angle M=m\angle Y\\52^\circ=(4x)^\circ\\52=4x\\13=x[/tex]
Therefore, x=13
ABC Inc. recently issued $1,000 par bonds at a 8.40% coupon rate. If the bonds have 18 years to maturity and current price of $885, what is the yield to maturity? Assume semi-annual compounding.
Note: Convert your answer to percentage and round off to two decimal points. Do not enter % in the answer box.
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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help me please i need it fast!! ill give brainliest please
Find x
(4x+6)
The measure of x in the circle is 21 degrees
Finding the measure of x in the circleFrom 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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you deposit $500 inna saving account tgat earns 2% intrest componded anually each year. How much money is in your account after 4 years? HINT y=a(l+r) ^t
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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What is equivalent of square root of 200 in simplest form
Answer:
10[tex]\sqrt{2}[/tex]
Step-by-step explanation:
√200 = √(2 × 2 × 2 × 5 × 5)
√200 = (√2)2× (√5)2× √2
√200 = 10√2
Answer:
The square root of 200 in its simplest form is 10√2 is the answer.
This can be done if we know the prime factorization of a number we can right the radical form of the square root of that number.
As a result the prime factorization of 200 is 2×2×2×5×5 so in that way the simplest form of square root of 200 is 10√2.
Step-by-step explanation:
in many cases, property taxes when you own a home are paid every six months, homeowner's insurance is paid once per year, and car insurance is paid every six months. One homeowner pays 1470.00 in property taxes twice a year, 918.00 in homeowner's insurance annually, and makes car insurance payments of 285.78 and 359.79 every six months. If this homeowner wants to spread these expenses out by putting some money each month into a savings account, how much should she put aside monthly? Round your answer to the nearest cent.
The homeowner should put aside $375.30 each month in order to save up for these expenses. Rounded to the nearest cent, this is $375.31.
The question asks us to determine how much a homeowner should put aside each month in order to save up for property taxes, homeowner's insurance, and car insurance expenses that come up every six months and annually.
To solve this problem, we can add up the total cost of all these expenses and divide by the number of months in a year, then round to the nearest cent.
Let's begin by finding the total cost of all these expenses. The homeowner pays property taxes twice a year, so that's a total cost of $1470 x 2 = $2940. The homeowner's insurance is paid once per year, with a cost of $918. The car insurance is paid twice a year, with costs of $285.78 + $359.79 = $645.57.
Adding up all these costs, we get: $2940 + $918 + $645.57 = $4503.57.
To determine how much to put aside each month, we divide this total by 12 (the number of months in a year): $4503.57 ÷ 12 = $375.30.
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Ralph chase plans to sell a piece of property for $145000. He wants the money to be paid off in two ways- and short term note at 9% and a long term note at 7% interest. Find the amount of each note if the total anual interest paid is $11650
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.
jewelry company makes copper heart pendants. Each heart uses 0.75 in of copper and there is o.323 pound of copper per cubic inch. If copper costs $2.25 per pound, what is the total cost of 24 copper hearts?
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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