The sum of the given polynomial [tex](7x^{3} - 4x^{2} ) + (2x^{3} - 4x^{2} ).[/tex]is [tex]9x^{3} - 8x^{2}[/tex].
How to add the polynomials?
Polynomials can be added or subtracted when they contain like terms, which are the same alphabets with the same powers.
Whereas there are no such rules for multiplication, any phrase with any power can be multiplied. The powers of the terms are then modified in accordance with exponentiation principles.
The following polynomial equation is [tex](7x^{3} - 4x^{2} ) + (2x^{3} - 4x^{2} ).[/tex]
Polynomial addition is accomplished by combining 'like terms'.
As a result, sorting and adding
= [tex](7x^{3} - 4x^{2} ) + (2x^{3} - 4x^{2} ).[/tex]
= [tex]7x^{3} + 2x^{3} - 4x^{2} - 4x^{2}[/tex]
= [tex]9x^{3} - 8x^{2}[/tex]
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Complete question:
What is the sum of the polynomials? (7x3 - 4x2) + (2x3 - 4x2)
The Wigwam Motel in Holbrook, Arizona is famous for its large tepees, which are shaped like cones. Each of these units has a base diameter of 14 feet and a height of 32 feet. (a) What is the slant height of the Teepees at the Wigwam Motel? Please make sure to use the Pythagorean Theorem and show your work. (b) (1. 5 pts) For extra credit, how much floor space, in square units, is available inside each tepee?
The Wigwam Motel in Holbrook, Arizona is famous for its large tepees shaped like cones. the floor space inside each tepee is approximately 153.94 square feet.
(a) To find the slant height of the tepee, we can use the Pythagorean theorem. The slant height is the hypotenuse of a right triangle with the height and the radius of the base as the legs.
The radius of the base is half of the diameter, so r = 14/2 = 7 feet. The height of the tepee is 32 feet. Let's call the slant height "s".
Using the Pythagorean theorem, we have:
s² = r² + h²
s² = 7² + 32²
s² = 49 + 1024
s² = 1073
s = sqrt(1073)
s ≈ 32.77 feet
Therefore, the slant height of the tepee is approximately 32.77 feet.
(b) To find the floor space inside the tepee, we need to calculate the area of the circular base. The formula for the area of a circle is A = πr², where A is the area and r is the radius.
A = π(7)²
A = 49π
A ≈ 153.94 square feet
Therefore, the floor space inside each tepee is approximately 153.94 square feet.
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a classroom is arranged with 8 seats in the front row 10 seats in the middle row and 12 seats in the back what is the probability that that the first student who enters the room will be assigned to the front row
The probability that the first student who enters the room will be assigned to the front row is 4/15.
What is probability?The probability of an event is calculated by dividing the total number of possible outcomes by the number of possible outcomes.
given that ,
A classroom is arranged with 8 seats in the front row 10 seats in the middle row and 12 seats
The total number of seats in the classroom is 8 + 10 + 12 = 30.
There are thirty seats to choose from because there is only one student entering the room.
However, we want to determine the likelihood that the student will be assigned to one of the eight seats in the front row.
Therefore, the probability of assigning the front row to the first student who enters the room is:
P(front row) = 8/30
Simplifying this fraction gives:
P(front row) = 4/15
As a result, there is a probability of 4/15, or roughly 0.267, that the first student who enters the room will be assigned to the front row.
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rebecca and michael took a survey of the number of siblings that each of their classmate had. what percent of the total classmates have 2 siblings
The percentage of total classmates that have 2 siblings is calculated as follows:
Percentage = number of students with 2 siblings / total number of students x 100%.
How to obtain the percentage?Before obtaining the percentage, we must obtain the proportion, which is given by the division of the number of desired outcomes by the number of total outcomes, as follows:
number of students with 2 siblings / total number of students.
Then the percentage is obtained multiplying by 100%, as follows:
Percentage = number of students with 2 siblings / total number of students x 100%.
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If the length of a rectangle prism is doubled, it’s width is tripled, and it’s height remains the same, what is the volume of the new rectangle prism?
If in a rectangular-prism, the length is doubled, width is tripled and height is same, then the volume of new rectangular prism will be 6 times the original-prism.
The "Volume" of a 3-D object is defined as the amount of space that object occupies in three-dimensional space. It is a measure of the total capacity or size of the object
Volume of a rectangular prism is ⇒ Volume = Length × Width × Height,
If the length of the rectangular prism is doubled, the new length would be 2 times the original length.
If the width is tripled, the new width would be 3 times the original width, and
If the height remains the same, it would be the same as the original height.
Let the original length be = "L", width be = "W", and height be = "H",
So, New Length = 2L , New Width = 3W, New Height = H (remains unchanged),
So, volume of new rectangular prism is :
⇒ New Volume = (New Length)×(New Width)×(New Height),
⇒ (2L) × (3W) × H
⇒ 6LWH
Therefore, volume of "new-rectangular prism' is 6 times volume of original rectangular prism.
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pls hlp thx so much !!!!!!!!!!!!!!
On solving the provided question, we can say that
the measurement of angle B is 40 degrees.
What is equation?A mathematical equation is a formula that connects two statements and denotes equivalence with the equals symbol (=). An equation is a mathematical statement that shows the equality of two mathematical expressions in algebra. In the equation 3x + 5 = 14, for example, the equal sign separates the variables 3x + 5 and 14.
A mathematical formula describes the connection between the two sentences that occur on opposite sides of a letter. The symbol and the single variable are frequently the same. As in 2x - 4 equals 2, for instance.
Supplementary angles add up to 180 degrees. Therefore, we can write the equation:
A + B = 180
Substituting the given expressions for A and B, we get:
(4x - 16) + (x + 1) = 180
Simplifying the left side, we get:
5x - 15 = 180
Adding 15 to both sides, we get:
5x = 195
Dividing both sides by 5, we get:
x = 39
Therefore, the measurement of angle B is:
B = x + 1 = 39 + 1 = 40 degrees.
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Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle C?
The measure of angle C is 80°
What is a cyclic quadrilateral?A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle. It can also be called inscribed quadrilateral.
A theorem if circle geometry states that the opposite angles of a cyclic quadrilateral are supplementary. This means the sum of. opposite angles of a cyclic quadrilateral is 180°
Therefore 3x-59+2x-1 = 180
5x -60 = 180
5x = 180+60
5x = 240
x = 240/5
x = 48
angle A = 2x+4 = 2×48+4
= 100°
therefore angle C = 180-(angle A)
C = 180-100
= 80°
therefore the measure of angle C is 80°
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A cone has a radius of 6 m and a height of 24 m. What is the volume of the cone in terms of π? 864π m3 432π m3 288π m3 144π m3
The volume of the cone in terms of π is 288π cubic meters, which corresponds to option (c) in the given answer choices.
The formula for the volume of a cone is:
V = (1/3)πr^2h
where V is the volume, r is the radius, and h is the height of the cone.
Plugging in the given values, we get:
V = (1/3)π(6 m)^2(24 m)
V = 288π m^3
Therefore, correct option is C.
This is because π is an irrational number that cannot be expressed as a finite decimal or fraction, so any approximation would be less precise than the exact value in terms of π.
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What is 2 X 2 X 8 + 25?
Answer:
57
Step-by-step explanation:
2 X 2 = 4
4 X 8 = 32
32 + 25 = 57
3. Find the area of the shape below. Break
the larger shape into smaller pieces if needed.
8.4m
4m
11.4m
8m
ak direst
boyut ved FI
So, the area of the shape is 164.4 square meters.
What is area?In geometry, area is the measure of the size of a two-dimensional surface or region. It is the amount of space inside the boundaries of a flat object such as a polygon, circle, or rectangle. Area is measured in square units, such as square meters (m²), square centimeters (cm²), square feet (ft²), square inches (in²), and so on. To calculate the area of a shape, you typically need to use a specific formula depending on the type of shape, such as base times height for a triangle, or length times width for a rectangle.
Here,
The area of the shape is equal to the sum of the areas of these smaller pieces. We can calculate each area as follows:
The area of the rectangle on the left is 4m x 8.4m = 33.6 square meters.
The area of the rectangle on the right is 8m x 11.4m = 91.2 square meters.
The area of the triangle on the top is (8.4m x 4m) / 2 = 16.8 square meters.
The area of the triangle on the bottom is (11.4m x 4m) / 2 = 22.8 square meters.
Therefore, the total area of the shape is:
33.6 + 91.2 + 16.8 + 22.8 = 164.4 square meters
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Need in deed classrooms participate in great service learning projects! One classroom took 254 photos of their Saving Honeybees project. Another classroom took 15 times as many pictures of their Advocacy Project for Homeless Pets. How many photos did the Advocacy Project for Homeless Pets classroom take? Show or explain your work
Answer:
To solve the problem, we can use multiplication. We know that one classroom took 254 photos and the other classroom took 15 times as many pictures. So, we can write an equation to represent the situation:
Number of photos taken by Advocacy Project for Homeless Pets classroom = 254 x 15
We can then solve this equation using multiplication.
254 x 15 = 3810
Therefore, the Advocacy Project for Homeless Pets classroom took 3,810 photos.
Find the measure
Find the measure
of the complement of a 14° angle.
of the supplement of a 14° angle.
The Complement of a 14° angle is 76°, while the supplement of 14° angle is 166°.
What is the Complement of an Angle?Recall that two angles that have a sum of 90 degrees are referred to as complementary angles. This implies that, if x is an angle, its complement is (90 - x).
Also, the supplement of an angle is the angle measure that is added to it to make it 180 degrees. This implies that if x is an angle, its supplement would be (180 - x).
Therefore, we have:
Complement of a 14° angle = 90 - 14 = 76°.
Supplement of 14° angle = 180 - 14 = 166°.
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The grid you see below is in the shape of a rectangle. What is the area, in square
units, of the shaded part?
Answer:
12 square units
Step-by-step explanation:
interior angles of rectangles are right angles
Area of the triangle: 6 x 4 / 2
Jordan studied for his science test for 2 ¼ hours on Saturday and 1 ½ hours Sunday. How many hours did he spend studying for science this weekend?
2 ¼ hours + 1 ½ hours = 3 ¾ hours
Jordan studied for his science test for 3 ¾ hours this weekend.
What is the purpose of science?Science is a systematic process that produces knowledge in the form of testable predictions and universe-related explanations that can be organized and placed into order.
In general, science entails an effort to learn about universal truths or how fundamental laws work. Learning about the components of the universe and how they operate right now, in the past, and perhaps in the future is done through science.
Although science is intricate and multifaceted, its most significant traits are simple: Learning understanding what is in the natural world, how it functions, and how it came to be the way it is through science.
2 ¼ hours + 1 ½ hours = 3 ¾ hours
Jordan studied for his science exam for 3 ¾ hours this weekend.
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Jordan spent a total of 3 hours and 45 minutes studying for his science test this weekend.
what is arithmetic sequence.
An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.
Jordan studied for 2 ¼ hours on Saturday and 1 ½ hours on Sunday for his science test. To find the total number of hours he studied, we can add these two amounts.
2 ¼ hours is the same as 2 + ¼ hours, or 2 hours and 15 minutes.
So, we have:
2 hours and 15 minutes (Saturday) + 1 hour and 30 minutes (Sunday)
To add these two amounts, we can first add the hours and then add the minutes separately.
2 hours + 1 hour = 3 hours
15 minutes + 30 minutes = 45 minutes
Therefore, Jordan spent a total of 3 hours and 45 minutes studying for his science test this weekend.
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Factor ax-2bx + ay-2by
You may need to use the appropriate appendix table or technology to answer this question. The following results are for independent random samples taken from two populations. Sample 1 Sample 2 n1 = 20 n2 = 30 x1 = 22.8 x2 = 20.1 s1 = 2.2 s2 = 4.6 (a) What is the point estimate of the difference between the two population means? (Use x1 − x2. ) 2.7 (b) What is the degrees of freedom for the t distribution? (Round your answer down to the nearest integer.) (c) At 95% confidence, what is the margin of error? (Round your answer to one decimal place.) (d) What is the 95% confidence interval for the difference between the two population means? (Use x1 − x2. Round your answers to one decimal place.)
a). The difference between the two population means is estimated at a location to be 2.7.
b). 49 different possible outcomes make up the t distribution. The margin of error at 95% confidence is 1.7.
c). The range of the difference between the two population means' 95% confidence interval is (0.0, 5.4).
d). The (0.0, 5.4) represents the 95% confidence interval for the difference among the two population means.
What is standard deviations?The variability or spread in a set of data is commonly measured by the standard deviation. The deviation between the values in the data set and the mean, or average, value, is measured. A low standard deviation, for instance, denotes a tendency for data values to be close to the mean, whereas a high standard deviation denotes a larger range of data values.
Using the equation [tex]x_1-x_2[/tex], we can determine the point estimate of the difference between the two population means. In this instance, we calculate the point estimate as 2.7 by taking the mean of Sample
[tex]1(x_1=22.8)[/tex] and deducting it from the mean of Sample [tex]2(x_2=20.1)[/tex].
With the use of the equation [tex]df=n_1+n_2-2[/tex], it is possible to determine the degrees of freedom for the t distribution. In this instance, the degrees of freedom are 49 because [tex]n_1[/tex] = 20 and [tex]n_2[/tex] = 30.
We must apply the formula to determine the margin of error at 95% confidence [tex]ME=t*\sqrt[s]{n}[/tex].
The sample standard deviation (s) is equal to the average of [tex]s_1[/tex] and [tex]s_2[/tex] (3.4), the t value with 95% confidence is 1.67, and n is equal to the
average of [tex]n_1[/tex] and [tex]n_2[/tex] (25). When these values are entered into the formula, we get [tex]ME=1.67*\sqrt[3.4]{25}=1.7[/tex].
Finally, we apply the procedure to determine the 95% confidence interval for the difference between the two population means [tex]CI=x_1-x_2+/-ME[/tex].
The confidence interval's bottom limit in this instance is [tex]x_1-x_2-ME2.7-1.7=0.0[/tex] and the upper limit is [tex]x_1+x_2+ME=2.7+1.7=5.4[/tex].
As a result, the (0.0, 5.4) represents the 95% confidence interval for the difference among the two population means.
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The perimeter of a rectangle is 24.
Write the function that describes its area in terms of one of the sides.
Answer:
2l + 2w = 24, so l + w = 12
A(l) = l(12 - l)
Use the formula from question 12 to estimate the amount of material required to cover Firm 1's structure, not including the floor. Show your calculations
formula: 2(lw + wh + lh)
Answer:
Step-by-step explanation:
Total enclosed space of the structure 1's = 6597.35ft³Firms 1's structure is in the form of the cylinder. So the formula used for the calculation of the enclosed space or volume of the cylinder is:
Volume of the cylinder = πr²h .........(i)
where r = radius of the structure
Diameter(d) = 70ft
Given r = 70/2 = 35ft
h = Height of the structure
Given h = 60ft
By substituting the values of radius (r) and height (h) in equation (i), we get
V = π(35)²(60)ft³
V = 3.14(35)(60)ft³
V = 6597.345ft³
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Can somebody please help me with some of these math questions.
The ratio of the areas of two similar polygons is equal to the square of the ratio of their corresponding side lengths. Since the scale factor of the polygons is 3:8, the ratio of their corresponding side lengths is 3/8. Therefore, the ratio of their areas is (3/8)^2 = 9/64.
How to explain the ratioThe ratio of the areas of two similar circles is equal to the square of the ratio of their radii. Since the scale factor of the circles is 2:3, the ratio of their radii is 2/3. Therefore, the ratio of their areas is (2/3)^2 = 4/9. Since the area of the larger circle is 64π, the area of the smaller circle is (4/9) * 64π = 28.44π.
The ratio of the areas of two similar polygons is equal to the square of the ratio of their corresponding side lengths. Since the ratio of the areas of the two regular pentagons is 150√3/54√3 = 25/9, the ratio of their corresponding side lengths is the square root of the ratio of their areas, which is √(25/9) = 5/3. Therefore, the ratio of their perimeters is 5:3, since the perimeters of regular polygons are directly proportional to their side lengths.
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Which scatter plot shows a negative nonlinear association?
A.
Scatter plot graph in quadrant 1 of a coordinate plane. 11 points are plotted approximated at (2, 5), (1.5, 11.5), (3.1, 6.1), (4, 9), (5.9, 12.5), (7, 6), (7.5, 8.5), (8, 11), (8.9, 4.1), (9, 8), and (11, 10).
B.
Scatter plot Graph on a coordinate plane. Closed points plotted at (3, 11), (3, 12), (4, 11), (4.2, 12), (5, 10.8), (5.4, 12), (6, 10), (6.5, 11), (6.9, 9), (7.1, 6), (7.1, 7.7), (7.8, 9), (8.1, 6.1), (8, 7.5).
C.
Scatter plot in quadrant 1 of a coordinate plane. 10 points are plotted at (2, 11), (2.5, 9), (3, 10), (4, 8), (5, 8.2), (5.5, 6.5), (6.5, 7), (6.5, 5), (8, 5.8), and (9, 4).
D.
Scatter plot in quadrant 1 of a coordinate plane. 10 points are plotted at (2, 3), (2.8, 4.2), (3.8, 3.2), (4, 4.6), (4, 6), (5, 5), (6, 8), (7, 7), (7.8, 9.2), and (8.9, 9.1).
The scatter plot that shows a negative nonlinear association is option C.
What is scatter plot?A scatter plot is a type of graph that displays the relationship between two variables. It is used to show how much one variable is affected by another variable. One variable is plotted on the horizontal axis (x-axis) and the other variable is plotted on the vertical axis (y-axis).
Here,
In this scatter plot, as the x-axis values increase, the y-axis values initially increase and then decrease. This type of association is referred to as a negative nonlinear association, where the direction of the association is negative (decreasing) and the shape of the association is nonlinear (not a straight line). The other options either show a positive association (increasing values of x and y) or a linear association (a straight line).
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Please help me.
Giving 40 points
a) i) The pressure on the ground by snowshoe hare is 0.07 N/cm².
ii) The pressure on the ground by European hare is 0.15 N/cm².
b) The snowshoe hare is suited to living in snow because it has a larger surface area of feet.
a) The pressure on the ground can be calculated by dividing the force on the ground due to weight by the total surface area of the feet.
i) For the snowshoe hare, the pressure on the ground is:
Pressure = Force on ground / Total surface area of feet
Pressure = 14 N / 200 cm²
Pressure = 0.07 N/cm²
ii) For the European hare, the pressure on the ground is:
Pressure = Force on ground / Total surface area of feet
Pressure = 38 N / 250 cm²
Pressure = 0.15 N/cm²
b) The snowshoe hare is suited to living in snow because it has a larger surface area of feet than the European hare and exerts less pressure on the ground. This allows the snowshoe hare to move more easily over the snow without sinking.
Additionally, the snowshoe hare has fur on the soles of its feet, which provides additional insulation against the cold snow. These adaptations help the snowshoe hare survive in its snowy environment by allowing it to move and find food more easily.
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Write an equation of the line that passes through (-4, 1) and is perpendicular to the line y = 2x + 3.
y=-1/2x-1 is equation of the line that passes through (-4, 1) and is perpendicular to the line y = 2x + 3
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
We have to find the equation of the line that passes through (-4, 1) and is perpendicular to the line y = 2x + 3.
The slope of given line is 2
The slope of perpendicular line is -1/2
Now let us find the y intercept
1=-1/2(-4)+b
1=2+b
b=-1
Now the equation is y=-1/2x-1
Hence, equation of the line that passes through (-4, 1) and is perpendicular to the line y = 2x + 3 is y=-1/2x-1.
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What is 15.98 round to the nearest tenth
Answer:
16
Step-by-step explanation:
To round 15.98 to the nearest tenth, we look at the digit in the hundredths place which is 8. Since 8 is greater than or equal to 5, we round up the digit in the tenths place which is 9. Therefore, rounding 15.98 to the nearest tenth gives us 16.
Answer:
16
Step-by-step explanation:
15 . 98
8 round up is 10
0.10 + 0.9 = 1
15 + 1 = 16
Look at this table:
X
0
1
2
3
4
y
3
6
12
24
48
Write a linear function (y = mx + b) or an exponential function (y = a(b)*) that models the
data.
The exponential function that represents the data in the table is given as follows:
y = 3(2)^x.
How to define an exponential function?The standard definition of an exponential function is given as follows:
y = a(b)^x.
In which the parameters are given as follows:
a is the initial value, representing the value of y when x = 0.b is the rate of change.From the table, when x = 0, y = 3, hence the parameter a is given as follows:
a = 3.
When x is increased by one, y is multiplied by 2, hence this is an exponential function and the parameter b is given as follows:
b = 2.
Hence the function is defined as follows:
y = 3(2)^x.
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A deck of cards is shuffled, if we want to know the chance that the top card is the ace of spades or the bottom card is the ace of spades, we will use: Neither of the rules Addition rule Multiplication rule & Either of the rules
We will use the "Either of the rules" to calculate the probability that either the top card is the ace of spades or the bottom card is the ace of spades.
The either of the rules states that the probability of either of two mutually exclusive events occurring is the sum of their individual probabilities. In this case, the events are the top card being the ace of spades and the bottom card being the ace of spades. Since the two events are mutually exclusive (the ace of spades cannot be both at the top and at the bottom of the deck), we can add their probabilities to get the total probability.
The probability of the top card being the ace of spades is 1/52 (since there is only one ace of spades in the deck of 52 cards), and the probability of the bottom card being the ace of spades is also 1/52 (assuming that the deck has been sufficiently shuffled). Therefore, the probability of either the top card or the bottom card being the ace of spades is:
P(top or bottom is ace of spades) = P(top is ace of spades) + P(bottom is ace of spades)
= 1/52 + 1/52
= 2/52
= 1/26
So the chance that either the top card is the ace of spades or the bottom card is the ace of spades is 1/26 or approximately 0.038 or 3.8%.
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The probability is 2/52 or 1/26.
To find the chance that the top card is the ace of spades or the bottom card is the ace of spades, you will use the
Addition rule.
Calculate the probability of the top card being the ace of spades:
There are 52 cards in a deck, and 1 ace of spades, so the probability is 1/52.
Calculate the probability of the bottom card being the ace of spades:
This is also 1/52 since there's still 1 ace of spades among the 52 cards.
Apply the Addition rule:
Add the probabilities together, then subtract the probability of both events happening at the same time (which is 0, as
the ace of spades can't be in both positions).
So, the probability is (1/52) + (1/52) - 0 = 2/52 or 1/26.
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Question 1
Find the future value twenty-five years from now of an account in which you have $19,675.13 today and into which you make annual $3,000 deposits. Assume the account earns 9.25%.
As a result, the account will be worth $398,634.52 in 25 years as by estimating the future worth of the yearly deposits.
what is interest ?Interest is the fee incurred when paying interest or the compensation given when lending money. The principal, which is the obtain desired or lent, is typically stated as a percentage. The period, and or duration for which the principal is lent or invested, as well as the interest rate determine how much interest is charged or generated. There are two types of interest: simple and compound. Compound interest is calculated based on the original and the total interest.
given
Let's begin by estimating the future worth of the yearly deposits:
[tex]$3000 * ((1 + 0.0925)25 - 1) / 0.0925[/tex] = $263,361.05 FV annuity
Then, let's determine the initial deposit's future value:
FV initial is $19,675.13 multiplied by (1 + 0.0925)25 to get $135,273.47.
Let's finally combine the two future numbers to determine the account's total future value:
$135,273.47 + $263,361.05 = $398,634.52
where FV total = FV initial + FV annuity
As a result, the account will be worth $398,634.52 in 25 years as by estimating the future worth of the yearly deposits.
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Please help! Equation is below.
The values of a that make (x - a) a factor of x^4 - 5x³ - 21x² - 23x - 8 are given as follows:
a = 8 and a = -1.
How to obtain the values of a?The polynomial is given as follows:
f(x) = x^4 - 5x³ - 21x² - 23x - 8
By the factor theorem, x - a is a factor of a polynomial f(x) if f(a) = 0.
The numeric value at x = a is given as follows:
f(a) = a^4 - 5a³ - 21a² - 23a - 8.
Hence the values of a are obtained solving the equation presented as follows:
a^4 - 5a³ - 21a² - 23a - 8 = 0.
Using a calculator, the values of a are given as follows:
a = 8 and a = -1.
(the root of -1 has a multiplicity of 3).
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Bob's gift shop sold a record number of cards for Mother's Day. One salesman sold 46 cards, which was 10% of the cards sold for Mother's Day. How many cards were sold for Mother's Day?
The total 460 cards are sold on Mothers day.
Given that, Bob's gift shop sold a record number of cards for Mother's Day.
One salesman sold 46 cards, which was 10% of the cards sold for Mother's Day.
Let the number of cards sold on mothers day be x.
Here, 10% of x =46
10/100 ×x= 46
10x=4600
x=460
Therefore, total 460 cards are sold on Mothers day.
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Why are there two different formulas for circumference?
Answer: Perimeter of semi-circle πr + 2r
Area of semi-circle πr2/2
Step-by-step explanation:
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A trip to St. Louis from Atlanta will take 7¾ hours. Assuming you're two-thirds of the way there, how much longer, in hours, will the trip take?
Answer:
5 and 1/6 hours
Step By Step Explanation:
for the integer data set containing 11, 13, 15, 17, x, and y, the unique mode, median, and mean form an increasing arithmetic sequence, in that order. what is the greatest possible value of y?
Given the integer data set containing 11, 13, 15, 17, x, and y, we know that the mode, median, and mean form an increasing arithmetic sequence.
Since the mode is the unique number that appears most frequently, either x or y must be equal to one of the existing numbers (11, 13, 15, or 17). Let's assume x is the mode. For the sequence to be increasing, the mode must be the smallest, so x = 11.
The median of the data set is the average of the two middle numbers when they are arranged in ascending order. With x = 11, the sorted sequence will be 11, 11, 13, 15, 17, and y. The median will be the average of 11 and 13, which is 12.
For the mean, we have (11+11+13+15+17+y)/6. We know the mean is greater than the median, which is 12. If we increase the mean to 13, we can solve for y:
(11+11+13+15+17+y)/6 = 13
67 + y = 78
y = 11
However, this would make the mode 11 as well, so it doesn't meet the unique requirement. Let's increase the mean to 14 and solve for y:
(11+11+13+15+17+y)/6 = 14
67 + y = 84
y = 17
Now, the mode, median, and mean are unique and form an increasing arithmetic sequence (11, 12, 14). Therefore, the greatest possible value of y is 17.
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