Simplify 6^2/6 x 6^12/6^8
Step-by-step explanation:
6^2 / 6^1 x 6^12 / 6^8 =
6^(2-1) x 6^(12-8) =
6^1 x 6^4 =
6^(1+4) = 6^5 or = 7776
the 3rd and 6th term in fibonacci sequence are 7 and 31 respectively find the 1st and 2nd terms of the sequence
Answer:
Step-by-step explanation:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,144,233,377,610,987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, ... Can you figure out the next few numbers?
A coordinate plane with 2 lines drawn. The first line is labeled f(x) and passes through the points (0, negative 2) and (1, 1). The second line is labeled g(x) and passes through the points (negative 4, 0) and (0, 2). The lines intersect at about (2.5, 3.2)
How does the slope of g(x) compare to the slope of f(x)?
The slope of g(x) is the opposite of the slope of f(x).
The slope of g(x) is less than the slope of f(x).
The slope of g(x) is greater than the slope of f(x).
The slope of g(x) is equal to the slope of f(x)
Therefore, the correct answer is: The slope of g(x) is less than the slope of f(x).
Where do the X and Y axes intersect on the coordinate plane, at position 0 0?The origin is the location where the two axes meet. On both the x- and y-axes, the origin is at 0. The coordinate plane is divided into four portions by the intersection of the x- and y-axes. The term "quadrant" refers to these four divisions.
We can use the slope formula to get the slopes of the lines f(x) and g(x):
slope of f(x) = (change in y)/(change in x) = (1 - (-2))/(1 - 0) = 3/1 = 3
slope of g(x) = (change in y)/(change in x) = (2 - 0)/(0 - (-4)) = 2/4 = 1/2
The slope of g(x) is 1/2, which is less than the slope of f(x), which is 3.
Therefore, the correct answer is: The slope of g(x) is less than the slope of f(x).
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Suppose you have $1600 in your savings account at the end of a certain period of time. You invested $1500
at a 6.49% simple annual interest rate. How long, in years, was your money invested?
Thus, the time taken for the sum of $1500 to become $1600 with 6.49% simple annual interest rate is found as 1.027 years.
Explain about the simple interest:Simple interest is the percentage that is charged on the principal sum of money that is lent or borrowed. Similar to this, when you deposit a particular amount in a bank, you can also earn interest.
Calculating simple interest is as easy as multiplying the principal borrowed or lent, the interest rate, and the loan's term (or repayment time).
Given data:
Principal P = $1500
Amount after interest A = $1600
Rate of simple interest R = 6.49%
Time = T years
The formula for the simple interest:
SI = PRT/100
A = P + SI
A = P + PRT/100
PRT/100 = A - P
1500*6.49*T/100 = 1600 - 1500
1500*6.49*T = 100 *100
T = 10000 / 9735
T = 1.027 years
Thus, the time taken for the sum of $1500 to become $1600 with 6.49% simple annual interest rate is found as 1.027 years.
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the area of Rectangle is 112 in sq. if the height is 8 in, what is the base length
Answer:
14cm
Step-by-step explanation:
112÷8=14
base length=14cm
Answer:
To find the base length of a rectangle, given its area and height, you can use the formula for calculating the area of a rectangle, which is:
Area = Length x Width
In this case, you are given that the area is 112 square inches and the height is 8 inches. Let's denote the base length as "x" inches.
So, the equation for the area of the rectangle becomes:
112 = x * 8
To solve for "x", you can divide both sides of the equation by 8:
112 / 8 = x
x = 14
Therefore, the base length of the rectangle is 14 inches.
what’s the surface area of this figure ?
Thus, the total surface area of pentagonal prism is found to be 308.6 sq. ft.
Explain about the pentagonal prism:A prism having a pentagonal base is referred to as a pentagonal prism. It has two hexagonal bases, five parallelogram faces, and seven faces. Seven faces, fifteen edges, and ten vertices make up a pentagonal prism.
The two bases of each of the seven faces—two pentagons—and the remaining five faces—parallelograms—connect the bases of the pentagons.
Given data:
base area B = 84.3 sq. ftLength of rectangular side L = 7 ftwidth of rectangular side w = 4 ftsurface area of pentagonal prism = 2* base area + 5*rectangle area
surface area of pentagonal prism = 2* B + 5*L*w
surface area of pentagonal prism = 2* 84.3 + 5*7*4
surface area of pentagonal prism = 168.6 + 140
surface area of pentagonal prism = 308.6 sq. ft
Thus, the total surface area of pentagonal prism is found to be 308.6 sq. ft.
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The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for 35 minutes of calls is $16.83 and the monthly cost for 52 minutes is $18.87. What is the monthly cost for 39 minutes of calls?
Answer: We can use the two given points to find the equation of the line and then plug in 39 for the calling time to find the corresponding monthly cost.
Let x be the calling time (in minutes) and y be the monthly cost (in dollars). Then we have the following two points:
(x1, y1) = (35, 16.83)
(x2, y2) = (52, 18.87)
The slope of the line passing through these two points is:
m = (y2 - y1) / (x2 - x1) = (18.87 - 16.83) / (52 - 35) = 0.27
Using point-slope form with the first point, we get:
y - y1 = m(x - x1)
y - 16.83 = 0.27(x - 35)
Simplifying, we get:
y = 0.27x + 7.74
Therefore, the monthly cost for 39 minutes of calls is:
y = 0.27(39) + 7.74 = $18.21
Step-by-step explanation:
Complete the truth table for (A ⋁ B) ⋀ ~(A ⋀ B).
The truth table for (A ⋁ B) ⋀ ~(A ⋀ B) is:
A B (A ⋁ B) ⋀ ~(A ⋀ B)
0 0 0
0 1 0
1 0 0
1 1 0
The truth table is what?A truth table is a table that displays all possible combinations of truth values (true or false) for one or more propositions or logical expressions, as well as the truth value of the resulting compound proposition or expression that is created by combining them using logical operators like AND, OR, NOT, IMPLIES, etc.
The columns of a truth table reflect the propositions or expressions themselves as well as the compound expressions created by applying logical operators to them. The rows of a truth table correspond to the various possible combinations of truth values for the propositions or expressions.
To complete the truth table for (A ⋁ B) ⋀ ~(A ⋀ B), we need to consider all possible combinations of truth values for A and B.
A B A ⋁ B A ⋀ B ~(A ⋀ B) (A ⋁ B) ⋀ ~(A ⋀ B)
0 0 0 0 1 0
0 1 1 0 1 0
1 0 1 0 1 0
1 1 1 1 0 0
So, the only case where the expression is true is when both A and B are true, and for all other cases it is false.
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$2000 are invested in a bank account at an interest rate of 5 percent per year.
Find the amount in the bank after 7 years if interest is compounded annually.
Find the amount in the bank after 7 years if interest is compounded quaterly.
Find the amount in the bank after 7 years if interest is compounded monthly.
Finally, find the amount in the bank after 7 years if interest is compounded continuously.
The amount in the bank after 7 years increases as the compounding frequency increases, and it is highest when interest is compounded continuously.
Simple interest calculation.
Using the formula A = P(1 + r/n)^(nt), where:
A = the amount in the account after t years
P = the principal (initial amount)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
a) If interest is compounded annually:
A = 2000(1 + 0.05/1)^(1*7) = $2,835.08
b) If interest is compounded quarterly:
A = 2000(1 + 0.05/4)^(4*7) = $2,888.95
c) If interest is compounded monthly:
A = 2000(1 + 0.05/12)^(12*7) = $2,905.03
d) If interest is compounded continuously:
A = Pe^(rt) = 2000e^(0.05*7) = $2,938.36
Therefore, the amount in the bank after 7 years increases as the compounding frequency increases, and it is highest when interest is compounded continuously.
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Given the expression 3x+2 evaluate the expression for the given values of x when x=(-2)
Answer:
...............................
3+4x greater than 27
subtract 3 from both sides to get
4x > 27
divide both sides by 4 to get
x > 27/4 or 6 3/4
Please I’ll give brainliest
A Ferris wheel reaches a maximum height of 60 m above the ground and takes twelve minutes to complete one revolution. Riders have to climb a m staircase to board the ride at its lowest point.
(a) [4 marks] Write a sine function for the height of Emma, who is at the very top of the ride when t = 0.
(b) [2 marks] Write a cosine function for Eva, who is just boarding the ride.
(c) (2 marks] Write a sine function for Matthew, who is on his way up, and is at the same height as the central axle of the wheel.
If Riders have to climb a m staircase to board the ride at its lowest point.
a. sine function for the height of Emma, who is at the very top of the ride when t = 0 is: h(t) = 60 sin(π/6 t).
b. a cosine function for Eva, who is just boarding the ride is: h(t) = m + 60 cos(π/6 t).
c. a sine function for Matthew is: h(t) = 30 sin(π/6 t).
What is the sine function for the height of Emma?(a) Let's assume that the Ferris wheel completes one full revolution in 12 minutes. The height of the Ferris wheel can be modeled by a sine function as it moves up and down periodically. When the Ferris wheel completes one revolution, it returns to its original position, so the period of the sine function is 12 minutes.
The maximum height of the Ferris wheel is 60 m, so the amplitude of the sine function is 60 m. When t = 0, Emma is at the very top of the ride, which means she is at the maximum height of the Ferris wheel. Therefore, the sine function for Emma's height, h(t), can be written as:
h(t) = 60 sin(2π/12 t)
Simplifying this equation, we get:
h(t) = 60 sin(π/6 t)
(b) Eva is just boarding the ride, which means she is at the lowest point of the ride when t = 0. The cosine function is ideal for modeling this situation, as it starts at its maximum value and reaches its minimum value after one-fourth of the period. Therefore, the cosine function for Eva's height, h(t), can be written as:
h(t) = m + 60 cos(2π/12 t)
Simplifying this equation, we get:
h(t) = m + 60 cos(π/6 t)
where m is the height of the staircase that Eva has to climb to board the ride.
(c) Matthew is at the same height as the central axle of the Ferris wheel, which means he is halfway between the maximum and minimum height of the ride. Therefore, the sine function for Matthew's height, h(t), can be written as:
h(t) = 30 sin(2π/12 t)
Simplifying this equation, we get:
h(t) = 30 sin(π/6 t)
Therefore sine function for the height of Emma, who is at the very top of the ride when t = 0 is: h(t) = 60 sin(π/6 t).
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Aeronautical researchers have developed three different processes to pack a parachute. They want to compare the different processes in terms of time to deploy and reliability. There are 1,200 objects that they can drop with a parachute from a plane. Using a table of random digits, the researchers will randomly place the 1,200 items into three equally sized treatment groups suitable for comparison. Which design is the most appropriate for this experiment
- Randomly number each item with 1, 2, or 3. Assign the items labeled 1 to the process 1 group, assign the items labeled 2 to the process 2 group, and assign the items labeled 3 to the process 3 group.
- Number each item from 1 to 1,200.
Reading from left to right from a table of random digits, identify 800 unique numbers from 1 to 1,200. Assign the items with labels in the first 400 numbers to the process 1 group. Assign the items with labels in the second 400 numbers to the process 2 group. Assign the remaining items to the process 3 group.
- Number each item from 0000 to 1199.
Reading from left to right on a random number table, identify 800 unique four-digit numbers from 0000 to 1199. Assign the items with labels in the first 400 numbers to the process 1 group. Assign the items with labels in the second 400 numbers to the process 2 group. Assign the remaining items to the process 3 group.
- Select an item, and identify the first digit reading from left to right on a random number table. If the first digit is a 1, 2, or 3, assign the item to the process 1 group.
If the first digit is a 4, 5, or 6, assign the item to the process 2 group. If the first digit is a 7, 8, or 9, assign the item to the process 3 group. If the first digit is a 0, skip that digit and move to the next one to assign the item to a group. Repeat this process for each item.
Answer: The most appropriate design for this experiment is the third option:
- Number each item from 0000 to 1199.
- Reading from left to right on a random number table, identify 800 unique four-digit numbers from 0000 to 1199. Assign the items with labels in the first 400 numbers to the process 1 group. Assign the items with labels in the second 400 numbers to the process 2 group. Assign the remaining items to the process 3 group.
This design ensures that the groups are equally sized and selected randomly without any biases. The use of a random number table to assign the groups helps to avoid any systematic patterns or preferences that might arise from numbering or labeling the items directly.
Step-by-step explanation:
The count in a bateria culture was initially 300, and after 35 minutes the population had increased to 1600. Find the doubling period. Find the population after 70 minutes. When will the population reach 10000?
Write an equation for the polynomial graphed below
The polynomial in factor form is y(x) = - (1 / 6) · (x + 3) · (x + 1) · (x - 2) · (x - 3).
How to derive the equation of the polynomial
In this problem we find a representation of polynomial set on Cartesian plane, whose expression is described by the following formula in factor form:
y(x) = a · (x - r₁) · (x - r₂) · (x - r₃) · (x - r₄)
Where:
x - Independent variable.r₁, r₂, r₃, r₄ - Roots of the polynomial.a - Lead coefficient.y(x) - Dependent variable.Then, by direct inspection we get the following information:
y(0) = - 3, r₁ = - 3, r₂ = - 1, r₃ = 2, r₄ = 3
First, determine the lead coefficient:
- 3 = a · (0 + 3) · (0 + 1) · (0 - 2) · (0 - 3)
- 3 = a · 3 · 1 · (- 2) · (- 3)
- 3 = 18 · a
a = - 1 / 6
Second, write the complete expression:
y(x) = - (1 / 6) · (x + 3) · (x + 1) · (x - 2) · (x - 3)
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Find the value of x from the given figure.
The value of x from the given figure is given as follows:
144º.
What is a straight angle?An angle that measures 180 degrees is called a straight angle, and it is formed by two opposite rays that extend in opposite directions from a common endpoint, creating a straight line. A straight angle forms a straight line, and it can also be thought of as a half-turn or a semicircle.
The two opposite rays in this problem have the measures given as follows:
x.x/4.Hence the equation to find the value of x is given as follows:
x + x/4 = 180
x + 0.25x = 180
1.25x = 180
x = 180/1.25
x = 144º.
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The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 0 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 10. There are two dots above 1 and 4. There are three dots above 2 and 5. There are 4 dots above 3.
Which of the following is the best measure of variability for the data, and what is its value?
The IQR is the best measure of variability, and it equals 3.
The IQR is the best measure of variability, and it equals 9.
The range is the best measure of variability, and it equals 3.
The range is the best measure of variability, and it equals 9.
The range is the best measure of variability for this data, and its value is 4.
Which of the following is the best measure of variability for the data, and what is its value?The line plot displays the number of roses purchased per day at a grocery store, with the data values ranging from 0 to 4 (since there are no dots above 4).
The best measure of variability for this data is the range, which is the difference between the maximum and minimum values in the data set. In this case, the minimum value is 0 and the maximum value is 4, so the range is:
Range = Maximum value - Minimum value = 4 - 0 = 4
Therefore, the range is the best measure of variability for this data, and its value is 4.
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Identify the correct equation of the graph.
-10
O f(b) = (6+4)² +8
O f(b) = (b+8)² +4
Of(b)=(6-8)²-4
O
-5
10
5
-5
-10
V
5
O f(b) = (b-8)² +4
Of(b) = (6-4)²-8
Of(b) (6-4)² +8
10
Check
Thus, the correct equation for the given parabolic graph is found as: f(b) = (b – 8)² + 4.
Explain about the quadratic function in vertex form:A parabola has a lowest point if it opens upward. A parabola has a highest point if it opens downward.
The vertex of the parabola is located at this lowest or highest point.
Vertex form of a quadratic function:
f(x) = a(x – h)² + k, where a, h, and k are constants.
The vertex of the parabola is at because it is translated h horizontal units and k vertical units from the origin (h, k).
(h,k) are the vertex of parabola.
From the given graph:
f(b) is the given function:
Vertex (h,k) = (8, 4)
Thus, h= 8 and k = a = 1, x = b.
Put the values in quadratic function:
f(b) = 1(b – 8)² + 4
f(b) = (b – 8)² + 4
Thus, the correct equation for the given parabolic graph is found as: f(b) = (b – 8)² + 4.
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A survey stopped men and women at random to ask them where they purchased groceries, at a local grocery store or online.
What percent of the people surveyed shop at a local grocery store? Round your answer to the nearest whole number percent.
63% of people Surveyed shop at a local grocery store.
What is percentage ?A number can be expressed as a fraction of 100 using a percentage. The word "%" stands for percentage.
For instance, 50% represents 50 out of 100, or 0.5 in decimal form. Frequently, proportions, rates, and changes in quantity are represented as percentages.
In many aspects of daily life, including the calculation of sales tax, loan interest rates, and price discounts, percentages are frequently utilised. They are also employed in many academic disciplines, including math, physics, economics, and statistics.
What are proportions ?The equality of two ratios is referred to as a percentage in mathematics. A ratio is a comparison of two amounts or values;
it is frequently stated as a fraction.
For instance, "3/5" can be used to represent the proportion of boys to girls in a classroom.
An assertion of equality between two ratios is a proportion.
For instance, the ratio of males to girls is the same as the ratio of boys to all pupils,
hence the sentence "3/5 = 6/10" is a proportion.
Analysis: -
people surveyed at store = 45
total no. of people = 72
the
Percent of peopla = 45/72 x100
= 0.625 × 100
= 62.5 %
= 63 %
63% of people Surveyed shop at a local grocery store.
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0\left\{-10\le x\le10\right\}
Describe the transformations (vertical translation, horizontal translation, and dilation/reflection) from the parent function that happened to these formulas
The formula g(x) = 2 * 0{-10≤x+3≤10} represents a function that has been horizontally shifted left by 3 units, reflected about the y-axis, and vertically scaled by a factor of 2.
What is Function?A function is a mathematical rule that assigns each input from a set (domain) a unique output from another set (range), typically written as y = f(x).
The notation "0{-10≤x≤10}" typically represents the domain of a function or an inequality. It means that the function is defined only for the values of x that are between -10 and 10 (including -10 and 10).
Assuming that the function in question is a constant function equal to zero, the parent function is f(x) = 0.
To describe the transformations that happened to this function, we need more information about the specific formula. For example, if the formula is:
g(x) = 0{-10≤x≤10}
Then there are no transformations from the parent function. The function is simply a constant function that is equal to zero over the interval [-10, 10].
However, if the formula is something like:
g(x) = 2 * 0{-10≤x+3≤10}
Then we can describe the transformations as follows:
Horizontal translation: The function has been shifted horizontally to the left by 3 units. This means that the point (3, 0) on the parent function is now located at the origin (0, 0) on the transformed function.
Dilation/reflection: The function has been reflected about the y-axis and vertically scaled by a factor of 2. This means that the point (-1, 0) on the parent function is now located at (-4, 0) on the transformed function, and the point (1, 0) on the parent function is now located at (2, 0) on the transformed function.
Vertical translation: There is no vertical translation in this case, since the constant function is already centered at y = 0.
To summarize, the formula g(x) = 2 * 0{-10≤x+3≤10} represents a function that has been horizontally shifted left by 3 units, reflected about the y-axis, and vertically scaled by a factor of 2.
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The formula g(x) = 2 * 0{-10≤x+3≤10} represents a function that has been horizontally shifted left by 3 units, reflected about the y-axis, and vertically scaled by a factor of 2.
What is Function?A function is a mathematical rule that assigns each input from a set (domain) a unique output from another set (range), typically written as y = f(x).
The notation "0{-10≤x≤10}" typically represents the domain of a function or an inequality. It means that the function is defined only for the values of x that are between -10 and 10 (including -10 and 10).
Assuming that the function in question is a constant function equal to zero, the parent function is f(x) = 0.
To describe the transformations that happened to this function, we need more information about the specific formula. For example, if the formula is:
g(x) = 0{-10≤x≤10}
Then there are no transformations from the parent function. The function is simply a constant function that is equal to zero over the interval [-10, 10].
However, if the formula is something like:
g(x) = 2 * 0{-10≤x+3≤10}
Then we can describe the transformations as follows:
Horizontal translation: The function has been shifted horizontally to the left by 3 units. This means that the point (3, 0) on the parent function is now located at the origin (0, 0) on the transformed function.
Dilation/reflection: The function has been reflected about the y-axis and vertically scaled by a factor of 2. This means that the point (-1, 0) on the parent function is now located at (-4, 0) on the transformed function, and the point (1, 0) on the parent function is now located at (2, 0) on the transformed function.
Vertical translation: There is no vertical translation in this case, since the constant function is already centered at y = 0.
To summarize, the formula g(x) = 2 * 0{-10≤x+3≤10} represents a function that has been horizontally shifted left by 3 units, reflected about the y-axis, and vertically scaled by a factor of 2.
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HELP FAST PLEASEEE!!!!
The correct matches for the probability of falling below the z-score are:
-0.08: 0.4681
0.63: 0.7357
-2.7: 0.0035
1.95: 0.9744
Explain probability
Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain. Probability is calculated by dividing the number of favourable outcomes by the total number of possible outcomes. Probability is used in many fields, including mathematics, statistics, science, economics, and finance, to make predictions and decisions based on uncertain events.
According to the given information
To match the probability of falling below a given z-score, we need to use a standard normal distribution table or a calculator with a built-in normal distribution function. Here are the probabilities for each z-score:
For a z-score of -0.08, the probability of falling below it is 0.4681.For a z-score of 0.63, the probability of falling below it is 0.7357.For a z-score of -2.7, the probability of falling below it is 0.0035.For a z-score of 1.95, the probability of falling below it is 0.9744.To know more about probability visit
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A farmer is building a fence to enclose a rectangular area against an existing wall, shown in the figure below. Three of the sides will require fencing and the fourth wall already exists. If the farmer has 176 feet of fencing,
what is the largest area the farmer can enclose?
Answer: 46 ft by 92 ft
Step-by-step explanation:
The largest area is enclosed when half the fence is used parallel to the wall and the other half is used for the two ends of the fenced area perpendicular to the wall. Half the fence is 184 ft/2 = 92 ft. Half that is used for each end of the enclosure.
Is each number rounded correctly to the nearest hundred thousand?
yes is answer for all option .we can check it by rules of rounding off numbers .
what is rounding ?
Rounding is the process of approximating a number to a nearby value that is easier to work with or more appropriate for a given context. When rounding, we take a number with many decimal places or significant figures and adjust it to a simpler or more convenient value with fewer decimal places or significant figures.
In the given question,
Yes, each number is rounded correctly to the nearest hundred thousand based on the rules of rounding.
To round to the nearest hundred thousand, we look at the digit in the hundred thousand place and the digit to its right (i.e., in the ten thousand place).
If the digit in the ten thousand place is 5 or greater, we round up the digit in the hundred thousand place by adding 1.
If the digit in the ten thousand place is less than 5, we leave the digit in the hundred thousand place as it is.
Using these rules, we can see that:
350000 rounded to the nearest hundred thousand is 400000 because the digit in the ten thousand place is 5, so we round up the digit in the hundred thousand place.
555555 rounded to the nearest hundred thousand is 560000 because the digit in the ten thousand place is 5, so we round up the digit in the hundred thousand place.
137998 rounded to the nearest hundred thousand is 200000 because the digit in the ten thousand place is 7, so we round up the digit in the hundred thousand place.
792314 rounded to the nearest hundred thousand is 800000 because the digit in the ten thousand place is 3, so we leave the digit in the hundred thousand place as it is.
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Here is another question DUE SOON PLEASE ASAP
Question 5(Multiple Choice Worth 1 points)
(08.07 MC)
The table describes the quadratic function p(x).
x p(x)
−1 10
0 1
1 −2
2 1
3 10
4 25
5 46
What is the equation of p(x) in vertex form?
p(x) = 2(x − 1)2 − 2
p(x) = 2(x + 1)2 − 2
p(x) = 3(x − 1)2 − 2
p(x) = 3(x + 1)2 − 2
The equation of p(x) in vertex form is;
p(x) = 9.67(x + 1.04)² - 10.25
The closest answer choice is:
p(x) = 3(x - 1)² - 2, which is not correct.
What is vertex?In the context of a quadratic function, the vertex is the highest or lowest point on the graph of the function. It is the point where the parabola changes direction. The vertex is also the point where the axis of symmetry intersects the parabola.
To find the vertex form of the quadratic function p(x), we need to first find the vertex, which is the point where the function reaches its maximum or minimum value.
To find the vertex, we can use the formula:
x = -b/2a, where a is the coefficient of the x² term, b is the coefficient of the x term, and c is the constant term.
Using the table, we can see that the highest value of p(x) occurs at x = 5, and the value is 46.
We can then use the formula to find the vertex:
x = -b/2a = -5/2a
Using the values from the table, we can set up two equations:
46 = a(5)² + b(5) + c
1 = a(0)² + b(0) + c
Simplifying the second equation, we get:
1 = c
Substituting c = 1 into the first equation and solving for a and b, we get:
46 = 25a + 5b + 1
-20 = 5a + b
Solving for b, we get:
b = -20 - 5a
Substituting b = -20 - 5a into the first equation and solving for a, we get:
46 = 25a + 5(-20 - 5a) + 1
46 = 15a - 99
145 = 15a
a = 9.67
Substituting a = 9.67 and c = 1 into b = -20 - 5a, we get:
b = -20 - 5(9.67) = -71.35
Therefore, the equation of p(x) in vertex form is:
p(x) = 9.67(x - 5)² + 1
Simplifying, we get:
p(x) = 9.67(x² - 10x + 25) + 1
p(x) = 9.67x² - 96.7x + 250.85 + 1
p(x) = 9.67x² - 96.7x + 251.85
Rounding to the nearest hundredth, we get:
p(x) = 9.67(x - 5² + 1 = 9.67(x + 1.04)² - 10.25
Therefore, the answer is:
p(x) = 9.67(x + 1.04)² - 10.25
The closest answer choice is:
p(x) = 3(x - 1)² - 2, which is not correct.
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Please help with this math question!
The exponential function of the population is P(x) = 15000 * 1.046^x
Calculating the exponential function of the populationFrom the question, we have the following parameters that can be used in our computation:
Initial, a = 15000
Rate, r = 4.6%
The equation of the function is represented as
P(x) = a * (1 + r)^x
Substitute the known values in the above equation, so, we have the following representation
P(x) = 15000 * (1 + 4.6%)^x
Evaluate
P(x) = 15000 * 1.046^x
Hence, the function is P(x) = 15000 * 1.046^x
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Four family members attended a
family reunion. The table below
shows the distance each person
drove and the amount of time each
person traveled.
If each person drove at a constant rate,than Laura drove the fastest
What is the distance ?Displacement is the measurement of the how far an object is out of place,therefore distance refers to the how much ground an object has covered during its motion.so, examine the distinction between distance and displacement in this article.
What is the speed?The means of Speed is :he speed at which an object of location changes in any direction. The distance traveled in relation to the time it took to travel that distance is how speed is defined. The speed simply has no magnitude but it has a direction, Speed is a scalar quantity.
to compute who drove the quickest by Using this formula
speed=Distance /time,
first of all the convert times into hours:
Hank: 3.2 hours x 3 hours and 12 minutes.
Laura: 2.5 hours is 2 hours and 30 minutes.
Nathan: 2.25 hours is 2 hours and 15 minutes.
Raquel: 4 hours plus 24 minutes equals 4.4 hours.
now to calculate the speed by above formula
Hank: 55 miles per hour for 176 miles in 3.2 hours.
Laura: 60 miles per hour equals 150 miles in 2.5 hours.
Nathan: 50 miles per houris equal to 112.5 miles in 2.25 hours.
Raquel: 65 miles for 286 miles in 4.4 hours.
As a result, Laura moved the fastest, clocking in at 60 miles. The solution, Laura, is B.
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La Suma delos cuadrados de dos números naturales consecutivos es 181 halla dichos numeros
The two consecutive natural numbers whose sum of squares is 181 are 9 and 10
Let's assume that the two consecutive natural numbers are x and x+1. Then, we can write an equation based on the given information:
x² + (x+1)² = 181
Expanding the equation:
x² + x² + 2x + 1 = 181
Combining like terms:
2x² + 2x - 180 = 0
Dividing both sides by 2:
x² + x - 90 = 0
Now, we can use the quadratic formula to solve for x:
x = (-b ± √(b² - 4ac)) / 2a
where a = 1, b = 1, and c = -90
x = (-1 ± √(1 + 360)) / 2
x = (-1 ± √(361)) / 2
x = (-1 ± 19) / 2
We discard the negative value, as it does not correspond to a natural number:
x = 9
Therefore, the two consecutive natural numbers are 9 and 10, and their sum of squares is 81 + 100 = 181.
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I need helppp!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
The distance formula is
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
x1 is a,
x2 is 0,
y1 is 0 and
y2 is b. Fitting those into the formula where they belong:
[tex]d=\sqrt{(0-a)^2+(b-0)^2}[/tex] and
[tex]d=\sqrt{(-a)^2+(b)^2}[/tex]
Since a negative squared is a positive, then
[tex]d=\sqrt{a^2+b^2}[/tex]
which is the second choice down.
You take out a loan in the amount of your tuition and fees cost $70,000. The loan has a monthly interest rate of 0.25% and a monthly payment of $250. How long will it take you to pay off the loan? Use the formula N= (-log(1-i*A/P))/(log(1+i)) to determine the number of months it will take you to pay off the loan. Let N represent the number of monthly payments that will need to be made, i represent the interest rate in decimal form, A represent the amount owed (total amount of the loan), and P represent the amount of your monthly payment. Be sure to show your work for all calculations made.
Therefore, it will take 173 months to pay off the loan, or approximately 14 years and 5 months.
What is percentage?A percentage is a way of expressing a number as a fraction of 100. The symbol for a percentage is "%". For example, 50% is the same as 50/100 or 0.5 as a decimal. Percentages are often used to express a portion or share of a whole. For instance, if you scored 90% on a test, it means you got 90 out of 100 possible points. In finance, percentages are commonly used to express interest rates, returns on investments, or changes in stock prices.
First, we need to convert the monthly interest rate from a percentage to a decimal by dividing by 100.
0.25% / 100 = 0.0025
Now we can plug in the values into the formula:
N= (-log (1-0.0025*70000/250))/ (log (1+0.0025))
Simplifying the equation in the parentheses:
N= (-log (1-175))/ (log (1.0025))
N= (-log (0.9964))/ (0.002499)
N= 172.9
Rounding up to the nearest whole number since we can't make partial payments:
N= 173
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solve the equation
a) y''-2y'-3y= e^4x
b) y''+y'-2y=3x*e^x
c) y"-9y'+20y=(x^2)*(e^4x)
Answer:
a) To solve the differential equation y''-2y'-3y= e^4x, we first find the characteristic equation:
r^2 - 2r - 3 = 0
Factoring, we get:
(r - 3)(r + 1) = 0
So the roots are r = 3 and r = -1.
The general solution to the homogeneous equation y'' - 2y' - 3y = 0 is:
y_h = c1e^3x + c2e^(-x)
To find the particular solution, we use the method of undetermined coefficients. Since e^4x is a solution to the homogeneous equation, we try a particular solution of the form:
y_p = Ae^4x
Taking the first and second derivatives of y_p, we get:
y_p' = 4Ae^4x
y_p'' = 16Ae^4x
Substituting these into the original differential equation, we get:
16Ae^4x - 8Ae^4x - 3Ae^4x = e^4x
Simplifying, we get:
5Ae^4x = e^4x
So:
A = 1/5
Therefore, the particular solution is:
y_p = (1/5)*e^4x
The general solution to the non-homogeneous equation is:
y = y_h + y_p
y = c1e^3x + c2e^(-x) + (1/5)*e^4x
b) To solve the differential equation y'' + y' - 2y = 3xe^x, we first find the characteristic equation:
r^2 + r - 2 = 0
Factoring, we get:
(r + 2)(r - 1) = 0
So the roots are r = -2 and r = 1.
The general solution to the homogeneous equation y'' + y' - 2y = 0 is:
y_h = c1e^(-2x) + c2e^x
To find the particular solution, we use the method of undetermined coefficients. Since 3xe^x is a solution to the homogeneous equation, we try a particular solution of the form:
y_p = (Ax + B)e^x
Taking the first and second derivatives of y_p, we get:
y_p' = Ae^x + (Ax + B)e^x
y_p'' = 2Ae^x + (Ax + B)e^x
Substituting these into the original differential equation, we get:
2Ae^x + (Ax + B)e^x + Ae^x + (Ax + B)e^x - 2(Ax + B)e^x = 3xe^x
Simplifying, we get:
3Ae^x = 3xe^x
So:
A = 1
Therefore, the particular solution is:
y_p = (x + B)e^x
Taking the derivative of y_p, we get:
y_p' = (x + 2 + B)e^x
Substituting back into the original differential equation, we get:
(x + 2 + B)e^x + (x + B)e^x - 2(x + B)e^x = 3xe^x
Simplifying, we get:
-xe^x - Be^x = 0
So:
B = -x
Therefore, the particular solution is:
y_p = xe^x
The general solution to the non-homogeneous equation is:
y = y_h + y_p
y = c1e^(-2x) + c2e^x + xe^x
c) To solve the differential equation y" - 9y' + 20y = x^2*e^4x, we first find the characteristic equation:
r^2 - 9r + 20 = 0
Factoring, we get:
(r - 5)(r - 4) = 0
So the roots are r = 5 and r = 4.
The general solution to the homogeneous equation y" - 9y' + 20y = 0 is:
y_h = c1e^4x + c2e^5x
To find the particular solution, we use the method of undetermined coefficients. Since x^2*e^4x is a solution to the homogeneous equation, we try a particular solution of the form:
y_p = (Ax^2 + Bx + C)e^4x
Taking the first and second derivatives of y_p, we get:
y_p' = (2Ax + B)e^4x + 4Axe^4x
y_p'' = 2Ae^4x +