Answers
a) The exponential function that models the population in t years after 2000 is of: P(t) = 14300(1.06)^t.
b) The estimate for the population in 2008 is of: 22792.
How to define the exponential function?Considering it's standard format, the increasing exponential function is defined as follows:
P(t) = P(0)(1 + r)^t.
In which the parameters of the function are defined as follows:
P(0) is the population in the reference year of 2000.r is the growth rate, as a decimal.Hence the values of these parameters are given as follows:
P(0) = 14300, r = 0.06.
Thus the function is given by:
P(t) = 14300(1.06)^t.
2008 is eight years after 2000, thus the estimate is P(8), which is obtained as follows:
P(8) = 14300 x (1.06)^8 = 22792.
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Related Questions
Is 5/6 greater than 10/12
Answers
Answer:
Step-by-step explanation:
Clearly, it can be seen that 10/12 represents the largest fraction. Hence 5/6 (which is equivalent to 10/12) is larger than 2/3 or 3/4.
Answer: no they are equal either simplified to 5/6 or decimal 0.83 repeating decimal.
Step-by-step explanation:
tell how you can use the structure of mathematics to complete the task
Answers
Answer: It is crucial for students to look for and make use of a structure because this practice requires them to reason about the underlying mathematical structure and unity of mathematics ideas.
Find the values of a b and c for the equation y = 4x2- 8x - 12
Answers
Answer:
[tex]a=4, b=-8, c=-12[/tex]
Step-by-step explanation:
Compare the given equation with the general form [tex]y=ax^2 + bx+c[/tex].
Help Please! This is 6th grade k12
Answers
Answer:Put a one under the five then sop he last faction and start multiplying
Step-by-step explanation:
Miguel drove his car 315 miles, which was 7 inches on his road map. Which equation represents the actual miles traveled, m, relative to the distance shown on the map, d.
m=d/45
m=45xd
d=45xm
d=45/m
Answers
The equation representing the actual miles traveled, m, relative to the distance shown on the map, d is m = 45 × d, so option B is correct.
What is the equation?Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign. It shows that the expressions printed on the left and right sides have an equal relationship.
Given:
The distance travelled = 315 miles,
The distance on the map = 7 inches,
Calculate the equation represents the actual miles traveled,
Actual distance = The distance traveled / The distance on the map × The distance on the map
m = 315 / 7 × d
m = 45 × d
Therefore, the equation representing the actual miles traveled, m, relative to the distance shown on the map, d is m = 45 × d.
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help meeeeeeeeeee pleaseee
Answers
The pressure of 28 inches of mercury occurs about 6 miles from the eye of the hurricane. We get this from the given algebraic expression.
What is an expression?An expression is formed by variables, constants, and algebraic operations. Since the operation among them is an algebraic or arithmetic operation, it is said to be an algebraic expression.
Calculation:It is given that the algebraic expression that relates the barometric pressure and the eye of the hurricane as
f(x) = 0.48 ln(x+2) + 27
Here x is the distance in miles from the eye of the hurricane.
f(x) is the pressure of the mercury in a barometer in inches
So, the required distance from the eye of the hurricane when the pressure of 28 inches of mercury in the meter is
(Here f(x) = 28)
f(x) = 0.48 ln(x+2) + 27
⇒ 28 = 0.48 ln(x+2) + 27
⇒ 0.48 ln(x+2) = 28 - 27
⇒ ln (x+2) = 1/0.48
⇒ ln(x+2) = 2.0833
Applying exponential base "e" on both sides, we get
(x+2) = [tex]e^{2.0833}[/tex]
⇒ x + 2 = 8.0309
⇒ x = 8.0309 - 2 = 6.0309
When the result is rounded to the nearest whole number, we get x = 6 miles.
Thus, for the pressure of 28 inches of mercury, the eye of the hurricane is 6 miles far from the barometer.
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A sample of 38 observations is selected from one population with a population standard deviation of 3.0. The sample mean is 100.5. A sample of 50 observations is selected from a second population with a population standard deviation of 5.2. The sample mean is 98.8. Conduct the following test of hypothesis using the 0.02 significance level.
P value?
Answers
A hypothesis is an assumption, an idea that is proposed for the sake of argument so that it can be tested to see if it might be true.
What is the hypotheses in research?A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.Hypotheses are used to support scientific research and create breakthroughs in knowledge. These brief statements are what form the basis of entire research experiments. Thus, a flaw in the formulation of a hypothesis may cause a flaw in the design of an entire experiment.a. two-tailed test
b. reject H0 if Z>1.96 or Z<-1.96
c. Z = 1.73
d. we have failed to reject the null hypothesis
e. P-value = 0.0418
We will use a Z test to resolve this, an it will be a two-tailed test because the hypothesis statements are not indicating a specific direction for the significant difference (H0 : μ1 = μ2 ; H1 : μ1 ≠ μ2), this also means that the significanclevel will be divided between the both tails (2.5% en each tail for the rejection regions). See attached drawing for reference.We need to find our critical value:
Zα/2 = Z(0.05/2) = 0.025
If we look for 0.025 in a Z table we will find that the critical value is 1.96 to the right, and by symmetry -1.96 to the left. So our decision rule will be to reject H0 if Z>1.96 or Z<-1.96The Z test will be done using the next equation:
Z = (x⁻1 - x⁻2) - (μ1 - μ2) / √( σ²1/n1 + σ²2/n2
Because we are testing the null hypothesis we know that μ1 - μ2 must be zero if they are supposed to be equal (H0 : μ1 = μ2), so we calculate as follows:Z = (100.5 - 98.8) - (0) / √( (3.4)²/38 + (5.8)²/51 = 1.7/0.9817 = 1.73
Z<1.96, therefore we have failed to reject the null hypothesis
The P-value for this test would be represented by the probability of Z being greater than 1.73, so we can look for it in any Z table, finding that its value is 0.0418, and because P-value>0.025 we again confirm that we don't have evidence statistically significant to reject the null hypothesis
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When determining if triangles are congruent, what additional angles/sides should you mark in each triangle? Select all that apply.
Reflexive Angles
Reflexive Sides
Vertical Angles
nothing
Answers
Triangles are congruent, then there is no additional angles/sides should we mark in each triangle.
What is congruent triangles?
If and only if we can use rigid transformations to map one figure onto the other, then two figures are said to be congruent. All corresponding sides and angles are congruent because rigid transformations maintain distance and angle measure. Therefore, measuring all of the sides and angles of a pair of triangles would be one method of determining whether they are congruent.
Since reflexive angles means is an angle that is more than 180 degrees and less than 360 degrees.
And the reflexive sides means the reflexive property of congruence states that any shape is congruent to itself.
Vertical angles are angles opposite each other where two lines cross.
But to check the congruence of two triangles we only have the angles and sides of the two triangles are same.
So, there is no additional angles/sides should we mark in each triangle.
Hence, triangles are congruent, then there is no additional angles/sides should we mark in each triangle.
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Are the two expressions x-5 and x-5 equivalent? Give evidence to support your yes or no answer.
Remember, for expressions to be equivalent, they must have the same value for all values of the input
variable, x.
Answers
The expressions x - 5 and x - 5 gives the equal value for the different values of x, therefore expressions are equivalent.
What is an algebraic expression?An algebraic expression is consists of variables, numbers with various mathematical operations,
The given expressions are,
x - 5 and x - 5
To determine the expressions are equivalent,
Since, in the both, the expression x is a variable, and 5 is an integer,
Therefore, for the values of x the value of expression should be equal.
Substitute x = 0,
x - 5 = 0 - 5 = - 5
And
x - 5 = 0 - 5 = - 5
Substitute x = 1
x - 5 = 1 - 5 = - 4
and
x - 5 = 1 - 5 = - 4
Since, for the different values of x the values of expressions are equal.
Hence, expression x - 5 and x - 5 are equivalent.
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Find the area of the triangle below.
Be sure to include the correct unit in your answer.
10yd
4yd
7yd
Answers
The area of the triangle below 8 yards
What is triangle?
A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
A polygon having three edges and three vertices is called a triangle. It is one of the fundamental geometric forms. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
Triangles are three-sided shapes. The many kinds of triangles go by various names. The size of the angles and the length of the sides determine the type of triangle (corners). Equilateral, isosceles, and scalene triangles are the three varieties of triangles based on the length of the sides.7-15=8
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if you roll die, what is the probability of rolling a numbe rless than 4 or rolling an odd number
Answers
The probability of rolling an odd number or a number less than 4 is 2/3.
What is probability?
The degree to which something is likely; the probability that something will occur or will be the case.
Here, we have
Given
A single die is rolled.
Sample space = {1, 2, 3, 4, 5, 6}
Let P(A) be the probability of getting an odd number, where A = {1, 3, 5}
Let P(B) be the probability of getting a number less than 4,
where B = {1,2,3}
A ⋂ B ={1, 3}
P(A) = 3/6 = 1/2
P(B) = 3/6 = 1/2
P(A ⋂ B) = 2/6 = 1/3
Let P be the required probability of getting an odd number or a number less than 4
P = P( A ⋃ B ) = P(A) + P(B) - P(A ⋂ B)
P( A ⋃ B ) = 1/2 + 1/2 - 1/3
P( A ⋃ B ) = 1 - 1/3
P( A ⋃ B ) = 2/3
Hence, the probability of rolling an odd number or a number less than 4 is 2/3.
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Dontrell bought 5 1/2 pounds of potatoes for $3.52. What equation can be used to represent the total amount he paid, y, for x pounds of potatoes?
Enter the correct equation in the box.
____________________
Answers
The equation for total amount to be paid represented as y and pounds of potatoes represented as x will be y = 0.64x
What is linear equation?Ax + By + C = 0 can be used to express a linear equation in two variables, where x and y are the two variables, and each has a degree of one.
Ex. -2x+3y=8
Total weight of potatoes in pounds Dontrell bought= x
Let total amount Dontrell he pays= $ y
It is given 5.5 pounds are bought by paying $3.52
5.5 pounds = $3.52
1 pound = $ 3.52/5.5
1pound=$0.64(Using Unitary method)
Dontrell buy x pounds potatoes and he pays $y
Therefore,
y=0.64x
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Question content area top Part 1 A motorboat is capable of traveling at a speed of 10 miles per hour in still water. On a particular day, it took 15 minutes longer to travel a distance of 6 miles upstream than it took to travel the same distance downstream. What was the rate of current in the stream on that day? PLEASE HURRY
Answers
We can determine the stream's current velocity by solving a set of equations, which gives us S is 2 mi/h.
Calculate the stream's current flow rate on that particular day?The total speed of a motorboat traveling downstream is equal to the speed of the boat in still water plus the speed of the stream, whereas the total speed of a motorboat traveling upstream is equal to the speed of the stream minus one.
Therefore, the speed upstream is: (14 mi/h - S)
The speed downstream is (14 mph + S), where S is the stream's current flow rate.
We can construct the equations below after we know that it takes 15 minutes longer to walk 12 miles downstream:
14 mph plus speed (S) times the time (T minus 15 minutes) equals 12 miles.
In order to solve this, one of the variables in one of the equations needs to be isolated. I'll isolate T in the first equation:
T = (12 miles)/(14 miles per hour Plus S)
By substituting it in the other equation, we will obtain the following value: (14 mi/h - S)*((12 mi)/(14 mi/h + S) - 15 min) = 12 mi.
Taking only the favorable outcome, we obtain:
S = (24 - 25)/(-0.5) = 2 mph
2 mi/hr is the stream's current velocity.
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16
22
34
52
76
?
Select one:
a.
106
b.
137
c.
89
d.
105
Answers
Answer:
106
Step-by-step explanation:
The pattern goes +6, +12, +18, etc
Thus, the final term is simply +30.
76+30 = 106
Hope it helps :) and let me know if you want me to elaborate.
If cos (∅)=-1/4 and ∅ is in the 3rd quadrant. find the exact value for sin (∅).
sin(∅)=
Answers
The exact value for sin (∅) is √15/4 if cos (∅)=-1/4 and ∅ is in the 3rd quadrant.
What are trigonometric functions?In mathematics, the trigonometric functions—also known as circle, angle, or goniometric functions—are real functions that connect the angle of a right-angled triangle to the ratios of its two side lengths. As some of the most basic periodic functions, they are frequently employed in Fourier analysis to examine periodic phenomena.
The sine, cosine, and tangent are the trigonometric functions that are most commonly utilized in contemporary mathematics. The cotangent, secant, and their less common reciprocals, the cosecant, are each of their reciprocals.
Given, cos (∅)=-1/4 and ∅ is in the 3rd quadrant.
cos²∅+sin²∅=1
sin²∅=1-cos²∅
sin²∅=(1-(-1/4)²)
sin²∅=1-(1/16)
sin²∅=15/16
sin∅=√15/4
Therefore, the exact value for sin (∅) is √15/4 if cos (∅)=-1/4 and ∅ is in the 3rd quadrant.
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The first three terms of a sequence are given. Round to the nearest thousandth (if
necessary).
205, 201, 197, ...
Find the 35th term.
Answers
The first three terms of a sequence are given, so the 35th term is: [tex]a_n = 69[/tex]
What is sequence?A grouping of numbers in a specific order is known as a sequence. On the other hand, a series is described as the accumulation of a sequence's constituent parts. A sequence is a list of elements that has been arranged in a certain way.
An ordered list of numbers is a sequence. The three dots indicate that the established pattern should go forward. A phrase is used to describe each number in the series. The first word in the order 1, 3, 5, 7, 9,... is 1, the second is 3, the third is 5, and so on.
The first three terms are : 205, 201, 197, .......
The general term through the pattern is:
[tex]a_n = - 4n+209[/tex]
or, [tex]a_n = - 4(35)+209[/tex]
here, n = 35
or, [tex]a_n = 69[/tex]
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The sample space of an experiment involving graduating seniors is {No job offers, Exactly one job offer, Exactly two job offers, Exactly three job offers, More than three job offers}, where P(No job offers) = 0.33, P(One job offer) = 0.22, P(Two job offers) = 0.15, P(Three job offers) = 0.11, P(More than three job offers) = 0.19. Find the probability that a graduating senior receives two or three job offers. 0.26 0.36 0.46 0.56
Answers
0.26 is probability that a graduating senior receives two or three job offers.
What is probability in math?
Calculating or estimating how likely or "possible" something is to occur is the subject of probability. Words like "certain," "impossible," or "probable" can be used to express the likelihood of an event occurring.
Probabilities in mathematics are always represented as fractions, decimals, or percentages with values ranging from 0 to 1.
P(2 or 3 jobs)=P(2 jobs)+P(3 jobs)-P(2 jobs and 3 jobs)=P(2 jobs) + P(3 jobs) since a student can not have 2 jobs as well as three jobs at a time.
So,
P(2 or 3 jobs)=0.15+0.11 = 0.26
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Select the correct answer. What happens if the correlation coefficient equals 0? A. There is a strong negative linear relationship between x and y. B. There is not a linear relationship between x and y. C. There is a strong positive linear relationship between x and y. D. There is a weak negative linear relationship between x and y. Reset Next
Answers
By the Definition of a Correlation Coefficient,
x and y do not have a linear relationship.
Option B is the correct answer.
What Is the Definition of a Correlation Coefficient?The correlation coefficient describes the movement of one variable in relation to another. A positive correlation indicates that the two are moving in the same direction, with 1 denoting a perfect positive correlation. A value of -1 indicates a perfect negative, or inverse, correlation, while a value of zero indicates that no linear correlation exists.
What does a correlation between 0 and +1 mean?The number's value indicates the strength of the relationship: r = 0 indicates that there is no correlation. r = 1 indicates that there is a perfect positive correlation. r = -1 shows a perfect negative correlation.
According to the question, If the correlation coefficient is zero, there is no linear relationship.
If the correlation coefficient is zero, the relationship between x and y is not linear. Another possible relationship (such as an exponential or quadratic) could exist, but this is dependent on the scatter plot provided.
By the Definition of a Correlation Coefficient,
Option B is the correct answer.
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By the Definition of a Correlation Coefficient, X and Y do not have a linear relationship. Option B is the correct answer.
What Is the Definition of a Correlation Coefficient?The correlation coefficient describes the movement of one variable in relation to another. A positive correlation indicates that the two are moving in the same direction, with 1 denoting a perfect positive correlation. A value of -1 indicates a perfect negative, or inverse, correlation, while a value of zero indicates that no linear correlation exists.
What does a correlation between 0 and +1 mean?The number's value indicates the strength of the relationship: r = 0 indicates that there is no correlation. r = 1 indicates that there is a perfect positive correlation. r = -1 shows a perfect negative correlation.
According to the question, If the correlation coefficient is zero, there is no linear relationship.
If the correlation coefficient is zero, the relationship between x and y is not linear. Another possible relationship (such as an exponential or quadratic) could exist, but this is dependent on the scatter plot provided.
By the Definition of a Correlation Coefficient,
Option B is the correct answer.
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$4232 invested for 4 years at 6% compounded annually
Answers
The final amount of the money according to compound interest model is $ 5342.80.
What is the resulting amount after four years by compound interest model?
Herein we find a case of a money deposited that increases its amount in time by compound interest, that is, the amount increases continuously in time. The compound interest model is described below:
C' = C · (1 + r / 100)ⁿ
Where:
C - Initial amount.C' - Current amount. r - Interest rate, in percentage.n - Number of periods, in years.If we know that C = 4232, r = 6 and n = 4, then the final amount of the money is:
C' = 4232 · (1 + 6 / 100)⁴
C' = 5232.802
The final amount is $ 5342.80.
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Please do this I have to turn it in to pass
Answers
Answer:
I've solved all of the above for you :)
Step-by-step explanation:
3q² + 7 = 55
3q² = + 7 - 7 = 55 - 7
3q² = 48
3q²/3 = 48/3
q² = 12
q = 2√3
√p - 4 = - 5
p - 4 = (-5)²
p - 4 + 4 = 25 + 4
p = 29
5√a/2 = 40
5√a/2 × 2 = 40 × 2
5√a = 80
5√a/5 = 80/5
√a = 16
a = 256
c³ - 4 = 23
c³ - 4 + 4 = 23 + 4
c³ = 27
c = 3
(k + 3)² = 4
k² + 6k + 9 = 4
k² + 6k + 9 - 4 = 0
k² + 6k + 5 = 0
k² + k + 5k + 5 = 0
k(k + 1) + 5(k + 1) = 0
(k + 5) (k + 1) = 0
k = (-5) or (-1)
√s + 4 = 6
s + 4 = (6)²
s + 4 - 4 = 36 - 4
s = 32
(√f - 5) = (√7 - f)
(√f - 5)² = (√7 - f)²
f - 5 = 7 - f
f - 5 + 5 + f = 7 + 5 - f + f
2f/2 = 12/2
f = 6
∛j + 9 = 0
∛j + 9 - 9 = -9
∛j = (-9)
j = (-9)³
j = (-729)
b² - 1 = 24
b² - 1 + 1 = 24 + 1
b² = 25
√b² = √25
b = 5
13 = (w - 2)² + 5
13 = w² - 4w + 4 + 5
13 - 9 = w² - 4w
w² - 4w = 4
w² - 4w - 4 = 0
w² - 2w - 2w - 4 = 0
w(w - 2) - 2(w - 2) = 0
(w - 2) (w - 2) = 0
w = 2 or 2
12 = 4√2x + 1
12/4 = 4√2x + 1/4
3 = √2x + 1
√2x + 1 = 3
2x + 1 = 9
2x + 1 - 1 = 9 - 1
2x/2 = 8/2
x = 4
(g + 1)³ = (-8)
g³ + 1³ + 3g(g + 1) = (-8)
g³ + 1 + 3g² + 3g = (-8)
g³ + 3g² + 3g = (-8) - 1
g³ + 3g² + 3g = -9
g³ + 3g² + 3g + 9 = 0
g = (-3)
∜(5m + 1) = 4
[∜(5m + 1)]⁴ = (4)⁴
5m + 1 = 256
5m + 1 - 1 = 256 - 1
5m/5 = 255/5
m = 51
∛(y³ - 19) = 2
(y³ - 19) = (2)³
y³ - 19 = 8
y³ - 19 + 19 = 8 + 19
y³ = 27
y = 3
Write 0.00317 in scientific notation.
Answers
Answer:
3.17×10^3
Step-by-step explanation:
Hope it helps!
Write a function g whose graph is a horizontal shrink by a factor of 1/3
of the graph of f. F(x)=2|x+3|-2
Answers
Answer:
g(x) = 6|x + 1| - 2-----------------------------------------
Given:
Function f(x) = 2|x + 3| - 2Find a function g which is a horizontal shrink by a factor of 1/3 of f(x).
Horizontal shrink by a factor of k is:
g(x) = f(x/k)Apply this to the given function:
g(x) = f(x : 1/3) = f(3x) = 2|3x + 3| - 2 = 6|x + 1| - 2The graph shows the proportional relationship between the number of gems collected and the number of levels that has been completed in a video game.
Determine the constant of proportionality for the relationship.
Answers
The constant of proportionality for the relationship is 70.
From the given graph (2, 140), (4, 280), (6, 420), (8, 560) and (10, 700).
What is a proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".
From the graph we can see it is direct proportion.
Here, y∝x
⇒ y=kx
⇒ k=y/x
⇒ k=140/2
⇒ k=70
Hence, the constant of proportionality for the relationship is 70.
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= |4|+|−3|
= |1,2| − |−1,2|
= 2|4 − 10| + |7 − 5|
Answers
Answer:
Step-by-step explanation:
12=666
What is the length of side AB? please help
Answers
top I think he or she is right
The length of the AB in the given right triangle is √3/6
Given that, a right triangle with the base measure 6 units and an acute angle 30°,
We need to find the measure of side AB,
So, we will use the concept of trigonometric ratios,
Tan 30° = AB / AC
Tan 30° = AB / 6
1 / √3 = AB / 6
AB = √3/6
Hence the length of the AB in the given right triangle is √3/6
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The classroom outside bag had 5 frisbees in it. If 25% of the outside toys are frisbees, then how many total toys are in the bag?
Answers
The total number of toys in the bag is 20
How to determine the number of total toys in the bag?From the question, we have the following parameters that can be used in our computation:
Frisbees = 5
Proportion of these Frisbees = 25%
Using the above as a guide, we have the following:
Number of Frisbees = Total number of Frisbees * The proportion of these Frisbees
Substitute the known values in the above equation, so, we have the following representation
Total number of Frisbees * 25% = 5
Divide both sides by 25%
Total number of Frisbees = 20
Hence, the total is 20
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estimate the difference between 3,894,256 and 756,533 by rounding each number to the nearest thousand. 4,561,000 3,137,000 3,138,000 3,139,000
Answers
The difference between 3894256 and 756533 by rounding each number to the nearest thousand is 3138000
The first number = 3894256
The second number = 756533
To find the difference between the numbers we have to use the subtraction
Difference between 3894256 and 756533 = 3894256 - 756533
Subtract the numbers
= 3137723
Rounding of a number is write the numbers to the nearest place values like tens, hundreds and thousand etc.
Here, the number is 3137723 and we have to round the number to nearest thousand
Round to nearest thousand = 3137000
Therefore, the result nearest to the thousand is 3138000
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A person works at a vegetable farm and a paddy field. He earns Rs 200/- per hour from
vegetable farm and Rs 250/- per hour from paddy field. Last week, he worked for both jobs for a total of 30 hours, and earned a total of Rs 6900/-. How long did the person work at the vegetable farm last week, and how long did he work at the paddy field.. ?
Answers
Answer:
He worked 26 hours at the vegetable farm and 4 hours at the paddy field.
Step-by-step explanation:
Let us take the working hour at a vegetable farm be x and at paddy field be y
He worked for both jobs for a total of 30 hours.
So,
x + y = 30 ...(1)
He earns Rs 200/- per hour from vegetable farm and Rs 250/- per hour from paddy field, total of Rs 6900.
So,
200x + 250y = 6900
2x + 5y = 138 ...(2)
From equation 1 we get,
x = 30 - y
Put the value of x = 30 - y in equation 2 we get,
2x + 5y = 138
2(30 - y) + 5y = 138
60 - 2y + 5y = 138
60 + 3y = 138
3y = 138 - 60
3y = 78
y = 26
Now, put the value of y in equation 1 we get,
x + y = 30
x + 26 = 30
x + 26 - 26 = 30 - 26
x = 4
Thus, He worked 26 hours at the vegetable farm and 4 hours at the paddy field.
An object was launched from the top of a hill with an upward vertical velocity of 100 feet per second. The height of the object can be modeled by the function h(t)=-16 t^2+100 t+300, where t represents the number of seconds after the launch. Assume the object landed on the ground at sea level. Find the answer using graphing technology,
The object's height was } \quad \text { when it was launched.
Answers
The object's height was 300 ft above sea level when it was launched.
What is a quadratic equation?
An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as a[tex]x^{2}[/tex] + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.
Given, the height of the object can be modeled by the function
h(t)=-16t^2+100 t+300
Height of object when it was launched
At the time of launched, t=0
h = -16(0)^2 + 100(0) + 300 = 300 ft above sea level
Hence, the object's height was 300 ft above sea level when it was launched.
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The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is nine times the measure of the first angle. The third angle is 20 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.
Answers
(X=60,Y=47,Z=73), the measures of the three angles.
What are angles?When two rays are linked at their ends, they create an angle in geometry. The sides or arms of the angle are what are known as these rays.
When two lines meet at a point, an angle is created.
An "angle" is the measurement of the "opening" between these two rays. It is symbolized by the character.
The circularity or rotation of an angle is often measured in degrees and radians.
Angles are a common occurrence in daily life.
Angles are used by engineers and architects to create highways, structures, and sports venues.
According to our question
x+y+z=180
The second and third angles' combined measurements equal twice the first angle's combined measurement, therefore
y+z−2x+y+z=2=0
Third angle has 26 more degrees than second angle, therefore
z−y+z=y+26=26
As a result, we obtain the equation system.
x+y+z=180−2x+y+z=0−y+z=26
(1)(2)(3)
By removing y and z, use equations (1) and (2) to determine x. To get rid of y and z, multiply equation (2) by one before adding it to equation (1).
x+y+z2x−y−z3xx=180=0=180=60(4)
To get rid of z, use equations (1) and 3). To get rid of z, multiply equation (3) by 1 and then add it to equation (1).
x+y+zy−zx+2y=180=−26=154(5)
To determine, substitute x=60 into equation (5).
x+2y(60)+2y2yy=154=154=94=47
In order to find, we can now change x=60 and y=47 in equation (1).
x+y+z(60)+(47)+zz+107z=180=180=180=73
Therefore, there is a solution.
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