Answer:
heres your answers
Step-by-step explanation:
George Washington was defeated when he went to fight the French in the Ohio River Valley.
The British then sent a trained army to attack the French Fort Duquesne.
The British suffered a defeat in the first battle of the French Indian War.
The population of a city, P , in millions, is a function of ????, the number of years since 2010, so P = ???? (????). Explain the meaning of the statement ????(5) = 7 in terms of the population of this city.
Answer:
The population of city is 7 million in 2015.
Step-by-step explanation:
It is given that the population of a city, P, in millions, is a function of t, the number of years since 2010.
It means, P = f(t).
We need to explain the meaning of the statement f(5) = 7 in terms of the population of this city.
f(5) = 7 means the population is 7 millions at t=5.
t = 5 means 5 years after 2010, i.e., 2010+5 = 2015
Therefore, the population of city is 7 million in 2015.
What is the Translation Postulate?
Answer: to suggest or accept that a theory or idea is true as a starting point for reasoning or discussion.
Step-by-step explanation:
Here's an example: Astronomers postulate that the comet will reappear in 4000 years.
A, B, and C are midpoints of ∆GHJ. When AB = 3x+8 and GJ = 2x+24, what is AB?
Answer:
AB = 14 units
Step-by-step explanation:
Given:
A triangle GHJ with the following aspects:
A, B, C are midpoints of sides GH, HJ and GJ respectively.
AB = [tex]3x+8[/tex]
GJ = [tex]2x+24[/tex]
Midsegment Theorem:
The line segment joining the midpoints of any two sides of a triangle is parallel to the third side and the length of the midsegment is one-half of the length of the third side.
Therefore, AB is the midsegment of sides GH and HJ and thus, is parallel to GJ and equal to one-half the length of GJ.
[tex]\therefore AB=\frac{1}{2}\times\ GJ[/tex]
Now, plug in the values of AB and Gj and solve for 'x'.
This gives,
[tex]3x+8=\frac{1}{2}(2x+24)\\\\3x+8=x+12\\\\3x-x=12-8\\\\2x=4\\\\x=\frac{4}{2}=2[/tex]
Now, the length of AB is given by plugging in 2 for 'x'.
[tex]AB=3\times2+8=6+8=14[/tex]
Therefore, the length of midsegment AB is 14 units.
Answer:
14 Units
Step-by-step explanation:
The length of midsegment AB is equal to one-half the length of side GJ. In this case, AB is given by the expression 3x + 8 and GJ is given by the expression 2x + 24.
To find the value of x, we can set the expressions for AB and GJ equal to each other and solve for x.
3x + 8 = 1/2(2x + 24)
We can simplify this equation by distributing the 1/2 to the terms inside the parentheses:
3x + 8 = x + 12
Next, we can subtract x from both sides to isolate the x term:
3x - x + 8 = 12
2x + 8 = 12
Then, we can subtract 8 from both sides:
2x = 4
Finally, we can solve for x by dividing both sides by 2:
x = 2
Now that we have the value of x, we can substitute it back into the expression for AB:
AB = 3(2) + 8
AB = 6 + 8
AB = 14
Therefore, the length of midsegment AB is 14 units.
You deposited $10,000 into a savings account at 6%. After a certain amount of time, you earned $4,800. How long did you have your money in the savings account?
Answer:
800 months
Step-by-step explanation:
The formula for interest is:
(Capital * saving account * time) / 100
So:
(10000 * 0.06 * x) / (100) = 4800
We clear x:
(10000 * 0.06 * x) = (100) * 4800
x = 480,000 / (10000 * 0.06)
x = 800 months (66.67 years)
To determine the duration for which the deposited $10,000 at 6% interest grew to a total of $14,800 ($10,000 principal + $4,800 interest), the formula for compound interest can be re-arranged to solve for the time variable. You'll use the amount of money accumulated, the principal amount, the annual interest rate, and the assumption that the interest is compounded annually. Plug these values into the formula to calculate the number of years.
Explanation:You deposited $10,000 into a savings account at 6% interest. To determine how long it took for you to earn $4,800 in interest, we can use the formula for compound interest, which is A = P(1 + r/n)^(nt), where:
A is the amount of money accumulated after n years, including interest.P is the principal amount (the initial amount of money).r is the annual interest rate (decimal).n is the number of times that interest is compounded per year.t is the time the money is invested for, in years.In this case, we can rearrange the formula to solve for t, because you want to find out how many years it took for your investment to turn into A = $10,000 + $4,800 = $14,800. Assuming the interest is compounded annually (n = 1), the formula becomes:
t = ln(A/P) / n * ln(1 + r/n)
Plugging in the numbers gives us:
t = ln($14,800 / $10,000) / ln(1 + 0.06)
By calculating this, you can get the number of years you had the money in the savings account.
The process of using sample statistics to draw conclusions about the population parameters is referred to as
A. inferential statistics
B. sampling
C. the scientific method
D. descriptive statistics
Answer:
Option A) inferential statistics
Step-by-step explanation:
We describe inferential statistic as:
Inferential Statistic:
It s the process of estimating population parameter with the help of a sample from the population.A random sample from the population is used to describe the population with the help of sample statistic.A smaller subset is used to inference about the larger set.Thus, the correct answer is
Option A) inferential statistics.
Answer:
Step-by-step explanation:
A machine is supposed to mix peanuts, hazelnuts, cashews, and pecans in the ratio 5:2:2:1. A can containing 500 of these mixed nuts was found to have 269 peanuts, 112 hazelnuts, 74 cashews, and 45 pecans. At the 0.05 level of significance, test the hypothesis that the machine is mixing the nuts in the ratio 5:2:2:1.?
Answer:
the machine is mixing the nuts are not in the ratio 5:2:2:1.
Step-by-step explanation:
Given that a machine is supposed to mix peanuts, hazelnuts, cashews, and pecans in the ratio 5:2:2:1.
A can containing 500 of these mixed nuts was found to have 269 peanuts, 112 hazelnuts, 74 cashews, and 45 pecans.
Create hypotheses as
H0: Mixture is as per the ratio 5:2:2:1
Ha: Mixture is not as per the ratio
(Two tailed chi square test)
Expected values as per ratio are calculated as 5/10 of 500 and so on
Exp 250 100 100 50 500
Obs 269 112 74 45 500
O-E 19 -12 -26 -5 0
Chi 1.343 1.286 9.135 0.556 12.318
square
df = 3
p value = 0.00637
Since p value < alpha, we reject H0
i.e. ratio is not as per the given
We perform a chi-square goodness of fit test to analyze if the machine is mixing nuts according to the ratio. We set a null and alternate hypothesis, calculate expected frequencies for each group, calculate chi-square test statistic and compare it with the critical value. If the calculated chi-square is greater than the critical value, we reject the null hypothesis.
Explanation:This question asks about hypothesis testing using chi-squared tests. In this particular case, we're testing the observed distribution of mixed nuts against the expected distribution given by the ratio 5:2:2:1.
First, set null and alternate hypotheses. Here, the null hypothesis is that the machine is mixing the nuts in the correct ratio of 5:2:2:1, while the alternative hypothesis is that the machine is not mixing the nuts in the ratio of 5:2:2:1.Calculate the expected frequencies for each group. The total number of nuts is 500, and they should be distributed in the ratio 5:2:2:1. So we'd have 250 peanuts, 100 hazelnuts, 100 cashews, and 50 pecans.Calculate the chi-square test statistic using the formula x^2 = Σ[(O-E)^2 / E], where O refers to the observed frequencies from the question, and E refers to the expected frequencies calculated above. Compare the calculated chi-square test statistic with the critical value from the chi-square distribution table. If our calculated chi-square test statistic is greater than the critical value, we reject the null hypothesis and conclude that the machine is not mixing the nuts in a ratio of 5:2:2:1. Learn more about hypothesis testing here:https://brainly.com/question/34171008
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A house with an original value of increased in value to in years. What is the ratio of the increase in value to the original value of the house?
Answer:
Ratio of the increase in value to the original value will be 1 : 5
Step-by-step explanation:
This question is incomplete; Here is the complete question.
A house with an original value to $150,000 increased in value to $180,000 in 5 years. what is the ratio of the increase in value to the original value of the house?
Original value of the house = $150000
Value of the house after 5 years = $180000
Appreciation in value of the house after 5 years = $180000 - $150000
= $30000
Now the ratio of the increase in value to the original value = [tex]\frac{\text{Increased value}}{\text{Original value}}[/tex]
= [tex]\frac{30000}{150000}[/tex]
= [tex]\frac{1}{5}[/tex] or 1 : 5
Therefore, ratio of the increase in value to the original value of the house is 1 : 5
Final answer:
To find the ratio of the increase in house value to the original value, subtract the original price from the increased price, then divide by the original price. For a house purchased at $200,000 and increased to $250,000, the ratio would be 0.25, or a 25% increase from the original value.
Explanation:
To calculate the ratio of the increase in value to the original value of a house, you must take the difference between the final value and the original value, then divide this by the original value. Suppose a house was bought for $200,000 and is now worth $250,000, this would be an increase of $250,000 - $200,000 = $50,000. The ratio of increase to original value would thus be $50,000 / $200,000 = 0.25 or 1:4. This indicates that, for every dollar of the original value, the house increased in value by 25 cents. If we wanted to express this as a percentage, we would multiply by 100, giving us a 25% increase in value. However, it's important to remember other factors such as transaction costs, market conditions, and loan repayment when considering the rate of return on a house.
The formula for the surface area of a sphere is A=4pi r*2, where r is the length of the radius. Find the surface area of the sphere with a radius of 14. Use 22/7 as pi
Answer:
Step-by-step explanation:
area=4×22/7×14²=4×22×28=2464 units²
The surface area of a sphere with a radius of 14 is 2464 square units. When considering significant figures, this is rounded to 2500 square units to match the two significant digits of the given radius.
To find the surface area of a sphere with a radius of 14, using the given value of 22/7 for , the formula A = 4*pi*r2 is used. Plugging in the numbers:
A = 4 * (22/7) * (14)²
A = 4 * (22/7) * 196
A = 4 * 22 * 28
A = 88 * 28
A = 2464
Thus, the surface area of the sphere is 2464 square units.
A certain shop repairs both audio and video components. Let A denote the event that the next component brought in for repair is an audio component, and let B be the event that the next component is a compact disc player (so the event B is contained in A). Suppose that P(A) = .625 and P(B) = .05. What is P(B/A)?
Answer:P(A/B)=0.08
Step-by-step explanation:
The probability formula to find p(A/B) is :
P(A/B) = p(A n B) / p(A)
Which means that B is contain in A and p(A n B) is p(B)
p(A n B)=p(B)=0.05
p(A)=0.625
Therefore
P(A/B) = p(A n B) / p(A)=p(B) / p(A)
P(A/B)=0.05 / 0.625
P(A/B)=0.08
Let f be integrable over R show that the funciton F defined by F(x) indefinite integral is properly defined and continuous is it necessarily lipschitz mathexchange?
Answer:
Step-by-step explanation:
A continuous function is one that has a set of unique solutions. a function is also said to be continuous if at every interval, there exist no sudden change in the assumed values otherwise the function will be discontinuous.
for example, the sine and cosine function are continuous over a set of real integers.
from the question, any assumed expression of x and integrating over the interval x and infinity will render the function continuous.
Assumed f(x) = cuberoot of x
Integrating and evaluating will prove that the function is continuous, as such a defined function is always a continuous function and not necessarily lipschitz.
In a sheet metal operation, three identical notches and four identical bends are required. If the operations can be done in any order, how many different possible sequences are there to complete the manufacturing?
The problem can be solved using combinatorics, specifically the permutation of a multiset. Using the formula P(n; n1, n2, ..., nk) = n! / (n1! * n2! *...* nk!), where n is total number of operations and n1, n2,... are the number of each identical operation, the number of different possible sequences to complete the manufacturing operation are 35.
Explanation:The number of sequences of the operations can be found by using the formula for permutations of multiset - a concept in combinatorics part of mathematics. Permutations of a multiset are the number of ways in which we can arrange all the elements of the multiset considering the repetition of elements. We have 7 operations in total: three identical notches (type A) and four identical bends (type B). The formula is:
P(n; n1, n2, ..., nk) = n! / (n1! * n2! *...* nk!), where n is the total number of items(7 in this case), n1,n2,...,nk are the number of each type of item.
Therefore, the number of different possible sequences to complete the manufacturing is: P(7 ; 3, 4) = 7! / (3! * 4!). This evaluates to 35.
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The endpoints of a diameter of a circle are (3, -2) and (-5, 8). What is the equation of the circle in standard form?
Answer:
(x + 1)² + (y − 3)² = 41
Step-by-step explanation:
The center of the circle is the midpoint of the diameter.
(h, k) = ((x₂ + x₁)/2, (y₂ + y₁)/2)
(h, k) = ((3 + -5)/2, (-2 + 8)/2)
(h, k) = (-1, 3)
The radius is half the length of the diameter.
r = ½ √((x₂ − x₁)² + (y₂ − y₁)²)
r = ½ √((3 − -5)² + (-2 − 8)²)
r = ½ √(8² + 10²)
r = √41
Therefore, the equation of the circle is:
(x − h)² + (y − k)² = r²
(x + 1)² + (y − 3)² = 41
The standard form of equation of the circle is (x + 1) + (y - 3) = (6.40)².
What is distance between two points?The length of the line segment bridging two points on a plane is known as the distance between the points.
The formula to find the distance between the two points is usually given by d=√{(x₂-x₁)² + (y₂-y₁)²}
Given is that the endpoints of a diameter of a circle are (3, -2) and (-5, 8).
The center: (3-5/2, -2+8/2) = (-1, 3)
The diameter d = √{(x₂-x₁)² + (y₂-y₁)²}
d = √{(-5-3)² + (8 + 2)²}
d = √{64 + 100}
d = √164
d = 12.81
The radius r = 6.40
The standard form of equation of the circle is,
(x + 1) + (y - 3) = (6.40)²
Therefore, the standard form of equation of the circle is,
(x + 1) + (y - 3) = (6.40)²
To learn more about the distance between two points;
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Use the three steps to solve the problem.
One number is five more than another and their sum is three less than three times the smaller. Find the numbers.
List your answers in numerical order, separated by a comma.
The two numbers are 8,13.
Step-by-step explanation:
Let,
smaller number = x
Larger number = x+5
According to given statement;
Smaller number + Bigger number = 3x-3
[tex]x+(x+5)=3x-3\\x+x+5=3x-3\\2x+5+3=3x\\8 = 3x-2x\\8=x\\x=8[/tex]
Smaller number = 8
Larger number = 8+5 = 13
The two numbers are 8,13.
Keywords: algebraic equation, addition
Learn more about addition at:
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Answer:
The two numbers are 8,13.
Find the height of a right square pyramid that has a rectangular base area of 70 square units and a volume of 140 cubic units. A. 2 units B. 6 units C. 1 units D. 18 units
Answer:
B) 6 units
Step-by-step explanation:
The formula of the volume of the Pyramid is 1/3×area of the base×height
1/3×70×height=140
Dividing both sides by 70
1/3×height=2
Multiplying both sides by 3
Height = 6
Final answer:
The height of a right square pyramid with a rectangular base area of 70 square units and a volume of 140 cubic units is 6 units, by using the volume formula of the pyramid.
Explanation:
The question asks us to find the height of a right square pyramid with a given base area and volume. To find the height, we need to use the formula for the volume of a pyramid, which is given by the formula: Volume = (Base Area * Height) / 3. We are given the base area as 70 square units and the volume as 140 cubic units.
Using the formula to solve for the height we get:
Height = (Volume * 3) / Base Area = (140 * 3) / 70 = 6 units. Therefore, the height of the pyramid is 6 units.
The area of a rectangle is 32a^3b^4 square units. The length is 4a^2b. Find the width. show your work
Answer:
The answer to your question is width = 8ab³
Step-by-step explanation:
Data
Area = 32a³b⁴ u²
length = 4a²b u
Formula
Area of a rectangle = width x length
Solve for width
width = [tex]\frac{Area}{length}[/tex]
Substitution
width = [tex]\frac{32a^{3}b^{4}}{4a^{2}b}[/tex]
Simplify using rules of exponents, just remember that in a division we subtract the exponents and divide the coefficients normally.
width = 8 a²b³
Answer:
Step-by-step explanation: 32a^3 is -8 < a < - 8 axis interceptions 32a^3 vertical asymphotes None Extreme points of a32a^3 0,0
A flying squirrel's nest is 56 feet high in a tree. From its nest, the flying squirrel glides 70 feet to reach an acorn that is on the ground. How far is the acorn from the base of the tree?
Answer:
Step-by-step explanation:
Which is the graph of f(x) = StartRoot x EndRoot?
Answer:
The 4th graph
Step-by-step explanation:
To determine which graph corresponds to the [tex]f(x) = \sqrt{x}[/tex] we will start with inserting some values for x and see what y values we will obtain and then compare it with graphs.
[tex]f(1) = \sqrt{1} = 1\\f(2) = \sqrt{2} \approx 1.41\\f(4) = \sqrt{4} = 2\\f(9) = \sqrt{9} = 3[/tex]
So, we can see that the pairs (1, 1), (2, 1.41), (4, 2), (3, 9) correspond to the fourth graph.
Do not be confused with the third graph - you can see that on the third graph there are also negative y values, which cannot be the case with the [tex]f(x) =\sqrt{x}[/tex], the range of that function is [tex][0, \infty>[/tex], so there are only positive y values for [tex]f(x) = \sqrt{x}[/tex]
Answer:
if your on edge its the last one
Step-by-step explanation:
use the graphing calculator and input the equation and it will be fourth graph
Tessa is cooking steak for her family. She wants to be sure the steak has an internal temperature of at least 160 degrees Fahrenheit. She uses a thermometer to measure the internal temperature at two randomly chosen places. The minimum reading in the sample is 165 degrees Fahrenheit. Identify the population, the parameter, the sample, and the statistic______________.
Answer:
Population : all the steaks Tessa can cook
Parameter : minimum internal temperature of 160 degrees Fahrenheit
Sample : two random thermometer readings
Statistic : minimum sample reading of 165 degrees Fahrenheit
Step-by-step explanation:
Let's recall the definitions of these statistical concepts and match it with the information that were provided to us:
Populations can be the complete set of all similar items that exist, in our case, all the steaks that Tessa can cook.Parameter is is a value that describes a characteristic of an entire population, such as the minimum temperature of the steaks Tessa is cooking in Fahrenheit degrees.Sample is a subset of the population, in our case, the two random readings of the thermometer Tessa did.Statistic is a characteristic of a sample, for our problem, it's the minimum reading of 165 degrees Fahrenheit.2.) Fill in the blank.
csc^2 0 = cot ^2 0 + ___
A.) sec ^2 0
B.) -cos ^2 0
C.) -tan ^2 0
D.) 0
E.) 1
Answer:
E.) 1
Step-by-step explanation:
Firstly we will solve for L.H.S.
L.H.S. =[tex]Csc^2\theta[/tex]
Since we know that [tex]Csc^2\theta[/tex] is the inverse of [tex]Sin^2\theta[/tex].
So we can say that;
[tex]csc^2\theta=\frac{1}{sin^2\theta}[/tex]
Now For R.H.S.
[tex]Cot^2\theta+1[/tex]
Since we can rewrite [tex]cot^2\theta[/tex] as [tex]\frac{cos^2\theta}{sin^2\theta}[/tex].
Now we can say that the R.H.S. is;
[tex]\frac{cos^2\theta}{sin^2\theta}+1[/tex]
Now we add the fraction and get;
[tex]\frac{cos^2\theta+sin^2\theta}{sin^2\theta}[/tex]
Now according to trigonometric identity;
[tex]cos^2\theta+sin^2\theta=1[/tex]
So, [tex]\frac{cos^2\theta+sin^2\theta}{sin^2\theta}=\frac{1}{sin^2\theta}[/tex]
Here,
[tex]csc^2\theta=\frac{1}{sin^2\theta}[/tex] and [tex]Cot^2\theta+1[/tex] = [tex]\frac{1}{sin^2\theta}[/tex]
L.H.S. = R.H.S.
Hence [tex]csc^2\theta=cot^2\theta+1[/tex]
⇒How many solutions does the equation 10-3x +10x-7=5x-5+2x+8 have? a. One solution b. Two solutions c. No solutions d. Infinitely many solutions
Answer: d. Infinitely many solutions
Step-by-step explanation:
The given equation is expressed as
10-3x +10x-7 = 5x-5+2x+8
The first step is to make all the terms containing the variable to be on the left hand side of the equation and the constants to be on the right hand side of the equation.
10-3x +10x-7=5x-5+2x+8
10 - 7 + 10x - 3x = 5x + 2x - 5 + 8
7x + 3 = 7x + 3
Subtracting 7x and 3 from the left hand side and the right hand side of the equation, it becomes.
7x - 7x + 3 - 3 = 7x - 7x + 3 - 3
0 = 0
It has infinitely many solutions because as any value of x would satisfy both sides of the equation.
The French club sold rose bouquets and chocolate hearts for Valentine's Day. The roses sold for $5 and the hearts sold for $3. The number of bouquets sold was 15 more than the number of hearts sold. If the club collected a total of $339, how many of each gift was sold?
Answer:
33 hearts sold, 48 roses sold
Step-by-step explanation:
x- number of roses sold
y- number of hearts sold
x=15+y <- " The number of bouquets sold was 15 more than the number of hearts sold"
5x+3y=339
5(15+y)+3y=339
75+5y+3y=339
8y=339-75
8y=264
y=33
x=15+33=48
The number of chocolate hearts sold was 33, and the number of bouquets sold was 48 for a total revenue of $339.
Explanation:Let's assume the number of chocolate hearts sold was 'x'. Since the number of bouquets sold was 15 more than the number of hearts sold, the number of bouquets sold would be 'x + 15'.
The price of each rose bouquet is $5, so the total revenue from selling bouquets would be '5(x + 15)'.
Similarly, the price of each chocolate heart is $3, so the total revenue from selling hearts would be '3x'.
Since the total revenue collected was $339, we can set up an equation: '5(x + 15) + 3x = 339'.
Simplifying the equation, we get '8x + 75 = 339'.
Subtracting 75 from both sides of the equation, we get '8x = 264'.
Dividing both sides of the equation by 8, we get 'x = 33'.
Therefore, 33 chocolate hearts were sold, and the number of bouquets sold would be '33 + 15 = 48'.
Similar right triangles
Solve for x include a explanation
Answer:
x = 12
Step-by-step explanation:
The figure in the question was split into the triangles in the attachment to the solution.
Now applying the principle of similar triangles, we have:
[tex]\frac{16}{x} = \frac{x}{9}[/tex]
cross-multiplying, we have:
[tex]x^{2} = 16*9 = 144[/tex]
solving for x,
x = 12
The Derby Dragons have a mean height of 72.0 inches and a standard deviation of 1.2. The Aviston Aces have a mean height of 70.8 inches and a standard deviation of 0.7. The Ballwin Bears have a mean height of 73 inches and a standard deviation of 1.0. On average, which team is a taller? Which team has players whose heights are more consistent?
Answer: Ballwin Bears
Step-by-step explanation:
Answer:
The Ballwin Bears are taller on average, and the Aviation Aces have players whose are more consistent.
Step-by-step explanation:
(This is the correct answer on Knewton-alta)
The following formula for the sum of the cubes of the first n integers is proved. Use it to evaluate the area under the curve y = x³ from 0 to 1 as a limit,
1³ + 2³ + 3³ +...+ n³ = [n(n+1)/2]².
Answer:
Therefore, area under the curve is [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
We have to find the area under curve y = x³ from 0 to 1 as limit.
Since Area 'A' = [tex]\lim_{n \to \infty} \sum_{i=1}^{n}f(x_{i})\triangle x[/tex]
The given function is f(x) = x³
Since [tex]x_{i}=a+\triangle x.i[/tex]
Here a = 0 and [tex]\triangle x=\frac{1-0}{n}=\frac{1}{n}[/tex]
[tex]f(x_{i})=(\frac{i}{n})^{3}[/tex]
Now A = [tex]\lim_{n \to \infty} \sum_{i=1}^{n}f(x_{i})\triangle x= \lim_{n \to \infty}\sum_{i=1}^{n}(\frac{i}{n})^{3}(\frac{1}{n})[/tex]
[tex]= \lim_{n \to \infty}\frac{1}{n^{4}}\sum_{i=1}^{n}i^{3}[/tex]
[tex]= \lim_{n \to \infty}\frac{1}{n^{4}}( \frac{n(n+1)}{2})^{2}[/tex] Since 1³ + 2³ + 3³..............n³ = [tex][\frac{n(n+1)}{2}]^{2}[/tex]
[tex]= \lim_{n \to \infty}\frac{n^{2}(n+1)^{2}}{4n^{4}}[/tex]
[tex]= \lim_{n \to \infty}\frac{1}{4}(1+\frac{1}{n})^{2}[/tex]
[tex]=\frac{1}{4}(1+0)[/tex]
[tex]=\frac{1}{4}[/tex]
Therefore, area under the curve is [tex]\frac{1}{4}[/tex]
What is a good science fair projects for 5th graders
I'm not sure of whether or not you're aware of this, but you asked this question in the math section. Nevertheless, I remember in 5th grade I did a project on whether or not it is possible to use solar energy to heat up different colored bags filled with water, and to determine which one would heat up the quickest. If that one doesn't pique your interest, you can go to sciencebuddies.com and search through a variety of project ideas if you'd like. That's where I found mine.
Final answer:
A good science fair project for 5th graders could be the 'Race of the Cans' experiment. Students can collect cans with different types of food and predict which can will win a race down an inclined plane.
Explanation:
A good science fair project for 5th graders could be the 'Race of the Cans' experiment. In this experiment, students can collect several cans containing different types of food and predict which can will win the race down an inclined plane. They can then explain their prediction and see if it is correct. Another option is to collect empty cylindrical containers of the same size and fill them with different materials like wet or dry sand to see how it affects the race.
The expression $x^2 15x 54$ can be written as $(x a)(x b),$ and the expression $x^2 - 17x 72$ written as $(x - b)(x - c)$, where $a$, $b$, and $c$ are integers. What is the value of $a b c$?
Answer: a=6 b=9 c=8
Step-by-step explanation:
The problem consists of finding the roots of the quadratic equations:
[tex]x^2+15x+54=0\\[/tex]
[tex]x^2-17x+72=0\\[/tex]
The roots can be found with the following equation for solving quadratic equations:
[tex]x_{12}=\frac{-B\pm\sqrt{B^2-4AC}}{2A}[/tex] for equation: [tex]Ax^2+Bx+C=0[/tex]
After solving the equations you can write the result as:
[tex]x^2+15x+54=(x+6)(x+9)\\[/tex]
[tex]x^2-17x+72=(x-9)(x-8)[/tex]
Answer:
b = 9
a = 6
c= 8
Therefore, a,b,c = 6,9,8
Question:
The expression $x^2 - 15x - 54$ can be written as $(x-a)(x-b),$ and the expression $x^2 - 17x + 72$ written as $(x - b)(x - c)$, where $a$, $b$, and $c$ are integers. What is the value of $a b c$?
Step-by-step explanation:
To determine the values of a,b and c.
We need factorize the two equations.
i) x^2 -15x +54
x^2 -6x -9x +54
x(x-6) -9(x-6)
=(x-6)(x-9)
ii) x^2 -17x +72
x^2 -9x -8x +72
x(x-9) -8(x-9)
=(x-9)(x-8)
From the question:
Comparing
(x-a)(x-b) to (x-6)(x-9)
And
(x-b)(x-c) to (x-9)(x-8)
We can see that b is common in the two cases and also 9 is common in the two factorised equations.
So,
b = 9
a = 6
c= 8
Therefore, a,b,c = 6,9,8
A one year membership to metro gym costs $460. There is a fee of $40 when you join, and the rest is paid monthly. Write an equation to represent the situation that can help members find how much they pay per month
Answer: The equation that would help members to find how much they would pay per month is
40 + 12x = 460
Step-by-step explanation:
Let x represent the amount of money that members would pay per month.
Let y represent the number of months for which a member uses the gym.
There is a fee of $40 when you join, and the rest is paid monthly. This means that the cost of using the gym for x months would be
40 + xy
A one year membership to metro gym costs $460. Therefore are 12 months in a year. Therefore,
40 + 12x = 460
12x = 460 - 40 = 420
x = 420/12 = 35
The equation that would help members to find how much they would pay per month is
Albert went shopping with half of his monthly allowance. He spent $35.50 on a shirt and 3/5 of the remainder on a book. He had $25.80 left after his shopping trip. What was Albert's monthly allowance?
Answer:
$ 213.50
Step-by-step explanation:
From the question;
Albert spent;
$35.5 on a shirt 3/5 on the remainder on a book Remainder is $25.80We are required to determine Albert's monthly allowance;
If we assume that the allowance was x dollars He therefore, went with half of his allowance for shopping, which is, x/2Then;
Deducting $35.5, we get,
$(x/2 - 35.5)
Then, 3/5 of the remainder is on a book
Thus, 1 - 3/5 = 2/5 of the remainder (represents the amount that remained after buying a book and a shirt.
Therefore;
2/5 (x/2 - 35.5) = 28.5
We get;
x/2 - 35.5 = 28.5 (5/2)
x/2 - 35.5 = 71.25
x/2 = 71.25 + 35.5
x/2 = $ 106.75
x = $ 106.75 × 2
= $ 213.50
Therefore, Albert's monthly allowance is $ 213.50
Francisco's recipe for cookies calls for 3/4 cups of sugar, 2 1/2 cups of flour and 3 eggs.If you want to use half as much sugarAnd then triple the recipe Size how much sugar will he need
Answer:
the answer is 9/8 or 1 and 1/8
Step-by-step explanation:
divide 3/4 by 2 to get 3/8 and then multiply 3/8 by 3 (since its tripling) to get 9/8 which can also be written as 1 1/8. Hope this helps!
Casandra is training for the 10 mile race. On the first day of training she runs 4 miles,each day after that she adds on 0.5 mile. On what day will Casandra run 8 miles?
Answer:
Casandra will run 8 miles on the 9th Day.
Step-by-step explanation:
Given:
Casandra on first day of training she runs 4 miles
So we can say that;
[tex]a_1=4\ miles[/tex]
Also Given:
each day after that she adds on 0.5 mile.
So we can say that;
Common difference [tex]d=0.5\ miles[/tex]
We need to find on what day she will run 8 miles.
So we can say that;
[tex]T_n = 8[/tex]
Let the number of the day be denoted by 'n'
Solution:
Now By using the formula of Arithmetic Progression we get;
[tex]T_n= a_1+(n-1)d[/tex]
Now substituting the values we get;
[tex]8=4+(n-1)0.5[/tex]
Now by using distributive property we get;
[tex]8 =4+0.5n-0.5\\\\8=3.5+0.5n[/tex]
Now subtracting both side by 3.5 we get;
[tex]8-3.5=3.5+0.5n-3.5\\\\4.5=0.5n[/tex]
Dividing both side by 0.5 we get;
[tex]\frac{4.5}{0.5}=\frac{0.5n}{0.5}\\\\9=n[/tex]
Hence Casandra will run 8 miles on the 9th Day.