Answers
Answer:
1.14200738982×10^26
Step-by-step explanation:
Substitution can make this integral much easier to evaluate.
SubstitutionLet u = 7x² -x. Then du = (14x -1)dx. The limits on x become different limits for u:
for x = 1: u = 7(1²) -1 = 6
for x = 3: u = 7(3²) -3 = 60
Integral[tex]\displaystyle\int_1^3{(14x-1)e^{(7x^2-x)}}\,dx=\int_6^{60}{e^u}\,du=\left.e^u\right|^{60}_6\\\\=e^{60}-e^6\approx e^{60}\approx\boxed{1.14200738982\times10^{26}}[/tex]
Related Questions
(a) Your Mom has a sum of x. She spent 3,000 on grocery and 2,000 on milk.
Write the algebraic expression for the amount left with her.
Answers
Answer:
y=x-5000
Step-by-step explanation:
Given,
total sum of money mom has=x
money spent on grocery=Rs 3000
money spent on milk= Rs 2000
total money spent by mom=Rs 5000
Let the money left with the mom =y
then the algebric expression for the amount left with her is given by
y=x-5000
Work out the value of 10 squared takeaway 4 cubed
Give your answer as a power of 6
Answers
Answer:
[tex]6^2=36[/tex]
Step-by-step explanation:
[tex]10^2-4^3=100-64=36=6^2[/tex]
Can anyone explain to me how to solve this for h? I was given the volume and radius and I still got it wrong. My incorrect answer is in red, and the coreect one was filled in, but I still don't understand how to solve it for h.
What is the 8[tex]\pi[/tex]mean? does it mean 8 times pi?
Answers
The graph at the right illustrates the rate at which Dave and Joe are saving money.
a. Estimate the solution to the system.
b. Explain what this means in the context of
the saving money scenario.
Answers
The solution of the System of Equation is (5.71, 514.2) and this means that at that point the money they save are the same .
What is System of Equation ?A finite collection of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.
A system of equations consists of two or more equations and looks for common answers. "A collection of equations fulfilled by the same set of variables is called a system of linear equations."
The point provides a singular solution to the system of equations if the two lines cross at the same location. There are an endless number of solutions in the situation when the two lines meet, and there is none in the case where the two lines are parallel.
From the graph :
i)The stipper line have 2 points at (0,300) and (4,450)
ii)The other line having points (0,400) and (5,500)
The slope of the line (i) is
The slope in the line (ii) is
The equation of lie (i) is
y = 37.5x + c
putting (0,300) in the equation we get,
300 = 37.5*0 + c
⇒ c = 300
The equation is y = 37.5x + 300
And the 2nd line putting (0,400) in the equation (ii) we get,
y = 20x + c
400 = 20*0 + c
⇒ c = 400
The equation is y = 20x + 400
Solving the both equation we get
37.5x + 300 - 20x - 400 = 0
⇒ 17.5x = 100
⇒ x = 5.71 and y = 514.2
The solution of the system is (5.71, 514.2) and this means that at that point the money they save are the same .
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HELP ASAP! there are other answers similar to this but aren’t the same so don’t steal from them and answer it yourself
The Top-Notch Middle School had athletes from all the grades playing on a sports team.
6th grade 7th grade 8th grade
Basketball 2 4 7
Baseball 1 6 5
Soccer 7 4 4
Football 8 15 10
Explain what the ratio 15:73 represents.
The ratio 15:73 represents the ratio of total athletes to 7th grade football players.
The ratio 15:73 represents the ratio of 8th grade baseball players to total athletes.
The ratio 15:73 represents the ratio of 7th grade football players to total athletes.
The ratio 15:73 represents the ratio of 6th grade athletes to total athletes.
Answers
Since the Top-Notch Middle School had athletes from all the grades playing on a sports team, the ratio 15:73 represents the following: C. The ratio 15:73 represents the ratio of 7th grade football players to total athletes.
How to explain the given ratio?In order to interpret and explain the meaning of the given ratio 15:73, we would first of all determine the total number of athletes from all grades in Top-Notch Middle School as follows;
Total number of athletes, T = 2 + 4 + 7 + 1 + 6 + 5 + 7 + 4 + 4 + 8 + 15 + 10
Total number of athletes, T = 73 athletes.
For the number of Basketball athletes, we have:
Number of Basketball athletes, B = 2 + 4 + 7
Number of Basketball athletes, B = 13 Basketball athletes.
Ratio of B to T = 13:73.
For the number of Baseball athletes, we have:
Number of Baseball athletes, B = 1 + 6 + 5
Number of Baseball athletes, B = 12 Baseball athletes.
Ratio of Ba to T = 12:73.
For the number of Football athletes, we have:
Number of Football athletes, B = 8 + 15 + 10
Number of Football athletes, B = 33 Football athletes.
Ratio of F to T = 33:73.
For the ratio of Football athletes in 7th grade to total number of athletes, we have:
Ratio of F7 to T = 15:73.
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Hurry! Did i do it right?
Answers
Answer: Yes its right
Step-by-step explanation:
You substitute 10 in for x
-3(10) + 1
-30 + 1
=-29
culating Volume
Which expression can be used to represent the
volume of this prism?
6 x 11 unitsª
48 x 3 units
14 x 3 units³
8x9 units³
Answers
This prism's volume can be expressed using an expression of 48 x 3 units.
How may the volume of a prism be expressed?The area of the base is multiplied by the prism's height to determine its volume. The volume of a prism can be calculated using the formula V = B H, where V stands for the volume, B for the base area, and H for the height.
The volume of the prism is given in cubic units by the formula V = A H cubic units, where A is the prism's base area and H is its height.
The expression for the volume of this prism is 48 x 3 units.
The area of the base is multiplied by the prism's height to determine its volume.
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Complete Question -
Lina had 1 points located at (4,2) and (9,0). Line 2 is represented by the equation y=2/5x+5.
A.Line has 1 greater rate of change equal to 2/5
B. Line 1 had a greater rate of change equal to -5/2
C. Line 2 has a greater rate of change equal to 2/5
D. Line 2 has a greater rate of change equal to -5/2
Answers
So on solving the provided question, we can say that the equation is = > y = 2/5x ; at (4,2) and at (9,0) Line 1 had a greater rate of change equal to -5/2
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
the equation is = > y = 2/5x
at (4,2) and at (9,0) Line 1 had a greater rate of change equal to -5/2
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Two motorcycles leave home at the same time, heading directly toward each other. They are a total of 300 miles apart. The first motorcycle travels at 65 miles per hour. The second motorcycle travels at 85 miles per hour. How long will it take for the two motorcycles to meet?
Answers
Answer:
150 miles
Step-by-step explanation:
Total miles by the two motorcycles
300 miles
The first motorcycle travel 65 miles per hour
The second motorcycle travel 85 miles per hour
Total miles the two motorcycles travels
65 mile + 85 miles
=150 miles
Long it will take for the two motorcycles to meet
= 300 miles + 150 miles
=150 miles.
Hence it will take 150 miles for the two motorcycles to meet.
HELP PLEASE TYYY easy
Answers
The angle measure of the circle graph is as follows:
Train = 90 degreesAirplane = 198 degreesBoat = 72 degrees.How to find the angles in a pie chart?A travel magazine surveyed 500 of its adult readers about their favourite ways to travel. The circle graph below shows that 125 people like to travel by train, 275 like to travel airplane and 100 people like to travel by boat.
Therefore, let's use the data to create a pie chart with the measured angles.
Hence,
angle for train travellers = 125 / 500 × 360
angle for train travellers = 45000 / 500
angle for train travellers = 90 degrees
angle for the airplane travellers = 275 / 500 × 360
angle for the airplane travellers = 99000 / 500
angle for the airplane travellers = 198 degrees
Finally,
angle for the boat travellers = 360 - 198 - 90 = 72 degrees.
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A white rectangular board 28 cm long and 16 cm wide is placed in the centre of a large rectangular wooden board. It creates a border of 3 cm around it. Find the area not covered by the white board.
Answers
The area not covered by the white board is 192 cm².We can find by using area of rectangular formula.
What is rectangle?A rectangle is a quadrilateral that has its parallel sides equal to each other and all the four vertices are equal to 90 degrees. Hence it is also called quadrilateral. Since the opposite sides are equal and parallel in rectangle.
What is the formula to find area of rectangle?The area is measurement of the surface of a shape. To find the area of a rectangle or a square you need to multiply the length and the width of a rectangle.The formula for the Area of a Rectangle is A = l × b. The area of any rectangle is calculated once its length and width are known.
Now we find
A white rectangular board 28 cm long and 16 cm wide.
Substitute the respective values
Area of White Board = 28 *16
The area of white board is 448 cm²
Wooden board creates a border of 2 cm around it.
Wooden Board dimension = (28 + 2 + 2) cm long and (16 + 2 + 2) cm wide
Wooden Board dimension = 32 cm long and 20 cm wide.
The area of Wooden board = 32*20=640
The area not covered by the white board is
640 cm² - 448 cm² = 192 cm²
The area not covered by the white board is 192 cm².
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Solve the oblique triangle using the Law of Sines and/or the Law of Cosines. Find all side lengths rounded to
the nearest whole and all angles rounded to the nearest whole.
Answers
Side a of the oblique triangle is 25.57 units and side b is 9.42 units.
What is the law of sines?The number of sides of a triangle and how their individual sine angles are equal are determined by the law of sines. Other names for the sine law are sine rule, sine formula, and sine law. The law of sine is used to determine the side or unknown angle of an oblique triangle.
Given:
∠A = 107
∠B = 21
∠C = 52
c = 21
So, using the law of sines
b/sin B = c/ sin C
b/sin 21 = 21/sin 52
b = (21 × sin 21) / sin 52
= (21 × 0.35) / (0.78)
b ≈ 9.42
Similarly, side a of the triangle is given by
a/ sin A = c/ sin C
a/sin 107 = 21/sin 52
a = (21 × sin 107) / sin 52
= (21 × 0.955) / (0.78)
a ≈ 25.57
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The price for printing a small photo is $0.19. If the cost per square inch stays constant, how much should the large version of that photo cost, whose dimensions are 140% of the original?
Explain please!!
Answers
The cost of the large version of the photo is $0.456.
What is the cost?
Percentage is the fraction of an amount that is expressed as a number out of hundred. The sign that is used to represent percentage is %.
Cost of the large version of the photo = cost of the small photo x (1 + percent/100)
Cost of the large version of the photo = $0.19 x (1 + 140/100)
= $0.19 x (1 + 1.40)
= $0.19 x 2.40
= $0.456
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cuemath
THE MATH EXPERT
probability
probability
of B getting a job is 3/4. What is the
that only one of them gets the job.
Answers
By the total number of potential outcomes, divide the total number of events. Divide the total number of ways the event could occur by the total number of possible outcomes once the probability event and its accompanying consequences have been determined.
What is probability?The likelihood that an event or several events will occur is known as probability. Utilizing a straightforward formula, probability can be determined and is used to describe the likelihood of obtaining a specific result.Probability can alternatively be defined as the ratio of the number of expected outcomes of an event to its likelihood of occurring. When there are several events, the probability is calculated by dividing each likelihood into a single computation, multiplying the results, and then summing the results to determine the probability of each event.The probability of an event happening is defined by the probability formula. The proportion of favorable outcomes to all possible outcomes serves as the basis for the formula used to determine an event's probability. Always between 0 and 1 are the possible outcomes. One way to say the generic probability formula is:Number of Favorable Outcomes / Total Number of Outcomes is the formula for probability.
or P(A) = f / N
Where:P(A) = Chance of Event A Occurring f = Number of Possible Ways for Event A
N represents all conceivable outcomes.
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0.1 | 0.4 | ? | 1.6 | 2.5
Answers
Answer:
? = 1
Step-by-step explanation:
You are trying to mind the MEDIAN of the given expression.
The MEDIAN is the middle number of a set of given values.
1. Arrange the terms in ascending order.
= 0.1 , 0.4 , 1.6 , 2.5
2. The median is the middle term in the arranged data set. In the case of an even number of terms, the median is the average of the two middle terms.
= (0.4 + 1.6)/2
Write as a fraction where (0.4 + 1.6) is the NUMERATOR & 2 is the DENOMINATOR. Include parentheses.
3. Remove parentheses.
= 0.4 + 1.6/2
Write as a fraction where 0.4 + 1.6 is the NUMERATOR & 2 is the DENOMINATOR.
4. Add 0.4 and 1.6.
= 2/2
5. Divide 2 by 2.
= 1
6. Convert the median 1 to decimal.
= 1
help pls and thanks !!! i’ll mark brainliest !!!
Answers
How to figure this out is simple. Angle FD gives you the measure of 14, which is the same length as Angle DG. Therefore your answer is 14
Which is the BEST estimate for the sum of 5/12+2/5?
Answers
The probabilities of events R and S satisfy the following conditions: • P(R) = 1 4 If events R and S are independent, which represents P(R and S)? • P(S) = 3 O 42 0 H
Answers
If events R and S are independent, the probability of both occurring (P(R and S)) is the product of their individual probabilities which will give 3/32.
What is the probability of independent events?To calculate the probability that if events R and S are independent, both events occurring (P(R and S)) is the product of the individual probabilities of each event.
So, P(R and S) = P(R) x P(S) = (1/4) x (3/8) = 3/32
This is because when events are independent, the occurrence of one event does not affect the probability of the other event, so the probability of both events occurring is just the product of the individual probabilities of each event.
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4. Fabian harvests 10 pounds of tomatoes from his gar
2 2/5 pounds to make a batch of soup. If he sets aside 2.8 pounds of
tomatoes to make spaghetti sauce, how many batches of soup can
Fabian make? Write and solve an equation.
Answers
There will be a total of 3 batches of soup can Fabian make.
Explain how to calculate the total weight of ingredients needed for making a specific number of batches of a recipe.
To calculate the total weight of ingredients needed for making a specific number of batches of a recipe, you can multiply the weight of each ingredient per batch by the number of batches you want to make. This will give you the total weight of ingredients needed for the desired number of batches. For example, if a recipe requires 1 pound of flour per batch and you want to make 3 batches, the total weight of flour needed is 1 pound per batch * 3 batches = 3 pounds.
To find out how many batches of soup Fabian can make, we need to divide the total weight of tomatoes by the weight of tomatoes used per batch of soup.
Let x be the number of batches of soup Fabian can make. We know that:
10 pounds of tomatoes - 2.8 pounds of tomatoes = 7.2 pounds of tomatoes are available to make soup
The weight of tomatoes used per batch of soup is 2 2/5 pounds, we can write this as:
x * 2.4 = 7.2
To find the number of batches of soup Fabian can make, we can divide both sides by 2.4
x = 7.2/2.4
x = 3
So Fabian can make 3 batches of soup.
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y= 2x- 2
y = 2x - 2
How many solutions does the system of equations have?
• One solution
• Infinitely many solutions
• No solution
Answers
Answer:
Infinitely many solutions
System of EquationsA system of equations is solving for 2 or more lines. Solving it means finding the point where they intersect.
One solution means the lines only intersect once and have a different slope.
No solution means the lines never intersect and have the same slope but a different y-intercept.
Infinitely many solutions means the lines are always intersecting, meaning the lines have the same y-intercept and slope.
Q)y= 2x - 2
y = 2x - 2
They have the same slope and y-intercept, so there are infinitely many solutions.
Which of the following is an improper form of the null and alternative hypotheses? a. H_0: mu lessthanorequalto mu_0 and H_a: mu > mu_0 b. H_0L: mu = mu_0 and H_a: mu = mu_0 c. H_0: mu < mu_0 and H_a: mu greaterthanorequalto mu_0 d. H_0: mu greaterthanorequalto mu_0 and H_a: mu < mu_0
Answers
They are known as the two types of first is null hypothesis and the second is alternative hypothesis. These two hypotheses bear opposite viewpoints.
H0: also known as null hypothesis: It is a statement about the population that either is taken to be true or is used to put forth an argument until it can be shown to be incorrect behind a reasonable doubt.
Ha: also known as the alternative hypothesis: It is a state about the population that is contradictory to H0 and what we conclude when we reject H0.
H0 every time has a symbol with an equal in it. It never has a symbol with an equal in it. The option of the symbol depends on the wording of the hypothesis test.
Yet, be aware that many researchers use = in the null hypothesis, even with > (greater) or < (less) as the symbol in the alternative hypothesis.
We can accept this practice because we only decide to reject or not reject the null hypothesis.
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Airplane A flies 300 miles due east of an airport and then flies 200 miles at 15° north of east. Airplane B flies 200 miles due north and then flies 300 miles at 20° west of north. Which airplane is closer to the airport? Explain how you know.
Answers
Answer:
It is not possible to determine which airplane is closer to the airport without additional information. The distance and direction of each airplane's flight are given, but the starting point for each airplane is not specified. If we knew the starting point of each airplane, we could use the information provided to calculate the final position of each airplane and determine which one is closer to the airport.
Step-by-step explanation:
Which of the contexts below could not be modeled by a linear function?
A car depreciates at a rate of 8.3% per year.
Snow was falling at a rate of 2.25 inches per hour.
A sunflower was growing at a rate of 1.5 inches per week.
A taxí charges a flat fee of $2.50 for pick-up, then an additional fee of $3.75 per
mile.
Answers
Therefore , the solution of the given problem of function comes out to be we cannot consider the fourth statement as linear function.
Describe function.Mathematicians frequently use the word "function" to refer to a connection that describes how two variables are connected to one another. There are two: a predictor variable, which is the function's output, and a variable, which can be any input of an equation.
Here,
Given:
A car loses value at a rate of 8.3% annually.
2.25 inches of snow were falling every hour.
A sunflower was expanding by 1.5 inches every week.
A set rate of $2.50 is charged by taxis for pickup, and an additional $3.75 is added for each subsequent mile.
thus,
From the following above expression we cannot consider the fourth statement
As if we write it in the formula it comes out to be linear equation not function.
Therefore , the solution of the given problem of function comes out to be we cannot consider the fourth statement as linear function.
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An apple in a dessert contributes one-thirtieth the number of fat grams that the cup of cottage cheese contributes. If the total number of fat grams in the dessert is 4.03 g, how many fat grams are in the apple and how many are in the cup of cottage cheese?
Answers
The cottage cheese contains 3.9 g of fat and the apple has 0.13 g, making a total of 4.03 g of fat in the dessert.
what is proportionality ?Relationships that always have the same ratio are said to be proportional. For instance, the number of trees in an orchard and the number of apples in a harvest of apples are determined by the average number of apples per tree. A linear relationship between two numbers or variables is referred to as proportional in mathematics. When the first quantity doubles, the other number does as well. When one of the variables is reduced to 1/100th of its previous value, the other also decreases. If two quantities are proportional, it means that when one rises, the other rises as well, and the ratio between the two quantities remains constant throughout all values. The diameter and circumference of a circle serve as an example.
given
fat grams from the apple, where a
a +30a = 4.03g
31a/31 = 4.03 / 31
a = 0.13
The cottage cheese has 30(0.13) = 3.9 g fat, compared to the apple's 0.13 g.
The cottage cheese contains 3.9 g of fat and the apple has 0.13 g, making a total of 4.03 g of fat in the dessert.
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can someone please help work this sum out please
Answers
We can conclude that we have sufficient data to reject the null hypothesis and that the mean breaking strength is different from 8000 at 5% of significance if we compare the p value and the significance threshold, for example, α = 0.05.
The information provided and notation
X = 7750 indicate the sample's mean breaking strength, which is 145.
n = 6 sample size μ o= 8000 reflect the sample standard deviation indicate the quantity we want to test, and
α = 0.05 denotes the level of significance for the hypothesis test.
The statistic (interesting variable) would be represented by t, and the test's p value would be represented by P u (variable of interest)
Name the prevailing and competing hypotheses.
It is a test with two tails.
How do H₀ and Hₐ relate to this study?We wish to determine whether or not the genuine mean is equal to 8000.
Null hypothesis μ = 8000.
Alternate hypothesis μ₀ ≠ 800
Determine the test statistic.
[tex]t = \frac{X-\mu}{\frac{s}{\sqrt{n} } }[/tex]
t-test: "enables the comparison of group means. One of the most widely used tests, it is used to assess whether the mean is (greater, lower, or not equal) to a given value ".
Determine the statistic.
We can substitute the following information in the above formula
[tex]t = \frac{7750-8000}{\frac{145}{\sqrt{6} } } = -4.22[/tex]
Give the test's appropriate conclusion -
To begin with, we must determine the degrees of freedom indicated by: df = n-1 = 6-1 = 5.
Given that the test has two possible outcomes, the p value is
Pv = 2 × P(t(5) < -4.22) = 0.0083.
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Please help if you can what are the factors for 45 (math)
Answers
Answer:
Step-by-step explanation:
The number in consideration here is 45 and the integers that divide it evenly are known as the factors of 45. There are a total of six factors of the number 45: 1, 3, 5, 9, 15 and 45. The numbers that are multiplied in pairs to produce 45 are the factor pairs of 45.
Can someone help with this?
Answers
Answer: Its definitely 7.2 for the first two and 4.5 on the last one to the right
Step-by-step explanation: i did the quiz
find the area that the curve encloses and then sketch it. r2 = 9 cos(2θ)
Answers
Emma scores 72 marks out of 80 in her English exam. Convert her
marks into percent.
Answers
Answer:
Emma scored 90% in her English exam, as 80 marks out of 80 is equivalent to 100%. Thus, 72 marks out of 80 is equivalent to 90%.
Hurry - Fill in the blanks
Answers
Answer:
The first value of a relation is an input value and the second value is the output value. A function is a specific type of relation in which each input value has one and only one output value.
An input is an independent value, and the output value is the dependent value, as it depends on the value of the input.