W =∫ lower power (-r) to higher power (r + h) (h + r - x) 2pgl [tex]\sqrt{r^2+x^2}[/tex] dx is the integral for the effort needed to pump water out of a spout that is 2 m above the tank.
What is meant by Integral?Integral: In mathematics, an integral is either a number representing the region under a function's graph for a certain interval or a new function, the derivative of which is the original function (indefinite integral).
r = 2m
l= 5m
sinθ=x/r
[tex]dv=2l\sqrt{r^2+x^2} dx[/tex]
Let g be the acceleration brought on by gravity, and let p be the density of water.
dm = p dv
dw = dmg (h + r - x)
dw = pg (h + r - x) dx
dw = 2lpg (h + r - x) [tex]\sqrt{r^2+x^2}[/tex] dx
w = ∫dw
w = ∫ lower power (-r) to upper power (r + h) 2pgl (h + r - x) [tex]\sqrt{r^2+x^2}[/tex] dx
Therefore, the integral for the work required to pump the water out of a
spout that rises 2 m above the tank is
w = ∫ lower power (-r) to upper power (r + h) 2pgl (h + r - x) [tex]\sqrt{r^2+x^2}[/tex] dx
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Which sequence of transformations will change figure PQRS to figure P′Q′R′S′? (5 points)
Counterclockwise rotation about the origin by 180 degrees followed by reflection about the x-axis
Counterclockwise rotation about the origin by 180 degrees followed by reflection about the y-axis
Counterclockwise rotation about the origin by 270 degrees followed by reflection about the x-axis
Counterclockwise rotation about the origin by 270 degrees followed by reflection about the y-axis
The sequence of transformations to change figure PQRS to figure P′Q′R′S′ will be;
⇒ Counterclockwise rotation about the origin by 180 degrees followed by reflection about the x-axis.
What is Translation?A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Given that;
Sequence of transformations will change figure PQRS to figure P′Q′R′S′.
Now,
Since, Sequence of transformations will change figure PQRS to figure P′Q′R′S′.
And, The coordinates of figure PQRS are,
P = (1, 2)
Q = (2, 1)
R = (3, 2)
S = (3, 3)
And, The coordinates of figure P'Q'R'S' are,
P' = (1, -2)
Q' = (2, -1)
R' = (3, -2)
S' = (3, -3)
We know that,
The transformation rule for Counterclockwise rotation about the origin by 180 degrees followed by reflection about the x-axis will be,
⇒ (x , y) → (x, - y)
Thus, We get;
The sequence of transformations to change figure PQRS to figure P′Q′R′S′ is,
''Counterclockwise rotation about the origin by 180 degrees followed by reflection about the x-axis.''
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At a water park, 42 out of 56 tickets sold were child tickets. What percentage of the tickets
were child tickets?
Write your answer using a percent sign (96).
Answer:
75%
Step-by-step explanation:
42/56 * 100% = 0.75 * 100
= 75%
Find the circumference of a circle with a radius of 5 inches
Answer: The answer should be 31.42 in
Graph g(x) = −2x − 8 and identify its x-intercept.
(−8, 0)
(−4, 0)
(0, −4)
(0, −8)
Based on the graph of the function g(x) = −2x − 8, the x-intercept is equal to -4.
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate respectively.
What is the x-intercept?In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" is equal to zero (0).
By critically observing the graph of g(x) = −2x − 8, the x-intercept is -4. This ultimately implies that, the function g(x) = −2x − 8 would cross the x-coordinate (x-axis) at point (-4, 0.
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Suppose f(x)is a continuous differentiable function and you are given that f"(x) is always positive. Which of the following statements must be true? f(x) is always increasing. f'(x) is always increasing. f"(x) is always increasing. None of the above must be true.
According to the facts provided in the question and we know that the derivative of the function f(x) is f'(x) which refers to the slope at the point. The answer is f(x) is always increasing.
What do you mean by derivative?The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument. Calculus's core tool is the derivative. The rate at which a function changes in relation to a variable Calculus and differential equations issues must be solved using derivatives.
What do you mean by slope of the line?A line's steepness can be determined by looking at its slope. The ratio of the change in the y-value to the change in the x-value can also be used to determine slope.
f(x) is the function.
f'(x) is the derivative of the function.
f'(x) is always positive which explains that the line has positive slope that is moving upwards in graph.
So, f(x) is always increasing.
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In ΔA B G, if m ∠C is nine less than m ∠A and m ∠B is fifteen less than four times m ∠A, find the measure of ∠B
A) 125° hula hooping
B) 121° doing the Nae Nae
C) 57° finger painting
D) 34° playing clarinets
The measure of angle B is 121°
The correct option is B) 121° doing the Nae Nae
"Information available from the question"
In the question:
In ΔA B C, if m ∠C is nine less than m ∠A and m ∠B is fifteen less than four times m ∠A,
To find the measure of ∠B.
Now, According to the question:
We know that:
The sum of the measures of the angles of a triangle are 180
m<A + m<B + m<C = 180°
m<C = m<A - 9
m<B = 4*m<A - 15
m<A + 4*m<A - 15 + m<A - 9 = 180°
6m<A - 24 = 180°
6m<A = 204
m<A = 34°
Now, To find the measure of ∠B
m<B = 4*m<A - 15
m<B = 4* 34 - 15
m<B = 121°
The correct option is B) 121° doing the Nae Nae
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The diagram below shows all the possible totals from adding together
the results of rolling two fair dice.
Calculate P(total is neither 5 nor 7).
Give your answer as a fraction in its simplest form.
Answer:
1/6
Step-by-step explanation:
ia fair dice only has 6 numbers so you can't get 7 so there is two 5 since its two fair dice it's out of 12,2/12 divide both by 2 because that the highest common factor and you get 1/6 that your answer
Find the value of x from the figure
Answer:
x = 20
Step-by-step explanation:
the figure is a parallelogram, therefore the sum of angle A and angle B is 180°, we solve with an equation
180 = 5x + 5 + 4x - 5
180 = 9x
x = 180 : 9
x = 20
------------------------
check
180 = 5x + 5 + 4x - 5
180 = 5 × 20 + 5 + 4 × 20 - 5 (remember PEMDAS)
180 = 180
the answer is good
Answer:
The angle x is equal to 20 degrees
√3ab
rewrite the equation in radical form
Answer:
√3√ab
Step-by-step explanation:
Please look in the attachment! Hope this helps! :D
A company shipped 3 boxes which each weighed 3.894 pounds and one box which weighed 6.7 pounds. What was the total weight of the 4 boxes?
The total weight of the 4 boxes was - 18.382 pounds.
A company shipped 3 boxes which each weighed 3.894 pounds.
As per the rule, we shall have to multiply the weight of the boxes of similar weight into 3 followed by the addition of the weight of the other box.
Then, we can get the final answer.
one box weighed = 3.894 pounds
Three boxes weighed = 3 * 3.894 pounds
= 11.682 pounds
Another box weighed = 6.7 pounds
The total weight of the 4 boxes was = ( 11.682 + 6.7 ) pounds
= 18.382 pounds
Hence, The total weight of the 4 boxes was - 18.382 pounds.
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Help pls I don’t understand
Step-by-step explanation:
QUESTION 3[tex]\triangle ABC[/tex] is inscribed in circle with centre O. OA, OB and OC are it's radii.Now, In [tex]\:\triangle AOB[/tex] and [tex]\:\triangle COB[/tex] [tex]OA\cong OC[/tex] (radii of same circle)[tex]\angle AOB \cong\angle COB[/tex] (Given)[tex]OB\cong OB[/tex] (common side)[tex] \rightarrow \:\red{\triangle AOB\cong \triangle COB}[/tex](By SAS congruence postulate)QUESTION 4In [tex]\:\triangle ABE [/tex] and [tex]\:\triangle CBE[/tex] [tex]AB\cong CB[/tex] (Given)[tex] \angle ABE \cong\angle CBE[/tex] (Given)[tex]BE\cong BE[/tex] (common side)[tex] \rightarrow \:\orange{\triangle ABE\cong \triangle CBE}[/tex](By SAS congruence postulate)At the beginning of the year, Kaylee had $60 in savings and saved an additional $12 each week thereafter. Jack started the year with $95 and saved $5 every week. Let K represent the amount of money Kaylee has saved t weeks after the beginning of the year and let J represent the amount of money Jack has saved t weeks after the beginning of the year. Write an equation for each situation, in terms of t, and determine the number of weeks after the beginning of the year until Kaylee and Jack have the same amount of money saved.
After 5 week the savings of both Kaylee and Jack will be same.
The equation for Kaylee's savings, in terms of t, is K = 60 + 12t.
The equation for Jack's savings, in terms of t, is J = 95 + 5t.
To determine the number of weeks after the beginning of the year until Kaylee and Jack have the same amount of money saved, we set K equal to J and solve for t.
K = J
60 + 12t = 95 + 5t
7t = 35
t = 5
Kaylee and Jack have the same amount of money saved after 5 weeks.
What are savings?
The funds one has saved, particularly through a bank or government programme is known as savings.
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a sales manager analyzed the sales, in dollars, y, of snow shovels compared to the outside temperature, in degrees fahrenheit, x. the manager calculated the correlation coefficient of r
The correlation coefficient of r measures how closely the two variables, x and y, are related. If the coefficient is close to 1, it means that the two variables are strongly related, whereas if it is close to 0, it means that there is no relation between them.
The correlation coefficient of r is a measure of how closely related two variables are to each other. It is calculated by taking the covariance of the two variables and dividing it by the product of their standard deviations. The coefficient ranges from -1 to +1, with -1 indicating a perfectly negative linear relationship, 0 indicating no relationship, and +1 indicating a perfectly positive linear relationship. In the case of the sales manager analyzing the sales of snow shovels compared to the outside temperature, the correlation coefficient of r can be used to measure the strength of the relationship between the two variables. If the coefficient is close to 1, it indicates that the two variables are strongly related, while a coefficient close to 0 indicates that there is no relation between them.
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if angle GHJ is an equilateral triangle, GH = 5x - 13, HJ = 11x - 61, and GJ = 7x - 29, find x and the
measure of each side. Draw and label a picture and show all work for full credit. (10 pts)
Answer:
x is 8
And each side is 27
Step-by-step explanation:
check out the photo
hope it will help
In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse.
If b = 16 units and c = 20 units, what is the perimeter? If necessary, round your answer to the nearest tenth.
Answer: 48
Step-by-step explanation: Use this to help you!
The equation for line g can be written as y–1= – 1/10 (x+8). Parallel to line g is line h, which passes through the point ( – 5,5). What is the equation of line h?
Answer:
point-slope form: [tex]y+5=-\frac{1}{10}(x-5)[/tex]
slope-intercept form: [tex]y = -\frac{1}{10}x - \frac{9}{2}[/tex]
Step-by-step explanation:
Point-Slope Form:We can express any one-variable linear equation as: [tex]y-y_1=m(x-x_1)[/tex], where "m" is the slope, and [tex](x_1, y_1)[/tex] is some point on the graph.
We're given the equation in point-slope form: [tex]y-1=-\frac{1}{10}(x+8)[/tex], and if we want to make a line parallel to this line, we just need the slopes to be the same. So let's just look at the value in front of the parenthesis. This is given to be: [tex]-\frac{1}{10}[/tex]
We can use this same form, to develop an equation parallel to the given line, and passing through: [tex](-5, 5)[/tex]
Plugging the values into the point-slope formula, we get:
[tex]y-(-5)=-\frac{1}{10}(x-5)\\\\y+5=-\frac{1}{10}(x-5)[/tex]
From here we can also convert this into slope-intercept form, where "y" is isolated.
[tex]\\y+5=-\frac{1}{10}(x-5)\\\\y+5=-\frac{1}{10}x + \frac{5}{10}\\\\y + \frac{10}{2} = -\frac{1}{10}x + \frac{1}{2}\\\\y + \frac{10}{2} - \frac{10}{2} = -\frac{1}{10}x + \frac{1}{2} - \frac{10}{2}\\\\y = -\frac{1}{10}x - \frac{9}{2}[/tex]
: A cell phone manufacturer claims that the average battery life of its newest flagship smartphone is exactly 20 hours. Javier believes the population mean battery life is less than 20 hours. He tests this claim by selecting a random sample of 33 phones of this model. Javier found that the sample mean battery life is 19.5 hours with a sample standard deviation of 1.9 hours. Should Javier reject or fail to reject the null hypothesis given the sample data below? • H:u=20 versus H, u <20 . a=0.05 (significance level) . to = -1.51 • 0.05
There is not sufficient evidence to conclude that the population mean battery life is less than 20 hours, based on the sample data.
To test the null hypothesis, Javier can use a one-sample t-test. In this test, the null hypothesis is that the population mean is equal to the claimed value of 20 hours, and the alternative hypothesis is that the population mean is less than 20 hours. To determine whether to reject or fail to reject the null hypothesis, Javier can compare the t-statistic, calculated from the sample data, to the critical t-value at a significance level of 0.05. The critical t-value is the value beyond which the null hypothesis can be rejected.
In this case, the t-statistic is given as -1.51. To find the critical t-value, Javier can use a t-table or a statistical software package. At a significance level of 0.05 and a sample size of 33, the critical t-value is approximately -1.68. Since the t-statistic (-1.51) is less than the critical t-value (-1.68), Javier should fail to reject the null hypothesis.
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what is an expression equivalent to 5 1/4d - 5?
Answer:
Step-by-step explanation:
23
Find the volume of the composite solid
Marcus worked 45 hours this week. His hourly rate of pay is $9.00. What was the pay
for Overtime hours only?
Marcus' overtime pay for the week is $67.50.
How is the overtime pay determined?The overtime pay is paid at the hourly rate and a half.
This translates to the regular rate of pay x 1.5 x overtime hours worked.
The total hours worked this week = 45 hours
Normal working hours per week = 40 hours (5 days x 8 hours)
Overtime hours = 5 hours (45 - 40)
Hourly rate = $9.00
Overtime rate = $13.50 ($9 x 1.5)
Overtime pay = $67.50 ($13.50 x 5)
Thus, for this week, Marcus has earned overtime pay of $67.50 above his normal weekly pay of $360.
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Find a positive and a negative coterminal angle for each given angle.
A positive and a negative co - terminal angle for each given angle is 1) -π/2 and -9π / 2 and 2) 7π / 2 and -π / 2 .
Given :
a positive and a negative co - terminal angle for each given angle
1 )
= -5π / 2
To find positive and negative co - terminal angle we need to add and subtract by 2π .
= -5π / 2 + 2π
= -5π + 4π / 2
= -π/2
= -5π / 2 - 2π
= -5π - 2 * 2π / 2
= -5π - 4π / 2
= -9π / 2
or =
2 )
= 3π / 2
= 3π / 2 + 2π
= 3π + 2 * 2π / 2
= 3π + 4π / 2
= 7π / 2
= 3π / 2 - 2π
= 3π - 4π / 2
= -π / 2
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Talhah and Rosina are doing push ups for PE class. They both want to complete the same number of push ups, but Talhah wants to do 6 push ups per set and Rosina wants to do 8 push ups per set. After they finished they realized that while they did the same total number of push ups, Rosina needed 3 fewer sets to finish hers. How many push ups did each girl do?
The number of push ups done by each girl from the given parameters is; 72 push ups
How to solve Algebra Word Problems?We are given;
Rate of Push ups for Talhah = 6 push ups per set
Rate of Push ups for Rosina = 8 push ups per set
Let the number of sets of push ups done by each girl be denoted as x
Thus, since after they finished, they realized that while they did the same total number of push ups, Rosina needed 3 fewer sets to finish hers, then the equation here is;
6x = 8(x - 3)
Expanding the bracket gives;
6x = 8x - 24
8x - 6x = 24
2x = 24
x = 12 sets
Thus, number of push ups done by each = 6 * 12 = 72
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For the 2009 regular season, the MLB batting leaders in number of hits were Ichiro Suzuki and Derek Jeter. These two players had a total of 437 hits. Suzuki had 13 more hits than Jeter. How many hits did each player have?
a 50.0 cmcm, uniform, 50.0 nn shelf is supported horizontally by two vertical wires attached to the sloping ceiling (figure 1). a very small 20.0 nn tool is placed on the shelf midway between the points where the wires are attached to it.
the tension in each wire will be equal. The tension in each wire, T ,the tension in each wire is 85.36 N with its weight.
Assuming that the tool has negligible mass so that its weight does not contribute to the tension in the wires, the tension in each wire will be equal. The tension in each wire, T, can be calculated using the equation:
T = (W/2) + (L/2)*sin(θ),
where W is the weight of the shelf and L is the length of the shelf. The angle θ is the angle between the ceiling and the shelf.
In this case, W = 50 N, L = 50 cm and θ = 45°. Therefore, T = (50/2) + (50/2)*sin(45) = 50 + 35.36 = 85.36 N.
So, the tension in each wire is 85.36 N.
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Justin was out at a restaurant for dinner when the bill came. His dinner came to $35. After adding in a tip, before tax, he paid $44.10. Find the percent tip.
Justin paid a tip that was 26% of his bill.
Step-by-step explanation:1. Form the expression.[tex]\frac{44.10-35}{35}[/tex]
2. Calculate.[tex]\frac{44.10-35}{35}=0.26[/tex]
3. Conclude.Justin paid a tip that was 26% of his bill.
$5400 is invested, part of it at 11% and part of it at 9%. For a certain year, the total
yield is $546.00. How much was invested at each rate?
Answer:$2400 invested at $9% $3000 invested at $11%
Step-by-step explanation:
Suman has a piece of land, which is in the shape of a rhombus. She wants her two sons to work on the land and produce different crops. She divides the land in two equal parts by drawing a diagonal. If its perimeter is 400 m and one of the
diagonals is of length 120 m, how much area each of them will get for his crops ?
Please help me with the question along with steps.
Answer:
Step-by-step explanation:
Perimeter = 400
Diagonal= 120
Each Side= 400/4 = 100
Then, find the length of a straight line:
400= 120(2)+2x
400= 240+ 2x
400-240=2x
160=2x
x=80
Area of Triangle= 1/2(b)(h)
= 1/2(80)(120)
= 1/2(9600)
= 4800
34 In the appeal of the People v. Collins case (see Exercise 4.1.28), the counsel for the defense argued as follows: Suppose, for example, there are 5,000,000 couples in the Los Angeles area and the probability that a randomly chosen couple fits the witnesses’ description is 1/12,000,000. Then the probability that there are two such couples given that there is at least one is not at all small. Find this probability. (The California Supreme Court overturned the initial guilty verdict.)
The probability that there are two such couples given that there is at least one is 1 - (4999999/12000000) = 4/12 = 1/3.
What is probability?Probability is the measure of the likelihood that a given event will occur. It is expressed as a number between 0 and 1 (or 0% to 100%). A probability of 1 indicates that the event is certain to occur, while a probability of 0 indicates that it is impossible for the event to occur. Probability is used in a wide range of disciplines including mathematics, science, engineering, finance, and philosophy. Probability can be used to make predictions and help inform decision-making. By understanding probability, we can better understand the chances of certain outcomes and make more informed decisions.
This is because the probability that the first couple matches the description is 1/12000000, and the probability that the second couple matches the description, given that the first couple does, is 1/(12000000-1). Since there are 4999999 other couples, the probability that the second couple matches the description is (4999999/12000000). Thus, the probability that there are two such couples is 1 minus the probability that the second couple does not match the description, which is 1 - (4999999/12000000) = 4/12 = 1/3.
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1. Assume that there is a party consisting of people between the ages of 18 and 24 inclusive. How many people would have to be at the party to guarantee that at least three people share the same birth date, birth month, and birth year? Note: assume the range of birth years include 2 leap years. (10 points)
at least 24 people must be in the party to guarantee that at least 3 people have the same date of birth, date of birth, date of birth.
To warrant that at least three people have the same date, month, and year of birth, we need to find the minimum number of people such that there is a probability that at least three people have the same date, month, and year. there is. Birth year she is 1 or more. Non-leap years have 365 days, and leap years have her 366 days. The birth year range includes two leap years, so there are 3652 + 3662 = 2,922 possible births. This means that the probability that a particular person's birthday is unique is (2922-1)÷2922 = 1÷2922.
Now we can use the birthday puzzle to calculate the probability that at least three people have the same birthday. The probability that no one has the same birthday is (1 - 1÷2922)^n, where n is the number of people in your party. At least he has 1-(1-1÷2922)^n probability that 3 of them have the same birthday. You can set this probability to 1 or more and solve for n.
1 - (1 - 1÷2922)^n >= 1
(1 - 1÷2922)^n <= 0
n >= log(0) ÷ log(1 - 1÷2922)
The logarithm of 0 is not defined, so you can use a small value on the right hand side instead. B. 10^-6. This will tell you:
n >= log(10^-6) ÷ log(1 - 1/2922)
n >= log(10^-6) ÷ log(2921/2922)
n >= log(10^-6) ÷ log(2921) - log(10^-6) / log(2922)
n >= log(10^-6) × log(2922) ÷ log(2921) - log(10^-6)
n >= log(10^-6) × log(2922) ÷ log(2921) - log(10^-6)
n >= 23.
Hence, at least 24 people must be in the party to guarantee that at least 3 people have the same date of birth, date of birth, date of birth.
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What are the vertex and range of y = |2x + 6| + 2?
(0, 2); 2 < y < ∞
(0, 2); −∞ ≤ y < ∞
(−3, 2); 2 < y < ∞
(−3, 2); −∞ ≤ y < ∞
The vertex and the range of y = |2x + 6| + 2 are (c) (-3, 2); 2 ≤ y < ∞
How to determine the vertex and the range?The equation is given as
y = |2x + 6| + 2
The above equation is an absolute value function
An absolute value function represented as
y = a|x - h| + k
Where
Vertex = (h, k)
So, we have
y = |2x + 6| + 2
This gives
y = 2|x + 3| + 2
This means that the vertex is
Vertex = (-3, 2)
Remove the x value
y = 2
Because the leading coefficient is positive, then the vertex is a minimum
i.e.
y ≥ 2
So, the range is 2 ≤ y < ∞
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