The area of region R is given by the integral ∫[0,5] (x^2+2) dx = 41.6667,The volume of the solid is given by the integral ∫[0,5] (x^2+2)^2 dx and the equation to find the value of k is given by the equation ∫[0,k] (x^2+2) dx = ∫[k,5] (x^2+2) dx.
a) We must integrate the function (x2+2) over the range [0,5] in order to determine the area of region R. The ensuing integral provides this information:
∫[0,5] (x^2+2) dx = 41.6667
b) To get the solid's volume, we must integrate the function (x2+2)2 over the range [0,5]. The ensuing integral provides this information:
∫[0,5] (x^2+2)^2 dx \sc) We must construct an equation that asserts that the area of the region below the line y=k is equal to the area of the region above the line y=k in order to get the value of k. The following equation yields this:
∫[0,k] (x^2+2) dx = (x2 + x2)[k,5] dx
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2) Given that Y and P are two events and P(Y) = 0.57, P(P) = 0.5 and P(Y UP) = 0.84,
Draw a Venn Diagram and find:
a) P(Yn P)
b) P(Y|P)
c) P(P|Y)
d) P(Y/P')
a) The value of P(Y∩P) =0.23
b) The value of (Y|P) = 0.34
c) The value of (P|Y) = 0.27
d) The value of P(Y/P') = 0.68
What is Venn diagram?
A Venn diagram can also be referred to as a set diagram or a logic diagram that illustrates various set operations including the intersection, union, and difference of sets. Subsets of a set are also represented using it. A subset of whole numbers, which is a subset of integers, is a collection of natural numbers, as an example.
Given that there are two events Y and P.
P(Y) = 0.57
P(P) = 0.5
P(Y∪P) = 0.84
The formula of intersection is P(Y∩P) = P(P) + P(Y) - P(Y∪P)
Putting P(Y) = 0.57, P(P) = 0.5, P(Y∪P) = 0.84
P(Y∩P) = 0.5 + 0.57 - 0.84
P(Y∩P) = 0.23.
b)
P(Y|P) = P(Y) - P(Y∩P)
P(Y|P) = 0.57 - 0.23
P(Y|P) = 0.34
c)
P(P|Y) = P(P) - P(Y∩P)
P(P|Y) = 0.5 - 0.23
P(P|Y) = 0.27
d) P(Y/P') = P(Y∩P') / P(P')
P(Y/P') = P(Y|P)/[1 - P(P)]
P(Y/P') = 0.34/(1- 0.5)
P(Y/P') = 0.68
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Blaine is going bowling and will need to
pay $4 for shoes and then $3 for every
game. Write an equation for the
situation, if Blaine spends 16 dollars.
Answer: $16 = 4s + 3g
Step-by-step explanation:
s = shoes
g = games
Coach Burgess drew a right triangle on the board. He said the hypotenuse was 13 inches and one of the legs was 5 inches. What is the length of the other leg? Round to the the tenths place
The length of the other leg is 12 inches.
What is the Pythagorean theorem?
The Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
The hypotenuse of a right triangle is the side opposite the right angle, and the legs of a right triangle are the two sides that are adjacent to the right angle.
If we know the length of the hypotenuse and one leg of a right triangle, we can use the Pythagorean theorem to find the length of the other leg.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.
We can use this theorem to write the equation:
c² = a² + b²
where c is the length of the hypotenuse, and a and b are the lengths of the legs.
In this problem, the hypotenuse is 13 inches and one of the legs is 5 inches. We can substitute these values into the equation to find the length of the other leg:
c² = a² + b²
(13)² = a² + (5)²
169 = a²+ 25
144 = a^2
a = 12
Hence, the length of the other leg is 12 inches.
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Geometric Transformations
The four letter code from the transformations is given as follows:
FB H.
How to obtain the four letter code?The four letter code is obtained applying the transformations to the given points.
The coordinates of point 1 are given as follows:
(-4,2).
The transformation is a reflection over the x-axis, which has the rule given as follows:
(x,y) ->(x,-y).
Hence the coordinates of the image of point 1 are given as follows:
1'(-4,-2).
Meaning that the first letter is of F.
The coordinates of point 2 are given as follows:
(-2,3).
The transformation is a reflection over the y-axis, which has the rule given as follows:
(x,y) ->(-x,y).
Hence the coordinates of the image of point 2 are given as follows:
2'(2,3)
Meaning that the second letter is of B.
The coordinates of point 4 are given as follows:
(-1,2)
The transformation is a reflection over the line y = x, which has the rule given as follows:
(x,y) ->(y,x).
Hence the coordinates of the image of point 4 are given as follows:
4'(2,-1)
Meaning that the fourth letter is of H.
Missing InformationThe third transformation is missing.
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The equation 4(2x 1) = 6x − 12 models the change in water level in a lake in one month. solve for x, which is change in height in inches. x equals negative thirteen halves x = −8 x = 8 x equals eleven halves
From the given options, option 2. x= -8 is the correct option. Here, the x is change in height in inches so the, change in height is -8 inches.
A linear equation is simply an equation with the highest degree always being 1. The standard form of a linear equation in one variable is Ax + B = 0. x is a variable in this equation, and A and B are constants. A two-variable linear equation has the standard form Ax + By = C. The variables x and y are variables, their coefficients A and B are variables, and C is a constant.
Given, linear equation is
[tex]4(2x+1)=6x-12\\\\8x+4=6x-12\\\\8x-6x=-4-12\\\\2x=-16\\\\x=-8[/tex]
Hence, the x equals to -8.
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Consider this right triangle. 20 m 37° Enter the length of side AB, to the nearest tenth.
Answer:
15.1
Step-by-step explanation:
tan(angle) = opposite/adjacent
tan 37 = AB/20
AB = 20 x tan 37 = 20 x 0.754 = 15.08 or 15.1
three hot dogs cost $82.86 and 2 hamburgers cost $55.12. which food has the lower unit price
Answer:
Hamburgers
Step-by-step explanation:
82.86/3 = 27.62
55.12/2 = 27.56
27.56 is smaller so hamburgers it is!
for a particular clothing store a marketing firm finds that 16% of $10-off coupons delivered by mail are redeemed. suppose six customers are randomly selected and are mailed $10-off coupons. what is the probability that three of the customers redeem the coupon?
The anticipated quantity of coupons as calculated from the data given is 1.6 .
We learn from the question that
The probability of a $10 voucher being redeemed via mail is p = 0.16.
n = 10 is the sample size.
In general, the projected number of coupons redeemed is represented numerically as
E(x) = np [ of PDF ]
= 10 x 0.16
= 1.6
When data follows a normal distribution, the probability density function (PDF) and cumulative distribution function (CDF) assist us in determining probabilities and ranges of probabilities. The CDF is the PDF integration, from left to right. We may construct many forms of probability estimates from our normally distributed data using these two normal distribution functions.
The standard deviation is a technique for us to explain how "spread out" the data is - how far it "deviates" from the mean value. Both and are known as normal distribution parameters.
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Julie buys a pair of earrings for $7. Now she would like to buy the same earrings for 2 of her friends. How much will she spend for all 3 pairs of earrings
Please help me with this question!
Answer:
Step-by-step explanation:
the answer is 11/12
If slope of a line is 7 and y-intercept is 4, then write the equation of that line.
Answer: The answer is y=7x+4
M is the slope and the y-intercept is b
Help with question 1
Answer: D
Step-by-step explanation:
Given the tally marks its 16ths, and the point is on the 3rd tally so it would be 10-3/16 Hope this helps!
1. Which of the following is a perfect cube. (A) 100 (B) 68600 (C) 343000 (D) 400
Answer: 68600
hope it helps!
Hard A level Maths question, please help ASAP cheers
The value of the shaded area from the rectangle ACDE is approximately 52.124 square centimeters.
How to determine the value of the shaded area
In this problem we must calculate the shaded area of the section within the rectangle ACDE, this can be found by the subtracting the area of the region ABDE, which is the combination of the areas of the right triangle ABE and the arc BDE, whose formulas are shown below:
Triangle ABE
S = (1 / 2) · AB · AE
Arc BDE
S = (1 / 2) · α · ED²
Where α is the central angle, in radians.
Rectangle ACDE
S = ED · AE
If we know that AE = 20 cm, ED = 28 cm, α = π / 4 and AB = 20 cm, then the area of the shaded area is:
S = (28 cm) · (20 cm) - (1 / 2) · (π / 4) · (28 cm)² - (1 / 2) · (20 cm) · (20 cm)
S ≈ 52.124 cm²
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Express 80 as the product of its prime factors.
Write the prime factors in ascending order.
Answer: [tex]2^4 \times 5[/tex]
Step-by-step explanation:
[tex]80=2 \times 40\\\\80=2 \times 2 \times 20\\\\80=2 \times 2 \times 2 \times 10\\\\80=2 \times 2 \times 2 \times 2 \times 5\\\\80=2^4 \times 5[/tex]
The pep squad is making mascot flags. They used 1.5 yards each of crimson, gold, and navy fabric to make 90 flags. How much fabric is needed to make 1 flag?
It will take 0.05 yards of fabric to make one flag.
What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that a pep squad is making mascot flags. They used 1.5 yards each of crimson, gold, and navy fabric to make 90 flags.
Assume that the total fabric needed is [x] yards. So -
(1.5 x 3) yards is needed to make 90 flags.
4.5 yards is need to make 90 flags.
1 flag will need (4.5/90) yards or 0.05 yards of fabric is needed.
Therefore, it will take 0.05 yards to make 1 flag.
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PLEASE HELP ME I TOOK A PICTURE
The inequality to describe the possible side length for the third side is 1 < x ≤ 19.
What is the inequality of a triangle?
According to the triangle inequality theorem, the sum of any two sides of a triangle is greater than or equal to the third side of a triangle. This statement can symbolically be represented as; a + b > c. a + c > b.
The triangle inequality tells that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.
We have given,
Two sides of a triangle have lengths 9 and 10.
The third side is represented by x.
So by triangle inequality, we have the following inequality:
x ≤ 9 + 10
x ≤ 19
Also, the difference between the lengths of any two sides of a triangle is less than the length of the third side.
10 - 9 < x
1 < x
Hence, the inequality to describe the possible side length for the third side is 1 < x ≤ 19.
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Select ALL the correct answers.
Consider the graph given below.
Determine which sequences of transformations could be applied to the parent function, f(x) = x, to obtain the graph above.
1)Shift left 3 units, reflect over the y-axis, and then vertically stretch by a factor of 2
2)Shift up 6 units, reflect over the x-axis, and then vertically stretch by a factor of 2
3)Shift right 3 units, reflect over the y-axis, and then vertically stretch by a factor of 2
4)Reflect over the y-axis, vertically stretch by a factor of 2, and then shift up 6 units
5)Shift left 2 units, reflect over the y-axis, and then vertically stretch by a factor of 6
6)Reflect over the x-axis, vertically stretch by a factor of 2, and then shift up 6 units
The sequences of transformations that could be applied to the parent function are Reflected over the y-axis, vertically stretch by a factor of 2, and then shift up 6 units i.e. Option (4).
What is transformation?
An operation that manipulates a polygon or other two-dimensional object on a plane or coordinate system is known as a transformation. Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.
The two-dimensional shape without any transformations is known as a preimage or inverse image. The transformed figure is shown in the image.
Given, the parent function, f(x) = x
From the given graph, the equation will be
y = -2x + 6
Then, the transformation will be
Shifted up 6 units
Vertical stretch by a factor of 2
Reflected over the y-axis
Hence, the required answer is Option 4.
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Which of the following values is not an irrational number?
5.73, ,√73, √40
O 5.73
O TT
3/73
O√40
The number that is non-irrational is 5.73, because it can be written as a quotient of two integers.
Which of the following options is not an irrational number?A rational number is a number that can be written as a quotient of two integer numbers, while an irrational number can't be written like that.
Also, the square root of a non perfect square is also irrational.
Here the options are:
5.73, ,√73, √40
Notice that neither of the square roots of non perfect square numbers, so these are irrational numbers.
In other hand, if we see the first one:
5.73
We can rewrite this as:
5.73 = 573/100
So this is a quotient of two integers, then this is a rational number, so this is the correct option.
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At a football stadium, 4% of the fans in attendance were teenagers. If there were 170 teenagers at the football stadium, what was the total number of people at the stadium?
Answer:
4,250
Step-by-step explanation:
If 4% of all fans were teenagers, and 100 divided by 4 is 25, simply math of 170 times 25 gives you 4,250
Therefore, the answer is 4,250
Answer:
Total number of people = 4,250
Step-by-step explanation:
4% of 4,250 = 170
Describe the error in finding the distance between A(6, 2) and B(1,−4). What is the actual length?
Using the formula for the distance between two points and using the provided points, The error is missing a square root. The actual length is [tex]\sqrt{61}[/tex] units.
What do you mean by distance?A line or line segment's length between two points along the line or line segment.
What is the formula to calculate distance between two points?
The required formula is:
[tex]d = \sqrt{(x2-x1)^{2}+(y2-y1)^{2}}[/tex]
(x1,y1)= (6,2)
(x2,y2)=(1,-4)
[tex]d = \sqrt{(1-6)^{2}+(-4-2)^{2}}[/tex]
[tex]d=\sqrt{25+36}[/tex]
[tex]d=\sqrt{61}[/tex] units.
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Using the formula for the distance between two points and using the provided points, The error is missing a square root. The actual length is units.
What do you mean by distance?
Distance refers to the amount of space between two or more points, or the measure of how far apart two or more points are. It can be measured in various ways, including miles, kilometers, inches, centimeters, and more. Distance is often used to measure the length of a journey or the amount of space between two physical objects. It can also refer to the amount of time between two events, such as the distance between two birthdays. Distance can also be used to describe the relative or emotional separation between two people, such as the distance between a parent and a child.
What is the formula to calculate distance between two points?
The required formula is:
[tex]d =\sqrt{(x2-x1)^2 +(y2-y1)^3}[/tex]
(x1,y1)= (6,2)
(x2,y2)=(1,-4)
[tex]d = \sqrt{(1-6)^2 + (-4 -2)^2}[/tex]
[tex]d = \sqrt{25+36}[/tex]
[tex]d = \sqrt{61} units[/tex]
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DUE BY SATURDAY!! please help
Answer:
Step-by-step explanation:
so you don't understand at all
Answer:
a.+1,-1
b.+√13,-√13
c.no real solutions
d.no real solutions
Step-by-step explanation:
question no c&d has no real solutions but they have complex solutions
if you are not taught about complex numbers then the Answers to c&d are no real solutions but for complex solutions
c.+3i,-3i
d.+√5i,-√5i
1.
The band and the orchestra are each having a party to celebrate the
results of their latest competition. The band would like to order cupcakes
from Walmart at a cost of $3.35 per cupcake and a $13.00 order fee
The orchestra would like to order cupcakes from Publix at $2.90 each
and a $22.50 order fee. This system {2.90c +22.50 represents the
total cost, T, and the number of cupcakes. Determine how many
cupcakes each club can order if they both have the same amount of
money to spend. Is the solution viable or not viable?
By solving a linear equation, it can be calculated that
Each club can order 21.1 cupcakes if they both have the same amount of
money to spend
What is a linear equation?
Equation shows the comparison between two algebraic expressions by connecting the two algebraic expressions by an equal to sign
A one degree equation is called linear equation
Let the number of cupcakes ordered by each club be c
The band would like to order cupcakes from Walmart at a cost of $3.35 per cupcake and a $13.00 order fee
Total amount spent = $(13 + 3.35c)
The orchestra would like to order cupcakes from Publix at $2.90 each
and a $22.50 order fee
Total amount spent = $(22.5 + 2.90c)
By the problem,
The linear equation is
13 + 3.35c = 22.5 + 2.90c
3.35c - 2.90c = 22.5 - 13
0.45c = 9.5
c = 21.1
This solution is not viable as the number of cupcakes must be an integer not a decimal.
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a doctor claims that people are at most 6 pounds overweight. to test the claim, the doctor randomly selects 81 people and calculates the difference between their ideal weight and actual weight. the sample mean and sample standard deviation of that difference were 7 pounds and 2 pounds respectively. can we conclude at the 1% level of significance that the claim is true? group of answer choices yes, conclude the claim is true by rejecting h0. no, conclude the claim is not true by rejecting h0. no, conclude the claim is not true by accepting h0. yes, conclude the claim is true by accepting h0.
we conclude at the 1% level of significance that the claim is true by accepting H₀
What is Hypothesis?
A hypothesis outlines your expectations for the results of your investigation. It is a speculative, untested response to your research question.
Given,
n = 81
x bar = 7
s= 2
Here, a doctor claims that people are atmost 6 pound over weight
H₀ : μ ≤ 6 versus
H₀ : μ > 6 versus
Now,
The Test Stastistic is
t = x bar - μ / s√n
t = 7-6/2√81
t = 4.5
let ∝ = 0.10, then p value = 0.000
p value >∝
yes, conclude the claim is true by accepting H₀
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Joe bought a box of laundry that contains 195 scoops. Each load of laundry uses 2 1/2 scoops. If the box of detergent costs $19.99, how much is he paying per load of laundry?
Answer:
a) Number of laundry he can do with this box = 78 laundries.b) Price he paying for each load = 0.256
what is this pleasee i give brainliest
The Slope of the line is -3/2
How to find Slope of the Line ?By Substituting x=26
=1/9/8*26+8/3
=-3/2
The slope formula is as follows if P(x1,y1) and Q(x2,y2) are the two points on a straight line:Slope, m = Y-coordinate change / X-coordinate changem = (y2 – y1)/(x2 – x1) (x2 – x1)As a result, using the formula above, we can quickly determine the slope of a line connecting two locations.The rise of the line from one point to another (along the y-axis) over the run is another way to describe the slope of a line between two points (along x-axis). A line's slope provides information on the steepness and direction of the line. By calculating the difference between the coordinates of the two points, (x1,y1) and (x2,y2), it is simple to calculate the slope of a straight line between them.To learn more about Slope of the Line refer to:
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Container A has 1000.75 mL of water and is draining 10.8 mL per minute. Container B has 800.75 mL of water and is draining 5.8 mL per minute. After how many minutes will the two containers have the same amount of water?
After 40min. water in both container A & B will be equal.
Let after 't' min. water in both the containers is same.
Water in Container A is 1000.75 ml & is draining at rate of 10.8ml/ min.
after 't' min. water will be = 1000.75 - 10.8t .......(eq 1)
Water in Container B is 800.75 ml & is draining at rate of 5.8ml/ min.
after 't' min. water will be = 800.75 - 5.8t ........(eq 2)
Now, we know that after 't' min. water in both container A & B is equal, so we can equate equation 1 with equation 2 and find out the value of 't' .
1000.75 - 10.8t = 800.75 - 5.8t
1000.75 - 800.75 = 10.8t - 5.8t
200 = 5t
t = 40 min.
Hence, after 40min. water in both container A & B will be equal.
What is a Container?
Something that can hold or move something is known as a container.
Eg- water, oil etc.
What is meaning of Draining Rate?
A channel or drain for water drainage.
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Simplify each expression.
8x+13 - 3x + 9/1/2
Answer:5x+22
there you gooo
Answer:
5x+ 45/2
Step-by-step explanation:
Manish borrowed some amount from bank at 4% per annum compounding yearly He lent the whole amount on anish at 6% per annum compound interest compounded half yearly if at the end of the year Manish gained Rs 104.5 find the amount that he borrowed from the bank
Answer:
Below
Step-by-step explanation:
Amount borrowed = x
Amount owed to bank at end of 1 year = 1.04 x
Manish lent out x then the amount owed to him
at end of 1 year = x (1 + .06/2)^2 = 1.0609x
GAIN = 1.0609x - 1.04x = 104.5 solve for x = 5000. Rs
The amount that Manish borrowed from the bank is ₹5000.
What is the compound interest?Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
If borrowed is ₹100 compound interest is ₹104
So, interest to be paid is 4.
If the shopkeeper got ₹100 then 6 months interest is 3 and next 3 months interest is ₹3.09 so interest to be paid is ₹6.09
Difference 6.09-4=2.09
If ₹2.09 is the difference principle is ₹100
₹104.50 is the difference the principle = (100×104.50)/2.09
= ₹5000
Therefore, the amount that Manish borrowed from the bank is ₹5000.
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Fátima, Gabriel y José tienen un total de $1080 en sus carteras. Gabriel tiene 3 veces lo que José tiene. Fátima tiene $70 menos
que José. ¿Cuanto dinero tienen en sus carteras?
Fátima tiene un total de $ 160, Gabriel tiene un total de $ 690 y José tiene un total de $ 230.
¿Cómo determinar el dinero requerido en sus carteras?
En este problema tenemos a tres personas, Fátima, Gabriel y José, que reúnen un total de $ 1.080. A continuación, traducimos las variables y ecuaciones asociadas a la situación:
x - Cantidad de dinero de Fátima.
y - Cantidad de dinero de Gabriel.
z - Cantidad de dinero de José.
Ecuaciones: Fátima, Gabriel y José tienen un total de $ 1080.
x + y + z = 1080
Gabriel tiene 3 veces lo que José tiene.
y = 3 · z
Fátima tiene $ 70 menos que José.
x = z - 70
A continuación, resolvemos el sistema de ecuaciones lineales:
x + y + z = 1080
(z - 70) + 3 · z + z = 1080
5 · z - 70 = 1080
5 · z = 1150
z = 1150 / 5
z = 230
x = z - 70
x = 230 - 70
x = 160
y = 3 · z
y = 3 · 230
y = 690
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