The solution of compound interest problem using formula of amount is
Anna have$2,734 more money than Hudson.
what is compound interest ?Compound interest is a type of interest in which the interest gained is added to the principal sum before the interest for the subsequent period is calculated using the updated total sum. In other words, in addition to the initial principal, the accumulated interest from prior periods is also taken into account for calculating interest. As a result, as time passes, the interest earned increases, increasing the total amount earned or due. Savings accounts, loans, and investments frequently use compound interest.
According to given informationFor continuous compounding, the formula is:
A = Pe^(rt)
Where:
A = the amount after t years
P = the principal amount
r = the annual interest rate (as a decimal)
t = the time in years
For daily compounding, the formula is:
A = P(1 + r/n)^(nt)
Where:
A = the amount after t years
P = the principal amount
r = the annual interest rate (as a decimal)
n = the number of times compounded per year
t = the time in years
Using these formulas, we can calculate the amount that Anna and Hudson will have after 10 years, and then find the difference between them.
For Anna's investment:
r = 8.5% = 0.085 (as a decimal)
t = 10 years
P = $69,000
A = Pe^(rt) = 69000 * e^(0.085*10) = $156,794.63
For Hudson's investment:
r = 8 3/8% = 8.375% = 0.08375 (as a decimal)
n = 365 (daily compounding)
t = 10 years
P = $69,000
A = P(1 + r/n)^(nt) = 69000(1 + 0.08375/365)^(365*10) = $154,060.52
Therefore, the difference between the two amounts is:
$156,794.63 - $154,060.52 = $2,734.11
So Anna will have approximately $2,734 more in her account than Hudson after 10 years.
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Jamal is comparing two different kinds of fruit at the store .He wants to buy the one that is the best value per pound. what is the cost per pound for each kind of fruit? Which kind of fruit gives him the best value per pound?
Answer:
apples per pound: 0.25
pears per pound: 0.33
Apples give him the best value per pound
Step-by-step explanation:
to find apple per pound: 4/16= 0.25
to find pears per pound: 7/21= 0.33
find the surface area of the prism.
Step-by-step explanation:
There are six sides... 3 pairs of equal sides
2 x ( 4x5 + 4x7 + 5x7) = 166 cm^2
Answer:
166 cm²
Step-by-step explanation:
5x7=35
35x2=70
4x7=28
28x2=56
5x4=20
20x2=40
70+56+40= 166cm²
hope this helps!
You are applying fertilizer to the football field field is 360 feet long is 160 feet why do you use 8 pounds of fertilizer per thousand square feet the fertilizer comes and 50 pound bags how many bags of fertilizer what you need to co
To cover the full football pitch, you will want 10 bags of fertiliser, rounded up to the nearest whole number.
What is area?The term "area" refers to the volume of space occupied by a two-dimensional (2D) form or surface.
It's represented by squares.
You must multiply the length by the breadth of the football pitch to determine its total area:
field size for football = length x width
field size for football = 360 feet x 160 feet
field size for football = 57,600 square feet
You must now calculate how many thousands of square feet the football pitch has in order to get the total amount of fertiliser required:
the size of a football pitch in square feet = the size of the football pitch overall / 1,000
the size of a football pitch in square feet = 57,600 / 1,000
the size of a football pitch in square feet = 57.6
You must spread 8 pounds of fertiliser per 1,000 square feet of the football pitch because it is 57.6 thousand square feet in size.
Total required fertiliser quantity = 8 pounds per 1,000 square feet x 57.6 thousand square feet
Total required fertiliser quantity = 460.8 pounds
Given that the fertiliser is sold in 50-pound bags, you will require:
number of fertiliser bags = Total amount of fertilizer needed / Weight of each bag
number of fertiliser bags = 460.8 pounds / 50 pounds/bag
number of fertiliser bags = 9.216 bags
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Use the given conditions to find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas. sin(u) = 5/13, pi/2 < u < pi.
According to the information, the exact values of sin(2u), cos(2u) and tan(2u) are sin(2u) = -120/169, cos(2u) = -1, and tan(2u) = -120/119.
How to calculate the exact values of sin(2u), cos(2u) and tan(2u)?We can use the double-angle formulas to find the values of sin(2u), cos(2u), and tan(2u) in terms of sin(u) and cos(u).
sin(2u) = 2 sin(u) cos(u)cos(2u) = cos²(u) - sin²(u)tan(2u) = (2 tan(u)) / (1 - tan²(u))First, we need to find cos(u) using the Pythagorean identity:
cos²(u) + sin²(u) = 1cos²(u) = 1 - sin²(u)cos(u) = ±sqrt(1 - sin²(u))Since pi/2 < u < pi, we know that sin(u) is positive and cos(u) is negative. Therefore:
cos(u) = -sqrt(1 - (5/13)²) = -12/13Now we can substitute sin(u) and cos(u) into the double-angle formulas:
sin(2u) = 2 sin(u) cos(u) = 2 (5/13) (-12/13) = -120/169cos(2u) = cos²(u) - sin²(u) = (-12/13)² - (5/13)² = -144/169 - 25/169 = -169/169 = -1tan(2u) = (2 tan(u)) / (1 - tan²(u)) = (2 (5/12)) / (1 - (5/12)²) = (10/12) / (119/144) = -120/119Therefore, sin(2u) = -120/169, cos(2u) = -1, and tan(2u) = -120/119.
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A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a velocity of
33 ft/s. Its height in feet after t seconds is given by y = 33t - 20t².
A. Find the average velocity for the time period beginning when t=3 and lasting
.01 s:
4
.005 s:
.002 s:
.001 s:
NOTE: For the above answers, you may have to enter 6 or 7 significant digits if you are using a calculator.
Estimate the instanteneous velocity when t=3.
Answer:
The average velocity for a time period is given by the change in position divided by the change in time. For the time period beginning when t=3 and lasting 0.01 seconds, we have:
Initial time: t1 = 3 secondsFinal time: t2 = 3.01 secondsInitial position: y1 = 33t1 - 20t1^2 = 9 feetFinal position: y2 = 33t2 - 20t2^2 = 8.397 feetThe change in position is y2 - y1 = -0.603 feet, and the change in time is t2 - t1 = 0.01 seconds. Therefore, the average velocity for this time period is:
average velocity = change in position / change in time = (-0.603 feet) / (0.01 seconds) ≈ -60.3 feet/second
Similarly, for the time periods beginning when t=3 and lasting 0.005 seconds, 0.002 seconds, and 0.001 seconds, we have:
Time period of 0.005 seconds:Initial time: t1 = 3 secondsFinal time: t2 = 3.005 secondsInitial position: y1 = 33t1 - 20t1^2 = 9 feetFinal position: y2 = 33t2 - 20t2^2 = 8.8025 feetChange in position: y2 - y1 = -0.1975 feetChange in time: t2 - t1 = 0.005 secondsAverage velocity: (-0.1975 feet) / (0.005 seconds) = -39.5 feet/secondTime period of 0.002 seconds:Initial time: t1 = 3 secondsFinal time: t2 = 3.002 secondsInitial position: y1 = 33t1 - 20t1^2 = 9 feetFinal position: y2 = 33t2 - 20t2^2 = 8.8808 feetChange in position: y2 - y1 = -0.1192 feetChange in time: t2 - t1 = 0.002 secondsAverage velocity: (-0.1192 feet) / (0.002 seconds) = -59.6 feet/secondTime period of 0.001 seconds:Initial time: t1 = 3 secondsFinal time: t2 = 3.001 secondsInitial position: y1 = 33t1 - 20t1^2 = 9 feetFinal position: y2 = 33t2 - 20t2^2 = 8.9408 feetChange in position: y2 - y1 = -0.0592 feetChange in time: t2 - t1 = 0.001 secondsAverage velocity: (-0.0592 feet) / (0.001 seconds) = -59.2 feet/secondTo estimate the instantaneous velocity when t=3, we can calculate the derivative of the position function with respect to time:
y = 33t - 20t²
dy/dt = 33 - 40t
At t=3, we have:
dy/dt = 33 - 40(3) = -87
Therefore, the estimated instantaneous velocity when t=3 is -87 feet/second.
Real-life Problems Question 9
The Results:
a) Cost of the bouncy castle for 20 children = £149
b) Number of children who went to the party = 14.
How to find the cost of the bouncy castle for 20 children?a) To find the cost of the bouncy castle for 20 children, we can substitute the number of children, which is 20, into the formula provided:
Cost = £3.65 * number of children + £76
Cost = £3.65 * 20 + £76
Now we can estimate the cost:
Cost = £73 + £76
Cost = £149
Thus, the cost of the bouncy castle for 20 children = £149.
b) To find the number of children who went to the party based on the given cost of £127.10, we can rearrange the formula to solve for the number of children:
Cost = £3.65 * number of children + £76
£127.10 = £3.65 * number of children + £76
Subtracting £76 from both sides of the equation:
£127.10 - £76 = £3.65 * number of children
£51.10 = £3.65 * number of children
Now we can divide both sides of the equation by £3.65 to isolate the variable:
£51.10 / £3.65 = number of children
14 = number of children
Therefore, the number of children who went to the party = 14.
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Amy is planning an event for her company where at least 1,640 guests are expected to attend. She is reserving rooms at a large hotel-convention center. Each ballroom (x) can hold 139 people and each conference room (y) can hold 30 people. Select the inequality that Amy could use to determine how many of each type of room she will need to reserve. a. 30x + 139y<1640 b. 30x + 139y>1640 c. 30y + 139x<1640 d. 30y + 139x>1640
The inequality states that the sum of the number of conference rooms and ballrooms should be greater than the number of guests, so that all the guests can be accommodated. The correct answer is d. 30y + 139x>1640.
What is inequality?It is usually written using symbols such as “<”, “>”, “≤”, and “≥”, where one side of the expression is greater than, less than, or equal to the other side.
This is the appropriate inequality to determine how many of each type of room Amy will need to reserve because it expresses the total number of guests (1,640) that must be accounted for in the total number of conference rooms (30y) and ballrooms (139x).
To solve the inequality, Amy can start by assuming the number of conference rooms (y) she will need to reserve.
If she decides to reserve 10 conference rooms, the inequality will become 30(10) + 139x > 1640.
This can be simplified to 1390x > 1640 - 300, which reduces to x > 7.64. This means that Amy will need to reserve at least 8 ballrooms to accommodate all 1,640 guests.
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3. What two assumptions must be met when you are using
the z test to test differences between two means? Can the
sample standard deviations s, and so be used in place of
the population standard deviations o, and o₂?
Brainiest please.
Tulips should be planted 3 inches apart to give a full look. You have a trapezoidal plot for a flower garden, as shown in the figure. You plan to put tulips along the parallel sides of the garden. The midsegment to the garden is 10 feet long
Answer: 3 and 14
Step-by-step explanation: x ft = 3ft and x + 4 x = 10 (as you stated) x would be 10 so (10 + 4)ft= 14ft
At a large high school, 20% of the students prefer to have a salad for lunch. If you take a random sample of 10 students from this population, the probability that exactly 2 students prefer salad is
The probability that exactly 2 students prefer salad is 0.302
Calculating the probability that exactly 2 students prefer saladFrom the question, we have the following parameters that can be used in our computation:
n = 10
r = 2
p = 20%
The probability is then calculated as
P(x = 2) = nCr * p^x * (1 - p)^(n - x)
substitute the known values in the above equation, so, we have the following representation
P(x = 2) = 10C2 * (20%)^2 * (1 - 20%)^8
Evaluate
P(x = 2) = 0.302
Hence, the probability is 0.302
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1A. Draw a Venn diagram for (A–B) nC
Answer:
Draw three overlapping circles to represent the sets A, B, and C.
Label the regions inside each circle with the name of the corresponding set (i.e., A, B, and C).
Shade the region that represents the set A - B, which includes all the elements that belong to A but not to B.
Finally, shade the region that represents the intersection of (A - B) and C, which includes all the elements that belong to both (A - B) and C.
The resulting diagram should show three overlapping circles, with the region for A shaded but with a part removed (to represent the exclusion of elements in B from A), and the region for (A - B) n C shaded within that.
The numbered disks shown are placed in a box and one disk is selected at random. Find the probability of selecting an number, given that a disk is selected.
The probability of selecting a 2 given that a blue disk is selected is 1/8, or 0.125.
How did we arrive at the conclusion above?1. Let's calculate the probability of selecting a blue disk
We can select a blue disk with number 2, 6 or 8 out of a total of 8 disks, it means that the probability of selecting a blue disk is
3/8
2. Let's calculate the probability of selecting the blue disk labeled with number 2:
We can select the blue disk labeled with number 2 out of three blue disks, it means that the probability of selecting the blue disk labeled with number 2 is 1/3
3. These are dependent events because the fact that we select the disk labeled with number 2, depends on selecting a blue disk before, thus:
Probability of selecting a 2 given that a blue disk is selected =
3/8 * 1/3 = 3/24 = 1/8
So we can state that the probability of selecting a 2 given that a blue disk is selected is 1/8, or 0.125.
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Full Question:
See the attached image.
let U={1,2,...,10}, A={3,5,6,8,10}, B=1,2,4,5,8,9} and C={1,2,3,4,5,6,8} Then, find each following
¡) (A n B) u C
¡¡) (A-B) u C
¡¡¡) (A u B)'
The set of all elements that are in either A or B is the union of A and B, which is 1, 2, 3, 4, 5, 6, 8, 9, 10. As a result, A u B = 1, 2, 3, 4, 5, 6, 8, 9, 10
What is set operations?Set operations are done on two or more sets to produce a combination of components based on the operation. There are three primary sorts of operations done on sets in a set theory, such as: Intersection of sets () Union of sets () Set difference (-).
¡) (A n B) u C:
The value of the intersection of A and B is 5, 8. As a result, (A n B) = 5, 8. The union of this set with C is thus 1, 2, 3, 4, 5, 6, 8. As a result, (A n B) u C = 5, 8 u 1, 2, 3, 4, 5, 6, 8 = 1, 2, 3, 4, 5, 6, 8.
¡¡) (A-B) u C:
A-B is the set of elements in A that are not in B, which is 3, 6. The union of this set with C is thus 1, 2, 3, 4, 5, 6, 8. As a result, (A-B) u C = 3, 6 u 1, 2, 3, 4, 5, 6, 8 = 1, 2, 3, 4, 5, 6, 8.
¡¡¡) (A u B):
The set of all elements that are in either A or B is the union of A and B, which is 1, 2, 3, 4, 5, 6, 8, 9, 10. As a result, A u B = 1, 2, 3, 4, 5, 6, 8, 9, 10.
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¡) (A ∩ B) ∪ C = {1,2,3,4,5,6,8}.
¡¡) (A-B) ∪ C = {1,2,3,4,5,6,8,10}.
¡¡¡) (A ∪ B)' is the set of elements that are in U but not in {1,2,3,4,5,6,8,9,10}. This is simply the set {7}.
What is probability?
Probability is a measure of the likelihood of an event occurring.
Recall that:
A ∩ B denotes the intersection of sets A and B, i.e., the set of elements that are in both A and B.
A ∪ B denotes the union of sets A and B, i.e., the set of elements that are in either A or B or both.
A' denotes the complement of set A, i.e., the set of elements that are not in A.
Using these notations, we can solve each part of the question as follows:
¡) (A ∩ B) ∪ C
First, we need to find A ∩ B, which is the set of elements that are in both A and B. We can see that A={3,5,6,8,10} and B={1,2,4,5,8,9}. So, A ∩ B={5,8}.
Next, we take the union of (A ∩ B) and C. We have C={1,2,3,4,5,6,8}, so the final set is:
(A ∩ B) ∪ C = {5,8} ∪ {1,2,3,4,5,6,8} = {1,2,3,4,5,6,8}
Therefore, (A ∩ B) ∪ C = {1,2,3,4,5,6,8}.
¡¡) (A-B) ∪ C
First, we need to find A-B, which is the set of elements that are in A but not in B. We can see that A={3,5,6,8,10} and B={1,2,4,5,8,9}. So, A-B={3,6,10}.
Next, we take the union of (A-B) and C. We have C={1,2,3,4,5,6,8}, so the final set is:
(A-B) ∪ C = {3,6,10} ∪ {1,2,3,4,5,6,8} = {1,2,3,4,5,6,8,10}
Therefore, (A-B) ∪ C = {1,2,3,4,5,6,8,10}.
¡¡¡) (A ∪ B)'
Recall that A ∪ B denotes the union of sets A and B, i.e., the set of elements that are in either A or B or both. So, (A ∪ B)' denotes the complement of A ∪ B, i.e., the set of elements that are not in A or B.
We can see that A={3,5,6,8,10} and B={1,2,4,5,8,9}. So, A ∪ B={1,2,3,4,5,6,8,9,10}. Therefore, (A ∪ B)' is the set of elements that are not in {1,2,3,4,5,6,8,9,10}.
The universal set U={1,2,...,10}, so (A ∪ B)' is the set of elements that are in U but not in {1,2,3,4,5,6,8,9,10}. This is simply the set {7}.
Therefore, (A ∪ B)'={7}.
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whats angle A pls help
Answer:
x = 19.6
Step-by-step explanation:
The sum of the angles of a triangle is 180.
<A + <B+ < C = 180
x + 5x + 4x - 16 = 180
Combine like terms.
10x-16=180
Add 16 to each side.
10x-16+16 = 180+16
10x = 196
Divide each side by 10.
10x/10 = 196/10
x = 19.6
Answer :
Angle A = 19.6°Step-by-step explanation :
According to the question It is given that,
Angle A = x Angle B = 5x Angle C = 4x - 16We will apply angle sum property in the question.
Angle sum property states that sum of all the angles of triangle is 180°
[tex]\: :\implies [/tex] ∠A + ∠B + ∠ C = 180
[tex]\: :\implies [/tex] x + 5x + 4x - 16 = 180
[tex]\: :\implies [/tex] 10x - 16 = 180
[tex]\: :\implies [/tex] 10x = 180 + 16
[tex]\: :\implies [/tex] 10x = 196
[tex]\: :\implies [/tex] x = 196/10
[tex]\: :\implies [/tex] x = 19.6
Therefore, The Measure of Angle A is 19.6°
PLEASE HELP ASAP
Polygon JKLM is drawn with vertices J(−2, −5), K(−4, 0), L(−1, 2), M (0, −1). Determine the image coordinates of M′ if the preimage is translated 4 units up.
M′(−4, −1)
M′(4, −1)
M′(0, −5)
M′(0, 3)
The image coordinates of M′ are M′(0, 3).
What is translation?
A translation is a geometric transformation when each point in a figure, shape, or space is moved in a specific direction by the same amount. A translation can also be thought of as moving the origin of the coordinate system or as adding a constant vector to each point.
Here, we have
Given: Polygon JKLM is drawn with vertices J(−2, −5), K(−4, 0), L(−1, 2), M (0, −1).
When the shape is moved up by k units, then replace y with y + k.
The translation is as follows:
Here, J(-2, -5) → (-2, -5+4) → J'(-2, -1)
K(-4, 0) → (-4, 0+4) → K'(-4, 4)
L(-1, 2) → (-1, 2+4) → (-1, 6)
M(0, -1) → (0, -1+4) → (0, 3)
Hence, the image coordinates of M′ are M′(0, 3).
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solve this problem using leibnitz's theorem with details explanation.
We have shown that dⁿ⁺¹ / d xⁿ⁺¹ (xⁿ ln x) = n!/x using Leibniz's theorem.
What is the Leibniz's theorem?
Leibniz's theorem, also known as the product rule for derivatives, is a rule for finding the nth derivative of a product of two functions. It states that if u(x) and v(x) are functions of x, then the nth derivative of their product
To apply Leibniz's theorem, we need to express the function in terms of a product of two functions: u and v.
Let u = xⁿ and v = ln(x)
Then, du/dx = n*xⁿ⁻¹ and dv/dx = 1/x
Using the formula,
d/dx(xⁿ ln(x)) = u(dv/dx) + v(du/dx)
= xⁿ * (1/x) + ln(x) * n * xⁿ⁻¹
= xⁿ⁻¹ + n*xⁿ⁻¹ ln(x)
To find the nth derivative, we differentiate n times using the product rule.
First, we need to find the first few derivatives:
f(x) = xⁿ⁻¹ + n*xⁿ⁻¹ ln(x)
[tex]f'(x) = nx^{(n-2)} + (n-1)*x^{(n-2)} ln(x)[/tex]
[tex]f''(x) = n(n-2)x^{(n-3)} + 2(n-1)x^{(n-3)} ln(x) - (n-1)x^{(n-3)}/(x^2)[/tex]
[tex]f'''(x) = n(n-2)(n-3)x^{(n-4)} + 3(n-1)(n-2)x^{(n-4)} ln(x) - 3(n-1)x^{(n-4)}/(x^2) - 2(n-1)x^{(n-4)} ln(x)/(x^2)[/tex]
and so on...
The pattern becomes apparent and the nth derivative can be expressed as:
[tex]f^{(n)}(x) = n!/(x^{(n+1)})[/tex]
So,
dⁿ⁺¹ / d xⁿ⁺¹ (xⁿ ln x) = [tex]f^{(n)}(x) = n!/(x^{(n+1)})[/tex]
Hence, we have shown that dⁿ⁺¹ / d xⁿ⁺¹ (xⁿ ln x) = n!/x using Leibniz's theorem.
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Color can be used to highlight parts of a painting, but it cannot work to bring together parts of a painting.
OA. True
OB. False
The statement "color cannot work to bring together parts of a painting" is false. OB. False
what is proportionality ?
The interaction of two variables that changes as a single ratio or proportion is referred to as proportionality.
The use of a cohesive color palette can help to create a sense of unity throughout the painting, tying together disparate elements and creating a harmonious whole. Color can also be used to create visual connections between different parts of the painting, leading the viewer's eye from one area to another and creating a sense of flow and movement within the composition.
So, the statement "color cannot work to bring together parts of a painting" is false.
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Obtain the HCF of 420 and 272 by using Euclid's division algorithm and verify the using fundamental therorem of arthmetic
The HCF of 420 and 272 is 4.
To find the HCF of 420 and 272 using Euclid's division algorithm, we can proceed as follows:
Step 1: Divide 420 by 272
420 = 272 x 1 + 148
Step 2: Divide 272 by 148
272 = 148 x 1 + 124
Step 3: Divide 148 by 124
148 = 124 x 1 + 24
Step 4: Divide 124 by 24
124 = 24 x 5 + 4
Step 5: Divide 24 by 4
24 = 4 x 6 + 0
So, we can see that the last non-zero remainder obtained by Euclid's division algorithm is 4. Therefore, the HCF of 420 and 272 is 4.
Now, let's verify this using the Fundamental Theorem of Arithmetic.
The Fundamental Theorem of Arithmetic states that every positive integer greater than 1 can be expressed as a product of prime numbers in a unique way, up to the order of the factors.
The prime factorization of 420 is:
420 = 2^2 x 3 x 5 x 7
The prime factorization of 272 is:
272 = 2^4 x 17
To find the HCF using the prime factorizations, we need to take the product of the common prime factors with the smallest exponent. In this case, the only common prime factor is 2, and it appears with an exponent of 2 in 420 and an exponent of 4 in 272. So, the HCF is:
HCF(420, 272) = 2^2 = 4
This matches the result obtained using Euclid's division algorithm. Therefore, we have verified that the HCF of 420 and 272 is indeed 4.
Use a net to find the surface area of the prism.
A. 469 in.2
B. 315 in.2
C. 539 in.2
D. 784 in.2
The surface area of the triangular prism is 511 in²
What is an equation?An exponential equation is an expression that shows how numbers and variables using mathematical operators.
The surface area of the prism is gotten by summing the individual area of each surface of the prism.
The surface area = (0.5 * 11 in * 7 in) + (0.5 * 11 in * 7 in) + (11 in * 14 in) + (9 in * 14 in) + (8 in * 14 in) = 511 in²
The surface area is 511 in²
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There are 60 children in a club.
In the club, the ratio of the number of girls to the number of boys is 3:1
3/5 of the girls play a musical instrument.
4/5 of the boys play a musical instrument.
What fraction of the 60 children play a musical instrument?
(4 marks)
Evaluate the expression for the given values. If x=−5 and y=29, find y−x2.
Answer:
We have,
y - x^2 = 29 - (-5)^2
= 29 - 25
= 4
Therefore, y - x^2 = 4 when x = -5 and y = 29.
Each side of a square classroom is 20 feet long. What is the room's area?
Answer:
Area = length * width
Step-by-step explanation:
If all the sides of the room are equal, all you have to do is 20*20 = area
which of the following points (A, B, C or D) correctly represents 5/2 on the number line?
Answer:
C
Step-by-step explanation:
if we have a number line that has fractions listed, it should be C, because if 6/2 makes 3, which would be D, 5/2 should be C.
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Answer:
The answer is -3
Step-by-step explanation:
log(1/1000)=x
log 10(1/1000)=x
10^x=(1/1000)
10^x=10⁰/10³
10^x=10^-3
x= -3
Answer:
-3
Step-by-step explanation:
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What is the particular solution to the differential equation?
Answer:
y = (1/3)(e^(-9(x+2)/(x+1)) -1)
Step-by-step explanation:
You want the particular solution to the differential equation ...
y' = 3(1+3y)/(1+x)^2 with y(-2) = 0
Separation of variablesThe differential equation can be rewritten as ...
[tex]\dfrac{dy}{3(1+3y)}=\dfrac{dx}{(1+x)^2}[/tex]
We can define u = 1+3y, then du = 3 and the left side becomes ...
dy/(3(1+3y)) = (1/9)du/u
and its integral is ...
∫(1/9)du/u = (1/9)ln(u) = (1/9)ln(1 +3y)
The integral of the right side is ...
[tex]\int{(1+x)^{-2}}\,dx=-(1+x)^{-1}+C[/tex]
ResultThen the result of integrating both sides of this rewritten differential equation is ...
[tex]\dfrac{1}{9}\ln{(1+3y)}=-\dfrac{1}{1+x}+C[/tex]
The boundary condition can be used to find C:
[tex]\dfrac{\ln(1+3\cdot0)}{9}=-\dfrac{1}{1-2}+C\\\\0=1+C\\\\C=-1[/tex]
Particular solutionSolving this equation for y, we get ...
[tex]\ln(1+3y)=-9\left(\dfrac{1}{1+x}+1\right)\\\\\\1+3y=e^{\left(-\dfrac{9(x+2)}{x+1}\right)}\\\\\\\boxed{y=\dfrac{e^{\left(-\dfrac{9(x+2)}{x+1}\right)}-1}{3}}[/tex]
Consider the following set of equations:
Equation R: -3y = -3X-9
Equation S: y=x+3
Which of the following best describes the solution to the given set of equations? (4 points
No solution
One solution
Infinite solutions
OTwo solutions
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0 8. A function f(x) is said to have the jump discontinuity at a point x = a if lim a)x+a+ c) x→a+ f(x) = lim x→a+ f(x) = lim x→a¯ lim X-a f(x). b) lim x→a f(x) = lim x→a¯ _ f(x) f(x) = f(a) d) lim f(x) → +00 x→a+
The correct option for the given question is c) lim x→a¯ f(x) = f(a) when the function f(x) is said to have jump discontinuity at a point x=a.
What is jump discontinuity?Jump continuity is a concept in calculus that describes the behaviour of a function at a specific point where the function jumps from one value to another value without any intermediate values. In other words, a function is considered jump continuous at a point if the function approaches a finite limit from both the left and right sides of that point, but the function values on the left and right sides of the point are not equal.
According to the given information:
The correct notation for the left-hand limit as x approaches a from the left side is lim x→a¯, where the horizontal line above the "a" indicates approaching from the left side.
The statement "lim x→a¯ f(x) = f(a)" means that the limit of f(x) as x approaches a from the left side is equal to the value of f(a) at x = a. This indicates that the function f(x) has a jump discontinuity at x = a, where the function jumps from one value to another value at that specific point.
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Which ordered pairs represent points on the graph of this equation? Select all that apply. y = 2x - 3 a)3-3 b) 0,-3 c) 5,7 d) -2,-7 e) 2,1 or f) 4,5
The ordered pairs that represent points on the graph of y = 2x - 3 are (0,-3), (5,7), (-2,-7), (2,1), and (4,5).
What is equation?An ordered pair is a pair of numbers written in a specific order (x,y) that represents a point in the coordinate plane.
What is graph?A graph is a visual representation of data or a mathematical function that is plotted on a coordinate plane, usually with an x and y-axis. It is used to analyze trends and relationships between variables.
According to the given information:
To determine whether a given ordered pair represents a point on the graph of the equation y = 2x - 3, we need to substitute the values of x and y into the equation and see if the equation is true.
a) (3,-3):
y = 2x - 3
-3 = 2(3) - 3
-3 = 3
This is not true, so (3,-3) is not on the graph.
b) (0,-3):
y = 2x - 3
-3 = 2(0) - 3
-3 = -3
This is true, so (0,-3) is on the graph.
c) (5,7):
y = 2x - 3
7 = 2(5) - 3
7 = 7
This is true, so (5,7) is on the graph.
d) (-2,-7):
y = 2x - 3
-7 = 2(-2) - 3
-7 = -7
This is true, so (-2,-7) is on the graph.
e) (2,1):
y = 2x - 3
1 = 2(2) - 3
1 = 1
This is true, so (2,1) is on the graph.
f) (4,5):
y = 2x - 3
5 = 2(4) - 3
5 = 5
This is true, so (4,5) is on the graph.
Therefore, the ordered pairs that represent points on the graph of the equation y = 2x - 3 are: (0,-3), (5,7), (-2,-7), (2,1), and (4,5). Answer: b), c), d), e) and f).
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El radio de la lente circular de una lupa es de 4 centímetros. ¿Cuál es el área, en centímetros cuadrados, del vidrio?
Por lo tanto, el área del vidrio de la lupa es de aproximadamente 50.24 centímetros cuadrados.
What is el área?
"El área" is a Spanish phrase that translates to "the area" in English. "The area" is a mathematical term that refers to the measure of the size of a two-dimensional region, usually measured in square units such as square centimeters (cm²) or square meters (m²). The area of a figure can be calculated using various mathematical formulas, depending on the shape of the figure.
El área del vidrio de una lupa circular se puede calcular usando la fórmula del área del círculo, que es A = πr², donde "A" es el área, "π" es una constante aproximadamente igual a 3.14 y "r" es el radio de la lupa.
En este caso, el radio de la lupa es de 4 centímetros. Sustituyendo este valor en la fórmula, obtenemos:
A = πr²
A = 3.14 x 4²
A = 3.14 x 16
A = 50.24
Por lo tanto, el área del vidrio de la lupa es de aproximadamente 50.24 centímetros cuadrados.
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The lengths of two sides of a triangle are 4 inches and 7 inches. What is a possible length, in inches, of the third side? Select all that apply.
2
3
4
5
6
8
11
Pls tell me the ones that are right! It’s select all that apply
The right answers outoff these options are: 3,5,6,8
Define length?Length is a measure of the size or distance of an object or space in one dimension, usually referring to the longest dimension of an object. It is typically measured in units such as inches, meters, or feet.
What is triangle?In geometry, a triangle is a closed two-dimensional shape that is formed by connecting three non-collinear points with straight line segments. The line segments are called sides, and the points where they meet are called vertices. A triangle has three angles, which are formed by the intersection of its sides.
To determine the possible length of the third side of a triangle, we need to apply the triangle inequality theorem which states that the sum of the lengths of any two sides is always greater than the third side.
Using this theorem, we can see that the possible lengths for the third side are:
- 3 inches
- 5 inches
- 6 inches
- 8 inches
Therefore, the correct answers are:
3,5,6,8.
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