JAMB UTME - Mathematics - 2017

Answer Details

The integral of x^2 + 3x - 5 with respect to x is: ∫(x^2 + 3x - 5) dx To solve this, we can use the power rule of integration, which states that the integral of x^n with respect to x is (x^(n+1))/(n+1) + C, where C is the constant of integration. Using this rule, we can integrate each term of the polynomial separately: ∫(x^2 + 3x - 5) dx = ∫x^2 dx + ∫3x dx - ∫5 dx = (x^3/3) + (3x^2/2) - (5x) + C Therefore, the antiderivative or indefinite integral of x^2 + 3x - 5 with respect to x is: (x^3/3) + (3x^2/2) - (5x) + C, where C is the constant of integration.

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2x + x = 180°, => 3x = 180°, and thus x = 60°
Each exterior angle = 60° but size of ext. angle = 360°/n
Therefore 60° = 360°/n
n = 360°/60° = 6 sides

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From the diagram

sin 70o = $\frac{x}{10}$

x = 10sin 70o

= 9.3969

Hence, length of chord MN = 2x

= 2 x 9.3969

= 18.7938

= 19cm (nearest cm)

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To solve this problem, we substitute x = 2 into the given expression: x + x(x*x) = 2 + 2(2*2) = 2 + 2(4) = 2 + 8 = 10. Therefore, the value of x + x(x*x) when x = 2 is 10. Here's a step-by-step breakdown of how we got this answer: 1. We start by substituting the value of x into the expression, which gives us: x + x(x*x) = 2 + 2(2*2) 2. We simplify the expression inside the parentheses first, which gives us: x + x(4) 3. Then we multiply x by 4, which gives us: x + 4x 4. We combine the two terms to get: 5x 5. Finally, we substitute x = 2 into this expression, which gives us: 5(2) = 10 Therefore, the value of x + x(x*x) when x = 2 is 10.

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2, 1, $\frac{1}{2}$, $\frac{1}{4}$.....
There are 4 terms in the series
Therefore the next number will be the 5th term
Tn = ar${}^{n-1}$ (formular for geometric series)
a = first term = 2
r = common rate = $\frac{\text{next term}}{\text{previous term}}$ = $\frac{1}{2}$
n = number of terms
T5 = 5th term = ?
T5 = ar${}^{5-1}$
= ar${}^4$
= 2 × (ar${}^{n-1}$)4
= 2 × $\frac{1}{16}$
= $\frac{1}{8}$

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MN || PQ || RS
MN = PQ = RS (parallel lines)
Label the angle in the lines
a = i (corresponding angles are equal)
b = x (corresponding angles are equal)
If |MN| = |RS|
If a = i
and a = 63 = i
a + b = 180 (Adjacent interior angles are supplementary i.e add to 180)
∴ i + x = 180
63 + x = 180
x = 180 - 63
x = 1170

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Let's simplify each term first: - √27 can be simplified as √(3^3), which equals 3√3. - √12 can be simplified as √(2^2 × 3), which equals 2√3. - √75 can be simplified as √(3 × 5^2), which equals 5√3. Substituting these simplifications into the original expression, we get: 427(3√3) + 512(2√3) - 375(5√3) Simplifying the coefficients of √3, we get: 1281√3 + 1024√3 - 1875√3 Combining like terms, we get: 330√3 Therefore, the simplified expression is 330√3. Answer:  73" tabindex="0" class="mjx-chtml MathJax_CHTML" id="MathJax-Element-38-Frame">√3  divided by 3.

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Sum of angle at a point = 360o
2x + 3x + 4x = 360
9x = 360
x = $\frac{360}{9}$
x = 40o

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To find the size of angle x, we can start by using the fact that the sum of the opposite angles in an inscribed quadrilateral is 180 degrees. In this case, angle RST is opposite to angle O, and angle OST is opposite to angle x. We are given that angle RST is 60 degrees, so we can use this to find angle O: angle RST + angle RTO + angle STO + angle OST = 360 degrees 60 + angle RTO + angle STO + angle OST = 360 angle RTO + angle STO + angle OST = 300 Since angle RTO and angle STO are both equal to angle O (because they are both subtended by the same arc), we can write: 3 x angle O = 300 angle O = 100 degrees Now that we know angle O, we can find angle x: angle OST = 180 - angle RST - angle O angle OST = 180 - 60 - 100 angle OST = 20 degrees Therefore, the size of angle x is 20 degrees, which corresponds to option D.

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The operation * on the set R of real numbers is defined as x * y = 3x + 2y − 1. To find 3 * −1, we need to substitute x = 3 and y = −1 into the equation and simplify. So, we have: 3 * −1 = 3 * 3 + 2 * −1 − 1 = 9 + −2 − 1 = 6 So, the answer is 6.

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MACICITA is an eight letter word = 8!
Since we have repeating letters, we have to divide to remove duplicates accordingly. There are 2A, 2C, 2I
∴ $\frac{8!}{2!2!2!}$

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The curved surface area of a cylinder is given by the formula 2πrh, where r is the radius of the base and h is the height of the cylinder. We are given that the cylinder is 5 cm high and its curved surface area is 110 cm². Therefore, 2πrh = 110 Substituting the value of π as 22/7, we get: 2 x 22/7 x r x 5 = 110 Multiplying both sides by 7/22 and simplifying, we get: r = 3.5 Therefore, the radius of the base of the cylinder is 3.5 cm. Hence, the correct answer is option (B) 3.5cm.

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Total angle at a point = 3600
∴ To get the angle occupied by fertilizer we have,
40 + 50 + 80 + 70 + 30 + fertilizer(x) = 360
270 + x = 360
x = 360 - 270
x = 90
Total amount allocated to the farm
= ₦ 80,000
∴Amount allocated to the fertilizer
= $\frac{\text{fertilizer (angle) × Total amount}}{\text{total angle}}$
= $\frac{90}{360}$ × 80,000
= ₦20,000

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$\frac{2\sqrt{3}-\sqrt{2}}{\sqrt{3}+2\sqrt{2}}$= m + n√6
$\frac{2\sqrt{3}-\sqrt{2}}{\sqrt{3}+2\sqrt{2}}$ x $\frac{\sqrt{3}-2\sqrt{2}}{\sqrt{3}-\sqrt{2}}$

$\frac{2\sqrt{3}(\sqrt{3}-2\sqrt{2})-\sqrt{2}(\sqrt{3}-2\sqrt{2})}{\sqrt{3}(\sqrt{3}-2\sqrt{2})+2\sqrt{2}(\sqrt{3}-2\sqrt{2})}$
$\frac{2\times 3-4\sqrt{6}-6+2\times 2}{3-2\sqrt{6}+2\sqrt{6}-4\times 2}$
= $\frac{6-4\sqrt{6}-\sqrt{6}+4}{3-8}$
= $\frac{0-4\sqrt{6}-6}{5}$
= $\frac{10-5\sqrt{6}}{5}$
= − 2 + √6
∴ m + n$\sqrt{6}$ = − 2 + √6
m = − 2, n = 1

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y = xsinx
$\frac{dy}{dx}$ = $1\sin x+x\cos x$
= $\sin x+x\cos x$
At x = $\frac{\pi }{2}$
= sin$\frac{\pi }{r}$ + $\frac{\pi }{2}\cos \frac{\pi }{2}$
= 1 + $\frac{\pi }{2}$ × 10
= 1

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The locus of a point P(x,y) such that PV = PW where V = (1,1) and W = (3,5). This means that the point P moves so that its distance from V and W are equidistance.
PV = PW
$\sqrt{(x-1{)}^2+(y-1{)}^2}=\sqrt{(x-3{)}^2+(y-5{)}^2}$.
Squaring both sides of the equation,
(x-1)2 + (y-1)2 = (x-3)2 + (y-5)2.
x2-2x+1+y2-2y+1 = x2-6x+9+y2-10y+25
Collecting like terms and solving, x + 2y = 8.

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The temperature (t) and heat (h) are directly proportional, which means that as the temperature increases, so does the heat. This can be written as an equation: h = kt, where k is a constant of proportionality. Given that when t = 20°C, h = 50 J, we can find the value of k by using the equation: 50 = k * 20. Solving for k gives us k = 2.5. Now that we know the value of k, we can use the equation h = kt to find the temperature when h = 60 J: 60 = 2.5 * t Solving for t gives us t = 24°C, so the answer is 24°C.

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M = $\frac{\sqrt{SL}}{T}$,
make T subject of formula square both sides
M2 = $\frac{N^{2}SL}{T}$
TM2 = N2SL
T = $\frac{N^{2}SL}{M^2}$

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To find the intersection of T and N, we need to find the numbers that are common to both sets. T is the set of even numbers from 1 to 12, so T = {2, 4, 6, 8, 10, 12}. N is the set of common factors of 6, 8, and 12. To find the common factors, we can list the factors of each number and look for the factors that they have in common: Factors of 6: 1, 2, 3, 6 Factors of 8: 1, 2, 4, 8 Factors of 12: 1, 2, 3, 4, 6, 12 The common factors of 6, 8, and 12 are 1, 2, and 3. Therefore, the intersection of T and N, written as T ∩ N, is the set of numbers that are in both T and N. In this case, the only even number that is also a common factor of 6, 8, and 12 is 2. So, T ∩ N = {2}. Therefore, {2} is the correct answer.

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To find the product of (2x^2 - x + 1) and (3 - 2x), we need to multiply every term in the first expression with every term in the second expression, and then simplify the result. We can use the distributive property of multiplication to do this. First, we multiply 2x^2 by 3 and by -2x: 2x^2 * 3 = 6x^2 2x^2 * -2x = -4x^3 Then, we multiply -x by 3 and by -2x: -x * 3 = -3x -x * -2x = 2x^2 Finally, we multiply 1 by 3 and by -2x: 1 * 3 = 3 1 * -2x = -2x Now we can add up all these products: 6x^2 - 4x^3 - 3x + 2x^2 + 3 - 2x Simplifying this expression, we get: -4x^3 + 8x^2 - 5x + 3 Therefore, the answer is option B: -4x^3 + 8x^2 - 5x + 3.

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We can use the formula for the volume of a cylinder to solve this problem. The formula is: Volume = πr^2h where π is the value of pi, r is the radius of the base, h is the height (or depth) of the cylinder. We are given that the diameter of the base of the cylinder is 14 m, which means the radius is 7 m (since radius is half the diameter). We are also given that the volume of the cylinder is 3080 m^3. Substituting these values into the formula, we get: 3080 = (22/7) * 7^2 * h Simplifying this expression, we get: 3080 = 22 * 7 * h 3080 = 154h h = 3080/154 h = 20 Therefore, the depth of the cylinder is 20 m, which means the answer is option C: 20 m.

Answer Details

?

$1?(\frac{1}{5}\times \frac{2}{3})+(5+\frac{2}{3})1\; -\; \backslash left(\; \backslash frac\{1\}\{5\}\; \backslash times\; \backslash frac\{2\}\{3\}\; \backslash right)\; +\; \backslash left(\; 5\; +\; \backslash frac\{2\}\{3\}\; \backslash right)$

Step 1: Evaluate $\frac{1}{5}\times \frac{2}{3}\backslash frac\{1\}\{5\}\; \backslash times\; \backslash frac\{2\}\{3\}$

$\frac{1}{5}\times \frac{2}{3}=\frac{1\times 2}{5\times 3}=\frac{2}{15}\backslash frac\{1\}\{5\}\; \backslash times\; \backslash frac\{2\}\{3\}\; =\; \backslash frac\{1\; \backslash times\; 2\}\{5\; \backslash times\; 3\}\; =\; \backslash frac\{2\}\{15\}$

51?×32?=5×31×2?=152?

Step 2: Subtract $\frac{2}{15}\backslash frac\{2\}\{15\}$ from 1

$1?\frac{2}{15}=\frac{15}{15}?\frac{2}{15}=\frac{13}{15}1\; -\; \backslash frac\{2\}\{15\}\; =\; \backslash frac\{15\}\{15\}\; -\; \backslash frac\{2\}\{15\}\; =\; \backslash frac\{13\}\{15\}$

1?152?=1515??152?=1513?

Step 3: Simplify $5+\frac{2}{3}5\; +\; \backslash frac\{2\}\{3\}$

First, convert $55$ to a fraction with a denominator of 3:

$5=\frac{15}{3}5\; =\; \backslash frac\{15\}\{3\}$

So,

$5+\frac{2}{3}=\frac{15}{3}+\frac{2}{3}=\frac{17}{3}5\; +\; \backslash frac\{2\}\{3\}\; =\; \backslash frac\{15\}\{3\}\; +\; \backslash frac\{2\}\{3\}\; =\; \backslash frac\{17\}\{3\}$

Step 4: Combine the results

$\frac{13}{15}+\frac{17}{3}\backslash frac\{13\}\{15\}\; +\; \backslash frac\{17\}\{3\}$

To combine these fractions, find a common denominator. The least common multiple of 15 and 3 is 15:

Convert $\frac{17}{3}\backslash frac\{17\}\{3\}$ to a fraction with a denominator of 15:

$\frac{17}{3}=\frac{17\times 5}{3\times 5}=\frac{85}{15}\backslash frac\{17\}\{3\}\; =\; \backslash frac\{17\; \backslash times\; 5\}\{3\; \backslash times\; 5\}\; =\; \backslash frac\{85\}\{15\}$

Now add the fractions:

$\frac{13}{15}+\frac{85}{15}=\frac{13+85}{15}=\frac{98}{15}\backslash frac\{13\}\{15\}\; +\; \backslash frac\{85\}\{15\}\; =\; \backslash frac\{13\; +\; 85\}\{15\}\; =\; \backslash frac\{98\}\{15\}$

Simplify the fraction if possible:

$\frac{98}{15}=6\frac{8}{15}\backslash frac\{98\}\{15\}\; =\; 6\; \backslash frac\{8\}\{15\}$

Thus, the evaluated expression is:

$\boxed{{\displaystyle 6\frac{8}{15}}}\backslash boxed\{6\; \backslash frac\{8\}\{15\}\}$

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Percentage error is a measure of how accurately a measurement represents the true value of a quantity. It is calculated as the difference between the measured value and the true value, divided by the true value, and multiplied by 100 to get a percentage. In this case, the true value of the rod's length is 10 cm and the measured value is 10.5 cm. To calculate the percentage error, we use the formula: Percentage error = (|measured value - true value| / true value) * 100 = (|10.5 - 10| / 10) * 100 = (0.5 / 10) * 100 = 5% Therefore, the percentage error is 5%.

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When two quantities, such as x and y, are inversely proportional, it means that as one quantity increases, the other quantity decreases at a consistent rate. In mathematical terms, we can write the inverse proportionality as: y = k/x where k is a constant of variation that relates the two quantities. To find the constant of variation, we can use the given information that "y and 6 when x = 7". Substituting these values into the equation, we get: 6 = k/7 Multiplying both sides by 7, we obtain: k = 42 Therefore, the constant of variation is 42, and the answer is.

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Total cost = N(250,000 + 70,000) = ₦320,000
Selling price = ₦400,000 (given)
Gain = SP - CP = N(400,000 - 320,000) = ₦80,000
Gain % = gain/CP x 100 = (80,000/320,000) x 100
Gain % = 25%

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Dividing polynomials is a process similar to dividing numbers. To divide 4x^3 - 3x + 1 by 2x - 1, we need to find a polynomial that when multiplied by 2x - 1 gives us 4x^3 - 3x + 1. The polynomial that fits the bill is 2x^2 + x - 1. This can be verified by multiplying 2x^2 + x - 1 by 2x - 1, which gives us 4x^3 - 3x + 1. Therefore, the answer is 2x^2 + x - 1.

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The sum of the range of a set of numbers is simply the difference between the largest and smallest number in the set. To find the mode, we need to look for the number that appears most frequently in the set. In this set of numbers, the smallest number is 4 and the largest number is 10, so the range would be 10 - 4 = 6. The mode of this set is the number 10, since it appears the most times (7 times). So, the sum of the range and the mode of the set is 6 + 10 = 16.

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To solve the problem, we need to use the fact that the two graphs intersect at x = 2, which means that they have the same y-coordinate at that point. Let's first find the y-coordinate of the point of intersection by plugging x = 2 into both equations: y = p(2)^2 + q = 4p + q y = 2(2)^2 - 1 = 7 Since the two graphs intersect at x = 2, we know that their y-coordinates are equal at that point. Therefore, we can set the two expressions for y equal to each other: 4p + q = 7 Now we can solve for p in terms of q by isolating p on one side of the equation: 4p = 7 - q p = (7 - q) / 4 So the value of p in terms of q is (7 - q) / 4.

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m * n = $\frac{m}{n}$ - $\frac{m}{n}$
m = − 3
n = 4
∴ − 3 × 4 = $\frac{-3}{4}$ - $\frac{-4}{-3}$
= $\frac{3(-3)-(-4\times 4)}{12}$
= $\frac{-9+16}{12}$
= $\frac{7}{12}$

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hypotenuse
sin = $\frac{1}{2}$
$\sin 45=\frac{1}{\sqrt{2}}$
= $\frac{2}{2}$
∴ (sin45 + sin30)
= $\frac{1}{\sqrt{2}}+\frac{1}{2}$
= $\frac{\sqrt{2}}{2}$ + $\frac{1}{2}$
= $\frac{\sqrt{2}+1}{2}$
= $\frac{1+\sqrt{2}}{2}$

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To evaluate the given expression step-by-step, let's break it down:

$1-(\frac{1}{5}\times \frac{2}{3})+{\left(\frac{5+\frac{2}{3}}{4}\right)}^{3}1\; -\; \backslash left(\; \backslash frac\{1\}\{5\}\; \backslash times\; \backslash frac\{2\}\{3\}\; \backslash right)\; +\; \backslash left(\; \backslash frac\{5\; +\; \backslash frac\{2\}\{3\}\}\{4\}\; \backslash right)^3$

Step 1: Evaluate $\frac{1}{5}\times \frac{2}{3}\backslash frac\{1\}\{5\}\; \backslash times\; \backslash frac\{2\}\{3\}$

$\frac{1}{5}\times \frac{2}{3}=\frac{1\times 2}{5\times 3}=\frac{2}{15}\backslash frac\{1\}\{5\}\; \backslash times\; \backslash frac\{2\}\{3\}\; =\; \backslash frac\{1\; \backslash times\; 2\}\{5\; \backslash times\; 3\}\; =\; \backslash frac\{2\}\{15\}$

51​×32​=5×31×2​=152​

Step 2: Subtract $\frac{\mathrm{<span\; style="font-family:\; Ubuntu;\; font-size:\; 16px;">2</span>}}{\mathrm{<span\; style="font-family:\; Ubuntu;\; font-size:\; 16px;">15</span>}}$\frac{2}{15} from 1

$1-\frac{2}{15}=\frac{15}{15}-\frac{2}{15}=\frac{13}{15}1\; -\; \backslash frac\{2\}\{15\}\; =\; \backslash frac\{15\}\{15\}\; -\; \backslash frac\{2\}\{15\}\; =\; \backslash frac\{13\}\{15\}$

Step 3: Simplify

$\frac{5+\frac{2}{3}}{4}\backslash frac\{5\; +\; \backslash frac\{2\}\{3\}\}\{4\}$

First, convert $55$ to a fraction with a denominator of 3:

$5=\frac{15}{3}5\; =\; \backslash frac\{15\}\{3\}$

So,

$5+\frac{2}{3}=\frac{15}{3}+\frac{2}{3}=\frac{17}{3}5\; +\; \backslash frac\{2\}\{3\}\; =\; \backslash frac\{15\}\{3\}\; +\; \backslash frac\{2\}\{3\}\; =\; \backslash frac\{17\}\{3\}$

Then divide by 4:

$\frac{17}{3}÷4=\frac{17}{3}\times \frac{1}{4}=\frac{17}{12}\backslash frac\{17\}\{3\}\; \backslash div\; 4\; =\; \backslash frac\{17\}\{3\}\; \backslash times\; \backslash frac\{1\}\{4\}\; =\; \backslash frac\{17\}\{12\}$

Step 4: Cube $\frac{\mathrm{<span\; style="font-size:\; 16px;">17</span>}}{\mathrm{<span\; style="font-size:\; 16px;">12</span>}}$\frac{17}{12}

${\left(\frac{17}{12}\right)}^3=\frac{17^3}{12^3}=\frac{4913}{1728}\backslash left(\; \backslash frac\{17\}\{12\}\; \backslash right)^3\; =\; \backslash frac\{17^3\}\{12^3\}\; =\; \backslash frac\{4913\}\{1728\}$

Step 5: Combine the results

$\frac{13}{15}+\frac{4913}{1728}\backslash frac\{13\}\{15\}\; +\; \backslash frac\{4913\}\{1728\}$

To combine these fractions, find a common denominator. The least common multiple of 15 and 1728 is 1728 (since 15 is a factor of 1728):

Convert $\frac{13}{15}\backslash frac\{13\}\{15\}$ to a fraction with a denominator of 1728:

$\frac{13}{15}=\frac{13\times 115.2}{15\times 115.2}=\frac{1497.6}{1728}\backslash frac\{13\}\{15\}\; =\; \backslash frac\{13\; \backslash times\; 115.2\}\{15\; \backslash times\; 115.2\}\; =\; \backslash frac\{1497.6\}\{1728\}$

Now add the fractions:

$\frac{1497.6}{1728}+\frac{4913}{1728}=\frac{1497.6+4913}{1728}=\frac{6410.6}{1728}\backslash frac\{1497.6\}\{1728\}\; +\; \backslash frac\{4913\}\{1728\}\; =\; \backslash frac\{1497.6\; +\; 4913\}\{1728\}\; =\; \backslash frac\{6410.6\}\{1728\}$

Simplifying the fraction is a bit complex and since none of the provided options directly match our detailed calculation, it looks like we might need to revisit some steps or compare our answer directly to the provided options to see if any approximation matches closely.

Given the complexity, let's directly compare the options:

Considering the given options, the closest approximate value

we calculated is around $\frac{6410.6}{1728}\backslash frac\{6410.6\}\{1728\}$ which seems close to $3.73.7$.

Hence, the closest match would be: 

$\boxed{{\displaystyle 3\frac{2}{3}}}\backslash boxed\{3\; \backslash frac\{2\}\{3\}\}$

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Let's denote the man's speed on his first trip as "s". On his first trip, he covered a distance of 50 miles, so his time would be: time = distance / speed = 50 / s On his later trip, he traveled 300 miles while going 3 times as fast, so his new speed would be: new speed = 3s His time for the later trip would then be: time = distance / speed = 300 / (3s) = 100 / s So the ratio of his new time to his old time would be: new time / old time = (100/s) / (50/s) = 100/50 = 2 Therefore, his new time compared to his old time is twice as much. In simpler terms, the man covered a longer distance on his second trip but also traveled faster. Even though he traveled faster on the second trip, the increased distance resulted in his new time being twice as much as his old time.

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Sum to infinity
? = arn ? 1
= $\frac{a}{1}$ ? r
a = $\frac{1}{4}$
r = $\frac{1}{8}$ ÷ $\frac{1}{4}$
r = $\frac{1}{s}$ × $\frac{4}{1}$
= $\frac{1}{2}$
S = $\frac{1÷4}{1}$ ? $\frac{1}{2}$
= $\frac{1}{4}$ ÷ $\frac{1}{2}$
= $\frac{1}{4}$ × $\frac{2}{1}$
= $\frac{1}{2}$

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To find the probability that an integer randomly picked from U is not in E2, we need to find the number of integers in U that are not in E2 and divide it by the total number of integers in U. First, let's find the number of integers in U that are not in E2. We can do this by finding the complement of E2 in U, which is the set of integers in U that are not in E2. Since E2 is the set of multiples of 4 in U, we can write the complement of E2 as the set of integers in U that are not multiples of 4. We can express this set using set-builder notation as follows: U \ E2 = {x : x is an integer and x is not a multiple of 4} To find the number of integers in this set, we can count the number of integers in U that are multiples of 4 and subtract it from the total number of integers in U. The largest integer in U that is a multiple of 4 is 99996, which we can find by dividing 100000 by 4 and taking the floor. Therefore, the number of integers in U that are multiples of 4 is: floor(100000/4) = 25000 Since U contains all integers from 1 to 100000, the total number of integers in U is: 100000 - 1 + 1 = 100000 Therefore, the number of integers in U that are not in E2 is: 100000 - 25000 = 75000 To find the probability that an integer randomly picked from U is not in E2, we divide the number of integers in U that are not in E2 by the total number of integers in U: 75000/100000 = 0.75 So the probability that an integer randomly picked from U is not in E2 is 0.75 or 75%. Answer: The correct option is not provided in the question.

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Principal, P = Amount, A - Interest, I.
A = P + I
I = (P.T.R)/100 = (P x 5 x 2)/100 = 10P/100 = P/10
But A = P + I,
=> 5500 = P + (P/10)
=> 55000 = 10P + P
=> 55000 = 11P
Thus P = 55000/11 = ₦5,000

Answer Details

3${}^{n+1}$ × 27$\frac{n+1}{{81}^n}$
= 3${}^{n+1}$ × 3 $\frac{3^{(n+1)}}{3^{4n}}$
= 3${}^{n+1+3n+3-4n}$
= 3${}^{4n-4n-1+3}$
= 32
= 9