find the value of (3^0+4^-1)×2^2 ​

Subsets with bit strings:

To find the subsets with bit strings:

We need to express a) b) and c) into bit strings.

Firstly, a number of elements in the universal set represent the number of bits in the bit string.

Secondly, 1 = yes element is present in both universal sets as well as in subset.

0 = No, the element is not present in the subset but present in the universal set.

Hence, we have:

a) Subset {3,4,5} = 0011100000  (As there are 3 1's which means only 3,4,5 are present in both universal set and subset.

Similarly,

b) Subset {1, 3, 6, 10} = 1010010001

c) Subset {2, 3, 4, 7, 8, 9} = 0111001110

Therefore, Subsets with bit strings:

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Complete question:

Suppose that the universal set is U={1,2,3,4,5,6,7,8,9,10}. Express each of the following subsets with bit strings (of length 10) where the ith bit (from left to right) is 1 if i is in the subset and zero otherwise.

a) {3, 4, 5}

b) {1, 3, 6, 10}

c) {2, 3, 4, 7, 8, 9}.

Answer:CB,CH,AE,AB

Step-by-step explanation:

Answer:

200

Step-by-step explanation:

Let's call the number x :
12.5% of x = 25

Changing 12.5% into decimal would be 0.125

Now we have the equation :

0.125x = 25

Divide both sides by 0.125 to make x the subject :

x = 25 ÷ 0.125

x = 200

To check we can substitute this value into the question :

12.5% of 200 = 25

Hope this helped and have a good day

The angle A of the triangle ABC has a measure of approximately 34°. (Right choice: D)

To determine the missing angle of a triangle by the law of the cosine, we must know the lengths of the three sides of the figure. Please notice that angle A is opposite to the side a in accordance with the law of the cosine. Then:

[tex]\cos \theta = \frac{(10\,cm)^{2}-(17\,cm)^{2}-(11\,cm)^{2}}{-2\cdot (17\,cm)\cdot (11\,cm)}[/tex]

θ ≈ 34.016°

The angle A of the triangle ABC has a measure of approximately 34°. (Right choice: D)

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Based on the table showing the percentage of households playing games over the net, the average rate of change from 1999 to 2003 is 3.9% per year.

This can be found as:

= (27.9 - 12.3) / 4 years

= 3.9% per year

In 2000, the instantaneous rate of change would be:

= (Rate in 2001 - Rate in 1999) / difference in years

= (24.4 - 12.3) / (2001 - 1999)

= 6.05%

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The volume of the oblique cylinder is 6867.18 cubic units

The given parameters are:

Height = 27

Radius = 9

The volume is calculated as:

[tex]V = \pi r^2 h[/tex]

So, we have:

[tex]V = 3.14 * 9^2 * 27[/tex]

Evaluate

V = 6867.18

Hence, the volume of the oblique cylinder is 6867.18 cubic units

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E and F are two events and that P(E)=0.3 and P(F|E)=0.5. Thus, P(E and F)=0.15

Bayes' theorem is transforming preceding probabilities into succeeding probabilities. It is based on the principle of conditional probability. Conditional probability is the possibility that an event will occur because it is dependent on another event.

P(F|E)=P(E and F)÷P(E)

It is given that P(E)=0.3,P(F|E)=0.5

Using Bayes' formula,

P(F|E)=P(E and F)÷P(E)

Rearranging the formula,

⇒P(E and F)=P(F|E)×P(E)

Substituting the given values in the formula, we get

⇒P(E and F)=0.5×0.3

⇒P(E and F)=0.15

∴The correct answer is 0.15.

If, E and F are two events and that P(E)=0.3 and P(F|E)=0.5. Thus, P(E and F)=0.15.

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Answer:

77 m (nearest metre)

Step-by-step explanation:

Angle of Elevation

If a person stands at a point and looks up at an object, the angle between their horizontal line of sight and the object is called the angle of elevation.

To find how tall the flagpole is, model as a right triangle and solve using the tan trigonometric ratio.

Tan trigonometric ratio

  [tex]\sf \\tan(\theta)=\dfrac{O}{A}[/tex]

where:

Given information:

Therefore:

As the person is 1.6 m tall, we model the line of sight as 1.6 m above ground level.  Therefore, when calculating the height of the flagpole, we will need to add the height of the person to the value found using the trig ratio.

Substitute the given values into the formula and solve for O:

[tex]\implies \sf \tan(65^{\circ})=\dfrac{O}{35}[/tex]

[tex]\implies \sf O=35\tan(65^{\circ})[/tex]

Therefore the height of the flagpole is:

[tex]\implies \sf 35\tan(65^{\circ})+1.6=76.65774222...[/tex]

[tex]\implies \sf Height\:of\:flagpole=77\:m\:(nearest\:metre)[/tex]

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The rational function that matches with the graph of the picture is f(x) = (2 · x + 7.2)/(x + 3).

Herein we have the graph of a rational function of the form f(x) = p(x)/q(x) . The domain of these kind of functions is all real numbers except those values of x such that q(x) = 0. Graphically speaking, there is a vertical asymptote when a discontinuity exists and an horizontal asymptote for x → ± ∞.

In accordance with the picture, there are one horizontal asymptote and one vertical asymptote. As the horizontal asymptote of the function is distinct of 0, then the grade of p(x) is the same grade of q(x). Therefore, we have a rational function of the form:

f(x) = (2 · x + k)/(x + 3)     (1)

If we know that x = 0 and y = 2.4, then the value of k is:

2.4 = (2 · 0 + k)/(0 + 3)

2.4 = k/3

k = 7.2

Therefore, the rational function that matches with the graph of the picture is f(x) = (2 · x + 7.2)/(x + 3).

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The solution of the inequality -2(3x + 2) - 6x ≥ -4 is undefined

-2(3x + 2) - 6x ≥ -4

-6x - 4 - 6x ≥ -4

-12x ≥ - 4 + 4

-12x ≥ 0

x ≥ 0 / -12

x is undefined

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The proportion cranberry juice should be mixed with 84 ounces of apple juice 1:5 that is 1 parts of cranberry juice and 5 parts of lemon juice.

According to the question,

A punch recipe calls for mixing 2 parts of cranberry juice with 5 parts of apple juice.

84/2 = 42

5*42=210

Hence, the proportion cranberry juice should be mixed with 84 ounces of apple juice 1:5 that is 1 part of cranberry juice and 5 parts of lemon juice.

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1 ) 6

2) 6

3) -2

4) 2

5) -2

6) 2

The equivalent value of the given expression is -21.4

Decimals are values that include decimal points. Given the expression below

-8.2 - 5−8.2

Collect like terms

-8.2 −8.2 - 5

Convert to fractions

-82/10- 82/10 -  5

-164/10 - 5

-16.4 - 5

Take the sum

-21.4

Hence the equivalent value of the given expression is -21.4

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The missing data item for the given set of data if the median is 14 is 18.

The Median is the "middle" of a sorted list of numbers.

Therefore, the missing data item for the given set of data if the median is 14 can be calculated as follows:

10 10, 11, 11, 12, 12, 14, 15, 16, 18, 19, 19,

Therefore, if you add 18 the middle number of the sorted numbers will be 14.

10 10, 11, 11, 12, 12, 14, 15, 16, 18, 18, 19, 19,

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I don't think this question is complete but here's ur answer

The value of f(3) is 8

The weight of A is 75kg.

Total weight of A + B + C = 84 x 3 = 252kg

Total weight of A + B + C + D = 80 x 4 =.320 kg

Weight of D = 320 - 252 = 68 kg

Given, E = D + 3 = (68 + 3) kg = 71 kg

Total weight of B + C + D + E = (79 x 4) = 316 kg

Weight of B + C = 316 kg - 71 kg - 68 kg = 177 kg

Weight of A only will be:

= 320 kg - 177 kg - 68 kg

= 75 kg

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Answer:

  3 1/2 quarts

Step-by-step explanation:

The fraction of the lemonade that is water can be determined from the ratio of water to lemon juice. That fraction of a gallon is the quantity of interest.

Of the 7+1 = 8 parts that make up the lemonade, 7 of those are water. That is, water is 7/8 of the lemonade.

Of the 4 quarts of lemonade, the quantity that is water will be ...

  (7/8)(4 quarts) = 7/2 quarts = 3 1/2 quarts . . . of water

160 ounces is the answer

16 ounces per pound

16x10=160

First put to find the weight in ounces, *multiply* the number of pounds by the unit rate, 16 ounces per pound. Then put 10 pounds = *160 ounces.*

An ounce is the designation of several different units of mass, weight, or volume, and is largely unchanged from the ancient Roman unit of measurement, uncia. Avoirdupois ounces are 1⁄16 Avoirdupois pounds. This is a US standard and an ounce of the British Empire.

oz [Ouns] n. A unit of weight in the US customary unit, an avoirdupois unit equal to 437.5 grains or 28.35 grams. A pharmacist's weight unit is equivalent to 480 grains or 31.10 grams.

oz, equivalent to 1/16 pound (437 1/2 grain) on the Avoirdupois system and 480 grains or 1/12 pound on the Troy and pharmacist system. Avoirdupois ounces are equivalent to 28.35 grams and pharmacist ounces are equivalent to 31.103 grams.

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Answer:

x = 2

Step-by-step explanation:

To solve the equation, you need to set both functions equal to each other and simplify to find the value of "x".

f(x) = 2x + 1

g(x) = -x + 7

f(x) = g(x)                                              <----- Given equation

2x + 1 = -x + 7                                      <----- Insert functions

3x + 1 = 7                                             <----- Add "x" to both sides

3x = 6                                                  <----- Subtract 1 from both sides

x = 2                                                    <----- Divide both sides by 3

Step-by-step explanation:

remember, the sum of all angles in a triangle is always 180°.

and the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

with a, b, c being the sides opposite of their associated angles (A, B, C).

1)

17/sin(26) = 12/sin(C)

sin(C) = 12×sin(26)/17 = 0.309438457...

C = 18.02539254...° ≈ 18°

3)

180 = 27 + 115 + C

C = 38°

19/sin(38) = AC/sin(27)

AC = 19×sin(27)/sin(38) = 14.01065332... in ≈ 14 in

In first triangle side angle m∠C is 18° and in first triangle side AC is 14 in. This can be obtained by using the law of sine.

We know the law of sine which is,

If in a triangle, Δ ABC,

[tex]\frac{sin A}{a} =\frac{sin B}{b}= \frac{sinC}{c}[/tex], where a is the side opposite to the angle m∠A, b is the side opposite to the angle m∠B and c is the side opposite to the angle m∠C.

sine of the angle scan be found using calculator.

From the question,

1) In first triangle side,

AB = 12ft, BC = 17 ft and m∠A=26°

⇒By using the law of sine,

[tex]\frac{sin A}{a} =\frac{sin B}{b}= \frac{sinC}{c}[/tex]

sin 26°/17 = sin B/AC = sin C/12

sin 26°/17 = sin C/12

12×sin 26° = 17×sin C

sin C = 5.26/17 = 0.3091

C = 18.023° ≈ 18°

3) In second triangle side,

m∠B = 27°, AB = 19 in and m∠A = 115°

m∠A + m∠B +m∠C = 180°

115° + 27° + m∠C = 180°

142° + m∠C = 180°

m∠C = 38°

⇒By using the law of sine,

[tex]\frac{sin A}{a} =\frac{sin B}{b}= \frac{sinC}{c}[/tex]

sin 115°/BC = sin 27°/AC = sin 38°/19

sin 27°/AC = sin 38°/19

sin 27° × 19 = sin 38° × AC

8.63 = 0.62 × AC

AC = 13.91 in ≈ 14 in.

Hence in first triangle side angle m∠C is 18° and in first triangle side AC is 14 in.

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Answer:

7 hot dogs

Step-by-step explanation:

Set up an equation:

2.5x + 1.25 = 21

2.5x = 19.75

x = 7.9

You cannot buy .9 of a hot dog, so the answer is 7

Dave is 18 years old.

A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation. Word illustration: The product of 8 and 3. Word illustration: The product of 8 and 3 is 11

Given

Let x be Dave’s age today. Then:

x=3(x+3)-3(x-3)

x=3x+9–3x+9

x=18

Dave is 18 years old.

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Answer:

[tex]x^2+8x+8+\frac{-9}{x+4}[/tex]

Step-by-step explanation:

it would be simpler to do synthetic division by removing the variables and using the coefficients:

i hope this helped!

Answer:

x = 157/60

Step-by-step explanation:

x + 2/3 - x + 1/5 = x - 3/4 - 1

x - x - x = -2/3 - 1/5 - 3/4 - 1

-60x/60 = -40/60 - 12/60 - 45/60 - 60/0

-60x = -40 - 12 - 45 - 60

-60x = -157

x = -157/-60

x = 157/60

157/60 + 2/3 - 157/60 + 1/5 = 157/60 - 3/4 - 1

2/3 + 1/5 = 157/60 - 3/4 - 1

40/60 + 12/60 = 157-60 - 45/60 - 60/60

40 + 12 = 157 - 45 - 60

52 = 157 - 105

It is the definition of  Midpoint

Disclaimer!!!

The question is incomplete and the correct question is shown below

What definition would justify the following statement?

If T is the midpoint of segment RS then, Segment RT is congruent to segment TS..

If t is the midpoint of segment rs then, segment rt is congruent to segment ts. is the definition of the midpoint

The line segment of a triangle connecting the midpoint of two sides of the triangle is said to be parallel to its third side and is also half the length of the third side, according to the midpoint theorem.

Hence It is the definition of the midpoint

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Answer: C:  Definition of Midpoint

Step-by-step explanation: Hope that helped!

Answer:

12  and 3

Step-by-step explanation:

Let  x= length

If you draw a rectangle.  two sides would be the length x.  The other two sides would be (x-9).

(length)(width) = Area

(x)(x-9) = 36

x^2 - 9x = 36 Substitute in x and x-9 for the length and width

x^2 - 9x - 36 =0  Subtract 36 from both sides

(x-12)(x+3) = 0   We are looking for 2 number that add to -9 and mult. to -36

x-12=0 and x+3=0  Set both factors to 0 and solve

x = 12 and x =-3.  It does not make sense that a length could be -3 so we reject that answer.  If the length is 12, then the width is 3

Based on the height of the ball suspended from a spring, the height of the ball at equilibrium is K feet.

The model for the height of the ball when it is suspended from a spring is shown as:

= aSin(b ( t - h)) + k

Given this, we can infer the value of h by looking at the general form of the Sin function which is:

y = Asin(Bx) + c

In the above:

A = amplitude

B = (2 x pi) / Period

C = midline

Comparing the function and the general Sin function, we notice that:

C = K

If C = K then it means that K is the height of the ball at its equilibrium because C as the midline represents the equilibrium height.

In conclusion, the height of the ball at equilibrium is K feet.

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