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A painter is placing a ladder to reach the third story window, which is 39 feet above the ground and
makes an angle with the ground of 80°.
How far out from the building does the base of the ladder need to be positioned? Round your answer to
the nearest tenth.
The base of the ladder needs to be positioned
feet out from the building.

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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The length of the belt around the two pulleys is approximately 49.2 centimeters.

In this question we must determine the perimeter of a belt around two pulleys, whose centers are 10 centimeters apart. This perimeter is the sum of part of the circumference of small pulley, part of the circumference of the big pulley and two times the segment tangent to the two pulleys.

Now we proceed to determine the parts of the perimeter of the belt:

Big pulley

s' = (214.92° / 180°) · π · (6 cm)

s' ≈ 22.506 cm

Small pulley

s'' = (145.08° / 180°) · π · (3 cm)

s'' ≈ 7.596 cm

Tangent segments

l = (10 cm) · sin 72.54°

l ≈ 9.539 cm

Lastly, the perimeter of the belt is:

L = s' + s'' + 2 · l      (1)

L = 22.506 cm + 7.596 cm + 2 · (9.539 cm)

L = 49.180 cm

The length of the belt around the two pulleys is approximately 49.2 centimeters.

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Answer:

F+V=E+2

F=6

V=8

E=?

PUT THEIR VALUE

6+8=E+2

= 14=E+2

=14-2=E

=12=E

VALUE OF E IS 12

The value of f(3) is 8

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!

The point which is the center of the ellipse whose equation is; (y+5)²/121+(x-9)²/49=1 s in the task content is; (-5, 9).

It follows from convention that the equation of an ellipse usually takes the form;

(y-h)²/a²+(x-k)²/b²=1 in which case, the center of the ellipse is given by the point; (h, k).

On this note, By comparison of the actual equation and the standard equation, it follows that;

+5 = -h and consequently, h = -5,

-9 = -k and consequently, k = 9.

Ultimately, the point which is the center of the

ellipse is; (-5, 9).

Remark: The equation of the ellipse which is missing in the task content is; (y+5)²/121+(x-9)²/49=1

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Answer: D. (9, −5)

Not (-5, 9)

Step-by-step explanation:

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

Probability that a freshman selected at random who took the course and did not get lost and Probability of freshmen who took course at MSU in outdoor survival skills is 0.8333

According to the question,

Probability of freshmen who took course at MSU in outdoor survival skills is 0.6.

Probability that a freshmen selected at random who did not get lost during a hike is 0.9.

Probability that a freshman selected at random who took the course and did not get lost is 0.50

Conditional probability = P(A and B)/ P(A)

P(did not get lost/took the course) = P( freshmen did not get lost who took the course and freshmen took the course)/P(freshmen did not get lost)

= 0.5/0.6

= 0.8333

Hence, Probability that a freshman selected at random who took the course and did not get lost and Probability of freshmen who took course at MSU in outdoor survival skills is 0.8333

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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

The true statement about the plane include:

It should be noted that a vertical plane simply passes through a vertical line.

In this case, Point H is not on plane R and the e line containing points F and G is on plane R.

The correct options are 1,2,4, and 5.

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Answer:

a,b,d,e

Step-by-step explanation:

Its related to the mixing in the Analysis.

Quantitative data:

They are used when a researcher is trying to quantify a problem, or address the "what" or "how many" aspects of a research question. It is data that can either be counted or compared on a numeric scale.

Qualitative data :

It describes qualities or characteristics. It is collected using questionnaires, interviews, or observation, and frequently appears in narrative form. For example, it could be notes taken during a focus group on the quality of the food at Cafe Mac, or responses from an open-ended questionnaire.

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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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1 ) 6

2) 6

3) -2

4) 2

5) -2

6) 2

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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The error made while find the mean absolute deviation was: C. When calculating the distances to the mean, the student forgot to take the absolute values.

The mean absolute deviation is simply the average of the sum of the "absolute difference" of the mean and each data point.

In the calculation of the student, after getting the difference of the mean and each data point, the student failed to take the absolute value, and still kept the minus sign included.

Therefore, the error was: C. When calculating the distances to the mean, the student forgot to take the absolute values.

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In circuit training, exercises are usually set up so that the same muscle group is worked in back to back exercises is a "false" statement.

A circuit workout consists of six or more exercises that are alternated with brief rest intervals and performed for either a predetermined number of reps or a certain duration of time.

Some features of circuit training exercise are-

Benefits of doing circuit training exercise-

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The complete question is -

In circuit training, exercises are usually set up so that the same muscle group is worked in back to back exercises.(True/False)

The ways that can be used to solve a quadratic equation include:

Factorization

Using the quadratic formula.

Completing the squares.

It should be noted that a quadratic equation simply means an algebraic equation of the second degree in x.

Here, the factorization, using the quadratic formula, and completing the squares method can be used.

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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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Answer:

They are similar.  Triangle abc is similar to triangle edc.

Step-by-step explanation:

To prove that triangles are similar, you must show that the 3 angles in one triangle are equal to the 3 angles in the other triangle.  We know that they both have a 50 degree angle.  We can also see that they both have a right angle.  That means that the 3rd angle must also equal 40 (180-90-50).  So by AAA the two triangles are congruent.

Triangle ABC is similar to triangle EDC.

Answer:

triangle ABC is similar to triangle DCE

Step-by-step explanation:

Reason being that angles in triangle ABC Correspond to That of triangle DCE Eg triangle ABC=CDE

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}.

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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Answer: If the product of any two numbers in the list is equal to 0, you can't conclude that the list is composed only by zeroes. In fact, suppose that you have a list of N numbers which are all zeroes except one. Whenever you multiply two elements of this list, you either multiplies two zeroes, or you multiply the non-zero element by a zero element, and so the result is zero, but the list is not composed by zeroes only.

Step-by-step explanation:

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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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!

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:

  1,123,449,768

Step-by-step explanation:

The smallest number composed from 8 different digits that is divisible by each of those digits appears to be the 10-digit number ...

  1,123,449,768

If the number is to be divisible by an even digit, it must be even. That means it cannot end in the digit 5, so 5 cannot be one of the digits. We disallow division by 0, so 0 cannot be one of the digits.

The remaining 8 digits total 40, so cannot form a number divisible by 3, 6, or 9. In order to make such a number, we must add 5 to the digit total, but cannot do so using the single digit 5.

Choices for added digits include {1, 4} and {2, 3}. Adding 9+5 = 14 to the digit total would also work but would guarantee the resulting number is not the minimum possible.

The digits we have to work with are now {1, 1, 2, 3, 4, 4, 6, 7, 8. 9}. We know that an even number constructed from these digits will be divisible by 1, 2, 3, 6, and 9. To make it divisible by 4, 7, and 8, it must be a multiple of the LCM of those numbers.

The least possible number will use the smallest digits first, so will start ...

  112344...

The remaining digits, 6, 7, 8, 9, need to form a number that will be divisible by 56 when appended to the 6 digits already used. Those 6 digits form a number, 1123440000, that has a remainder of 32 when divided by 56. Hence we need to use the digits 6, 7, 8, 9 to make a number with a remainder of 24 when divided by 56. There are 24 permutations of the digits 6, 7, 8, 9. Half of these are odd numbers

The one number formed from digits 6, 7, 8, 9 that is divisible by 56 with a remainder of 24 is 9768.

The smallest number comprised of 8 different digits and divisible by each of them is the 10-digit number 1,123,449,768.

Answer:

53

Step-by-step explanation:

Let yazid's score be x

x + x + 17 + 2x = 161

4x + 17 = 161

4x = 144

x = 36

jack = x + 17

jack = 53

Answer:

Jack:  36

Bonus:  Yazid:  53 and Susan:  72

Step-by-step explanation:

Let J, Y, and K stand for Jack, Yazin, Susan's scores.

We are told that:

J = Y + 17  [Jack scored 17 marks more than Yazid]

S = 2Y  [Susan scored twice Yazid's score]

J + Y + S = 161  [total score is 161]

Substitute the first two expressions into the last equation:

J + Y + S = 161

(Y+17) + Y + (2Y) = 161

4Y = 144

Y = 36

Use Y = 36 to find the other scores:

J = Y + 17

J = 36 + 17

J = 53

S = 2Y

S = 2*(36)

S = 72

CHECK:

Does 36+53+72 = 161?

YES

Answer:

75 degrees.

Step-by-step explanation:

Central angle = subtending arc.

Answer:

x^3-4x^2+25x-100

Step-by-step explanation:

We have 2 roots -5i and 4. Using the conjugate root theorem for the root -5i, we know that 5i should be another root

Combining the roots into a polynomial gives us:

(x+5i)(x-5i)(x-4)

Expand:

(x^2 + 25)(x-4)

x^3-4x^2+25x-100

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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