toddler triplets whose names are red, green and blue each have a coat whose colour is given by their name, but they aren't clear on which coat belongs to which of them. when they go out, red chooses a coat at random among the three coats, green chooses a coat at random among the remaining two coats and blue is left to take the remaining coat. how many ways are there for exactly one of the toddler triplets to end up with their coat? help

The equation of the tangent line at x = 4 is:

y = 179*x  - 490

(your teacher or the person who wrote this problem made a mistake somewhere, as none of the options is near correct)

We have:

f(x) = 4x³ - 2x² + 3x - 10

When x = 4 we have:

f(4) = 4*4³ - 2*4² + 3*4 - 10 = 226

So we want a line tangent to the curve at the point (4, 226)

To find the slope of that line, we need to evaluate the derivative of f(x) in x = 4.

The derivative is:

f'(x) = 3*4x² - 2*2x + 3

f'(x) = 12x² - 4x + 3

Then the slope is:

f'(4) = 12*4² - 4*4 + 3 = 179

Then the tangent line is something like:

y = 179*x + b

To find the value of b, we replace the values of the point (4, 226)

226 = 179*4 + b

226 - 179*4 = b = -490

The line is:

y = 179*x  - 490

Notice that this is not in the options, meaning that the problem (or the options) are written incorrectly.

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Applying the area of the parallelogram formula, it can be concluded that the area is 56 square units.

The area of the parallelogram is the magnitude of the cross-product of the adjacent edges (base and height).

Given information:

A parallelogram is made up of 4 vertices: A(−3, 0), B(−1, 6), C(8, 5), and D(6, −1).

So first we find the adjacent edges as follows:

AB = B - A

     = ( (-1-(-3)) , (6-0) )

     = (2,6)

AD = D - A

     = ((6-(-3)) , (-1-0))

     = (9,-1)

We want to find the area of the parallelogram, we do the following step:

[tex]AB x AD = \left[\begin{array}{ccc}i&j&k\\2&6&0\\9&-1&0\end{array}\right][/tex]

               = i(0 - 0) + j(0 - 0) + k(-2 - 54)

               = -56k

The area of the parallelogram = | AB x AD |

                                                  = √(-56)²

                                                  = 56 square unit

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Answer:

398.32

Step-by-step explanation:

647.82 - 249.50 = 398.32

The probability that the hand contains 4 jacks is solved to be

0.003697

Probability is solved using the formula

= required outcome / possible outcome

The required outcome

= number of ways of picking 4 jacks * number of ways of 10 cards from 48

= ⁴C₄ * ⁴⁸C₁₀

= 1 * 6540715896

= 6540715896

The possible outcome

= number of ways of picking 14 card from possible 52 cards

= ⁵²C₁₄

= 1.768966345 * 10¹²

The probability

= required outcome / possible outcome

=  6540715896 / 1.768966345 * 10¹²

= 11 / 2975

= 0.00369747

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Answer:

ΔMDA ≅ ΔMBC by ASA

Step-by-step explanation:

∠DMA ≅ ∠BMC          

MD ≅ MB

∠MDA ≅ ∠MBC

Two angles are congruent and the sides in between the congruent angles are equal. So, the two triangles are congruent by Angle Side Angle congruency.

Answer:

234565432344343

Answer:

-4a²b

5a²b

Step-by-step explanation:

A monomial is a polynomial that has one term only but can have multiple variables.

Given monomial:

[tex]-20a^4b^2[/tex]

The coefficient of the given monomial is -20.

Therefore, we need to find two numbers that multiply to -20 and sum to 1.

Factors of -20:

Therefore, the two numbers that multiply to -20 and sum to 1 are:

Rewrite -20 as the product of -4 and 5:

[tex]\implies -4 \cdot 5 \cdot a^4b^2[/tex]

Rewrite the exponents as sums of equal numbers:

[tex]\implies -4 \cdot 5 \cdot a^{2+2} \cdot b^{1+1}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c[/tex]

[tex]\implies -4 \cdot 5 \cdot a^2 \cdot a^2\cdot b^{1}\cdot b^{1}[/tex]

Rearrange as the product of two monomials with the same variables:

[tex]\implies -4a^2 b^{1}\cdot 5 a^2 b^{1}[/tex]

[tex]\implies -4a^2 b\cdot 5 a^2 b[/tex]

Therefore, the two monomials whose product equals -20a⁴b², and whose sum is a monomial with a coefficient of 1 are:

Check the sum of the two found monomials:

[tex]\begin{aligned}\implies -4a^2b+5a^2b&=(-4+5)a^2b\\&=(1)a^2b\\&=a^2b\end{aligned}[/tex]

Thus proving that the sum of the monomials has a coefficient of 1.

The kite is flying 23.4ft far of the ground.

as per the details stated above,

the angle of elevation given is 67 degrees

the length at which the string is extended is 20 feet

the spool is 5ft above the ground

so if d is the height of the spool the the actual length of the kite flying will be ( the length of the kite flying + the height of the spool (d) )

according to the question

the hypotenuse side of the triangle or the length of the string is extended is 20 feet

we have to find the opposite side of the triangle using the sine rule

sin [tex]67^0 = \frac{h}{20}[/tex]

=> 20 sin [tex]67^0[/tex] = h

=> h = 18.4 feet

the kite is flying above the spool 5 feet of the ground that is

the kite flying at

h = 18.4 + d

=> 18.4 + 5

=> 23.4 feet

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The equations ( x1+4x2 ) = 11 and ( 2x1+7x2 ) = 18 give the solution as x1 = -5 and x2 = 4.

In order to solve the equation using elementary row operation it is required to multiply the first equation with -2, so that the term with x1 is eliminated from both equations and the value of x2 can be found.

Now

-2. ( x1+4x2 ) = -2 . 11

(-2x1 - 8x2 ) = -22

Now, this equation is added to the second equation (the left-hand sides of both equations are added together and the right-hand side of the equations are added together).

(-2x1 - 8x2 ) + ( 2x1+7x2 ) = ( -22 + 18 )

-2x1 + 2x1  - 8x2  + 7x2  = -4

-x2 =  -4

(x2 = 4)

The value of x2 = 4 is now put in equation 1 to get the value of x1,

( x1 + 4x2 ) = 11

x1+ 4 (4) =  11

x1 + 16 = 11

x1 = (11 - 16)

(x1 = - 5)

So solution is x1 =  -5 and x2 = 4.

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The exact value of  the cosine ( (4π)/3) ] is -0.5.

The exact value of  the cosine function [ Cos ( (4π)/3) ] is calculated by resolving the pi radian into degrees as shown below.

π radian = 180 degrees

The exact value of  the cosine ( (4π)/3) ] is calculated as

Cos ( ( 4π ) / 3 ) = cos ( 4 x 180 / 3 )

cos ( 4 x 180 / 3 )  = cos ( 4 x 60 )

cos ( 4 x 60 ) = cos ( 240 )

cos ( 240 ) = -0.5

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Answer:

Let G be Emily's gross pay.

Deductions:

FIT = 112

State Tax = 0.04G

City Tax = 0.015G

Social Security and Medicare

Net pay = Gross pay - Deductions

3,223 = G - 112 - 0.04G - 0.015G - Social Security - Medicare

We can then solve for G by isolating it on one side of the equation:

3,223 + 112 + 0.04G + 0.015G = G - Social Security - Medicare

3,223 + 0.055G = G - (Social Security + Medicare)

Now we can solve for G by dividing both sides by 1.055

G = 3223 / 1.055 + (Social Security + Medicare)

So we can find the gross pay but we don't have the exact amount for Social Security and Medicare that are being deduced.

Answer:

12.4

Step-by-step explanation:

Answer:

Gordon

Step-by-step explanation:

The domain is the x values and the range is the y values.  The y values are the not the same.  The y values for function A are all positive and the y values for function B are all negative.

The x values are the same for both functions, so the domain is the same for both functions.

The area of the triangle APB is 6.75 square inches.

We know that PA=PB=PC and that PC is perpendicular to FD. Thus C will be the midpoint of FD.

Draw a perpendicular from P to AB, let the point of intersection be Q.

We know that CQ = DB = 6 inches

That is PC + PQ = 6 inches

PQ = (6 - PC) inches

Consider triangle APQ, it is a right angled triangle, right angled at Q. So using Pythagorean theorem

PA² = PQ² + AQ²

PA² = (6 - PC)² + (AB/2)²

PA² = (6 - PA)² + (6/2)²

PA² = 36 - 12PA + PA² + 9

12PA = 45

PA = 3.75

So PA = PB = PC = 3.75 inches

Also PQ = 6 - PC = 2.25 inches

The area of a triangle can be found by using the formula:

area = (base * height) / 2.

In this case, the base, AB is equal to the length of the side of the square, which is 6 inches, and the height is equal to PQ. So the area of triangle APB is

= (6*2.25)/2

= 6.75 square inches.

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Hope it helps.

If you have any query, feel free to ask.

Answer:

Step-by-step explanation:

The formula for calculating the time it will take for an investment to reach a certain amount given a rate of return and regular withdrawals is:

Time = (ln(Final Balance/Initial Balance))/(ln(1 + Rate of Return))

In this case, the Initial Balance is $100,000, the Final Balance is $0, and the Rate of Return is 2.66%.

Time = (ln(0/100000))/(ln(1 + 0.0266))

Time = (-11.51)/(0.026101)

Time = -440.17

Since the time is given in years, we need to round the answer to the nearest year.

Answer: It will take 440 years for the account to have a balance of $0.

The manager of a garden shop wants to make a mixture that contains 74% rye grass. The weight of the 60% mixture used in this composition is 30 lb.

Percentage is used to denote a fraction of a hundred.

Suppose q represents the weight of the mix that contains 60% rye grass, then the weight of rye grass in this mix is:

w1 = 60% q = 0.6 q

Mix 2: 70 lb grass seed that contains 80% rye grass. The weight of rye grass in the second mix is:

w1 = 80% x 70 = 56 lb

The final mixture has 74% rye grass. Total weight of rye grass in the final mixture:

weight of rye grass = w1 + w2

                                = 0.6 q + 56

Total weight of the final mixture = (q + 70) lb

74% = 0.74 = (0.6 q + 56) / (q + 70)

0.6 q + 56 = 0.74 (q + 70)

0.74 q - 0.6 q = 56 - 0.74 x 70

0.14 q = 4.2

q = 4.2/0.14 = 30

Hence, the weight of 60% mixture is 30 lb.

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The number of pais of headphones that can be manufactured in a day = 576

Given that the time to manufacture a pair of headphones on each assembly line is 1/3 hour.

By unitary method the number of pairs of headphones can be manufactured in an hour :

1 ÷ (1/3)

= 1/ (1/3)

= 3

So, 3 pairs of headphones can be manufactured in an hour.

We need to determine the number of pairs of headphones that can be manufactured in a day.

Since we can operate assemply line 8 hours a day.

By unitary method the number of pairs of headphones can be manufactured in 8 hours:

3 × 8 = 24

And there are such 24 assembly lines.

So, the number of pais of headphones that can be manufactured in a day:

24 × 24 = 576

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The equation of the line would be y = 17/7x + 1.

What is the equation of the line?

The equation of a line is a mathematical expression that describes the position of a line in a coordinate plane. It typically takes the form of "y = mx + b", where "m" is the slope of the line and "b" is the y-intercept, the point where the line crosses the y-axis.

The whole question is:

Write an equation of the line passing through the point (8,7) that is perpendicular to the line  [tex]y + 7 = -\frac{7}{17}(x+8)[/tex]

To write the equation of a line that is perpendicular to a given line, we can use the slope of the given line and the point the new line passes through.

The slope of the line [tex]y + 7 = -\frac{7}{17}(x+8)[/tex] can be found by isolating y and then taking the derivative, which gives us: -7/17.

The slope of a line perpendicular to this line is the negative reciprocal of the given line's slope, which is 17/7.

We also know that the new line passes through the point (8,7). Using a point-slope form of a line which is (y-y1) = m(x-x1) where m is the slope, we can write the equation of the line as:

y - 7 = 17/7(x - 8)

So the equation of the line that passes through the point (8,7) and is perpendicular to the line [tex]y + 7 = -\frac{7}{17}(x+8)[/tex] is:

y = 17/7x + 1

Hence, the equation of the line would be y = 17/7x + 1.

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Answer:

To solve this problem, we will use the following steps:

Step 1: We know that the amount of time it takes Susan to get from her residence to class averages 50 minutes, with a standard deviation of 5 minutes. So we can use this information to calculate the proportion of Susan's trips to class that would take less than 40 minutes.

Step 2: To calculate the proportion of Susan's trips to class that would take less than 40 minutes, we need to find the z-score for the value of 40 minutes. We can use the following formula to find the z-score:

z = (x - μ) / σ

Where x is the value we are interested in (40 minutes), μ is the mean (50 minutes), and σ is the standard deviation (5 minutes).

z = (40 - 50) / 5 = -2

Step 3: We can use a standard normal table or a calculator to find the proportion of Susan's trips to class that would take less than 40 minutes.

The proportion of Susan's trips to class that would take less than 40 minutes is 0.0228 or 2.28%.

Step 4: To calculate the proportion of Susan's trips to class that would take more than 50 minutes or less than 40 minutes, we need to find the proportion of Susan's trips to class that would take more than 50 minutes and add it to the proportion of Susan's trips to class that would take less than 40 minutes.

Step 5: To find the proportion of Susan's trips to class that would take more than 50 minutes, we need to find the z-score for the value of 50 minutes.

z = (50 - 50) / 5 = 0

Using a standard normal table or a calculator, the proportion of Susan's trips to class that would take more than 50 minutes is 0.5 or 50%.

Step 6: Finally, we can add the proportion of Susan's trips to class that would take more than 50 minutes and the proportion of Susan's trips to class that would take less than 40 minutes to find the proportion of Susan's trips to class that would take more than 50 minutes or less than 40 minutes.

0.50 + 0.0228 = 0.5228 or 52.28%

Final Answer: The proportion of Susan's trips to class that would take more than 50 minutes or less than 40 minutes is 0.5228 or 52.28%.

The only option that represents the two possible transformations that together could have been used to create the image is; D. a translation of 6 units down followed by a reflection across the y axis

In geometry, a transformation is defined as an operation that moves, flips, or changes a shape that is called the preimage in order to create a new shape that is called the image. Some of the types of transformations includes; Translation, Reflection, Dilation e.t.c

Let us analyze each of the options;

A. This is not correct because the transformation rule for a reflection over the x -axis is (x, y) → (x, −y)  while the transformation rule for the reflection of point (x, y) across the y-axis is (-x, y). This will not correspond with the final transformation given.

B) This is not correct because it will not produce the complete match as the rotation given will not allow for proper mapping.

C) This is NOT correct just like is seen in option A above.

D) This is correct because after translation by 6 units downwards, when we reflect across the y-axis, it produces the final transformed image.

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if D is the incenter of ABC, DF=6, and DB=10 then EB is 8.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given that D is the incenter of ABC, DF=6, and DB=10

We need to find EB

As D is the incenter then DF=DG=DE

so DE is 6

We know DB and DE

DBE is a right triangle and we can find EB by pythagoras theorem

EB²+DE²=DB²

EB²+36=100

EB²=100-36

EB²=64

Take square root on both sides

EB=8

Hence, if D is the incenter of ABC, DF=6, and DB=10 then EB is 8.

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suppose the average number of hours worked per week for high-school aged teens in the united states is 17 hours per week with a standard deviation of 4 hours. So, the number of people selected from the public for a research is known as a sample.

Data dispersion in regard to the mean is quantified by a standard deviation, or "σ". Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high.

Because it makes measures easier to comprehend when the data is spread, standard deviation is significant. The data's standard deviation will increase as the data's distribution becomes more widely scattered. The deviation of each observed value from the mean is measured using this metric. The majority of data in any distribution will fall within a 2 standard deviation range of the mean.

For the given details the correct matching will be:

Parameter - 17 hrs per week

Population - All high-school-aged teens in the US

Statistic - 14.4 hours per week

Sample - 15 students

Population is everything that is taken into account for an experiment since parameters reflect population characteristics and statistics state sample parameters.

The number of people selected from the public for a research is known as a sample.

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The inequality 60 + 5x ≤ 130 shows the maximum width, in inches, of the box that meets the restrictions of the shipping service, given that the box has a height of 60 inches and a length of 2.5 times the width.

1. Let x = the width of the box, in inches.

2. The perimeter of the base of the box is calculated by the following formula: Perimeter = 2(Width) + 2(Length)

3. Therefore, the equation is: 60 + 5x + 2(2.5x) = 130

4. Simplify the equation by expanding the parentheses and combining like terms: 60 + 5x + 5x = 130

5. Solve for x: 5x = 130 - 60

6. Simplify: 5x = 70

7. Divide both sides by 5 to find x: x = 70/5

8. Simplify: x = 14

9. Therefore, the inequality 60 + 5x ≤ 130 shows the maximum width, in inches, of the box that meets the restrictions of the shipping service is 14 inches

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The Scale On A Map Is 1 Inch = 60 Miles. If Two Cities Are 2 3/4 Inches Apart On The Map,  the number of miles they are apart is, 165  Miles

So, Option B is correct.

Scale factor is a mathematical term, which we use to scale 2-dimensional and 3-dimensional shapes. Scale factor is a measure of similar figures. Those figures who look the same but are in different sizes.

For example, Two spheres look similar but could have different radii.

Given that,

The Scale On A Map Is 1 Inch = 60 Miles

Two Cities Are 2 3/4 Inches Apart On The Map

The number of miles they are apart =?

1 Inch = 60 Miles

11/4 Inch = 60 × 11/4 Miles

              = 165  Miles

So, The actual distance is 165  Miles

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The value of x 1/2 or 3/2.

The logarithm of any number N if interpreted as an exponential form, is the exponent to which the base of the logarithm should be raised, to obtain the number N. Here we shall aim at knowing more about logarithmic functions, types of logarithms, the graph of the logarithmic function, and the properties of logarithms.

The basic logarithmic function is of the form f(x) = logax (r) y = logax, where a > 0. It is the inverse of the exponential function ay = x. Log functions include natural logarithm (ln) or common logarithm (log). Logarithmic function properties are helpful to work across complex log functions. All the general arithmetic operations across numbers are transformed into a different set of operations within logarithms. The product of two numbers, when taken within the logarithmic functions is equal to the sum of the logarithmic values of the two functions. Similarly, the operations of division are transformed into the difference of the logarithms of the two numbers.

Here, we use:

1) loga/b = log a - log b

2) logba = (logc a)/(logc b)

Given logarithmic equation:

logₓ(8x-3) - logₓ4 = 2

logₓ (8x-3/4) = 2

(8x-3/4) = x²

8x - 3 = 4x²

4x² - 8x + 3 = 0

x = 1/2 or 3/2

Thus, the value of x 1/2 or 3/2.

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Answer:

1

Step-by-step explanation:

use Pythagoras as shown

The linear equation passing through both points is:

f(x) = 8x - 14 ,the quadratic equation passing through both points is:

[tex]f(k) = -1/28k^2 + 17/14k - 36/7[/tex]

Linear Equation:

f(x) = mx + b

Where, m is the slope and b is the y-intercept.

Calculation:

By substituting the two points (3,2) and (7,18) in the equation, we get:

2 = 3m + b

18 = 7m + b

Solving the equation we get:

m = 8

b = -14

Therefore, the linear equation passing through both points is:

f(x) = 8x - 14

Quadratic Equation:

f(k) = ax^2 + bx + c

Where, a, b and c are constants.

Calculation:

Substituting the two points (3,2) and (7,18) in the equation, we get:

2 = a(3)^2 + b(3) + c

18 = a(7)^2 + b(7) + c

Solving the equation we get:

a = -1/28

b = 17/14

c = -36/7

Therefore, the quadratic equation passing through both points is:

f(k) = -1/28k^2 + 17/14k - 36/7

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Answer: 25.0

Step-by-step explanation:

[tex]\frac{x}{\sin 65^{\circ}}=\frac{22}{\sin 53^{\circ}}\\\\x=\frac{22 \sin 65^{\circ}}{\sin 53^{\circ}}\\\\x \approx 25.0[/tex]

a) The probability of getting exactly 5 successes is  0.1029.

b)The  probability of getting 6 or more successes is 0.8497510126.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

Here, p = 0.7, q = 0.3 and n = 10

a) The probability of getting exactly 5 successes

P (x= 5) = C(10, 5) (0.7)⁵ (0.3)⁵

             = 10!/ 5! 5! x 0.16807 x 0.00243

             = 0.1029

b)The  probability of getting 6 or more successes

P(X≥6) = 1 - P(X<6)

           = 1 - P(X = 0, 1,2, 3, 4, 5)

           = 1 - [ P(0) + P(1)  P(2) + P(3) + P(4) + P(5)]

           = 1 - [C(10, 0) [tex](0.3)^{10[/tex] + C(10, 1) (0.7) [tex](0.3)^{9[/tex] +  C(10, 2) (0.7)² [tex](0.3)^{8[/tex]

                     + C(10, 3) (0.7)³ [tex](0.3)^{7[/tex] + C(10, 4) [tex](0.7)^4[/tex][tex](0.3)^{6[/tex]  + C(10, 4) [tex](0.7)^5[/tex]

                                                                                                    [tex](0.3)^{5[/tex]  ]

          = 1 - [ 0.0000059049 + 0.000137781 + 0.0014467005 +

                    0.009001692 + 0.036756909 +  0.1029]

          = 1 - 0.1502489874

          = 0.8497510126

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