The numbers of points scored in each basketball game are 49, 36, 61, 64, 39, 41, 43, and 39.

In what percent of the games were at least 55 points scored?

\(\quad \huge \quad \quad \boxed{ \tt \:Answer }\)

\(\qquad\displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{ \sqrt{x} (2x - 4) -( \frac{{x}^{2} - 4x + 5) }{2 \sqrt{x} } )}{x } \)

____________________________________

\( \large \tt Solution \: : \)

\(\qquad\displaystyle \tt \rightarrow \: y = \frac{ {x}^{2} - 4x + 5 }{ \sqrt{x} } \)

We know, division rule of differentiation :

\(\qquad\displaystyle \tt \rightarrow \: y = \frac{u}{v} \)

then,

\(\qquad\displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{v\frac{du}{dx} - u \frac{dv}{dx} }{(v) {}^{2} } \)

So, let's do the same in given equation :

\(\qquad\displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{ \sqrt{x} \frac{d}{dx}(x {}^{2} - 4x + 5) - ( {x}^{2} - 4x + 5) \frac{d}{dx}( \sqrt{x} ) }{( \sqrt{x} ) {}^{2} } \)

\(\qquad\displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{ \sqrt{x} (2x - 4) -( {x}^{2} - 4x + 5) \frac{1}{2 \sqrt{x} } }{x } \)

[ This is the required Answer, but you can simplify it however you want according to the choices given ]

\(\qquad\displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{x \bigg( \frac{\sqrt{x} (2x - 4)}{x} -( {x}^{2} - 4x + 5) \frac{1}{2x \sqrt{x} } \bigg)}{x } \)

\(\qquad\displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{\sqrt{x} (2x - 4)}{x} -( {x}^{2} - 4x + 5) \frac{1}{2x \sqrt{x} } \)

\(\qquad\displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{(2x - 4)}{ \sqrt{ x}} - \frac{( {x}^{2} - 4x + 5) }{2 \sqrt{x {}^{3} } }\)

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

(i) The first term (a) is 24 and the common difference (d) is -2.

(ii) The sum of the progression is 2520.

i) Finding the first term and common difference:

Given that the number of terms in the arithmetic progression is 40 and the last term is -54, we can use the formula for the nth term of an arithmetic progression to find the first term (a) and the common difference (d).

The nth term formula is: An = a + (n-1)d

Using the given information, we can substitute the values:

-54 = a + (40-1)d

-54 = a + 39d

We also know that the sum of the first 15 terms added to the sum of the first 30 terms is zero:

S15 + S30 = 0

The sum of the first n terms of an arithmetic progression can be calculated using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values for S15 and S30:

[(15/2)(2a + (15-1)d)] + [(30/2)(2a + (30-1)d)] = 0

Simplifying the equation:

15(2a + 14d) + 30(2a + 29d) = 0

30a + 210d + 60a + 870d = 0

90a + 1080d = 0

a + 12d = 0

a = -12d

Substituting this value into the equation -54 = a + 39d:

-54 = -12d + 39d

-54 = 27d

d = -2

Now we can find the value of a by substituting d = -2 into the equation a = -12d:

a = -12(-2)

a = 24

Therefore, the first term (a) is 24 and the common difference (d) is -2.

ii) Finding the sum of the progression:

The sum of the first n terms of an arithmetic progression can be calculated using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values:

S40 = (40/2)(2(24) + (40-1)(-2))

S40 = 20(48 - 39(-2))

S40 = 20(48 + 78)

S40 = 20(126)

S40 = 2520

Therefore, the sum of the arithmetic progression is 2520.

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If the base triangle has a base of 8 meters and a height of 6.9 meters. the surface area of the pyramid is 139.6 square meters.

First, let's find the area of the base triangle:

Area of base triangle = (1/2) * base * height

Area of base triangle = (1/2) * 8 * 6.9

Area of base triangle = 27.6 square meters

Now, let's find the area of one of the triangular faces:

Area of triangular face = (1/2) * base * height

Area of triangular face = (1/2) * 8 * 7

Area of triangular face = 28 square meters

Since the pyramid has four triangular faces, the total area of the triangular faces is 4 times the area of one triangular face, which is:

4 * 28 = 112 square meters

Total surface area = area of base triangle + area of triangular faces

Total surface area = 27.6 + 112

Total surface area = 139.6 square meters

Therefore, the surface area of the pyramid is 139.6 square meters.

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Applying the intersecting secants theorem, the length of segment KL is approximately, 45.8.

According to the intersecting secants theorem, if two lines from a point outside a circle intersect the circle, then the product of the length of one line segment and its portion outside the circle is equal to the product of the length of the other line segment and its portion outside the circle.

Using the theorem, we have:

MN * MO = ML * MK

Substitute:

21 * 48 = 22 * KL

1,008 = 22KL

1,008/22 = KL

KL = 45.8 (nearest tenth)

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Answer:

5/10 and 3/10

Step-by-step explanation:

because i believe that if u have 5 pencils and 5 pens all together thats 10 so it would be a 5/10 chance same with the second one hopefully this is right and i dont know if its simplified

The number of students enrolled in castle rock school is 625

information from the problem

At castle rock school 575 students ride their bikes to schoolin the theater

If this number is 92% of the school enrollment

how many students are enrolled = ?

The question is a percentage problem, percentage deals with a fraction hundred and used as follows

92%

= 92 percent

= 92 / 100

= 0.92

The factor 0.92 of the total number gives 575 students

let the total number be x

0.92 * x = 575

0.92x = 575

x = 575 / 0.92

x = 625

The total number of students is 625

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Answer:

-8.5m

Step-by-step explanation:

Answer:

20%

Step-by-step explanation:

The theoretical probability of drawing a red marble can be found by dividing the number of red marbles by the total number of marbles in the bag:

P(red) = number of red marbles / total number of marbles

P(red) = 5 / (5 + 8 + 12)

P(red) = 5 / 25

P(red) = 0.2

So the theoretical probability of randomly drawing a red marble is 20%, which corresponds to option (C).

The computation of the figure illustrates that 0.47 expressed as a fraction in simplest form is 43/90.

From the information given, let a = 0.47. Now 10a = 4.777 .... equation i

100a = 47.77 ..... equation ii

Subtract equation i from ii

100a - 10a = 47 - 4

90a = 43

Divide both side by 90

90a/90 = 43/90

a = 43/90

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Answer:

A e/f

Step-by-step explanation:

\(\frac{-e}{-f} = \frac{e}{f}\)

Two negatives always equal one positive

Recall:

Negative + Negative = Positive

Negative + Positive = Negative

Positive + Positive = Positive

The least common denominator needed to solve the equation is given as follows:

D. x(x - 3).

The equation in this problem is given as follows:

1/x + 2/(x - 3) = 5.

The denominators of each expression are given as follows:

x and x - 3 are not factors of each other, hence we multiply them and the least common denominator needed to solve the equation is given as follows:

D. x(x - 3).

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Answer:

f(- 2) = - 9

Step-by-step explanation:

Substitute x = - 2 into f(x) , that is

f(- 2) = (- 2)² + 5(- 2) - 3 = 4 - 10 - 3 = 4 - 13 = - 9

The number of points gained overall by Julia playing the game is 30 point

From the question, we have the following parameters that can be used in our computation:

Tax paid for a new quest = 2.5 points

Total points gained playing the game = 75 points

The above parameters can be represented as

The number of points gained overall = Total points gained playing the game/Tax paid for a new quest

Substitute the known values in the above equation, so, we have the following representation

The number of points gained overall = 75/2.5

Express as a correct fraction

So, we have the following representation

The number of points gained overall = 750/25

Evaluate the quotients

So, we have the following representation

The number of points gained overall = 30

Hence, the number of points gained overall =is30

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Answer:

C

Step-by-step explanation:

If you notice, this is what the tangent-difference identity resembles. The tangent-difference identity is:

\(\tan(\alpha-\beta)=\frac{\tan(\alpha)-\tan(\beta)}{1-\tan(\alpha)\tan(\beta)}\)

We have the expression:

\(\frac{\tan(\frac{\pi}{7})-\tan(\frac{\pi}{8})}{1-\tan(\frac{\pi}{7})\tan(\frac{\pi}{8})}\)

So, our α is π/7 and our β is π/8. Therefore:

\(\frac{\tan(\frac{\pi}{7})-\tan(\frac{\pi}{8})}{1-\tan(\frac{\pi}{7})\tan(\frac{\pi}{8})}=\tan(\frac{\pi}{7}-\frac{\pi}{8}})\)

Simplify:

\(\frac{\tan(\frac{\pi}{7})-\tan(\frac{\pi}{8})}{1-\tan(\frac{\pi}{7})\tan(\frac{\pi}{8})}=\tan(\frac{8\pi}{56}-\frac{7\pi}{56}})\)

Subtract:

\(\frac{\tan(\frac{\pi}{7})-\tan(\frac{\pi}{8})}{1-\tan(\frac{\pi}{7})\tan(\frac{\pi}{8})}=\tan(\frac{\pi}{56})\)

So, our answer is C.

And we're done!

Answer:

c

Step-by-step explanation:

Answer:

Step-by-step explanation:

y = \(\frac{5}{6}\) x - 12

m = \(\frac{5}{6}\)

( - 1, 2 )

y - 2 = \(\frac{5}{6}\) ( x - ( - 1 ))

Equation of the ║ line is y = \(\frac{5}{6}\) x + \(\frac{17}{6}\)

Slope of the perpendicular line is ( - \(\frac{6}{5}\) )

y - 2 = - \(\frac{6}{5}\) ( x - ( - 1 ))

Equation of the ⊥ line is y = - \(\frac{6}{5}\) x + \(\frac{4}{5}\)

The calculated length of the segment v is 267.1 cm

From the question, we have the following parameters that can be used in our computation:

V = 26 degrees

W = 80 degrees

w = 600 cm

See attachment for the triangle

Using the law of sines, the length of w is calculated as

sin(W)/w = sin(V)/v

So, we have

sin(80)/600= sin(26)/v

This gives

v = sin(26) * 600/sin(80)

Evaluate

v = 267.1

Hence, the length of the segment v is 267.1 cm

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Answer: Option (3)

Step-by-step explanation:

The slope of the given line is

\(\frac{-2-4}{-6-2}=\frac{-6}{-8}=\frac{3}{4}\)

Thus, the answer must be Option (3)

Answer

\(\pink\sf{y=-1}\)

Step-by-step explanation

I'm assuming that this exercise is asking us to simplify the equation \(\sf{y=0.5(6)-4}\).

We know that 0.5 (6) means 0.5 multiplied by 6. That is the same as 6 divided by 2, which is 3:

\(\sf{y=3-4}\)

And now we just simplify the last part:

\(\sf{y=-1}\)

∴ answer: y = -1

Answer:

The value is \(n = 188 \)

Step-by-step explanation:

From the question we are told that

    The margin of error is  \(E = 0.06\)

From the question we are told the confidence level is  90% , hence the level of significance is    

      \(\alpha = (100 - 90 ) \%\)

=>   \(\alpha = 0.10\)

Generally from the normal distribution table the critical value  of  \(\frac{\alpha }{2}\) is  

   \(Z_{\frac{\alpha }{2} } =  1.645\)

  Generally will assume that the sample proportion young adults in Louisville, Kentucky, who received help from their parents in buying a home is  \(\^ p = 0.5\)

Generally the sample size is mathematically represented as  

    \(n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p ) \)

=>  \(n = [\frac{1.645}{0.06 } ]^2 * 0.5 (1 - 0.5 ) \)

=>  \(n = 188 \)

Answer: the first thing is your answer :)

thx for the points

Step-by-step explanation:

g

(

x

)

=

x

2

−

3

The parent function is the simplest form of the type of function given.

f

(

x

)

=

x

2

The transformation being described is from

f

(

x

)

=

x

2

to

g

(

x

)

=

x

2

−

3

.

f

(

x

)

=

x

2

→

g

(

x

)

=

x

2

−

3

The horizontal shift depends on the value of

h

. The horizontal shift is described as:

g

(

x

)

=

f

(

x

+

h

)

- The graph is shifted to the left

h

units.

g

(

x

)

=

f

(

x

−

h

)

- The graph is shifted to the right

h

units.

In this case,

h

=

0

which means that the graph is not shifted to the left or right.

Horizontal Shift: None

The vertical shift depends on the value of

k

. The vertical shift is described as:

g

(

x

)

=

f

(

x

)

+

k

- The graph is shifted up

k

units.

g

(

x

)

=

f

(

x

)

−

k

- The graph is shifted down

k

units.

Vertical Shift: Down

3

Units

The graph is reflected about the x-axis when

g

(

x

)

=

−

f

(

x

)

.

Reflection about the x-axis: None

The graph is reflected about the y-axis when

g

(

x

)

=

f

(

−

x

)

.

Reflection about the y-axis: None

Compressing and stretching depends on the value of

a

.

When

a

is greater than

1

: Vertically stretched

When

a

is between

0

and

1

: Vertically compressed

Vertical Compression or Stretch: None

Compare and list the transformations.

Parent Function:

f

(

x

)

=

x

2

Horizontal Shift: None

Vertical Shift: Down

3

Units

Reflection about the x-axis: None

Reflection about the y-axis: None

Vertical Compression or Stretch: None

image of graph

Applying the sine rule the value of side w is calculated to be 6.2

The size of w is calculated using the sine rule which states that the ratio of a side and the opposite angles are equal

the formula is

Sin A / a = Sin B / b = Sin C / c

applying the formula for the problem

Sine W / w = Sine X / x

plugging in the values

Sine 38 / w = Sine 84 / 10

cross multiplying

w = 10 x Sin 38 / Sine 84

x = 6.185

x =  6.2 to the nearest tenth

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Answer:

P = I / rt is the formula we're going to use.

P is the principle (which is what we're solving for)

I = the interest accrued over the specified amount of time (2 years)

r = the interest rate (6%)

t = the time specified (2 years)

Change the percent to a decimal. Place the decimal two places to the left to make 0.06.

P = 264 / 0.06(2)

P = 264 ÷ 0.12 = 2,200

Principal borrowed would be $2,200

Answer:

B. The product of 5 and a number.

Product means multiplication is taking place. In this case, 5 is being multiplied with n.

Hope this helps!

Answer:

Step-by-step explanation:

34

Answer:

34

Step-by-step explanation:

The probabilities, using it's concept, are given as follows:

The probability of an event in an experiment is calculated as the number of desired outcomes in the context of the experiment divided by the number of total outcomes in the context of the experiment.

For the probability P(C|D), the outcomes are given as follows:

Hence the probability is:

P(C|D) = 20/55 = 4/11.

For the probability P(D|C), the outcomes are given as follows:

Hence the probability is:

P(Sweet Foods|Left-Handed) = 20/32 = 5/8.

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Answer:

0.364

0.625

Step-by-step explanation:

Answer:

the area of the rectangle is 35.25 square meters.

Step-by-step explanation:

To find the area of a rectangle, we multiply the length by the width.

First, we need to convert the mixed numbers to improper fractions to make the multiplication easier:

4 and 2/4 = 4 + 2/4 = 16/4 + 2/4 = 18/4

7 and 5/6 = 7 + 5/6 = 42/6 + 5/6 = 47/6

Now we can multiply the length and width:

Area = (18/4) * (47/6)

Area = (9/2) * (47/6) (canceling the common factor of 2 between 18/4 and 6 in 47/6)

Area = (9 * 47) / (2 * 6)

Area = 423/12

Area = 35.25

Therefore, the area of the rectangle is 35.25 square meters.

Answer:

7

Step-by-step explanation:

According to the question,

f(x)= 3x + 4 and g(x) = 5x - 10 are equal.

So,

3x + 4 = 5x - 10

- 2x = - 10 - 4

-2x = -14

2x = 14

x = 7

The measure οf the supplementary angle οf x = 61.33° is fοund tο be 118.67°.

An angle is a figure in plane geοmetry that is created by twο rays οr lines that have a shared endpοint. The twο rays are termed the sides οf an angle, and the cοmmοn terminatiοn is called the vertex. Angles are typically expressed as degrees. A "prοtractοr" is a crucial geοmetrical instrument that aids in measuring angles in degrees. Twο sets οf numbers οn a prοtractοr are οriented in οppοsitiοn tο οne anοther. On the οutside rim, οne set gοes frοm 0 tο 180 degrees, while οn the inner rim, the οther set gοes frοm 180 tο 0 degrees.

Let the angle be x.

Twο angles are cοmplementary when their sum is 90°.

Tοw angles are supplementary when their sum is 180°

If x is οne angle, then its cοmplementary angle is (90-x)°

Given x is 4 mοre than twice its cοmplement.

We can write the equatiοn as:

x = 4 + 2*(90-x)

Sοlving,

x = 4 + 180 - 2x

3x = 184

x = 61.33°

Nοw we are asked tο find the supplementary angle οf x.

Supplementary angle = 180 - x = 180 - 61.33 = 118.67°

Therefοre the measure οf the supplementary angle οf x = 61.33° is fοund tο be 118.67°.

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(42•16)•10 can be rewritten using the associative law of multiplication as (42×16)×4 = 42×(16×10)

The associative law of multiplication states that the way in which numbers are arranged in a multiplication problem does not change the product of those numbers.

This implies the product of three or more numbers remains the same irrespective of how they are arranged. For example: (2×3)×4 = 2×(3×4)

Given:  (42•16)•10

(42×16)×4 = 42×(16×10)

672×4  = 42×160

6720 =  6720

Therefore,  (42•16)•10 rewritten using the associative law of multiplication is (42×16)×4 = 42×(16×10)

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