Multiply the numbers.

The height of the ball is given as 7.74 ft.

We have the value of h(X) to be

-[tex]-\frac{44x^{2} }{v^{2} } +x+6[/tex]

The initial velocity is given as v which is = 26

v = 26² = 676

the value of x is given as 2

We have to put these values in the formula

[tex]-\frac{44(2)^{2} }{676 } +2+6[/tex]

= 44 * 4/676 + 2 + 6

= -0.26 + 2 + 6

= 7.74

Hence we can say that the height of the ball is given as 7.74 ft.

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[tex] \longrightarrow \: - 4 + \frac{x + 4}{3} - 2 = 2(x + 1) \\ \longrightarrow \: { -4} + \frac{x}{3} + \frac{4}{3} - {2} = 2x + 2 \\ \longrightarrow \: { - 4}+ \frac{4}{3} - {2} - 2 = 2x - \frac{x}{3} \\ \longrightarrow \: -4 - 2 - 2 + \frac{4}{3} = 2x - \frac{x}{3} \\ \longrightarrow \: - 8 + \frac{4}{3} = 2x - \frac{x}{3} \\ \longrightarrow \: \frac{ - 20}{3} = \frac{5}{3} x \\ \longrightarrow \:\frac{ - 20}{3} \times \:3\: = 5x \\ \longrightarrow \:-20 = 5x\\\longrightarrow \:\frac{-20}{5} = x \\\longrightarrow \:x = - 4[/tex]

The nth terms of the arithmetic sequences;

I. Tn = 3 + √2 + ( n - 1) √2

ii. Tn = 2/ √3 + ( n - 1) 1/ √3

The formula for the nth term of an arithmetic sequence is expressed as;

Tn = a + ( n - 1)d

Where;

i. a = 3 + √2

d = √2

Substitute the values, we have;

Tn = 3 + √2 + ( n - 1) √2

ii. a = 2/ √3

d = 1/ √3

Substitute the value, we have;

Tn = 2/ √3 + ( n - 1) 1/ √3

Thus, the nth terms of the arithmetic sequences are Tn = 3 + √2 + ( n - 1) √2 and Tn = 2/ √3 + ( n - 1) 1/ √3 respectively

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Answer:mkpewmg pmblembmfe

Step-by-step explanation:

7 t8gt385uhg

Answer:

72

Step-by-step explanation:

$48 + $20 = $68

$68 - $32 = $36

$36 × 2 = $72

Answer:

She had $160 at first

Step-by-step explanation:

Fiona spent of her money on a dress and $39 on a bag. If she had $121 left, how much money did she have at first?

In order to find how much she had at first

we have to add how much she spent plus how much she has left with her

➟ $121 + $39

➟ $160

∴ She had $160 at first

After the picture is reflected along the y-axis, its vertices will have the coordinates P'Q'R.:

[tex]P' = (-3,8)\\Q' = (5,7)\\R'=(0,2)[/tex]

What is coordinates of the vertices?

The triangle's vertices' coordinates are [tex](x_{1} ,y_{1} )[/tex], [tex](x_{2},y_{2})[/tex], and [tex](x_{3},y_{3} )[/tex]. The line that connects the first two is split in the ratio l:k, and the line that runs from the division point to the opposing angular point is divided in the ratio m:k+l.

Given:

Triangle PQR and vertices of triangle are

[tex]P=(3,8)\\Q=(-5,7)\\R=(0,2)[/tex]

The following rule results in a reflection about the y-axis:

                      [tex](x, y) ---- > (-x, y)[/tex]

Using the rule on each of our vertices, we have:

[tex](3, 8) ---- > (-3, 8)\\(-5, 7) ---- > (5, 7)\\(0, 2) ---- > (0, 2)[/tex]

Therefore,

After the picture is reflected along the y-axis, its vertices will have the coordinates P'Q'R.

[tex]P' = (-3,8)\\Q' = (5,7)\\R'=(0,2)[/tex]

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a. Straight-line method: $36,000 $36,000

b. Sum-of-the-years'-digits method: $60,000 $48,000

c. Double-declining-balance method: $79,200, $47,520

d. Activity method based on hours worked: $30,600, $21,600

e. Activity method based on units of output $40,000 $34,000

b. Straight line method

Depreciation expense = (Cost of asset - Salvage value) / Useful life

Depreciation expense=( $198,000 -  $18,000 ) / 5

Depreciation expense = $36,000

b.  Sum-of-the-years'-digits method

Sum-of-the-year digits = (Remaining useful life / Sum of the years ) x  (Cost of asset - Salvage value)

Sum of the years = (1 +2 +3 +4 + 5 )

Sum of the years = 15

Year 1 Depreciation expense = (5/15) × ( $198,000 -  $18,000 )

Year 1 Depreciation expense = $60,000

Year 2 Depreciation expense = (4/15) x ( $198,000 -  $18,000 )

Year 2 Depreciation expense = $48,000

c.  Double-declining-balance method

Depreciation factor = 2 x (1/Useful life)  

Depreciation factor =2 x(1/5)

Depreciation factor = 0.4

Year 1 Depreciation expense = 0.4 x  $198,000

Year 1 Depreciation expense= $79,200

Year 1 Book value =  $198,000 - $79,200

Year 1 Book value= $118,800

Year 2 Depreciation expense= 0.4 x $118,800

Year 2 Depreciation expense= $47,520

d.  Activity method based on hours worked

Activity method = (Hours worked  / Total machine hours) x  (Cost of asset - Salvage value)

Year 1 Depreciation expense = (1,700 / 10,000) x ( $198,000 -  $18,000 )

Year 1 Depreciation expense  = $30,600

Year 2 Depreciation expense = (1,200 / 10,000) x ( $198,000 -  $18,000 )

Year 2 Depreciation expense = $21,600

e. Activity method based on units of output

Activity method  = (Output produced / Total machine output capacity) x  (Cost of asset - Salvage value)

Year 1 Depreciation expense =  ( 40,000 / 180,000) x ( $198,000 -  $18,000 )

Year 1 Depreciation expense = $40,000

Year 2 Depreciation expense=  ( 34,000 / 180,000) x ( $198,000 -  $18,000 )

Year 2 Depreciation expense = $34,000

Therefore the Straight-line method is $36,000 $36,000.

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The linear inequality represented by the given graph in the attached image is y > -3x + 6.

Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.

The graph of the linear inequality. Let's pick two points from the graph to frame the linear equation

The slope-intercept form of the equation is Where m is the slope and b is the y-intercept is (0,6) from the graph so b=6.

Find out slope m by using the general formula. Pick two points (0,6) and (2,0).

Slope = ( y₂ - y₁)  / ( x₂ - x₁ )

Slope = ( 0 - 6 ) / ( 2 - 6 )

Slope = -3

m = -3

So the equation is y = -3x + 6

Now we check the inequality sign by testing any point on the shaded area let's pick (4,0). let's plug in 4 for x  and 0 for y

y= -3x + 6

0 = -3(4) + 6

0 > -6

Inequality:  y > -3x + 6.

Therefore, the inequality represented by the given graph is y > -3x + 6.

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Answer: y≥4x−6

Step-by-step explanation: I took the test and this was the right answer for me.

Answer:

  x = 155°

Step-by-step explanation:

Given hexagon ABCDEF, you want to find the measure of interior angle E. Angles at vertices A, B, C, D, and F are specified.

The sum of the interior angles of an n-sided polygon is ...

  angle sum = (n -2)180°

For the 6-sided polygon given, the sum of interior angles is ...

  (6-2)180° = 720°

The interior angle at vertex B is 360° -80° = 280°.

The interior angle at vertex D is 180° -115° = 65°.

Then the sum of interior angles is ...

  A +B +C +D +E +F = 720°

  85° +280° +30° +65° +x +105° = 720° . . . . . substitute known values

  565° +x = 720° . . . . . . . collect terms

  x = 155° . . . . . . . . . . subtract 565°

__

Additional comment

The angles in the attached figure are drawn to scale.

An alternate solution might draw segment CX through vertex B so that the figure containing angle x has no reflex interior angles. Then the interior angles of pentagon ABXEF will total 540°. Known angles in that figure are A=85°, B=100°, X=95°, F=105°. Then E=x=540° -385° = 155°.

We took this approach initially, to verify that the angle sum of the given hexagon remained 720° even with the reflex interior angle at B.

here u go I hope this is the answer ur looking for!

The number of terms in the sequence with d=5 , a₁ = -9 and aₙ=141 is 31 terms.

Arithmetic Sequence

The nth term of the sequence { a , a+d , a+2d , ... , a+(n-1)d } is given by

aₙ=a+(n-1)d       ...(i)

where , a = first term ,

d = common difference ,

n = number of terms ,

aₙ = nth term of the sequence .

It is given in the question that

first term (a) = -9

common difference (d) = 5

and nth term (aₙ) = 141

Substituting the values in equation (i) we get ,

141 = -9 + (n-1)5

simplifying further we get

141+9=(n-1)5

150 = 5n - 5

150+5 = 5n

155 = 5n

n=155/5

n=31.

Therefore , There are 31 terms in the sequence with d=5 , a1 = -9 and aₙ=141 .

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Question 1

Opposite sides of a trapezoid are parallel. So, by the same-side interior angles theorem,

[tex]-16x+10x+86=180 \\ \\ 10x+70=180 \\ \\ 10x=110 \\ \\ x=11[/tex]

Question 2

Opposite sides of a trapezoid are parallel. So, by the same-side interior angles theorem,

[tex]9x+30+7x-10=180 \\ \\ 16x+20=180 \\ \\ 16x=160 \\ \\ x=10[/tex]

Answer:

f(1) = 9

Step-by-step explanation:

where x is 1, y is 9

Answer:

-39

Step-by-step explanation:

Hello, to do this problem, we need to use substitution.

c=-4 and x=7

-5x+c

-5(7)+-4

-35-4

=-39

Hope that helps

:D

Answer:

c = -4

x = 7

- 5 (7) + (- 4)

- 35 + (- 4)

= - 39

Hope this helps :)

By using  Matrix method it denotes that the equations are consistent and have a single solution.

Matrix method, we will use the formula, [tex]X=A^{-1} B[/tex] where,

[tex]\[{\rm{X}} = \left[ {\begin{array}{*{20}{l}}x\\y\\z\end{array}} \right]\][/tex]

[tex]\[{A^{ - 1}} = \frac{{adjA}}{{|A|}}\][/tex]

[tex]\[{\rm{B}} = \left[ {\begin{array}{*{20}{c}}{33}\\{ - 26}\\{23}\end{array}} \right]\][/tex]

So, we will have to find [tex]A^{-1}[/tex], for that, we will first find the determinant of matrix A, that is |A|, then we will find the cofactors of matrix A, take its transpose, and that will be Adj A.

Therefore, we will be able to get the inverse of matrix A using

[tex]A^{-1}[/tex] =Adj A|A|

and hence We then substitute all the obtained values of [tex]A^{-1}[/tex] and B in the main formula and do necessary calculations to get the value of x, y and z accordingly.

Complete step-by-step answer:

It is given in the question that, we have to solve the system of equations,

2x-y+4z=33

X+2y-3z=−26

-5x−3y+5z=23

Applying the matrix approach.

Therefore, the first step is to convert the supplied equations into matrix form. Thus, it can be expressed as follows.

[tex]\[\left[ {\begin{array}{*{20}{c}}2&{ - 1}&4\\1&2&{ - 3}\\{ - 5}&{ - 3}&5\end{array}} \right]\left[ {\begin{array}{*{20}{l}}x\\y\\z\end{array}} \right]\]\[[/tex][tex]= \left[ {\begin{array}{*{20}{c}}{33}\\{ - 26}\\{23}\end{array}} \right][/tex]

[tex]\[|{\rm{A}}| = \left[ {\begin{array}{*{20}{c}}2&{ - 1}&4\\1&2&{ - 3}\\{ - 5}&{ - 3}&5\end{array}} \right]\][/tex]

= 2(10+9) + 1(5-15) + 4(-3+10)

= 38-10+28

=56

Since we have |A|≠0.

Hence, it denotes that the equations are consistent and have a single solution.

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The answer to this given simplification (3x^-4)6/9x^-12 is 2 x^8.

What are exponents?

The exponent of a number indicates how many times a number has been multiplied by itself. For instance, 34 indicates that we have multiplied 3 four times. Its full form is 3 3 3 3. Exponent is another name for a number's power. It could be an integer, a fraction, a negative integer, or a decimal. In this essay, let's study more about exponents.

given:

(3x^-4)6/9x^-12

=x^-4 . 3 . 6 / 9 . x^-12

= 2. x^-4 /  x^-12

=2 x^8

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The graph that shows the correct synthetic division process is given at the end of the answer.

For this problem, we have that:

Then, from the graph, we have that:

Hence, the result of the division of 3x² - x - 2 by (x + 4) is 3x - 13 with a remainder of 50.

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The probability of rolling a number less than 5 is 0.667.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event asked. The value is expressed from zero to one. An outcome is a value we can obtain.

As we are given a 6-sided dice therefore,

Total possible outcomes = 6

Favorable outcomes (that is less than 5) = 4                 [that are; 1, 2, 3, 4]

probability = number of favorable outcomes/number of possible outcomes

probability = 4/6

4/6 = 2/3

= 0.6666666666666

To round the value to three decimal places, we need to see if the fourth value after decimal is more than 5 or not. If it is more than 5, preceding digit is increased by 1. therefore, by applying the rule to the value we get

= 0.667                         [rounded to three decimal places as needed]

therefore, the probability of the event given, that is rolling a number less than 5 is 0.667.

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(a) X is distributed normally.

(b) The median recovery time is 3 days.

(c) The z score of the patient who takes 4.2 days to recover is 0.75.

(d) The probability of spending more than 2.3 days in recovery is 66.64 %.

(e) The probability of spending between 3.7 and 4.2 days in recovery is 10.7 %.

(f) The 85th percentile for recovery times is 5.24 days.

(a) We are informed that a certain surgical procedure's recuperation time for patients is typically distributed. As a result, X is distributed normally.

(b) The median will be equal to the mean because the patient recovery time has a normally distributed distribution. The median is therefore 3 days.

(c) The formula for z score is given as:

z = X - μ / σ

Now, we have the mean μ = 3 days.

Standard deviation, σ = 1.6 days

The observed value, X = 4.2 days

Therefore,

z = ( 4.2 - 3) / 1.6

z = 1.2 / 1.6

z = 0.75

(d) When X = 2.3 days

Then the z score will be:

z = X - μ / σ

z = 2.3 - 3 / 1.6

z = - 0.7 / 1.6

z = - 0.4375

The corresponding area for z = 0.4375 is 0.3336.

In order to determine the likelihood for a period longer than 2.3 days, we must look at the region to the right, which we can locate by deducting 0.3336 from 1.

Therefore, the probability will be:

p = 1 - 0.3336

p = 0.6664

p = 66.64 %

(e) Now, for the probability between X = 3.7 days and 4.2 days.

z₁ = (3.7 - 3) / 1.6 = 0.7/1.6 = 0.4375

z₂ = (4.2 - 3) / 1.6 = 1.2 / 1.6 = 0.75

The area for a z score of 0.4375 is 0.1664 and the area to left for a z score 0.75 is 0.2734.

Then the probability between 3.7 days and 4.2 days will be:

p = 0.2734 - 0.1664

p = 0.107

p = 10.7 %

(f) For the 85th percentile:

For 0.85 the z score from the table is 1.4.

So, z = 1.4

z = X - μ / σ

1.4 = ( X - 3) / 1.6

(1.4)(1.6) = X - 3

2.24 = X -3

X = 2.24 + 3

X = 5.24 days

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The complete question is mentioned below:

The patient recovery time from a particular surgical procedure is normally distributed with a mean of 3 days and a standard deviation of 1.6 days. Let X be the recovery time for a randomly selected patient. Round all answers to 4 decimal places where possible.

a. What is the distribution of X?

b. What is the median recovery time? __________days

c. What is the Z-score for a patient that took 4.2 days to recover?

d. What is the probability of spending more than 2.3 days in recovery?

e. What is the probability of spending between 3.7 and 4.2 days in recovery?

f. The 85th percentile for recovery times is _________days.

Answer:

5 square mile

Step-by-step explanation:

1 square km = 0.3 square mile

13 square km = 5.01 square mile

5.01 rounded equals 5

hope that helps <3

Answer:

89.14%

Step-by-step explanation:

279 Out of 313 is 89.14%. Follow the below steps to calculate what percent is 279 out of 313 or how to write 279/313 as a percentage.

Step 1: Percentage Formula = Number 1/Number 2 x 100

Step 2: plugin the 279 and 313 to the percentage formula and we get 279/313 x 100 = 89.14%

The number line which shows the solution to the inequality is option C

3x + 2 ≤ -11

or

4x - 3 > 9

3x + 2 ≤ -11

3x ≤ -11 - 2

3x ≤ -13

x ≤ -13/3

x ≤ -4.33

or

4x - 3 > 9

4x > 9 + 3

4x > 12

x > 12 / 4

x > 3

Ultimately, the answer to the inequalities is x ≤ -4.33 and x > 3

Therefore, the number line which shows the solution to the inequality is option C

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The number of pieces are 18 if the piece of wood was 12 feet long. Kendra cut the wood into pieces 2/3 foot.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

A piece of wood was 12 feet long. Kendra cut the wood into pieces __

2/3 foot.

Let x be the number of pieces:

12/x = 2/3

x = 36/2

x = 18

Thus, the number of pieces are 18 if the piece of wood was 12 feet long. Kendra cut the wood into pieces 2/3 foot.

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Answer:

4.69 x 10⁵

Step-by-step explanation:

Step 1

To find a, take the number and move a decimal place to the right one position.

Original Number: 469,000

New Number: 4.69000

Step 2

Now, to find b, count how many places to the right of the decimal.

New Number: 4 . 6 9 0 0 0

Decimal Count: 1 2 3 4 5

There are 5 places to the right of the decimal place.

Step 3

Building upon what we know above, we can now reconstruct the number into scientific notation.

Remember, the notation is: a x 10b

a = 4.69 (Please notice any zeroes on the end have been removed)

b = 5

Now the whole thing:

4.69 x 10⁵

Step 4

Check your work:

105 = 100,000 x 4.69 = 469,000

Answer:   [tex]4.61 \times 10^5[/tex]

Reason:

The original number is 461,000 or 461000

Place a decimal point between the first two nonzero values. Erase the zeros and we get 4.61

To get back to 461000, we need to move the decimal point 5 spaces to the right. This is the exponent for the [tex]10^5[/tex] portion.

So [tex]461,000 = 4.61 \times 10^5[/tex]

Answer:

11

Step-by-step explanation:

Opposite sides of a trapezoid are parallel. So, by the same-side interior angles theorem,

[tex]-16x+10x+86=180 \\ \\ 10x+70=180 \\ \\ 10x=110 \\ \\ x=11[/tex]

Answer:

40 yellow marbles

Step-by-step explanation:

1. Divide 64 by 8 (Determine how many sets there are)

64/8 = 8

2. Multiply 8 by 5 (Because for every 8 purple marbles there are 5 yellow ones)

8*5 = 40