10. What is the coefficient of the X^3 term
of the product?

Answer:

A C and E

Step-by-step explanation:

Edge

The choices that contain equivalent statements are:

a) ln 3x = 6 → 3x = e⁶

c) log 4x = 8 → 4x = 10⁸

e) 5.6554 = 10ˣ → log 5.6554 = x

To determine which choices contain equivalent statements, let's analyze each option one by one:

a) ln 3x = 6 → 3x = e⁶

This statement is true. It represents the inverse relationship between the natural logarithm (ln) and the exponential function with base e. Taking the exponential of both sides of the equation allows us to isolate the variable.

b) log 3x = 9 → 9x = 10³

This statement is not true. It seems to confuse the base of the logarithm. If the logarithm is not specified with a base, it is usually assumed to be base 10 (log base 10). In this case, the correct equivalent statement would be 3x = 10⁹.

c) log 4x = 8 → 4x = 10⁸

This statement is true. Similar to the previous option, assuming a base 10 logarithm (log base 10), the equivalent statement would be 4x = 10⁸.

d) 0.577 = e⁵ˣ → ln 5 = x / 0.577

This statement is not true. The equation given at the beginning, 0.577 = e⁵ˣ, cannot be transformed into the second equation using the properties of logarithms or exponentials. The two statements are unrelated.

e) 5.6554 = 10ˣ → log 5.6554 = x

This statement is true. It correctly represents the relationship between the logarithm and exponential functions. By taking the logarithm (base 10) of both sides of the equation, we can solve for x.

In summary, the choices that contain equivalent statements are:

a) ln 3x = 6 → 3x = e⁶

c) log 4x = 8 → 4x = 10⁸

e) 5.6554 = 10ˣ → log 5.6554 = x

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Answer:

28.4 (rounded)

Step-by-step explanation:

7.1 times 7.1 is 50. To calculate area, you need to multiply 2 of the sides. so, that is the side length.

then, you multiply it by 4 for all four sides. that would be 28.4.

Answer:

54 or 30

Step-by-step explanation:

Perimeter is adding all the sides together. Area is multiplying LxW and 50 can be gotten by multiplying 5 by 10, or 25 by 2. So if you went by 5x10, both lengths would be 5 and the widths would be 10 or vice versa. Same goes for if you multiplied 25 by 2.

The slope is -5/4 and the equation of the line in point-slope form is       y-5 = -5/4(x+4) + c.

The slope or gradient of a line is a number that describes both the direction X and Y and the steepness of the line. It is the ratio of the vertical change to the horizontal change between any two distinct points on a line.

For the given situation,

The points are  (x1,y1) is (−4,5) and (x2,y2) is (0,0)

The formula of slope is

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

⇒ [tex]m=\frac{0-5}{0-(-4)}[/tex]

⇒ [tex]m=\frac{-5}{4}[/tex]

The equation of the line in point-slope form is

[tex]y-y1=m(x-x1)[/tex]

⇒ [tex]y-5=\frac{-5}{4} (x-(-4))[/tex]

⇒ [tex]y-5=\frac{-5}{4} (x+4)[/tex]

Hence we can conclude that the slope is -5/4 and the equation of the line in point-slope form is y-5 = -5/4 (x+4).

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The area of the triangle RST is the amount of space on the triangle RST

The area of the triangle RST is 127135 square cm

The given parameters are:

r = 690 cm, s = 410 cm and ∠T=64°.

Using the sine function, the area of ΔRST is calculated as:

[tex]A = 0.5rs\sin(T)[/tex]

Subsitute known values

A = 0.5 * 690 * 410 * sin(64 degrees)

Evaluate the sine ratio

A = 0.5 * 690 * 410 * 0.8988

Evaluate the product

A = 127135.26

Approximate

A = 127135

Hence, the area of the triangle RST is 127135 square cm

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From the given table, the year values, and prices, we have the following

equation and values;

(a) The least squares regression equation is; y ≈ 0.1316·x - 261.73

(b) The estimate of the price per gallon in 2030 is approximately $5.418

(a) The coefficients of the least squares regression formula are

presented as follows;

[tex]a = \mathbf{\overline y - b \cdot \overline x}[/tex]

[tex]b = \mathbf{\dfrac{\sum \left(x_i - \bar x\right) \times \left(y_i - \bar y\right) }{\sum \left(x_i - \bar x\right )^2 }}[/tex]

Entering the given values in MS Excel, we have;

[tex]\overline x[/tex]  = 2005.1

[tex]\overline y[/tex] = 2.204

[tex]b = \dfrac{56.456 }{428.9} \approx 0.1316[/tex]

a = 2.204 - 0.1316 × 2005.1 ≈ -261.73

The least squares regression equation is therefore;

(b) In the year 2030, we have;

The price, y ≈ 0.1316 × 2030 - 261.73 = 5.418

In the year 2030, the price per gallon will be approximately $5.418

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Answer: The answer is where the n is the number of people in the club

Step-by-step explanation:

A)Write down an expression, in terms of n, for the number of people in the club.

B) Two of the people in the club are chosen at random. The probability that both these people are men is one tenth. Calculate the number of people in the club.

Answer:

no solution

Step-by-step explanation:

y = 2x - 1 → (1)

y = 2x + 4 → (2)

substitute y = 2x - 1 into (2)

2x - 1 = 2x + 4 ( add 1 to both sides )

2x = 2x + 5 ( subtract 2x from both sides )

0 = 5 ← not possible

This indicates the system has no solution

The dimension that maximize the are of the pen is 45 ft by 90 ft.

where

l = length

w= width

Therefore,

perimeter of a rectangle = 2(l + w)

The barn is occupying one part of the rectangle . Therefore,

perimeter = 2l + w

180 = 2l + w

w  = 180 - 2l

area = lw

Therefore,

area = l(180 - 2l)

area = 180l - 2l²

To maximize area

l = -b / 2a

l = - (180) / 2 × -2

l = -180 / -4

l = 45 ft

Therefore,

w = 180 - 2(45)

w = 180 - 90

w = 90 ft

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I can't see it redo it so I can answer

Answer:

I believe the answer is B

Answer:

hiiiiii

Step-by-step explanation:

Answer:

$134217728

Step-by-step explanation:

Day 1: $1

Day 2: $2

Day 3: $4

Day 4: $8

Day 5: $16

Day 6: $32

Day 7: $64

Day 8: $128

Day 9: $256

Day 10: $512

Day 11: $1024

Day 12: $2048

Day 13: $4096

Day 14: $8192

Day 15: $16384

Day 16: $32768

Day 17: $65536

Day 18: $131072

Day 19: $262144

Day 20: $524288

Day 21: $1048576

Day 22: $2097152

Day 23: $4194304

Day 24: $8388608

Day 25: $16777216

Day 26: $33554432

Day 27: $67108864

Day 28: $134217728

The table which most likely relates the height h(t), in meters, over time, t, in seconds  is: Option D:

If the height function is function of time 't', and the object's height is measured from the ground level and object never goes inside ground, then that means height can never be negative. It will always assume non-negative values.

There are three equations of motion that can be used when motion of the object is under constant acceleration and on a straight path.

They are listed below as:

[tex]v = u + at\\\\s = ut + \dfrac{1}{2} at^2\\\\v^2 = u^2 + 2as[/tex]

where the symbols have following meanings:

All the tables given except the last table have negative height values. That shows that if those negative valued tables are true, then the ball went inside ground.

Since no such event of ball going inside the ground is specified in the considered situation, thus, only the last table is valid here in terms of sign of height.

The last table is:

       t (in seconds)            h(t) (in meters)

       0                                180

       2                                160.4
       4                                101.6
       6                                3.6

Checking the truthfulness of the last table by using law of motion in straight path:

u = initial velocity of ball = 0

a = gravitational acceleration = -g ≈ -9.8 m/s sq.

Now, height of ball at time t = initial height of ball - distance it traveled from starting point in direction of reaching ground.

Thus, h(t) = 180 - |s| (assuming first value is true in the table)

where |s| = non-negative value of s

[tex]s= ut + (1/2)at^2\\s = 0t + (1/2)(-9.8)t^2\\\\|s| = 4.9t^2 \: \rm m/s^2[/tex]

Thus, h(t) = 180 - 5t² m/s sq.

[tex]h(2) = 180 - 4.9(2)^2 = 160.4\\h(4) = 180 - 4.9(4)^2 = 101.6\\h(6) = 180 - 4.9(6)^2 = 3.6\\[/tex]

Thus, the table which most likely relates the height h(t), in meters, over time, t, in seconds  is: Option D:

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Answer:

To measure the length of an object, choose the correct tool for measuring it, like a ruler for small, flat items, or a measuring tape for items with curves. Then, line up the zero mark on your measuring tool with one end of the object.

43 × 7 = 301

12 × 9 = 108

10 × 6 = 50

9 × 7 = 63

7 × 5 =35

6 × 3 = 18

0 × 8 = 0

30 × 3 =9

11 × 8 =88

73 × 2 =146

83 × 5 = 166

16 × 8 = 128

392 × 7 =2,744

29 × 4 = 116

761 × 9 = 6,849

4,829 × 6 = 28974

12 × 7 = 84

25,500 × 4 =102,000

Answer:

288m^2

Step-by-step explanation:

ratio is 4000/3, though the thousand does not matter because we can just exchange units

18*4/3=24

24 meters

9*4/3=12

12 meters

24*12=288

Answer:

No

Step-by-step explanation:

2 is a positive whole number with a value greater than 1. 3/4 is NOT greater than 1. So 2 is greater than both 0 AND 3/4 and cannot be between the two numbers.

No, Jan is wrong because 2 is not in between 0 and 3/4 on a number line.

Number line is a horizontal line where numbers are marked at equal intervals one after another form smaller to greater.

Given that;

Jan says that 2 is between 0 and 3/4 on a number line.

Here, The numbers on the number line are 0 and 3/4.

⇒ 3 / 4 = 0.75

So, We get;

⇒ 2 > 0

And, 3/4 < 2

Thus, The number 2 is not in between 0 and 3/4 on a number line.

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Answer: 40

Step-by-step explanation:

The concentration of pineapple when 2 gallons of pineapple juice are added to 6 gallons of the other juice is; 8.24

The function is a type of relation, or rule, that maps one input to a specific single output.

Given that the functions that model the concentration of apple juice in the drink after x gallons of the 20% drink are added to 2 gallons of pure juice.

f(x)=(2)(1.0)+x(0.2)²+x

If the concentration of apple when 2 gallons of apple juice are added to 6 gallons of the other juice;

f(6) = (2)(1.0)+ 6(0.2)²+ 6

f(6) = 2.0 + 6.24

f(6) = 8.24

Hence the concentration of pineapple when 2 gallons of pineapple juice are added to 6 gallons of the other juice is; 8.24

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Answer:

B

Step-by-step explanation:

I hope this helps! :) If you need an explanation, let me know. Other than that, have a lovely day!! <3

A(2;3) is ok on B and C

B(2 ; 6) is ok on B

C (8 ; 7) is ok on B as well

and

D (8 ; 3) is ok on B

=> B

Answer:

33+4^2

Step-by-step explanation:

Expression: Does not require an equal sign.

Sum: addition of

four squared: 4^2

thirty three: 33

The correct numerical expression that represents the sum of four squared and thirty three is,

⇒ 4² + 33

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

''the sum of four squared and thirty three''

Now, We get;

The correct numerical expression that represents the sum of four squared and thirty three is,

⇒ 4² + 33

Thus, The correct numerical expression that represents the sum of four squared and thirty three is,

⇒ 4² + 33

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[tex](\frac{1}{sin\alpha } -sin\alpha )(\frac{1}{cos\alpha } -cos\alpha )=cos\alpha *sin\alpha \\\\\\(\frac{1}{sin\alpha } -\frac{(sin\alpha)^2}{sin\alpha} )(\frac{1}{cos\alpha } -\frac{(cos\alpha)^2}{cos\alpha } )=cos\alpha *sin\alpha \\\\\\(\frac{1-(sin\alpha )^2}{sin\alpha } )(\frac{1-(cos\alpha)^2 }{cos\alpha } ) = cos\alpha *sin\alpha\\\\\\(\frac{(cos\alpha)^2 }{sin\alpha } )(\frac{(sin\alpha )^2}{cos\alpha } )=cos\alpha *sin\alpha\\\\\\cos\alpha *sin\alpha = cos\alpha *sin\alpha[/tex]

Identities used

Hope it helped!

p.s. If you can give me a brainly, it would help a lot since the formatting of these equations were a lot of work

Simple interest formula:

Total = start x ( 1 + rate x time )

Total = 14,000 x ( 1 + (0.015 x3))

Total = 14,000 x 1.045

Total = 14,630

Answer:

£14,630

Step-by-step explanation:

Simple interest formula:  A = P(1 + rt)

where:

Given:

⇒ A = 14000(1 + 0.015 · 3)

⇒ A = 14000(1.045)

⇒ A = £14,630

[tex] \tt \tiny \gray{thanks}[/tex]

118 - 4 x 8 = 118 - 32 = 86°

5 ori 5 fac 25 și cu 25 egal 14 și cu 14 egal 100 și cu 100 egal 12

Answer:

x = 24

Step-by-step explanation:

0.6x=0.1×x+7+5

0.6x=0.1×x+12

0.6x−0.1×x=12

0.5x=12

x=24

Answer:

x=24

Step-by-step explanation:

Answer:

He will drive 180 miles in 4 hours. ( I think)

Step-by-step explanation:

If he keeps going at his rate which is 45 mph then if you multiply that by 4 then your answer should just be 180 miles.

Answer:

180 miles

Step-by-step explanation:

so he goes 45 miles per hour

since you need to find 4 hours just multiply 45 by 4

45 x 4 = 180

there's your answer