Evaluate 4log4(3,100)

Answer:

80 cm^2

Step-by-step explanation:

Let the width of the rectangle equal x. This means the length is x + 2, as it is 2 cm longer than the width. The formula for perimeter is: P = 2l + 2w, and substitute in the values of the length, width, and perimeter:

P = 2l + 2w

36 = 2(x + 2) + 2(x)

36 = 2x + 4 + 2x

36 = 4x + 4

4x = 32

x = 8

x represents the width, so the width is 8 and the length is 10. Area is length times width, so the area is 8 x 10 or 80 cm^2.

Step-by-step explanation:

let x be the width

p=2l+2w

36=2(2)+2(x)

36=4+2x

36-4=2x

32/2=2x/2(simplify)

x=16

therefore the width is 16cm

area of the rectangle is l×w

=2×16

=32cm"

therefore the area is 32cm"

Answer:

acute

Step-by-step explanation:

That triangle is an obtuse triangle

Answer:

Scores between 71 and 80 give a C grade.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Scores on the test are normally distributed with a mean of 78.8 and a standard deviation of 9.8.

This means that [tex]\mu = 78.8, \sigma = 9.8[/tex]

Find the numerical limits for a C grade.

Above the bottom 20%(20th percentile) and below the top 45%(below the 100 - 45 = 55th percentile).

20th percentile:

X when Z has a p-value of 0.2, so X when Z = -0.84.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-0.84 = \frac{X - 78.8}{9.8}[/tex]

[tex]X - 78.8 = -0.84*9.8[/tex]

[tex]X = 70.57[/tex]

So it rounds to 71.

55th percentile:

X when Z has a p-value of 0.55, so X when Z = 0.125.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]0.125 = \frac{X - 78.8}{9.8}[/tex]

[tex]X - 78.8 = 0.125*9.8[/tex]

[tex]X = 80[/tex]

Scores between 71 and 80 give a C grade.

If one ball is selected at random, the odds for it being striped are 7 out of 15, or 7/15.

What do we know?

We know that there are 15 billiard balls.

We also know that balls numbered 1 through 8 are solid-colored, so we have 8 solid-colored balls.

And the other 7 balls are striped.

Now we want to find the probability for a randomly selected ball to be a striped ball.

Because all the balls have the same probability of being randomly selected, the probability of randomly selecting a striped ball is equal to the quotient between the number of striped balls (7) and the total number of balls (15).

Then we have:

P = 7/15 = 0.467

That quotient is also what is called the "odds"

So if one ball is selected at random, the odds for it being striped are 7 out of 15, or 7/15.

If you want to learn more, you can read:

https://brainly.com/question/23044118

Answer:

157 cm²

Step-by-step explanation:

A cylinder is given to us and we need to find out the lateral surface area of the cylinder . We can see that the ,

Height = 5cm

Radius = 5cm

We know that we can find the lateral surface area of the cylinder as ,

[tex]\rm\implies LSA_{cylinder}= 2\pi r h [/tex]

Substitute upon the respective values ,

[tex]\rm\implies LSA = 2 \times 3.14 \times 5cm \times 5cm [/tex]

Multiply the numbers ,

[tex]\rm\implies \boxed{\blue{\rm LSA = 157 \ cm^2 }}[/tex]

Hence the Lateral surface area of the cylinder is 157 cm² .

[tex] \setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{5cm}}\put(9,17.5){\sf{5cm}}\end{picture}[/tex]

Answer:

314.2 is the Surface area

Step-by-step explanation:

Hope it Helps! If you have any questions, feel free to comment! :)

2π(5)(5)+2π(5^2)

2π(25)+2[tex]\pi[/tex](25)

50π+50π=100π

314.2 is the answer. That's what we get after rounding up! :)

Answer:

Step-by-step explanation:

slope of line through (6,-1) and (11,2) = (-1 - 2)/(6 - 11) = 3/5

slope of line through (5,-7) and (8,-2) = (-7 - (-2))/(8 - 5) = -5/3

product of the slopes = -1, so the lines are perpendicular.

9514 1404 393

Answer:

  12

Step-by-step explanation:

Apparently, you want the sum a+b when ...

  [tex]\[\displaystyle\frac{\sqrt{600} + \sqrt{150} + 4\sqrt{54}}{6\sqrt{32} - 3\sqrt{50} - \sqrt{72}} = a\sqrt{b},\][/tex]

A calculator can show you the expression on the left evaluates to √243. In simplest terms, that is 9√3, so we have a=9, b=3 and ...

  a+b = 9+3 = 12

Answer:

12

Step-by-step explanation:

Answer: 3 shelves

Step-by-step explanation:

12 ÷ 3.1 = 3.87…

Since this is more than 3 but less than 4, we can build 3 full shelves with a leftover.

Answer:

D.

Step-by-step explanation:

Since the unit rate is in dollars per pound, we divide the cost (in dollars) by the weight (in pounds.)

($7.45)/(2.5 lb) = $2.98 per pound

Answer: D.

Answer:

1.047734151

Step-by-step explanation:

Type into calculator

1/2sin(2x)+cos(3x)

Answer:

Number of 7-digit numbers that can be made from the digit is 576

Step-by-step explanation:

Given the data in the question;

digits ⇒ 1, 2, 3, 4, 5, 6, 7

Number of odd numbers in the given digits = 4

Number of even numbers in the given digits = 3

now, we take the odd digits as a single unit.

so, number of ways the odd digits can be arranged with the unit will be 4!.

Now, lets consider the unit of 4 odd digits with 3 even digits.

there are 4 units.

so the number of possible arrangements of these 4 units = 4!

hence, Number of 7-digit numbers that can be made from the digits will be;

⇒ Number of possible arrangements of 4 units × Number of ways in which the odd digits can be arranged within the unit.

⇒ 4! × 4!

⇒ 576

Therefore, Number of 7-digit numbers that can be made from the digit is 576

Answer:

x=9

Step-by-step explanation:

[tex]\sqrt{x}[/tex]=3

[tex]\sqrt{x}[/tex]^2=3^2

x=9

Answer:

168).  C

169).  C

170).  C

Step-by-step explanation:

For the first angle, it is a right angle, so it measures 90 degrees.

x and 50 are complementary angles, meaning they add up to 90 degrees.

So, subtract 50 from 90 to get 40, which is equal to x.

45 and x are supplementary angles, meaning they add up to 180 degrees.

Subtract 45 from 180 to get 35 degrees, which is the measure of angle x.

All angles in a triangle add up to 180 degrees.

So, 70 + 56 = 126, 180 - 126 = 54.

Since the unknown angle is x - 5, 54 + 5 = 59, which the the measure of angle x - 5.

Answer:

32[tex]\pi[/tex]/3 cm³

Step-by-step explanation:

If the diameter is 4 cm, then the radius is 2 cm.

Use the sphere volume formula:

V = 4/3[tex]\pi[/tex]r³

Plug in the radius and solve:

V = 4/3[tex]\pi[/tex](2)³

V = 4/3[tex]\pi[/tex](8)

V = 32[tex]\pi[/tex]/3

So, the volume of the sphere is 32[tex]\pi[/tex]/3 cm³

A line of symmetry would separate a shape to make multiple shapes that are exactly the same.

The answer is C.2

Answer:

24

Step-by-step explanation:

The number of rows (x) should b equal to the number of columns (x).

x²=576

x=√576 taking the square root of the product

x=24

Answer:

marilyn isrestiring and wants to set up a 25-year annuity earns 7.

Notice that

[tex]\dfrac{4n+1}{8n+2}=\dfrac{4n+1}{2(4n+1)}=\dfrac12[/tex]

So by the root test,

[tex]\displaystyle\lim_{n\to\infty}\sqrt[n]{\left|\left(\frac12\right)^{2n}\right|} = \frac14 < 1[/tex]

and so the series converges (absolutely).

y' + 6y = f(t)

where

[tex]f(t)=\begin{cases}0&\text{if }0\le t\le2\\12&\text{if }2<t\le6\\0&\text{if }6<t<\infty\end{cases}[/tex]

You can write f(t) in terms of the unit step (i.e. Heaviside theta) function u(t), which is defined as

[tex]u(t)=\begin{cases}0&\text{if }t<0\\1&\text{if }t\ge0\end{cases}[/tex]

Then the DE is written as

y' + 6y = 12 u (t - 2) - 12 u (t - 6)

(a) Take the Laplace transform of both sides:

LT[y' + 6y] = LT[12 u (t - 2) - 12 u (t - 6)]

s Y - y (0) + 6Y = 12 (exp(-2s) - exp(-6s))/s

(b) Solve for Y :

(s + 6) Y = 12 (exp(-2s) - exp(-6s))/s + y (0)

Y = 12 (exp(-2s) - exp(-6s))/(s (s + 6)) + y (0)/(s + 6)

(c) Take the inverse transform:

LT⁻¹ [Y] = LT⁻¹[12 (exp(-2s) - exp(-6s))/(s (s + 6)) + y (0)/(s + 6)]

y = 12 LT⁻¹ [(exp(-2s) - exp(-6s))/(s (s + 6))] + y (0) LT⁻¹ [1/(s + 6)]

y = 12 u (t - 2) LT⁻¹ [1/(s (s + 6))] - 12 u (t - 6) LT⁻¹ [1/(s (s + 6))] + y (0) exp(-6t )

For the remaining inverse transform, break up into partial fractions:

1/(s (s + 6)) = a/s + b/(s + 6)

1 = a (s + 6) + bs

1 = (a + b) s + 6a

==>   6a = 1, a + b = 0   ==>   a = 1/6, b = -1/6

y = 2 u (t - 2) LT⁻¹ [1/s - 1/(s + 6)] - 2 u (t - 6) LT⁻¹ [1/s - 1/(s + 6)] + y (0) exp(-6t )

y = 2 u (t - 2) (1 - exp(-6t )) - 2 u (t - 6) (1 - exp(-6t )) + y (0) exp(-6t )

Answer:

- 9

Step-by-step explanation:

Let the four consecutive numbers be x, x + 1,

x + 2 and x + 3.

x + x + 1 + x + 2 + x + 3 = - 30

x + x + x + x + 1 + 2 + 3 = - 30

4x + 6 = - 30

4x = - 30 - 6

4x = - 36

x = - 36 / 4

x = - 9

Answer:

y=4x-5

Step-by-step explanation:

Slope-intercept form is y=mx+b where m is the slope and b is the y intercept.

Plug in what you know to solve for b.

3 = 4(2) + b

3 = 8 + b

3-8 = b

b = -5

now put b and m back into the slope- int form.

y = 4x-5

Step-by-step explanation:

5% of 483759 is 24187.95

Answer: The answer is 24,187.95

Step-by-step explanation:

483759 Multiplied by 0.05 = 24,187.95

Answer:

[tex]1.1x, 1.21x, 1.61051x[/tex]

Step-by-step explanation:

If you saving grows [tex]10 \%[/tex] every year, then your saving is [tex]1.1\\[/tex] times your saving from last year. Therefore, after one year, you will have [tex]1.1x\\[/tex], then after [tex]2[/tex] years, you will have [tex](1.1)^2 \cdot x=1.21x[/tex], then after [tex]5[/tex] years, you will have [tex](1.1)^5 \cdot x = 1.61051x[/tex].

Answer:

$1.1x, $1.21x, $1.61x

Step-by-step explanation:

Answer:

36 members

Step-by-step explanation:

Let x = the number of science club members

There are 24 people on the bus (1 seat empty on the 25 seat bus)

2/3 of the club attended and that equals 24 people on the bus

2/3x = 24

Multiply each side by 3/2

3/2 * 2/3x = 24 * 3/2

x = 36

Answer:

3.418

Step-by-step explanation:

3.4175

3.4178

u round if the number behind it is higher than 5

Answer:

240 NC rupees.

9514 1404 393

Answer:

  120

Step-by-step explanation:

I find it pretty easy to obtain the solution by graphing ...

  c(x) -13865 = 0

The positive value of x that makes this so is x = 120.

120 units will have a cost of 13,865 to manufacture.

__

If you like to solve this algebraically, you can probably do it most easily by completing the square.

  x^2 -5x = -65 +13865

  x^2 -5x +6.25 = 13806.25 . . . . . add the square of (-5/2)

  (x -2.5)² = 13806.25

  x -2.5 = √13806.25 = 117.5 . . . . only the positive square root is interesting

  x = 117.5 +2.5 = 120

Answer:

3x³+3x²+3x+8+[tex]\frac{4}{x-1}[/tex]

Step-by-step explanation:

You can use synthetic division for this problem since the divisor is in (x-a) form. The fraction is the remainder over the divisor.

Answer:

0.19

Step-by-step explanation:

Jane bought a shoe for 54.82 euros

She gave the store owner 55 euros

= 55-54.82

= 0.18 euros to franc

= 0.18× 1.08222

= 0.19 franc

9514 1404 393

Answer:

  8000π mm^3/s ≈ 25,133 mm^3/s

Step-by-step explanation:

The rate of change of volume is found by differentiating the volume formula with respect to time.

  V = 4/3πr^3

  V' = 4πr^2·r'

For the given numbers, this is ...

  V' = 4π(20 mm)^2·(5 mm/s) = 8000π mm^3/s ≈ 25,133 mm^3/s

_____

Additional comment

By comparing the derivative to the area formula for a sphere, you see that the rate of change of volume is the product of the area and the rate of change of radius. This sort of relationship will be seen for a number of different shapes.