A ball is thrown from an initial height of 4 ft with an initial upward velocity of 40 ft/s. The ball's height h (in feet) after t seconds is given by the following. H=4+40t-16t squared. Find all values of t for which the ball's height is 26 feet

It looks like the equation is

[tex]2\ln\left(e^{\ln(2x)}\right)-\ln\left(e^{\ln(10x)}\right) = \ln(30)[/tex]

Right away, we notice that any solution to this equation must be positive, so x > 0.

For any base b, we have [tex]b^{\log_b(a)}=a[/tex], so we can simplify this to

[tex]2\ln(2x)-\ln\left(10x\right) = \ln(30)[/tex]

Next, [tex]\ln(a^b)=b\ln(a)[/tex], so that

[tex]\ln(2x)^2-\ln\left(10x\right) = \ln(30)[/tex]

[tex]\ln\left(4x^2\right)-\ln\left(10x\right) = \ln(30)[/tex]

Next, [tex]\ln\left(\frac ab\right)=\ln(a)-\ln(b)[/tex], so that

[tex]\ln\left(\dfrac{4x^2}{10x}\right) = \ln(30)[/tex]

For x ≠ 0, we have [tex]\frac xx=1[/tex], so that

[tex]\ln\left(\dfrac{2x}5\right) = \ln(30)[/tex]

Take the antilogarithm of both sides:

[tex]e^{\ln\left((2x)/5\right)} = e^{\ln(30)}[/tex]

[tex]\dfrac{2x}5 = 30[/tex]

Solve for x :

[tex]2x = 150[/tex]

[tex]\boxed{x=75}[/tex]

Answer:

2500

Step-by-step explanation:

it is a geometric progression

r=5

The geometric sequence 4, 20, 100, 500 is [tex]\rm a_n = 4 \times 5^{n-1}[/tex].

A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant.

This ratio is known as a common ratio of the geometric sequence.

The given geometric sequence 4, 20, 100, 500.

The common difference between the geometric sequence is;

[tex]\rm \dfrac{a_2}{a_1}=\dfrac{20}{4} =5\\\\ \dfrac{a_3}{a_2}=\dfrac{100}{20} =5\\\\ \dfrac{a_4}{a_3}=\dfrac{500}{100} =5\\\\[/tex]

The formula geometric sequence is;

[tex]\rm a_n = a_1 \times r^{n-1}\\\\ a_n = 4 \times 5^{n-1}[/tex]

Where a1 is the first term and r is the common difference of the given geometric sequence.

Hence, the geometric sequence 4, 20, 100, and 500 is [tex]\rm a_n = 4 \times 5^{n-1}[/tex].

Learn more about geometric sequence here;

https://brainly.com/question/15486558

#SPJ2

Answer:

-3x^2 +7x -4

-------------------------------

(x-3)(x-2)(x+3)

Step-by-step explanation:

2              3x

--------   - ----------

X^2-9    x^2 -5x+6

Factor

2                 3x

--------   -      ----------

(x-3)(x+3)   (x-3)(x-2)

Get a common denominator

2  (x-2)               3x(x+3)

--------   -             ----------

(x-3)(x+3)(x-2)   (x-3)(x-2)(x+3)

2x-4  - (3x^2 -9x)

-------------------------------

(x-3)(x-2)(x+3)

Distribute

2x-4  - 3x^2 +9x

-------------------------------

(x-3)(x-2)(x+3)

Combine like terms

-3x^2 +7x -4

-------------------------------

(x-3)(x-2)(x+3)

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9514 1404 393

Answer:

  3x

Step-by-step explanation:

If x represents the number, then "3 times a number" is 3x.

__

Additional comment

"The quotient of the number and 4" is x/4.

The sum of those two expressions is ...

  3x + x/4

Answer:

quneotentendeiporoqenouteetendxdin

Step-by-step explanation:

Answer:

Length of all 3 sides: 7, 7, and 9

Length of the two sides that have the same length: 7

Step-by-step explanation:

Let the two sides with equal lengths have a length of [tex]x[/tex]. We can write the third side as [tex]2x-5[/tex].

The perimeter of a polygon is equal to the sum of all its sides. Since the perimeter of the triangle is 23 meters, we have the following equation:

[tex]x+x+2x-5=23[/tex]

Combine like terms:

[tex]4x-5=23[/tex]

Add 5 to both sides:

[tex]4x=28[/tex]

Divide both sides by 4:

[tex]x=\frac{28}{4}=\boxed{7}[/tex]

Therefore, the three sides of the triangle are 7, 7, and 9 and the length of the two sides that have the same length is 7.

Answer:

[tex]y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x+2)[/tex]

OR

[tex]y+2=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)[/tex]

Step-by-step explanation:

Hi there!

Point-slope form: [tex]y-y_1=m(x-x_1)[/tex] where [tex](x_1,y_1)[/tex] is a point and [tex]m[/tex] is the slope

1) Determine the slope

[tex]m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_2}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in the given points (-2, 6) and (3,-2):

[tex]m=\frac{\displaystyle -2-6}{\displaystyle 3-(-2)}\\\\m=\frac{\displaystyle -8}{\displaystyle 3+2}\\\\m=-\frac{\displaystyle 8}{\displaystyle 5}[/tex]

Therefore, the slope of the line is [tex]-\frac{\displaystyle 8}{\displaystyle 5}[/tex]. Plug this into [tex]y-y_1=m(x-x_1)[/tex]:

[tex]y-y_1=-\frac{\displaystyle 8}{\displaystyle 5}(x-x_1)[/tex]

2) Plug in a point [tex](x_1,y_1)[/tex]

[tex]y-y_1=-\frac{\displaystyle 8}{\displaystyle 5}(x-x_1)[/tex]

We're given two points, (-2, 6) and (3,-2), so there are two ways we can write this equation:

[tex]y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x-(-2))\\\\y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x+2)[/tex]

OR

[tex]y-(-2)=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)\\y+2=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)[/tex]

I hope this helps!

this is the answer

210.28

Answer:

Survey

Step-by-step explanation:

During data collection for a particular study, reaching all target Population might seem illogical or impossible. Therefore, a subset of the population of interest is chosen and the outcome used to infer about the population. This procedure could be referred to a a SURVEY. In the scenario samples drawn from the population of interest is used to make inference on population. During a survey, selected data ponuts or subjects must be drawn at random in other to ensure that it is representative of the larger population data.

Answer:

84.5

Step-by-step explanation:

Given :

Mean μ = 80

Standard deviation, σ = 5

Z = number of standard deviations from the mean, Z = 0.9

Teat score, x

Using the Zscore formula :

Zscore = (x - μ) / σ

Plugging in our values :

0.9 = (x - 80) / 5

Cross multiply

0.9 * 5 = x - 80

4.5 = x - 80

4.5 + 80 = x

x = 84.5

Test score = 84.5

Answer:

Step-by-step explanation:

The most repeated value is:

There are 4 of them.

Correct choice is A

Answer:

Minimum = 0

Maximum = 15

Step-by-step explanation:

Given

Optimization Equation: [tex]z = 2x + 5y[/tex]

Constraints:

[tex]2x- y \le 12[/tex]

[tex]4x + 2y \ge 0[/tex]

[tex]x + 2y \le 6[/tex]

[tex]x,y\ge 0[/tex]

Required

The maximum and the minimum values of z

To do this, we make use of graphical method.

Plot the constraints on a graph (see attachment)

Get the corner points from the points.

These are the points where [tex]x,y\ge 0[/tex]

So, we have:

[tex](x_1,y_1) = (0,0)[/tex]

[tex](x_2,y_2) = (0,3)[/tex]

[tex](x_3,y_3) = (6,0)[/tex]

Substitute these points in the optimization equation:

[tex](x_1,y_1) = (0,0)[/tex]

[tex]z = 2x + 5y[/tex]

[tex]z = 2 * 0 + 5 * 0 = 0[/tex]

[tex](x_2,y_2) = (0,3)[/tex]

[tex]z = 2 * 0 + 5 * 3 = 15[/tex]

[tex](x_3,y_3) = (6,0)[/tex]

[tex]z = 2 * 6 + 5 * 0 = 12[/tex]

So, the values are:

Minimum = 0

Maximum = 15

Answer:

max= 16 min= -24

Step-by-step explanation:

Answer:

ACT Score performed better.

Step-by-step explanation:

Given :

ACT :

Mean score, μ = 21.2

Standard deviation, σ = 5.1

Score, x = 26

SAT :

Mean score, μ = 1498

Standard deviation, σ = 347

Score, x = 1800

To know which score is better, we obtain the standardized, Z score of the two examination :

Zscore = (x - μ) / σ

ACT Zscore :

(26 - 21.2) / 5.1

Zscore = 4.8 / 5.1 = 0.941

ACT Zscore = 0.941

SAT Zscore :

(1800 - 1498) / 347

Zscore = 302 / 347 = 0.870

SAT Zscore = 0.870

The student with the higher Zscore performed better :

ACT Zscore > SAT Zscore

Answer:

0.054

Step-by-step explanation:

9 3/5% as a decimal is 0.054 (already to 3 decimal places)

Answer from Gauthmath

9 are just, well..., 9

3/5 are 0.6

because 1/5 is 0.2

so it's 9.6%, not so complicated I guess

Answer:

te qif y btubf

Step-by-step explanation:

Answer:

no solution

Step-by-step explanation:

Answer:

[tex]{ \tt{6x + 5 = - 29}} \\ { \tt{6x = - 36}} \\ { \tt{x = - 6}}[/tex]

Answer:

28

Step-by-step explanation:

78

Answer:

mean=256229+253657+218747+246163+235626+288694+316265+196721+285077+215152+253291+315011+199901+265443+291806+303556+215359+258554+293658+289935÷21

=5198845÷21

=247564.0

=247564 to the next whole number

B.6 times

Answer:

3 students

Step-by-step explanation:

since the total number of students is 25,when you add those that like baseball, basketball and football the total number must be 25 but in this case it's 22 meaning 2 student liked neither.

7+5+10+x=25

x=25-22

=3

I hope this helps

Answer:

3/ 7

Step-by-step explanation:

We know that it is an even ball

2,4,6,8,10,12,14 are even balls

2,4,6,8 are red and 10,12,14 are white

P ( white) = white even / total even

              = 3/ 7

Answer:

-243

Step-by-step explanation:

(-3) (-3) (-3) (-3) (-3) = - 243

[tex]\frac{1}{-243 }[/tex]

Answer:

10234

Step-by-step explanation:

one is the smallest number so its first

and then you can place zero

after that just place the second smallest number

and so on

Answer:

A. -510

Step-by-step explanation:

We are given the variable values:

Geometric series formula:

[tex]s = \frac{a( {r}^{n} \times - 1) }{r - 1} [/tex]

Plugging in values we have:

[tex]s = \frac{ - 2( {2}^{8} - 1) }{2 - 1} [/tex]

Simplifying the equation we are left with:

[tex] \frac{ - 2(255)}{1} = - 510[/tex]

Answer:

x=37.84

Step-by-step explanation:

We can write a ratio to solve

4 gallons        11 gallons

--------------- = ----------------

13.76              x dollars

Using cross products

4x = 11*13.76

4x=151.36

Divide by 4

4x/4 = 151.36/4

x=37.84

Answer:

Hari saves $ 10,320 in a year.

Step-by-step explanation:

Given that Hari earns $ 4300 per month, and he spends 80% from his income, to determine how much amount does he save in a year, the following calculation must be performed:

100 - 80 = 20

4300 x 0.20 x 12 = X

860 x 12 = X

10320 = X

Therefore, Hari saves $ 10,320 in a year.

Answer:

f(x) is compressed horizontally

Step-by-step explanation:

Given

[tex]f(x) = \log(4x)[/tex]

[tex]g(x) = f(13x)[/tex]

Required

The effect on f(x)

[tex]g(x) = f(13x)[/tex] implies that f(x) is horizontally compressed by 13.

So, we have:

[tex]f(13) = \log(4 * 13x)[/tex]

[tex]f(13) = \log(52x)[/tex]

So:

[tex]g(13) = \log(52x)[/tex]

3 | x - 7 | = 15

Divide both sides by 3

3 | x - 7 | ÷ 3 = 15 ÷ 3

| x - 7 | = 5

_________________________

" Reminder "

| a | = t ===》 a = + t OR a = - t

__________________________

| x - 7 | = 5

x - 7 = 5 ====》 x = 12

OR

x - 7 = - 5 ===》 x = 2

Answer:

4/5

Step-by-step explanation:

I'm not exactly sure what this question is asking but I'm guessing it's asking to create a fraction with the numerator as 4 and denominator as 5.