two identical rubber balls are dropped from different heights. Ball 1 is dropped from a height of 109 feet, and ball 2 is dropped from a height of 260 feet. Use the function f(t) -16t^2+h to determine the current height, f(t), of a ball from a height h, over given time t.

When does ball 1 reach the ground? Round to the nearest hundredth​

Subtracting 10 from the original equation will shift the graph down 10 units

The answer is D.

(a) Let [tex]A(t)[/tex] denote the amount of sugar in the tank at time [tex]t[/tex]. The tank starts with only pure water, so [tex]\boxed{A(0)=0}[/tex].

(b) Sugar flows in at a rate of

(0.07 kg/L) * (7 L/min) = 0.49 kg/min = 49/100 kg/min

and flows out at a rate of

(A(t)/1080 kg/L) * (7 L/min) = 7A(t)/1080 kg/min

so that the net rate of change of [tex]A(t)[/tex] is governed by the ODE,

[tex]\dfrac{\mathrm dA(t)}[\mathrm dt}=\dfrac{49}{100}-\dfrac{7A(t)}{1080}[/tex]

or

[tex]A'(t)+\dfrac7{1080}A(t)=\dfrac{49}{100}[/tex]

Multiply both sides by the integrating factor [tex]e^{7t/1080}[/tex] to condense the left side into the derivative of a product:

[tex]e^{\frac{7t}{1080}}A'(t)+\dfrac7{1080}e^{\frac{7t}{1080}}A(t)=\dfrac{49}{100}e^{\frac{7t}{1080}}[/tex]

[tex]\left(e^{\frac{7t}{1080}}A(t)\right)'=\dfrac{49}{100}e^{\frac{7t}{1080}}[/tex]

Integrate both sides:

[tex]e^{\frac{7t}{1080}}A(t)=\displaystyle\frac{49}{100}\int e^{\frac{7t}{1080}}\,\mathrm dt[/tex]

[tex]e^{\frac{7t}{1080}}A(t)=\dfrac{378}5e^{\frac{7t}{1080}}+C[/tex]

Solve for [tex]A(t)[/tex]:

[tex]A(t)=\dfrac{378}5+Ce^{-\frac{7t}{1080}}[/tex]

Given that [tex]A(0)=0[/tex], we find

[tex]0=\dfrac{378}5+C\implies C=-\dfrac{378}5[/tex]

so that the amount of sugar at any time [tex]t[/tex] is

[tex]\boxed{A(t)=\dfrac{378}5\left(1-e^{-\frac{7t}{1080}}\right)}[/tex]

(c) As [tex]t\to\infty[/tex], the exponential term converges to 0 and we're left with

[tex]\displaystyle\lim_{t\to\infty}A(t)=\frac{378}5[/tex]

or 75.6 kg of sugar.

Answer: 72576m7

Step-by-step explanation:

2m x 8m x 6m x 9m x 7m x 6m x 2m

All together equals my answer 72576m7

Hope this helps!

Answer:

1.649 approximately 2

Step-by-step explanation:

S.d = standard deviation = 0.5

Time taken = lead time = 2 weeks

Mean = demand for week = 5 boxes

We are required to find the safety stock to maintain at 99% service level.

At 99% level, the Z value is equal to 2.326.

Therefore,

Safety stock = z × s.d × √Lt

= 2.326 × 0.5 x √2

= 1.649

Which is approximately 2.

Answer:

a.  1-step transition matrix is be expressed as:

[tex]P= \left[\begin{array}{cc}0.75&0.25\\0.45&0.55\\\end{array}\right][/tex]

b. The probability that he will be in City A after two trips given that he is in City B  = 0.585

c. After many trips, the probability that he will be in city B = 0.3571

Step-by-step explanation:

Given that:

For each trip, if the driver is in city A, the probability that he has to drive passengers to city B is 0.25

If he is in city B, the probability that he has to drive passengers to city A is 0.45.

The objectives are to calculate the following :

a. What is the 1-step transition matrix?

To  determine the 1 -step transition matrix

Let the State ∝ and State β denotes the Uber Driver providing service in City A and City B respectively.

∴  The transition probability from state ∝ to state β is 0.25.

The transition probability from state ∝ to state ∝ is 1- 0.25 = 0.75

The transition probability from state β to state ∝ is 0.45. The transition probability from state β to state β is 1 - 0.45 = 0.55

Hence; 1-step transition matrix is be expressed as:

[tex]P= \left[\begin{array}{cc}0.75&0.25\\0.45&0.55\\\end{array}\right][/tex]

b. Suppose he is in city B, what is the probability he will be in city A after two trips?

Consider [tex]Y_n[/tex] = ∝ or β  to represent the Uber driver is in City A or City B respectively.

∴ The probability that he will be in City A after two trips given that he is in City B

=[tex]P(Y_0 = 2, Y_2 = 1 , Y_3 = 1) + P(Y_0 = 2, Y_2 = 2 , Y_3 = 1)[/tex]

= 0.45 × 0.75 + 0.55 × 0.45

= 0.3375 + 0.2475

= 0.585

c. After many trips between the two cities, what is the probability he will be in city B?

Assuming that Ф = [ p  q ] to represent the long run proportion of time that Uber driver is in City A or City B respectively.

Then, ФP = Ф  , also  p+q = 1  , q = 1 - p  and p = 1 - q

∴

[tex][ p\ \ \ q ] = \left[\begin{array}{cc}0.75&0.25\\0.45&0.55\\\end{array}\right] [ p\ \ \ q ][/tex]

0.75p + 0.45q = q

-0.25p + 0.45q = 0

since p = 1- q

-0.25(1 - q) + 0.45q = 0    

-0.25 + 0.25 q + 0.45q = 0

0.7q = 0.25

q = [tex]\dfrac{0.25} {0.7 }[/tex]

q =  0.3571

After many trips, the probability that he will be in city B = 0.3571

3x ⁴ = 3x ² • x ². Then

(3x ⁴ - 2x ³ + 4x - 5) - 3x ² (x ² + 4) = -2x ³ - 12x ² + 4x - 5

-2x ³ = -2x • x ². Then

(-2x ³ - 12x ² + 4x - 5) - (-2x) (x ² + 4) = -12x ² + 12x - 5

-12x ² = -12 • x ². Then

(-12x ² + 12x - 5) - (-12) (x ² + 4) = 12x + 43

So we've shown

[tex]\displaystyle \frac{3x^4-2x^3+4x-5}{x^2+4} = 3x^2 - \frac{2x^3+12x^2-4x+5}{x^2+4} \\\\ = 3x^2 - 2x - \frac{12x^2-12x+5}{x^2+4} \\\\ = \boxed{3x^2 - 2x - 7 + \frac{12x+43}{x^2+4}}[/tex]

Answer:

Step-by-step explanation:

Hello,

[tex]r^3s^{-2}\cdot 8r^{-3}s^4\cdot 4rs^5\\\\=r^{3-3+1}s^{-2+4+5}\cdot 8\cdot 4\\\\\boxed{=32\cdot r\cdot s^7}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

24/25

Step-by-step explanation:

In this triangle DF and FE are legs (because they form the right angle) , ED is the hypotenuse (it is the largest side, it is opposite to the right angle).

son of E is the ratio of the leg opposite to the angle E (DF) to the hypotenuse

it is 24/25

Answer:

The answer is 4 + 4 + 4 - 4 = 8

Step-by-step explanation:

The four fours problem is one of the problems given in the book "The Man Who Calculated" by Malba Tahan, a Brazilian-born professor of mathematical sciences.

There are many complicated problems in this book made with the intention of using logic to find a value.

The 4 fours problem is based on using these numbers and using any operation to result in the numbers 1 through 10.

Answer:

B is the correct answer.

Step-by-step explanation:

-2x+3y+z=-6

z=6

-2x+3y+6=-6

-2x+3y=-12

-2(3)+3(2)

-6+6=0 A is incorrect

-2(3)+3(-2)=-12

-6-6=-12

B is the correct answer.

I am not going to show C or D, because you have the right answer. Hope this helps you. Thank you.

[tex] \Large{ \boxed{ \bf{ \color{purple}{Solution:}}}}[/tex]

Let the smaller angle be x

Then, Larger angle would be x + 4°

❍ They are complementary angles.

So,

➙ x + x + 4° = 90°

➙ 2x + 4° = 90°

➙ 2x = 86°

➙ x = 86°/2 = 43°

Then, x + 4° = 47°

So, Our required answer:

❍ They are supplementary angles.

So,

➙ x + x + 4° = 180°

➙ 2x + 4° = 180°

➙ 2x = 176°

➙ x = 176°/2 = 88°

Then, x + 4° = 92°

So, Our required answer:

✌️ Hence, solved !!

━━━━━━━━━━━━━━━━━━━━

[tex]_nC_k=\dfrac{n!}{k!(n-k)!}\\\\\\_{34}C_{34}=\dfrac{34!}{34!0!}=1[/tex]

In general, [tex]_nC_n=1[/tex]

Answer:

A, B

Step-by-step explanation:

Square both sides

5x+1=sqr7        (sqr is square root)

Isolate x

x=sqr7-1/5

Because the square root can also be negative, -sqr7 is also an answer

Answer:

Drag the ruler over each side of the triangle to find its length.

The length of AB is

✔ 5

.

The length of BC is

✔ 4

.

Drag the protractor over each angle to find its measure.

The measure of angle C is

✔ 90°

.

The measure of angle B is

✔ 36.9°

.

Step-by-step explanation:

The length of sides AB and BC of the triangle will be 5 units and 4 units. And the measure of angle C and angle B of the triangle will be 90° and 37°.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Drag the ruler over each side of the triangle to find its length.

The length of side AB of the triangle is 5 units.

The length of side BC of the triangle is 4 units.

Drag the protractor over each angle to find its measure.

The measure of angle C of the triangle is 90°.

The measure of angle B of the triangle is 37°.

The length of sides AB and BC of the triangle will be 5 units and 4 units.

And the measure of angle C and angle B of the triangle will be 90° and 37°.

More about the right-angle triangle link is given below.

https://brainly.com/question/3770177

#SPJ2

Answer:

[tex]x=129[/tex] °

Step-by-step explanation:

A secant is a line that intersects a circle in two places. The secants interior angle theorem states that when two secants intersect a circle inside a circle, the measure of any one of the angles formed is equal to half of the sum of the two intersecting arcs. Therefore, one can apply this theorem here:

[tex]x=\frac{204+54}{2}[/tex]

Simplify,

[tex]x=\frac{204+54}{2}[/tex]

[tex]x=\frac{258}{2}[/tex]

[tex]x=129[/tex]

Answer:

C. 9

Step-by-step explanation:

Start plugging in the number 2

3(2)^2+3(2)-9

6^2+6-9

12+6-9

18-9

9

Answer:

32 DAT yang tersembunyi do 3 Dan 2 semoga membatu

Answer:

Step-by-step explanation:

The summary of the given data includes;

sample size for the first school [tex]n_1[/tex] = 42

sample size for the second school [tex]n_2[/tex]  = 34

so 16 out of 42 i.e [tex]x_1[/tex] = 16 and 18 out of 34 i.e [tex]x_2[/tex] = 18 have ear infection.

the proportion of students with ear infection Is as follows:

[tex]\hat p_1 = \dfrac{16}{42}[/tex] = 0.38095

[tex]\hat p_2 = \dfrac{18}{34}[/tex]  =  0.5294

Since this is a two tailed test , the null and the alternative hypothesis can be computed as :

[tex]H_0 :p_1 -p_2 = 0 \\ \\ H_1 : p_1 - p_2 \neq 0[/tex]

level of significance ∝ = 0.05,

Using the table of standard normal distribution, the value of z that corresponds to the two-tailed probability 0.05 is 1.96. Thus, we will reject the null hypothesis if the value of the test statistics is less than -1.96 or more than 1.96.

The test statistics for the difference in proportion can be achieved by using a pooled sample proportion.

[tex]\bar p = \dfrac{x_1 +x_2}{n_1 +n_2}[/tex]

[tex]\bar p = \dfrac{16 +18}{42 +34}[/tex]

[tex]\bar p = \dfrac{34}{76}[/tex]

[tex]\bar p = 0.447368[/tex]

[tex]\bar p + \bar q = 1 \\ \\ \bar q = 1 -\bar p \\ \\\bar q = 1 - 0.447368 \\ \\\bar q = 0.552632[/tex]

The pooled standard error can be computed by using the formula:

[tex]S.E = \sqrt{ \dfrac{ \bar p \bar q}{ n_1} + \dfrac{\bar p \bar p}{n_2} }[/tex]

[tex]S.E = \sqrt{ \dfrac{ 0.447368 * 0.552632}{ 42} + \dfrac{ 0.447368 * 0.447368}{34} }[/tex]

[tex]S.E = \sqrt{ \dfrac{ 0.2472298726}{ 42} + \dfrac{ 0.2001381274}{34} }[/tex]

[tex]S.E = \sqrt{ 0.01177284105}[/tex]

[tex]S.E = 0.1085[/tex]

The test statistics is ;

[tex]z = \dfrac{\hat p_1 - \hat p_2}{S.E}[/tex]

[tex]z = \dfrac{0.38095- 0.5294}{0.1085}[/tex]

[tex]z = \dfrac{-0.14845}{0.1085}[/tex]

z = - 1.368

Decision Rule: Since the test statistics is greater than the rejection region - 1.96 , we fail to reject the null hypothesis.

Conclusion: There is insufficient evidence to support the claim that a difference exists between the proportions of students who have ear infections at the two schools

Answer:

Hi, there!!!

I hope you mean to evaluate cosA+ sonA /cosA - sinA.

so, i hope the answer in pictures will help you.

Answer:

y=2x-3

Step-by-step explanation:

4x-2y=3

-2y=3-4x

2y=4x-3

y=4x/2-3/2

y=2x-1.5  m1=2 (the number near x)

If the searched line is parallel to the line 4x−2y=3, m1=m2= 2

y=m2x+b - the searched line

1=2*2+b

b=-3

y=2x-3

Answer:

1.86

Step-by-step explanation:

Given the following :

X : - - - - 0 - - - - 1 - - - - 2 - - - - - 3 - - - - 4

P(x) - 0.37 - - 0.28 - - 0.22 - - 0.22 - - 0.12

The mean of the distribution can be calculated by evaluated by determining the expected value of the distribution given that the data above is a discrete random variable. The mean value can be deduced multiplying each possible outcome by the probability of it's occurrence.

Summation of [P(x) * X] :

(0.37 * 0) + (0.28 * 1) + (0.22 * 2) + (0.22 * 3) + (0.12 * 4)

= 0 + 0.28 + 0.44 + 0.66 + 0.48

= 1.86

Answer:

Daniel sold 54 and Jack sold 42

Step-by-step explanation:

D = number of tickets that Daniel sold

J = number of tickets that Jack sold

D + J = 96

D = 12+ J

Substitute the second equation into the first equation

12 + J + J = 96

Combine like terms

12 + 2J = 96

Subtract 12 from each side

2J = 84

Divide by 2

J = 42

D = J+12

D = 54

Daniel sold 54 and Jack sold 42

Answer:

Jack sold 42 & Daniel sold 54.

Step-by-step explanation:

96 - 12 = 84

84 / 2 = 42

Jack sold 42.

42 + 12 = 54

Daniel sold 54.

42 + 54 = 96

Answer:

5

Step-by-step explanation:

This shape is formed by two right triangles.

Let's start by the little one.

Let y be the third side.

Using the Pythagorian theorem we get:

y^2 = 6^2 + 3^2

y^2 = 36 + 9

y^2 = 45

y = 3√(5)

●●●●●●●●●●●●●●●●●●●●●●●●

Now let's focus on the second triangle. Let z be the third side.

The Pythagorian theorem:

6^2 + x^2 = z^2

Using the Pythagorian theorem on the big triangle :

[3√(5)]^2 + z^2 = (3+x)^2

45 + z^2 = 3x^2 + 6x + 9

36 +z^2 = 3x^2 +6x

So we have a system of equations.

36+ x^2 = z^2

36 +z^2 = 3x^2 +6x

We want to khow the value of x so we will eliminate z .

Add (36+x^2 -z^2 =0) to the second one.

36 + x^2-z^2+36+z^2 = 3x^2+6x

72 + x^2 = 3x^2 +6x

72 - 2x^2 -6x = 0

Multipy it by -1 to reduce the number of - signs

2x^2 + 6x -72 = 0

This is a quadratic equation

Let A be the discriminant

● a = 2

● b = 6

● c = -72

A = b^2-4ac

A = 36 -4*2*(-72) = 36 + 8*72 =612

So this equation has two solutions

The root square of 612 is approximatively 25.

● (-6-25)/4 = -31/4 = -7.75

● (-6+25)/4 = 19/4 = 4.75 wich is approximatively 5

A distance cannot be negative so x = 5

Work Shown:

Replace x with 3, replace y with -8. Use order of operations PEMDAS to simplify.

x^2 + y^2 + x*y

3^2 + (-8)^2 + 3*(-8)

9 + 64 - 24

73 - 24

49

Answer:

49

Step-by-step explanation:

We are given the polynomial:

[tex]x^2+y^2+xy[/tex]

We want to evaluate when x=3 and y= -8. Therefore, we must substitute 3 for each x and -8 for each y.

[tex](3)^2+(-8)^2+(3*-8)[/tex]

Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

Solve the parentheses first. Multiply 3 and -9.

3*-8=-24

[tex](3)^2+(-8)^2 + -24[/tex]

[tex](3)^2+(-8)^2-24[/tex]

Now, solve the exponents.

3^2= 3*3 =9

[tex]9+ (-8)^2 -24[/tex]

-8^2= -8*-8= 64

[tex]9+64-24[/tex]

Add 9 and 64

[tex]73-24[/tex]

Subtract 24 from 73

[tex]49[/tex]

The polynomial evaluated for x=3 and y= -8 is 49.

Answer:

16% of 242 = 38.72

Step-by-step explanation:

16% = 16/100 = 0.16

242 * 0.16 = 38.72

Answer:

38.72

Step-by-step explanation:

242 * .16 = 38.72

Answer:

[tex]Probability = \frac{1}{3}[/tex]

Step-by-step explanation:

Given

[tex]Set:\ \{1, 2, 3, \ldots, 24\}[/tex]

[tex]n(Set) = 24[/tex]

Required

Determine the probability of selecting a factor of 4!

First, we have to calculate 4!

[tex]4! = 4 * 3 * 2 * 1[/tex]

[tex]4! = 24[/tex]

Then, we list set of all factors of 24

[tex]Factors:\ \{1, 2, 3, 4, 6, 8, 12, 24\}[/tex]

[tex]n(Factors) = 8[/tex]

The probability of selecting a factor if 24 is calculated as:

[tex]Probability = \frac{n(Factor)}{n(Set)}[/tex]

Substitute values for n(Set) and n(Factors)

[tex]Probability = \frac{8}{24}[/tex]

Simplify to lowest term

[tex]Probability = \frac{1}{3}[/tex]

Answer:

$247

Step-by-step explanation:

$95 = 5 h

1 h = 95 ÷ 5 = $19/h

$19 × 13h = $247

she would make $247 after 13 hours of work.

From eq(1)

[tex]\\ \sf\longmapsto x=3-3y\dots(3)[/tex]

Putting the value in eq(2)

[tex]\\ \sf\longmapsto 3y-2(3-3y)=12[/tex]

[tex]\\ \sf\longmapsto 3y-6-6y=12[/tex]

[tex]\\ \sf\longmapsto -3y-6=12[/tex]

[tex]\\ \sf\longmapsto -3y=12+6[/tex]

[tex]\\ \sf\longmapsto -3y=18[/tex]

[tex]\\ \sf\longmapsto y=\dfrac{18}{-3}[/tex]

[tex]\\ \sf\longmapsto y=-6[/tex]

Putting value in eq(3)

[tex]\\ \sf\longmapsto x=3-3(-6)[/tex]

[tex]\\ \sf\longmapsto x=3+18[/tex]

[tex]\\ \sf\longmapsto x=21[/tex]

Answer:

x=-3 & y=2

Step-by-step explanation:

x+3y=3----(i)

3y-2x=12----(ii)

Solving eqn--(i)

x+3y=3

or, x=3-3y---(iii)

Substituting the value of x from eqn --(iii) in eqn (ii) ,we get

3y-2x=12

or, 3y-2(3-3y)=12

or, 3y-6+6y=12

or,9y=18

y=18/9=2

Substituting the value of x in eqn--(iii),

x=3-3y=3-3*2=3-6=-3