The quadratic coefficient (the number multiplying t^2) depends only on gravity, and will be the same in all free-fall situations. Using the value determined from the experiment earlier, how tall is the balcony in the video, if it takes 1.4 seconds for the ball to hit the ground?


Height: ________ meters (to at least 1 decimal place)

Answer:

1. slope = -x, Y-intercept = 2

2. slope = -1/3,Y-intercept = 2

3. slope = 5/2, Y-intercept = 2

4. slope = -2, Y-intercept = 1

5. slope = -3/4, Y-intercept = 2

Step-by-step explanation:

To find the slope and y-intercept you have to solve the equation. You only have to solve for 2 and 3. 1, 4, and 5 already have the equations solved. For questions 1, 4, and 5 the first number is the slope and the second number is the y-intercept. For questions 2 and 5 you have to solve the equations. You have to bring the y to the right side of the equation. to do that you subtract the y. Then you have to bring the number that was already on the right side of the equation to the left side. To do this you also have to subtract that number to bring it to the other side. Now you have to get the y by its self, and to do this you divide the equation. You divide both sides of the equation. Then you can get the slope and y-intercept.

Answer

187.5 ml/hr

Step-by-step explanation:

1500ml/8hrs=187.5ml/hr

Answer:

The answer is "[tex]y=\frac{c}{1+a}[/tex]".

Step-by-step explanation:

Given:

[tex]\bold{y=\frac{c}{1+ae^{-rx}}}[/tex]

For the y-intercept, the value x is =0

[tex]y=\frac{c}{1+ae^{-r \times 0}}[/tex]

[tex]y=\frac{c}{1+ae^{0}}[/tex]

[tex]\therefore e^0 = 1[/tex]

[tex]y=\frac{c}{1+a\times 1}}[/tex]

[tex]\boxed{y=\frac{c}{1+a}}[/tex]

Answer:

The inverse is (x+6)/7

Step-by-step explanation:

y = 7x-6

To find the inverse, exchange x and y

x = 7y-6

Solve for y

x+6 = 7y

Divide each side by 7

(x+6)/7 = y

The inverse is (x+6)/7

Answer:

Her eye discourses; I will answer it.

I am too bold; ’tis not to me she speaks:

Two of the fairest stars in all the heaven,

Having some business, do entreat her eyes

To twinkle in their spheres till they return.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The p value (probability of obtaining results as extreme the z score if null is true) is usually the value derived to make a conclusion and in this case the p value is 0.03

The level of significance is the value usually compared with the p value which is 0.05

The sample promotion is 65 out of 100 = 65/100 = 0.65

The sample size is the total number of consumers which is 100

The null value is usually the default value. The null value would assume that there is no difference in the proportions who prefer each type in the population. There are two preferences: 100/2 = 50- 0.5 for each preference.

Answer:

(x + 2)(x - 6)

Step-by-step explanation:

We are given the equation: x² - 4x - 12. Let's factor this.

First, look at the integer factor pairs of -12:

-1, 12

-2, 6

-3, 4

1, -12

2, -6

3, -4

We would like to find a pair whose sum is -4. Inspecting each pair, we realise that only the pair 2, -6 works because 2 + (-6) = -4.

Thus, our factors are:

x + 2    (from the 2)

x - 6     (from the -6)

The factored form of our given quadratic is:

(x + 2)(x - 6)

~ an aesthetics lover

Answer:

G(2b) = 10b + 3

Step-by-step explanation:

To find G(2b), simply plug in 2b wherever there is an x in G(x).

G(x) = 5x + 3

G(2b) = 5(2b) + 3

G(2b) = 10b + 3

Answer:

3 + 10b maybe?

Step-by-step explanation:

Answer:

None of these choices are correct

Step-by-step explanation:

Law of exponents

3^(x+5) = 9^(-1)

3^(x+5) = (3²)^(-1)

3^(x+5) = 3^(-2)

Same base, same power or exponents

x+5 = -2

x = -2 -5

x = -7

Answersin -> 48

Step-by-step explanation:

solve for the length of the horizontal line by doing:

sin(55)=x/58

rearrange: x = sin(55) times 58 = 47.51

round UP to 48

Answer:

  1.2b

Step-by-step explanation:

When we say, "a number that is 20% greater than b," we're talking about a number that is ...

  b + 20%×b

  = b + 0.20b

  = b(1 + 0.20)

  = 1.2b

Answer: 0.0899.

Step-by-step explanation:

Given: CNNBC recently reported that the mean annual cost of auto insurance is 1048 dollars, the standard deviation is 282 dollars.

Sample size : n= 55

Let [tex]\overline{X}[/tex] be the sample mean.

The probability that a sample of size n =55 is randomly selected with a mean less than 997 dollars:

[tex]P(\overline{X}<997)=P(\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}<\dfrac{997-1048}{\dfrac{282}{\sqrt{55}}})[/tex]

[tex]=P(Z<-1.3412)\ \ \ [Z=\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=1-P(Z<1.3412)\\\\=1-0.9101\ \ \ \ [\text{By z-table}]\\\\ =0.0899[/tex]

Hence, the required probability = 0.0899 .

Answer:

6/4

Step-by-step explanation:

Answer:

6/4

Step-by-step explanation:

There are 6 brooms to 4 mops.

So you would write it that way as a fraction, but you could also write it like 6:4 or 6 to 4.

Answer:

Going from up to down

Box #1=0

Box #2=3

Box #3=5

Step-by-step explanation:

Answer:

Step-by-step explanation:

Going from up to down

Box #1=0

Box #2=3

Box #3=5

Answer:

The answer is "[tex]= \frac{\pi}{8}(15-41n^2 )\\[/tex]".

Step-by-step explanation:

The radius = x

the value of height is= [tex]e^{-x}[/tex]

The Formula for  the volume by the shell method:

[tex]\bold{V= \int\limits^b_a {(2\pi\ rad)(height)} \, dx }[/tex]

   [tex]= 2\pi \int\limits^{In 16}_0 {xe^{-x}} \, dx\\\\\\= 2\pi {(e^{-x}[-x-1])}_{0}^{In 16}\\\\ = 2\pi {(\frac{1}{16} \times (15-41n^2 ))}\\\\ = \frac{\pi}{8}(15-41n^2 )\\[/tex]

Answer:

Number:3.75

Equation:7 x-9=3(x+2)

Step-by-step explanation:

Let the number be x.

According to the question,

7 x-9=3(x+2)

7 x-9= 3 x+ 6

7 x- 3 x= 9+6

4 x= 15

x=15/4

x=3.75

If you verify the answer you will get,

11.25=11.25

Thank you!

Answer:

The principal must be = $8991.88

Step-by-step explanation:

Formula for compound interest is:

[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]

Where A is the amount after 't' years.

P is the principal amount

n is the number of times interest is compounded each year.

r is the rate of interest.

Here, we are given that:

Amount, A = $15000

Rate of interest = 13 % compounded quarterly i.e. 4 times every year

Number of times, interest is compounded each year, n = 4

Time, t = 4 years.

To find, Principal P = ?

Putting all the given values in the formula to find P.

[tex]15000 = P(1 + \frac{13}{400})^{4\times 4}\\\Rightarrow 15000 = P(1 + 0.0325)^{16}\\\Rightarrow 15000 = P(1.0325)^{16} \\\Rightarrow 15000 = P \times 1.66817253\\\Rightarrow P = \dfrac{15000}{1.66817253}\\\Rightarrow P \approx \$8991.88[/tex]

So, the principal must be = $8991.88

The principal required is $ 8993.

Using the formula;

A = P(1 + r/n)^nt

Where;

P = principal = ?

r = rate = 0.13

n = Number of times the interest is compounded = 4

t = time = 4years

Amount = $15,000

15,000 = P(1 +  0.13/4)^4(4)

15,000 = P(1.668)

P = 15,000/1.668

P =$ 8993

Learn more: https://brainly.com/question/7558603

Answer:

[tex]\boxed{A=\sqrt{s(s-a)(s-b)(s-c)}}[/tex]

Step-by-step explanation:

We can use Heron’s formula to determine the area of a triangle when three side lengths of a triangle are given.

[tex]s=\frac{a+b+c}{2}[/tex]

[tex]s : \mathrm{semi \: perimeter}[/tex]

[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]

[tex]A : \mathrm{area}[/tex]

Answer:

Heron's formula gives the area of a triangle when the length of all three sides are known. Use Heron's formula to find the area of triangle ABC, if AB=3,BC=2,CA=4 . Substitute S into the formula . Round answer to nearest tenth.

Step-by-step explanation:

Answer:

63m

Step-by-step explanation:

A pool that is 2.9m tall cast a shadow that is 1.76m

At the same time, a nearby building casts a shadow that is 38.25m long.

We are to find the height of the building.

If an object of length 2.9m cast an image of 1.76m ,

Then an image of 38.25m willl be cast by an object of what length?

Cross multiplying this gives:

[tex]\frac{38.25 * 2.9}{1.76}[/tex]  = 63.02556818  = 63m (rounded up to nearest meter)

Answer:

You'll need 2.8 gallons of the 80% solution.

Step-by-step explanation:

Let the volume of 30% alcohol =x gallons

Then the volume of 80% alcohol =(14-x) gallons

Since we want to obtain a 40% alcohol solution, we have:

0.3x+0.8(14-x)=0.4(14)

0.3x+11.2-0.8x=5.6

0.8x-0.3x=11.2-5.6

0.5x=5.6

x=11.2

Therefore, the volume of 80% alcohol

=14-11.2

=2.8 gallons

You'll need 2.8 gallons of the 80% solution.

Answer:

H0: μ=2; Ha: μ>2

Step-by-step explanation:

The null hypothesis is the default hypothesis while the alternative hypothesis is the opposite of the null and is always tested against the null hypothesis.

In this case study, the null hypothesis is that adults were eating, on average, the recommended 2 cups of vegetables a day: H0: μ=2 while the alternative hypothesis is adults were eating, on average, more than the recommended 2 cups of vegetables a day Ha: μ>2.

Answer:

[tex]\Large \boxed{\sf \ \ 7 \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

The polynomial function is

[tex]x^3-5x^2-12x+14[/tex]

The rational root theorem states that each rational solution

   [tex]x=\dfrac{p}{q}[/tex]    

, written in irreducible fraction, satisfies the two following:

   p is a factor of the constant term

   q is a factor of the leading coefficient

In this example, the constant term is 14 and the leading coefficient is 1. It means that p is a factor of 14 and q a factor of 1.

Let's proceed with the prime factorisation of 14:

14 = 2 * 7

Finally, the possible rational roots of this expression are :

   1

   2

   7

   14

and we need to test for negative ones too

   -1

   -2

   -7

   -14

From your list, the correct answer is 7.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

the answer is C.) 7

Answer:

j/2+7= -12

(j+14)/2= -12

cross-multiply

j+14= -24

j= -38

Answer:

[tex]\boxed{j=-38}[/tex]

Step-by-step explanation:

[tex]\frac{j}{2} +7=-12[/tex]

Subtract 7 on both sides.

[tex]\frac{j}{2} +7-7=-12-7[/tex]

[tex]\frac{j}{2}=-19[/tex]

Multiply both sides by 2.

[tex]\frac{j}{2}(2)=-19(2)[/tex]

[tex]j=-38[/tex]

Answer:

ans1 9/11

ans2 8/52

it is because the reciprocol means the opposite of the the give value

Answer:

Step-by-step explanation:

a.

[tex] \frac{11}{9} [/tex]

Just flip the fraction, you will get:

[tex] \frac{9}{11} [/tex]

b.

[tex]5 \frac{1}{8} [/tex]

The first thing you have to do is that convert the mixed fraction into improper fraction.

To convert mixed fraction into improper fraction, you have to rewrite the denominator which is 8 , Thenafter you have to multiply 5 and 8 and then add 1

It would be:

[tex] \frac{5 \times 8 + 1}{8} [/tex]

[tex] = \frac{40 + 1}{8} [/tex]

[tex] = \frac{41}{8} [/tex]

Now , you have to flip it in order to get reciprocal:

[tex] = \frac{8}{41} [/tex]

Answer: There is sufficient evidence to conclude that the proportion of agenda-less meetings is greater than 45%.

Step-by-step explanation:

Given: [tex]H_0:p=0.45 \\ H_a:p>0.45[/tex]

The p-value for this hypothesis test is 0.025.

The level of significance is α=0.05

As p-value< α  ∵0.025< 0.05

[if p-value< α , we reject [tex]H_0[/tex]]

then, we reject the null hypothesis.

i.e. We have sufficient evidence to support the alternative hypothesis.

Hence, the correct statement is : There is sufficient evidence to conclude that the proportion of agenda-less meetings is greater than 45%.

Answer:4

Step-by-step explanation:

Simplify what you can which is 0.1m-1.3m

you end up getting -1.2m

Now do the other side of the equation which is  2.1-2.7 which is -4.8

Divide -4.8 by -1.2 to get m=4

Answer: m=4

Step-by-step explanation:

[tex]0.1m-1.3m=-2.1-2.7[/tex]

add like terms

[tex]-1.2m=-2.1-2.7[/tex]

subtract

[tex]-2.1-2.7=-4.8[/tex]

[tex]-1.2m=-4.8[/tex]

multiply both sides by 10

[tex]-12m=-48[/tex]

divide -12 on both sides

m=4

Answer:

The 95% confidence interval for true average degree of polymerization is (431, 446).

Step-by-step explanation:

The data provided for the degree of polymerization for paper specimens for which viscosity times concentration fell in a certain middle range is:

S = {418, 421, 422, 422, 425, 429, 431, 434, 437,  439, 446, 447, 449, 452, 457, 461, 465}

Compute the sample mean and sample standard deviation:

[tex]\bar x=\frac{1}{n}\sum X=\frac{1}{7}\times 7455=438.5294\\\\s=\sqrt{\frac{1}{n-1}\sum (X-\bar x)^{2}}=\sqrt{\frac{1}{17-1}\times 3594.2353}=14.988[/tex]

As the population standard deviation is not provided use the t-statistic to compute the two-sided 95% confidence interval for true average degree of polymerization.

[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\cdot\frac{s}{\sqrt{n}}[/tex]

The critical value of the t is:

[tex]t_{\alpha /2, (n-1)}=t_{0.05/2, (17-1)}=t_{0.025, 16}=2.12[/tex]

*Use a t-table.

Compute the 95% confidence interval for true average as follows:

[tex]CI=438.5294\pm 2.12\cdot\frac{14.988}{\sqrt{17}}[/tex]

     [tex]=438.5294\pm 7.7065\\=(430.8229, 446.2359)\\\approx (431, 446)[/tex]

Thus, the 95% confidence interval for true average degree of polymerization is (431, 446).

Answer:

[tex]P(\overline X < 2.3) = 0.9999[/tex]

Step-by-step explanation:

Given that:

mean = 2

standard deviation = 0.5

sample size = 50

The probability that the sample mean is less than 2.3 hours is :

[tex]P(\overline X < 2.3) = P(Z \leq \dfrac{\overline x - \mu}{\dfrac{\sigma}{\sqrt{n}}})[/tex]

[tex]P(\overline X < 2.3) = P(Z \leq \dfrac{2.3 - 2.0}{\dfrac{0.5}{\sqrt{50}}})[/tex]

[tex]P(\overline X < 2.3) = P(Z \leq \dfrac{0.3}{0.07071})[/tex]

[tex]P(\overline X < 2.3) = P(Z \leq 4.24268)[/tex]

[tex]P(\overline X < 2.3) = P(Z \leq 4.24)[/tex]

From z tables;

[tex]P(\overline X < 2.3) = 0.9999[/tex]

Hi,

[tex]A=\frac{base_{1} +base_{2} }{2} *h\\\\A=(base_{1} +base_{2} ) *h *\frac{1}{2} \\\\A=(70ft + 130ft) * 50ft *\frac{1}{2} \\\\A=5000ft^{2}[/tex]

each bag covers 3000 ft²

[tex]N_{number of bags} = 5000ft^{2} / 3000ft^{2} \\\\N_{number of bags} = 1.6[/tex]

We need to purchase two bags fertilizer, but will use one and a half of them.

Have a good day.