Need help with two questions please

Answer:

  after 3.92 seconds

Step-by-step explanation:

Fill in the given value of h to find the formula for the height of the ball. Then set the value of that height to zero and solve for t.

  [tex]h_2(t)=-16t^2+246\\\\0=-16t^2+246\\\\0 = t^2-15.375 \quad\text{divide by -16}\\\\\sqrt{15.375}=t \quad\text{add 15.375, take the square root}\\\\t\approx 3.92[/tex]

Ball 2 reaches the ground after 3.92 seconds.

Answer:

This statement is true

Step-by-step explanation:

Remember that subset F of a metric (or topological) space X is said to be closed if X-F is open according to the metric (topology) of F.

Let F⊆X. For the "if" part, suppose that [tex]F=F_1\cap F_2\cap \cdots \cap F_n[/tex] where [tex]F_k[/tex] is a closed set for all k. Then by De Morgan's law, [tex]X-F=(X-F_1)\cup(X-F_2)\cup \cdots\cup(X-F_n)[/tex].

Now, since Fk is closed for all k, then X-Fk is open. In every metric (topological) space, the union of an arbitrary family of open sets open sets is open, thus X-F is open, that is, F is closed.

For the "only if" implication, suppose that F is closed. We always have that F=F∩F (y∈F if and only if y∈F and y∈F if and only if y∈F∩F). then F is a finite intersection of closed sets (F and F).

Answer:

number 1

Step-by-step explanation:

if you'd look at Number One X is negative and if you look at the two number problems the x that is negative is negative for and then the one that is positive is the Y which is 3

Answer:D

Step-by-step explanation:

Given

There are 52 cards out which we have to choose 3 cards

and starting 2 will have same denomination

For first card we can withdraw any card of any denomination and for second card we have to choose card of same denomination

There are total of 4 cards of same denomination and after 1 st card is drawn we need to choose 1 card out of  3 card

Probability[tex]=\frac{^3C_1}{^{51}C_1}[/tex]

[tex]=\frac{3}{51}[/tex]  

Answer:

16

Step-by-step explanation:

Monday: 3

Thursday:3

Saturday:4

Sunday: 4

Tuesday:2

3+3+4+4 + 2 = 16

Answer:

The finance charge is $19.68

Step-by-step explanation:

The finance charge on a credit card is given by the formula:

Finance Charge = The Average Daily Balance x Monthly Periodic Rate

We know that:

Average Daily Balance = $875

Monthly Periodic Rate = 2.25% = 0.0225

Using in Formula:

Finance Charge = $875 x 0.0225

Finance Charge = $19.68

To calculate the finance charge on the statement, multiply the average daily balance by the monthly periodic rate.

To calculate the finance charge on the statement, we can use the formula:
Finance Charge = Average Daily Balance × Monthly Periodic Rate

First, convert the percentage rate to decimal form:
2.25% = 0.0225

Then, substitute the given values into the formula:
Finance Charge = $875 × 0.0225

Using a calculator, multiply $875 by 0.0225:
Finance Charge = $19.69

Therefore, the finance charge on the statement should be $19.69.

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Answer:

uo

Step-by-step explanation:

Answer:

1 ) B. {-5 , -4 , 2}

2 ) A. {-1 , 1 , 3}

Step-by-step explanation:

1. The range of a relation is an ordered pair of real numbers to which all the real numbers in the domain relate to.

Given the Relation R: { ( 3, -5 ) , ( 1 , 2 ) , (  -1 ,  -4 ) , ( -1 , 2 ) }

Here The Range is the ordered pair of number towards the right in each relation.

Range = { -5 , 2 , -4 }

2. The domain of a relation is an ordered pair of real numbers which are related to any one of the element in the range of the relation.

Given the Relation R: { ( 3 , -2 ) , ( 1 , 2 ) , ( -1 , -4 ) , ( -1 , 2 ) }

Here the domain is the ordered pair of numbers towards the left in each relation.

Domain = { -1 , 1 , 3 }

Answer: the second one

Step-by-step explanation:

cuz i say so

Answer:

4). But the more correct answer is; y is less than or equal to 14.

Step-by-step explanation:

Graphing this function shows a downward facing parabola with the vertex at (-10,14).  The domain must be less than or equal to 14 because it's all values including and below the vertex since there is negative a value (-1/2).

Explanation:

Imagine that white rectangle as a blade that cuts the cylinder as the diagram shows. If you pull the top cylinder off and examine the bottom of that upper piece, then you'll see a circle forms. It's congruent to the circular face of the original cylinder. This is because the cutting plane is parallel to both base faces of the cylinder. Any sort of tilt will make an ellipse form. Keep in mind that any circle is an ellipse, but not vice versa.

Another example of a cross section: cut an orange along its center and notice that a circle (more or less) forms showing the inner part of the orange.

Yet another example of a cross section: Imagine an egyptian pyramid cut from the top most point on downward such that you vertically slice it in half. If you pull away one half, you should see a triangular cross section forms.

Good morning,

Answer:

Step-by-step explanation:

Because the plane is parallel to the cylinder base.

:)

Answer:

The Function formula is given by [tex]c = 150 -8s[/tex].

Step-by-step explanation:

Given:

Number of candies eaten each time he has snacks = 8

Number of snacks ate = 18

Now Number of candies eaten will be equal to number of snacks he ate multiplied by number of candies eaten each time he ate snacks

Hence. Number of candies he ate in 18 snacks = 18* 8 = 144 candies

Also given that 6 candies are remaining after eating 18 snacks;

Total Number of candies at the beginning will be = Number of candies he ate in 18 snacks + Number of candies remaining after 18 snacks

Total Number of candies at the beginning will be = 144 + 6 = 150 candies

Now, let The number of pieces of candy remaining in the bag be 'c'

Also Let the number of snacks Tyrone eats be 's'

Since it has been given that in number of candies in each snack is 8 candies.

Therefore,In 's' snacks , candies will be eaten by him = [tex]8s[/tex]

Total number of candies = 150

Now Remaining candies 'c' is equal to Total number of candies minus number of candies eaten in 's' snacks.

framing in equation form we get;

Remaining candies [tex]c = 150 -8s[/tex]

Hence the Function formula is given by [tex]c = 150 -8s[/tex].

Answ300er:

300

24+36=60

60x5=300

Step-by-step explanation:

Answer:he would earn 300 points

Step-by-step explanation:

Let x represent the number of pirates that Craig catches.

Let y represent the number of ghosts that Craig catches.

Craig earns 5 points each time he catches a bad guy in his game. The total number of points that Craig will earn if he catches x pirates and y ghosts would be

5x + 5y

Craig caught 24 ghost and 36 pirates. Therefore, total number of points earned would be

5×36 + 5×24 = 180 + 120 = 300 points.

Answer:

The answer is 18,019 days.

Step-by-step explanation:

Answer:

8y-11z=5

Step-by-step explanation:

2x + y − 4z = 4, -----------A

2x + 4y + z = 15,-----------B

6x − 5y − z = 7------------C

Solving A to find the value of x

2x= 4-y+4z

x=4-y+4z/2------------------D

Putting D in C

6(4-y+4z/2) -5y -z=7

3(4-y+4z) -5y-z=7

12-3y+12z-5y-z=7

12-8y + 11z=7

-8y +11z= 7-12

-8y +11z= -5

8y-11z=5--------------E

Answer:

Step-by-step explanation:

[tex]f(x)=36x^5-44x^4-28x^3\\\\g(x)=4x^2\\\\\dfrac{f(x)}{g(x)}=\dfrac{36x^5-44x^4-28x^3}{4x^2}\\\\\dfrac{f(x)}{g(x)}=\dfrac{(4x^2)(9x^3)-(4x^2)(11x^2)-(4x^2)(7x)}{4x^2}\\\\\dfrac{f(x)}{g(x)}=\dfrac{(4x^2)(9x^3-11x^2-7x)}{4x^2}\qquad\text{cancel}\ 4x^2\\\\\dfrac{f(x)}{g(x)}=9x^3-11x^2-7x[/tex]

Answer:option C is the correct answer

Step-by-step explanation:

f(x) = 36x^5 − 44x^4 − 28x^3

g(x) = 4x^2

We want to determine f(x)/g(x). It becomes

(36x^5 − 44x^4 − 28x^3) /(4x^2)

Looking at the numerator, each term in the numerator can divide the term in the denominator without remainder. it means that the term in the denominator is a common factor of the numerator and thus, 4x^2 can be factorized out of the numerator. It becomes

4x^2(9x^3 − 11x^2 − 7x) /(4x^2)

4x^2 in the numerator cancels out 4x^2 in the denominator. It becomes

9x^3 − 11x^2 − 7x

Answer:

d. H0: p = .25 vs. Ha: p < .25

Step-by-step explanation:

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".  

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

On this case the claim that they want to test is: "If the proportion of 2005 has decreased from the info of 2004". So we want to check if the population proportion for 2005 is less than 0.25 (the value for 2004), so this needs to be on the alternative hypothesis and on the null hypothesis we need to have the complement of the alternative hypothesis.

Null hypothesis:[tex]p \geq 0.25[/tex]

The null hypothesis can be on this way: [tex]p=0.078[/tex], but is better put the complement of the alternative hypothesis.    

Alternative hypothesis:[tex]p > 0.25/tex]

And the correct option would be:

d. H0: p = .25 vs. Ha: p < .25

Answer:

[tex] x = 35-4-5-3-5-4-4=10[/tex]

So then the value for Saturday should be equal or higher to 10 servings per day in order to have an average of 5 or higher.

Step-by-step explanation:

First we can begin finding the original average for the first 6 days of the week. We assume that the week start at Sunday, and we have data for Sunday, Monday, Tuesday, Wednesday, Thrusday, Friday. And we can find the average like this:

[tex]\bar X_i =\frac{4+5+3+5+4+4}{6}=4.167[/tex]

And for this case we have the original average under the goal of 5, so we need to find a value x, such that the final average taking in count the 7 days of the week would be 5.

[tex]\bar X_f = \frac{4+5+3+5+4+4+x}{7}=5[/tex]

So we can nultiply both sides by 7 and we got:

[tex]4+5+3+5+4+4+x = 35[/tex]

And then solving for x we got:

[tex] x = 35-4-5-3-5-4-4=10[/tex]

So then the value for Saturday should be equal or higher to 10 servings per day in order to have an average of 5 or higher.

Answer: the BEST approximation of the amount of water her fish tank can hold is 21ft^3

Step-by-step explanation:

The shape of Samantha's fish tank is rectangular. The volume of the rectangular fish tank would be expressed as LWH

Where

L represents length of the tank

W represents the width of the tank.

H represents the height of the tank.

The tank has a height of 2.6 ft, a width of 2.1 ft, and a length of 3.9 ft.

This means that the volume of the fish tank would be

Volume = 2.6 × 2.1 × 3.9

= 21.294 ft^3

Annie paid 12800 pounds at end of 10 years

Solution:

Given that Annie borrows 8000 pounds at simple interest rate of 6 %

She also agrees to pay the loan back over a 10 year period

To find: total money paid back at the end of 10 years

The total amount paid is given as:

Total amount = simple interest + principal amount borrowed

The simple interest is given as:

[tex]S.I = \frac{pnr}{100}[/tex]

Where, "p" is the principal sum

"n" is the number of years

"r" is the rate of interest

Here, p = 8000 ; r = 6 % ; n = 10 years

[tex]S.I = \frac{8000 \times 10 \times 6}{100}\\\\S.I = 4800[/tex]

Therefore total amount paid at end of 10 years is:

Total amount = 4800 + 8000 = 12800

Thus Annie paid 12800 pounds at end of 10 years

Final answer:

Annie will pay a total of 12800 pounds at the end of 10 years for her loan of 8000 pounds with an annual simple interest rate of 6%.

Explanation:

To calculate the total amount of money Annie will have paid back at the end of 10 years on her loan of 8000 pounds with an annual simple interest rate of 6%, we first need to find the total interest she will pay over the period. Simple interest can be calculated using the formula: Interest = Principal × Rate × Time. In this case, the Principal (P) is 8000 pounds, the Rate (r) is 6% or 0.06 as a decimal, and the Time (t) is 10 years.

Interest = P × r × t = 8000 × 0.06 × 10 = 4800 pounds

The total amount of interest Annie will pay over 10 years is 4800 pounds. To find the total repayment amount, we add this interest to the original loan amount.

Total repayment = Principal + Interest = 8000 pounds + 4800 pounds = 12800 pounds

At the end of 10 years, Annie will have paid back a total of 12800 pounds.

Answer:

After 8 minutes and 25 sec time will be 12:00

Step-by-step explanation:

We have given initial time is 11:51:35

And we have to find the time after 8 minute and 25 second

After 8 minutes time will be 51+8 = 59 minutes

So after 8 minutes time will be 11:59:35

And after 25 second time will 25 +35 = 60 sec

60 sec = 1 minute

So after 8 minutes and 25 sec time will be 11:59:35 plus 25 sec = 12:00

Answer will be 12:00

Answer: There are 72 seats in order to be very sure of having enough seating.

Step-by-step explanation:

Since we have given that

Total number of seats is being planned = 120

Percentage of customers demand a smoke free area = 60%

So, Number of seats that should be in the non smoking area in order to be very of having enough seating would be

[tex]\dfrac{60}{100}\times 120\\\\=0.6\times 120\\\\=72[/tex]

Hence, there are 72 seats in order to be very sure of having enough seating.

Answer:

With replacement

 21C2 = 210 outcomes

without replacement

20C2 = 190 outcomes

Step-by-step explanation:

For determining the number of possible outcomes you need count the number of possible combinations, because a combination is a selection of a number of items from a set of items where the order of selection does not matter.

The number of possible combinations is calculated thus

nCr = [tex]\frac{n!}{(n-r)!r!}[/tex]

           Where n: number of items of the set

                        r: number of selected items

a) If the group of states are selected with replacement then

   (n+r-1)Cr  

   n = 20 states

   r = 2 states

  then n +r -1 = 20 +2 -1 = 21

  21C2 = [tex]\frac{21!}{(21-2)!2!} = 210[/tex]

b) If the group of states are selected without replacement then

 nCr

 n = 20

 r = 2

20C2 = [tex]\frac{20!}{(20-2)!2!} = 190[/tex]

When two states are chosen with replacement from 20, there are 400 possible outcomes. Without replacement, there are 380 possible outcomes.

The question asks for the number of possible outcomes if two states are selected at random from a group of 20 states, with and without replacement. Replacement means a state can be chosen more than once, while without replacement means a state can only be chosen once.

When selecting with replacement, a state can be chosen, replaced, and then chosen again. Therefore, for each of the two selections, there are 20 possible states that can be chosen. This leads to a total of 20 * 20 = 400 possible outcomes.

In the scenario where states are chosen without replacement, the number of possible outcomes changes for the second selection because a state cannot be chosen twice. In this case, there are 20 options for the first state and 19 options for the second (since one state has been selected and is not replaced). Thus, the total number of possible outcomes is 20 * 19 = 380.

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Answer:

( 9x - 18 ) square inches

Step-by-step explanation:

Data provided in the question:

Side of the square piece of gift wrapping paper = x inches

Now,

According to the question:

He cut 6 inches off the right side of the paper and discarded the rectangular scrap

Therefore,

Dimension of the scrap formed will be 6x square inches

The dimensions of the paper left

Top width will be ( x - 6 ) and the right width will be x

Next he cut 3 inches off the top of the paper and again discarded the rectangular scrap

Therefore,

Dimension of the scrap will be

( x - 6 ) long wide and 3 inches wide

Hence,

The area of the scraps will be

⇒ 6x + 3(x - 6)

⇒ 6x + 3x - 18

⇒ ( 9x - 18 ) square inches

Answer: Devaughn's age is 48 and Sydney's age is 24

Step-by-step explanation:

72 divided by 3 gives you 24.

24+24 is 48 which is Devaughn's age.48-72 gives you 24 which is Sydney's age

Sydney is 24 and Devaughn is 48

Answer:

Step-by-step explanation:

In order to qualify for the NBA playoffs, the New York Knicks must win at least 3/7 of their remaining games. Number of games remaining to be played is 15.

3/7 × 15 = 6.43

Since it is above 6 and closest to 7,

It means that they must win at least 7 games in order to qualify for the playoffs.

So they were correct by thinking that if they won 7 games from 15, they will be eligible to compete in the playoffs.

Answer:  The proof is done below.

Step-by-step explanation:  We are given to prove that the following statement is true :

"For every natural number n, [tex]n^5+4n[/tex] is a multiple of 5."

We will prove the above statement by MATHEMATICAL INDUCTION.

Let n = 1. Then, we get

[tex]n^5+4n=1^5+4\times5=5,[/tex] a multiple of 5.

Let n = 2. Then, we get

[tex]n^5+4n=2^5+4\times2=40,[/tex] a multiple of 5.

Let the statement be true for n = m, where m is a natural number.

So,

[tex]m^5+4m=5k,[/tex] for any natural number k.

Then,

[tex](m+1)^5+4(m+1)\\\\=m^5+5m^4+10m^3+10m^2+5m+1+4m+4\\\\=(m^5+4m)+5m^4+10m^3+10m^2+5m+5\\\\=5k+5(m^4+2m^3+2m^2+m+1)\\\\=5(k+m^4+2m^3+2m^2+m+1),[/tex] which is a multiple of 5.

Therefore, if the statement is true for n = m, then it is true for n = m+1.

That is, the statement is true for all natural numbers n.

Hence proved.

The exponential equation representing the situation is A = A₀ * (0.5)^(t/h). The half-life of this substance is approximately 67 minutes.

To represent the radioactive decay of the substance, we can use the exponential decay model:

A = A₀ * (0.5)^(t/h)

where A is the amount of the substance at time t, A₀ is the initial amount, h is the half-life, and t is the time elapsed.

In this case, we have:

250 = 32 * (0.5)^(250/h)

To find the half-life, we can rearrange the equation:

(0.5)^(250/h) = 250/32

Take the logarithm of both sides:

(250/h) * ln(0.5) = ln(250/32)

Solve for h:

h = (250 * ln(0.5)) / ln(250/32)

Using a calculator, we find that h is approximately 67 minutes.

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The radioactive decay of a substance is an exponential process represented by the equation [tex]N = N0 * e^(^-^k^t^)[/tex]. In this case, the half-life of the substance, or the time it takes for half the substance to decay, is approximately 66 minutes.

The subject matter at hand is related to the decay of a radioactive substance and its half-life. It's important to understand that the decay of radioactive material is an exponential process.

This can be represented with an equation of the form [tex]N = N0 * e^(^-^k^t^)[/tex], where N is the remaining amount of the substance, N0 is the initial amount, k is the decay constant, and t is time. In this given scenario, the scientist starts with 250 grams of the substance, and after 250 minutes, only 32 grams are left. Hence, we have [tex]32 = 250 * e^(^-^k^ *^ 2^5^0^)[/tex].

To find the half-life, we use the equation T = ln(2) / k, where T is the half-life. By solving these equations, we get the half-life to be approximately 66 minutes. Here the term 'half-life' is defined as the time it takes for half of the substance to decay; hence when the substance has gone through one half-life, only 50% of it would remain.

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Answer:

50 miles per hour

Step-by-step explanation:

Given:

Distance planned to travel each day is, [tex]D=500\ mi[/tex]

Hours of driving for covering the above distance is, [tex]t=10\ h[/tex]

The question asks to find the number of miles per hour Anderson plan to drive.

In other words, we need to calculate the average speed with which Anderson has to drive in order to cover 500 miles in 10 hours daily.

Therefore, the formula to calculate speed when distance covered and time taken are known is given as:

Average speed = [tex]\frac{Distance}{Time}[/tex]

Average speed = [tex]\frac{D}{t}[/tex]

Plug in 500 miles for 'D', 10 h for 't' and solve for speed. This gives,

[tex]\textrm{Average speed}=\frac{500}{10}\ mi/h\\\textrm{Average speed}=50\ mi/h[/tex]

Therefore, Anderson need to drive at an average of 50 miles per hour to cover the distance of 500 miles in 10 hours.