what is the average rate of change of f(x), represented by the graph , over the interval [-1,2]

Projectile B begins its descent 1 seconds before Projectile A does.

In Mathematics and Geometry, the y-intercept of any graph or table such as a quadratic equation or function, generally occurs at the point where the value of "x" is equal to zero (x = 0).

By critically observing the table shown in the image attached above, we can reasonably infer and logically deduce the following y-intercept of Projectile A:

y-intercept = (0, 44).

Maximum height = (4, 300).

When t = 0, the y-intercept of Projectile B can be calculated as follows;

h(t) = -16t² + 96t

h(0) = -16(0)² + 96(0)

h(0) = 0.

For the maximum height, we have:

h(t) = -16t² + 96t

h'(t) = -32t + 96

32t = 96

t = 96/32

t = 3

Difference in time = 4 - 3

Difference in time = 1 seconds.

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(a) The errors made by the student are:

Incorrectly expanding 49(2) as 24 instead of 98.

Mistakenly factoring the quadratic equation as (y - 8)(y - 1) instead of

\(y^{2} - 9y + 8.\)

(b) The exact solution to the equation is x = 7/11.

(a) The student made two errors in their solution:

Error 1: In the step \("22x + 49(2) = 0,"\) the student incorrectly expanded 49(2) as 24 instead of 98. The correct expansion should be 49(2) = 98.

Error 2: In the step \("y^{2} - 9y + 8 = 0,"\) the student mistakenly factored the quadratic equation as (y - 8)(y - 1) = 0. The correct factorization should be \((y - 8)(y - 1) = y^{2} - 9y + 8.\)

(b) To find the exact solution to the equation, let's correct the errors made by the student and solve the equation:

Starting with the original equation: \(22x + 4 - 9(2) = 0\)

Simplifying: 22x + 4 - 18 = 0

Combining like terms: 22x - 14 = 0

Adding 14 to both sides: 22x = 14

Dividing both sides by 22: x = 14/22

Simplifying the fraction: x = 7/11

Therefore, the exact solution to the equation is x = 7/11.

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Answer:

The quadrilateral'area is 96cm².

A polar graph that is a limacon has a formula similar to \(r=a+bcos\theta\)

Option B is correct.

A  limacon has a formula similar to \(r=a+bcos\theta\)

Case 1 .  If  a < b  or  \(\frac{b}{a}>1\)

Then the curve is limacon with an inner loop.

Case 2.  If  a>b   or   \(\frac{b}{a}<1\)

Then the limacon does not have an inner loop.

Here, given that,  \(r=3+4cos\theta\)

It is observed that,  a < b  or \(\frac{b}{a}>1\)

Therefore, the curve is limacon with an inner loop.

Hence, option B is correct.

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Step-by-step explanation:

The formula:

�

�

=

�

2

(

�

1

+

�

�

)

S

n

=

2

n

(a

1

+a

n

)

is used to solve for the sum of the arithmetic sequence given the first term a₁, the number of terms n, and the last term in an.

Example:

3, 6, 9, 12, 15,...,123

The first term, a₁ = 3

The last term an = 123

Common difference, d = 3 (because the sequence are multiples of 3)

Number of terms, n= ?

Find the number of terms, n:

an = a₁ + (n-1) (d)

123 = 3 + (n-1) (3)

123 = 3 - 3 + 3n

123/3 = 3n/3

n = 41

To find the sum of the given sequence without adding 3 + 6 + 9, ... + 123, we use the formula:

S₄₁ = (41/2) (3 + 123)

S₄₁ = (41/2) (126)

S₄₁ = (41)(63)

S₄₁ = 2,583 ⇒ the sum of the given sequence

Answer:

3a^2

Step-by-step explanation:

one way of answering this question is by finding the area of the whole shape, including the non-shaded shape, then taking away the area of the non-shaded shape from the whole thing, leaving you the area of the shaded shape

Step-by-step

find the area of the whole shape

2a x 2a

= 4a^2 (or 4a to the power of 2)

Now that we have the area of the whole shape, we must find the area of the non-shaded shape and take it away from 4a^2, we do this by

a x a

= a^2 (or a to the power of 2)

now we minus the non-shaded shape away from the total area

4a^2 - a^2

= 3a^2 (or 3a to the power of 2)

Answer:

slope of -2

Step-by-step explanation:

the slope of this equation is -2 and the parallel slope would be the same slope.

The correct answer is use of randomized controlled experiments. Randomized controlled experiments are used to test the impact of a certain variable on the outcome, not to address omitted variable bias. The other solutions listed can be used to address omitted variable bias.

What is bias?

Bias is a form of prejudice or preconceived notion, typically for or against a particular group or individual. It is often based on incorrect or incomplete information, or a lack of understanding and can lead to unfair discrimination or judgement. Bias can be expressed in both subtle and overt ways through actions, decisions, and statements. It can influence decision-making, workplace behavior, and relationships in an unfair and negative way. Bias often manifests when people allow their own personal views to override impartial judgement, which can lead to unfair decisions and unequal treatment. It is important to be aware of biases and strive to remain open-minded, objective, and impartial in order to ensure fair and equitable treatment of all individuals.

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Answer: It would cost $47.3 to fill the same tank in 2010

Step-by-step explanation:

In 1970

Total cost to fill the tank = $6

Cost per capacity of tank = $0.36

Capacity of tank = Total cost / Cost per capacity of tank

Capacity = 6/0.36

Capacity = 16.6

Therefore

In 2010

Cost per capacity of tank = $2.84

And we now know it capacity = 16.6

Total cost to fill the tank = 2.84 * 16.6

Total cost = $47.3

Hope this helps have a awesome day ❤️✨

Answer:

  C and D

Step-by-step explanation:

Population density is the ratio of population to area. Its units are persons per square mile. Here, you're being asked to compare the population densities of several countries to the average population density in several US states.

__

The idea of "average population density of the 10 states listed" is somewhat ambiguous. It could mean either of (a) the ratio of the total of the states' population to the total of their land area, or (b) the average of the population densities of the states. (In the attached, we computed both, but the answer remains the same using either number.)

When there are numerous identical calculations to be performed, it is convenient to let a spreadsheet do them. The attached spreadsheet shows the population densities for the 10 states and 5 countries listed.

Depending on how you define it, the average population density of the 10 states is about 10.5 or about 15.7 people per square mile. (15.7 is the average of the density numbers, found using the spreadsheet AVERAGE function.)

__

The 5 countries have population densities ranging from about 7.7 to 236 people per square mile. Two of the countries have density below 10.5, so are the answers to the question asked.

  Canada (C) and Iceland (D) have population density below the US state average.

Step-by-step explanation:

hope it helps

see attached

Answer:

√38

Step-by-step explanation:

√38

step 1: Check which squared numbers can be multiplied by another number to get 38.

Start with these numbers: 4, 9, 16, and 25

Step 2: Testing out the numbers

√25 × __ = 25 can't be divided by 38

√16 × ___ = 16 can't be divided by 38

√9 × ____ = 9 can't be divided by 38

√4 × ____= 4 can't be divided by 38

Step 3: Answer

After trying the square root numbers that could possibly work with √38 none work; which means √38 can't be simplified. So the answer is √38

I hope this helps!

Hello !

68/17 = 4

=> yes for 68

84/17 = 4.941...

=> no for 84

357/17 = 21

=> yes for 357

1001/17 = 58.882...

=> no for 1001

Answer:

4 times larger

Step-by-step explanation:

-24.59, -8.38, -4.5, -0.99, -0.002, -0.0001

Answer:

-24.59, -8.38, -4.5, -0.99, -0.002, -0.0001

Step-by-step explanation:

hope this  helps!

Answer:

x=30o+n90on∈Z

Step-by-step explanation:

cos2x=sin(90o−2x)=sin(2x−30o)

Which mean 90o−2x=2x−30o+n360o

or 90o−2x+2x−30o=(2n+1)180o

The later cannot be true.

so x=30o+n90on∈Z

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The value of tan x is :

solution is in attachment !

The volume of the solid generated about the x-axis by revolving region r is equal to V  = \(\int\limits^a_b \pi {[y]^{2} } \, dx\) .

As given in the question,

Volume of the solid which is generated by revolving a plane region 'r' about vertical line which does not pass through the given plane:

'r' be the radius of the circle.

Area of the cross section is the circle area = πr²

As it is given it is about the x-axis then radius 'r' is the function of x

f(x) = r

Let 'V' be the volume.

Volume of the solid generated by revolving the region 'r' about the x‐axis on the interval [ a, b] is given by :

V = \(\int\limits^a_b \pi {[f(x)]^{2} } \, dx\)

As f(x) = y

⇒V  = \(\int\limits^a_b \pi {[y]^{2} } \, dx\)

Therefore, the integral used to represent the volume of the given solid generated by revolving about the x-axis is equal to V  = \(\int\limits^a_b \pi {[y]^{2} } \, dx\)

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Answer: 26

Step-by-step explanation:

Since we are given the value of y, all we need to do is plug it into the equation and solve it. Make sure if you plug this into a calculator that you put the substituted number in parenthesis that way it squares the number correctly without a negative sign.

(-3)²-5(-3)+2

9 - 5(-3) +2

9 - -15 + 2

9 + 15 + 2

24 + 2

26

Hope this helps!

The quartiles of the distribution are given as follows:

The sample size of the distribution is of:

n = 40.

The first quartile is the value that is greater than 25% of the distribution, hence it is the value at the position which is 25% of the sample size, hence:

The second quartile is the value that is greater than 50% of the  distribution, hence it is the value at the position which is 50% of the sample size, hence:

The third quartile is the value that is greater than 75% of the  distribution, hence it is the value at the position which is 75% of the sample size, hence:

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The bank reconciliation shows an adjusted bank balance of Br.5,301.42 and an adjusted ledger balance of Br.4,173.83.

To prepare the bank reconciliation and journal entry for ABC Company based on the given information, we need to compare the transactions recorded in ABC's ledger with the transactions shown in the bank statement. Here's the bank reconciliation:

1. Bank Statement Balance:

Cash on deposit at July 31: Br.4,964.47

2. Adjusted Bank Balance:

Bank Statement Balance: Br.4,964.47

3. Deposit not on the statement: + Br.410.90

(Adjusted Bank Balance: Br.5,375.37)

Erroneously charged check: + Br.79

(Adjusted Bank Balance: Br.5,454.37)

Outstanding checks:

Check 801: - Br.100.00

Check 888: - Br.10.25

Check 890: - Br.294.50

Check 891: - Br.205.00

(Adjusted Bank Balance: Br.4,844.62)

4. Incorrectly charged check: + Br.90

(Adjusted Bank Balance: Br.4,934.62)

5. Collection of interest-bearing note: + Br.500

(Adjusted Bank Balance: Br.5,434.62)

6. Interest earned: + Br.24.75

(Adjusted Bank Balance: Br.5,459.37)

7. Incorrectly recorded check: - Br.90

(Adjusted Bank Balance: Br.5,369.37)

8. Collection fee: - Br.5.00

(Adjusted Bank Balance: Br.5,364.37)

9. NSF check: - Br.50.25

(Adjusted Bank Balance: Br.5,314.12)

10. Service charge: - Br.12.70

(Adjusted Bank Balance: Br.5,301.42)

Adjusted Ledger Balance:

Bank Balance in ABC's Ledger: Br.4,173.83

Reconciled Bank Balance: Br.5,301.42

Reconciled Ledger Balance: Br.4,173.83

Journal Entry:

To record the bank reconciliation, we make the following journal entry:

Debit: Cash (Ledger Balance adjustment) - Br.5,301.42

Credit: Cash (Bank Statement Balance adjustment) - Br.4,964.47

Credit: Miscellaneous Income/Expense - Br.336.95 (the difference between the two balances)

This journal entry ensures that the ledger balance matches the reconciled bank balance by adjusting for the discrepancies identified during the reconciliation process.

The journal entry reflects the necessary adjustments to reconcile the two balances, with a debit to Cash (Ledger Balance adjustment), a credit to Cash (Bank Statement Balance adjustment), and a credit to Miscellaneous Income/Expense to account for the difference.

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Answer:3

Step-by-step explanation:

-3x+2=-7

subtract 2 from both sides

-3x+2-2-(-7-2

simplify the arithmetic

-3x=-7-2

simplify the arithmetic aging

-3x=-9

=3

The measure of ∠1 is 41°, ∠2 is 27° and ∠3 is 63°.

Same-side exterior angles are two external angles to the parallel lines that are on the same side of the transverse line. According to the theorem, same-side exterior angles are supplementary, which means they add up to 180 degrees.

⇒∠1 + ∠2 + 22°+90° =180°

⇒∠1 + ∠2 = 180° - 112° = 68°

⇒∠1 + ∠2 = 68°

Similarly,

⇒∠3 =180°-117°=63°

⇒63°+ 90°+∠2 = 180°

⇒153°+∠2 = 180°

⇒∠2 =180°-153° =27°

⇒∠1 = 68°-27°= 41°       (since ∠1 + ∠2 = 68°)

Hence, the measure of ∠1 is 41°, ∠2 is 27° and ∠3 is 63°.

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Answer:

18 years (to the nearest year)

Step-by-step explanation:

Compound interest formula:

\(A=P(1+\frac{r}{n})^{nt}\)

where A is amount, P is principal, r is interest rate (decimal format), n is the number of times interest is compounded per unit 't', and t is time

Given:

\(\implies 4490=2400(1+\frac{0.035}{12})^{12t}\)

\(\implies \dfrac{449}{240}=\left(\dfrac{2407}{2400}\right)^{12t}\)

\(\implies \ln\dfrac{449}{240}=\ln\left(\dfrac{2407}{2400}\right)^{12t}\)

\(\implies \ln\dfrac{449}{240}=12t\ln\left(\dfrac{2407}{2400}\right)\)

\(\implies t=\dfrac{\ln\dfrac{449}{240}}{12\ln\left(\dfrac{2407}{2400}\right)}\)

\(\implies t=17.92277136...\)

Therefore, it would take 18 years (to the nearest year) for the account to reach $4,490

Given:

Total people=19035

Number of days =5

The average number of skiers per day can be calculated as,

Answer: The average number of skiers per day is 3807.

Answer:

  about -4.7622

Step-by-step explanation:

You want the cube root of -108.

Your calculator will tell you the cube root of -108 is about -4.7622.

__

Additional comment

Some calculators compute roots using logarithms. Since the logs of negative number are not real, they will give you an error if you try to do this directly. You have to know that the odd index root of a negative number is the opposite of the same root of its absolute value.

The prime factoring of 108 is 2²·3³. Factoring out the perfect cube gives the simplified form ...

  ∛-108 = -3∛4

<95141404393>

According to the question there are 35 distinct website graphics that can be created by using at least four of seven different bitmap images.

A website is a collection of related web pages, images, videos, and other digital assets that are hosted on a web server and can be accessed by users over the internet. A website is typically identified by a unique domain name and can be accessed by typing the URL into a web browser.

Using the formula for calculating the number of combinations of size k from a set of size n (n choose k), we can calculate the number of distinct website graphics that can be created by using at least four of seven different bitmap images as follows:

n = 7 (7 different bitmap images)
k = 4 (at least 4 of the 7 bitmap images)
Number of distinct website graphics = (7 choose 4) = 35
Therefore, there are 35 distinct website graphics that can be created by using at least four of seven different bitmap images.

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Answer:

12.4m

Step-by-step explanation:

In order to solve this equation, we can use the length of a carriage as our unknown value (using the engine is a bit more difficult). The questions says that the whole train: 4 carriages and an engine = 86.8m

If we represent carriage length as 'x', we can write the following equation:

4x (length of 4 carriages) + (2/3)x (length of engine as it is 2/3 of a carriage) = 86.8m

4x+(2/3)x = 86.8

From here we can combine into one fraction:

\(4x+\frac{2}{3} x=\frac{14}{3}x\)

So now our equation looks like this:

\(\frac{14x}{3}=86.8\)

Now all we need to do is multiply both sides by 3 and then divide both sides by 14 to isolate and solve x:

\(\frac{14x}{3}*3=86.8*3\\ 14x=260.4\\\frac{14x}{14}=260.4/14\\ x=18.6\\\)

Now that we know the carriage length, we can use it to find the engine length:

Engine length = 2/3 Carriage length

\(E=\frac{2}{3}x\\ E=\frac{2}{3} (18.6)\\E = 12.4m\)

Hope this helped!

Length of a carriage = x

Length of four carriages = 86.8 m

Length of each carriage =

\(86.8 \div 4 \: m \\ = \: 21.7 \: m\)

Length of one carriage = 21.7 m

Length of the engine =

\( = \frac{2}{3} x\)

\( = \frac{2}{3} \times 21.7\)

\( = 43.4 \: m\)

\(43.4 \div 3 \: m \\ = 14.4666666667 \: m\)

∴ The length of the engine is 14.4666666667 m .

Respuesta:

2/9

Explicación paso a paso:

Dado que :

tarjeta numerada = 1 - 15

Probabilidad de obtener un número no menor o igual a 5

Número de cartas no menor o igual a 5:

Tarjeta no ≤ 5 = (6,7,8,9,10,11,12,13,14,15) = 10

Probabilidad = resultado requerido / Total de resultados posibles

P (Tarjeta no ≤ 5) = 10/15 = 2/3

Número de cartas menor o igual a 5:

Tarjetas ≤ 5 = 1, 2, 3, 4, 5

P (Tarjeta ≤ 5) = 5/15 = 1/3

P (Tarjeta no ≤ 5) * P (Tarjeta ≤ 5)

2/3 * 1/3 = 2/9

Calcularemos la probabilidad del evento combinado para obtener: P = 0.22

La probabilidad de sacar una carta menor o igual a 5 es igual al cociente entre el numero de cartas con un número menor o igual a 5 y el número total de cartas en el mazo.

Tenemos 5 cartas con un número igual o menor a 5 y un total de 15 cartas, así que la probabilidad es:

p = 5/15

La probabilidad de que no le salga una carta menor o igual a 5 es calculada de la misma forma, hay 10 cartas que no son menores o iguales a 5 y un total de 15 cartas, entonces tenemos:

q = 10/15

La probabilidad conjunta es simplemente el producto de esas dos probabilidades, así obtenemos:

P = (10/15)*(5/15) = 10/45 = 0.22

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