Find the surface area of this rectangular prism. Be sure to include the correct unit in your answer.

The values of the terms are a₂ = 15, a₃ = 30 and a₄ = 45

The definition of the function is given as

a₁= 0

aₙ = aₙ₋₁ + 15

The above definitions imply that we simply add 15 to the previous term to get the current term

Using the above as a guide,

So, we have the following representation

a₂ = 0 + 15

a₂ = 15

Also, we have

a₃ = 15 + 15

a₃ = 30

Lastly, we have

a₄ = 30 + 15

Evaluate the equation

a₄ = 45

Hence, the value of a₄ is 45

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From the set of numbers 9, 16, 25, 43 , the number does not belong to the group is prime number 43.

Set of numbers are 9, 16 , 25, 43.

9 is the composite number with 1, 3, 9 as factor.

It is perfect square of 3 also.

16 is the composite number with 1, 2, 4, 8,16 as factors.

It is perfect square of 4 also.

25 is the composite number with 1, 5, 25 as factors.

It is perfect square of 5 also.

43 is not a composite number.

It has only two factors 1, 43.

43 is a prime number.

It is not a perfect square of any number.

Here 43 does not belong to the group.

Therefore, the number which does not belong to the group from 9,16, 25, 43 is 43.

The above question is incomplete, the complete question is :

Which number does not belongs to group ?

9, 16, 25, 43.

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Answer:

See Below

Step-by-step explanation:

5. [tex]3.1 + (8.6 + m)\\3.1 + 8.6 + m\\11.7 + m[/tex]

take expression out of brackets by distribution (multiplying both by 1), then add

6. [tex]((\frac{2}{3})(t)) (1\frac{1}{2})\\(\frac{2}{3}t) (1\frac{1}{2})\\(\frac{2}{3}t) (\frac{3}{2})\\\frac{6}{6} t\\t[/tex]

Simplify the expression in the brackets by multiplying them together, once done turn the mixed fraction back into improper fraction in order to multiply the two together. Once done, simplify the expression

7. [tex]4(x + 8)\\4x + 32[/tex]

I would argue that factored form is the most simplified but regardless using the distribution rule you multiply both numbers within the bracket in order to get rid of it

8. [tex]4t + 7 + 2t - 2\\6t + 5[/tex]

This is just combining like terms and simplifying

Answer:

12.  & 2.5mins

Step-by-step explanation:

2 hours = 120 mins for 48 baguettes.  so 120/48 = 2.5 mins per baguette

30 mins is 1/4 of 2 hours. so 12  baguettes

Answer:

iam sorry

i don't know the answer

Two  cards are drawn in succession from a standard deck. The probability that both the drawn cards are diamonds is 143/2,652

Probability is defined as the ratio of the number of favorable events to the the number of possible outcomes. The probability of an event A is defined as:

P(A) = n(A)/n(S)

Where:

n(A) = number of possible ways the event A occurs

n(S) = total possible outcomes

In a standard deck, there are 52 cards. The number of diamond suit = 13 cards.

First drawn: number of diamond = 13

Hence, P1(diamond) = 13/52

In the second drawn, the number of diamonds left is 13 - 1 = 12, and total number of cards left is 52 - 1 = 51.

Hence, the probability of the second card will be a diamond is:

P2(diamond) = 12/51.

Since those 2 events are independent, the probability that both cards are diamonds is:

P(diamonds) = P1 (diamond) x P2 (diamond)

                     = (13/52) x (11/51) = 143/2,652

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The height of the antenna is 17m approximately to the nearest metre using the trigonometric ratio of tangent for angleof elevation 44°.

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

Considering the right triangle formed by the point of Nicole's eyes E with an angle of elevation 44°, top of the roof A (90°) and the top of the antenna B,

we shall evaluate for the height of the antenna AB as follows:

tan 44° = AB/18m {opposite/adjacent}

AB = 18m × tan 44° {cross multiplication}

AB = 18m × 0.9657

AB = 17.3826m

Therefore, the height of the antenna to the nearest metre is 17 metres using the trigonometric ratio of tangent for angleof elevation 44°.

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Answer:
2 meters

I got it correct in my hw (check the photos)

also mark me brainleist

Answer: x > -5

Step-by-step explanation:

-1.5x < 7.5

x > -5 (When multiplying both sides by a negative, the inequality is flipped)

[tex]-1.5x < 7.5[/tex]

Divide both sides by -1.5:

[tex]\dfrac{-1.5x}{-1.5} < \dfrac{7.5}{-1.5}[/tex]

When dividing by a negative number, the inequality sign will reverse.

Answer:

[tex]x > -5[/tex]

Answer: The given quadratic expression is -3x²+172x-20. To factor this expression, we look for two numbers that multiply to -20 and add to 172.

We can start by dividing -20 by different numbers and checking if the product and the sum of the divisors equals -20 and 172 respectively.

-20/1 = -20, 1+-20 = -19

-20/2 = -10, 2+-10 = -8

-20/4 = -5, 4+-5 = -1

-20/-1 = 20, -1+20 = 19

-20/-2 = 10, -2+10 = 8

-20/-4 = 5, -4+5 = 1

We can see that the divisors that multiply to -20 and add to 172 are (x+8)(x-5)

So, we can factor the quadratic expression as:

-3x²+172x-20 = -3(x+8)(x-5)

Hope this helps!

Step-by-step explanation:

The revenue is maximized when the derivative of R(p) is equal to 0.

R'(p) = -80p + 400 = 0

p = 5

A function is a mathematical relationship between two or more variables, where one variable (the output) is determined by the values of the other variables (the inputs). A function can be expressed as an equation, and it describes how the output changes in relation to the inputs.

Therefore, the maximum revenue is achieved when the price of each ticket is $5.

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Steven will have to pay $127. 50 for the insurance per year.

The correct answer is an option (C)

First, we need to find the corresponding value for the all-wood building in the city suburbs.

From given table, we will use the value 0.85 because he wishes to ensure his belongings.

Here, the value of the belongings in the apartment is about $15,000

Steven wants to insure his belongings while renting.

Now we can calculate the amount of money he will have to pay  for insurance per year as follows:

15000 × (0.85 / 100)

= 127. 50 dollars

Therefore, he will have to pay 127. 50 dollars for insurance.

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Lisa and Joe put $46 towards the gift

Let's call the amount of money that Sara put in "x".

Joe put in twice that amount, so he put in 2x.

Lisa put in ten dollars more than Sara, so she put in x + 10.

Together, Sara, Joe, and Lisa put in x + 2x + (x + 10) = $58.

Evaluate the like terms, so we have

4x + 10 = 58.

Subtracting 10 from both sides, we get

4x = 48.

Dividing both sides by 4, we find that

x = $12.

So Sara put in $12, Joe put in $24, and Lisa put in $22.

The total amount put by Lisa and Joe is  $24 + $22 = $46.

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Complete question

Three friends are put their money together to buy a $58 gift. Joe put in twice the amount of money as Sara. Lisa put in ten dollars more than Sara. How much money did Lisa and Joe put towards the gift?

A: The exponential function for the situation is P(t) = 36,000 × (1 + 0.15)^t.

B: The population in 2020 was 72,396.

What is an exponential function?

The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

The population of a city in 2015 is 36,000 and it is increasing at 15% per year.

Model this using an exponential equation of the form -

P(t) = P0 × (1 + r)^t

Where -

P(t) is the population after t years

P0 is the initial population in 2015 (36,000)

r is the rate of growth (0.15)

t is the number of years since 2015

So the exponential equation that models the population is -

P(t) = 36,000 × (1 + 0.15)^t

Part B:

To find the population in 2020, substitute t = 5 (2020 - 2015) into the equation -

P(5) = 36,000 × (1 + 0.15)^5

P(5) = 36,000 × 1.15^5

P(5) = 36,000 × 2.011

P(5) = 72396

Calculating this gives us a population of approximately 72,396 in 2020.

To obtain this answer, the exponential equation that models the population, P(t), is used where t represents the number of years since 2015, with the given information that population in 2015 was 36,000 and it's increasing at 15% per year and substitute the value of 5 for t.

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Answer:

23.37

Step-by-step explanation:

There ya go

:)

The expected value of the sum of the two extreme numbers is 1/2.

Random sampling is a part of the sampling technique in which each sample has an equal probability of being chosen.

The optimal strategy for you would be to choose the number 0.5, as it maximizes the probability that your pair will have the highest sum, and minimizes the probability that your pair will have the lowest sum.

This is because if all players choose a number uniformly at random, the expected value of the lowest and highest numbers will be 0 and 1 respectively, and the expected value of the middle two numbers will be 0.5. Therefore, by choosing 0.5, you have the best chance of having the highest sum, which means you will have to pay the least amount of money.

Therefore, the expected value of the sum of the two extreme numbers is 1/2.

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Answer:

123.6​30189899 or A. $1,257.72

Step-by-step explanation:

[tex]\frac{4.25}{100}=0.0425\\ 100(1 + \frac{0.0425}{12})^{12(5)} \\= 123.630189899[/tex]

No Chase's work is not correct. He has made a mistake in working the brackets out. The BODMAS Rule has to be used here.

We have 2(12 ÷ 2)2 – 14 + 6

Here according to the BODMAS rule which stands for Brackets  Of  Division  Multiplication  Addition  Subtraction, we will first solve the brackets.

Now any number to the left or right of the brackets without any sign in between the bracket and the number has to be multiplied by the answer we get by solving the bracket.

12 ÷ 2 = 6

Hence we get

2 X 6 X 2  -  14  +  6

Now we need to multiply.

2 X 6 X 2 = 12 X 2 = 24

Hence we get

24 - 14 + 6

Now we need to add the numbers up.

24 + 6 = 30 hence we get

30 - 14

= 16

Hence Chase's work is not correct.

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Answer: X has to be greater than or equal to 15/7 for the inequality to be true.

Step-by-step explanation:

here are the steps to solve the inequality 25-2x≤5(2-x):

Start by simplifying the right side of the inequality: 5(2-x) = 10 - 5x

Now we can substitute this back into the original inequality: 25 - 2x ≤ 10 - 5x

Next, we need to combine like terms on both sides of the inequality: 25 - 7x ≤ 10

Now we'll add 7x to both sides: 25 ≤ 10 + 7x

Subtract 10 from both sides: 15 ≤ 7x

Finally, divide both sides by 7: 15/7 ≤ x

The solution set is x ≥ 15/7.

So x has to be greater than or equal to 15/7 for the inequality to be true.

Answer:

-5 ≥ x  or x ≤ -5

Step-by-step explanation:

25 - 2x ≤ 5(2 - x)

distribute the 5 to eliminate the parentheses:

25 - 2x ≤ 10 - 5x

now combine like terms:

15 - 2x ≤ -5x

15 ≤ -3x

-5 ≥ x  or x ≤ -5

the inequality symbol gets switched whenever you multiply or divide by a negative value

We can assume linear inequality 8x>40 for x>8 for an indirect proof.

What are linear inequalities?

Inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in Maths. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠). The different types of inequalities in Maths are polynomial inequality, rational inequality, absolute value inequality.

The symbols ‘<‘ and ‘>’ express the strict inequalities and the symbols ‘≤’ and ‘≥’ denote slack inequalities. A linear inequality seems exactly like a linear equation but there is a change in the symbol that relates two expressions.

e.g. y>x+2

Now,

Given,

Quinn ran total distance>40 mile

No. of times he ran=5

average distance for each run>8

also let x>8 where x=average distance for each run

Hence,

           We can assume linear inequality 8x>40 for x>8

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Answer:

0.82

Step-by-step explanation:

A： area =2( 0.8*0.6*+0.6*1+0.8*1) =2(0.48+0.6+0.8)=2*1.88 =3.76

B：area = 2(1.4*0.5+0.5*1.2+1.4+1.2) =2(0.7+0.6+1.68)=2*2.98=5.96

total 9.72

cost = $6.79* 9.72/80 =$0.82

Answer:

0.92

Step-by-step explanation:

The statement below about the rocket is true:

A rocket travels at an approximate speed of 7.9 *10⁵ cm per second.

A statement of the connection between units that are used to alter the units of a measured quantity without affecting the value is called a conversion factor. A conversion ratio (or unit factor), if the numerator and denominator have the same value represented in various units, always equals one (1).

Given, A rocket travels at an approximate speed of 7.9 kilometers per second.

Since, some unit conversion:

1 kilometer = 1000 meteres

1 kilometer = 100000 centimeteres = 10⁵ cm

1 kilometer = 10000000 milimeteres = 10⁷ mm

thus we can say that from the given options only "f" is correct that states:

A rocket travels at an approximate speed of 7.9 *10⁵ cm per second.

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The minimum stopping distance is 800 ft.

Part A: The minimum stopping distance for a driver going at the speed limit (40 mph) is given by the equation: s = v2/2a, where s is the stopping distance, v is the speed (40 mph), and a is the deceleration rate (assumed to be 10 ft/s2). Therefore, the minimum stopping distance is 800 ft.

Part B: For a driver going at 45 mph, the minimum stopping distance is given by the equation: s = v2/2a, where s is the stopping distance, v is the speed (45 mph), and a is the deceleration rate (assumed to be 10 ft/s2). Therefore, the minimum stopping distance is 925 ft, which is 15.6% greater than the stopping distance for the speed limit.

Part C: For a driver going at 50 mph, the minimum stopping distance is given by the equation: s = v2/2a, where s is the stopping distance, v is the speed (50 mph), and a is the deceleration rate (assumed to be 10 ft/s2). Therefore, the minimum stopping distance is 1250 ft, which is 56.3% greater than the stopping distance for the speed limit.

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Answer:

(i) Let's call Jaren's current age J. According to the problem, the sum of J and Daniel's age is 40.

If we also know that four years ago, Daniel was 3 times Jaren's age, we can set up the following equation:

J + (J+4) = 40

Solving for J, we find that Jaren's present age is 18.

(ii) When Jaren was born, Daniel would have been 18 + 4 = 22 years old.

The number of months when the total cost is $1700 is 48 months

A function can be defined as an expression, equation, law or rule that shows the relationship between two variables.

These variables are;

From the information given, we have that;

Now, substitute the values, we have;

1700 = 35x + 20

collect like terms

35x = 1700 - 20

subtract the like terms

35x = 1680

Make 'x' the subject of formula

x = 48 months

Hence, the value is 48 months

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Answer:

c

Step-by-step explanation:

Answer:

We can use algebra to find the two consecutive even integers whose product is 168.

Let's call the first even integer x. Since it is consecutive to another even integer, the next one will be x+2. The product of these two integers is:

x * (x+2) = 168

We can solve for x by simplifying the equation:

x^2 + 2x = 168

x^2 + 2x - 168 = 0

We can factor the left side of the equation:

(x-14)(x+12) = 0

So the two solutions for x are -12 and 14.

The negative integers are -12 and -14.

The two integers that multiply to give 168 are -12 and -14, but keep in mind that they are not consecutive integers.