In Her Freshman Year, Wilhelmina Earned A B+ In Algebra, A B+ In English, An A- In Science, And A B- (2023)

Unit price of $0.60 per notebook (60 cents per 1 notebook = .60/1).

Step-by-step explanation:

A rate is a ratio matching quantities of various items. A unit rate is a value 1 in the denominator. The denominator is not going to have the value as 1 when an item has some rate like a cost per any quantity of things. Using division operation one can determine the unit rate.

Unit price of $0.60 per notebook (60 cents per 1 notebook = .60/1).

Answer:

14 students

Step-by-step explanation:

Let x be the number of students,

• If a gym class is divided into 4 equal teams, 2 students have to sit out, so

• If a gym class is divided into 5 equal teams, 1 student has to sit out, so

• If a gym class is divided into 6 equal teams, 4 students have to sit out, so

From the first congruence,

substitute it into the second congruence:

Substitute this into the third congruence:

Since then

The next number divisible by 4, 5 and 6, greater than 46 and less than 70 is 60, so 14 students should be added.

Answer:

3ax+2ay+6bx+4by

= 3ax+ 6bx+ 2ay + 4by

= 3x(a+2b) +2y(a+2b)

= (3x+2y)(a+2b)

Answer:

(a+2b)(3x+2y)

Step-by-step explanation:

3ax+2ay+6bx+4by​ = a(3x+2y)+2b(3x+2y) = (a+2b)(3x+2y)

Answer:

Gemma has 7 fewer games than Chris.

Step-by-step explanation

I got this answer by subtracting 6 by 13, (13-6) and I got 7.

Answer:

It would take five hours

Step-by-step explanation:

a page takes five minutes

10 pages per season

50 min per season

6 seasons

300min=5 hours

It would take five hours

Step-by-step explanation:

Let x be Ramen

Anthony=2x+4

Kasim=2x

Ramen=x

Therefore, if their ages add up to 64 we can add them all up

2x+4+2x+x=64

5x+4=64

5x=60

x=12

Now substitute

Ramen=12

Kasim=24

Anthony=28

It will take 51 days to fill the olympic sized pool.

What is relation between time and work?

The relation between time and work is

Work Done = Time Taken × Rate of Work ·

or, Rate of Work = 1 / Time Taken ·

or, Time Taken = 1 / Rate of Work ·

Now it is given that,

Volume of swimming pool = 6.6043×10^5 gallons = 6,600,430 gallons

Volume of water delivered by hose per minute = 9 gallons per minute

So, volume of water delivered by hose per hour = (9*60) gallons per hour

⇒ volume of water delivered by hosen per day = (9*60*24) gallons = 12,960 gallons per day

Thus, number of days required to fill the pool = 6,600,430/12960

⇒ number of days required to fill the pool = 50.9

⇒ number of days required to fill the pool ≈ 51 days

Thus, It will take 51 days to fill the olympic sized pool.

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6.6043×10^5 = 660,430 gallons.

660,430 / 9 = 73381.11... minutes.

73381.11... / 60 = 1223.01851852 hours.

1223.01851852 / 24 = 50.9591049383 days.

It would take about 51 days for the garden hose to fill the pool.

Answer:

You need at least 37 terms to have a sum of 2000 or more

Step-by-step explanation:

,

S(n):=3+6+9+12+⋯+3n=3⋅n(n+1)2

This is approximately 32⋅n2.

It should be around 2000, that is n2 should be around 2/3⋅2000≈1334. Using calculator, its square root is ≈36.52 and if you sustitue n=36 to S(n) gives S(36)=1998.

So since 36 is not enough you need 37 terms to have a sum of 2000 or more

Answer:

Step-by-step explanation:

1/20 is a tiny portion of the length that needs to be traveled. 20/20 is the whole length. If 1/20 gets traveled in 3/4 of a second, multiply 3/4 by 20 to see how long it takes to travel 20(1/20) which is equal to 1, the whole path.

20(3/4) = 15 seconds

The time taken for the object to travel the entire length (L) is 15 s.

The given parameters:

• Initial distance, d1 = 1/20 L
• Time of motion, t1 = 3/4 s

The time taken for the object to travel the entire length (L) is calculated as follows;

Thus, the time taken for the object to travel the entire length (L) is 15 s.

Learn more about fractions and proportions here: brainly.com/question/2328454

Car takes 1.53 seconds to pass over the bridge completely​

Solution:

Given that car of length 4.3m is travelling at 105km/h it passes over a bridge of length 36m

To find: time in seconds car takes to pass over the bridge completely​

From given information,

Speed of car = 105 km/hr

Let us convert the kilometer per hour to meter per second

To convert km/hr into m/sec, multiply the number by 5 and then divide it by 18

So speed of car = 29.167 m/sec

Length of car = 4.3 m

Length of bridge = 36 m

For the car to completely pass the bridge, back end of car should cross the endpoint of bridge

So the distance covered by car to pass over the bridge completely​ = 4.3 + 36 + 4.3 = 44.6 m

Time taken is given as:

So car takes 1.53 seconds to pass over the bridge completely​

Answer:

They lost parts of their culture.

Answer:

Step-by-step explanation:

Area of the rectangle = height * width

= 7x² * (3x² + 8x + 7)

= 7x² * 3x² + 7x² * 8x + 7x² * 7

= 21x⁴ + 56x³ + 49x²

P(B/A) is in the simplest form

Step-by-step explanation:

Let us explain how to solve the problem

• P(B|A) is called the "Conditional Probability" of B given A
• Conditional probability is the probability of one event occurring with some relationship to one or more other events that means event A has already happened, now what is the chance of event B
• The formula for conditional probability is P(B|A) = P(A and B)/P(A), where P(A and B) is P(A) . P(B given A occurred)

∵ There are 3 red marbles, 5 green marbles, and 2 blue

marbles in the jar

∴ The total number of the marbles in the jar = 3 + 5 + 2 = 10

∵ Two marbles are drawn from the bag, one after the other without

replacement

- That means red is already occurred when green is happened,

so it is a "Conditional Probability" of green given red

P(B/A) = P(A and B)/P(A)

∵ Event A is defined as drawing a red marble from the jar on

the first draw

∴ P(A) = P(red)

∵ P(red) =

∴ P(A) =

∵ Event B is defined as drawing a green marble on the second draw

∴ P(B) = P(green)

- The number of marbles after the red is chosen is 9

∵ P(green) =

∴ P(B) =

- Find P( A and B)

∴ P(A and B) = ( ) . ( )

∴ P(A and B) =

- Simplify the fraction by divide up and down by 15

∴ P(A and B) =

∵ P(B|A) = P(A and B)/P(A)

- Substitute the values of P(A and B) and P(A) in the rule above

∴ P(B/A) =

- Simplify the fraction

∵ ÷ = × =

- Divide up and down by 2

∴ P(B/A) =

P(B/A) is in the simplest form

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Answer:5/9

Step-by-step explanation:

Answer:

Territory is the correct answer

have a great day and i hope you do well on your grades ^-^

Answer:

See below.

Step-by-step explanation:

f(x) = -25x2 + 30x − 9

This is a parabola which opens downwards.

Part A.

The discriminant b^2 - 4ac = 30^2 - 4*(-25) * -9

= 900 - 900

= 0

This indicates that the graph of the function just touches the x-axis. So there is one root of multiplicity 2.

Factoring:

-25x2 + 30x − 9

= -(25x^2 - 30x + 9)

= -(5x - 3)(5x - 3)

so the roots are x = 3/5 multiplicity 2.

The x -intercept is at (0.6, 0).

Part B.

The y intercept is when x = 0 so here it is

y = -25(0)^2 + 30(0) -9

= -9

The constant at the end of the function (-9) indicates the y-intercept.

The y intercept is at (0, -9).

Part C.

The end behaviour of f(x):

The negative coefficient (-25) of x^2 indicates that the graph increases from negative infinity from the left.

Since it is a parabola that opens downwards ( because of the -25) it decreases to negative infinity on the right.

Answer:

Step-by-step explanation:

25x2 − 40x + 16 = (5x)² - 2*5*4 + 4² { (a - b)² = a² - 2ab + b² }

= (5x - 4)² { here a = 50 and b = 4}

Side of the square = 5x - 4 units

Part B:

25x2 − 16y2 = (5x)² - (4y)² { a² - b² = (a + b) * (a - b) }

= (5x + 4y) * (5x - 4y) { here a = 5x and b = 4y}

Dimensions of Rectangle: (5x + 4y) ; (5x - 4y)

Answer:

see explanation

Step-by-step explanation:

A

25x² - 40x + 16 ← is a perfect square of the form

(ax - b)² = a²x² - 2abx + b²

Comparing the coefficients of like terms in the 2 expressions

a² = 25 ⇒ a = 5, b² = 16 ⇒ b = 4

and 2 × 5 × 4 = 40, thus

25x² - 40x + 16 = (5x - 4)²

The side of the square = 5x - 4

B

25x² - 16y² ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b), thus

25x² - 16y²

= (5x)² - (4y)² = (5x - 4y)(5x + 4y)

Dimensions of rectangle are 5x - 4 and 5x + 4

Answer:

9y(2x - 1)(x - 2y)(x + 2y)

Step-by-step explanation:

Given

18x³y - 9x²y - 72xy³ + 36y³ ← factor out 9y from each term

= 9y(2x³ - x² - 8xy² + 4y²)

Factor the first/second and third/fourth term in the parenthesis

= 9y( x²(2x - 1) - 4y²(2x - 1)) ← factor out (2x - 1) from each term

= 9y(2x - 1)(x² - 4y²)

x² - 4y² is a difference of squares and factors in general as

a² - b² = (a - b)(a + b), thus

x² - 4y²

= x² - (2y)² = (x - 2y)(x + 2y), hence

18x³y - 9x²y + 72xy³ + 36y³

= 9y(2x - 1)(x - 2y)(x + 2y) ← in factored form

Answer: 452.16 cm²

Step-by-step explanation: To find the area of a circle, start with the formula for the area of a circle.

Area = πr²

Notice that the radius of our circle is 12 cm so we can plug a 12 in for the radius in our formula.

Area = (π)(12cm)²

12 cm² is equal to 12 cm × 12 cm or 144 cm².

Area = 144π cm²

So the area of the circle is 144π cm².

Now, remember that π is approximately equal to 22/7 or 3.14 so we can estimate the area of the circle by plugging in 3.14 for π.

So we have (144)(3.14) which is equal to 452.16 cm².

So the area of the circle is approximately equal to 452.16 cm².

Answer:

The area is 452 cm2

Step-by-step explanation:

We use the formula:

Area = π (raduis)2 =π (12cm)´2 = 452, 39 cm2

Answer:

Step-by-step explanation:

Area of circle = πr²

= 3.14 * 12 * 12

= 452.16 sq. cm

The domain and the range of a function are the set of input and output values of the function.

The true statements are:

• f(25) = -10 is true
• f(45) = -65 is true
• f(20) = -10 is true

The domain and the range of function f(x) are given as (-15, 45) and (-65 , -5).

This means that:

• The input value of the function is from between -15 and 45 (exclusive)
• The output value of the function is from between -65 and -5 (exclusive)

The above highlights mean that:

• f(50) = -35 is false, because the input is out of the domain
• f(25) = -10 is true
• f(5) = -42 is false, because f(5) = -17
• f(45) = -65 is true
• f(20) = -10 is true

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Answer:

True options f(25) = -10

f(45) = -65

f(20) = -10

Step-by-step explanation:

Note that domain of function f(x) is (-15, 45).

Range is (-65 , -5).

In first option f(50) = -35. Here 50 is not in domain thus this point is not on the graph of f(x).

In second f(25) = -10.Value of x and function both are in domain and range thus acceptable.

In third f(5) = -42. Already given that f(5)=-17 thus it is false.

In fourth f(45) = -65. This is extreme boundary for domain and range also it is true.

In fifth f(20) = -10. This is also true as this point lie on function graph.