Tim drives at an average speed of 80 km per hour for 3 hours 45 minutes.
Work out how many kilometres Tim drives.

Answer:

51.1 m² and 75 in²

Step-by-step explanation:

A cube has 6 congruent square faces

Given the surface area of the cube, that is the combined area of the 6 faces , then

divide the surface area by 6 for area of each face.

(a)

306.6 m² ÷ 6 = 51.1 m²

(b)

450 in² ÷ 6 = 75 in²

a) The area of each face of a cube 306.6 is 51.1 square units.

b) The area of each face of a cube 450 is 75 square units.

a) A cube has 6 faces

Area of each face is (side × side)

Area = side × side

So, total area is equal to 6 times the area of each side.

Area = 6 × (side × side)

Now,

306.6 = 6 (side)²

(side)² = 51.1

Therefore, the area of each face is 51.1 square units.

b) A cube has 6 faces

Area of each face is (side × side)

Area = side × side

So, total area is equal to 6 times the area of each side.

Area = 6 × (side × side)

now,

450 = 6 (side)²

(side)² = 75

Therefore, the area of each face is 75 square units.

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The difference between the best and worst credit score interest rates would be = 6.24%

An interest rate is defined as the particular amount of money an individual receives for a period of time due to an investment made.

The difference between the best and the worst credit score interest rates would be to substrate the best score from the worst score.

The best interest rate score = 3.65

The worst interest rate score = 9.89

Therefore the difference = 9.89 - 3.65 = 6.24 %

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It is true that when you design an algorithm, it should be general enough to provide a solution to many problem instances, not just one or a few of them.

In mathematics, an algorithm is a process, a description of a series of steps that may be used to solve a problem; however, they are now far more prevalent than that.

Although many areas of research (and daily life) employ algorithms, long division's step-by-step process is probably the most prevalent example.

Thus, It is true that when you design an algorithm, it should be general enough to provide a solution to many problem instances, not just one or a few of them.

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Answer:

[tex]\sqrt{\sqrt{2} }[/tex]

Step-by-step explanation:

f(1)=3; f(1)=f(0)^2+1
f(0)=[tex]\sqrt{2}[/tex]=f(3)^2+0; f(3)^2=sqrt*2; f(3)=sqrt*sqrt2

Answer:

Tn = 4 + (n – 1)3

is the arithmetic sequence for the nth term

Step-by-step explanation:

formula for an arithmetic sequence is

[tex]tn = a + ( n - 1)d[/tex]

where:-

Tn = nth term

a = first term

n = number of terms

d = common difference.

now back to the question

the 8th term of an arithmetic sequence is 25.

that will be written as

[tex]t8 = a \: + ( 8 - 1)d = 25[/tex]

[tex]a + (7 )d = 25 \: \: \: \: .....eqn1[/tex]

and the 14th term is 43

this will be written as

[tex]t14 = a + (14 - 1 )d = 43[/tex]

[tex]a + 13d = 43 \: \: \: \: .....eqn2[/tex]

subtract eqn 1 from 2

a – a, 13d – 7d, 43–25

[tex]6d = 18[/tex]

divide both sides by (6)

[tex] \frac{6d \\ }{6} = \frac{18}{6} [/tex]

d = 3

now that we know d = 3 let's substitute it in eqn 1 above.

a + 7d = 25

a + 7(3) = 25

a +21 = 25

a = 25 – 21

a = 4

now the normal arithmetic sequence given will be

[tex]tn = 4 + (n - 1 )3[/tex]

I hope this helps

Answer: x=4

Step-by-step explanation:

The required value of the expression 2c - a is 1.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

It's possible to multiply, divide, add, or subtract with this mathematical operation.

An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division, etc.)

So, we have:

x²+3x-28

x²+7x-4x-28     [28=7×2×2, 7-(2×2)=7-4=3]

x(x+7)-4(x+7)

(x+7)(x-4)$

In light of the fact that x2+3x-28 can be expressed as (x+a)(x-b).

in order to compare (x+7)(x-4) and (x+a)(x-b).

As a result, a = 7 and b = 4.

Similarly,

x²-10x-56$

x²-14x+4x-56       [ 56= 7×2×2×2, - (7×2)+(2×2) = -14+4=10]

x(x-14)+4(x-14)

(x-14)(x+4)

Given that (x+2b)(x+c) can be used to represent x2-10x-56.

Consequently, compare (x-14)(x+4)and (x+2b)(x+c).

Now,  c=4    [∵c>0].

Then,

2c-a

(2×4)-7

8-7

1

Therefore, the required value of the expression 2c - a is 1.

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Answer:

The third graph comes closest, but some difference suggest that the fifth graph, which is incorrectly displayed, may be the correct one.

Step-by-step explanation:

I will rewrite the equation to the form it seems to have been intended:  (x + 4)^2 + (y − 7)^2 = 49.  Note the addition of two "^" to indicate the 2's are both powers, and not "*2."

Plot the equation on a scientific calculator or a free web-based scientific calculator, such as DESMOS.  Compare the graph with the graph options.  See the attached worksheet.

The plotted graph comes close to the graph option selected (third from left), but there were differences, as noted.  It was the closest I saw on a first pass, but spend time ooking more closely at the options to see if there is a better choice.  The fifth option doesn't look like it belongs, and the correct option may not be listed.

The probability to find the spin projection along the x-axis to be 1 is 0.5. The operator corresponding to the spin projection along the x-axis is X, and the expectation value of X in this state is 0.

This result is a consequence of the fact that operator X is a Hermitian operator, which means that its eigenvalues are real. The eigenvalues of X are ±1, so the probability of measuring a spin projection of 1 is ½. This is because the eigenstate corresponding to the eigenvalue 1 is |+⟩, which is a superposition of |0⟩ and |1⟩.

Similarly, the eigenstate corresponding to the eigenvalue -1 is |-⟩, which is also a superposition of |0⟩ and |1⟩. Thus, the qubit is equally likely to be found in either the |+⟩ or the |-⟩ state, and so the probability of measuring a spin projection of 1 is 0.5.

In summary, since the qubit is in a superposition of the two computational basis states, the expectation value of any Hermitian operator is 0, and the probability of measuring a spin projection of 1 is 0.5.

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Answer:

(0,-3)

Step-by-step explanation:

C( 5,1)

5 is the horizontal value.  It is the distance from zero.  If we go 5 units left we will be at 0

1 is the vertical value.  Is is the distance above the x axis.  If we go down 4 units, we will be at -3

(0,-3)

Answer: The equation that represents the amount of money Mrs. Espinoza will pay to rent the bounce house for h hours is:

t = 15 + 5h

Step-by-step explanation: From the table, it can be seen that the rental cost is $15 for the first hour and $5 for each additional hour.

The rental cost t can be represented by the equation t = 15 + 5h

The first term, 15, represents the fixed cost of $15 for the first hour.

The second term, 5h, represents the variable cost of $5 for each additional hour.

So if Mrs Espinoza rents the bounce house for h hour, the cost will be 15+5h.

Labeling:

t represents the total amount that Mrs. Espinoza will pay to rent the bounce house

h represents the number of hours that Mrs. Espinoza rents the bounce house.

15 is the fixed cost of renting the bounce house for the first hour.

5 is the variable cost for each additional hour.

The equation t = 15 + 5h represents the total cost of renting the bounce house for h hours.

We need 600 grams of flour to make the recipe with 400 grams of sugar.

What is a ratio?

A ratio is a mathematical comparison of two or more values or quantities. It is represented as a fraction, with the numerator representing the first value or quantity and the denominator representing the second value or quantity.

An equation is a mathematical statement that asserts the equality of two expressions. In this case, the recipe uses 300 grams of flour for every 200 grams of sugar. To write an equation that represents this relationship, we can use the variable "f" to represent the number of grams of flour and "s" to represent the number of grams of sugar.

The equation that represents this relationship is f = (3/2)s. The coefficient of the "s" variable is 3/2, which represents the ratio of flour to sugar in the recipe (3 parts flour to 2 parts sugar). This equation states that the number of grams of flour, represented by f, is equal to 3/2 times the number of grams of sugar, represented by s.

So, in other words, if we know the number of grams of sugar we need, we can use this equation to find out how many grams of flour we need. For example, if we need 400 grams of sugar, we can substitute that into the equation:

f = (3/2)s

f = (3/2) * 400

f = 600

Hence, We need 600 grams of flour to make the recipe with 400 grams of sugar.

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1. a function that could be used to model the data in the table. Make sure to use h for height and d for distance is d = -0.425h + 39.25

2. If the balloon is 800 meters high,  the farthest distance that you would be able to see is  48 km

3. at the  height  of  67 does the balloon have to rise for the building to be visible.

The table in the question shows a relationship between the height of a balloon and the distance away from the balloon that can be seen. Using this data, a linear function can be determined that models this relationship. The function is d = -0.425h + 39.25, where h is the height of the balloon in meters and d is the distance in kilometers. Using this function, if the balloon is 800 meters high, the farthest distance that can be seen is 48 km, which is the y-intercept of the equation.

Inversely, if a building is 16 km away from the balloon, the height the balloon must rise for the building to be visible is 67 m. This can be determined by substituting 16 for d in the equation and solving for h.   Overall, the linear function d = -0.425h + 39.25 models the relationship between the height of the balloon and the distance away from the balloon that can be seen. The equation can be used to determine the height of the balloon needed to see a certain distance or the distance away from the balloon that can be seen when the balloon is at a certain height.

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Height in meters 15 30 45 60 75 90 105 , Distance in kilometers 13.833 19.562 23.959 27.665 30.931 33.833 36.598

1. Determine a function that could be used to model the data in the table. Make sure to use h for height and d for distance.

2. If the balloon is 800 meters high, what is the farthest distance that you would be able to see? Round the answer to the nearest whole number

3. Round answer to the nearest whole number A building is 16 km away. What height does the balloon have to rise for the building to be visible?

The relation in this problem that is a function is given as follows:

D. (3, 4), (-5, 2), (5, 1), (-8, 2).

To verify whether a relation represents a function, we need to observe if each input is mapped to only one output.

The relationships that are not functions in this problem, along with the justification, are given as follows:

Hence the relationship that is a function is given by option D, as the inputs 3, -5, 5 and -8 are each mapped to a single output.

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The correct option is A "Because the population sizes are so different, it's impossible to make the standard deviations equal by adjusting the two sample sizes ".

The collection of data is gathered and chosen from a statistical population with the use of some prescribed techniques in both statistics and quantitative methodology. Data sets may be divided into two categories: sample and population.

All the components of the data set are included in the population, which also contains quantifiable qualities like mean and standard deviation.

A sample is made up of one or more observations that are taken from the population, and a statistic is what makes a sample quantifiable. The act of sampling is the selection of a sample from a population.

Complete question:

Suppose you want to estimate the percentage of college students who are using electronic cigarettes on a regular basis. You have permission to sample two colleges, Grove City College and Penn State University. Grove City has an enrollment of 2,500 students and Penn State has an enrollment of 45,000 students. What should the relative size of our samples be from each school if we want the two sampling distributions to have approximately the same standard deviation?

A. Because the population sizes are so different, it's impossible to make the standard deviations equal by adjusting the two sample sizes

B. We should take a larger number of Penn State students since there are more of them.

C. We should take a larger number of Grove City students since there are fewer of them.

D. We should take the same size samples from each school.

E. We should take samples that are exactly 10% of each school's enrollment.

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On solving the provided question we can say that by factorization are

x(x-3) + 2(x-3) ⇒(x-3)(x+2) ⇒ x = 3, -2

A number or other mathematical object is factored, or written as the product of numerous factors—typically smaller or simpler things of the same kind—in mathematics. For instance, the integer 15 is factorized as 3 5, which is the factorization of the polynomial x2 – 4. Factorization in mathematics refers to the breakdown of a number into smaller numbers that are multiplied together to produce the original number. Factorization is the division of a number into its factors or factors. 12 is multiplied by 3 and 4 as an example.

the polynomial is as =  x^2 + 14x + 48

by factorization are

x(x-3) + 2(x-3)

(x-3)(x+2)

x = 3, -2

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.

Greetings!!

Lool at the attachment

Answer: A piecewise function is a function that is defined by multiple equations, each with its own domain. The equation for the situation can be represented as a piecewise function as:

f(x) = { 2x, 0<x<=5}

f(x) = { 1.5x, x>5}

Where f(x) is the cost of x number of cookies.

The first equation represents the cost of x number of cookies when x is between 0 and 5 (inclusive). The second equation represents the cost of x number of cookies when x is greater than 5.

So, the piecewise function that represents the cost of x number of cookies based on the given conditions is:

f(x) = { 2x, 0<x<=5}

f(x) = { 1.5x, x>5}

It means if you buy x number of cookies and if x is between 0 and 5 (inclusive) then you are charged $2 per cookie and if x is greater than 5 then you are only charged $1.50 per cookie.

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

(3,2) is a solution to the equationExplanation:If (3 ,2) is a solution then it must 'satisfy' the equation. That is make it True.To determine this, substitute x = 3 and y = 2 into the left side of the equation and if the result is 12 then it is a solution.⇒(2×3)+(3×2)=6+6=12LHS = RHS hence (3,2) is a solution

Answer:

the solution is 9/2 = X24

Answer:

8 mins 20000feet

Step-by-step explanation:

let mins be x

45600-3200x = 2500x

so 45600= 5700

x=8

2500*8 = 20000

The average rate of change in annual sales are as follows;

a) Between 2003 and 2004, the average rate of change of sales is -3 unit per year

b) The average rate of change between 2003 and 2006 is -9 units per year

The average rate of change of a set of values is the rate at which one variable changes with regards to the unit change in another variable, over an interval.

The values in the table are presented as follows;

The sales of a product in millions annually.

Year;  1998[tex]{}[/tex]  1999  2000  2001  2002  2003  2004  2005  2006

Sales; 174 [tex]{}[/tex]     201    222     237   246     249    246    237     222

The average rate of change between two data points, (x₁, y₁), and (x₂, y₂), can be obtained as follows;

[tex]Average \, rate \, of \, change= \frac{y_2-y_1}{x_2-x_1}[/tex]

a) The average rate of change between 2003 and 2004 is found using the formula for the average rate of change as follows;

[tex]Average = \frac{246-249}{2004-2003} =-3[/tex]

b) The average rate of change in sales of the product between 2003 and 2006 is found as follows;

Rate of change between 2006 and 2003; [tex]\frac{222-249}{2006-2003} =\frac{-27}{3} =-9[/tex]

Please find attached the screen grab of the table in the attachment that specifies the annual sales of the product (in millions).

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Answer: B

Step-by-step explanation:

On solving the provided question, we can say that the range is between the two sides' difference and their sum.

The variable's range is obtained by finding its largest observed value (maximum) and subtracting its smallest observed value (minimum). Variational bounds or possible range: various steel prices; various styles; The extent or magnitude of a procedure or action: insight. the maximum or expected range of a weapon's projectile. The range of a list or set is the number between the minimum and maximum. Prior to identifying the region, align all the numbers. Remove (remove) the lowest number from the highest number next. The list's range is provided in the solution.The solution provides the list's range.

T is length of the third side

[tex]18-13 < T < 18+13[/tex]

[tex]5 yards < third side < 31 yards[/tex]

The range is between the two sides' difference and their sum.

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The sum of the three integers is 57.

The term integer in math is known as the collection of whole numbers and negative numbers.

Here we have given that the product of three different positive integers is equal to 7³.

Here let us consider that x,y,z be three positive number.

Then based on the given is written as

=> xyz = 7³

When we expand the equation, then we get,

=> xyz = 343

Here we have expand the equation as,

=> xyz = 1 × 7 × 49

Then the equation written as

=> x + y + z = (1 + 7 + 49)

Then the sum equation is calculated as

=> x + y + z = 57

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Answer:

Step-by-step explanation:

To calculate the total amount Daniel LaRusso will have to pay back in 2 years, we first need to calculate the interest he will owe on the loan.Simple Interest (I) = P * r * t

where P is the principal (the amount borrowed), r is the annual interest rate (expressed as a decimal), and t is the time (in years) for which the loan is borrowed.In this case, the principal is $1,200, the annual interest rate is 8%, and the time is 2 years.I = $1,200 * 0.08 * 2 = $192So, he will have to pay back a total of $1,200 (principal) + $192 (interest) = $1,392So, Daniel LaRusso will have to pay back a total of $1,392 in 2 years.

Answer:

---------------------------------

The amount of interest at 8% simple for 2 years is 16% of the loan:

The total amount including both the principal and interest is:

Correct choice is D.