The figure shows the measurements, in inches, of a rectangular prism. 8 in 12 in 7 in What is the volume of the prism

A:92 in B: 236 in C: 472 D: 672

The probability that you pull a card at random from a regular 52 card deck and it is either a 3 or a heart is,

⇒ 17/52

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

We know that;

In a regular 52 card deck,

Number of 3 cards = 4

And, Number of heart cards = 14

Hence, The probability that you pull a 3 cards = 4 / 52

And, The probability that you pull a heart = 13/52

Thus, The probability that you pull a card at random from a regular 52 card deck and it is either a 3 or a heart is,

⇒ 4/52 + 13/52

⇒ 17/52

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The solution is Option A.

The value of the modulus function is | x - 42.80 | = 12

Regardless of the sign, a modulus function returns the magnitude of a number. The absolute value function is another name for it.

It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.

The value of the modulus function is always non-negative. If f(x) is a modulus function , then we have:

If x is positive, then f(x) = x

If x = 0, then f(x) = 0

If x < 0, then f(x) = -x

Given data ,

Let the modulus function be represented as A

Now , the equation will be

The amount James borrowed from Rita or Rita borrowed from James = $ 12

And , Let x be the amount of money James will have after he sees Rita

The amount of money with James in his wallet = $ 48

So ,

when James pays Rita , the equation will be

x = 42.80 - 12

On subtracting 42.80 on both sides of the equation , we get

x - 42.80 = -12   be equation (1)

And , when James receives the amount from Rita , the equation is

x = 42.80 + 12

On subtracting 42.80 on both sides of the equation , we get

x - 42.80 = 12   be equation (2)

Now , the modulus function will be

| x - 42.80 | = 12

Hence , the function is | x - 42.80 | = 12

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A characteristic of interest for the elements is called C) Variable.

A dataset is a grouping or set of data. This set is typically displayed in a tabular format. Each column provides information about a distinct variable. In accordance with the stated question, each row represents a certain component of the data set. The management of data includes datasets.

A sample is a condensed, controllable representation of a larger group. It is a subgroup of people with traits from a wider population. When population sizes are too big for the test to include all potential participants or observations, samples are utilized in statistical testing.

A qualitative variable, often known as a categorical variable, is one in which the variable categories are expressed verbally rather than as sets of numbers. Nominal and ordinal are the two subtypes of categorical data. Nominal variables don't have numerical values; they have "names."

Therefore, A characteristic of interest for the elements is called C) Variable.

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For completion of maze faster, time need to be decreased. therefore test is left tailed.

The significance level, also denoted as alpha or α, is the probability of rejecting the null hypothesis when it is true. For example, a significance level of 0.05 indicates a 5% risk of concluding that a difference exists when there is no actual difference.

These types of definitions can be hard to understand because of their technical nature. A picture makes the concepts much easier to comprehend!

The significance level determines how far out from the null hypothesis value we'll draw that line on the graph. To graph a significance level of 0.05, we need to shade the 5% of the distribution that is furthest away from the null hypothesis.

It is give that mean time for maze is

seconds.

We will conduct hypothesis for population parameter (not sample statistics).

The null and alternate hypothesis are as below:

H0 : µ = 18

Ha : µ < 18

For completion of maze faster, time need to be decreased. therefore test is left tailed.

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As the importance of having a powerful online presence continues to grow, many people are chosen to build their own websites using do-it-yourself (DIY) tools.

These tools, also known as website builders, are relatively easy to use and inexpensive. Examples include Wix, Square Space, Weebly, and more.

Web builder users lean to create two various types of websites, either personal sites a creative display, blog or portfolio or business sites for online ecommerce, sales, or an online business presence.

Understanding what users of web builders design with the DIY tools is an important step in pick out what makes these tools stand out.

While the mass of users is familiar with the techniques needed to build a site, the actual types of websites being built vary. Nearly half of respondents (48%) specify that their website was built for personal purposes, while 42% said that their website is for business.

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The equation that represents the total sales for the month is given as follows:

y = 0.05x + 1000.

The linear function for this problem is defined in slope-intercept format, as follows:

y = mx + b.

In which:

The parameters for this problem are given as follows:

b = 1000, m = 0.05.

Hence the function is defined as follows:

y = 0.05x + 1000.

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The area of the given figure would be = 508yd

The area of an object is defined as the total space that is being occupied by that object.

The are of the given shape above= area of a rectangle - area of square.

Area of the rectangle = length × width

= 36 × 18 = 648yd

Are of a square = length × width

= 10×14 = 140

Therefore, area of the figure, 648 - 140 = 508yd

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a. The number of people that enjoyed only skiing is 129

b. The number of people that enjoyed snow boarding and ice skating only is 13

c. The number of people that enjoyed snow board or ice skating is 221

d. The number of people that enjoyed none is 35

e. The number of people that enjoyed at least two is 62

sets is a collection of well-defined objects or elements.

The total number of visitors is 350

n(ski and snow board only) = 49-2 = 47

n( ski and skating) only= 2-2 = 0

n( snow board and skating) = 15-2 = 13

n( snow board only) = 154-(47+13+2) = 92

n( skating only) = 57-(13+2) = 32

a. The number of that that enjoyed skiing only = 178-(47+2) = 129

b. n( skating and snow board) only= 13

c. n ( ski or snow board) only = 129+92 = 221

d. the number of people that didn't enjoy any = 350-(129+47+92+13+32+2)

= 350-315 = 35

e. the number of people that enjoyed at least two = 13+2+47 = 62

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The function represents the domain of a function is x ≥ -2.

What is a graph of a quadratic function?

A graph of a quadratic function is a type of parabola, which is a symmetric, U-shaped curve that opens either upward or downward. The equation of a quadratic function is y = ax² + bx + c, where x and y are variables, and a, b, and c are constants.

The graph of a quadratic function is determined by the value of the coefficient a. If a is positive, the parabola opens upward, and if a is negative, the parabola opens downward. The vertex of the parabola is the highest or lowest point on the graph and it is the point of symmetry of the parabola. The x-coordinate of the vertex is given by -b/(2a) and the y-coordinate of the vertex is given by the value of the function at that point.

In the given figure, we can see that it is a parabola, and if we look towards the options, then the third option is a domain of the given function

x ≥ -2

So we can say this is the perfect match for the given figure.

Hence, the function represents the domain of a function is x ≥ -2.

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Two isosceles right triangles are the two triangles formed by the cut.

A quadrilateral is a four-sided polygon, having four edges and four corners.

Given that Nathan cut a square tile in half for his kitchen, he made one cut along a diagonal from one vertex to another,

We need to find the triangles formed by cutting the square diagonally.

Every square has 4 right angles, so each triangle will have one right triangle, which makes the triangles, right triangles.

They are isosceles because all sides of the square are the same, though the diagonal is not.

Hence,  Two isosceles right triangles are the two triangles formed by the cut.

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The slope of the line is 0.93 and the y intercept is 100.54

Value of tempareture at time 30 mins = 1/2 hr = 101.01°

Value of tempareture at 1 hr is = 101.47°

Value of temperature at 90 mins  =1.5 hr = 101.935°

An equation is a formula that uses the equals sign to connect two expressions to show that they are equal.

A line's slope is how steeply it slopes from LEFT to RIGHT. The slope of a line is determined by dividing its rise, or vertical change, by its run, or horizontal change.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it may take as input. After we enter an x value, the function outputs this sequence of values.

The collection of all a function's outputs is its range. Example: Let's have a look at the function f: A - > B, where f(x) = 2x and A and B each represent a "collection of natural numbers." The domain in this instance is A, and the co-domain is B. The range then appears as the function's output.

As per the problem

at starting that is x =0 hrs The temperature y = 99.9°

at x = 10/60 = 1/6 , y = 100.7° and at x = 2 , y = 102.4°

The equation of the line is

y-y₁ = (y₂ - y₁)/(x₂ - x₁) * (x - x₁)

(y - 100.7) = (102.4 - 100.7)/(2 - 1/6) * (x - 1/6)

y = 0.93x + 100.54

The slope of the line is 0.93 and the y intercept is 100.54

Value of tempareture at time 30 mins = 1/2 hr = 101.01°

Value of tempareture at 1 hr is = 101.47°

Value of temperature at 90 mins  =1.5 hr = 101.935°

Temperature at 4 hrs past current time  = 104.26°

The domain of the function will be the time which can go upto infinite.

The range will be the temperature and have a fixed value between the range of a human body temperature as the body temperature can not exceed that temperature.

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Answer:

No. The relation shows indirect variation.

Step-by-step explanation:

      In this relation the absolute value of one variable increases while the other gets decreased.

xy = k

  [tex]\sf x = \dfrac{k}{y}[/tex]

Here, xy = 3

           [tex]\sf x = \dfrac{3}{y}[/tex]

So, if the product of two variables is constant, then it is indirect or inverse variation.

Option C, yes, the opposite side are both parallel and congruent, is the correct answer.

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.

According to the definition of parallelogram the opposite sides of the parallelogram are equal and parallel.

Hence, option C, yes, the opposite side are both parallel and congruent, is the right answer.

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According to the area of parallelogram, the value of height is 4m.

In math the term parallelogram is defined as a special kind of quadrilateral in which the opposite sides are parallel and equal.

And the general form to calculate the area of parallelogram is written as,

=> A = base x height,

Here we know that the area of the parallelogram is 48 m² and the base is 12 m.

Then the value of height is calculated as,

=> 48 = 12 x height.

When we simplify this one then we get the value of height as,

=> height = 48/12

=> height = 4.

Therefore the correct option is A.

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There are 55 adults and 27 younglings attended the club.

let the number of adults attended the club be x

let the number of younglings  attended the club be y

total people attended the club = 82

so,

x + y = 82.....[1]

cost for the adult = $6

cost for the younglings = $4

so total amount collected = $438

so, equation formed is ,

6x + 4y = 438.......[2]

from equation [1]

x + y = 82

x = 82 - y

put this in equation [2]

6(82 - y) + 4y = 438

492 - 6y + 4y = 438

492 - 2y = 438

492 - 438 = 2y

2y = 54

y = 27

put this value in equation [1]

x + y = 82

x + 27 = 82

x = 82 - 27

x = 55

so, there are 55 adults and 27 younglings attended the club.

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a) A linear equation that describes the relationship between the number of buses and the number of vans needed for 120 students is 24x + 8y = 120.

b) If the teachers rent 4 buses, the number of vans they will need to transport all the students is 3.

c) If the teachers rent 6 vans, the number of buses they will need to transport all the students is 3.

d) If the teachers rent only vans, the number of vans needed will be 15.

e) Suppose the teachers rented only buses, the number of buses needed will be 5.

A linear equation is an algebraic equation of the form y = mx+b.

A linear equation involves a constant and a first-order (linear) term, with m as the slope and b as the y-intercept.

The total number of students on the field trip = 120

The number of students a bus can seat = 24

The number of students a van can seat = 8

Let the number of buses = x and the number of vans = y

24x + 8y = 120

b) Renting 4 buses, the number of vans needed:

24(4) + 8y = 120

96 + 8y = 120

8y = 24

y = 3

c) Renting 6 vans, the number of buses will be:

24x + 8(6) = 120

24x = 48 = 120

24x = 72

x = 3

d) Renting only vans, the number needed will be:

24(0) + 8y = 120

8y = 120

y = 15

e) Renting only buses, the number needed will be:

24x + 8(0) = 120

24x = 120

x = 5

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Answer:

the answer is to the question is 12

If the rental car company charges $54.75 per day to rent a car and $0.14 for every mile driven, then the inequality which can be used to determine number of days Camden can afford to rent is "54.75x + 0.14(75)  ≤ 120"  and the number of days are 2  .

the per day charge for the car by rental company is = $54.75  ;

the charge for per mile driven is = $0.14  ;

let the number of days Camden rents the car is = x days ;

let the number of miles driven by Camden be = y miles ,

the equation for the total cost (c) of the trip can be denoted as :

⇒ c = 54.75x + 0.14y    ...equation(1)

the atmost amount that Caden can afford is = $120  ;

So , the situation can be represented in inequality form as :

⇒ 54.75x + 0.14y ≤ 120  ;

the number of miles driven by Camden is = 75 miles ,

Substituting value of y = 75 in the inequality ,

we get ;

⇒ 54.75x + 0.14(75)  ≤ 120 ;

⇒ 54.75x + 10.5  ≤ 120 ;

⇒ 54.75x ≤ 120 - 10.5  ;

⇒ 54.75x ≤ 109.5 ;

⇒ x ≤ 109.5/54.75   ;

⇒ x ≤ 2 .

Therefore , Camden can afford to rent while staying within his budget for 2 days .

The given question is incomplete , the complete question is

A rental car company charges $54.75 per day to rent a car and $0.14 for every mile driven. Camden wants to rent a car, knowing that: He plans to drive 75 miles. He has at most $120 to spend.

Write and solve an inequality which can be used to determine "x", the number of days Camden can afford to rent while staying within his budget ?

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Answer:

Answers are in bold

Data set A:

Mean: 7

Median: 7

Mode: 7

Range: 11

Data set B:

Mean: 78

Median: 95

Mode: No mode or all the numbers (85, 105, 95, 90, 115)

Range: 30

Data set C:

Mean: 13

Median: 13

Mode: 11 and 16

Range: 7

Step-by-step explanation:

I just answered this but you're welcome.

The solution to the inequality:

(1/2)*|x + 1| ≤ 6

is:

x ≤  11 or x ≥  -13

Here we want to solve the inequality below:

(1/2)*|x + 1| ≤ 6

To solve it we need to isolate x, so let's start by multiplying both sides by 2:

2*(1/2)*|x + 1| ≤ 2*6

|x + 1| ≤ 12

Now we can break the absolute value part into two inequalities:

(x + 1) ≤ 12

(x + 1) ≥ -12

Solving these two we will get:

x ≤ 12 - 1 = 11

x ≥ -12 -1 = -13

That is the solution.

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For the energy use to double it will take approximately 69.66 years.

To find out how many years it will take for the energy use to double, we can use the formula for exponential growth:

P = P₀ * (1 + r)^t

where P is the final amount of energy use, P₀ is the initial amount of energy use, r is the growth rate (1% per year in this case), and t is the number of years.

Setting P = 2 * P₀ and solving for t, we get:

2 * P₀ = P₀ * (1 + r)^t

Dividing both sides by P₀:

2 = (1 + r)^t

Taking the natural logarithm of both sides:

ln(2) = t * ln(1 + r)

Dividing both sides by ln(1 + r):

t = ln(2) / ln(1 + r)

Plugging in the values for r = 0.01 and using the natural logarithm function, we get:

t = ln(2) / ln(1 + 0.01) = 69.66 years

So it will take approximately 69.66 years for the energy use to double.

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Answer:

Step-by-step explanation:

Answer:

Volume =936.3 ft³

Step-by-step explanation:

Solution Given:

The mathematics tells us that the cube of the ratio of the lengths is equal to the ratio of the volumes.

[tex]{(\frac{Side\: of\: bigger \: solid}{Side \: of \: smaller \: solid} )}^3 = \frac{volume\: of \: bigger \: solid}{volume \: of \: smaller \: solid} [/tex]

let volume of smaller solid be x.

by equation

[tex] {(\frac{12}{8} )}^3 = \frac{3160}{x} [/tex]

doing criss cross multiplication

12³*x=3160*8³

we get

[tex]x = \frac{3160 \times 8^3}{12^3} [/tex]

x= 936.296296296 ft³

[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &120000\\ r=rate\to 1.4\%\to \frac{1.4}{100}\dotfill &0.014\\ t=\textit{elapsed time}\dotfill &10\\ \end{cases} \\\\\\ A = 120000(1 + 0.014)^{10} \implies A \approx 137898.90 ~\hfill \boxed{A=120000(1.014)^t}[/tex]

Answer:

850

Step-by-step explanation:

Everything above 5 goes to the next tenth. Example:

17 = 20

Everything below 5 goes to the next below tenth. Example:

13 = 10

You get it or more expantion?

$85000 is the prize money is awarded in total.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that  top four winners in a golf tournament share the prize money in the ratio 9:5:2:1.

The top prize winner receives $45,000

We need to find the prize money is awarded in total.

9+5+2+1=17

9/17 x = 45000

Divide both sides by 9/17

x=$85000

Hence, $85000 is the prize money is awarded in total.

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The equation that represents the number of hours on the second week will be x / 184 = 13 / 119.60.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The equation to Eric works 13 hours the first week and earns 119.60. the second week, he earns 184.

Let 'x' be the number of hours. Then the equation is given as,

x / 184 = 13 / 119.60

Simplify the equation, then we have

x / 184 = 13 / 119.60

x = 184 x 13 / 119.60

x = 2392 / 119.60

x = 20 hours

The equation that represents the number of hours on the second week will be x / 184 = 13 / 119.60.

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The specified equations in the question are in logarithmic form. The exponential form of the equations are as follows;

The logarithmic form of an exponential equation is the form logₐ(c) = b

The exponential form from which the logarithmic form is obtained, is the form aᵇ = c

The form of the equations in the question are in the logarithmic form, the exponential form  of the equation are found as follows;

(1) 3 = logₓy

Therefore, x³ = y

(2) log₁₀100 = 2

Therefore, 10² = 100

(3) log₃27 = 3

Therefore, 3³ = 27

(4) log₁₀1 = 0

Therefore, 10⁰ = 1

(5) logₐa = 1

Therefore, a¹ = a

(6) log₁₀x = y

Therefore, [tex]10^y[/tex] = x

(7) log₅p = q

Therefore, [tex]5^q[/tex] = p

(8) [tex]log_yx=20[/tex]

Therefore, y²⁰ = x

(9) log₂16 = 4

Therefore, 2⁴ = 16

(10) log₅25 = 2

Therefore, 5² = 25

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So, there are 56 different committees possible, of 3 people, that could be elected to attend a political national convention from a ballot of 8 names.

When choosing a committee of 3 people from a group of 8 names, the order in which the names are chosen does not matter and repetition is not allowed, this is an example of a combination.

The number of different committees possible is given by the binomial coefficient (n choose k) where n is the number of items to choose from (in this case, 8 names) and k is the number of items to choose (in this case, 3 names for the committee).

The binomial coefficient is calculated as:

n!/(k!(n-k)!)

where ! denotes the factorial operator, meaning the product of all positive integers up to that number.

So in this case, the number of different committees possible is (8!/(3!(8-3)!) = 8!/(3!5!) = (876)/(321) = 56.

Therefore, there are 56 different committees possible, of 3 people, that could be elected to attend a political national convention from a ballot of 8 names.

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Step-by-step explanation:

the vertex form of a quadratic function is

y = (x - h)² + k

with (h, k) being the vertex.

luckily for us the function is already defined in that form.

so, when we compare

y = (x + 4)² - 9

with the general form about (h, k) above we see

h = -4

k = -9

so, the vertex is (-4, -9).