Someone help me, I don't understand this

The correct option to represents downloads and rentals this person purchases is, (6, 14) and (8, 12).

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

A digital download, x, costs $3 and a digital rental, y, costs $2 for a song. a person has $48 maximum to spend in a month.

Now, Let (x, y) represent number of downloads and rentals this person purchases.

Hence, We can formulate;

⇒ 3x + 2y ≤ $48

So, We can check all the options which satisfy the above equation.

By option C; (x, y) = (6, 14)

⇒ 3x + 2y ≤ $48

⇒ 3×6+ 2×14 ≤ $48

⇒ 18 + 28 ≤ 48

⇒ 46 ≤ 48

Hence, This option satisfy the equation.

By option D; (x, y) = (8, 12)

⇒ $3x + $2y ≤ $48

⇒ 3×8 + 2×12 ≤ 48

⇒ 24 + 24 ≤ 48

⇒ 48 = 48

Thus, It satisfy the equation.

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Step-by-step explanation:

the formula for the circumference of a circle is

2×pi×r

well, does this look familiar ?

our given circumference is

2×pi×sqrt(2)

so, clearly, r (radius) = sqrt(2).

the area of a circle is

pi×r²

so, for our circle that means

pi×sqrt(2)² = 2pi ft²

The minimum value of the expression is [tex]$\sqrt{\frac{abc(a+b+c)^2}{6}}$[/tex], with a, b, and c be positive real numbers.

What is the positive real number?

In mathematics, the set of positive real numbers is the subset of those real numbers that are greater than zero. The non-negative real numbers, also include zero.

We can simplify the expression as follows:

a^2 b^2 c = (ab)^2 c.

Now, we can use the AM-GM inequality to find the minimum value of the expression:

[tex][(ab)^2 c \ge \left(\frac{(ab)^2 + c}{2}\right)^2 = \left(\frac{(ab + c)^2 - 2abc}{4}\right)^2.][/tex]

As the minimum value is achieved when equality holds, we can set the equation to the original expression and simplify it.

[tex][(ab)^2 c \ge \left(\frac{(ab)^2 + c}{2}\right)^2 = \left(\frac{(ab + c)^2 - 2abc}{4}\right)^2.][/tex]

[tex]$a^2b^2c = \frac{(a^2b^2+ 2ab^2c+c^2b^2) - 2abc}{4}$[/tex]

[tex]$4a^2b^2c = (a^2b^2+ 2ab^2c+c^2b^2) - 2abc$[/tex]

4abc = (ab + c)(ab + c) - 2abc

4abc = (ab + c)^2 - 2abc

6abc = (ab + c)^2

so the minimum value is: [tex]$(\frac {(ab+c)^2}{6})^{\frac{1}{2}}$[/tex]

[tex]$\sqrt{\frac{abc(a+b+c)^2}{6}}$[/tex]

Hence, the minimum value of the expression is [tex]$\sqrt{\frac{abc(a+b+c)^2}{6}}$[/tex], with a, b, and c be positive real numbers.

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[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=7 \end{cases}\implies V=\cfrac{\pi (3)^2(7)}{3} \\\\\\ V=21\pi \implies {\Large \begin{array}{llll} V\approx 65.97 \end{array}} ~in^3 ~~ \approx 66~in^3[/tex]

Each puppy would weigh approximately 2.13 grams if all the puppies weighed the same amount.

To estimate the weight of each puppy, we need to subtract the weight of the basket from the total weight of the basket and puppies to find the total weight of the puppies.

Total weight of puppies = Total weight of basket and puppies - Weight of basket alone

= 2,977 - 1,077 = 1,900 grams

Then we divide the total weight of the puppies by the number of puppies to find the weight of each puppy:

Weight of each puppy = Total weight of puppies / Number of puppies

= 1,900 / 888

= approximately 2.13 grams

Each puppy would weigh approximately 2.13 grams if all the puppies weighed the same amount.

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Therefore ,as a result, the answer to the given circle problem is  

√ 1996/(√ 62)3 =0.0915, which is the curvature.

A circle is created in the plane by each point that is a specific distance from another point (center). Thus, it is a curve made up of points that are separated from one another by a defined distance in the plane. Additionally, it is rotationally symmetric the about center at every angle. Every pair of endpoints in a circle's closed, two-dimensional plane are evenly spaced apart from the "center." A circular symmetry line is made by drawing a line through the circle. Additionally, it is rotationally equal about the center at every angle.

Here,

Given: (7, 2t, 3t2) r'(t)

r''(t)= (0, 2, 6t) (0, 2, 6t)

r(t) x r(t) = (6t2, -42t, 14)

(36t4 + 1764t2 + 196) = sqrt (r'(t) x r"(t)

|r'(t)|= sqrt (49 + 4 T 2 + 9 T 4)

We know that t = 1 at (7,1,1), therefore sqrt (36 + 1764 + 196) = sqrt 1996 |r'(t)| = √ (49 + 4 + 9) = √ 62.

The curvature is then equal as√ 1996/(√ 62)3 =0.0915

Therefore ,as a result, the answer to the given circle problem is  √ 1996/(√ 62)3 =0.0915, which is the curvature.

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0.5x + 6 = 4x - 1

3.5x = 7

x = 2

Only one solution exists for the given equation.

Answer:

one

Step-by-step explanation

For a polynomial function, the number of solutions, or zeros, is generally equivalent to the highest degree. For example, a cubic function (e.g. [tex]x^3+2x^2[/tex]) has 3 real zeros (x=-2, x=0, and x=0) and a quadratic (e.g. [tex]x^2-1[/tex]) has 2 real zeros (x=-1 and x=1).

For your problem, [tex]\frac{1}{2} (x+12)=4x-1[/tex], the highest degree is 1 since this is a linear function. To prove there is only one solution, let's bring all the terms to one side, simplify, and solve for x.

There only one solution to the equation as shown above and as can be seen in step 4, the x is only to the first degree ([tex]x=x^1[/tex]) which indicates that there is only one solution, 2.

Answer:

yes

Step-by-step explanation:

Answer:

Step-by-step explanation:

First, find the length of the longer pipe, which is stated to be 5 times longer than the shorter piece. Substitute the longer piece as b. Same for the shorter piece, but as a.

[tex]a + b = 342\\5b\:+\:? = 342\\a = 5b[/tex]

Why a is 5b is because a is the correspondent value to b since they are both substituted, in short words this means that a will be the equivalent of |5 × b - 342|

Next, we substitute the problem in a ruled equation. Think of it this way: There are 2 values in the equation. One has a value of 5 and the other has a value of one. Add those together, and you get 6, right? This will be important for our final answer.

[tex]6b\div 6 = 342\div 6\\b = 57[/tex]

Lastly, substitute a.

[tex]a + b = 342\\a + \bold{57} = 342\\a = \left(342 - 57\right)\\\\a = 285\\b = 57[/tex]

Hope this helps!

Answer:

41

Step-by-step explanation:

area of square CDE = 4 × 4 = 16

area of triangle BCA = 1/2 × 10 × 5 = 25

total area = 16 + 25 = 41

Answer:

0.15

Step-by-step explanation:

Factors of 12 are 1, 2, 3, 4, and 6.

Only 5 is not a factor of 12.

The probability of rolling a 5 is 15 / 100, or 0.15, or 15%.

Therefore, the supplied variable problem's solution is found to be quantitative.

A variable is a quality that may be measured and take on several values. A few examples of variables are height, age, salary, province of birth, school grades, and kind of dwelling.

Here,

Quantitative variables are numerical variables, whereas categorical/qualitative variables assign the people into a category.

Because the length is quantified by numbers, it is (a) quantitative (such as 200 ft).

So , by observing the following information we can conclude that it is quantitative.

As a result, it is quantitative.

Therefore, the supplied variable problem's solution is found to be quantitative.

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The complete question is " All highway bridges in the United States are inspected periodically for structural deficiency by the Federal Highway Administration (FHWA). Data from the FHWA inspections are compiled into the National Bridge Inventory (NBI). Several of the nearly 100 variables maintained by the NBI are listed below. Classify and explain each variable as a) quantitative or qualitative; b) discrete or continuous; and c) by level of measurement. (10 points)

Route type (interstate, U.S., state, county, or city)

Length of maximum span (feet)

Number of vehicle lanes

Bypass or detour length (miles)

Condition of deck (good, fair, or poor)

Average daily traffic

Toll bridge (yes or no)"

The equation of function after a horizontal translation is y = 2*4ˣ⁺².

Initially, functions represented the idealized relationship between two changing quantities. A planet's position, for instance, depends on time. In the past, the idea was developed with the infinitesimal calculus at the end of the 17th century, and the functions that were taken into consideration until the 19th century were differentiable (that is, they had a high degree of regularity).

The realms of application of the concept of a function were substantially expanded at the conclusion of the 19th century when it was defined in terms of set theory.

An assignment of an element from set Y to each element of set X constitutes a function from set X to set Y. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

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The equation of the tangent line at any point on the curve is y = f'(x)x + c. For the line to be horizontal, its slope has to be zero, meaning that f'(x) = 0. Therefore, the coordinates of all points on the curve with a horizontal tangent line are those points (x, f(x)) such that f'(x) = 0.

The equation for any line tangent to a curve at a given point (x, f(x)) is given by the equation y = f'(x)x + c, where c is a constant. This equation is derived from the definition of the derivative, which is the instantaneous rate of change of a function at a given point. The slope of this line is equal to the derivative of the curve at the given point, or f'(x). A line is horizontal when its slope is equal to zero, meaning that f'(x) = 0. Therefore, the coordinates of all points on the curve at which the line tangent to the curve at that point is horizontal are all points (x, f(x)) such that f'(x) = 0. This is because a line with a slope of zero is always horizontal, regardless of the value of the constant c. So, in order to find the coordinates of all points on the curve at which the line tangent to the curve at that point is horizontal, we must find all points (x, f(x)) such that f'(x) = 0.

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The required graph has been attached below which represents the cube root function f(x) = ³√x.

The cube root function is given in the question, as follows:

f(x) = ³√x

We have to determine the graph of the given function.

The domain of the square root parent function is x ≥ 0 as the square root of only non-negative values exists and that of negative values does not exist, while the domain of the cube root parent function is the set of all real numbers as the cube root of all numbers exists.

Thus, the required graph has been attached below which illustrates the cube root function f(x) = ³√x.

Hence, the correct answer would be an option (B).

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The size of a television screen that is 21.6 inches wide and 16.2 inches high is approximately 27 inches (measured diagonally).

What is the Pythagorean theorem?

It's a relation in Euclidean geometry among the three sides of a right triangle. In it, the square of the hypotenuse is equal to the sum of the squares of the other 2 sides.

The size of a television screen can be found by using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the length of the diagonal of the screen is the hypotenuse, the width is 21.6 inches, and the height is 16.2 inches. We can use the theorem to find the length of the diagonal:

diagonal²= width² + height²

diagonal² = 21.6² + 16.2²

diagonal² = 467.76 + 262.44

diagonal² = 730.2

diagonal = √730.2

diagonal ≈ 27 inches

Hence, the size of a television screen that is 21.6 inches wide and 16.2 inches high is approximately 27 inches (measured diagonally).

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There is a 0.32768 or 32.77% probability that all 5 employees selected at random from the company have college degrees.

The probability of all 5 employees selected at random from the company having college degrees is calculated by using the following formula: P = (0.8)^5.  Substituting 0.8 for the probability of having a college degree, this equation simplifies to P = 0.32768.

Therefore, P = (0.8)^5 = 0.32768.

This implies that there is a 0.32768 or 32.77% probability that all 5 employees selected at random from the company have college degrees.

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The measurement that you can use in your future career depends on the exact career and there are many more options.

Depending on the exact career but measurements are plentiful in the healthcare business. First, you'll most likely deal with weight and height... since that's part of most healthcare consultations. Then, if you deal with medication, you'll use grams, milligrams, milliliters, and liters all the time. depending if the medication is in solid or liquid form.

Even as a nutritionist, you'll deal with grams and such for portion sizes. There are countless ways you'll use mathematics and measurements in the healthcare sector.  

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The union of two or more events is a single event that represents all the outcomes that belong to at least one of the original events.

16) It is often represented using the symbol "U" or "∪". For example, if event A is "rolling a 3 on a die" and event B is "rolling a 4 on a die", the union of A and B would be "rolling a 3 or a 4 on a die".

17)  The intersection of two or more events is a single event that represents all the outcomes that belong to all of the original events. It is often represented using the symbol "∩". For example, if event A is "rolling an even number on a die" and event B is "rolling a number greater than 3 on a die", the intersection of A and B would be "rolling a 4 on a die".

18)  The union of two or more events represents all the outcomes that belong to at least one of the original events, while the intersection of two or more events represents all the outcomes that belong to all of the original events. The union is a "larger" event that includes all outcomes from the original events, while the intersection is a "smaller" event that only includes outcomes that belong to all of the original events.

For example, if event A is "rolling an odd number on a die" and event B is "rolling a number less than 4 on a die", the union of A and B would be "rolling a 1,3, or a 2 on a die" while the intersection of A and B would be "rolling a 1 or a 3 on a die".

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A graphical plot with sales on the Y axis and time on the X axis is a:

a. Scatter diagram.

Using a single variable on each axis, the scatter diagram plots pairings of numerical data in an effort to identify any relationships between them. A line or curve will be formed by the points if the variables are correlated. The points will hug the line closer the more highly correlated the data is. You may also visualise the strength of any relationship. If the researcher believes there may be a correlation, a line of greatest fit can also be drawn on the graph.

Data points are shown on a horizontal and vertical axis using scatter plots in an effort to demonstrate the degree to which one variable is influenced by another.

Thus, correct option: a

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The sides given as 16cm , 12cm and 20cm  forms a right triangle because the sides satisfies the condition of Pythagoras Theorem .

What is Pythagoras Theorem ?

The Pythagoras Theorem states that the square of the longest side (hypotnuse) is equal to the sum of the square of the other two sides .

The sides of the triangle are given as ⇒ 16cm , 12cm and 20cm ;

here the hypotnuse (longest side) is = 20 cm ;

According to Pythagoras theorem ,

⇒ [tex]20^{2} =12^{2} +16^{2}[/tex] ;

⇒ [tex]400 =144+256[/tex] ;

⇒ [tex]400=400[/tex] ;

So , The condition of Pythagoras theorem is satisfied .

Therefore , the given sides can form a Right Triangle .

The given question is incomplete , the complete question is

Does the sides 16cm , 12cm and 20cm form a right triangle ?

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Jamal should multiply his current balance by 1.07 to find his total balance in one year.

Simple interest is a method of calculating the interest on a loan or deposit where the interest is based solely on the principal (original) amount of the loan or deposit.

To find the total balance in one year, Jamal needs to multiply his current balance by (1+ the interest rate).

Since the interest rate is 7%, the interest rate in decimal form is 0.07

Therefore, he needs to multiply his current balance by (1+0.07) = 1.07

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The volume of the composite solid, given the dimensions for the cylinder and cone, is D. 1, 099 cm ³

First, find the volume of the cone which can be found by the formula:

= π x radius ² x ( height / 3 )

Height = 3 inches

Radius = 3 inches

The volume is:

= π x radius ² x ( height / 3 )

= π x 3 ² x ( 2.5 / 3 )

= 28.27 inches ³

The volume of the cylinder is :
= π x radius ² x  height

= π x 3² x 2. 5

= 70. 69 inch ³

The volume of the composite solid is:

= 28. 27 + 70. 69

= 98.96 inch³

In cm³, this is:

= 98. 96 x 16.3871

= 1, 099 cm ³

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Answer:

20

Step-by-step explanation:

Given the function:

[tex]p(x)=3x^3-x^2[/tex]

We need to find p(2)

This means we need to find the value of the function when x is 2

[tex]p(2)=3*2^3-2^2=3*8-4=24-4=20[/tex]

Hope this helps :)

Have a great day!

The turning point of the function is x = 1 and it is a local minima.

The curve of a function has peaks and troughs called maxima and minima. A function may have any number of peaks and minima. Calculus allows us to determine any function's maximum and lowest values without ever consulting the function's graph. Maxima will be the curve's highest point within the specified range, while minima will be its lowest.

Extrema is the result of maxima and minima combined. The graph in the graphic below shows several peaks and falls. We obtain the function's maximum and lowest values at x = a and 0 respectively, and at x = b and c respectively. The valleys are the minima and all the peaks are the maximum.

In a function, maxima and minima can be of two different types:

Local Maxima and Minima

Global or Absolute Maxima and Minima

The function is

y = [tex](x-1)^{2}[/tex] for -3 ≤ x ≤ 3

differentiating both side with respect to x we get

[tex]\frac{dy}{dx} = 2(x-1)[/tex]

for maxima and minima [tex]\frac{dy}{dx} = 0[/tex]

or, 2(x-1) = 0

or x = 1

Now, for x > 1 [tex]\frac{dy}{dx} > 0[/tex]

So, the function's turning point is a minima.

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Lower bound: a number that is less than or equal to all of the elements in a data collection. Upper bound: a number larger than or equal to every element in a data collection.

A)1600×40%=640

Because of the onion in the

(0- 640)Kg

The upper bound for the mass of

Onion sold is 640 kg

B)The lower bound is the minimum quantity  for sale

The lower limit is the least amount that, when rounded up, equals the estimated value. The upper bound is the minimum possible value that would be rounded up to the next estimated value. A mass of 70 kg, for example, rounded to the closest 10 kg, has a lower bound of 65 kg since 65 kg is the lowest mass that rounds to 70 kg.

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The probability of flipping four coins is 0.0625

Total coins = 4

The study of chances, which are determined by the ratio of favourable occurrences to probable cases, is known as probability.

When flipping a coin, there are two possible outcomes (heads or tails), hence the likelihood of flipping a head-up coin is equal to the likelihood of flipping a tail-up coin.

Thus, the probability is = 1/2

Calculating the probability of getting all heads or all tails when flipping 4 coins -

= 1/2 x 1/2 x 1/2 x 1/2

= 1/16

In decimal form, this will be 0.0625

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Answer:

1. Pt. A: -6               3. Pt. C: 3               5. Pt. E: 0

2. Pt. B: -2              4. Pt. D: 5

Step-by-step explanation:

By looking at the number line, you can see that a few points are labled from letter A to letter E.

In order to know the value of each point, you just have to look at their placement in the number line. For example, we can see that Point B is plotted at -2 on the number line, this means that the value of Point B is -2.

I hope this helps! :)

Class limits indicate the largest and smallest data values that can be included in the class. Class limits are referred to actual data values. On the other hand, class boundaries give values that remove gaps between the classes in the frequency distribution. Class boundaries are considered to be one decimal place more accurate in comparison to the data. Options A, B, D, and F correctly describe differences between a class boundary and a class limit.

Following are the potential differences between a class boundary and a class limit.

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Answer:

38

Step-by-step explanation:

4/2+33-2+5=2+33-2+5=35-2+5=33+5=38