Can someone please help me with this math

The exact dimensions of the rectangular prism are:

Width = [tex]((\sqrt{282} + \sqrt{1975})/3)/2[/tex]

Height = [tex](141 - (\sqrt{282} + \sqrt{1975})/3) / 2[/tex]

(I may have formatted my response incorrectly. If so, please let me know. I will update my response accordingly.)

The rectangular prism with a fixed surface area of 282 square units and maximum volume has dimensions of 9 by 9 by 14 units.

To find the dimensions of the rectangular prism with a fixed surface area of 282 square units and maximum volume, we need to use the fact that the volume of a rectangular prism is given by V = lwh and the surface area is given by SA = 2lw + 2lh + 2wh. Since we want to maximize the volume, we can use the surface area formula to solve for one of the dimensions in terms of the other two, and then substitute into the volume formula to obtain a function of two variables.

We can then take the derivative of this function and set it equal to zero to find the maximum volume. Solving this equation, we obtain l = w = 9 and h = 14, which gives the desired dimensions.

Therefore, the rectangular prism with a fixed surface area of 282 square units and maximum volume has dimensions of 9 by 9 by 14 units.

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Two fractions that also represent 60% are 6/10 and 12/20, which can be simplified to 3/5.

Percent is a way of expressing a number as a fraction of 100. It is denoted by the symbol "%". Percentages are used in many areas, including finance, statistics, and science, to represent relative values or changes.

I choose 60%.

60% means 60 out of 100 or 60/100 or 3/5. It represents a fraction of a whole or a part of a group that is equivalent to 60 parts per 100 parts, or 3 parts per 5 parts.

For example, if there are 100 students in a class and 60 of them are girls, then 60% of the class are girls. Another example could be if a store is offering a 60% discount on a $100 item, then the discounted price would be $40.

Two fractions that also represent 60% are 6/10 and 12/20, which can be simplified to 3/5.

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There is a linear relationship between the number of absences and grade point average.

The total number of absences depend on the number of students enrolled in a class. Therefore, a measure independent of the number of students is needed. This leads to the introduction of the concept of normalized absences.

It is defined as: Number of Absences / (Number of Students x Number of Contact Hours).

A Final Grade is the installation of specific materials - such as screened topsoil - on top of a clay base called, "Rough Grade" that promotes proper drainage and flow of excess water away from existing structures.

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Answer:

Range, because it measures the difference between the highest and lowest values in a dataset, providing a clear measure of variability for both sets of data. It is not affected by skewness or symmetry, which makes it a useful measure of variability for comparing the temperature consistency between Desert Landing and Flower Town.

Step-by-step explanation:

Hope this helps!=D

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The number such that twice a number is fourteen is 7

If we let the number be "x", we can write the given information as an equation:

2x = 14

To solve for x, we need to isolate it on one side of the equation. We can do this by dividing both sides by 2:

2x/2 = 14/2

x = 7

Therefore, the number is 7.

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Answer:

x ≈ 22,6°

Step-by-step explanation:

Use trigonometry:

[tex] \cos(x°) = \frac{12}{13} [/tex]

Use the reverse (SHIFT, cos (12/13)) function on your calculator to find the approximate value of x:

x ≈ 22,6°

Step-by-step explanation:

- - 4 turns into + 4

then   3/4 + 7/12 + 4   find common denominator to add or subtract fractions

    9/12  + 7/12  + 48/12   = ( 9+7+48 ) / 12 = 64/12 = 5  1/3

Answer: wassup, so basically the price just increases by like 20% because of how many more people are coming thats the best way i can say to help u understand it. hope I helped a bit

After answering the presented question, we can conclude that Therefore, the factorization of the quadratic expression  is: x =2 , x= -3

A quadratic equation is x[tex]ax2+bx+c=0,[/tex]which is a single variable quadratic polynomial. a 0. Because this polynomial is of second order, the Basic Theorem of Algebra implies that it has at least one solution. Simple or complex solutions are possible. A quadratic equation is a quadratic equation. This means it has at least one word that must be squared. One of the most common solutions for quadratic equations is [tex]"ax2 + bx + c = 0.[/tex]" where a, b, and c are numerical coefficients or constants. where the variable "X" is unnamed.

In a quadratic equation

[tex]ax2+bx+c=0, to solve one splits the middle term in two parts so that their sum is b and product is ac.Hence, in x2+x−6=0 one needs to split 1×(−6)=−6 in two parts whose sum is 1. It is apparent that these are 3 and −2, hence x2+x−6=0 can be written asx2+3x−2x−6=0 orx(x+3)−2(x+3)=0 or(x−2)(x+3)=0i.e. either x−2=0 i.e. x=2or x+3=0 i.e. x=−3[/tex]

Therefore, the factorization of the quadratic expression  is:

x = 2, x=-3

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question is - How do you factor and solve

[tex]x2+x−6=0?[/tex]

there are 312 cubic inches of wood left after cutting out a square hole with side lengths of 5 inches from a cube-shaped block with side lengths of 8 inches.

How to find the volume ?

To find the volume of the remaining wood, first find the volume of the cube-shaped block. To find the volume of a cube use V = s³ where s is the side of the cube. In this case, s = 8 inches, so V = 8³ = 512 cubic inches.

Then, find the volume of the hole using the side lengths of the hole and the same depth as the cube, which is 8 inches. The hole has side lengths of 5 inches, so its volume is V = 5² * 8 = 200 cubic inches.  

To find how much wood is left after cutting out the hole, subtract the volume of the hole from the volume of the cube:

512 - 200 = 312 cubic inches

Therefore, there are 312 cubic inches of wood left after cutting out a square hole with side lengths of 5 inches from a cube-shaped block with side lengths of 8 inches.

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Answer:

41.05

Step-by-step explanation:

Given that-

Solve-

Let, "p" represents his original cost.

0.4p = $16.42        

0.4p/0.4 = $16.42/0.4    >> Divide both sides by 0.4          

   p  = $16.42/0.40         >> $16.42/0.40 = $41.05

Answer- $41.05

The price of the item was $41.05 if he had not used the coupon.

RevyBreeze

Answer:

$41.05

Step-by-step explanation:

.40c = $16.42

c = $41.05

Answer: Dog show 1 was a dog show for smaller dogs while dog show 2 was a dog show for larger dogs.

Step-by-step explanation:

The probability that the part can be assembled in 7 minutes or less is 0.2592.

To solve the problem, we need to use the cumulative distribution function (CDF) of the exponential distribution. The CDF gives the probability that the random variable X (in this case, the time required to assemble the part) is less than or equal to a certain value x.

The CDF of the exponential distribution is given by:

F(x) = [tex]1 - e^{(-λx)}[/tex]

where λ is the rate parameter of the exponential distribution, which is equal to 1/mean. In this case, the mean is 14 minutes, so λ = 1/14.

To find the probability that the part can be assembled in 7 minutes or less, we plug x = 7 and λ = 1/14 into the CDF formula: F(7) = [tex]1 - e^{(-(1/14)*7)} \approx 0.2592[/tex]

So, there is a chance of about 25.92% (rounded to four decimal places) that the part can be assembled in 7 minutes or less.

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Answer:

All of the above.

Step-by-step explanation:

It is 2 and 3 because they are next to each other and when added together equal to 180 degrees.

It is 5 and 8 for the same reason and so on for the rest.

Answer:

All of the above

Step-by-step explanation:

Supplementary means two angles that add up to 180 degrees.

now, since all of the angles are beside each other, it's automatic that they add up to 180 degrees.

I'm guessing you are learning about transversals and rules on lines.

I did this ixl as well and I understand why you're confused

based on my guessing on what you are learning in school, 4 and 5 would also be supplementary because they are consecutive interior angles

I don't know if you learned this term but that's the best I can explain it.

The area of the shaded region in this shape that has a rectangle and a circle within is 27.73 square cm.

The area of the rectangle can be found using the formula:

Area rectangle = length × width

Area rectangle = 8 cm × 7 cm = 56 square cm

The area of the circle can be found using the formula:

Area circle = π × radius^2

Given the radius is 3 cm, we have:

Area circle = π × (3 cm)^2 = 9π square cm  =  28.27 square cm

Now, to find the area of the shaded region (which is the rectangle minus the circle):

Area shaded = Area rectangle - Area circle

Area shaded = 56 square cm - 28.27 square cm = 27.73 square cm

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The given expression 14 - 0.6t  is representing the amount of fuel that has been remaining after "t" days of use.

14 - 0.6t is an algebraic expression. The car had 14 gallons of fuel at first and after each day of use, the car used 0.6 gallons which means that the amount of fuel that is remaining in the car at the end of the day is continuously decreasing by 0.6 per day. So, after "t" days of use, the car must have 0.6×t gallons of fuel, and the amount of fuel that remains in the car will be 14 - 0.6t.

When the warning light comes on, the remaining fuel is 1.5 gallons or less. So we can set the expression 14 - 0.6t to 1.5 and solve for t to find the number of days it takes for the warning light to come on:

14 - 0.6t = 1.5

0.6t = 12.5

t = 20.83

Therefore, it takes approximately 20.83 days of use for the warning light to come on.

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Since Demand is higher than then supply at $3.99 price, hence, correct answer is Option (b).

A graph is a visual representation of data that is used to show the relationship between two or more variables. Graphs are commonly used in mathematics, science, engineering, and other fields to help visualize and analyze data.

There are many different types of graphs, each with its own unique features and applications. Some of the most common types of graphs include:

Line graphs: Line graphs are used to show the trend or change in a variable over time. They consist of a set of data points that are connected by straight lines.

Bar graphs: Bar graphs are used to compare data across different categories or groups. They consist of rectangular bars that are proportional in height to the values they represent.

Pie charts: Pie charts are used to show the proportion or percentage of each category within a larger whole. They consist of a circle that is divided into sections, with each section representing a different category.

If Leroy set the price at $3.99, then based on the given chart, Demand will be 1,500 units whereas Supply will be 500 units. Since Demand is higher than then supply at $3.99 price, hence, correct answer is Option (b).

Therefore, Correct answer is Option (b), The demand will exceed the supply.

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The complete question is:

The sοlutiοns οf the quadratic equatiοn [tex]x^2 + 8x + 3 = 0[/tex] are:

[tex]x = -4 + \sqrt{(13)[/tex] and [tex]x = -4 - \sqrt{(13)[/tex]

it's a secοnd-degree quadratic equatiοn which is an algebraic equatiοn in x.

Tο find the sοlutiοns οf the quadratic equatiοn [tex]x^2 + 8x + 3 = 0[/tex], we can use the quadratic fοrmula:

[tex]x = (-b \± \sqrt{(b^2 - 4ac)}) / 2a[/tex]

where a = 1, b = 8, and c = 3.

Substituting these values intο the fοrmula, we get:

[tex]x = (-8 \± \sqrt{(8^2 - 4(1)(3))}) / 2(1)[/tex]

[tex]x = (-8\± \sqrt{(64 - 12)}) / 2[/tex]

[tex]x = (-8 \± \sqrt{(52)}) / 2[/tex]

[tex]x = (-8 \± 2\sqrt{(13)}) / 2[/tex]

[tex]x = -4 \± \sqrt{(13)[/tex]

Therefοre, the sοlutiοns οf the quadratic equatiοn [tex]x^2 + 8x + 3 = 0[/tex]are:

[tex]x = -4 + \sqrt{(13)[/tex] and[tex]x = -4 - \sqrt{(13)[/tex]

Sο the answer is οptiοn C.

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Complete Question:

What are the solutions of this quadratic equation?

x² + 8x + 3 = 0 A. B. C. D.

Answer:

the scale factor is 2

Step-by-step explanation:

Take each x and y value and multiply it by 2 and you get the coordinates for the image.

Helping in the name of Jesus.

The scale factor is 2. Point B goes from (3,3) to (6,6). 6/3 is 2. Similar triangles have the same shape and the three angles' measurements are likewise the same.

Their sides are the only thing that differs. The scale factor, which is what is referred to here as this, is the ratio of one triangle's sides to those of another triangle. To calculate the scale factor for the smaller triangle to the bigger triangle, divide one of the sides in the bigger triangle by its corresponding side in the smaller triangle. In the example, the scale factor would be 2 if you divided 40 by 20.

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Answer:

x = -30

y = 18

Step-by-step explanation:

-2,4x - 3y is equal to both 18 and y

Since there are two equal signs, we have a double equation (we can write each equation seperately and put them in a system):

{y = -2,4x - 3y,

{-2,4x - 3y = 18;

.

We move 3y to the left, so we change the sign to the opposite:

{4y = -2,4x, / : 4 (put y and 3y together)

{-2,4x - 3y = 18;

.

y = -0,6x,

-2,4x - 3y = 18;

Replace y in the 2nd equation with its value from the 1st equation:

-2,4x - 3 × (-0,6x) = 18

-2,4x + 1,8x = 18

-0,6x = 18 / : (-0,6)

x = -30

y = -0,6 × (-30) = 18

The median in this situation is the average of the two middle values, which are 48 and 76: (48 + 76) / 2 = 62

When a dataset is sorted in order of magnitude, the median, a statistical measure of central tendency, reflects the middle value of the dataset. The values must first be arranged from lowest to highest in order to determine the median (or largest to smallest). The median is the middle value when the dataset has an odd number of values. The median is indeed the average of the two middle values when the dataset does have an even number of values.

given

We must first determine the values of the first and third quartiles in order to determine the interquartile range (IQR) of a data set.

The median of the lower half of the data set makes up the first quartile (Q1), and the median of the higher half, the third quartile (Q3).

For this data set's Q1 and Q3, you can:

Sort the information from smallest to largest:

23 33 45 48 76 78 94 94

Determine the data set's overall median.

The median in this situation is the average of the two middle values, which are 48 and 76: (48 + 76) / 2 = 62 .

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Step-by-step explanation:

These are the steps to this Question...

To simplify this expression, we can follow the order of operations:

1. Simplify the expression inside the parentheses first:

(3x2^y - 2 - 7x2^(y-2))

2. Combine like terms:

3x2^y - 7x2^(y-2) - 2

3. Rewrite the denominator with a common base of 2:

5x2^(y-2)

4. Divide the numerator by the denominator:

(3x2^y - 7x2^(y-2) - 2) ÷ (5x2^(y-2))

5. Simplify by dividing each term in the numerator by 5x2^(y-2):

(3x2^y)/(5x2^(y-2)) - (7x2^(y-2))/(5x2^(y-2)) - (2/(5x2^(y-2)))

6. Simplify the exponents:

(3/5)x^(y-2) - (7/5) - (2/5)x^(-2)

So the final simplified expression is:

(3/5)x^(y-2) - (7/5) - (2/5)x^(-2)

In the circle graph, the amount budgeted for marketing is

A circle graph is another term for a pie chart, which is a type of data visualization that represents data as a circle, divided into sectors or slices, each representing a proportion or percentage of the total data set.

The size of each sector is proportional to the value it represents, so larger sectors indicate larger values, and smaller sectors indicate smaller values.

In the circle graph, when the total annual budget is $12,500,000. The amount budgeted for marketing is

= 38/100 * 12,500,000

= 4,750,000

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Answer:

[tex] {( - 7)}^{2} - 4(6)( - 1) = 49 + 24 = 73[/tex]

Josephine did not distribute the -1 correctly. -4(6)(-1) = 24.

Here are the correct solutions:

x = (7 + √73) / 12

x = (7/12) + (1/12)√73

Answer:

Step-by-step explanation:

$7

Answer:

7$

Step-by-step explanation:

By using a protractor or visual estimation, we can estimate the measure of angle ABC to the nearest degree.

To answer your question, let's first start with defining what an angle is. An angle is formed by two rays or line segments that share a common endpoint, called the vertex. The measure of an angle is usually given in degrees and is determined by how much the two rays are turned away from each other.

Now, let's look at the specific angle you asked about, angle ABC. Without a diagram or any additional information about the position of point B and C, it is impossible to determine the measure of angle ABC. However, we can make some general assumptions based on the fact that angle measures range from 0 to 360 degrees.

Assuming that angle ABC is a standard angle and not a reflex angle (i.e. it measures less than 180 degrees), we can estimate the measure of angle ABC to the nearest degree by using a protractor or by visual estimation. A protractor is a tool used to measure angles in degrees, and can be found at most office supply stores or online.

If we don't have access to a protractor, we can still estimate the measure of angle ABC by comparing it to other angles we know the measure of. For example, if angle ABC looks to be about halfway between a right angle (90 degrees) and a straight angle (180 degrees), we can estimate that angle ABC measures around 135 degrees.

In summary, without additional information about the specific position of points B and C, we cannot determine the exact measure of angle ABC. However, by using a protractor or visual estimation, we can estimate the measure of angle ABC to the nearest degree.

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Answer:

x ≥ 5

Step-by-step explanation:

Let's represent the number of action figures in a complete set by the variable "x".

Carlos has 5 complete sets plus 4 individual figures, which is a total of:

5x + 4

Josh has 3 complete sets plus 14 individual figures, which is a total of:

3x + 14

The problem states that Carlos has at least as many action figures as Josh, so we can set up the inequality:

5x + 4 ≥ 3x + 14

Simplifying this inequality, we can subtract 3x from both sides:

2x + 4 ≥ 14

Then, we can subtract 4 from both sides:

2x ≥ 10

Finally, we divide both sides by 2:

x ≥ 5

Therefore, the inequality that represents how many action figures can be in a complete set is:

x ≥ 5

The correct explicit rule is f(n) = 50 + 30n

An explicit rule is a mathematical formula that directly gives the n-th term of a sequence or the value of a function for a given input, without the need to find other terms first. It can be expressed using variables, constants, and operations such as addition, subtraction, multiplication, and division.

To determine who is correct, we need to first understand the meaning of the variables in the explicit rules.

Let n be the number of days the car is rented for.

Let f(n) be the cost of renting the car for n days.

The deposit is a one-time charge and is not dependent on the number of days rented. Therefore, the constant term in the explicit rule should be 50.

Now, for each day rented, the cost is $30. This means that the cost for n days should be 30n.

So the correct explicit rule is:

f(n) = 50 + 30n

Therefore, Kevin is correct with the explicit rule f(n) = 50 + 30(n-1). This is because we subtract 1 from n since the deposit is charged only once at the beginning and is not included in the daily rate.

Suzanne's explicit rule, f(n) = 80 + 30(n-1), adds an extra $30 to the cost of renting the car, which is not correct.

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An equation to represent the mass of nickel-63, in milligrams, as a function of 9.8 [tex]e^{(-.00001899 d)}[/tex]  .

What's a linear equation in  calculation?

A linear equation is an algebraic equation of the form y =  mxb. involving only a constant and a first- order( linear) term, where m is the  pitch and b is the y- intercept. sometimes, the below is called a" linear equation of two variables," where y and x are the variables.

The equation for half life is

n = no  [tex]e^{ (-kt)}[/tex]

Where no is the initial amount of a substance , k is the constant of decay and t is the time

no = 9.8

1/2 of that amount is 4.9 so n = 4.9 and t = 100 years

4.9 = 9.8 [tex]e^{ (-k 100)}[/tex]

Divide each side by 9.8

1/2 = [tex]e^{-100k}[/tex]

Take the natural log of each side

ln(1/2) = ln([tex]e^{(-100k)}[/tex]

ln(1/2) = -100k

Divide each side by -100

-ln(.5)/100 = k

Our equation in years is

n = 9.8  [tex]e^{(ln.5)/100 t)}[/tex]

Approximating ln(.5)/100 =-.006931472

n = 9.8 [tex]e^{(-.006931472 t) }[/tex] when t is in years

Now changing to days

100 years = 100*365 days/year

36500 days

Substituting this in for t

4.9 = 9.8 [tex]e^{(-k 36500)}[/tex]

Take the natural log of each side

ln(1/2) = ln([tex]e^{(-36500k))}[/tex]

ln(1/2) = -36500k

Divide each side by -100

-ln(.5)/36500 = k

Our equation in years is

n = 9.8  [tex]e^{(ln.5)/36500 d)}[/tex]

Approximating ln(.5)/365=-.00001899

n = 9.8 [tex]e^{(-.00001899 d)}[/tex]  when d is in days

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