12sec²x-16=0

Solve for the following equation by the quadratic formula or factoring

The answer is 38.7% which is option b., is Jordan's DTI (debt-to-income) ratio to the nearest tenth.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

To calculate Jim's DTI (debt-to-income) ratio, we need to divide his total monthly debt payments by his gross monthly income.

His total monthly debt payments are:

$2,600 (mortgage payment)

$250 (lease payment)

$500 (credit card payments)

$400 (speed boat payment)

then,

Total Monthly Debt Payments =  $3750

now,

His gross monthly income is his annual salary of $102,000 divided by 12 months which is $8,500

we get,

DTI = Total Monthly Debt Payments / Gross Monthly Income

= $3,750 / $8,500 + 1200

=0.387

=38.7%

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explanation: In order to find what two numbers have a Product and Sum write down what you know initially.

Let's assume the values we need to find are x, y whose product and sum are known.

Write the given data in the form of equations.

By using basic substitution, you will get an expression from which you can find the values easily.

If you aren't sure whether the results arrived are accurate or not cross-check the results obtained in the equations framed with input data.

Sum of two numbers = 24

Let's consider the numbers we need to find as x and y

To solve the problem x.y = 44

x+y = 24

y=24-x

Replace the value of y in the equation x.y=44. It's not necessarily y if you want you can interchange with the value of x too as x and y are interchangeable. . (24-x)=44

On solving the equation we get two numbers as 2 and 22

That's it the two numbers whose product is 44 and the sum is 24 are 2, 22. so you should be able to do the same with your question hope that helps!

2425÷ 45 can be solved by using long division. The first step is to divide the first number (2425) by the divisor (45). The result, 54, is the first number in the answer.

What does math's long division mean?

The mathematical operation of breaking up huge numbers into several smaller groups or sections is known as long division. The number we divide by is known as the divisor, and the number we divide into smaller groups is known as the dividend. A problem can be handled by breaking it down into smaller, more manageable parts.

Next, subtract 54 x 45 (2430) from 2425, which leaves a remainder of -5.

To continue long division, we bring down the next number in the dividend (2425), which is a 5. Next, divide the remainder (-5) by the divisor (45). The result, -1/9, is the second number in the answer.

Finally, subtract -1/9 x 45 (-5) from the remainder (-5), which leaves a remainder of 0. The answer is 54 1/9.

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The information provided doesn't mention Nobu's tomato, so it's not possible to determine how much heavier Anya's tomatoes are than Nobu's tomato without more information.

Answer:

[tex]4g^5[/tex]

Step-by-step explanation:

[tex]\sqrt{16g^{10}}=\sqrt{16}*\sqrt{g^{10}}=4g^5[/tex]

The solution of the given problem of expression comes out to be the standard form of 9.335 × 10⁵ is 933,500.

Addition, multiplication, and division in mathematics are required. When united, they produce the following: A mathematical function, some data, and an equation A declaration of fact contains values, parameters, and mathematical operations like additions, subtractions, multiplications, and divisions. It is possible to contrast and evaluate various phrases and words.

Here,

9.335 • 10⁵  is already in standard form, also known as scientific notation, which is a way of representing numbers as a coefficient multiplied by a power of 10.

To clarify, 10⁵  means "10 raised to the power of 5", which is equivalent to multiplying 10 by itself 5 times:

10^5 = 10 x 10 x 10 x 10 x 10 = 100,000

So 9.335 • 10⁵ can be written as:

933,500

Therefore, the standard form of 9.335 • 10^5 is 933,500.

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There are a total of 816 different subsets of {1,2,3,4,5,6,7,8,9,10,11,12} contain at least one element in common with each of the given sets

There are 12 elements in the original set, and each of the three smaller sets has different elements. To find the number of subsets that contain at least one element in common with each of the three sets, we need to count the number of subsets that contain at least one element from each set. To do this, we can consider each set separately and multiply the number of subsets that contain at least one element from each set.

The first set has 6 elements, the second set has 4 elements, and the third set has 5 elements. The number of subsets of the first set that contain at least one element is [tex]2^6-1[/tex]=63, the number of subsets of the second set that contain at least one element is [tex]2^4-1[/tex] =15, and the number of subsets of the third set that contain at least one element is [tex]2^5-1[/tex]=31. The number of subsets of the original set that contain at least one element from each of the three sets is 63 * 15 * 31 = 816.

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The explicit rule for the sequence is f(n) = a(3)^n-1

From the question, we have the following parameters that can be used in our computation:

a_(n)=a_(n-1)*3

The above definitions imply that we simply multiply the current from by 3 to get the next term

This means that the function is a geometric function with the following parameters

Common ratio, r = 3

So, the function is

f(n) = a(3)^n-1

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Expanding the expression a(b + c) = ab + ac, the value of ac is positive if both a and c are positive or if both a and c are negative.

By Multiplying the term outside the brackets by each term inside the brackets

Using this method you can distribute the outer terms into the inner terms. You can multiply the term outside the brackets by the first term inside the brackets. Then multiply the outside term by the second term. If there are more than two tribes, then continue to distribute the tribes until the tribe has no remainder. Keep the signs (positive or negative) in parentheses.

For example:

2(x-3) = 10

2(x) – (2)(3) = 10

2x – 6 = 10

We also know that the distribution characteristic state is a(b + c) = ab + ac.

Because plus times plus is plus and minus times minus is plus. When expanding the phrase a(b + c) = ab + ac, the value of ac is positive if both a and c are positive, and the value of ac is negative if both a and c are negative.

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a. Each marble has a volume of 0.013 liters.

b. 23.4 liters of water would be necessary if William uses 200 marbles.

a. To determine the volume of each marble, we can use the information that 85 marbles fill a tank with a volume of 20.9 liters of water:

Volume of each marble = (26 liters - 20.9 liters) / 85 marbles = 0.26 liters - 0.247 liters/marble = 0.013 liters/marble

So, each marble has a volume of 0.013 liters.

b. To determine the amount of water necessary if William uses 200 marbles, we can use the formula:

Volume of water = Total volume of tank - Volume of marbles

Volume of water = 26 liters - (200 marbles * 0.013 liters/marble) = 26 liters - 2.6 liters = 23.4 liters

So, 23.4 liters of water would be necessary if William uses 200 marbles.

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Complete question:

William has a 26-liter glass tank. First, he wants to put some marbles in it, all of the same volume. Then, he wants to fill the tank with water until it is completely full. If he uses 85 marbles, he will have to add 20.9 liters of water.

a. What is the volume of each marble?

b. How much water is necessary if William uses 200 marbles?

Step-by-step explanation:

To find the volume of this solid, we will use the method of cylindrical shells. We will integrate the cross-sectional area of a cylinder, given by πr^2, over the height of the solid. The height of the solid is given by the difference between the upper and lower bounds of the region, which are y = x^2 and y = 0, respectively. The radius of each cylindrical shell is given by the distance of the cross-sectional circle from the y-axis, which is x.

So, the volume of the solid is given by the integral:

V = ∫[0, 1] π * x^2 dx

Using the antiderivative of π * x^2, which is π * x^3 / 3, we can find the definite integral:

V = (π * x^3)/3 from 0 to 1

Evaluating the definite integral and simplifying, we get:

V = π/3 units^3

So, the volume of the solid is π/3 units^3.

Answer:

Step-by-step explanation:

Find the volume of the solid generated by rotating the region bounded by y = x^2, y = 0, and x = 1, about the y-axis.

a) The mode of the list is 7

b) The median of the list is 7.

c) The mean is 5.4

d) The range is 7

What is the Mean, Mode and Median?

Mean: The mean is the average of a set of numbers, calculated by adding up all the numbers and dividing by the total number of numbers in the set.

Mode: The mode is the most frequently occurring number in a set of numbers.

Median: The median is the middle value in a set of numbers when the set is sorted in ascending or descending order.

a) Mode: The mode of the list is 7, as it is the number that occurs most frequently (3 times).

b) Median: To find the median, the list must first be sorted in ascending order:

1, 2, 3, 4, 5, 7, 7, 7, 8, 8

The median of the list is 7.

c) Mean: The mean is found by adding up all the numbers in the list and dividing by the total number of items:

(3 + 7 + 2 + 4 + 7 + 5 + 7 + 1 + 8 + 8)/10 = 54/10 = 5.4

d) Range: The range is the difference between the largest and smallest numbers in the list:

8 - 1 = 7

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Let x be the number of fruit pies sold by Mr. Sanchez's class, and y be the number of bottles of fruit juice sold by Mr. Kelly's class.

(a) We can set up a system of equations to model the problem:

x + y = 53   (total number of items sold)

1.45x + 1.25y = 70.85   (total amount earned)

To solve this system using substitution, we can rearrange the first equation to solve for one variable in terms of the other:

x + y = 53

x = 53 - y

Then substitute x = 53 - y into the second equation:

1.45x + 1.25y = 70.85

1.45(53 - y) + 1.25y = 70.85

76.85 - 1.45y + 1.25y = 70.85

0.2y = 6

y = 30

Substituting y = 30 into the equation x + y = 53 gives:

x + y = 53

x + 30 = 53

x = 23

So Mr. Sanchez's class sold 23 fruit pies and Mr. Kelly's class sold 30 bottles of fruit juice.

(b) To find out which class earned more money, we can calculate the total amount earned by each class:

Mr. Sanchez's class: 1.45 x 23 = $33.35

Mr. Kelly's class: 1.25 x 30 = $37.50

Mr. Kelly's class earned more money.

(c) The amount by which Mr. Kelly's class earned more than Mr. Sanchez's class is:

$37.50 - $33.35 = $4.15

well, we know angle θ is in the III Quadrant, that means the sine or opposite side and cosine or adjacent side are both negative, whilst of course the hypotenuse is just a radius amount thus is always positive.

[tex]\sin(\theta )=\cfrac{\stackrel{opposite}{-3}}{\underset{hypotenuse}{4}}\hspace{5em}\textit{let's find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - b^2}=a ~~ \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \pm\sqrt{4^2 - (-3)^2}=a \\\\\\ \pm\sqrt{7}=a\implies \stackrel{III~Quadrant}{-\sqrt{7}=a}\hspace{5em} \boxed{\cos(\theta )=\cfrac{\stackrel{adjacent}{-\sqrt{7}}}{\underset{hypotenuse}{4}}}[/tex]

The standard error of the sample proportion p is approximately 0.281

The standard error of the sample proportion p can be calculated by taking the square root of the sample proportion's variance, which is given by-

p(1-p)/n, where p is the sample size,

The random sample(n) is equal to 500

The adults who indicate the unemployment is 304

Now the sample proportion

p=304/n

p=304/500

p= 0.608

Now the standard error is

SE= √p(1-p)/n

Now put the value here

SE=√0.608(1-0.608)/500

SE=0.021833

Therefore, the standard error of the sample proportion is 0.0218

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The slope is -2/5

You have a point at (0,3) and (5,1).  If you create a slope triangle, it'll go down 2 and right 5.

Answer:

D

Step-by-step explanation:

A and B would move the functional graph unchanged 6 units up and down.

but that is clearly not what happened.

so, A and B are out.

h(x) is instead f(x) shifted 6 units to the left.

that means the functional value h(x) is the same as f(x') just 6 units "earlier". that means x = x' - 6 or x' = x + 6.

therefore,

h(x) = f(x + 6) = sqrt(x + 6)

Answer:

81/100

Step-by-step explanation:

First we need to find a common multiple of 10 and 100.  It's going to be 100, so we chance 7/10 to 70/100.

Now that the denominator matches for both of them, now we add.

70/100 + 11/100 = 81/100

The letter on the number line that stands in for the numerals after it On the number line, B stands for -38.

The number line that displays negative numbers is presented to us. On the number line, we are aware that the number rises as we travel to the right.

As per the data given in the above question are as bellow,

The details provided are as bellow,

We can observe that the number line has a grading scale of 1, meaning that each subsequent mark is separated by one unit.

B is four points away from a 42.

This suggests that to get B, we just need to add 4 to -42.

So:

B = -42 + 4

B = -38

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Note : The complete question would be as bellow,

What integer does the letter B represent on the number line above?

What integer does the letter B represent on the number - 1

The distance of the probe is given by the equation A = 2.546 light years

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

The distance traveled by the space probe = 1.7 light years

Now , the value of 1 light year = 9.461 x 10¹³

So , the distance traveled by the space probe = 1.7 x value of 1 light year

On simplifying the equation , we get

The distance traveled by the space probe D = 1.7 x 9.461 x 10¹³

The distance traveled by the space probe D = 16.0837 x 10¹³ km

The distance traveled by the space probe D = 1.60837 x 10¹⁴ km

The distance to Proxima Centauri = 4.246 light years

So , the remaining distance is A = distance to Proxima Centauri - distance traveled by the space probe

On simplifying the equation , we get

The remaining distance is A = 2.546 light years

Hence , the equation is A = 2.546 light years

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Step-by-step explanation:

[tex]x = \frac{ - (b) \frac{ + }{} \sqrt{ {(b)}^{2} - 4(a)(c) } }{2(a)} [/tex]

If you believe that bit plane slicing is lossy, then 1st-order extrapolation or 2D bilinear interpolation cannot fully recover the original image.

What is extrapolation and interpolation?

Extrapolation is an estimation based on extending a known sequence of data beyond what is absolutely known.

Interpolation is the estimation of a value in a sequence of values between two known values.

Bit plane slicing is a lossy compression technique, which means that some information from the original image is lost during the compression process. The purpose of bit plane slicing is to reduce the size of an image by removing less significant bits from each pixel. As a result, the quality of the image is reduced.

1st-order extrapolation and 2D bilinear interpolation are techniques used to estimate or predict missing or unknown values from a given set of data. These techniques can be used to enhance the quality of an image, but they cannot recover the original image in cases where information has been lost through compression or degradation. In other words, they can only improve the quality of the image to a certain extent, but they cannot restore it to its original state.

So, if you believe that bit plane slicing is lossy, then 1st-order extrapolation or 2D bilinear interpolation cannot fully recover the original image, although they may help to improve its quality to some extent.

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Answer:

The area of a rectangle with length 4 cm and width 6 cm is 24 square cm. To find the area of a semi-circle, we use the formula for the area of a circle and divide by 2. The formula for the area of a circle is πr^2, where r is the radius. The radius of the semi-circle is half the width of the rectangle, so r = 6/2 = 3 cm. Thus, the area of the semi-circle is π(3^2) = 9π square cm.

The total area of the figure would be the sum of the area of the rectangle and the semi-circle, so the answer would be 24 + 9π square cm.

To subtract two fractions, we must find a common denominator and subtract the numerators.

The entire circle represents one whole.

To find the fraction for the shaded region, we must subtract [tex]\dfrac{1}{2}[/tex] and [tex]\dfrac{3}{7}[/tex] from one whole:

[tex]1-\dfrac{1}{2}-\dfrac{3}{7}[/tex]

One whole minus half the whole would leave us with just half:

[tex]\dfrac{1}{2}-\dfrac{3}{7}[/tex]

Now, to find a common denominator, multiply the numerator and denominator of each fraction by the denominator of the other fraction:

[tex]\dfrac{1*7}{2*7}-\dfrac{3*2}{7*2}\\\\= \dfrac{7}{14}-\dfrac{6}{14}[/tex]

Now, subtract normally:

[tex]\dfrac{7}{14}-\dfrac{6}{14}\\\\= \dfrac{1}{14}[/tex]

[tex]\dfrac{1}{14}[/tex]

well, first off, let's see how much was it in tax for the $200 purchase, since we know it was a whooping $14.50.

now, if 200(origin amount) is the 100%, what's 14.50 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 200 & 100\\ 14.50& x \end{array} \implies \cfrac{200}{14.50}~~=~~\cfrac{100}{x}\implies 200x=1450 \\\\\\ x=\cfrac{1450}{200}\implies x=\stackrel{\%}{7.25}[/tex]

now, let's check how much will that be for $76

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{7.50\% of 76}}{\left( \cfrac{7.50}{100} \right)76}\implies 5.7[/tex]

Metric System is a decimal system of measurement that is based on the meter, kilogram, and second and is used in most countries around the world. It is also known as the International System of Units (SI).

The Metric System is the most common measuring system used in the world today. It is a decimal system based on the meter, kilogram, and second and is officially known as the International System of Units (SI). This system was initially developed in France in the late 18th century and is now used in most countries around the world. The Metric System is based on powers of 10 and each unit is related to the next unit by a factor of 10. For example, a kilometer is equal to 1000 meters, a milliliter is equal to 0.001 liters, and a centimeter is equal to 0.01 meters. The Metric System is used to measure length, area, mass, weight, temperature, and volume. It is used in many different industries and applications including science, engineering, medicine, and agriculture. The Metric System has become the international standard for scientific measurements and is accepted by most countries as the preferred system of measurement. The Metric System is also easier for students to learn and use than other systems of measurement.

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The length of the base, AB, can be found to be 12. 49 cm

The base length can be found using the Pythagoras Rule which is:

c ² = a ² + b ²

a = CD which is the height

c = AC

So we can find half od base length when we divide the shape into a right angled triangle :

8 ² = 5 ² + b²

b ² = 64 - 25

b = √ 39

b = 6. 24 cm

Double of this would be:

= 12. 49 cm

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Answer:

1. 12 yards.

2. 15 meters.

3. 217 centimeters.

Step-by-step explanation:

[tex]\frac{1}{2}[/tex] · [tex]b[/tex] · [tex]h[/tex] is the formula. (for the area of a triangle.)

Hope it helped!