10.
(08.06 LC)

Variable c is 5 more than variable a. Variable c is also 3 less than variable a. Which pair of equations best models the relationship between c and a?

c = a − 5
c = a + 3

a = c + 5
a = 3c − 3

a = c − 5
a = 3c + 3

c = a + 5
c = a − 3

The simplified value of  \(\sqrt[4]{1296} /25\) is 0.24.

Simply put, to simplify is to make something simpler. Simplifying an equation, fraction, or issue in mathematics entails taking something complex and making it simpler. The issue is made simpler by calculations and problem-solving strategies. We can simplify fractions by removing all common elements from the numerator and denominator and putting the fraction in its simplest/lowest form.

Given  \(\sqrt[4]{1296} /25\)

factors of 1296 are = 2⁴ x 3⁴

\(\sqrt[4]{1296}\) = \((2^{4} *3^{4}) ^{\frac{1}{4} }\)

\(\sqrt[4]{1296}\) = 6

\(\sqrt[4]{1296} /25\)  = 6/25

\(\sqrt[4]{1296} /25\) = 0.24

Hence the value is 0.24.

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Answer:

(46 permutation 3)

Step-by-step explanation:

We have to choose any three with ranking from 46. So we can do this in (46 combination 3 ) ways. But for every three persons, there will be a 3 ! ways to interchange their ranks . so (46 combination 3)* 3! = (46 permutation 3)

Given:

The equation of a circle is:

\(x^2+y^2-x-2y-\dfrac{11}{4}=0\)

To find:

The center of the circle and its radius.

Solution:

The standard form of a circle is:

\((x-h)^2+(y-k)^2=r^2\)          ...(i)

Where, (h,k) is center and r is the radius of the circle.

The given equation of the circle is:

\(x^2+y^2-x-2y-\dfrac{11}{4}=0\)

Write the given equation in standard form of a circle.

\((x^2-x)+(y^2-2y)-\dfrac{11}{4}=0\)

\(\left(x^2-x+\left(\dfrac{1}{2}\right)^2\right)+(y^2-2y+1^2)-\dfrac{11}{4}-\left(\dfrac{1}{2}\right)^2+1^2=0\)

\(\left(x-\dfrac{1}{2}\right)^2+(y-1)^2-\dfrac{11}{4}-\dfrac{1}{4}-1=0\)

\(\left(x-0.5\right)^2+(y-1)^2-\dfrac{12}{4}-1=0\)

On further simplification, we get

\(\left(x-0.5\right)^2+(y-1)^2-3-1=0\)

\(\left(x-0.5\right)^2+(y-1)^2-4=0\)

\(\left(x-0.5\right)^2+(y-1)^2=4\)

\(\left(x-0.5\right)^2+(y-1)^2=2^2\)            ...(ii)

On comparing (i) and (ii), we get

\(h=0.5,k=1,r=2\)

Therefore, the center of the circle is (0.5,1) and radius is 2 units.

The seller purchased the product at a cost of 7500 and sold it for 7950, which resulted in a gain of 6%. So, the cost price is 7500.

In business, it is essential to keep track of cost prices and profit margins to ensure profitability. If the selling price is 7950 and the gain is 6%, we can use the following formula to calculate the cost price:

Cost price = Selling price / (1 + Gain%)

Substituting the given values, we get:

Cost price = 7950 / (1 + 0.06)

Cost price = 7500

Therefore, the cost price of the product is 7500, the gain percentage is calculated based on the cost price and not the selling price.

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Answer:

56mph I am pretty sure the answer is 56 mph

\(\text{To get the total surface area, all we have to do is multiply } 18 \text{ by } 12, \text{which gets us}\)\($18\cdot12 = \boxed{216\text{ ft}^2}\).

\(\text{So, our answer is } \boxed{216\text{ ft}^2}.\)

Larry needs 216 square feet of carpeting for her rectangular living room.

To find the amount of carpeting Larry needs, we need to calculate the area of her rectangular living room. The area of a rectangle can be found by multiplying its length by its width. In this case, the length of the living room is 18 feet and the width is 12 feet.

So, the area of the living room is:

Area = Length * Width

Area = 18 feet * 12 feet

Area = 216 square feet

Therefore, Larry needs 216 square feet of carpeting for her living room.

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Answer:

991 Ants

Step-by-step explanation:

amount of area excluding the area needed for food and resources= 1000-9=991 Square inches

area each ant needs= 1 square inch

number of ants= 991÷1= 991 ants

Answer:

( 2 , 1 ) , ( 4 , 1 ) , ( 4 , 4 ) .......

Answer:

Points of B are (-4,-1), (-2,-1) and (-4,-4)

Step-by-step explanation:

Points of A are (-4, 1), (-2, 1) and (-4,4)

Name the reflected trangle B.

If you have a point (x,y) and you reflect in the x-axis. That point becomes (x,-y).

Therefore. Points of B are (-4,-1), (-2,-1) and (-4,-4)

Answer: Varies

Step-by-step explanation:

x + 4 = 8 x = 4

4 + 4 = 8

8 = 8

The answer varies.

In case of :

x > 3

x = 4 because x is greater than 3.

Oʀ

x < 5

x = 4 because x is less than 5.

_______________________

The inequality : 20x < 100

→ x < 100/20

→ x < 5

→ x = 4 as x is less than 5.

_______________________

Answer:

5cm

Step-by-step explanation:

Answer: 1.905

Step-by-step explanation:

75 percent *2.54

= (75/100)*2.54

= (75*2.54)/100

= 190.5/100 = 1.905

Answer:

i think it is 1.905

Step-by-step explanation:

With a probability value of .02, one could conclude that there is evidence of a significant correlation between the variables, as the observed correlation coefficient is unlikely to be due to random chance alone.

If a correlation coefficient has an associated probability value of .02, it typically means that the probability of observing such a correlation coefficient by chance, assuming the null hypothesis (no true correlation), is .02 or 2%.

In statistical hypothesis testing, the probability value (p-value) is used to assess the statistical significance of a correlation coefficient. It represents the probability of obtaining a correlation coefficient as extreme or more extreme than the observed value, assuming the null hypothesis is true.

In this case, a probability value of .02 suggests that the observed correlation coefficient is unlikely to occur by chance alone, assuming no true correlation between the variables. Generally, a p-value less than a predetermined significance level (such as 0.05) is considered statistically significant, indicating evidence against the null hypothesis and suggesting the presence of a correlation.

Therefore, with a probability value of .02, one could conclude that there is evidence of a significant correlation between the variables, as the observed correlation coefficient is unlikely to be due to random chance alone.

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The Orthogonal diagonal augmented matrix of A is  \(\left[\begin{array}{cccccc}-8.6037 & 0 & 0 &-2.807 & 0.7596 & -0.60288\\0& 4.6575 & 0 &-2.319 & -0.4774 & 1.1351\\0&0& 15.94621 & 1 & 1 &1\end{array}\right]\\\)

The given matrix is A = \(\left[\begin{array}{ccc}-1 & -9 & 0\\-9 & 5 & 7\\0 & 7 &8\end{array}\right]\)

A can be diagonalized if there exists a invertible matrix P and the diagonal matrix D such that A = PDP⁻¹

So , We've to find eigen values of A

| A - λI | = 0

=> \(\left|\begin{array}{ccc}(-1- \lambda) & -9 & 0\\-9 & (5- \lambda) & 7\\0 & 7 &(8- \lambda)\end{array}\right| = 0\)

=> (-1 - λ)(-9 - 13λ +λ²) +9(-72 + 9λ) + 0(-63) = 0

=> (9 + 22λ + 12λ² -λ³) + (-648 + 81λ) = 0

=> ( -λ³ + 12λ² +103λ + 639) = 0

=>  λ³ - 12λ² - 103λ - 639 = 0

Roots can be found using Newton Raphson method ,

=> λ₁ =  4.6575

Now , using long division

=>  λ₂ = -8.6037 and  λ₃ = 15.9462

Now , the eigenvectors for λ = -8.6037

=> \(v_1 = \left[\begin{array}{c}-2.8075\\ -2.3719\\1\end{array}\right]\)

Eigenvectors for λ=  4.6575

Using row operations ,

=> \(v_2 = \left[\begin{array}{c}0.7596\\ -0.4774\\1\end{array}\right]\)

Eigenvectors for  λ₃ = 15.9462

=> \(v_3 = \left[\begin{array}{c}-0.028 \\ 1.1351 \\1 \end{array}\right]\)

Therefore. P matrix is compose by eigenvectors

P= \(\left[\begin{array}{ccc}-2.807 & 0.7596 & -0.60288\\-2.319 & -0.4774 & 1.1351\\1 & 1 & 1\end{array}\right]\)

The diagonal matrix D is composed of the eigenvalues ,

D = \(\left[\begin{array}{ccc}-8.6037 & 0 & 0\\0& 4.6575 & 0\\0&0& 15.9462\end{array}\right]\)

Hence , the augmented matrix

[D P] = \(\left[\begin{array}{cccccc}-8.6037 & 0 & 0 &-2.807 & 0.7596 & -0.60288\\0& 4.6575 & 0 &-2.319 & -0.4774 & 1.1351\\0&0& 15.94621 & 1 & 1 &1\end{array}\right]\\\)

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Answer:

11) I haven't done these yet don't go by my answers wait for more responses.

So if TR looks exactly half way from the middle and it says its 11, and if PS is basically two of TR then it would be 22. It looks to me that TR is 11 which is exactly half way I think, and PS looks double of TR so 2 x 11 = 22. Please go by the way you learned i don't know if I'm right.

12) If MK is exactly straight and its 10, half of 10 would be 5. I did half of 10 because L to M looks as if it is 10 already but since its L to the point in the middle that would be half way of the total line from L to M. So L to the point must be 5, MK is already given which is 10 so now we add 5 since L to the point in the middle is half way of 10 which is 5.

10(MK) + 5(L to the point in the middle of the circle) = 15

I don't want to be the one who brings your grades down so do by the way you learned.

(–2, 6) are the points that justify the shaded area

We can substitute the values of x and y from each point into the inequality and check if the inequality is satisfied or not.

Let's check each point:

For points (12, 6):

\((y+1)^2/6 -(x+2)^2/24\\ = (6+1)^2/6 - (12+2)^2/24 \\= 49/6 - 196/3 \\= -57.33\)

Here, the value of the expression is less than 1, so this point does not justify the shaded area.

For points (–2, 6):

\((y+1)^2/6 -(x+2)^2/24\\ = (6+1)^2/6 - (-2+2)^2/24 \\= 49/6\)

Here, the value of the expression is greater than or equal to 1, so this point does justify the shaded area.

For points (8, –6):

\((y+1)^2/6 -(x+2)^2/24 \\= (-6+1)^2/6 - (8+2)^2/24 \\= 25/6-100/24\)

Here, the value of the expression is greater than or equal to 1, so this point does not justify the shaded area.

For point (–1, –2):

\((y+1)^2/6 -(x+2)^2/24 \\= (-2+1)^2/6 - (-1+2)^2/24 \\= 1/6 - 1/24 \\= 1/8\)

Here, the value of the expression is less than 1, so this point does not justify the shaded area.

Therefore, the points that justify the shaded area are (–2, 6).

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The value of X and Y are not independent of each other.

To determine if X and Y are independent or not from each other with the given information, we have to check if the given joint density function satisfies the following property:

f(x,y) = g(x) × h(y)

where g(x) and h(y) are the marginal density functions of X and Y respectively.

If the above equation holds, then X and Y are said to be independent of each other.If not, X and Y are dependent on each other.

Let's find the marginal density functions of X and Y.

The marginal density function of X:

fX(x) = ∫f(x,y)dy

∫0∞xe^-(x+y)dy = x

∫0∞e^-(x+y)dy∫0∞e^-(x+y)dy = x

The marginal density function of Y:fY(y) = ∫f(x,y)dx∫0∞xe^-(x+y)dx = e^-y

The joint density function doesn't satisfy the property:

f(x,y) ≠ g(x) × h(y)f(x,y) = x × e^-(x+y)

fX(x) = x

fY(y) = e^-y

Since the joint density function can not be expressed as the product of the marginal density functions of X and Y, X and Y are dependent on each other.

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Domain and Range of the given rational functions are:Given rational function f(x) = 3/(x-1)The denominator of f(x) cannot be zero.x ≠ 1 Therefore the domain of f(x) is {x | x ≠ 1}

The range of f(x) is all real numbers except zero.Given rational function f(x) = (2x)/(x-4)The denominator of f(x) cannot be zero.x ≠ 4 Therefore the domain of f(x) is {x | x ≠ 4}The range of f(x) is all real numbers except zero.Given rational function f(x) = (x+3)/(5x-5)The denominator of f(x) cannot be zero.5x - 5 ≠ 0x ≠ 1 Therefore the domain of f(x) is {x | x ≠ 1}The range of f(x) is all real numbers except 1/5.Given rational function f(x) = (2+x)/(2x)The denominator of f(x) cannot be zero.x ≠ 0 Therefore the domain of f(x) is {x | x ≠ 0}The range of f(x) is all real numbers except zero.Given rational function f(x) = (x^2+4x+3)/(x^2-9)For the denominator of f(x) to exist,x ≠ 3, -3

Therefore the domain of f(x) is {x | x ≠ 3, x ≠ -3}The range of f(x) is all real numbers except 1, -1. Function Domain Rangef(x) = 3/(x-1) {x | x ≠ 1} All real numbers except zerof(x) = (2x)/(x-4) {x | x ≠ 4} All real numbers except zerof(x) = (x+3)/(5x-5) {x | x ≠ 1} All real numbers except 1/5f(x) = (2+x)/(2x) {x | x ≠ 0} All real numbers except zerof(x) = (x^2+4x+3)/(x^2-9) {x | x ≠ 3, x ≠ -3} All real numbers except 1, -1

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Answer:

Step-by-step explanation:

I am assuming  that the number 1 is not included.

This is an arithmetic sequence of integers with first term 1 and last term 999.

Number required  = (999-1) / 2

                              = 499.

There are 20 integers between 1 and 1000 that meet the given criteria.

To find this answer, we can start by noticing that there are only five odd digits: 1, 3, 5, 7, and 9. Therefore, any integer that meets the criteria must be made up of some combination of these digits.

Next, we can focus on the requirement that the digits be distinct. This means that we cannot repeat any of the odd digits within the same integer. We can use combinations to count the number of ways to choose three distinct odd digits from the set {1, 3, 5, 7, 9}:
5C3 = (5!)/(3!2!) = 10

Finally, we need to consider the requirement that the digits be in ascending order. Once we have chosen our three distinct odd digits, there is only one way to arrange them in ascending order. So each combination of three odd digits corresponds to exactly one integer that meets all the criteria.

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As the hospital's capacity increases, the solution to healthcare related problems improves significantly.

As the hospital's capacity increases, the solution to various healthcare-related problems changes significantly. In the current healthcare landscape, the demand for hospital beds and related services is ever-increasing. With the growing population, the need for healthcare services has increased significantly. Therefore, it is essential to understand how the solution changes as the hospital's capacity increases.
Firstly, with the increase in the hospital's capacity, the number of available hospital beds increases. This implies that more patients can be admitted, reducing the waiting time and allowing patients to receive timely and necessary care. This increase in capacity also allows for the addition of more specialized services, such as ICU beds, which can cater to critically ill patients.
Secondly, the increase in capacity also allows for the hiring of more healthcare professionals, including doctors, nurses, and administrative staff. This means that there will be more people to attend to the needs of patients, leading to better care and improved outcomes. Furthermore, with more staff, the workload per employee decreases, leading to a better work-life balance and job satisfaction.
Lastly, with an increase in capacity, the hospital can cater to a broader range of medical conditions. This allows for a more comprehensive range of treatments, including advanced surgeries and other medical procedures that may not have been possible with limited capacity.
In conclusion, as the hospital's capacity increases, the solution to healthcare-related problems improves significantly. With an increase in beds, healthcare professionals, and specialized services, patients can receive timely care, better outcomes, and a more comprehensive range of treatments. Therefore, increasing the hospital's capacity is essential to cater to the growing needs of the population and improve the quality of healthcare services.

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Answer:

there are 4 sides to the given data I can conclude that CD is 6 cm as the figure seems to be a rectangle as AB is the breadth and AC is the length.

Step-by-step explanation:

hope it helps

Over 8 months, an investment of $84,000 at a simple interest rate of 12% would earn $8,400 in interest.

To calculate the interest earned on a simple interest investment, we use the formula: Interest = Principal × Rate × Time. In this case, the principal is $84,000 and the rate is 12% or 0.12 (converted to decimal form). The time is 8 months.

First, we convert the time to years by dividing 8 months by 12 (number of months in a year). This gives us 0.67 years.

Next, we plug in the values into the formula: Interest = $84,000 × 0.12 × 0.67.

Calculating this, we find that the interest earned over 8 months is $8,400. This means that after 8 months, the investment would have grown to a total of $92,400 ($84,000 principal + $8,400 interest).

It's important to note that simple interest assumes a constant interest rate over the entire period and does not take compounding into account. If compounding were involved, the interest earned would be higher.

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16  is the approximate interquartile range (iqr) of the ages .

What does IQR, or interquartile range, mean?

The spread of the middle half of your data is measured by the interquartile range (IQR). The IQR shows the difference between the lowest and highest readings for that particular week. The spread in the center of the data for that week is roughly represented by the IQR.

                       It is the range for your sample's middle 50%. To evaluate the variability where the majority of your results are located, use the IQR. Larger values suggest a wider dispersion of the central component of your data. The first quartile (Q1) and third quartile (Q3) of these values (Q3). What separates Q3 from Q1 is known as the IQR.

IQR  = Q3 - Q1

       = 20 - 4

       = 16

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A relation R on Z is an equivalence relation if and only if it is reflexive, symmetric, and transitive. Specifically, in this case, xRy if and only if x^2+y^2 is even.

Reflexive: for any x in Z, x^2+x^2 is even, thus xRx. So, R is reflexive.

Symmetric: for any x,y in Z, if xRy, then x^2+y^2 is even, which implies y^2+x^2 is even, thus yRx. So, R is symmetric.

Transitive: for any x,y,z in Z, if xRy and yRz, then x^2+y^2 and y^2+z^2 are both even, thus x^2+z^2 is even, thus xRz. So, R is transitive.

Therefore, R is an equivalence relation.

To describe the equivalence classes, we need to find all the integers that are related to a given integer x under the relation R.

Let [x] denote the equivalence class of x.

For any integer x, we can observe that xR0 if and only if x^2 is even, which occurs when x is even.

Therefore, every even integer is related to 0 under R, and we have:[x] = {y in Z: xRy} = {x + 2k: k in Z}, for any even integer x.

Similarly, for any odd integer x, we can observe that xR1 if and only if x^2 is odd, which occurs when x is odd. Therefore, every odd integer is related to 1 under R, and we have:[x] = {y in Z: xRy} = {x + 2k: k in Z}, for any odd integer x.

In summary, the equivalence classes of R are of the form {x + 2k: k in Z}, where x is an integer and the parity of x determines whether the class contains all even or odd integers.

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Answer:

the second option

Step-by-step explanation:

SAS is side angle side. so, we need 2 sides and the enclosed angle.

since G is the transformed M, and GL is the transformed side TM, that also means L correlates to T and S to D.

for SAS we need both sides of the angles M and G.

TD and SL are not satisfying this condition.

only MD and SG do.

Hey there!

\(\fbox{2x²+16x-7}\)

\(\fbox{2(x + 4)² - 39}\)

Declan's reasoning does make sense. This is because 3/4 and 1/2 have the same denominator, and 3/4 is a larger fraction than 1/2.

Therefore, it is reasonable to assume that 3/4 is greater than 6/12 because 6/12 simplifies to 1/2. Simplifying fractions means dividing the numerator and denominator by the same number, in this case, 6 is divisible by 2, so we can reduce the fraction to 1/2.

So, Declan is correct in his reasoning that 3/4 is greater than 6/12. It is important to understand the relationship between fractions and their denominators to make such comparisons accurately.

3/4 = 9/12

1/2 = 6/12

6/12 = 6/12

Since 9/12 (which is equivalent to 3/4) is greater than 6/12 (which is equivalent to 1/2), we can say that 3/4 is indeed greater than 6/12.

Therefore, Declan's reasoning is correct.

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The volume of the pyramid is 18.86 cubic meters.

Now, For the volume of a pyramid with a square base, we can use the formula:

Volume = (1/3) x Base Area x Height

Given that;

the area of the base is 6.5 m² and the height of the pyramid is 8.6 m,

Hence, we can substitute these values in the formula to get:

Volume = (1/3) x 6.5 m² x 8.6 m

Volume = 18.86 m³

(rounded to two decimal places)

Therefore, the volume of the pyramid is 18.86 cubic meters.

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Answer:

254.34

Step-by-step explanation:

\(r^{2}\)x3.14(\(\pi\))

so then substitute

9x9=81

81x3.14=254.34

Answer:

The horizontal distance of the ball from Noli when it reached maximum height is approximately 4.1 feet

Step-by-step explanation:

The horizontal distance from the hoop at which Noli threw the ball, y₀ = 7 feet

The height of the hoop = 10 feet

The height from which the ball was thrown = 6 feet

The height to which the ball is thrown = 2 × The initial horizontal distance from the hoop

∴ The height to which the ball is thrown, \(y_{max}\) = 2 × 7 feet = 14 feet

The coordinates of points on the path of the ball are;

(0, 6), (7, 10), (x, 14)

The projectile in vertex form is y = a·(x - h)² + k

Where;

(h, k) = The x, and y-coordinate of the maximum height

The y-coordinate of the maximum height reached = k = 14 feet

The x-coordinate of the maximum height = h = The horizontal distance of the ball from Noli when it reached maximum height

At y = 6, x = 0, therefore, we get;

6 = a·(0 - h)² + 14 = a·h² + 14

6 = a·h² + 14

a = -8/h²

At y = 10, x = 7, we get;

10 = a·(7 - h)² + 14 = (-8/h²)·(7 - h)² + 14

10·h² = -8·(7 - h)² + 14·h²

-4·h² =  -8·(7 - h)²

4·h² - 8·(7 - h)² = 0

-4·h² + 112·h - 392 = 0

h = (-112 ± √(112² - 4 × (-4) × (-392)))/(2 × -4)

h ≈ 4.1, or h ≈ 23.9

We reject the value, h ≈ 23.9 feet given that the distance between the where the Noli threw the ball and the hoop = 7 feet

Therefore, the horizontal distance of the ball from Noli at which the ball reached its maximum height, h ≈ 4.1 feet