solve the system of equations. 2x + 7y =3
x = -4y
x =
y =​

We can see that the coefficients of the expanded expression match the terms of the 5th row of Pascal's triangle.

To evaluate the given expression, we need to use Pascal's triangle to expand the expression (b+c)^4. The coefficients of the expanded expression will be the terms of the 5th row of Pascal's triangle.

Using the formula for the coefficients of the expanded expression, we get:

4(b)(c)^3 + 6(b)^2(c)^2 + 4(b)^3(c) + (b)^4

Comparing this expression to the 5th row of Pascal's triangle, we see that the coefficients are:

1 4 6 4 1

We can rearrange the terms to match the expanded expression:

(b)^4 + 4(b)^3(c) + 6(b)^2(c)^2 + 4(b)(c)^3 + (c)^4

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Using the normal distribution formula, we know that the z score that is equivalent to 25 is 1.5.

A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.

The characteristics of normal distributions are as follows: Bell-like in its symmetry.

The distribution's mean and median, which are both at its center, are equal.

68 percent of the data, or approximately, falls within one standard deviation of the mean.

So, the formula is used to determine the Z score for a data point x in a normal distribution:

Z = z - mean/standard deviation

Now, use the formula to calculate the z value as follows:

Z = z - mean/standard deviation

Z = 25 - 16/6

Z = 9/6

Z = 3/2

Z = 1.5

Therefore, using the normal distribution formula, we know that the z score that is equivalent to 25 is 1.5.

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a. To represent the value of the house t years after the house was purchased, we can use the formula for compound interest:

Value = Principal * (1 + Rate)^Time

In this case, the principal (P) is the initial purchase price of the house, which is $135,000.

The rate (R) is the annual appreciation rate, which is 4% or 0.04. The time (T) is the number of years after the house was purchased.

Therefore, the function to represent the value of the house t years after the purchase is:

Value(t) = $135,000 * (1 + 0.04)^t

b. To find the value of the house in 10 years, we can substitute t = 10 into the function:

Value(10) = $135,000 * (1 + 0.04)^10

Calculating this expression gives us the value of the house after 10 years based on the given rate of appreciation.

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The probability of exactly two flaws in a 50-yard piece of material is approximately 0.2706 or 27.06%.

In order to determine the probability of exactly two flaws in a 50-yard piece of material, we will use the Poisson distribution formula.

The Poisson distribution is used to calculate the probability of a given number of events occurring in a fixed interval of time or space when these events happen independently of each other and at an average rate.

To find the probability of exactly two flaws in a 50-yard piece of material, we will use the following formula:

P(X = k) = (e^(-λ) * λ^k) / k!

Where: P(X = k) is the probability of k flaws occurring in a 50-yard piece of material

λ = the average rate of flaws per unit of material (in this case, 50 yards)

k = the number of flaws we want to calculate is the mathematical constant ≈ 2.71828...

k! is the factorial of k, which is the product of all positive integers up to k

Let's plug in the values we have for this problem:

P(X = 2) = (e^(-λ) * λ^2) / 2!

λ = 2 flaws per 50 yards of material produced = 2/50 = 0.04 flaws per yard.

Therefore, the average number of flaws in a 50-yard piece of material is:

λ = 0.04 * 50 = 2e is a mathematical constant that equals ≈ 2.71828...

Then, let's plug in these values into the formula:

P(X = 2) = (e^(-2) * 2^2) / 2!P(X = 2) = (0.1353 * 4) / 2P(X = 2) = 0.2706

The probability of exactly two flaws occurring in a 50-yard piece of material is 0.2706 or approximately 27.06%.

Therefore, the probability of exactly two flaws in a 50-yard piece of material is approximately 0.2706 or 27.06%.

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Answer:

the answer is C

Step-by-step explanation:

hope its help

Answer:

C ) 374

Step-by-step explanation:

I took the test and got it right.

Answer:

------------------------

After 3 half-lives the remaining amount becomes:

Convert 1/8 to percent:

The measure of KM in the circle ⊙F is 270 units.

To find the measure of KM in the circle ⊙F, we need to use the given information.

First, we know that GK is equal to 14 units.

Next, we are told that the measure of angle GHK is 142 degrees.

In a circle, the measure of an angle formed by two chords intersecting inside the circle is half the sum of the intercepted arcs.

So, we can set up the equation:
142 = (m GK + m KM)/2
We know that m GK is 14, so we can substitute it into the equation:
142 = (14 + m KM)/2
Now, we can solve for m KM by multiplying both sides of the equation by 2 and then subtracting 14 from both sides:

284 = 14 + m KM
m KM = 270

Therefore, the measure of KM in the circle ⊙F is 270 units.
The measure of KM in the circle ⊙F is 270 units.

To find the measure of KM in the circle ⊙F, we can use the given information about the lengths of GK and the measure of angle GHK.

In a circle, an angle formed by two chords intersecting inside the circle is half the sum of the intercepted arcs. In this case, we have the angle GHK, which measures 142 degrees.

Using the formula for finding the measure of such an angle, we can set up the equation (142 = (m GK + m KM)/2) and solve for m KM.

Since we know that GK measures 14 units, we can substitute it into the equation and solve for m KM. By multiplying both sides of the equation by 2 and then subtracting 14 from both sides, we find that m KM is equal to 270 units.

Therefore, the measure of KM in the circle ⊙F is 270 units.

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Answer:

Step-by-step explanation:

20.00

Answer:

Step-by-step explanation:

A

Never terminates. The answer is 6.1111111 ....

B

3^3 and 27 cancel. 3^3 is 27

5^2 and 5^3 partially cancel, you are left with 5 in the denominator.

2 is raised to the 1

1/(2 * 5 ) = 1/10 = 0.1 which terminates right where it is.

A non terminating repeating expansion

B terminating decimal expansion

Answer:

Step-by-step explanation:

\(8-7x-6-8x=5\\\\\mathrm{Group\:like\:terms}\\-7x-8x+8-6=5\\\\\mathrm{Add\:similar\:elements:}\:-7x-8x=-15x\\-15x+8-6=5\\\\\mathrm{Add/Subtract\:the\:numbers:}\:8-6=2\\-15x+2=5\\\\\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}\\-15x+2-2=5-2\\\\Simplify\\-15x=3\\\\\mathrm{Divide\:both\:sides\:by\:}-15\\\frac{-15x}{-15}=\frac{3}{-15}\\\\Simplify\\x=-\frac{1}{5}\)

Answer:

\(1\) and \(6\).

Step-by-step explanation:

Let \(x\) denote one of the integers. Since the two integers add up to \(7\), the other integer would be \((7 - x)\).

The sum of the squares of these integers is \(37\). In other words:

\(x^{2} + (7 - x)^{2} = 37\).

Expand \((7 - x)^{2}\) using binomial expansion. Simplify and rewrite this equation and solve for \(x\).

\(2\, x^{2} - 14\, x + 12 = 0\).

\(x^{2} - 7\, x + 6 = 0\).

Using the quadratic formula or factorization, \(x = 1\) or \(x = 6\). Thus, the two integers are \(1\) and \(6\).

The length of the diagonal of the rectangle is 6.4 meters

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

Length = 5 meters

Width = 4 meters

The length of the diagonal can be calculated as

diagonal = √(length² + width²)

substitute the known values in the above equation, so, we have the following representation

diagonal = √(5² + 4²)

Evaluate

diagonal = 6.4

Hence, the diagonal is 6.4 meters

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Answer:

I don t understand what you are saying

Answer:

tomorrow        

Step-by-step explanation:

Answer:

the answer for that is 35 letter D

Answer:the mean is the best measure of central tendency for the science class

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Assuming that the Skateboard is $180, and you are asking for the price when it is 30% off.

180 * .70 = $126

Another way of solving the question is finding 10 % of 180, which is 18. And you are looking for 30% less, so 18 * 3 = 54, which is 30% of 180.

180 - 54 = 126

The probability of the event A' (not A) or the complement of event A, which represents a disk not having high shock resistance, is 7/50.

To calculate this probability, we need to find the number of disks that do not have high shock resistance. From the given data, we can see that there are a total of 159 disks. Out of these, 70 disks have high shock resistance (event A), so the number of disks without high shock resistance is 159 - 70 = 89.

Therefore, the probability of A' is 89/159, which simplifies to 7/50.

In terms of interpretation, this probability represents the likelihood of randomly selecting a disk that does not have high shock resistance from the given sample of 159 disks. It indicates the proportion of disks that do not meet the criteria for high shock resistance.

It's worth noting that the calculation of P(A' U B) (the probability of either A' or B occurring) was not provided. If you provide the necessary information, I can assist you in calculating that probability as well.

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Answer:

4 feet 11 inches

Step-by-step explanation:

all you need to do is see how many groups of 12 is in 59

its 4 because 5 times 12 is 60

12 times 4 is 48

59-48= 11

4 feet 11 inches

Brainliest would be appreciated!

The ratios that could be the lengths of the two legs in a 30-60-90 triangle are √3:3 (option E) and 12√3 (option D).

In a 30-60-90 triangle, the angles are in the ratio of 1:2:3. The sides of this triangle are in a specific ratio that is consistent for all triangles with these angles. Let's analyze the given options to determine which ones could be the ratio between the lengths of the two legs.

A. √2:√2

The ratio √2:√2 simplifies to 1:1, which is not the correct ratio for a 30-60-90 triangle. Therefore, option A is not applicable.

B. 15

This is a specific value and not a ratio. Therefore, option B is not applicable.

C. √√√√5

The expression √√√√5 is not a well-defined mathematical operation. Therefore, option C is not applicable.

D. 12√3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which simplifies to √3:3. Therefore, option D is applicable.

E. √3:3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which is equivalent to √3:3. Therefore, option E is applicable.

F. √2:√5

This ratio does not match the ratio of the sides in a 30-60-90 triangle. Therefore, option F is not applicable. So, the correct option is D. 1 √2.

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Answer:

We have a right isoceles triangle, so y = 5 and x = 5√2.

Answer:

y= 5

x= 7.07

Step-by-step explanation:

- in the file attached, is the one with more mathematically proven.

- in simpler ways to solve this, you dont have to do 'TOA' as the question already show the triangle being isosceles so y is automatically 5.

- x can be found by using theorem pythagoras formula.

Answer:

Step-by-step explanation:

The function f(x) = 1/x is not defined for x = 0 since division by zero is undefined. Therefore, f(x) is not a function from R to R since it does not assign a unique value to every element in the domain.

The statement "A - (A ∩ B) = A - B" is true.

To demonstrate this, we'll need to show that every element in A - (A ∩ B) is also in A - B, and vice versa.

Let x be an arbitrary element of A - (A ∩ B). This implies that x is an element of A and not an element of A ∩ B, meaning that it is either an element of B or not.

Assume, for the sake of argument, that x is in B. This means that x is not in A ∩ B.

Since x is in A, it is also in A - B since it is not in B.

As a result, x is in A - B if x is in B.

On the other hand, if x is not in B, then it cannot be in A ∩ B, as A ∩ B includes all the elements that are both in A and B.

As a result, x must be in A - B since it is in A. In conclusion, we've shown that if x is in A - (A ∩ B), then it must be in A - B and vice versa.

Therefore, A - (A ∩ B) = A - B is proven.

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To start calculating the volume of the cone, we obtain the following data:

To calculate the volume of a cone, we apply the following formula:

\(\boldsymbol{\sf{V=\dfrac{\pi r^{2}h }{3} }}\), where

We solve, substituting our data in the formula:

taking the square root

Multiplying

Dividing

Therefore the volume of the cone is 144 cm³.

\(\huge\text{Hey there!}\)

\(\huge\textbf{What is the formula for finding the}\\\\\huge\textbf{the volume of a cone?}\)

\(\large\boxed{\mathsf{\dfrac{\pi \times r^2\times h}{3} = volume}}\)

\(\bullet\large\textsf{ Whereas, \boxed{r} is your \underline{radius}, \boxed{h} is your \underline{height}, \& \boxed{\pi} is your pi.}\)

\(\bullet\large\textsf{The pi }\boxed{(\pi)}\large\textsf{ is approximately equal to 3.14.}\)

\(\huge\textbf{What are the labels in your equation?}\)

\(\star\ \large\boxed{{Radius}}\rightarrow \textsf{\underline{4\ centimeters}}}}}\)

\(\star\ \large\boxed{{Height}}\rightarrow \textsf{\underline{9\ centimeters}}}}}\)

\(\star\ \large\boxed{{\pi}}\rightarrow \textsf{\underline{3}}}}}\)

\(\huge\textbf{What does should the equation look}\\\\\huge\textbf{like?}\)

\(\large\boxed{\mathsf{\dfrac{3 \times 4^2 \times9}{3}}}\)

\(\huge\textbf{What are the steps to solve for the}\\\\\huge\textbf{question to get the result?}\)

\(\large\boxed{\mathsf{\dfrac{3 \times 4^2 \times9}{3}}}\)

\(\large\boxed{\mathsf{= \dfrac{3\times4\times4\times9}{3}}}\)

\(\large\boxed{= \mathsf{\dfrac{3\times16\times9}{3}}}\)

\(\large\boxed{\mathsf{= \dfrac{48\times9}{9}}}\)

\(\large\boxed{\mathsf{= \dfrac{432}{3}}}\)

\(\large\boxed{\mathsf{= \dfrac{432 \div 3}{3\div3}}}\)

\(\large\boxed{= \mathsf{\dfrac{144}{1}}}\)

\(\large\boxed{\mathsf{= 144\div1}}\)

\(\large\boxed{= \textsf{144}}\)

\(\huge\textbf{What is the result to this question?}\)

\(\huge\boxed{\frak{144\ cm^3}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

The volume of the given object would be the addition of the volume of the cone and the volume of the rectangular prism = 3,648 in³.

The volume of cone = v = πr²h/3

where π = 3

r = 8/2 = 4ft

h = 12ft

Volume = 3× 4² × 12/3

= 576/3 = 192ft³

The volume of the rectangular prism = l×w×h

where;

l = 7ft

w = 2ft

h = 8ft

volume = 7×2×8 = 112ft³

Therefore the volume of the object = 192+112 = 304ft³

To convert to inches the following is carried out;

1 ft = 12 inches

304 ft = 304× 12 = 3,648 in³

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Answer:

f²r-nr=d

Step-by-step explanation:

f²r-N=d/r

multiply both sides by r to get d by itself

f²r-nr=d

(all variables need to be there in your final equation)

The correlation coefficient that represents the strongest relationship between two variables is -0.75.

In correlation coefficients, the absolute value indicates the strength of the relationship between variables. The strength of the association increases with the absolute value's proximity to 1.

The maximum absolute value in this instance is -0.75, which denotes a significant negative correlation. The relevance of the reverse correlation value of -0.75 is demonstrated by the noteworthy unfavorable correlation between the two variables.

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Answer:

\((-\infty,-9)\cup(-9,\infty)\)

Step-by-step explanation:

The domain of a rational function is all real numbers except for when the denominator equals 0.

So, to find the domain restrictions, set the denominator to 0 and solve for x.

We have the rational function:

\(s(y)=\frac{7y}{y+9}\)

Set the denominator to 0:

\(y+9=0\)

Subtract 9:

\(y\neq-9\)

So, the domain is all real numbers except for -9.

In other words, our domain is all values to the left of negative 9 and to the right of negative 9.

In interval notation, this is:

\((-\infty,-9)\cup(-9,\infty)\)

And we're done :)

The simplified expression for the polynomial is 2y = 8x³− 14x²− 25x+ 42

A mathematical formula that uses integer variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, multiplication, division, and exponentiation by a rational exponent).

The given function is p(x)=1/2(x-2)(2x-3)(4x+7)

The simplified form of the function can be written as

2y = 8x³− 14x²− 25x+ 42

Now we know that the roots of the equation are 2 ,3/2 and -7/4.

The graph of the function is attached below.

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Answer:

1. 42 cm²

2. 128 cm²

6. 66 cm²

Step-by-step explanation:

In each case, I am using the front and back faces as bases with length and width. The bottom right dimension is the height.

1.

SA = 2(L + W)H + 2LW

SA = 2(3 cm + 2 cm)(3 cm) + 2(3 cm)(2 cm)

SA = 42 cm²

2.

SA = 2(L + W)H + 2LW

SA = 2(6 cm + 4 cm)(4 cm) + 2(6 cm)(4 cm)

SA = 128 cm²

6.

SA = 2(L + W)H + 2LW

SA = 2(3 cm + 3 cm)(4 cm) + 2(3 cm)(3 cm)

SA = 66 cm²

Answer:

1=40 2=252 3=200 4=36

Step-by-step explanation:

I dint do the top two so start on 3

3#= 1