rachel states that -5.5 is an integer because it is negative. is she correct? why or why not?

The value of x is 10

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

The large triangle is divided into 2 similar triangles

The ratios of corresponding sides are equal

8/12 = x+4/2x+1

=> 8( 2x+1) = 12( x+4 )

=>  16x+8 = 12x+48

=> 16x-12x = 48-8

=> 4x = 40

=> x= 40/4 = 10

The value of x is 10

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1000 cubic centimeters would need to be placed in a tub of water to displace 1 Lter of water

Conversion of units simply refers to the method used in determining the equivalent of one unit in relation to another.

From the information given, we have that;

Number of cubic centimeters that would be placed in a tub of water to displace 1 L of water

So, we have that there is 1 liter of water in the tub

In order to displace, you need to put something in that is the same amount

Now, let's convert the units

1 liter = 1000 cubic cm

Hence, you need 1000 cubic cm to displace 1 liter

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The given matrix A is:
A = [−20−4−20−4102]

We know that the matrix has one real eigenvalue of algebraic multiplicity 3.
To find this eigenvalue, we can use the formula:
det(A - λI) = 0
Where I is the identity matrix and det(A - λI) is the determinant of the matrix A - λI.
Substituting the given matrix A, we get:
det([−20−4−20−4102] - λ[1111])
= |−20-λ   -4     |
 |−2      -4-λ  |
= (-20-λ)(-4-λ) - (-2)(-20)
= λ^2 + 24λ + 80
To find the eigenvalue, we set det(A - λI) = 0 and solve for λ:
λ^2 + 24λ + 80 = 0
Using the quadratic formula, we get:
λ = (-24 ± sqrt(24^2 - 4(1)(80))) / (2(1))
λ = (-24 ± sqrt(256)) / 2
λ = -12 ± 8
Therefore, the eigenvalues of the given matrix are:
λ1 = -20
λ2 = -4
λ3 = -12
Since the matrix has one real eigenvalue of algebraic multiplicity 3, the eigenvalue we are looking for is:
λ3 = -12
Therefore, the answer is:
The eigenvalue of the given matrix A=[−20−4−20−4102] with algebraic multiplicity 3 is -12.

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An angle is the two rays sharing a common endpoint.

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Answer:

(a) \(x=\frac{19}{4}=4.75\)

(b) \(x=-\frac{1+\sqrt{193}}{6}\approx-2.4821, x=-\frac{1-\sqrt{193}}{6}\approx2.1487\)

Step-by-step explanation:

The detailed explanation is shown in the attached documents below.

Answer:

70cm2

Please mark

Step-by-step explanation:

Answer:

396 cm²

Step-by-step explanation:

The figure is composed of 2 rectangles.

The vertical rectangle on the left has area (A) calculated as

A = 27 × 10 = 270 cm²

The horizontal rectangle on the right has area (A) calculated as

A = 9 × (24 - 10) = 9 × 14 = 126 cm²

Thus area of figure = 270 + 126 = 396 cm²

Answer:

R (I think it has a typo)

Step-by-step explanation:

18 times 13 equals 234 ounces.

There are 16 ounces in 1 pound, so to find how many pounds we have, we must divide by 16.

234 divided by 16 is 14.625.

R has a typo but I'm assuming is R.

Examples of such data include stock prices, economic indicators, and meteorological data such as temperature, wind speed, and barometric pressure.

These types of data often have a trend or pattern, but the difference between the data points has meaning and does not necessarily have a defined starting point.

1. Data where the difference between data values has meaning but there is no defined starting point can be defined as data that is not linearly dependent.

2. Examples of such data include stock prices, economic indicators, and meteorological data. These types of data often have a trend or pattern, but the difference between the data points has meaning and does not necessarily have a defined starting point.

3. Stock prices, economic indicators, and meteorological data all have different scales and can move in different directions, making it difficult to track the exact difference between data points.

4. Despite this, these types of data still allow for meaningful analysis and can be used to make predictions and draw conclusions.

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Answer:

the answer is 90%, 90% of 30 is 27

Answer:

The horizontal distance the ball travels before it hits the ground is 22.\(\overline{857142}\) feet

Step-by-step explanation:

The given parameter are;

The function modelling the path of the ball tossed by Nate y = -14·x² + 335·x

x = The horizontal distance the ball travels from Nate in feet

y = The height of the ball in feet

The line equation modelling the hill is y = 15·x

The point where the ball hits the ground is given by the point the graph of the equation for the path of the ball and the path of the model of the line of the hill meet as follows;

Ball path is y = -14·x² + 335·x

Hill path is y = 15·x

The point both paths meet and the ball hits the ground is -14·x² + 335·x = 15·x

Which gives;

-14·x² + 335·x - 15·x = 0

-14·x² + 320·x = 0

320·x - 14·x² = 0

x × (320 - 14·x) = 0

x = 0, or x = 320/14 = 22 6/7 = 22.\(\overline{857142}\) feet

Therefore;

The horizontal distance the ball travels before it hits the ground = x = 22.\(\overline{857142}\) feet.

The path of ball will be parabolic in nature .Parabolic path is defined as the angle of trajectory of a projectile.

Ball travel 22.86 feet horizontally before it hits the ground.

Since, The path of the ball is modeled by the function \(y = -14x^{2} + 335x\)

where x is the ball’s horizontal distance from Nate in feet and y is the ball’s height in feet.

And hill is modeled by equation, \(y=15x\)

To find out how much ball will travel horizontally before it hits ground , we have to find intersection of given two model equation.

\(y = -14x^{2} + 335x\)

\(y=15x\)

So,  \(-14x^{2} + 335x=15x\\\\-14x^{2} + 335x - 15x = 0\\\\320x - 14x^{2} = 0\\\\x(320-14x)=0\\\\x=0, x=320/14=22.86\)

Thus, Ball travel 22.86 feet horizontally before it hits the ground.

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Answer: there would be 8 defective phones.

Step-by-step explanation: assuming that only 2 percent is defective and the other 98 are not, every hundred phones ordered, two would be defective.

The standard deviation for the total portfolio returns can be calculated using the weighted average of the standard deviations of the index fund and the risk-free asset. The standard deviation for the total portfolio returns is 10.5%.


The standard deviation of a portfolio measures the variability or risk associated with the portfolio's returns. In this case, the portfolio is 70% invested in an index fund (with a standard deviation of returns of 15%) and 30% invested in a risk-free asset.

To calculate the standard deviation of the total portfolio returns, we use the weighted average formula:

Standard deviation of portfolio returns = √[(Weight of index fund * Standard deviation of index fund)^2 + (Weight of risk-free asset * Standard deviation of risk-free asset)^2 + 2 * (Weight of index fund * Weight of risk-free asset * 1Covariance  between index fund and risk-free asset)]

Since the risk-free asset has a standard deviation of zero (as it is risk-free), the second term in the formula becomes zero. Additionally, the covariance between the index fund and the risk-free asset is also zero because they are independent. Therefore, the formula simplifies to:

Standard deviation of portfolio returns = Weight of index fund * Standard deviation of index fund

Plugging in the values, we get:

Standard deviation of portfolio returns = 0.70 * 15% = 10.5%

Hence, the standard deviation for the total portfolio returns is 10.5%. This means that the total portfolio's returns are expected to have a variability or risk represented by this standard deviation.

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Therefore , the percentage of case 1 is 68% and percentage of case 2 is 47.4%

One percent (symbolized as 1%), being the hundredth component, is represented as 100 percent, while 200 percent signifies twice the amount specified. As an illustration, 1% of 1,000 chickens is equal to 1/100 of 1,000, or 10 birds, and 20% of the quantity is equal to 20% of 1,000, or 200.

Here,

Given: Total number of freshman =500

mean =75 and standard deviation =7

a) the percentage of scores that fell between 68 and 82

340 is the number of freshman whose  scores that fell between 68 and 82

thus,

percentage = 340 /500 * 100

=> percentage = 68%

b)the percentage of scores that fell between 61 and 75

237 is the number of freshman whose  scores that fell between 61 and 75

thus,

percentage = 237/500 * 100

=> percentage = 47.4%

Therefore , the percentage of case 1 is 68% and percentage of case 2 is 47.4%

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Answer:

a. \(\frac{x+2}{x+6}\)

Step-by-step explanation:

\(\frac{x^2 + 5x+6}{x^2 +9x+18}=\frac{(x+2)(x+3)}{(x+3)(x+6)}=\frac{x+2}{x+6}\)

There are 6 pennies in a total of 150 coins.

Given that,

Ninety of the 150 coins are quarters. 40 percent of the remaining coins are nickels, with the remainder being dimes and pennies.

and also,

For every penny, there are five dime.

Total = 150 coins

Out of it, 90 are quarters so the remaining coins are 60

It is said that,

In that 60 coins 40% are nickels which means

40% of 60 is 24

So remaining coins are 36 (by subtracting 24 from 60)

It is said that there are 5 dimes for every penny which means

Using Algebra,

x + 5x = 36

6x= 36

x= 6

Therefore, there are 6 pennies in a total of 150 coins.

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In school suspension

Hey there!

4x + 1/2 + 2x - 3

COMBINE the LIKE TERMS

= (4x + 2x) + (1/2 - 3)

TRYING to SIMPLIFY THEM

4x + 2x

= 6x

1/2 - 3

= -5/2

ANSWER

6x + (-5/2)

Therefore, your answer should be: 6x + -5/2

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Given:

There are given the equation:

Explanation:

According to the question:

We need to find the solution to the given quadratic.

Then,

To find the solution, we will use the quadratic equation formula.

Then,

From the equation:

Where,

Then,

Put all the value into the formula:

Then,

Then,

Therefore, the solution of the given quadratic equation:

Final answer:

Hence, the correct options are B and E.

Answer:

You're looking for the graph \(y=2x\)

Step-by-step explanation:

If Estelle is raking in leaves at a constant rate, which we usually assume for cases like this, we're looking for a function of the form

\(y=kx+m\)

x here is going to be the number of hours, or time.

y is going to be the number of bags she has raked in.

First of all, we know that at time 0, she hasn't raked in any leaves. So when x is 0, we know y is 0. Let's put these values in our function.

\(0 = k * 0 + m\)

\(0 = 0 + m\)

\(m = 0\)

We now know m is 0.

We also know that after 1 hour, Estelle has 2 bags of leaves. So when x is 1, y will be 2. Let's put these values in.

\(2 = k*1\)

We're excluding m as we know it's 0.

\(k=2\)

So k is 2, and m is 0. Let's put these values in our original function \(y=kx+m\):

\(y = 2x + 0\)

\(y=2x\)

The equation is y=2x.

Putting this into a graphing calculator, we get this graph (attached).

Answer:

35

Step-by-step explanation:

700 / 100 = 7

7 = 1%

7 x 5 = 35

35 = 5%

Answer:

35

Step-by-step explanation:

Answer:

hi

Step-by-step explanation:

we should collect 2 and 9 and add -

2+9 is 11 then we add -

-11

hope it helps

Answer:

(x+5)(x-5)

X²-5x+5x-25

X²-25

Answer:

12

Step-by-step explanation:

Ppopp

For the given problem, the integral of \(\frac{1}{\sqrt{a^2-x^2}}\)  is  \($\sin^{-1}\frac{x}{a} + C$.\)

A mathematical notion that depicts the area under a curve or the accumulation of a quantity over an interval is known as an integral. Integrals are used in calculus to calculate the total amount of a quantity given its rate of change.

The process of locating an integral is known as integration. Finding an antiderivative (also known as an indefinite integral) of a function, which is a function whose derivative is the original function, is what integration is all about. The antiderivative of a function is not unique since it might differ by an integration constant.

For given problem,

\($\int \frac{1}{\sqrt{a^2-x^2}} dx$\)

Let \($x = a \sin\theta$\) , then \($dx = a \cos\theta d\theta$\)

\($= \int \frac{1}{\sqrt{a^2-a^2\sin^2\theta}} a\cos\theta d\theta$\)

\($= \int \frac{1}{\sqrt{a^2\cos^2\theta}} a\cos\theta d\theta$\)

\($= \int d\theta$\)

\($= \theta + C$\)

Substituting back for\($x = a\sin\theta$:\)

\($= \sin^{-1}\frac{x}{a} + C$\)

Therefore, the integral of \(\frac{1}{\sqrt{a^2-x^2}}\) is \($\sin^{-1}\frac{x}{a} + C$.\)

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Matrix equations:

a) (A + B)² = 8 -3 -7/4

-8/3 21/4 -39/16

3/2 -7/6 99/16

b) A¹⁶ = 256 0

-384 1

c) det(A) = |A| = -4

d) det(A) = -4

The following matrix equations can be solved as follows:

a) For A = 3 0 2

-3 2 1

1 -1 4

and B = -3 2 -1

0 1/2 -3/4

1/3 -2/3 1/2

We have (A + B) = 0 2 1

-3 5 5/4

4/3 -1/3 9/2

Therefore, (A + B)² = (A + B)(A + B) = 0 2 1 3 -2 -2 8 -3 -3/4

-3 5 5/4 + 9/2 -5/2 -15/8 -8/3 5/3 5/4

4/3 -1/3 9/2 2 -1 -3/2 3/2 -1/2 81/16

Simplifying the above expression, we get:

(A + B)² = 8 -3 -7/4

-8/3 21/4 -39/16

3/2 -7/6 99/16

b) For A = 2

-3

1

We have A¹⁶ = A⁸ x A⁸

A⁴ = A² x A² = 4 0

-6 1

A⁸ = A⁴ x A⁴ = 16 0

-24 1

Therefore, A¹⁶ = A⁸ x A⁸ = 256 0

-384 1

c) For A = 1 2 3

2 0 1

3 0 0

We have det(A) = |A| = 1(0x0 - 0x0) - 2(0x3 - 1x0) + 3(0x0 - 0x2) = -4

d) For A = 1 2 3

2 0 1

3 0 0

We have det(A) = |A| = 1(0x0 - 0x0) - 2(0x3 - 1x0) + 3(0x0 - 0x2) = -4

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Answer:

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

Ratios of corresponding sides are equal.

The number of questions to be answered in the worst case is 10 questions.

The best approach would be to divide the overall range in half, for example, by asking:

If he says no, she now knows that the number is between 1 and 499.

If he responds yes, she will know that the figure is between 500 and 1000.

Assume that the response is yes.

She can now inquire whether the number is equal to or greater than 750.

We now have two sets of possibilities. (500, 749) and (750 , 1000). (750 , 1000).

Depending on the response, we can now divide those sets again.

Assume we obtained the collection of (750, 1000)

We can split it into two groups, and so on.

We must discover the smallest n that maintains the aforesaid inequality.

999/2^n ≤ 1.

we must find the smaller n that keeps the above inequality true.

999 ≤ 2^n

knowing that 2^10 = 1024.

999/1024 = 1024

In the worst-case scenario, she should ask ten questions.

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Using Chebyshev's theorem, we can conclude that at least 56% of the gym members' ages fall between 26 and 70.

Chebyshev's theorem states that for any given dataset, regardless of its distribution, at least 1 - 1/k² of the data will fall within k standard deviations from the mean.

We can use Chebyshev's theorem to determine the percentage of gym members aged between 26 and 70. We need to determine how many standard deviations away from the mean these ages are.

To do this, we calculate the z-scores for both ages using the formula z = \((x - μ) / σ\), where x is the value (in this case, either 26 or 70), \(μ\) is the mean (48), and σ is the standard deviation (10). For x = 26: z = (26 - 48) / 10 = -2.2 For x = 70: z = (70 - 48) / 10 = 2.2

Both ages are 2.2 standard deviations away from the mean. Using Chebyshev's theorem, we know that at least 1 - 1/2.2² = 56% of the gym members' ages fall within this range.This is a lower bound - the actual percentage of gym members aged between 26 and 70 could be higher than 56%, as the distribution of ages may not be perfectly symmetrical or may have outliers.

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The given statement, "In a contingency table, when all the expected frequencies equal the observed frequencies the calculated statistic equals zero" is true because when all the expected frequencies equal the observed frequencies, the calculated statistic equals zero.

A contingency table is a table used in statistics that shows the distribution of one variable in rows and another variable in columns. It is also known as a cross-tabulation table or a two-way frequency table. In a contingency table, expected frequencies are calculated based on the assumption that there is no association between the variables being analyzed.

Observed frequencies, on the other hand, are the actual frequencies of the data being analyzed. When all the expected frequencies in a contingency table are equal to the observed frequencies, it means that there is no association between the variables, and the calculated statistic equals zero. This is because the difference between the observed and expected frequencies is used to calculate the statistic, and if there is no difference, the statistic will be zero.

Therefore, the statement "In a contingency table, when all the expected frequencies equal the observed frequencies the calculated statistic equals zero" is true.

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