Write a compound inequality that represents the following phrase. Graph the solutions. all real numbers that are between -6 and 7, inclusive

Answer:

469,225

Step-by-step explanation:

685² = 469,225

I hope this helps!

Answer:

(a) 5.714s

(b) 0.625m

Step-by-step explanation:

Acceleration due to gravity=a=±9.8m/s/s (+ when falling, - when going upwards)

(a)

STAGE A: between start and first bounce

Initial speed=u=0m/s, Distance=s=40m, and Final velocity=v

v²=u²+2as

v²=0²+2(10)(40)

v²=794

v=28m/s (As the ball hits the ground)

v=u+at

28=0+9.8t\(_{a}\)

t\(_{a}\)=28/9.8=2.85714285714s

STAGE B: from the first bounce until it starts to fall

u=half the speed it hit the ground with=(28/2)=14m/s, and v=0m/s(when it starts to fall)

v=u+at

0=14-9.8t\(_{b}\)

t\(_{b}\)=14/9.8=1.42857142857s

STAGE C: between when it starts to fall after bounce 1, and bounce 2

We can assume that the time it takes to go from the ground to max height after bounce 1 is equal to the time it takes to fall from that same height to the ground. Therefore, t \(_{c}\)=1.42857142857s

The time from when the ball was released to when it hit the ground for the second time = t

t = t\(_{a}\) + t\(_{b}\) + t\(_{c}\)

t=2.85714285714+1.42857142857+1.42857142857

t=5.71428571428s≈5.714s

(b)

Before bounce 1, u=28m/s (see stage a)

After bounce 1, u= 28/2= 14m/s

After bounce 2, u= 14/2 = 7m/s

After bounce 3, u= 7/2 =3.5m/s

u=3.5m/s and v=0m/s(when it starts to fall)

v²=u²+2as

0²=3.5²+2(-9.8)s

19.6s=12.25

s=0.625m (max height after third bounce)

Answer:

\(6\).

Step-by-step explanation:

A line that goes through \((x_{0},\, y_{0})\) and \((x_{1},\, y_{1})\) where \(x_{0} \ne x_{1}\) would have a slope of \(m = (x_{1} - x_{0}) / (y_{1} - y_{0})\).

The slope of the line that goes through \((8,\, 4)\) and \((-1,\, 1)\) would thus be:

\(\begin{aligned}m_{2} &= \frac{1 - 4}{(-1) - 8} \\ &= \frac{(-3)}{(-9)} \\ &= \frac{1}{3}\end{aligned}\).

Two lines in a cartesian plane are perpendicular to one another if and only if the product of their slopes is \((-1)\).

Thus, if \(m_{1}\) and \(m_{2}\) denote the slope of the first and second lines in this question, \(m_{1}\, m_{2} = (-1)\) since the two lines are perpendicular to one another. Since \(m_{2} = (1/3)\), the slope of the first line would be:

\(\begin{aligned} m_{1} &= \frac{(-1)}{m_{2}} \\ &= \frac{(-1)}{(1/3)} \\ &= (-3)\end{aligned}\).

Given that the first line goes through the point \((1,\, 0)\), the point-slope equation of that line would be:

\((y - 0) = (-3)\, (x - 1)\).

\(y = -3\, x + 3\).

Substitute in \(x = (-1)\) to find the \(y\)-coordinate of the point in question:

\(y = -3\times (-1) + 3 = 6\).

a) To re-express the given differential equation as a first-order differential equation using matrix and vector notation, we can rewrite it in the form:

\(x' = Ax\)

where x is a vector and A is a square matrix.

b) To determine the stability of the system obtained in part (a), we need to analyze the eigenvalues of matrix A.

If all eigenvalues have negative real parts, the system is stable.

If at least one eigenvalue has a zero real part, the system is neutrally stable.

If at least one eigenvalue has a positive real part, the system is unstable.

c) To compute the eigenvalues and eigenvectors of matrix A, we solve the characteristic equation

\(det(A - \lambda I) = 0\),

where λ is the eigenvalue and I is the identity matrix.

By solving this equation, we obtain the eigenvalues.

Substituting each eigenvalue into the equation

\((A - \lambda I)v = 0\),

where v is the eigenvector, we can solve for the eigenvectors.

d) Once we have computed the eigenvalues and eigenvectors of matrix A, we can construct the diagonalization relationship as follows:

\(A = PDP^{(-1)}\)

where P is a matrix whose columns are the eigenvectors of A, and D is a diagonal matrix whose diagonal elements are the eigenvalues of A.

To show that this relationship is valid, we can compute \(PDP^{(-1)}\) and verify that it equals A.

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Answer:

12

Step-by-step explanation:

96/8 = 12

Answer:

12

Step-by-step explanation:

Answer:

$4

Step-by-step explanation:

We can write a ratio to solve

15 stickers       30 stickers

----------------- = -------------

2 dollars           x stickers

Using cross products

15x = 2*30

15x = 60

Divide by 15

15x/15 = 60/15

x = 4

Answer:

The answer varies depending if your teacher wants the answer in cents only, or in dollars only.

====================================================

Explanation:

Based on that, we know,

and ultimately

p+5n+50p = 51p+5n

represents the total value of all the coins, and this value is in cents. We would divide by 100 to convert from cents to dollars. So we can say that 51p+5n cents = (51p+5n)/100 dollars

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

As an example, let's say

So we have

This would mean we have

Overall we have p+5n+25q = 4+25+200 = 229 cents which converts to 229/100 = $2.29

We can also say 51p+5n = 51*4+5*5 = 204+25 = 229 which is a slight shortcut to get the same result (that result being in cents).

Answer:

Is there suppose to be a picture?

Step-by-step explanation:

Answer:

Because she liked Augle more than the other child

Step-by-step explanation:

She didn't want him to go to school so that she could spend the day with her favorite child

Answer:

2...

Step-by-step explanation:

1 + 1 = 2

Step-by-step explanation:

the scale factor is 1/1

both triangles are similar, and the scale factor is 1/1

Answer:0.916

The decimal multiplier to decrease by 8.4% is 0.916.

Step-by-step explanation:

Answer: 6x3y2

Step-by-step explanation:

Answer:

I wasn't too sure of your question, but this is what made sense to me.

Step-by-step explanation:

cross multiplication seems to be the best fit for this.

Like this:

\(\frac{9}{2}=\frac{x}{24}\\ 2(x)=9(24)\\ 2x=216\\x= \frac{216}{2}\\ x=108\)

Hope this helped in any way.

Answer:

8 peices

Step-by-step explanation:

Sorry it went without any work.

work: 27.2/3.4 = 8

Answer:

8 pieces

Step-by-step explanation:

27.2 divide 3.4 then you will get as answer which is 8 pieces from 27.2 meters string.

The inequality on the graph is the third option:

(2/5)*x - 3/2 ≥ y

Let's analyse the graph if the inequality.

We can see that there is a solid linear equation with a positive slope, and the shaded area is below that line, then the inequality is of the form:

y ≤ linear equation.

We know that the symbol "≤" must be used because of the solid line.

We also can see that when x = 0, y takes a velue between -1 and -2.

With that in mind the correct option is the third one:

(4/5)*x - 2y ≥ 3

Isolating y we get:

(4/5)*x - 3 ≥ 2y

(2/5)*x - 3/2 ≥ y

Changing the order:

y ≤ (2/5)*x - 3/2

That is the graphed inequality.

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Answer:

81%

Step-by-step explanation:

P (Defective item) = 10% , P (Defective identified) = 90% of defective = 90% of 10% = 9%

P (Non defective item) = 1 - 10% = 90% , P (Non defective identified) = 80% of non defective = 80% of 90% = 72%

Prob (Scanner identifies correctly) = Pr (non defective mentioned non defective) & Pr (defective mentioned defective)

= 9% + 72% = 81%

Answer:

i think its b i could be wrong if i am im so sorry

Step-by-step explanation:

The value of y is 11 and the value of x is 1/3.

For the equation 16 - y = 5, we can represent 16 and 5 by two bundles of chopsticks each, and y by a smaller bundle of chopsticks. Then, we can remove five chopsticks from each side of the equation to make the variables match as follows:

| | | | | | | | | | | | | | | |  - | | | | | =  | | | | | |

| | | | | | | | | | | |          + | | | | | |  + | | | | | |  y

After removing five chopsticks from the left and the right side of the equation, we are left with 11 chopsticks on the left, which equals to y on the right.

| | | | | |  + | | | | | | | | |

| | | | | | | | | | | | | | | | y

After adding eight chopsticks to the left and the right side of the equation, we get 13 chopsticks on the left, which equals y on the right. Therefore, the value of y is 13 - 8 = 5.

For the equation 10-3x=1, we can represent 10 and 1 by two bundles of chopsticks each, and 3x by a smaller bundle of chopsticks. Then, we can remove 9 chopsticks from each side of the equation to make the variables match as follows:

| | | | | | | | | | | - | | | = | | | | | |

| | | | | | | | | | | | | | | | | 3x

After removing 9 chopsticks from the left and the right side of the equation, we are left with one chopstick on the left, which corresponds to 3x on the right. Therefore, the value of 3x is 1.

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The total surface area of the triangular prism using the net is 96 square units

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

The net of a triangular prism

The surface area of the triangular prism from the net is calculated as

Surface area = sum of areas of individual shapes that make up the net of the triangular prism

Using the above as a guide, we have the following:

Area = 2 * 3 * 7 + 6 * 7+ 2 * 1/2 * 2 * 6

Evaluate

Area = 96

Hence, the surface area is 96 square units

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Answer:

\((a) \: 6n-2\\(b)\: 5 \times 3^{n-1}\\(c)\: 5({-1^n}+3)\)

Step-by-step explanation:

\(6(1)-2=4\)

\(6(2)-2=10\)

\(5 \times 3^{(3)-1}=45\)

\(5 \times 3^{(4)-1}=135\)

\(5(-1^{(5)}+3)=10\)

\(5(-1^{(6)}+3)=20\)

a) The formula that generates the sequence 4, 10, 16, 22, 28, 34, 40 is an = 4 + 6 * (n - 1)

b) The formula that generates the sequence 5, 15, 45, 135, 405 is an = 5 * 3ⁿ⁻¹

c) The formula that generates the sequence 10, 20, 10, 20, 10, 20, 10 is  an = 10 + 10 * ((n + 1) % 2)

(a) The sequence increases by 6 at each step. To generate the sequence, we can use the formula: an = 4 + 6 * (n - 1), where "an" represents the nth term in the sequence, and "n" is the position of the term in the sequence.

(b) The sequence is a geometric progression with a common ratio of 3. To generate the sequence, we can use the formula: an = 5 * 3ⁿ⁻¹ where "an" represents the nth term in the sequence, and "n" is the position of the term in the sequence.

(c) The sequence alternates between 10 and 20. To generate the sequence, we can use the formula: an = 10 + 10 * ((n + 1) % 2), where "an" represents the nth term in the sequence, and "%" represents the modulo operation, which results in 0 when n is even and 1 when n is odd. So, when n is even, an = 10, and when n is odd, an = 10 + 10 = 20.

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Answer:

\(n=(\frac{1.440(2.3)}{0.12})^2 =761.76 \approx 762\)

So the answer for this case would be n=762 rounded up to the nearest integer

Step-by-step explanation:

Information given

\(\bar X = 17\) represent the mean

\(\mu\) population mean (variable of interest)

\(\sigma= \sqrt{5.29}= 2.3\) represent the standard deviation

Solution to the problem

The margin of error is given by this formula:

\( ME=z_{\alpha/2}\frac{s}{\sqrt{n}}\)    (a)

And on this case we have that ME =0.12 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

\(n=(\frac{z_{\alpha/2} \sigma}{ME})^2\)   (b)

The confidence level is 85%, the significance level would be \( \alpha=1-0.85 = 0.15\) and \(\alpha/2 =0.075\) the critical value for this case would be \(z_{\alpha/2}=1.440\), replacing into formula (b) we got:

\(n=(\frac{1.440(2.3)}{0.12})^2 =761.76 \approx 762\)

So the answer for this case would be n=762 rounded up to the nearest integer

Answer:

To find the answer, we can use the formula:

number of won games / total number of games played = percentage won

Let x be the total number of games played. We know that the percentage won is 65%, or 0.65 as a decimal. So we can set up the equation:

number of won games / x = 0.65

To solve for x, we can cross-multiply:

number of won games = 0.65x

We want to find a whole number value for x that makes sense. One way to do this is to try each answer choice and see if it gives a whole number value for the number of won games. Let's start with choice A:

If the team played 22 games, then the number of won games is:

number of won games = 0.65 * 22 = 14.3

This is not a whole number value, so we can rule out choice A.

We can repeat this process for each answer choice. When we try choice C, we get:

number of won games = 0.65 * 18 = 11.7

This is also not a whole number value, so we can rule out choice C.

When we try choice D, we get:

number of won games = 0.65 * 14 = 9.1

This is also not a whole number value, so we can rule out choice D.

Therefore, the only remaining answer choice is B, which gives us:

number of won games = 0.65 * 20 = 13

This is a whole number value, so the team could have played 20 games in total last season.

Answer:

x=20

Step-by-step explanation:

Let's solve your equation step-by-step.

4x−4+3x−2+2x+6=180

Step 1: Simplify both sides of the equation.

4x−4+3x−2+2x+6=180

4x+−4+3x+−2+2x+6=180

(4x+3x+2x)+(−4+−2+6)=180(Combine Like Terms)

9x=180

9x=180

Step 2: Divide both sides by 9.

9x

9

=

180

9

x=20

Answer:

x=20

Answer:

x=20

Step-by-step explanation:

im pretty sure this is right. you can't take away 4 from 4 x, so you do it like this: -4+(-2)+6 =0. 4x + 3x + 2x =9x. 180/9 = 20

Answer:

m=-25

Step-by-step explanation:

m=Δh/Δt

(Im choosing for the difference in height and time (Δh and Δt) to be the difference between the data in the first two rows)

m=(4500-5000)/(20-0)

m=-500/20

m=-25

Answer:

line segment A B

Step-by-step explanation:

it's really a ray, not a line segment

In circle D, the AB line segment is tangent to the circle.

The circumference, which is the distance around the object, the diameter, which is the length of a circle measured from one end to the other and passing through its center, and the radius, which is equal to half of the diameter, are the three key characteristics.

The general coordinate equation of a circle is:

(x-h)² + (y - k)² = r²

Where,

(h, k) is the center of a circle,

"r" is the radius of the circle.

Since A line that only has one point where it crosses a circle is said to be tangent to the circle. The point of contact is the location where the circle and the tangent meet.

Thus, in the given figure AB is the tangent line segment of the circle D.

From the properties of the circle, we can state that,

FE is Diameter,

The CD is representing the radius, and

GH is representing the Secant line of the circle D.

Therefore, In circle D, the AB line segment is tangent to the circle.

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Answer: c

Step-by-step explanation:

Answer: C

Step-by-step explanation:

In the word problem,  The present ages of Ramesh and his elder brother are 20 years and 28 years.

What  is word problem ?

Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided expression are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.

Here let us take present age of Ramesh and His elder brother are 5x and 7x.

Now After 4 years their ages will be 3:4. Then,

=> \(\frac{5x+4}{7x+4}=\frac{3}{4}\)

=> 20x+16=21x+12

=> 21x-20x=16-12

=> x= 4

Then Present age of Ramesh = 5*4=20 years.

Present age of his elder brother = 7*4=28 years.

Hence The present ages of Ramesh and his elder brother are 20 years and 28 years.

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The probability that the student is a sophomore, given that they are in work, is given as follows:

P(sophomore|work) = 30%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The outcomes for this problem are given as follows:

Hence the probability is obtained as follows:

P(sophomore|work) = 3/10 = 0.3 = 30%.

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