WHAT IS A TAPE DIAGRAM AND WHAT DOES IT LOOK LIKE?

The value of x must be between -18 and -6. The solution has been obtained using Triangle inequality theorem.

What is Triangle inequality theorem?

The triangle inequality theorem explains how a triangle's three sides interact with one another. This theorem states that the sum of the lengths of any triangle's two sides is always greater than the length of the triangle's third side. In other words, the shortest distance between any two different points is always a straight line, according to this theorem.

We are given three sides of a triangle as 8, 6 and x+20

Using Triangle inequality theorem,

⇒8+6 > x+20

⇒14 > x+20

⇒-6 > x

Also,

⇒x+20+6 > 8

⇒x+26 > 8

⇒x > -18

Also,

⇒x+20+8 > 6

⇒x+28 > 6

⇒x > -22

From the above explanation it can be concluded that x is less than -6 but greater than -22 and -18.

This means that x must lie between -18 and -6.

Hence, the value of x must be between -18 and -6.

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Here is some info that might help


-2 factors is a hint



+0 +2 +4 is a fractor of 4/1


if not 41

To determine the surface area of the prism we need add the following areas:

• Two triangles with base of 6 in and height 4 in.

• Two rectangles with length 10 in and width 5 in

• One rectangle with length 10 in and width 6 in.

Then the surface area is:

Therefore, the surface area is 184 square inches

Answer:

Mean: 6.8

Median: 2

Mode: There's no mode

Step by step explanation:

Hope it helps ;)

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The statement "The median number of minutes outside in the summer is equal to the maximum number of minutes outside in the winter" is best supported by the data (option B).

Looking at the plot;

Winter: Minimum= 0   Maximum= 60   Median= 30

Range = 60 - 0 = 60

Summer: Minimum= 20   Maximum= 90    Median= 60

Range = 90 - 20 = 70

So the median number of minutes outside in the summer is

equal to the maximum number of minutes outside in the winter.

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Missing information:

The question is incomplete and the complete question is shown in the attached image.

The vector x = [c1 - e^-9t, c2 + 3e^7t, c1 + 5e^7t] is a solution of the initial-value problem x' = [1/10, 6, -3]x, x(0) = [2, 0, 1].

To verify that the given vector x is a solution to the initial-value problem, we need to take its derivative and substitute it into the differential equation, and then check that it satisfies the initial condition.

Taking the derivative of x, we have:

x' = c1(-1/10)e^(-9t) + c2(35)e^(7t) -1/10

5c2e^(7t)

Substituting x and x' into the differential equation, we have:

x' = Ax

x' = [ 1 10 6 −3 ] [ c1 −1 1 e−9t c2 5 3 e7t ] = [ (−1/10)c1 + 5c2e^(7t) , c1/10 − c2e^(7t) , 6c1e^(-9t) + 3c2e^(7t) ]

So, we need to verify that the following holds:

x' = Ax

That is, we need to check that:

(−1/10)c1 + 5c2e^(7t) = c1/10 − c2e^(7t) = 6c1e^(-9t) + 3c2e^(7t)

To check that the above equation holds, we first observe that the first two entries are equal to each other. Therefore, we only need to check that the first and third entries are equal to each other, and that the initial condition x(0) = [c1, 0] is satisfied.

Setting the first and third entries equal to each other, we have:

(−1/10)c1 + 5c2e^(7t) = 6c1e^(-9t) + 3c2e^(7t)

Multiplying both sides by 10, we get:

-c1 + 50c2e^(7t) = 60c1e^(-9t) + 30c2e^(7t)

Adding c1 to both sides, we get:

50c2e^(7t) = (60c1 + c1)e^(-9t) + 30c2e^(7t)

Dividing both sides by e^(7t), we get:

50c2 = (60c1 + c1)e^(-16t) + 30c2

Simplifying, we get:

50c2 - 30c2 = (60c1 + c1)e^(-16t)

20c2 = 61c1e^(-16t)

This equation must hold for all t. Since e^(-16t) is never zero, we must have:

20c2 = 61c1

Therefore, c2 = (61/20)c1. Substituting this into the initial condition, we have:

x(0) = [c1, 0] = [2, 0]

Solving for c1 and c2, we get:

c1 = 7/2 and c2 = -3/2

Thus, the solution to the initial-value problem is:

x(t) = [ (7/2) −1 1 e^(-9t) (−3/2) 5 3 e^(7t) ]

and we can verify that it satisfies the differential equation and the initial condition.

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The price after discount is $33 and option 1 is the correct answer.

A discount is a drop in a product's or service's price. Discounts can be provided for a variety of purposes, such as to entice consumers to make larger purchases, to get rid of excess inventory, or to draw in new clients. Discounts can be represented as a set monetary amount or as a %, as in the example above. For instance, a shop may give customers $10 off any purchase of more than $50.

Given that, one-day discount rate of 45% is applied.

Thus,

Discount = 60.20 * 0.45 = 27.09

Price after discount = 60.20 - 27.09 = 33.11

Hence, the price after discount is $33 and option 1 is the correct answer.

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Answer:

As radius=3

area=pie×r^2

=28.274

1. To convert -21 to 2's complement binary using 6 bits:

- First, convert the absolute value of the number (21) to binary: 10101.

- Then, invert all the bits: 01010.

- Finally, add 1 to the inverted value: 01011.

So, the 6-bit 2's complement binary representation of -21 is 01011.

2. To represent -4 in excess-16 using 5 bits:

- Add the excess value (16) to the absolute value of the number (4): 20.

- Convert 20 to binary: 10100.

So, the 5-bit excess-16 representation of -4 is 10100.

3. To represent -26 in sign-magnitude using 6 bits:

- Convert the absolute value of the number (26) to binary: 11010.

- Set the leftmost bit as the sign bit (1 for negative).

- So, the 6-bit sign-magnitude representation of -26 is 111010.

4. To convert the 6-bit excess-26 binary number (101101) to decimal:

- Subtract the excess value (26) from the binary value: 101101 - 26 = 101075.

- The resulting decimal value is 75.

So, the decimal equivalent of the 6-bit excess-26 binary number 101101 is 75.

5. In IEEE-754 floating-point representation, the exponent is expressed in binary, excess-k. The value of k is determined by the number of bits used for the exponent. Since 7 bits are used for the exponent in this case, the value of k would be 2^(7-1) - 1 = 63. So, an appropriate value for k is 63.

6. In IEEE-754 floating-point representation, the largest positive value that can be represented depends on the number of bits used for the exponent and the fractional mantissa.

Since 3 bits are used for the fractional mantissa and 4 bits are used for the exponent in this case, the largest positive value that can be represented is determined by the maximum exponent value of 2^(4-1) - 1 = 7. Therefore, the largest positive value that can be represented is 2^7 = 128 in decimal (base 10).

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Two consecutive whole numbers representing the estimated square root of 50 are 7 and 8.

Number need to estimate square root  = 50

To estimate √50,

Neal found that the two perfect squares nearest 50 are 49 and 64.

Since 50 is closer to 49 than to 64,

Square root of 49 is equal to 7

Square root of 64 is equal to 8.

We know that √50 is closer to the square root of 49 which is 7.

Estimated two consecutive whole numbers are 7 and 8.

Therefore, estimated √50 is between the two consecutive whole numbers 7 and 8.

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The above question is incomplete, the complete question is:

Neal estimated √50 by determining that the two perfect squares nearest 50 are 49 and 64. Select the two consecutive whole numbers that the √50 is between to complete the sentence.

In the given figure, the measure of angle ABD is 120 degrees

From the given figure

The measure of angle CBD = 60 degrees

We know the sum of angles on a straight line add up to 180 degrees.

Here the line AC is straight line

Therefore, the sum of the measure of angle ABD and measure of angle CBD is equal to 180 degrees, so the angle ABD and angle CBD are supplementary angles

Angle ABD + Angle CBD = 180 degree

Substitute the values in the equation

∠ABD + 60 = 180

∠ABD = 180 - 60

∠ABD = 120 degree

Therefore, the angle ABD is 120 degrees

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The correct option is (OB) -7; -2.

By analyzing the graph, it is observed that as x approaches -1 from the right side (i.e., x → -1+), lim f(x) = -7. And as x approaches -1 from the left side (i.e., x → -1-), lim f(x) = -2.

Limits are values that a function approaches as the input value gets closer to a certain point. The limit can be either a real number or infinity. The limit of a function is defined in a variety of ways, but a common approach is to define it as the value that the function approaches as the input approaches a certain point. The left and right limits of a function are computed using a similar method, except the input approaches the point from either the left or right side, respectively.

The graph of a function f(x) is shown in the figure, and we have to evaluate the limits of the function as x approaches -1. The limits of a function are the values that the function approaches as the input value approaches a particular point. It can either be a real number or an infinity. The given function has a jump discontinuity at x = -1. At x = -1, the left-hand limit and the right-hand limit do not exist, but the overall limit does exist, which is a finite number. As x approaches -1 from the right side (i.e., x → -1+), the value of the function approaches -7. And as x approaches -1 from the left side (i.e., x → -1-), the value of the function approaches -2. Therefore, we can conclude that the limits of the given function as x approaches -1+ and x approaches -1- are -7 and -2, respectively. In summary,lim f(x) = -7 and lim f(x) = -2 as x approaches -1+ and x approaches -1-, respectively. Hence, the correct option is (OB) -7; -2.

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Answer:

Step-by-step explanation:

To convert square meters to square centimeters, we need to multiply by the conversion factor (100 cm / 1 m)^2.

So,

3.9 m² = 3.9 × (100 cm / 1 m)²

3.9 m² = 3.9 × 10,000 cm²

3.9 m² = 39,000 cm²

Therefore, 3.9 square meters is equal to 39,000 square centimeters.

The vertical asymptote of the function = ln(x-6) + 5 is option C: x = 6.

The given function is f(x) = ln(x - 6) + 5.

A vertical asymptote is a vertical line that a function approaches but never crosses as it approaches infinity or negative infinity. For a logarithmic function like ln(x), the domain of the function is restricted to positive values only since the natural logarithm is undefined for non-positive arguments.

In the given function, we have f(x) = ln(x - 6) + 5. To find the vertical asymptote, we need to identify the value of x that would make the argument of the natural logarithm equal to zero.

Let's set the argument of the natural logarithm to zero:

x - 6 = 0

Now, solve for x:

x = 6

Thus, the value of x that would make the argument of the natural logarithm zero is x = 6.

So, the correct answer is option C: x = 6.

This means that the vertical asymptote of the function f(x) = ln(x - 6) + 5 is the vertical line x = 6. As x approaches 6 from either side (but never equaling 6), the function's values approach infinity. Similarly, as x approaches negative infinity, the function's values also approach infinity. The function never crosses the vertical line x = 6.

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To differentiate \(2F(x) = 2x^2 - 8x^2 + 6\), we need to find the derivative of each term separately. The derivative of \(2x^2\) is 4x, and the derivative of \(-8x^2\) is -16x.

To differentiate \(2F(x) = 2x^2 - 8x^2 + 6\), we can differentiate each term separately. The derivative of \(2x^2\) is found using the power rule, which states that the derivative of \(x^n\) is \(nx^{(n-1)}\). Applying this rule, the derivative of \(2x^2\) is 4x.

Similarly, the derivative of \(-8x^2\) is found using the power rule as well. The derivative of \(-8x^2\) is -16x.

Lastly, the derivative of the constant term 6 is zero since the derivative of a constant is always zero.

Combining the derivatives of each term, we have 4x - 16x + 0. Simplifying this expression gives us -12x.

Therefore, the derivative of \(2F(x) = 2x^2 - 8x^2 + 6\) is -12x.

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To find the curve of intersection of two surfaces, we need to set the equations of the two surfaces equal to each other and solve for the variables that describe the curve of intersection.

In this case, we will consider the intersection of two elliptic paraboloids. An elliptic paraboloid can be represented by the equation z = x^2/a^2 + y^2/b^2, where a and b are positive constants that determine the shape of the paraboloid.

To find the curve of intersection of two elliptic paraboloids, we set their equations equal to each other:

x^2/a^2 + y^2/b^2 = z = c^2/d^2 + w^2/e^2

where c, d, w, and e are also positive constants.

We can rearrange this equation to solve for one of the variables, say z:

z = x^2/a^2 + y^2/b^2 = c^2/d^2 + w^2/e^2

Now we can set z equal to a constant, say k:

k = x^2/a^2 + y^2/b^2

This equation represents the curve of intersection of the two elliptic paraboloids. To plot this curve, we can choose a range of values for x and y, and solve for the corresponding values of z. We can then plot these points in three-dimensional space to obtain the curve of intersection.

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Performing a Chi-Square test is a statistical tool used to determine if there is a significant difference between observed and expected data. The test helps to analyze categorical data by comparing observed frequencies to the expected frequencies. The p-value in a Chi-Square test refers to the probability of obtaining the observed results by chance alone.

If a p-value lower than 0.01 is obtained in a Chi-Square test, it means that the results are statistically significant. In other words, there is strong evidence to reject the null hypothesis, which states that there is no significant difference between the observed and expected data. This means that the observed data is not due to chance alone, but rather to some other factor or factors.

The mean, or average, is not directly related to the Chi-Square test or the p-value. The Chi-Square test is specifically used to determine the significance of the observed data. However, the mean can be used as a measure of central tendency for continuous data, but it is not applicable to categorical data.

In conclusion, obtaining a p-value lower than 0.01 in a Chi-Square test means that there is strong evidence to reject the null hypothesis, and that the observed data is statistically significant.

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Answer: The ride descends 168 feet.

Step-by-step explanation:

24 Feet x 7 seconds = 168 feet

For every second it is 24 feet, so 24 x 7.

The total change in elevation will be descending 168 feet when the ride lasts for 7 seconds.

In mathematics, Multiplication operations perform Multiplying values on either side of the operator.

For example 4×2 = 8

Given that a ride at an amusement descends 24 feet each second.

We have to determine the total change in elevation when the ride lasts for 7 seconds.

The total change in elevation is equal to the multiplication of 24 feet each second and the ride lasts for 7 seconds.

According to the given question, the solution would be

Total change in elevation = 24 Feet × 7 seconds

Apply the Multiplication operation,

Total change in elevation = 168 feet

Thus, the total change in elevation will be descending 168 feet when the ride lasts for 7 seconds.

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Answers:

Length = 270 feet

Width = 45 feet

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

Work Shown:

x = width

6x = length, since it is 6 times the width

P = perimeter of rectangle

P = 2*(Length + Width)

P = 2*(6x + x)

P = 2*(7x)

P = 14x

Plug in the given perimeter P = 630 and solve for x.

P = 14x

14x = P

14x = 630

x = 630/14

x = 45

The width is 45 feet.

The length must be 6x = 6*45 = 270 feet.

The required length and width of the lawn is given as Length = 270 feet and Width = 45 feet.

Given that,
A landscaper buried a water line around a rectangular lawn to serve as a supply line for a sprinkler system. The length of the lawn is 6 times its width. If 630 feet of pipe was used to do the job, what is the length and the width of the lawn is to be determined.

Perimeter is the measure of the figure on its circumference.

Here,
let the length be l and the width be w,
According to the question,
l = 6w
and
Perimeter of the lawn = 630
2 [l + w] = 630
2 [6w + w] = 630
14w = 630
w = 45
Now,
l = 45[6] = 270

Thus, the required length and width of the lawn is given as Length = 270 feet and Width = 45 feet.

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Answer:

(0,6)

Step-by-step explanation:

The y intercept is where the line crosses the y axis or the coordinate where x = 0.

Here, when x is equal to 0, y is equal to 6 meaning that the y intercept is at (0,6)

Answer:

20 students

Step-by-step explanation:

Weight lifting:

8% = 0.08

250(0.08) = 20

Because the formula of quadratic equations is y = ax² + bx + c where you can see the only equation with the power of two is equation B

Equation B into quadratic equation

5x² + x = y - 4

y = 5x² + x +4

Function 5x² + x = y - 4 is quadratic .

Hence option B is correct .

Given , Linear and Quadratic function.

Standard form of quadratic function : y = ax² + bx +c

a = coefficient of x² .

b = coefficient of x .

c = constant .

Rearranging the function,

5x² + x = y - 4

y = 5x² + x - 4

Comparing the equation with standard form,

a = 5

b = 1

c = -4

Hence option B is correct .

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Answer:

use google  

Step-by-step explanation:

A score of x = 60 on an exam with μ = 72 and σ = 12 is comparatively better than a score of x = 70 on an exam with μ = 82 and σ = 8.

To compare the two scores, we can convert them to z-scores, which tell us how many standard deviations a particular value is from the mean. The formula for z-score is:

z = (x - μ) / σ

where x is the value, μ is the mean, and σ is the standard deviation.

For the first score of x = 70 on an exam with μ = 82 and σ = 8, the z-score is:

z = (70 - 82) / 8 = -1.5

For the second score of x = 60 on an exam with μ = 72 and σ = 12, the z-score is:

z = (60 - 72) / 12 = -1.0

The z-score for the first score is lower than the z-score for the second score, which means that the first score is further below its mean than the second score is below its mean. Therefore, we can say that a score of x = 60 on an exam with μ = 72 and σ = 12 is comparatively better than a score of x = 70 on an exam with μ = 82 and σ = 8.

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The answe is D. 3.75

hope this helps^^

Answer:

x cannot = -2

Step-by-step explanation:

if x = -2 then the denominator is 0 and a fraction with 0 as a denominator is undefined.

Answer:

A

Step-by-step explanation:

f(x) = \(\frac{x-3}{x+2}\)

The denominator cannot be zero as this would make f(x) undefined.

Equating the denominator to zero and solving gives the value that x cannot be.

x + 2 = 0 ⇒ x = - 2 ← excluded value in the domain

The domain of f(x) is all real values of x such that x ≠ - 2

Answer:

6.3e-8

Step-by-step explanation:

Answer:

469.875 square feet

Step-by-step explanation:

All you have to do for this question is multiply 3.75 bags of soil * 125.3 feet per bag.

\(3.75 * 125.3 = 469.875\) square feet