Six identical right-angled triangles are arranged to make a rectangle.
7 cm
? cm
Calculato the length of the rectangle.

Answer: Holly has not made a mistake, she has correctly identified the lower bound of x as 1.8 based on the fact that x truncated to 1 decimal place is 1.8. However, she has not identified the upper bound of x, which should be 1.9 based on the fact that x truncated to 1 decimal place could not be greater than 1.9. Therefore, the correct answer is: 1.8 ≤ x ≤ 1.9.

Step-by-step explanation:

(a) Approximately 65.91% of SAT verbal scores are less than 550.

(b) Out of 1000 randomly selected SAT verbal scores, we can expect approximately 16 scores to be greater than 525.

(a) To find the percent of SAT verbal scores less than 550, we need to find the area under the normal curve to the left of 550. We can use the z-score formula to convert 550 to a z-score

z = (x - μ) / σ

where x is the score we're interested in, μ is the mean, and σ is the standard deviation.

z = (550 - 501) / 119 = 0.41

Using a standard normal distribution table or a calculator, we can find that the area to the left of z = 0.41 is 0.6591.

Therefore, approximately 65.91% of SAT verbal scores are less than 550.

(b) To find the number of SAT verbal scores greater than 525 out of 1000 randomly selected scores, we can use the normal distribution formula

z = (x - μ) / (σ / √(n)

where n is the sample size (1000 in this case).

z = (525 - 501) / (119 / √(1000)) = 2.12

Using a standard normal distribution table or a calculator, we can find that the area to the right of z = 2.12 is 0.0162.

Therefore, out of 1000 randomly selected SAT verbal scores, we can expect approximately 16 scores to be greater than 525.

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Answer:

[tex]9\frac{1}{3}[/tex] cans

Step-by-step explanation:

Gianna used 3[tex]\frac{1}{2}[/tex] cans, which can be written as [tex]\frac{7}{2}[/tex] (since 3 is 6 halves, plus the one half). Seyon used 2 and [tex]\frac{2}{3}[/tex] times as many, which is [tex]\frac{8}{3}[/tex] times as many (2 is six thirds, plus the two thirds).

Now, we multiply [tex]\frac{7}{2}[/tex] by [tex]\frac{8}{3}[/tex]:

[tex]\frac{7}{2}[/tex] * [tex]\frac{8}{3}[/tex] = [tex]\frac{56}{6}[/tex] = [tex]\frac{28}{3}[/tex] = [tex]9\frac{1}{3}[/tex] cans

Hope this helps! :D

Step-by-step explanation:

A: 3x-4y=-2

3x=-2+4y

x =(-2+4y)/3

B: x-y⁴=0

x=y⁴

C: x²-3y=0

x²=3y

x=±√3y

D: |x| + |y| =2

x + y= 2

x =2-y

The inequality that describes and suitable for this situation is 9.99+1.29n≤50 under the condition that Lin got a $50 gift card to an online music store. She uses the gift card to buy an album for $9.99. Then the correct option is Option C.

Given,
Lin has a $50 gift card and she spends $9.99 on an album. The amount of money left on the gift card is $50 - $9.99
= $40.01.

In the event that Lin buys n songs at $1.29 each, the total cost of the songs will be evaluated as  $1.29n.

The total amount spent on the album and songs cannot reach the level to exceed the amount left on the gift card, which is determined as $40.01.

So we can write the inequality equation
9.99 + 1.29n ≤ 50

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The complete question is
Lin got a $50 gift card to an online music store. She uses the gift card to buy an album for $9.99. She also wants to use the gift card to buy some songs. Each song costs $1.29. Which of these inequalities describes this situation, where n is the number of songs Lin wants to buy?9.99+1.29n≥50

a) 9.99+1.29n≤50

b) 9.99−1.29n≥50

c) 9.99−1.29n≤50

Answer:

Rise/run = - 4/3

The rise is vertical, run is from left to right.  I counted 4 units down from (-3, 2) to (-3, -2) and since it is down, it's negative.  Then, I counted 3 units to the right from (-3, -2) to (0, -2) and the run will always be positive.  Because there is a negative in one of the numbers, the slope will be negative: - 4/3

The graph of y= √x-1 is given by the image presented at the end of the answer.

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The parent function in the context of this problem is given as follows:

y= √x

Which has vertex at the origin.

The translated function is given as follows:

y = √x-1

Which is a translation down one unit of the parent function, hence it will have vertex at (0,-1).

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The 95% confidence interval for the proportion of people who reported problems getting to sleep after watching a horror film is approximately (0.550, 0.810).

CI is the confidence interval, p is the sample proportion, Z is the Z-score corresponding to the desired confidence level (1.96 for 95%), and n is the sample size.

First, calculate the sample proportion (p):

p = 34 / 50 = 0.68

Next, apply the formula:

CI = 0.68 ± 1.96 * sqrt(0.68 * (1 - 0.68) / 50)

CI = 0.68 ± 1.96 * sqrt(0.68 * 0.32 / 50)

CI = 0.68 ± 1.96 * sqrt(0.2176 / 50)

CI = 0.68 ± 1.96 * sqrt(0.004352)

CI = 0.68 ± 1.96 * 0.065975

CI = 0.68 ± 0.129512

Lower limit: 0.68 - 0.129512 = 0.550488

Upper limit: 0.68 + 0.129512 = 0.809512

So, the 95% confidence interval for the proportion of people who reported problems getting to sleep after watching a horror film is approximately (0.550, 0.810).

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If Mario asked "5-friends" about the amount they spent on boxes of cards last year, then only 3 friends spent less than $32.

We need to analyze the data given in the table and determine how many friends spent less than $32.00 on boxes of cards last year.

We are given the following data:

⇒ Friend 1 = $36,

⇒ Friend 2 = $32,

⇒ Friend 3 = $31,

⇒ Friend 4 = $12,

⇒ Friend 5 = $30.

We need to determine how many friends spent less than $32.00.

From the data given, we see that Friend 2 spent exactly $32.00, which is not less than $32.00.

So, we need to look at the remaining four friends to determine how many of them spent less than $32.00.

We can see that Friend 3 spent $31.00, which is less than $32.00.

So, at least one friend spent less-than $32.00.

Friend 4 spent only $12.00, which is much less than $32.00.

So, at least two friends spent less than $32.00.

Friend 5 spent $30.00, which is also less than $32.00.

So, at least three friends spent less than $32.00 on boxes of cards last year.

Therefore, three friends spent less than $32.00.

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The given question is incomplete, the complete question is

Mario asked 5 friends how much they spent on boxes of cards last year.

He organized the data in a table.

Friend 1  = $36,

Friend 2 = $32,

Friend 3 = $31,

Friend 4 = $12,

Friend 5 = $30.

How many friends spent less than $32.00?

Answer:

Step-by-step explanation:

The relationship between magnitude (M) and intensity (I) of an earthquake is given by:

I ~ 10^(1.5M + 4.8)

We can use this relationship to compare the intensities of the two earthquakes:

I1/I2 = (10^(1.5M1 + 4.8))/(10^(1.5M2 + 4.8))

= 10^(1.5(M1 - M2))

Substituting the given magnitudes, we get:

I1/I2 = 10^(1.5(8.6 - 8.2))

= 10^(1.5(0.4))

≈ 2.24

Therefore, the intensity of the first earthquake was approximately 2.24 times greater than the intensity of the second earthquake.

The vertex form of the quadratic equation is:

y  = -(x - 1)^2 + 4

The standard form is:

y = -x^2 + 2x + 3

If the leading coefficient is a and the vertex is (h, k), we can write:

y = a*(x - h)^2 + k

Here the vertex is at (1, 4), then:

y = a*(x - 1)^2 + 4

And it also passes through (0, 3), then we can write:

3 = a*(0 - 1)^2 + 4

3 = a + 4

3 - 4 = a

-1 = a

The vertex form is:

y  = -(x - 1)^2 + 4

b) Now expand that, we will get:

y = -(x^2 - 2x + 1) + 4

y = -x^2 + 2x - 1 + 4

y = -x^2 + 2x + 3

That is the standard form.

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Given:

[tex]0.1(-90 + 50a)[/tex]

Apply the distributive law: [tex]a(b+c)=ab+ac[/tex]

[tex]0.1(-90 + 50a)=0.1(-90)+0.1\times50a[/tex]

[tex]=0.1(-90)+0.1\times50a[/tex]

Simplify [tex]0.1(-90)+0.1\times50a[/tex]:

[tex]\boxed{\bold{=-9+5a}}[/tex]

Answer: y = |x - 1| - 1

Step-by-step explanation:

We will use this form of absolute value equations. a is the slope, which is 1. h is the horizontal shift and k is the vertical shift.

     y = a|x - h| + k

First, we see this graph is shifted one unit down from the parent function (absolute value). We will subtract 1 from the parent function.

     y = |x| - 1

Next, we see it is shifted one unit right from the parent function. We will add this to the equation above. Since we are adding one unit, we will subtract one unit as it's reversed (" -h" in the equation above).

     y = |x - 1| - 1

3! = 6

In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers from 1 up to n. For example

1! = 1

2! = 2 x 1 = 2

4! = 4 x 3 x 2 x 1 = 24

The factorial function is defined only for non-negative integers, but it is often extended to other types of numbers, such as complex numbers or even some non-integer real numbers, using techniques from complex analysis.

Factorials are used in a variety of mathematical contexts, such as combinatorics, probability theory, and calculus. For example, in combinatorics, factorials are used to count the number of ways to arrange a set of objects, or the number of ways to choose a subset of objects from a larger set. In calculus, factorials appear in Taylor series, which are used to approximate functions as a sum of powers of x.

Hence, the correct option is D.

The expression 3! (read as "3 factorial") is a mathematical shorthand for the product of all positive integers from 1 to 3. It is written as

3! = 3 x 2 x 1

Evaluating this expression gives

3! = 6

Hence, the correct option is D.

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[tex]\cos(18^o )=\cfrac{\stackrel{adjacent}{x}}{\underset{hypotenuse}{23}} \implies 23\cos(18^o)=x \implies 21.87\approx x[/tex]

Make sure your calculator is in Degree mode.

The area of the triangle outlined on the origami figure is 3.2 square centimeters or 3200 square millimeters (since 1 cm = 10 mm).

Area is the measurement of the extent of a two-dimensional surface or shape, typically measured in square units such as square meters or square feet.

Origami is a Japanese art form of paper folding where intricate and beautiful designs are created by folding a single piece of paper without cutting or gluing it.

According to the given information:

the area of a triangle using base (b) and height (h) measurements. The formula is:

Area = (1/2) x b x h

To convert this area into square millimeters, you would need to ensure that the base and height measurements are also in millimeters. If the base is 5 cm, this would be equivalent to 50 mm (since there are 10 millimeters in each centimeter). If the height is 1.28 cm, this would be equivalent to 12.8 mm.

Using these measurements in the formula, we get:

Area = (1/2) x 50 mm x 12.8 mm

Area = 320 mm²

Therefore, the area of the triangle outlined on the origami figure would be 320 square millimeters.

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The correct option is B, The null hypothesis to test if the population variances differ is population variance 1 differs from population variance 2.

Variance is calculated as the average of the squared differences of each data point from the mean. In other words, variance measures how far the data points are from their average value. A high variance indicates that the data points are spread out over a wider range, while a low variance indicates that the data points are clustered more tightly around the mean.

Variance is an important concept in statistical analysis because it helps to assess the reliability of data and to make inferences about the population from a sample. It is also used in many areas of research, such as finance, economics, and engineering, to measure the risk or uncertainty associated with a set of data. Variance is closely related to other statistical measures such as standard deviation, covariance, and correlation, and is often used in conjunction with these measures to gain a deeper understanding of the data.

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Complete Question:-

Before comparing means, we need to test the relationship of the population variances. what null hypothesis would you use to determine if the population variances differ?

a. population variance 1 equals population variance 2

b. population variance 1 differs from population variance 2

c. population variance 1 is less than population variance 2

d. population variance 1 exceeds population variance 2

The requried estimate of the real height of the man is 1.7 meters and the height of the tree is 10.2 meters.

Since the man is of average height, we can assume he is about 1.7 meters tall.

From the diagram, the man is approximately 1/6 the height of the tree. Therefore, the tree is about 6 times taller than the man.

Thus, an estimate for the real height of the tree is 6 times the height of the man, which is 6 x 1.7 = 10.2 meters.

Therefore, the requried estimate of the real height of the man is 1.7 meters and the height of the tree is 10.2 meters.

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Step-by-step explanation:

A  true   opposite side are congruent and parallel

B   false   opposite sides are not perpindicular

C  true opposite sides are equal and parallel

D  false   not perpindicular

E false    not necessarily 90 degrees  

The stack of  paper will be 3355.4432 meters high after stacking halves of it tearing up for 25 times by method of unit conversion from millimeters to meters.

A sheet of paper is 0.1 mm thick.
It is folded in halves for 25 times by tearing it.
The above information can be represented in an equation form as,
Height of the paper stack = (0.1)* ([tex]2^{n}[/tex]) in millimeters
where, n denotes the number of times paper is folded.
Thus, height of the paper stack after tearing it in halves for 25 times we get,
Height = (0.1)* ([tex]2^{25}[/tex]) in millimeters
= 3355443.2 millimeters
We can convert milimmillimeters in meters by the following way as,
1 millimeter = 0.001 meter
Therefore, 33355443.2 millimeters = (0.001)(3355443.2) meters
= 3355.4432 meters

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Answer:

f(3) = 23,750(0.09)^3 = 6412.5

Step-by-step explanation:

The number of students who would have a pet out of a population of 134 is equal to 90.

Percent of students did not have pet = 33%

Total number of students = 134

Number of students who do not have a pet

= 33% × 134

= 0.33 × 134

= 44.22

Since we cannot have a fraction of a student.

Round 44.22 to the nearest whole number which is 44.

This means that 44 out of the 134 students surveyed did not have a pet.

The number of students who have a pet

= subtract the number of students who do not have a pet from the total number of students.

⇒ Number of students who have a pet = 134 - 44

⇒ Number of students who have a pet  = 90

Therefore, approximately 90 students out of a population of 134 have a pet.

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The lateral surface area of the cylinder will be 32.34 square cm.

Given that:

Radius, r = 3 cm

Height, h = 10.5 cm

Let r be the radius and h be the height of the cylinder. Then the surface area of the cylinder will be given as,

SA = 2πr (h + r) square units

The lateral surface area is calculated as,

SA = 2 x 3.14 x 3 x (10.5 + 3)

SA = 18.84 x 13.5

SA = 32.34 square cm

The lateral surface area of the cylinder will be 32.34 square cm.

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Answer:

x = 4, -1

Step-by-step explanation:

Move all terms to the left side and set equal to zero. Then set each factor equal to zero.

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The volume, in cubic feet, of the sandbox is 12 cubic feet.

The volume V of a rectangular prism is given by the formula:

V = lwh

Where:

l is the representation of length, w is the representation of width, and h is the representation of height.

As per the given information, the length l = 4 1/2 feet, the width w = 5 1/3 feet, and the height h = 1/2 foot.

We need to convert the mixed numbers to improper fractions:

l = 4 1/2 = 9/2

w = 5 1/3 = 16/3

h = 1/2

Substitute the values to the given  formula,

V = (9/2) x (16/3) x (1/2)

V = 48/4

V = 12 cubic feet.

Therefore, the volume of the sandbox is 12 cubic feet.

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Answer: D

Step-by-step explanation:

To determine the minimum speed of a particle moving in 3-space with position function r(t) = t^2 i + 6t j + (t^2 - 24t) k, we need to find the magnitude of the velocity vector, which is the derivative of the position vector with respect to time.

v(t) = r'(t) = 2ti + 6j + (2t - 24)k

The speed of the particle at any given time t is the magnitude of the velocity vector, which is:

|v(t)| = √(4t^2 + 36 + (2t - 24)^2) = √(4t^2 + 4t^2 - 96t + 576) = √(8t^2 - 96t + 576)

To find the minimum speed, we need to find the minimum value of |v(t)|. We can do this by finding the vertex of the parabolic function 8t^2 - 96t + 576, which corresponds to the minimum value of the function.

The vertex of a parabola of the form ax^2 + bx + c is at x = -b/2a. In this case, a = 8, b = -96, and c = 576, so the vertex is at t = -b/2a = 96/16 = 6.

So the minimum speed of the particle is:

|min speed| = |v(6)| = √(8(6)^2 - 96(6) + 576) = √(288) = 12√2

Therefore, the minimum speed of the particle moving in 3-space with position function r(t) = t^2 i + 6t j + (t^2 - 24t) k is approximately 16.97 units/sec (rounded to two decimal places). Option 4, min speed = 17 units/sec, is the closest answer.

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(a) Yes the wavelengths is shorter for the finite square well compared with the infinite well.

(b) The physical arguments to decide whether the energies are smaller for the finite square-well than for the infinite square well.

(c) The energy levels of each potential can also be calculated using the Schrödinger equation, and the comparison of the energies involves comparing the magnitude of the potential energy term for each potential.

When considering the wavelengths of particles in the square well potentials, we can use the de Broglie wavelength, which relates the momentum of a particle to its wavelength.

Finally, the finite square well has a finite number of bound energy states because as the width of the well increases, the energy of the particle becomes less negative and eventually becomes positive, allowing the particle to escape from the well.

Mathematically, the comparison of the two potentials involves solving the Schrödinger equation for each potential. In the case of the infinite square well, the solution is a sine wave, with wavelengths determined by the width of the well. In the case of the finite square well, the solution is a combination of sine and exponential functions, with the wavelength depending on the width of the well.

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Complete Question:

Compare the results of the infinite and finite square-well potentials. (a) Are the wavelengths longer or shorter for the finite square well compared with the infinite well? (b) Use physical arguments to decide whether the energies (for a given quantum number n) are (i) larger or (ii) smaller for the finite square-well than for the infinite square well? (c) Why will there be a finite number of bound energy states for the finite potential?

Answer:

15

Step-by-step explanation:

[tex]\frac{5}{3}[/tex] = [tex]\frac{25}{x}[/tex]

5 x 5 = 25

3 x 5 = 15

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