Suppose the temperature x miles above ground level is given by T= 74minus29x. Write and solve an inequality that describes when the temperature is below 50degreesF.

To find the estimated population mean from the given equation, we will use the fact that the data are normally distributed. The equation provided is a linear equation that represents the best-fit line for the data:
y = 0.918x - 0.175. The correct option is B.

Since the data follows a normal distribution, the mean will be located at the point where the line is at its highest. In a normal distribution, the peak (or the highest point) occurs when the probability density is the greatest. In the case of the given linear equation, this peak corresponds to the y-intercept, which is the point where the line crosses the y-axis (when x = 0).

Plugging x = 0 into the equation:
y = 0.918(0) - 0.175
y = -0.175
Thus, the estimated population mean is -0.175.

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Answer:

f(x) = (2x + 3)(2x + 1)

Explanation:

The form that best reveals the zeros of the function is:

f(x) = (x - a)(x - b)

Where a and b are the zeros of the function.

So, we need to apply the distributive property as:

Then, we can factorize the quadratic function as:

So, now we can identify the zeros of the function if we solve the following equation:

Therefore, the form that best reveals the zeros in the function is:

f(x) = (2x + 3)(2x + 1)

The  number of cycles to first acoustic emission in a notched tensile fatigue test on a titanium specimen can vary depending on several factors such as the applied stress level, the size and geometry of the notch, and the material properties.

acoustic emission is a non-destructive testing method that detects the high-frequency sound waves generated by the formation and propagation of cracks in a material. In the case of fatigue testing, acoustic emission is often used to monitor the initiation and growth of cracks as a function of the number of cycles.

Generally speaking, the number of cycles to first acoustic emission is a useful indicator of the crack initiation resistance of a material, with higher values indicating better performance. However, it's important to note that this value is just one of several parameters used to assess the fatigue behavior of a material and should be interpreted in conjunction with other data such as the S-N curve and fracture toughness.

the expected number of cycles to first acoustic emission in a notched tensile fatigue test on a titanium specimen is influenced by various factors and should be viewed as a part of the larger picture of the material's fatigue properties.

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According to the information, the 95% confidence interval for the proportion of Americans who drink tea daily is approximately (0.2485, 0.2766). The margin of error is approximately 0.0140.

To construct a confidence interval for the proportion of Americans who drink tea daily, we can use the formula:

Where,

p = the sample proportion

Z = the critical value corresponding to the desired confidence level

n = the sample size

Given:

Now, let's calculate the confidence interval and margin of error:

According to the information, the 95% confidence interval for the proportion of Americans who drink tea daily is approximately (0.2485, 0.2766), with a margin of error of approximately 0.0140.

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Answer:

7

Step-by-step explanation:

You divide 56 by 8 to find the certain amount of seconds

Answer:

-7

Step-by-step explanation:

Answer:

( x - 2) ( x + 2 ) ( x² + 4 ) - ( x² - 3 ) ( x² + 3 )

(x² – 4) (x²+4) – ( x⁴ – 9 )

(x⁴ – 16 ) – ( x⁴ – 9)

(x⁴ – 16 ) + ( – x⁴ + 9) = – 7

I hope I helped you^_^

Answer:

x = 5 and y = 22

Step-by-step explanation:

See attached image.

Answer:

Step-by-step explanation:

4-2(3+7)=4-2.3+2.7

4-2(10)=4+0.4

4-20=4.4

-16=4.4 which clearly is false

Answer: 4

1/2 + (-1/2)- (-4)

1/2 -1/2 +4

8/2

4

Answer:

-p^3

Step-by-step explanation:

( p - 2 p ) ^ 3

combine p and 2p to get -p

》expand (-p)^3

》(-1)^3p^3

calculate -1 to the power of 3 and get -1

and this equals -p^3

We can say that approximately 23 out of the 34 practice trials would fall between 59 and 61 seconds.

To determine the number of practice trials out of 34 that would fall between 59 and 61 seconds, we can utilize the properties of a normal distribution with the given mean and standard deviation.

Given that Alejandro's finishing times are normally distributed with a mean of 60 seconds and a standard deviation of 1 second, we can represent this distribution as follows:

μ = 60 (mean)

σ = 1 (standard deviation)

To find the proportion of trials that fall between 59 and 61 seconds, we need to calculate the area under the normal curve within this range. Since the normal distribution is symmetrical, we can determine this area by calculating the area under the curve between the mean and the upper and lower limits.

Using a standard normal distribution table or a statistical calculator, we can find the z-scores for the values 59 and 61, based on the mean and standard deviation. The z-score represents the number of standard deviations a data point is away from the mean.

For 59 seconds:

z = (59 - 60) / 1 = -1

For 61 seconds:

z = (61 - 60) / 1 = 1

Next, we find the area under the curve between these z-scores. By referring to a standard normal distribution table or using a calculator, we can determine the area associated with each z-score.

The area to the left of z = -1 is approximately 0.1587.

The area to the left of z = 1 is approximately 0.8413.

To find the area between these two z-scores, we subtract the smaller area from the larger area:

Area between z = -1 and z = 1 = 0.8413 - 0.1587 = 0.6826

This means that approximately 68.26% of the trials will fall between 59 and 61 seconds.

To find the number of trials out of 34 that fall within this range, we multiply the proportion by the total number of trials:

Number of trials between 59 and 61 seconds = 0.6826 * 34 ≈ 23.23

Rounding this to the nearest whole number, we can say that approximately 23 out of the 34 practice trials would fall between 59 and 61 seconds.

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The solutions of the given equation in the interval [0, 2π) are: x = 0, x = π/2, x = π, x = 3π/2

solve the equation sin(2x)cos(x) = 0 in the interval [0, 2π).

First, we'll use the double-angle formula to simplify the equation. The double-angle formula for sine is:

sin(2x) = 2sin(x)cos(x)

Now, substitute this into the given equation:

2sin(x)cos(x)cos(x) = 0

This simplifies to:

2sin(x)cos^2(x) = 0

Now, we can solve the equation by setting each factor equal to zero:

1) sin(x) = 0
2) cos^2(x) = 0 or cos(x) = 0

For the first case (sin(x) = 0), the solutions within the interval [0, 2π) are:

x = 0, x = π

For the second case (cos(x) = 0), the solutions within the interval [0, 2π) are:

x = π/2, x = 3π/2

So, the solutions of the given equation in the interval [0, 2π) are:

x = 0, x = π/2, x = π, x = 3π/2

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In a Cartesian coordinate system for a three-dimensional space, let the sphere S be represented by the equation:

(x - a)^2 + (y - b)^2 + (z - c)^2 = r^2

where (a, b, c) are the coordinates of the center of the sphere, and r is the radius.

Let the plane P be represented by the equation:

Ax + By + Cz + D = 0

where (A, B, C) is the normal vector to the plane.

Since the line d is parallel to P and passes through the origin, it can be represented by the equation:

lx + my + nz = 0

where (l, m, n) is a vector parallel to the plane P.

To find the intersection points of the sphere S and the line d, we can substitute the equation of the line into the equation of the sphere, which gives us a quadratic equation in t:

(lt - a)^2 + (mt - b)^2 + (nt - c)^2 = r^2

Expanding this equation and collecting terms, we get:

(l^2 + m^2 + n^2) t^2 - 2(al + bm + cn) t + (a^2 + b^2 + c^2 - r^2) = 0

Since the line d passes through the origin, we have:

l(0 - a) + m(0 - b) + n(0 - c) = 0

which simplifies to:

al + bm + cn = 0

Therefore, the quadratic equation reduces to:

(l^2 + m^2 + n^2) t^2 + (a^2 + b^2 + c^2 - r^2) = 0

This equation has two solutions for t, which correspond to the two intersection points of the line d and the sphere S:

t1 = -(a^2 + b^2 + c^2 - r^2) / (l^2 + m^2 + n^2)

t2 = -t1

The coordinates of the intersection points can be obtained by substituting these values of t into the equation of the line d:

A = lt1, B = mt1, C = nt1

and

D = lt2, E = mt2, F = nt2

To find the distance between A and B, we can use the distance formula:

AB = sqrt((A - D)^2 + (B - E)^2 + (C - F)^2)

To maximize this distance, we can differentiate the distance formula with respect to t1 and set the derivative equal to zero:

d/dt1 (AB)^2 = 2(A - D)l + 2(B - E)m + 2(C - F)n = 0

This equation represents the condition that the direction vector (A - D, B - E, C - F) is orthogonal to the line d. Therefore, the vector (A - D, B - E, C - F) is parallel to the normal vector (l, m, n) of the plane P.

Using this condition, we can find the values of t1 and t2 that correspond to the maximum distance AB. Then we can substitute these values into the distance formula to find the maximum length of AB.

The total number of cups of chocolate is A = 12 cups

Given data ,

To find the total number of cups of hot chocolate that Stanley made, we need to add together the amounts of milk, cream, and melted chocolate.

6 cups of milk

1 pint of cream (1 pint = 2 cups)

On simplifying the equation ,

4 cups of melted chocolate

Now , the total number of cups is A

where A is

6 cups of milk + 2 cups of cream + 4 cups of melted chocolate = 12 cups of hot chocolate

Hence , Stanley made 12 cups of hot chocolate

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Answer:

Step-by-step explanation:

f(x) = x²

1. Vertex ( 0 ,0)

2) a > 0 , opening upward

3) minimum

4) Axis of symmetry : x = 0

5) Range:  y ≥ 0  

The number of cones it would take to completely fill the cylinder is 6 cones.

Let us assume that the dimensions of the cylinder are:

Volume of a cylinder = πr²h

π = 22/7

r = radius

6² X 10 X π= 360π

Volume of a cone = 1/3(πr²h)

Volume =1/3 x  5 x 6² x π = 60π

Number of cones it would take to fill the cylinder = 360 / 60 = 6 cones

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Given the values for the length and width of the rectangle, area of the rectangle is 16.625 square centimeter.

A rectangle simply a is a 2-dimentional shape in geometry with 2 equal opposite sides and 4 corners each at 90 degrees.

The area of a rectangle is;

A = Length × Width

A = L × W

Given the data in the question;

To determine the area of the retcangle, we substitute our given values into the expression above.

A = L × W

A = 4.5cm × 3.25cm

A = 16.625cm²

Therefore, the area of the rectangle with the given length and width is 16.625cm².

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Answer:

s=555

Step-by-step explanation:

The rate of return (RoR) needed for an population to increase from its starting balance to its ending balance, providing growth were repopulated at the conclusion of each period of the population life span

To determine an population CAGR:

Divide the population worth at the end of the time by the value it had at the start of the period.

The result should be multiplied by one and divided by the number of years.

The outcome is then reduced by one.

To convert the response into a percentage, multiply by 100.

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Answer:

\(39.8^{\circ} C\)

Step-by-step explanation:

We are given that the temperature each hour in Elma Texas on October 1 is modelled by the equation

\(t(h)=10cos(15h-10)^{\circ}+30\)

Where h=Hour of the day with 0 meaning midnight

t=Temperature in degree Celsius

We have to find the temperature on October 1.

Substitute h=0

\(t(0)=10cos(15(0)-10)+30\)

\(t(0)=10cos(-10)+30\)

\(t(0)=39.8^{\circ} C\)

Hence, the temperature in Elma on October 1=\(39.8^{\circ} C\)

The measure of the central angle that subtends the given arc is approximately 34.38°. It can be found using the formula: Central Angle = (Arc Length / Circumference) * 360°

In this case, the arc length is given as 3 miles and the radius of the circle is given as 5 miles. To find the circumference of the circle, we can use the formula: Circumference = 2 * π * radius
Substituting the given radius value, we get: Circumference = 2 * π * 5 miles
Now, we can calculate the central angle: Central Angle = (3 miles / (2 * π * 5 miles)) * 360°
Simplifying the expression, we get: Central Angle = (3 / (2 * π * 5)) * 360°
Calculating the value, we get: Central Angle ≈ 34.38°
Therefore, the measure of the central angle that subtends the given arc is approximately 34.38°.

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Answer:

Option (1)

Step-by-step explanation:

Coordinates of the vertices of a quadrilateral WXYZ drawn in the figure are,

W(-1, 4), X(2, 2), Y(0, -1), Z(-3, 1)

Length of a segment having ends as \((x_1, y_1)\) and \((x_2, y_2)\) is represented by,

d = \(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Length of WX = \(\sqrt{(-1-2)^2+(4-2)^2}\)

                       = \(\sqrt{9+4}\)

                       = \(\sqrt{13}\)

Length of XY = \(\sqrt{(2-0)^2+(2+1)^2}\)

                      = \(\sqrt{13}\)

Length of YZ = \(\sqrt{(0+3)^2+(-1-1)^2}\)

                      = \(\sqrt{13}\)

Length of ZW = \(\sqrt{(-1+3)^2+(4-1)^2}\)

                      = \(\sqrt{13}\)

Slope of side WX (\(m_1\)) = \(\frac{y_2-y_1}{x_2-x_1}\)

                                  = \(\frac{4-2}{-1-2}\)

                                  = \(-\frac{2}{3}\)

Slope of side XY (\(m_2\)) = \(\frac{2+1}{2-0}\)

                                    = \(\frac{3}{2}\)

By the property of perpendicular lines,

\(m_1\times m_2=-1\)

\((-\frac{2}{3})(\frac{3}{2})=-1\)

therefore, WX and XY are perpendicular.

Slope of YZ (\(m_3\)) = \(\frac{-1-1}{0+3}=-\frac{2}{3}\)

\(m_2\times m_3=(\frac{3}{2})\times (-\frac{2}{3})=-1\)

Therefore, XY ⊥ YZ

Similarly, we can prove YZ ⊥ ZW.

Therefore, quadrilateral WXYZ is a SQUARE.

Option (1) will be the answer.

Answer:

Its A, square

Step-by-step explanation:

I just took the quiz. :)

Answer:

25 students take both subjects.

Step-by-step explanation:

Solve for 60% of 300 students:

60/100 = x/300

Cross multiply:

60 × 300 = 100 × x

18000 = 100x

Divide both sides by 100:

180 = x

Solve for 20% of 300 students:

20/100 = x/300

20 × 300 = 100 × x

6000 = 100x

60 = x

Solve for the percentage of students in chemistry:

x/100 = 35/300

x × 300 = 100 × 35

300x = 3500

x = 11.66666...7

x = about 11.7%

Find the difference in percentages:

100 - 60 - 20 - 11.7

8.3

8.3% take both subjects

Solve for 8.3% of students:

8.3/100 = x/300

8.3 × 300 = 100 × x

2490 = 100x

24.9

About 25 students

Check your work by adding all the students together (to get to 300):

25 + 60 + 180 + 35

300 students total

This is correct!

Check the picture below.

\(tan(A)=\cfrac{\stackrel{opposite}{55}}{\underset{adjacent}{48}}\implies A=tan^{-1}\left( \cfrac{55}{48} \right)\implies A\approx 48.9^o \\\\\\ tan(B)=\cfrac{\stackrel{opposite}{48}}{\underset{adjacent}{55}}\implies B=tan^{-1}\left( \cfrac{48}{55} \right)\implies B\approx 41.1^o\)

Make sure your calculator is in Degree mode.

An equation of the line with the given gradient and points is \(y=\frac{2x}{3} -\frac{7}{3}\)

Given the following data:

To find an equation of the line with the given gradient and points:

Mathematically, the equation of a line is given by this formula:

\(y-y_1 =m(x-x_1)\)

Where:

Substituting the given parameters into the formula, we have;

\(y-(-3) =\frac{2}{3} (x-[-1])\\\\y+3=\frac{2}{3} (x+1)\\\\3y+9=2x+2\\\\3y=2x+2-9\\\\3y=2x-7\\\\y=\frac{2x}{3} -\frac{7}{3}\)

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Answer:

I guess, as long as this is an act of kindness. Thanks?

Answer:

x=7

Step-by-step explanation:

Solution of your latest question

because i can't get any answer option there ....so posting it heree .....

hope you get it before it got deleted

On solving the provided question we can say that - The Range of the given function, f(x) = sin(x) , Range = \(-1 < y < 1\)

Range: the discrepancy between the top and bottom numbers. To get the range, locate the greatest observed value of the variable and deduct the least observed value (the minimum). The data points between the two extremes of the distribution are not taken into consideration by the range; just these two values are considered. Between the lowest and greatest numbers, there is a range. Values at the extremes make up the range. The data set 4, 6, 10, 15, 18, for instance, has a range of 18-4 = 14, a maximum of 18, a minimum of 4, and a minimum of 4.

The Range of the given function, f(x) = sin(x)

\(-1 < y < 1\)

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Answer:

B) 6<x<90

Step-by-step explanation:

48+42=90

48-42=6

There will be a number greater than and a number less than x.

90>6

6<x<90

Hope this helps :)

1.5

The given function is:

f(x) = 2x² + 5x – 12

To find the zeros, equate f(x) to zero.

f(x) = 0

2x² + 5x – 12 = 0

2x² - 3x + 8x - 12 = 0

x(2x - 3) + 4(2x - 3) = 0

(x + 4)(2x - 3) = 0

x + 4 = 0

x = -4

2x - 3 = 0

2x = 3

x = 3/2

x = 1.5

The zeros of the function f(x) = 2x² + 5x – 12 are -4 and 1.5

Since only x = 1.5 is positive, x = -4 is not positive, the value of the positive zero is 1.5