Zachary says that the equation 0 = (x – 4)(x – c) has one unique real number solution. What must be the value of c for his statement to be true?

c = 4

The surface area of the first triangular prism is 174.58 square feet and second triangular prism is 1721.6 square feet.

To calculate the surface area of a triangular prism, we need the measurements of the base and the height of the triangular bases, as well as the length of the prism.

For the first triangular prism with measurements:

Base: 5 ft

Height: 8 ft

Length: 6 ft

To calculate the surface area, we need to find the areas of the two triangular bases and the three rectangular faces. The formula for the surface area of a triangular prism is:

Surface Area = 2 * (Area of triangular base) + (Perimeter of triangular base * Length)

The area of a triangle can be calculated using the formula: Area = 1/2 * Base * Height.

Area of triangular base = 1/2 * 5 ft * 8 ft = 20 ft²

The perimeter of a triangle is the sum of its three sides.

Perimeter of triangular base = 5 ft + 8 ft + √(5 ft² + 8 ft²) = 5 ft + 8 ft + √89 ft ≈ 5 ft + 8 ft + 9.43 ft ≈ 22.43 ft

Surface Area = 2 * 20 ft² + (22.43 ft * 6 ft) = 40 ft² + 134.58 ft² = 174.58 ft²

Therefore, the surface area of the first triangular prism is approximately 174.58 square feet.

For the second triangular prism with measurements:

Base: 6 ft

Height: 2.5 ft

Length: 115 ft

Area of triangular base = 1/2 * 6 ft * 2.5 ft = 7.5 ft²

Perimeter of triangular base = 6 ft + 2.5 ft + √(6 ft² + 2.5 ft²) = 6 ft + 2.5 ft + √40.25 ft ≈ 8.5 ft + 6.34 ft ≈ 14.84 ft

Surface Area = 2 * 7.5 ft² + (14.84 ft * 115 ft) = 15 ft² + 1706.6 ft² = 1721.6 ft²

Therefore, the surface area of the second triangular prism is approximately 1721.6 square feet.

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The surface area of the triangular prism is x - 0 = -3

If the solution to an absolute value equation is x = -3, then we know that the distance between x and 0 is 3 units. Since the absolute value of a number is the distance between the number and 0 on the number line, we can write the absolute value equation that corresponds to x = -3 as:

| x - 0 | = 3

To write this equation in the form x - b = c, we can simplify the absolute value expression by removing the absolute value bars. This gives us two possible equations:

x - 0 = 3 or x - 0 = -3

Simplifying further, we get:

x = 3 or x = -3

Therefore, the absolute value equation in the form x - b = c that has the solution set {x = -3} is:x - 0 = -3

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Recall that the exponential growth function is defined as f(x) = [tex]a^x[/tex], where a is a positive constant greater than 1. Since any real number can be plugged in for x, the domain of the function is all real numbers.

Since the exponential growth function increases without bound as x goes to infinity, the range of the function is all positive real numbers (y > 0). Similarly, as x approaches negative infinity, the function approaches zero but never equals zero. Therefore, the range of the function does not include zero or any negative numbers (y > 0).

So, the complete answer is:

Domain: all real numbers; Range: y > 0.

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Ajay's profit on each orange is Rs. 25, and the profit percentage is 125%.

Ajay makes a profit of Rs. 25 on each orange he sells, which is the difference between the selling price and the cost price. The profit percentage is calculated by dividing the profit by the cost price and then multiplying it by 100.

In this case, the cost price of each orange is Rs. 20 and the profit on each orange is Rs. 25. So, the profit percentage is (25/20) x 100 = 125%.

This means that Ajay is making a profit of 125% on each orange he sells, which is a significant profit margin. It also shows that buying in bulk at a lower price and selling at a higher price can be a profitable business strategy.

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The cost of 100 donuts is $ 1 if a dozen of donuts cost 12 cents.

This question is solved using the unitary method. The unitary method is a method in which you find the value of a unit and then the value of the required number of units.

1 dozen refers to a group of 12.

Cost of 1 dozen donuts or 12 donuts = 12 cents

Cost of 1 donut = [tex]\frac{12}{12}[/tex] = 1 cent

Cost of 100 donuts = 1 * 100 = 100 cents

100 cents = 1 dollar.

Thus, the cost of 100 donuts is 100 cents or 1 dollar.

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Answer:

12

Step-by-step explanation

60/100 to get the probability of success

0.6 * 20 attempts = 12

An expression to represent the number of miles both boys ran this month is 3j + 4d + 10.

To begin solving this problem, we need to use the given information and create an expression to represent the number of miles both boys ran this month.
We know that James runs 3 miles per day, so in j days, he would have run 3j miles.

Similarly, Denis runs 4 miles per day and ran an additional 10 miles this month.

So in d days, he would have run 4d + 10 miles.
To find the total number of miles both boys ran this month, we need to add the number of miles James ran to the number of miles Denis ran.

Therefore, our expression is:
Total Miles = 3j + 4d + 10
This expression represents the total number of miles both boys ran this month.

To solve for j and d, we would need more information, such as the total number of miles the boys ran or the number of days they both ran.
In summary, we can use the given information about James and Denis's daily running habits to create an expression that represents the total number of miles both boys ran this month.

This expression is 3j + 4d + 10.

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The z scοre is negative the actual probability would be

1-0.7995 = 0.2005

What is the probability?

A number that expresses hοw likely it is that an event will occur is called the probability of οccurrence. It is written as a number from 0 to 1, or frοm 0% to 100%, in percentage notation. The probability of an event occurring increases with probability.

here,

mean = 20.20

standard deviatiοn = 2.60

we knοw that,

Z scοre = (X-mean)/standard deviation

fοr X = 18:

Z scοre = (18-20.20)/2.6 = -0.8461

nοte that the z score is negative because the measured value is less than the mean value.

fοr Z score 0.8461 probability is 0.7995

and since the z scοre is negative the actual probability would be

1-0.7995 = 0.2005

a. For nοt within 1 hour of the population mean

We apply the formula here and we get the value οf P.

P(19.20>x>21.20) = P(19.20-20.20/2.60√18) > X-μ/σ√n >21.20-20.20/2.60√18

P(19.20>x>21.20) = P(-1.63>z>1.63)

Now, we find the value οf z.

P(19.20>x>21.20) = P(z>1.63) + P(z<-1.63)

P(19.20>x>21.20) = 0.0516 + 0.0516

P(19.20>x>21.20) = 0.1032

b. Fοr 20. 0 to 20. 5 hours

P(20<x<20.5) = P(20-20.20/2.60√18) < X-μ/σ√n<20.50-20.20/2.60√18

P(20<x<20.5) = P(-0.33<z<0.49)

Nοw, we find the value of the z-score and we get

P(20<x<20.5) = P(z<0.49) - P(z<-0.33)

P(20<x<20.5)  = 0.6879 - 0.2707

P(20<x<20.5)  = 0.3172

c. Fοr at least 22 hours

We apply the t-test fοrmula here and we get

P(x≥22) = P(X-μ/σ√n≥22-20.20/2.60√18)

Nοw, we find the value of z.

P(x≥22) = P(z≥2.94)

P(x≥22) = 0.0016

d. Fοr not more than 21 hours.

P(x<21) = P(X-μ/σ√n<21-20.20/2.60√18)

We find here the value οf P for x<21 and we get

P(x<21) = P(z<1.31)

Now, we find the value οf the z- score.

P(x<21) = 0.9049

Hence, a. 0.1032

b.  0.3172

c. 0.0016

d. 0.9049

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Complete question is,

Among college students who hold part-time jobs during the school year, the distribution of the time spent working per week is approximately normally distributed with a mean of 20.20 hours and a standard deviation of 2.60 hours. Find the probability that the average time spent working per week of 18 randomly selected college students who old part-time jobs during the school year is.

The probability of selecting an M&M that is not red is 11/15.To find the probability of selecting an M&M that is not red, we need to first find the total number of M&Ms in the bag,

It is the sum of the number of M&Ms of each color: 4 + 8 + 6 + 12 = 30.

Next, we need to find the number of M&Ms that are not red, which is the sum of the number of M&Ms of all other colors: 4 + 6 + 12 = 22.

Therefore, the probability of selecting an M&M that is not red is 22/30, which can be simplified by dividing both the numerator and the denominator by 2:

22/30 = 11/15

So the probability of selecting an M&M that is not red is 11/15.

In other words, there is an 11/15 chance that the selected M&M will be blue, orange, or green, and a 4/15 chance that it will be red.It is important to note that this assumes that each M&M is equally likely to be selected, and that the bag is well-mixed so that each M&M has an equal chance of being chosen.

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Min still needs 175 centimeters of ribbon to make 100 name tags with ribbons attached to them.

To help Min with her name tags, we first need to determine the total amount of ribbon needed for 100 name tags. Each name tag requires 5 centimeters of ribbon, so for 100 name tags, we can calculate the total requirement as follows:

Total ribbon needed = (Number of name tags) x (Ribbon per name tag) = 100 x 5 = 500 centimeters

Min has 3.25 meters of ribbon, which we need to convert to centimeters to compare with the total requirement:

3.25 meters = 3.25 x 100 = 325 centimeters

Now, we can find out how many more centimeters of ribbon Min needs by subtracting the available ribbon from the total requirement:

Additional ribbon needed = Total ribbon needed - Available ribbon = 500 - 325 = 175 centimeters

So, Min still needs 175 centimeters of ribbon to make 100 name tags with ribbons attached to them.

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Answer:it would still be a 50/50 chance of it be tails

Step-by-step explanation:

a coin has 2 sides. The probability would be 1/2. That means if you flip it a even amount, there would be a 50/tip chance. Let me know if I’m correct.

Weight difference between the large box and the small box is [tex](1/2)*(w2 - w1)[/tex] pounds.

Let's assume that Gina has n boxes in total, and let x be the weight of each box in pounds. We can then express the weight of the boxes that weigh less than [tex]1/2[/tex] pound as [tex](1/2)*w1[/tex], where [tex]w1[/tex] is the number of boxes that weigh less than [tex]1/2[/tex] pound. Similarly, we can express the weight of the boxes that weigh more than 1/2 pound as [tex](1/2)*w2[/tex], where [tex]w2[/tex] is the number of boxes that weigh more than [tex]1/2[/tex] pound.

Since Gina puts all the boxes weighing less than [tex]1/2[/tex] pound into a small box, the weight of the small box will be the sum of the weights of all the boxes that weigh less than [tex]1/2[/tex] pound, which is [tex](1/2)*w1[/tex].

Similarly, since Gina puts all the boxes weighing more than [tex]1/2[/tex] pound into a large box, the weight of the large box will be the sum of the weights of all the boxes that weigh more than [tex]1/2[/tex] pound, which is [tex](1/2)*w2[/tex].

The weight difference between the large box and the small box will be:

[tex](1/2)*w2 - (1/2)*w1[/tex]

Simplifying this expression, we get:

[tex](1/2)*(w2 - w1)[/tex]

Therefore, the weight difference between the large box and the small box is [tex](1/2)*(w2 - w1)[/tex] pounds.

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Answer: A voting system

Step-by-step explanation:

The standard deviation for the prices paid for this particular model of car is $6,250.

Based on the figure you provided, we know that the data is normally distributed and approximately 68% of car buyers pay within one standard deviation of the mean, approximately 95% pay within two standard deviations, and approximately 99.7% pay within three standard deviations.

Since we know that 95% of the prices paid fall within two standard deviations of the mean, we can say that the distance between the mean and the upper or lower limit of this range is equal to two standard deviations. This is also known as the "95% confidence interval."

Therefore, to find the standard deviation, we can calculate the distance between the mean and either the upper or lower limit of the 95% confidence interval and then divide it by two.

From the figure, we can see that the 95% confidence interval extends from approximately $23,500 to $48,500. The midpoint of this interval is approximately $36,000, which we can take as the mean.

So, the distance between the mean and either end of the 95% confidence interval is:

$48,500 - $36,000 = $12,500

Dividing this by two gives us the standard deviation:

$12,500 / 2 = $6,250

Therefore, the standard deviation for the prices paid for this particular model of car is $6,250.

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Weak correlation observed in scatter plot, inaccurate r=0.01 value; possible causal relationship - new fertilizer's effect on strawberry yields.

Based on the scatter plot, a correlation coefficient of r=0.01 is not an accurate value for this data. This is because the scatter plot shows an upward trend with moderately spread out points from the line of best fit, indicating a weak positive correlation. A correlation coefficient of 0.01 suggests a near-zero correlation, which is inconsistent with the observed pattern in the scatter plot.

A possible scenario for a causal relationship for strawberries picked on the farm could be the application of a new fertilizer that is known to increase strawberry yields. The farmer could divide the field in half, applying the new fertilizer to one half and the traditional fertilizer to the other half, and then compare the yields of each half. This would allow for a comparison of the effect of the two different fertilizers on strawberry yields and establish a causal relationship between the fertilizer and the yield of strawberries.

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Option C is correct. No, the least value is smaller than the critical value.

Null hypothesis (H₀): The average first-year teacher salary is $52,000.

Alternative hypothesis (Ha): The average first-year teacher salary is not $52,000.

The significance level is 5% (or 0.05), which means we will reject the null hypothesis if the probability of obtaining the observed result is less than 5%.

Calculate the standard error of the mean:

Standard Error = Standard Deviation / √n

where n is the number of samples (n = 25 in this case).

Standard Error = $1500 / √25

= $1500 / 5

= $300

Now, perform the hypothesis test using a t-test since the sample size is relatively small (n < 30) and the population standard deviation is unknown.

t-score = (Sample Mean - Population Mean) / Standard Error

t-score = ($52,525 - $52,000) / $300

t-score = $525 / $300

t-score = 1.75

To find the critical value at a 5% significance level with 24 degrees of freedom (n - 1), we can consult a t-table. At a 5% significance level (two-tailed test), the critical t-value is approximately ±2.064.

Since the calculated t-score (1.75) is not greater than the critical t-value (2.064), we fail to reject the null hypothesis.

Therefore, option C is correct. No, the least value is smaller than the critical value.

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Complete question:

The average first year teacher salary in a certain state is known to be $52,000 with a standard deviation of $1500. A researcher tests this claim by averaging the salaries of 25 first year teachers and finding their average salary to be $52,525. Is there significant evidence to suggest that the claim is wrong at the 5% significance level?

A. Yes, the least value is greater than the critical value

B. No, the least value is larger than the critical value

C. No, the least value is smaller than the critical value

D. yes, the least value is smaller than the critical value

If An oil globe made of hand-blown glass of a diameter of 22.6. Therefore, the volume of the oil globe is approximately 5704.8 cm^3.

The volume of a spherical object can be calculated using the formula:

V = (4/3)πr^3

where V is the volume, π is the mathematical constant pi (approximately equal to 3.14159), and r is the radius of the sphere.

In this case, we are given the diameter of the oil globe, which is 22.6. The radius is half of the diameter, so we can calculate the radius as:

r = d/2 = 22.6/2 = 11.3 cm

Substituting this value of radius in the formula for the volume of a sphere, we get:

V = (4/3)π(11.3)^3

V = 5704.8 cm^3 (rounded to one decimal place)

Therefore, the volume of the oil globe is approximately 5704.8 cm^3.

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We have shown that ⊙O and ⊙P are similar using similarity transformations.

To prove that ⊙O and ⊙P are similar using similarity transformations, we need to show that they have the same shape . Let's consider a dilation transformation with a scale factor of 2, centered at point A, which is the midpoint of the line segment connecting the centers of ⊙O and ⊙P:

1.Draw a line segment connecting the centers of ⊙O and ⊙P, and label the midpoint of this line segment as point A.

2.Draw two radii from the centers of ⊙O and ⊙P to a point B on the circumference of ⊙O, and label the intersection point of AB and ⊙P as point C.

3.Draw a perpendicular line from point A to BC, and label the intersection point as point D.

4.Since AD is the perpendicular bisector of BC, we have BD = DC.

5.By the properties of dilation, the length of any line segment on ⊙O is doubled when it is transformed by a dilation with a scale factor of 2 centered at A.

6.Therefore, the length of BD is doubled to become BE, and the length of DC is doubled to become CF.

7.Since ⊙O is transformed to a circle with center A and radius 10, and ⊙P is transformed to a circle with center A and radius 24, we can see that they have the same shape but different sizes.

Therefore, we have shown that ⊙O and ⊙P are similar using similarity transformations.

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After solving the word problem, the large bag contains enough sugar to make 40 cakes

Since the large bag is 2.5 times larger than the small bag, and the small bag contains enough sugar to make 9 cakes, the large bag contains enough sugar to make:

2.5 * 9 = 22.5 cakes

However, since there are only 30 cups of sugar in the large bag, and we don't know how much sugar is needed to make a single cake, we cannot determine the exact number of cakes that can be made with a large bag of sugar.

As for the small bag, if it had enough sugar to make 9 cakes and there are 0.75 cups of sugar remaining, then each cake requires:

(sugar in bag - remaining sugar) / number of cakes

= (9 - 0.75) / 9

= 0.75 cups of sugar

Therefore, the large bag contains enough sugar to make:

30 cups / 0.75 cups per cake

= 40 cakes

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Uranus rotates on its axis at an angular speed of 0.355 radians per day, and a point on its equator travels at a linear speed of approximately 9,522 miles per day.

Uranus is one of the gas giants in our solar system, and it has a unique orientation compared to the other planets. Its axis of rotation is tilted at an angle of 97.77 degrees relative to its orbit around the Sun, which means that it essentially spins on its side. This also means that its equator is located in a plane perpendicular to its orbit, unlike Earth's equator, which is in the plane of its orbit.

Given that Uranus rotates on its axis once every 17.2 hours and its equator lies on a circle with a radius of 15,881 miles, we can calculate the angular and linear speed of a point on its equator.

Angular speed is a measure of the rate of change of an angle with respect to time. In this case, we want to know the angular speed of a point on Uranus' equator in radians per day. To find this, we can start by calculating the angle that a point on the equator travels in one day, which is equal to the angular speed times the time, or 2π radians (a full circle).

So, the angular speed of a point on Uranus' equator is:

(2π radians)/(24 hours) = 0.2618 radians per hour

To convert this to radians per day, we multiply by the number of hours in a day:

0.2618 radians/hour × 24 hours/day = 0.355 radians per day

Therefore, a point on Uranus' equator travels at an angular speed of 0.355 radians per day.

Linear speed is a measure of the rate of change of position with respect to time. In this case, we want to know the linear speed of a point on Uranus' equator in miles per day. To find this, we can use the formula:

Linear speed = angular speed × radius

Where the radius is the distance from the center of Uranus to a point on its equator, which we are given as 15,881 miles.

So, the linear speed of a point on Uranus' equator is:

0.355 radians/day × 15,881 miles = 9,521.9 miles per day

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To find g(x), the translation 1 unit left of f(x) = x², we need to replace x with (x+1) because moving left means we need to subtract 1 from x. Therefore, g(x) = f(x+1) = (x+1)².

To write g(x) in the form a(x-h)² + k, we need to expand (x+1)² first. Using the formula (a+b)² = a² + 2ab + b², we get:

g(x) = (x+1)² = x² + 2x + 1

Now we can write g(x) in the vertex form by completing the square. We add and subtract (2/2)² = 1 to the expression to get:

g(x) = x² + 2x + 1 - 1 + 1
    = (x+1)² + 0

Therefore, g(x) = (x+1)² + 0 is the vertex form of g(x), where a=1, h=-1, and k=0. This means that the vertex of the parabola g(x) is (-1,0), and it opens upwards. The translation 1 unit left of f(x)=x² results in a horizontal shift of the parabola to the left by 1 unit without changing its shape or orientation.

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Answer:

1)3 pm

Step-by-step explanation:

1st) so till 12 15 he will have checked 3 patients and after the break the other two, I think he will finish at 3 pm

The solid obtained by rotating the region bounded by y = r^2 and y = 2 about the axis y = -2 would be a three-dimensional shape with a hole in the middle. The axis of rotation is the line y = -2, which means that the solid will be formed by rotating the given region around this axis. The resulting shape will have a cylindrical section and two hemispherical sections on either end. The cylinder will have a height of 4 and a radius of 2, while the hemispheres will have radii of 2 and 4, respectively.

b) The solid obtained by rotating the region bounded by y = Vx, y = 1, and x = 4 about the axis r = -1 would be a three-dimensional shape with a conical section and a cylindrical section. The axis of rotation is the line r = -1, which means that the solid will be formed by rotating the given region around this axis. The resulting shape will have a cone-shaped section with a height of 4 and a base radius of 4, as well as a cylindrical section with a height of 1 and a radius of 4.
a) The solid obtained by rotating the region bounded by y = x^2 and y = 2 about the axis y = -2 is a parabolic cylinder. This is formed when the parabolic region between the two given functions is rotated around the specified axis, creating a three-dimensional shape with parabolic cross-sections.

b) The solid obtained by rotating the region bounded by y = √x, y = 1, x = 4, about the axis x = -1 is a torus-like shape. This is formed when the region enclosed by the square root function, the horizontal line at y = 1, and the vertical line at x = 4 is rotated around the specified axis, creating a donut-like shape with varying thickness.

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The equation of the circle with a center at (-3, 6) and passing through the point (9, 1) is (x + 3)^2 + (y - 6)^2 = 169.

To write the equation of a circle with a center at the point (-3, 6) and passing through the point (9, 1), we can use the general equation of a circle: (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle, and r is the radius.

1. Identify the center (h, k) as (-3, 6).
2. Calculate the radius using the distance formula between the center and the given point (9, 1):
  r = √((x2 - x1)^2 + (y2 - y1)^2)
  r = √((9 - (-3))^2 + (1 - 6)^2)
  r = √((12)^2 + (-5)^2)
  r = √(144 + 25)
  r = √169
  r = 13

3. Substitute the values of h, k, and r into the equation of a circle:
  (x - (-3))^2 + (y - 6)^2 = 13^2
  (x + 3)^2 + (y - 6)^2 = 169

So, the equation of the circle with a center at (-3, 6) and passing through the point (9, 1) is (x + 3)^2 + (y - 6)^2 = 169.

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Answer: C

Step-by-step explanation:

since slope is rise/run its 2 and since the line is a negative slope the slope of the line is -2. and the y-intercept of the line is -2.

y = mx+b

m = -2

b= -2

Answer: C. y= -2x -2

The side length of the base of the rectangular prism is approximately 1.2 cm.

The top, bottom, and lateral faces of a rectangular prism are all rectangles, and all the pairings of the opposing faces are congruent. A rectangular prism is a three-dimensional structure with six faces.

Let's denote the side length of the base of the rectangular prism as "x" cm.

We know that the volume of a rectangular prism is given by the formula:

Volume = Base Area x Height

In this case, the base is a square, so its area is given by:

Base Area = x²

We are given that the volume is 24.768 cm³ and the height is 17.2 cm.

Therefore, we can write the equation:

24.768 = x² * 17.2

To find the value of x, we can rearrange the equation:

x² = 24.768 / 17.2

x² = 1.4376

Taking the square root of both sides, we get:

x = √1.4376

x ≈ 1.2

Therefore, the side length of the base of the rectangular prism is approximately 1.2 cm.

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So after 6 hours, there will be approximately 262,144 bacteria.

An exponent (also called a power or index) is a mathematical notation that indicates the number of times a quantity is multiplied by itself. It is written as a superscript to the right of the quantity being multiplied. Exponents are commonly used in algebra and other branches of mathematics to represent repeated multiplication or to simplify complex expressions. They also have important applications in science, engineering, and computer programming.

Here,

We can use the formula for exponential growth to find the number of bacteria after a certain amount of time:

N = N0 * [tex]2^{(t/d)} ^[/tex]

where N is the final number of bacteria, N0 is the initial number of bacteria (which is 1 in this case), t is the time elapsed (in minutes), and d is the doubling time (in minutes).

Since the doubling time is 20 minutes, we have:

d = 20

To find the number of bacteria after 6 hours (which is 360 minutes), we plug in these values:

N = 1 * [tex]2^{(360/20)}[/tex]

Simplifying the exponent, we get:

N = 1 * [tex]2^{18}[/tex]

Using a calculator or by hand, we can evaluate this expression to get:

N ≈ 262,144

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Answer:6

Step-by-step explanation:3*4/2=6

The estimated contribution for Rosemary's first-year college fee is $6,500 including all her savings and available funds.

Savings of Rosemary = $2,500

Savings from bond = $1000

To calculate the contribution needed for Rosemary from other sources, to pay her college fee, we need to add all the available funds and subtract the money for her college fee.

Let us imagine that the total cost of Rosemary's college = $10,000

Total available funds = $2,500  + $1,000

Total available funds = $3500

The remaining amount needed = $10,000 - $3,500 = $6,500

Therefore, we can conclude that Rosemary would need an estimated contribution of $6,500.

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Answer:

Step-by-step explanation:

Since the distribution is approximately normal, we can use the empirical rule to estimate the mean and standard deviation.

According to the empirical rule:

Approximately 68% of the data falls within 1 standard deviation of the mean

Approximately 95% of the data falls within 2 standard deviations of the mean

Approximately 99.7% of the data falls within 3 standard deviations of the mean

From the information given in the problem, we know that:

10% of women are less than 60.8 inches tall

10% of women are more than 67.6 inches tall

So, we can estimate the mean height as the midpoint between 60.8 and 67.6:

mean = (60.8 + 67.6) / 2 = 64.2 inches

We also know that 80% of women are between 60.8 and 67.6 inches tall. Since this is approximately 1 standard deviation from the mean (on either side), we can estimate the standard deviation as:

standard deviation = (67.6 - 64.2) / 1 = 3.4 inches

Therefore, the mean height is approximately 64.2 inches and the standard deviation is approximately 3.4 inches.