The answer to this question is x = 6
a cylinder has a radius of 3 cm and a height of 8 cm. what is the longest segment, in centimeters, that would fit inside the cylinder?
The longest segment that would fit inside the cylinder is approximately 9.06 centimeters.
The longest segment that would fit inside the cylinder would be the diagonal of the cylinder's base, which is equal to the diameter of the base. The diameter of the base is equal to twice the radius, so it is 6 cm. Using the Pythagorean theorem, we can find the length of the diagonal:
[tex]diagonal^2 = radius^2 + height^2 \\diagonal^2 = 3^2 + 8^2 \\diagonal^2 = 9 + 64 \\diagonal^2 = 73 \\diagonal = sqrt(73)[/tex]
Therefore, the longest segment that would fit inside the cylinder is approximately 8.54 cm (rounded to the nearest hundredth).
To find the longest segment that would fit inside the cylinder, we need to calculate the length of the space diagonal of the cylinder. This is the distance between two opposite corners of the cylinder, passing through the center. We can use the Pythagorean theorem in 3D for this calculation.
The terms we'll use are:
- Radius (r): 3 cm
- Height (h): 8 cm
To find the space diagonal (d), we can use the following formula:
[tex]d = \sqrt{r^2 + r^2 + h^2}[/tex]
Plug in the values:
[tex]d = \sqrt{((3 cm)^2 + (3 cm)^2 + (8 cm)^2)} d = \sqrt{(9 cm^2 + 9 cm^2 + 64 cm^2)} d = \sqrt{(82 cm^2)}[/tex]
d ≈ 9.06 cm
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The longest segment that can fit inside the cylinder is. [tex]$\sqrt{73}$ cm[/tex].
The longest segment that can fit inside a cylinder is a diagonal that connects two opposite vertices of the cylinder.
The length of this diagonal by using the Pythagorean theorem.
Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.
It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.
This theorem can be written as an equation relating the lengths of the sides a, b and the hypotenuse c, often called the Pythagorean equation:[1]
[tex]{\displaystyle a^{2}+b^{2}=c^{2}.}[/tex]
The theorem is named for the Greek philosopher Pythagoras, born around 570 BC.
The theorem has been proven numerous times by many different methods – possibly the most for any mathematical theorem.
The proofs are diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years.
Consider a right triangle with legs equal to the radius.
[tex]$r$[/tex] and the height [tex]$h$[/tex] of the cylinder, and with the diagonal as the hypotenuse.
Then, by the Pythagorean theorem, the length of the diagonal is:
[tex]$\sqrt{r^2 + h^2} = \sqrt{3^2 + 8^2} = \sqrt{73}$[/tex]
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why would you use a trigonometric function to set-up an application problem instead of a non-trigonometric function
Trigonometric functions are used to model relationships between angles and sides of a right triangle. They are particularly useful in solving problems that involve angles, distances, heights, and lengths that are difficult to measure directly.
For example, consider a problem that involves finding the height of a building. By measuring the length of the shadow cast by the building at a particular time of day, the angle of the sun's rays can be calculated using trigonometry. Once the angle is known, the height of the building can be determined using the tangent function.
In contrast, a non-trigonometric function may not be able to model the relationship between the given quantities in such problems, and may not provide an accurate solution. Therefore, when a problem involves angles or distances that are not directly measurable, trigonometric functions are typically the best tool for setting up and solving the problem.
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ASAP I really need help doing a two column proof for this please.
The two column proof is written as follows
Statement Reason
MA = XR given (opposite sides of rectangle)
MK = AR given (opposite sides of rectangle)
arc MA = arc RK Equal chords have equal arcs
arc MK = arc AK Equal chords have equal arcs
Equal chords have equal arcsAn arc is a portion of the circumference of a circle, and a chord is a line segment that connects two points on the circumference.
If two chords in a circle are equal in length, then they will cut off equal arcs on the circumference. This is because the arcs that the chords cut off are subtended by the same central angle.
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Find the exact value of sin a, given that cos a=-5/9 and a is in quadrant 3
Since cosine is negative and a is in quadrant III, we know that sine is positive. We can use the Pythagorean identity to solve for sine:
sin^2(a) + cos^2(a) = 1
sin^2(a) + (-5/9)^2 = 1
sin^2(a) = 1 - (-5/9)^2
sin^2(a) = 1 - 25/81
sin^2(a) = 56/81
Taking the square root of both sides:
sin(a) = ±sqrt(56/81)
Since a is in quadrant III, sin(a) is positive. Therefore:
sin(a) = sqrt(56/81) = (2/3)sqrt(14)
Part B
Based on your construction, what do you know about ΔABD and ΔBCD?
The construction and the resulting triangles are interesting because they allow us to explore the properties of perpendicular lines and the angles they form.
Now, let's look at the two triangles that are formed as a result of this construction - ΔABD and ΔBCD. Since line BD is perpendicular to line AC, we know that angle ABD and angle CBD are both right angles. This is because any line that is perpendicular to another line forms a right angle with that line.
Now, let's look at the other sides of the triangles. In ΔABD, we have side AB, which is different from side BC in ΔBCD. Similarly, in ΔBCD, we have side CD, which is different from side AD in ΔABD.
So, although the two triangles share a common side (BD), they have different lengths for their other sides. This means that the two triangles are not congruent, since congruent triangles must have the same length for all their sides.
However, we can still find some similarities between the two triangles. For example, since angle ABD and angle CBD are both right angles, we know that they are congruent. Additionally, we can use the fact that angle ADB is congruent to angle CDB, since they are alternate interior angles formed by a transversal (line BD) intersecting two parallel lines (line AC and the line perpendicular to it passing through point B).
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Complete Question:
Draw a line through point B that is perpendicular to line AC Label the intersection of the line and line AC as point D. Take a screenshot of your work, save it, and insert the image in the space below.
Part B
Based on your construction, what do you know about ΔABD and ΔBCD?
The cost of 1 cup of tea and 6 cakes is £13. The cost of 1 cup of tea and 4 cakes is £9 a) How much do 2 cakes cost? b) How much does 1 cake cost?
The answers are:
a) 2 cakes cost £5
b) 1 cake costs £2.5.
What is an algebraic expression?
An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations. It may also include exponents and/or roots. Algebraic expressions are used to represent quantities and relationships between quantities in mathematical situations, often in the context of problem-solving.
To find the cost of 1 cupcake, we need to subtract the cost of the tea from the total cost of 3 cupcakes:
3 cupcakes + 1 tea = £9
3 cupcakes = £9 - 1 tea = £9 - £1.5 (assuming the cost of 1 tea is the same in both cases) = £7.5
1 cupcake = £7.5 ÷ 3 = £2.5
So 2 cupcakes would cost:
2 cupcakes = 2 × £2.5 = £5
Therefore, the answers are:
a) 2 cakes cost £5
b) 1 cake costs £2.5.
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An industrial/organizational psychologist has been consulting with a company that runs weekend job-seeking workshops for the unemployed. She collected data on several issues related to these workshops and, after conducting statistical tests, obtained statistically significant findings. She needs to find a way to evaluate effect size so that she can make recommendations to the company. One of the psychologist's findings is that 18 months after the workshop, a sample of 81 job seekers who received training on using the Internet to find job listings worked more than 30 hours per week an average of 8. 7 months in the last year, with a standard deviation of 4. 1. The typical job seeker works 7. 4 months. The psychologist finds that the estimated Cohen's d is _____, the t statistic is 2. 83, and r^2 is ______. Using Cohen's d and Cohen's guidelines for interpreting the effect size with the estimated Cohen's d, there is a ______ treatment effect. Using r^2 and the extension of Cohen's guidelines for interpreting the effect size using r^2, there is a ______ treatment effect. Another one of the psychologist's findings is that a sample of 81 job seekers who received training on interview skills scored an average of 8. 1 as measured on a 9-point job search motivation scale, with a standard deviation of. 8. The typical job seeker scores 7. 4 points. She finds that the estimated Cohen's d is _____, the t statistic is 7. 78, and r^2 is _____ Using Cohen's d and Cohen's guidelines for interpreting the effect size with the estimated Cohen's d, there is a treatment effect. Using r^2 and the extension of Cohen's guidelines for interpreting the effect size with r^2, there is a ___ treatment effect
The psychologist finds that the estimated Cohen's d is 0.32, the t statistic is 2. 83, and r² is 0.073. Using r² and the extension of Cohen's guidelines for interpreting the effect size using r², there is a small treatment effect. job seeker finds that the estimated Cohen's d is 0.88, the t statistic is 7. 78, and r² is 0.479.Using r² and the extension of Cohen's guidelines for interpreting the effect size with r², there is a large treatment effect
To calculate the estimated Cohen's d, we use the formula
d = (M - M0) / SD
where M is the mean of the treatment group (job seekers who received training on using the Internet to find job listings), M0 is the mean of the control group (typical job seeker), and SD is the pooled standard deviation of the two groups. Using the given values, we have
M = 8.7 months
M0 = 7.4 months
SD = 4.1 months
So, d = (8.7 - 7.4) / 4.1 = 0.32
Using Cohen's guidelines for interpreting effect size with Cohen's d, a value of 0.2 is considered a small effect, 0.5 a medium effect, and 0.8 a large effect. Therefore, with an estimated Cohen's d of 0.32, there is a small treatment effect.
To calculate r², we use the formula
r² = t² / (t² + df)
where t is the t statistic, df is the degrees of freedom (n-2 for a two-group design), and n is the sample size. Using the given values for the Internet training group, we have
t = 2.83
n = 81
df = 79
So, r² = 2.83² / (2.83² + 79) = 0.073
Using the extension of Cohen's guidelines for interpreting effect size with r², a value of 0.01 is considered a small effect, 0.09 a medium effect, and 0.25 a large effect. Therefore, with an r² of 0.073, there is a small treatment effect.
For the job seekers who received training on interview skills, we can calculate Cohen's d and r² in a similar way
d = (M - M0) / SD = (8.1 - 7.4) / 0.8 = 0.88
t = 7.78
n = 81
df = 79
r² = 7.78² / (7.78² + 79) = 0.479
Using Cohen's guidelines for interpreting effect size with Cohen's d, a value of 0.2 is considered a small effect, 0.5 a medium effect, and 0.8 a large effect. Therefore, with an estimated Cohen's d of 0.88, there is a large treatment effect.
Using the extension of Cohen's guidelines for interpreting effect size with r², a value of 0.01 is considered a small effect, 0.09 a medium effect, and 0.25 a large effect. Therefore, with an r² of 0.479, there is a medium to large treatment effect.
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Answer:.317
.091
Small to med
Med
.875
.431
Large
Large
Step-by-step explanation:
three bolts and three nuts are in a box. two parts are chosen at random. find the probability that one is a bolt and one is a nut.
The probability of picking one bolt and one nut is 1/2 or 50%.
To find the probability that one is a bolt and one is a nut, we need to use the formula for calculating the probability of two independent events happening together: P(A and B) = P(A) × P(B)
Let's first calculate the probability of picking a bolt from the box:
P(bolt) = number of bolts / total number of parts = 3/6 = 1/2
Now, let's calculate the probability of picking a nut from the box:
P(nut) = number of nuts / total number of parts = 3/6 = 1/2
Since the events are independent, the probability of picking a bolt and a nut in any order is:
P(bolt and nut) = P(bolt) × P(nut) + P(nut) × P(bolt)
P(bolt and nut) = (1/2) × (1/2) + (1/2) × (1/2)
P(bolt and nut) = 1/2
Therefore, the probability of picking one bolt and one nut is 1/2 or 50%.
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the probability that one chosen part is a bolt and the other chosen part is a nut is 1, or 100%. This makes sense because if we choose two parts at random, we must get one bolt and one nut since there are three of each in the box.
To find the probability that one chosen part is a bolt and the other chosen part is a nut, we need to use the formula for probability:
Probability = (number of desired outcomes) / (total number of outcomes)
There are two ways we could choose one bolt and one nut: we could choose a bolt first and a nut second, or we could choose a nut first and a bolt second. Each of these choices corresponds to one desired outcome.
To find the number of ways to choose a bolt first and a nut second, we multiply the number of bolts (3) by the number of nuts (3), since there are 3 possible bolts and 3 possible nuts to choose from. This gives us 3 x 3 = 9 total outcomes.
Similarly, there are 3 x 3 = 9 total outcomes if we choose a nut first and a bolt second.
Therefore, the total number of desired outcomes is 9 + 9 = 18.
The total number of possible outcomes is the number of ways we could choose two parts from the box, which is the number of ways to choose 2 items from a set of 6 items. This is given by the formula:
Total outcomes = (6 choose 2) = (6! / (2! * 4!)) = 15
Putting it all together, we have:
Probability = (number of desired outcomes) / (total number of outcomes)
Probability = 18 / 15
Probability = 1.2
However, this answer doesn't make sense because probabilities should always be between 0 and 1. So we made a mistake somewhere. The mistake is that we double-counted some outcomes. For example, if we choose a bolt first and a nut second, this is the same as choosing a nut first and a bolt second, so we shouldn't count it twice.
To correct for this, we need to subtract the number of outcomes we double-counted. There are 3 outcomes that we double-counted: choosing two bolts, choosing two nuts, and choosing the same part twice (e.g. choosing the same bolt twice). So we need to subtract 3 from the total number of desired outcomes:
Number of desired outcomes = 18 - 3 = 15
Now we can calculate the correct probability:
Probability = (number of desired outcomes) / (total number of outcomes)
Probability = 15 / 15
Probability = 1
So the probability that one chosen part is a bolt and the other chosen part is a nut is 1, or 100%. This makes sense because if we choose two parts at random, we must get one bolt and one nut since there are three of each in the box.
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Given that £1 = $1.62
a) How much is £650 in $?
b) How much is $405 in £?
Answer:
a 1053
b 250
multiply 650 by 1.62 for part a.
for part b divide by 1.62 since pound is less than dollar
hope this helps :)
angles of triangles- does anyone know how to do this?
(1) m∠1=45°(sum of 3 angles of a triangle is always 180°)
(2) m∠1=180°-129°=51°(sum of two interior angles on the same side is equal to the exterior angle)
(3) m∠1= 152°-115°=37°
(4) m∠1=88°m∠2=42° m∠3=113°
What is an angle?An angle is a geometric figure formed by two rays that share a common endpoint, called the vertex. The measure of an angle is typically expressed in degrees or radians, and it describes the amount of rotation needed to bring one of the rays into coincidence with the other.
Define triangle?A triangle is a closed two-dimensional shape with three straight sides and three angles.
(1) m∠1=45°(sum of 3 angles of a triangle is always 180°)
(2) m∠1=180°-129°=51°(sum of two interior angles on the same side is equal to the exterior angle)
(3) m∠1= 152°-115°=37°(sum of two interior angles on the same side is equal to the exterior angle)
(4) m∠1=88°(sum of 3 angles of a triangle is always 180°),m∠2=42°(vertically opposite angle theorem), m∠3=113°(sum of 3 angles of a triangle is always 180°)
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Fifteen children split $9 among themselves so that each child receives the same amount. How much did each child receive?
The total amount of money received by each child after splitting $9 among 15 children is equal to $0.60.
Total number of children is equal to 15
Total amount of money distributed among 15 children = $9
To find out how much each child receives,
We can divide the total amount of money by the number of children.
In this case, there are 15 children and $9 to split.
So, the amount of money each child receives is equal to,
(Total amount of money )/ ( total number of children )
= $9 ÷ 15
= $0.60
Therefore, amount of money received by each child in the group of 15 children is equal to $0.60.
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Find the measure of the missing side.
1. 8.2
2. 9.9
3. 7.4
4. 10.9
Answer:
1
Step-by-step explanation:
First of all we use the "law of sines"
to get the measure/length we need the opposing angle of it of the side, now in this case the missing side is x
and its opposing angle is missing so using common sense, the sum of angles in the triangle is 180°
180°=70°+51°+ x
x = 180°-121°
=59°
Using law of sines:
(sides are represented by small letters/capital letters are the angles)
a/sinA= b/sinB= c/sinC
We have one given side which is "9"
so,
9/sin70= x/sin59
doing the criss-cross method,
9×sin59=sin70×x
9×sin59/sin70=x
x=8.2 (answer 1)
I hope this was helpful <3
a trapezoid has an area of 96 ft. if the base is 11 feet and the height is 8 feet, what is the length of the other base
Answer:
The formula for the area of a trapezoid is:
Area = (b1 + b2) / 2 x h
where b1 and b2 are the lengths of the two parallel bases, and h is the height.
We are given that the area of the trapezoid is 96 ft, the height is 8 ft, and one of the bases (b1) is 11 ft. We can use this information to find the length of the other base (b2).
Substituting the given values into the formula for the area of a trapezoid, we get:
96 = (11 + b2) / 2 x 8
Multiplying both sides by 2 and dividing by 8, we get:
24 = 11 + b2
Subtracting 11 from both sides, we get:
b2 = 13
Therefore, the length of the other base is 13 ft.
state the nameof this quadrilateral...70 points
Answer:
Step-by-step explanation:
its a rectanlge
when a researcher uses the pearson product moment correlation, two highly correlated variables will appear on a scatter diagram as what?
When a researcher uses the Pearson product-moment correlation, two highly correlated variables will appear on a scatter diagram as a tightly clustered group of points that form a linear pattern.
The scatter diagram is a visual representation of the correlation between two variables, where one variable is plotted on the x-axis, and the other variable is plotted on the y-axis. If the two variables have a high positive correlation, then the points on the scatter diagram will form a cluster that slopes upwards to the right.
On the other hand, if the two variables have a high negative correlation, then the points will form a cluster that slopes downwards to the right. The tighter the cluster of points, the higher the correlation between the variables.
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The answers are in the picture. I need help ASAP!
The perimeter and the area of the regular polygon are 20 inches and 27.53 square inches.
How to calculate the area and the perimeter of a regular polygon
The figure representing a regular polygon with five sides of same length, whose perimeter and area is well described by following formulas:
Perimeter
p = n · l
Area
A = (n · l · a) / 2
Where:
A - Area of the polygon, in square inches. n - Number of sides.l - Side length, in inches. a - Apothema, in inches. p - Perimeter, in inches.Where the apothema is:
a = 0.5 · l / tan (180° / n)
If we know that l = 4 in and n = 5, then the perimeter and the area of the polygon are:
Perimeter
p = 5 · (4 in)
p = 20 in
Area
a = 0.5 · (4 in) / tan (180° / 5)
a = 0.5 · (4 in) / tan 36°
a = 2.753 in
A = [5 · (4 in) · (2.753 in)] / 2
A = 27.53 in²
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in a role playing game two special dice are rolled. one die has 4 faces numbered 1 through 4 and the other has 6 faces numbered 1 thorugh 6. what is the probabilty that the total shown on the two dice after they are rolled is greater than or equal to 8?
The probability that the total shown on the two dice after they are rolled is greater than or equal to 8 is 1/9.
5. Select Yes or No to indicate whether each ordered pair is a point of intersection
between the line x - y = 6 and the circle y² - 26 = -x².
Ordered Pair
(1,-5)
(1,5)
(5,-1)
To determine if each ordered pair is a point of intersection between the line x - y = 6 and the circle y² - 26 = -x², we need to substitute the values of x and y in both equations and see if they are true for both.
Select Yes or No to indicate whether each ordered pair is a point of intersectionFor the ordered pair (1, -5):
x - y = 6 becomes 1 - (-5) = 6, which is true.
y² - 26 = -x² becomes (-5)² - 26 = -(1)², which is false.
Therefore, (1, -5) is not a point of intersection.
For the ordered pair (1, 5):
x - y = 6 becomes 1 - 5 = -4, which is false.
y² - 26 = -x² becomes (5)² - 26 = -(1)², which is true.
Therefore, (1, 5) is a point of intersection.
For the ordered pair (5, -1):
x - y = 6 becomes 5 - (-1) = 6, which is true.
y² - 26 = -x² becomes (-1)² - 26 = -(5)², which is false.
Therefore, (5, -1) is not a point of intersection.
So the answer is:
(1,-5) - No
(1,5) - Yes
(5,-1) - No
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I need help with this question can you help?
Answer:
The Correct answer is sinA/3.2=sin110°/4.6
3 out of 7 questions. PLEASE help me.
Translate the solid circle 2 units to the left and 2 units down and dilate the solid circle by a scale factor of 2. and the circles are similar
Transforming the circles(a) To move the solid circle exactly onto the dashed circle, we need to perform the following transformations:
Translate the solid circle 2 units to the left and 2 units down.Dilate the solid circle by a scale factor of 2.Therefore, the blank spaces should be filled as follows:
Translate the solid circle 2 units to the left and 2 units down.
Dilate the solid circle by a scale factor of 2.
(b) Yes, the original solid circle and the dashed circle are not similar, because they have different radii.
This is because all circles are similar
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Question:
The current (in amps) in a simple
electrical circuit varies inversely to
the resistance measured in ohms.
The current is 24 amps when the
resistance is 20 ohms. Find the
current (in amps) when the
resistance is 12 ohms.
The current in the circuit when the resistance is 12 ohms is 40 amps.
What is fraction?
A fraction is a mathematical term that represents a part of a whole or a ratio between two quantities.
We can use the inverse proportionality formula to solve this problem, which states that:
current (in amps) x resistance (in ohms) = constant
Let's call this constant "k". We can use the information given in the problem to find k:
24 amps x 20 ohms = k
k = 480
Now we can use this constant to find the current when the resistance is 12 ohms:
current x 12 ohms = 480
current = 480 / 12
current = 40 amps
Therefore, the current in the circuit when the resistance is 12 ohms is 40 amps.
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help me please please
Given the quadratic equation x^(2)+4x+c=0, what must the value of c be in order for the equation to have solutions at x=-3 and x=-1 ?
Answer:
Step-by-step explanation:
If the solutions are x = -3 and x = -1, then (x - 3) (x - 1) will give us our answer. Using the FOIL method,
(x - 3) (x - 1)
x^2 - x - 3x + 3
x^3 - 4x + 3 = 0
Your answer is 3
A small can of tomato paste has a radius of 2 inches and a height of 4 inches. Suppose the larger, commercial-size can has dimensions that are related by a scale factor of 3. Which of these is true?
The correct statement about scale factor is the radius of the larger can will be 8 inches. (option c).
Let's first consider the dimensions of the small can of tomato paste. We are given that it has a radius of 2 inches and a height of 4 inches. Therefore, its volume can be calculated using the formula for the volume of a cylinder, which is V = πr²h, where V is the volume, r is the radius, and h is the height. Substituting the given values, we get:
V_small = π(2²)(4) = 16π cubic inches
Using these dimensions, we can calculate the volume of the larger can using the same formula:
V_large = π(6²)(12) = 432π cubic inches
Now, let's compare the volumes of the small and large cans. We have:
V_large = 432π cubic inches > 16π cubic inches = V_small
Therefore, we can conclude that the volume of the larger can is greater than the volume of the smaller can. But is it three times greater? Let's compare:
V_large = 432π cubic inches 3
V_small = 3(16π) cubic inches = 48π cubic inches
We see that 432π cubic inches is not equal to 48π cubic inches, so option b) is not correct.
Finally, let's consider the radius of the larger can. We found earlier that it is 6 inches, which is greater than the radius of the smaller can, but it is not 8 inches. Therefore, option c) is correct.
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Complete Question:
A small can of tomato paste has a radius of 2 inches and a height of 4 inches. Suppose the larger, commercial-size can has dimensions that are related by a scale factor of 3. Which of these true?
a) The radius of the larger can will be 5 inches.
b) The volume of the larger can will be 3 times the volume of the smaller can
c) The radius of the larger can will be 8 inches.
d) The volume of the larger can is 3 times the volume of smaller can
What is the answer to this problem?
The area of the shaded area is 3.27 ft²
How to the area of the shaded area?We can find the area of the shaded area by subtracting the area of the triangle from the area of the sector. That is;
Area of shaded area = Area of sector - area of triangle
Area of shaded area = (60/360 * π * 6²) - (1/2 * 6 * 6 * sin 60)
Area of shaded area = (60/360 * 22/7 * 36) - (1/2 * 36 * 0.866)
Area of shaded area = 3.27 ft²
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A tram moved downward 12 meters in 4 seconds at a constant rate. What was the change in the tram's elevation each second?
Therefore , the solution of the given problem of unitary method comes out to be during the 4-second period, the tram's elevation changed by 3 metres every second.
What is an unitary method?To complete the assignment, use the iii . -and-true basic technique, the real variables, and any pertinent details gathered from basic and specialised questions. In response, customers might be given another opportunity to sample expression the products. If these changes don't take place, we will miss out on important gains in our knowledge of programmes.
Here,
By dividing the overall elevation change (12 metres) by the total time required (4 seconds),
it is possible to determine the change in the tram's elevation every second. We would then have the average rate of elevation change per second.
=> Elevation change equals 12 metres
=> Total duration: 4 seconds
=> 12 meters / 4 seconds
=> 3 meters/second
As a result, during the 4-second period, the tram's elevation changed by 3 metres every second.
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Evan takes 100 milligrams of medicine. The amount of medicine in his bloodstream decreases by 0.4 milligram each minute for a number of minutes, m, after that. He writes the expression 100 - 0.4m to find the amount of medicine in his bloodstream after m minutes. Which statement about his expression is true?
The statement that is true about Evan's expression is that it represents a linear function of the amount of medicine in his bloodstream, where the initial amount is 100 milligrams and the rate of change is -0.4 milligrams per minute.
What is the equivalent expression?
Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.
The expression 100 - 0.4m represents the amount of medicine in Evan's bloodstream after m minutes, where the amount of medicine decreases by 0.4 milligrams each minute.
The coefficient of the variable m (-0.4) represents the rate of change of the amount of medicine in Evan's bloodstream per minute. It tells us that for every one minute that passes, the amount of medicine in his bloodstream decreases by 0.4 milligrams.
The constant term (100) represents the initial amount of medicine in Evan's bloodstream before the medicine starts to decrease.
Therefore, the statement that is true about Evan's expression is that it represents a linear function of the amount of medicine in his bloodstream, where the initial amount is 100 milligrams and the rate of change is -0.4 milligrams per minute.
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c. what is the probability that the duration of a rainfall event at this location is between 2 and 3 hours? d. what is the probability that a rainfall duration exceeds the mean value by more than 2 standard deviations?
The probability that a rainfall event exceeds the mean by more than 2 standard deviations is approximately 0.0498.
a. The exponential distribution with a mean of 2.725 hours can be expressed as λ = 1/2.725. Using this parameter, we can calculate the probabilities as follows:
P(X ≥ 2) = [tex]e^{(-λ2) }= e^{(-1/2.7252)[/tex] ≈ 0.4800
P(X ≤ 3) = 1 - [tex]e^{(-λ3)} = 1 - e^{(-1/2.7253)[/tex] ≈ 0.6674
P(2 ≤ X ≤ 3) = [tex]e^{(-λ2)} - e^{(-λ3)} = e^{(-1/2.7252)} - e^{(-1/2.7253)}[/tex] ≈ 0.1474
b. The standard deviation of an exponential distribution is equal to the mean, so 2 standard deviations above the mean would be 2*2.725 = 5.45 hours. The probability that a rainfall event exceeds this duration can be calculated as follows:
P(X > 5.45) =[tex]e^{(-λ5.45)} = e^{(-1/2.7255.45)}[/tex] ≈ 0.0498
Therefore, the probability that a rainfall event exceeds the mean by more than 2 standard deviations is approximately 0.0498.
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Complete Question:
Suppose that rainfall duration follows an exponential distribution with mean value 2.725 hours.
a. What is the probability that the duration of a particular rainfall event is at least 2 hours? At most 3 hours? Between 2 and 3 hours? (.4800, .6674, .1474)
b. What is the probability that rainfall duration exceeds the mean value by more than 2 standard deviations? (.0498)
Becca is construction triangle d e f using the following angles 50°, 65°, 65°,
what mistake did she make?
Becca made a mistake while constructing triangle DEF by using the angles 50°, 65°, and 65°. The mistake she made was violating the triangle inequality theorem.
According to the theorem, the sum of any two sides of a triangle must be greater than the third side. In other words, if we add the lengths of two sides of a triangle, it must be greater than the length of the third side.
Since Becca only used angles to construct the triangle, she did not consider the side lengths of the triangle. Therefore, there is a possibility that the triangle she constructed does not satisfy the triangle inequality theorem, and it may not be a valid triangle.
In order to ensure the triangle is valid, Becca needs to consider the side lengths while constructing the triangle. She could use trigonometric ratios or a ruler and protractor to measure the side lengths and angles accurately.
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All help is appreciated thank you.
Using the fact that the triangles are similar we can see that the value of x is 36
How to find the value of x?We can see that the triangles are similar due to the same interior angles, then ther is a scale factor k between them.
So we can write:
20*k = 48
k = 48/20 = 2.4
Then:
x = 15*2.4
x = 36
That is the value of x.
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