The strengthening of National Ambient Air Quality Standards for maximum daily concentration of PM2.5 from 65 micrograms to 35 micrograms is expected to have a positive impact on public health.
The PM2.5 is defined as a fine particulate matter which penetrate deep into the lungs and cause a range of health problems, including asthma attacks, heart disease, and lung cancer.
By lowering the maximum daily concentration of PM2.5, the EPA is aiming to reduce the amount of air-pollution that people are exposed to, which should lead to improvements in public health.
Therefore, the strengthening of the National Ambient Air Quality Standards for PM2.5 is a positive step towards protecting public health and reducing the burden on medical facilities.
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puzzle 4 can you find the slope intercept equation of each line and type the correct code
Equation of line: y = -3/4 x + 3. Here , slope m = -3/4 and y intercept is 3.
Explain about the slope intercept equation?We need to knowing the slope of the line and indeed the intercept where the line crosses the y-axis in order to use the slope-intercept formula. Suppose a straight line with y-intercept b and slope m. For one straight line with slope "m" and y-intercept "b," the slope intercept program is designed is: y = mx + b.
Given coordinates are:
(2,3) and (4,0).
Slope m = (y2 - y1)/(x2 - x1)
m = (0 - 3)/(4 - 0)
m = -3/4
Equation of line:
y - y1 = m(x - x1)
y - 0 = -3/4(x - 4)
y = -3/4 x + 3
Here , slope m = -3/4 and y intercept is 3.
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Complete question:
Find the slope intercept equation of line passing through (2,3) and (4,0).
An isosceles trapezoid has a perimeter of 45 millimeters. Its shorter base measures 6.3 millimeters and its longer base measures 16.1 millimeters. The two remaining sides have the same length; what is that length?
The length of the two equal sides of the isosceles trapezoid is 11.3 millimeters.
What is trapezoid?
A trapezoid, also known as a trapezium in some countries, is a two-dimensional geometric shape with four sides. It is a quadrilateral that has at least one pair of parallel sides, which are called bases.
Let's start by labeling the sides of the isosceles trapezoid as follows:
The shorter base: b1 = 6.3 mm
The longer base: b2 = 16.1 mm
The two equal sides: s
We know that the perimeter P of the trapezoid is given by:
P = b1 + b2 + 2s
Substituting the values we have, we get:
45 mm = 6.3 mm + 16.1 mm + 2s
Simplifying this equation, we get:
22.6 mm = 2s
Dividing both sides by 2, we get:
s = 11.3 mm
Therefore, the length of the two equal sides of the isosceles trapezoid is 11.3 millimeters.
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what is the probability that betty is first in line or mary is last in line as a function of n? simplify your final expression as much as possible and include an explanation of how you calculated this probability.
The probability that Betty is first in line or Mary is last in line is (n^2 - n - 1)/n(n-1), as a function of n.
We can approach this problem by considering the probability of the complementary event, i.e., the probability that neither Betty is first in line nor Mary is last in line, and then subtracting this probability from 1 to get the probability we want.
The total number of ways the n kids can line up is n!, since there are n choices for the first person in line, n-1 choices for the second person, and so on down to 1 choice for the last person.
The number of ways in which neither Betty is first in line nor Mary is last in line is (n-2)!, since there are (n-2) choices for the first person in line (excluding Betty and Mary), (n-3) choices for the second person, and so on down to 1 choice for the second-to-last person.
Therefore, the probability that neither Betty is first in line nor Mary is last in line is
[(n-2)! / n!] = 1/n(n-1)
The probability we want is
1 - 1/n(n-1) = (n^2 - n - 1)/n(n-1)
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The given question is incomplete, the complete question is:
A class with n kids lines up for recess. The order in which the kids line up is random with each ordering being equally likely. There are two kids in the class named Betty and Mary. The use of the word “or” in the description of the events, should be interpreted as the inclusive or. That is “A or B” means that A is true, B is true, or both A and B are true.
What is the probability that Betty is first in line or Mary is last in line as a function of n? Simplify your final expression as much as possible and include an explanation of how you calculated this probability.
A cube has edges of length 'n', where 'n' is a positive integer. Three faces, meeting at a corner, are painted red. The cube is then cut into n³ smaller cubes of unit length. That is, the side lengths of the new cubes are 1 unit. f exactly 125 of these cubes have no faces painted red, determine the value of n.
Please do show workings, I would really appreciate it. Thank you so much!
The calculated value of n in the cube with the given properties is 5
Calculating the value of nIf we cut the original cube into smaller cubes of side length 1 unit, then the total number of smaller cubes is given by the formula:
Total number of smaller cubes = (number of cubes along each edge of the original cube)^3 = n^3
So, we have
n^3 = 125
Take the cube root of both sides
n = 5
Hence, the value of n is 5
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All sophomores at McKinley High are required to select one instrument to play for their music class
The answer is 3/20. By calculating the probability of selecting a female who plays the clarinet out of the total number of sophomores, we can get an accurate representation of the selection of the current sophomore class.
how to calculate probability?It is calculated by dividing the number of possible outcomes by the total number of possible outcomes.
This can be calculated by taking the number of females who play the clarinet (18) and dividing it by the total number of sophomores (120).
This gives us 18/120= 3/20.
This is the correct answer because it shows the probability of selecting a female who plays the clarinet out of the total number of sophomores. Option 1, 31/120, would show the probability of selecting a female or a clarinet player out of the total number of sophomores.
Option 3, 3/11, would show the probability of selecting a female who plays the clarinet out of the total number of female sophomores.
Option 4, 18/31, would show the probability of selecting a female out of the total number of clarinet players.
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Malik grills a steak minutes longer than he grills a serving of fish. The fish takes twice as long as the asparagus to grill. Malik grills halved tomatoes for minutes, which is minute longer than he grills the asparagus.Write an expression that represents the amount of time Malik grills the steak if the asparagus grills for x minutes.
As a result, 2x + 10 is the expression that describes how long Malik will cook the sirloin for if the asparagus grills for x minutes.
What is a good expression of the phrase?So, 1+1 is a straightforward illustration of a statement. This expression has one action, two constant elements, and (addition). Another illustration is x3.
Let's start by using the given information to create expressions for each item:
Let's call the time it takes to grill the fish "f". Then, according to the problem, Malik grills the steak for "f + 10" minutes.
Grilling time for the seafood is double that of the vegetables. Thus, if it requires "x" minutes to grill asparagus, "2X" minutes are needed to grill salmon.
For "x + 1" minutes, and this is one minute more than he roasts the asparagus, Malik cooks the tomatoes that have been cut in half.
Using these expressions, we can create an equation for the time it takes to grill the steak:
Time to grill steak = Time to grill fish + 10
(f + 10) = 2x + 10
Therefore, if the asparagus cooks for x minutes, the phrase that denotes how long Malik will grill the sirloin is:
2x + 10
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A cylindrical glass 7 cm in diameter and 10 cm tall is filled with water to a height of 9 cm. If a ball 5 cm in diameter is dropped into the class and sinks to the bottom, will the water in the glass overflow? If it does overflow, how much water will be lost? Explain and justify your response.
I
On solving the provided question we can say that The amount of water lost is: [tex]V_lost = V1 - V2 = 346.36 cm^3 - 401.94 cm^3 = -55.58 cm^3[/tex]
what is cylinder?A cylinder is a three-dimensional geometric shape made up of two parallel congruent circular bases and a curving surface connecting the two bases. The bases of a cylinder are always perpendicular to its axis, which is an imaginary straight line passing through the centre of both bases. The volume of a cylinder is equal to the product of its base area and height. A cylinder's volume is computed as V = r2h, where "V" represents the volume, "r" represents the radius of the base, and "h" represents the height of the cylinder.
[tex]V1 = \pi r^2h = \pi (3.5 cm)^2(9 cm) = 346.36 cm^3\\[/tex]
Next, let's calculate the volume of the ball:
The radius of the ball is 5/2 = 2.5 cm. The volume of the ball is:
[tex]V_ball = (4/3)\pi r^3 = (4/3)\pi (2.5 cm)^3 = 65.45 cm^3\\V_disp = V_ball = 65.45 cm^3\\h_new = 9 + (V_disp/\pi r^2) = 9 + (65.45 cm^3)/(\pi (3.5 cm)^2) = 10.77 cm\\V2 = \pi r^2h_new = \pi (3.5 cm)^2(10.77 cm) = 401.94 cm^3\\[/tex]
The amount of water lost is:
[tex]V_lost = V1 - V2 = 346.36 cm^3 - 401.94 cm^3 = -55.58 cm^3[/tex]
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in a class, 2/5 of the students play basketball, and 7/10 play soccer. of the students who play basketball, 2/3 also play soccer. there are 30 students in the class. how many students play soccer but do not play basketball?
If there are 30 students in the class, then the number of students who play soccer but do not play basket-ball are 13 students.
The total-students in the class is = 30 students,
The Number of students who play basketball is = (2/5) × 30 = 12,
The Number of students who play soccer is = (7/10) × 30 = 21,
⇒ Number of basketball players who also play soccer = (2/3) × 12 = 8,
So, out of the 21 students who play soccer, 8 also play basketball.
To find the number of students who play soccer but not basketball, we can subtract the number of students who play both from the total number of soccer players:
⇒ 21 - 8 = 13 students play soccer but not basketball.
Therefore, the required number of students are 13 students.
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what are the vertices of this ellipse? graph (-4, 2) and (4, 2) (2 , 2) and (2 , 2) (-5, 5) and (-5, -1) (-9, 2) and (-1, 2)
The vertices of the ellipse are (-4,2) and (4,2), since these points lie on the major axis of the ellipse which is horizontal.
Two of the focuses given in the issue, (−4,2) and (4,2), are both situated on a similar even line. This implies that the significant hub of the oval should be level. Two different focuses given in the issue, (2,2) and (- 9,2), are likewise situated on this level line. Thusly, the focal point of the oval is the midpoint between the focuses (- 4,2) and (4,2), which is (0,2).
The other two focuses given in the issue, (−5,5) and (−5,−1), are situated on an upward line that goes through the focal point of the oval. This implies that the minor pivot of the oval should be vertical.
The vertices of the oval are the places where the significant hub meets the circle. Since the significant hub goes through the focuses (−4,2) and (4,2), the vertices of the oval are (- 4,2) and (4,2).
In this way, the vertices of the oval are (- 4,2) and (4,2).
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Christina wanted to fence in her yard. How many feet of fence will be needed? 60 ft 50 ft 40 ft 25 ft
Christina will need 220 feet of fence to enclose her yard.
What is a Perimeter?The perimeter of a form is the space surrounding its edge. Find the perimeter of various forms by summing the lengths of their sides.
To solve this, we need to calculate the perimeter of the rectangular yard:
Perimeter = 2 × (Length + Width)
Plugging in the given dimensions:
Perimeter = 2 × (60 ft + 50 ft)
Perimeter = 2 × (110 ft)
Perimeter = 220 ft
Christina will need 220 feet of fence to enclose her yard.
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Christina wants to fence in her rectangular yard. The length of her yard is 60 feet, and the width is 50 feet. How many feet of fence will she need to enclose the entire yard?
data collected at toronto pearson international airport suggests that an exponential distribution with mean value 2.725 hours is a good model for rainfall duration (urban stormwater management planning with analytical probabilistic models, 2000, p. 69). a. what is the probability that the duration of a particular rainfall event at this location is at least 2 hours? at most 3 hours? between 2 and 3 hours?
The probability that the duration of rainfall at least 2 hours is 0.473, at most 3 hours is 0.683, and between 2 and 3 hours is 0.156.
How to find probability?1. Find the rate parameter (λ):
λ = 1/2.725 ≈ 0.367
2. To find P(X ≥ 2):
P(X ≥ 2) = 1 - P(X < 2).
The (pdf) is:
P(X < x) = 1 - e^(-λx)
P(X < 2) = 1 - e^(-0.367 * 2) ≈ 0.527
P(X ≥ 2) = 1 - 0.527 ≈ 0.473
3. To find P(X ≤ 3):
P(X ≤ 3) = 1 - e^(-0.367 * 3) ≈ 0.683
4. To find P(2 ≤ X ≤ 3):
P(2 ≤ X ≤ 3) = P(X ≤ 3) - P(X ≤ 2) = 0.683 - 0.527 ≈ 0.156
The probability that duration at least 2 hours is 0.473, at most 3 hours is 0.683, and between 2 and 3 hours is 0.156.
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10. A bag contains 3 red marbles, 7 white marbles, and 5 blue marbles. You draw 3 marbles, replacing each one before drawing the next. What is the probability of drawing a red, then a blue, and then a white marble?
the probability of drawing a red, then a blue, and then a white marble is [tex]=\frac{7}{225}[/tex]
To find probability, we take the number of ways the specific event can occur and divide it by the number of ways any event can occur.
The probability of drawing a red marble is: (of red marbles) / (total # of marbles) = 3/(3 + 7 + 5) = 3÷15 = 1÷5.
The probability of drawing a blue marble is: ( of blue marbles) / (total # of marbles) = 5/(3 + 7 + 5) = 5÷15 = 1÷3.
The probability of drawing a white marble is: ( of white marbles) / (total # of marbles) = 7/(3 + 7 + 5) = 7÷15.
Now, we want these events to all to occur for us. So, we must multiply them by each other: (1/5) * (1/3) * (7/15) [tex]=\frac{7}{225}[/tex]
Thus, the probability is [tex]=\frac{7}{225}[/tex]
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Lorenzo's rectangular bedroom is 16 feet by 12
feet. What is the diagonal distance from one
corner to the opposite corner?
feet
Pythagorean theorem word problem
Answer:
20
Step-by-step explanation:
c²=a²+b²
c²=16²+12²
c²=400
c=20
(co 1) in a normally distributed data set of how long customers stay in your store, the mean is 44.8 minutes and the standard deviation is 2.6 minutes. within what range would you expect 95% of your customers to stay in your store? g
You can expect 95% of your customers to stay in your store between range of 39.7 minutes and 49.9 minutes.
To determine the range in which 95% of your customers would stay in your store, we will use the properties of a normally distributed data set with a mean of 44.8 minutes and a standard deviation of 2.6 minutes.
Identify the mean and standard deviation.
The mean is 44.8 minutes, and the standard deviation is 2.6 minutes.
Determine the z-score for a 95% confidence interval.
A 95% confidence interval corresponds to a z-score of 1.96. This means that 95% of the data lies within 1.96 standard deviations from the mean.
Calculate the range using the z-score, mean, and standard deviation.
To find the lower and upper limits of the range, we will multiply the standard deviation (2.6 minutes) by the z-score (1.96) and then subtract or add the result to the mean (44.8 minutes).
Lower limit: Mean - (Z-score × Standard deviation)
44.8 - (1.96 × 2.6) = 44.8 - 5.096 ≈ 39.7 minutes
Upper limit: Mean + (Z-score × Standard deviation)
44.8 + (1.96 × 2.6) = 44.8 + 5.096 ≈ 49.9 minutes
State the range in which 95% of customers would stay in the store.
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PLS Give answer for 7. 8. 9.
Answer:
7. shifted right 8 units
8. shifted left 4 and up 12 units
9. shifted up 8 units
Step-by-step explanation:
You want to compare the given functions with p(x) = a(x -h)² +k and tell the value and effect of a, h, and k on the vertex.
TransformationsIn the equation for p(x) above, the value 'a' represents a vertical scale factor. It expands the graph vertically by the factor 'a'. If a < 0, the graph is reflected across the x-axis.
The values 'h' and 'k' in the equation for p(x) represent a right shift of the graph by 'h' units and a shift up by 'k' units. That is, the graph is translated by (h, k).
7. g(x)We have h = 8. The graph is shifted right 8 units.
8. h(x)We have (h, k) = (-4, 12). The graph is shifted left 4 units and up 12 units.
9. f(x)The values of the transformation parameters are a = -1/2 and k = 8. The vertical compression and reflection do not affect the vertex. The vertex is shifted up 8 units.
9. A box contains 8 identical soup cans. The soup cans are tightly packed, as shown below.
(4 pts)
10 in.
16 in.
8 in.
What is the total volume, in cubic inches, of all 8 soup cans?
Round your answer to the nearest tenth of a cubic inch.
Answer: 1280 in³
Step-by-step explanation:
Volume of 8 Soup Cans = Volume of box
V = l x b x h
V = 10 x 16 x 8
V = 1280
help asappp will give brainliest !!!!!!!!!!!!
Step-by-step explanation:
Remember that in order to find the volume you need to multiply 6.3 x 2.4 x 8. I don't know for sure but if that is true the answer should be 120.96. If they ask you to round I think you know how to do that.
Hope this helps.
how can i get equation b from equation a
1) You will Rewrite both side by combining like terms. Thus, option D is correct.
2) Yes, they have same solution x = 2.
How to balance an equation?Balancing an equation in math typically refers to solving an equation for a specific variable. The goal is to isolate the variable on one side of the equation and simplify the other side. The steps for balancing an equation in math can vary depending on the type of equation, but here are some general steps to follow:
1) Identify the variable you want to solve for.
You have given:
5x - 2 + x = x - 4
Also
5x - x = x - 4
Here, as you can see x - 4 is common in both equation, (option D) Rewrite one side (or both) by combining like terms i.e. x - 4:
5x - 2 + x = 5x - x = x - 4
4x - 2 = 4x = x - 4
4x - 4x - 2 = x - 4
- 2 = x - 4
4 - 2 = x
x = 2
Thus, You will Rewrite both side by combining like terms. Thus, option D is correct.
2) Yes, they have same solution x = 2
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a basket contains 14 apples, of which two are rotten. a sample of three apples is selected at random. what is the probability that the sample contains two rotten apples?
The probability that the sample contains two rotten apples is 0.0612.
The sample of three apples can be selected in 14C3 (14 choose 3) ways and the probability that we select a rotten apple will be 2/14 and the probability of selecting an apple that is not rotten is 12/14.
Now we can apply the binomial distribution formula, to calculate the probability as follows,
P = (3 choose 2) × (2/14)² × (12/14)
P = (3! / (2! × 1!)) × (2/14)² × (12/14)
P = 3 × (1/49) × (12/14)
P = 0.06122449
So, the probability of selecting a sample of three apples in which 2 are rotten and one is not rotten is 0.0612 or approximately 6.12%.
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What are the equations in graphing form for each parabola?
The parabola's equation is therefore for A: y = 7x2 - 5$1.
As a result, the parabola's equation for B is y = -1/2(x - 1)² + 4.
A parabola with vertex (h,k) has the basic equation y = a(x-h)² + k². In this instance, h=0 and k=-5 are equal because the vertex is at $(0,-5)$. Moreover, the parabola has a point at (-1 . 2). When we substitute these numbers in the general parabola equation, we obtain:
2 = a(-1-0)² -5
7 = a
The parabola's equation is therefore y = 7x2 - 5$1.
What is a parabola?A cone and a plane perpendicular to its side cross to create a symmetrical open plane curve known as a parabola1. It is a U-shaped curve whose vertex and axis of symmetry characterise it. The line dividing the parabola into its two mirror counterparts is known as the axis of symmetry. The parabola's vertex is where the axis of symmetry intersects it.
A parabola's vertex is represented by the equation y = a(x - h)²+ k, where (h,k) represents the vertex. We may utilise the vertex version of the equation and substitute the values of h, k, and the x and y coordinates of the point to determine the equation of a parabola that passes through a particular point and has a certain vertex.
B. Here, the vertex is (1, 4), and the point (5,-4). In the vertex form equation, we may therefore substitute h=1, k=4, x=5, and y=-4 to obtain:
-4 = a(5 - 1)²2 + 4 \s-8 = 16a
a = -1/2
As a result, the parabola's equation is y = -1/2(x - 1)² + 4.
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Find the missing dimension of the cylinder. Round your answer to the nearest tenth.
D
14 in.
Volume = 7433 in.³
d=
the missing dimension (diameter) of the cylinder is approximately 18.9 inches, rounded to the nearest tenth.
what is cylinder ?
A cylinder is a three-dimensional shape that consists of two parallel circular bases connected by a curved surface. It can be thought of as a tube or a can, and is a common shape found in many everyday objects such as soda cans, tubes, and pipes.
In the given question,
To find the missing dimension (diameter) of the cylinder, we can use the formula for the volume of a cylinder:
V = πr²h
where V is the volume of the cylinder, r is the radius of the cylinder, and h is the height of the cylinder.
Since the diameter (D) is twice the radius (r), we can also write:
V = π(D/2)²h
Simplifying this expression, we get:
V = πD²h/4
Multiplying both sides by 4/πh, we get:
D² = 4V/(πh)
Taking the square root of both sides, we get:
D = 2√(V/πh)
Substituting the given values, we get:
D = 2√(7433 in.³/π(14 in.))
D ≈ 18.9 in.
Therefore, the missing dimension (diameter) of the cylinder is approximately 18.9 inches, rounded to the nearest tenth.
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PLEASE HELP ME!!!!!!! 20 points & i’ll mark brainliest
see picture for equation
a-write the first four terms
b- does this series diverge or converge?
c- if the series has a sum, find the sum
Step-by-step explanation:
a) from n = 1 to 4 this equals
-4 -4 (2/3) -4 (2/3)^2 - 4 (2/3)^3
= -4 - 8/3 - 16/9 - 32/27
b) converges === since common ratio, r= (2/3) is less than 1
c ) sum = -4 / ( 1-r) = -4 / (1- 2/3 ) = -12
What are the zeros of f(x) = x² + x - 30?
OA. x=-15 and x = 2
OB. x= -6 and x = 5
OC. x = -2 and x = 15
D. x = -5 and x = 6
SUB
Answer:
x=6 and x=−5.
Mia is buying a computer monitor that is 18
inches tall and has a distance of 30 inches
between opposite corners. What is the width of
Mia's new monitor?
inches
This problem is a Pythagorean theorem word problem
Answer:
To solve this problem, we can use the Pythagorean theorem, which states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse.In this case, the height of the monitor is one leg of the right triangle, and the width of the monitor is the other leg. The distance between opposite corners is the hypotenuse.Let w be the width of the monitor in inches. Then we have:w^2 + 18^2 = 30^2Simplifying and solving for w, we get:w^2 + 324 = 900
w^2 = 576
w = 24Therefore, the width of Mia's new monitor is 24 inches.
Step-by-step explanation:
can someone please help thank you
Answer:
I'm sorry your paper is not clear please retake the picture and again attached it
Step-by-step explanation:
Pls answer fast!!! Whoever gets it correct first gets a brainly!!!!
Answer:
[D] No, it is not a polynomial
Step-by-step explanation:
Polynomial- (Have)
constantsvariablesexponents that are combined using mathematical operators: additionsubtractionmultiplicationdivisionPolynomial -(Can't/Don't)
Don't have negative exponentCan't be divided by a variableVariables can't be inside a radicalit must contain no square roots of variablesNo variables in the denominators of any fractions etc..There are 3 different types of polynomials:
monomial: has 1 termbinomial: has 2 termstrinomial: has 3 termsAs we can see based on the given;
5x²y⁴ + x√3 isn't a polynomial.
As a result, the answer is [D] No, it is not a polynomial
RevyBreeze
an artist needs to enlarge a statue by making each linear dimension 75% greater. if n cm3 of clay was used to make the original sculpture, how many cubic centimeters of clay are needed to make the larger sculpture?
To make the larger sculpture with each linear dimension 75% greater, the artist needs to use 265.625% or 3.65625 times more clay than the original sculpture.
Let's assume that the original sculpture is a cube with side length x cm. Therefore, its volume would be x³ cm³.
To make the larger sculpture, each linear dimension needs to be increased by 75%, which means that each side length will become 1.75x cm. Thus, the new volume of the sculpture will be (1.75x)³ = 5.378125 x³ cm³.
To find the amount of clay required to make the larger sculpture, we need to find the ratio of the new volume to the original volume (5.378125 x³ cm³) / (x³ cm³) = 5.378125
This means that the artist needs to use 5.378125 times more clay than the original amount used to make the larger sculpture.
Therefore, to find the actual amount of clay needed, we multiply the original amount of clay by 5.378125: n cm³ x 5.378125 = 5.378125n cm³
So, the artist needs to use 3.65625 or 265.625% times more clay than the original sculpture to make the larger sculpture with each linear dimension 75% greater.
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What is the side of the triangle of area is (2/5) And one side is (6/5)
By answering the presented question, we may conclude that Therefore, Pythagorean the length of the third side of the triangle is [tex]2/\sqrt(5)[/tex]and the height is 4/5.
what is Pythagorean theorem?The Pythagorean theorem is a fundamental mathematical principle that describes the connection between the sides of a right triangle. It asserts that the sum of the squares of the other two sides' lengths equals the square of the hypotenuse's length (the side opposite the right angle). The mathematical theorem is as follows: c2 = a2 + b2 Where "c" denotes the hypotenuse length and "a" and "b" indicate the lengths of the other two sides, known as the legs.
Let's use the formula for the area of a triangle:
[tex]A = 1/2 * b * h2/5 = 1/2 * (6/5) * h\\h = 4/5\\a^2 = (6/5)^2 - (4/5)^2\\a^2 = 36/25 - 16/25\\a^2 = 20/25\\a^2 = 4/5\\[/tex]
[tex]a = \sqrt(4/5)\\a = 2/\sqrt(5)[/tex]
Therefore, the length of the third side of the triangle is [tex]2/\sqrt(5)[/tex]and the height is 4/5.
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Problems 11 & 12. Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar. If the triangles are similar, write a valid similarity statement.
The triangles KJL and GJL are not similar in figure 1 whereas in figure 2 the triangles RST and RPQ are similar by SSS similarity criteria.
What is similar triangle?The triangles are said to be similar if all the angles in one triangle are equal or congruent to the corresponding angles in another triangle and the sides are proportional. There are different criterias for similarity of triangles namely SSS, SAS, ASA/AAS and RHS. According to the criteria/rule
SSS(SIDE-SIDE-SIDE):two triangles are said to be similar if three sides of one triangle are proportional to the corresponding sides of another triangle.
SAS(SIDE-ANGLE-SIDE):The triangles are said to be similar if two sides are proportional and an included angle is congruent to the two sides and included angle of another triangle.
ASA(ANGLE-SIDE-ANGLE):The triangles are said to be similar if two angles are congruent and an included side is proportional to the two angles and included side of another triangle.
RHS(RIGHT-HYPOTENUSE-SIDE):The triangles are said to be similar if one angle is right angle in both triangles, also the hypotenuse and any one side is proportional to the hypotenuse and any one side of another triangle.
Q11)In ΔKJL and ΔGJH,
∠KJL = ∠GJH {vertically opposite angles}
But the sides aren't proportional to each other.
∴The given triangles are not similar.
Q12)Consider the triangles ΔRST and ΔRPQ ,
∠SRT = ∠PRQ {Common angle}
As we know that, = { and }
By basic proportionality theorem, we can say that ST is parallel to PQ.
∴∠RST = ∠RPQ {corresponding angles} and
∠RTS = ∠RQP {corresponding angles}
All angles of ΔRST are congruent to corresponding angles of ΔRPQ.
The sides are proportional to each other:
RS= 35 units; RP= 35+14=49 units
ST=25 units; PQ=35 units
RT=30 units ; RQ=30+12=42 units
All three sides are proportional.
∴ ΔRST and ΔRPQ are similar by SSS.
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The jacobs family is planning to buy a home they have some money for. Down payment already they see a home they like and compute that they would need to borrow 213,000 from a bank over a 30-year period the apr is 3.75%
3 part question
A. What is the monthly payment to the nearest 10th
b. What is total if all of the monthly payments over the 30 years
C. What is her total interest for the 30 years
Step-by-step explanation:
A. To calculate the monthly payment, we can use the formula for a fixed-rate mortgage:
M = P * (r*(1+r)^n) / ((1+r)^n - 1)
where:
M = monthly payment
P = principal (amount borrowed) = $213,000
r = monthly interest rate = APR / 12 = 0.0375 / 12 = 0.003125
n = total number of payments = 30 years * 12 months/year = 360
Plugging in these values, we get:
M = 213000 * (0.003125*(1+0.003125)^360) / ((1+0.003125)^360 - 1)
M ≈ $988.32
So the monthly payment, rounded to the nearest 10th, is $988.30.
B. The total amount paid over the 30-year period would be the monthly payment multiplied by the total number of payments:
Total = M * n
Total = $988.30 * 360
Total = $355,788.00
So the total amount paid over 30 years would be $355,788.00.
C. To calculate the total interest paid over the 30-year period, we can subtract the principal from the total amount paid:
Total Interest = Total - P
Total Interest = $355,788.00 - $213,000
Total Interest = $142,788.00
So the total interest paid over the 30-year period would be $142,788.00.