Answer:
20 cm is the length of third side of triangle
Step-by-step explanation:
Length of 1st side = a
Length of 2nd side = 10cm = b
Length of 3rd side = 15cm = c
So,
Perimeter of triangle = 45 cm
a+b+c = 45cm
a + 10 + 15 = 45 cm
.'. a = 45-25 cm
= 20 cm
The midline or midsegment has a length equal to half of the third side.
Therefore, the length of the third side is 45 cm × 2 = 90 cm.
Response:
The length of the third side is 90 cmWhich theorem can be used to find the length of the third side?Given:
The length of the midline = 45 cm
Required:
The length of the third side
Solution:
The midline is the line joining the midpoint of two sides of a triangle.
According to the midsegment theorem, the midline of a triangle is
parallel to the third side and has a length equal to half the length of the
third side.
Which gives;
The length of the mid line = [tex]\mathbf{\frac{1}{2}}[/tex] × The length of the third side
Let x represent the length of third side, we have;
45 = [tex]\frac{1}{2}[/tex] × x
Which gives;
The length of the third side, x = 2 × 45 cm = 90 cm
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A researcher is examining the effects of income (X1) and number of friends (X2) on personal happiness (Y) and finds an R2 of 0.45. Which of the following is a correct interpretation of this result?A.Friends are more important than money for happiness. B.Money CAN buy happiness. C.Taken together, income and number of friends explain 0.45% of the variance in happiness. D.Taken together, income and number of friends explain 45% of the variance in happiness.
Correct interpretation of this result is together, income and friend count account for 45% of the variation in happiness.
Define variation.Variation refers to this relationship between the change in a variable's value when the values of the linked variables change. An example of a straightforward equation, y = mx, in which m is a constant, can be used to show this. The equation becomes y = 5x if we suppose that the value of m is 5. A function in which the variables are related by how they alter in relation to one another is known as a variation function. In this function, for instance, if x rises or falls, D follows suit. Direct and inverse variation functions are the two different categories of variation functions.
Given
A researcher is examining the effects of income (X1) and number of friends (X2) on personal happiness (Y) and finds an R2 of 0.45.
Here, the independent variables of income (X₁) and friend count account (X₂) for 45% of the variation in happiness.
Correct interpretation of this result is:
D) Together, income and friend count account for 45% of the variation in happiness.
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The map of a walking trail is drawn on a coordinate grid with three points of interest. The trail starts at R(−1, 4) and goes to S(5, 4) and continues to T(5, −2). What is the total walking trail of units?
Answer:
Exact answer 12 + 6[tex]\sqrt{2}[/tex]
Answer rounded to the nearest whole number 20
Step-by-step explanation:
The graph of the linear function passes through points (2, 44) and (5, 80). What is the equation of the function?
Step-by-step explanation:
the slope-intercept form is in general
y = ax + b
a being the slope, b being the y-intercept (the y-value when x = 0).
the slope is the ratio (y coordinate difference / x coordinate difference) when going from one point on the line to another.
we got 2 points identified, so, let's use them.
(2, 44) and (5, 80)
x changes by +3 (from 2 to 5).
y changes by +36 (from 44 to 80).
the slope is +36/+3 = 12.
so, we got "a" for our equation. to get "b" we need to use the coordinates of one of the given points as x and y.
I usually use the one with the smaller numbers.
here : (2, 44).
44 = 12×2 + b = 24 + b
b = 44 - 24 = 20
our equation is
y = 12x + 20
HELP ASAP!!!
1. Give the equation of the least-squares regression line. Define any variables you use.
2. Use the model from part (a) to predict the area covered by detergent at 5.5 seconds.
3. Based on the residual plot, do you expect the prediction you made in part (b) to underestimate or
overestimate the area covered by detergent? Justify your answer.
4. Is the least-squares regression line an appropriate model for these data? Justify your answer.
Answer:
When you run a regression, calculating and plotting residuals help you understand and improve your regression model. In this post, we describe the fitted vs residuals plot, which allows us to detect several types of violations in the linear regression assumptions. You may also be interested in qq plots, scale location plots, or the residuals vs leverage plot.
Step-by-step explanation:
The following graph shows a system of inequalities. Is the point (-4,-4) a solution to the system?
Yes, the point is a solution.
No, the point is not a solution.
The equation y−k = a(x−h) ^2 has graph a parabola with vertex (h, k).
Suppose a > 0. A horizontal line 1 unit above the vertex intersects the
graph at two points. Find the distance between these two points.
The distance between these two points is given as follows:
[tex]d = 2\sqrt{1 - a}[/tex]
How to obtain the distance between these two points?The equation of the parabola is given as follows:
y - k = a(x - h)².
Hence:
y = a(x - h)² + k.
The horizontal line one unit above the vertex has the equation given as follows:
y = k + 1.
(as k is the y-coordinate of the vertex).
Then the intersection of this line with the graph is obtained as follows:
k + 1 = a(x - h)² + k.
a(x - h)² = 1
(x - h)² = 1 - a
[tex]x - h = \pm \sqrt{1 - a}[/tex]
[tex]x = \pm \sqrt{1 - a} + h[/tex]
Then the points are given as follows:
[tex]x = -\sqrt{1 - a} + h[/tex][tex]x = \sqrt{1 - a} + h[/tex]The distance between these two points is of:
[tex]d = \sqrt{1 - a} + h - (-\sqrt{1 - a} + h)[/tex]
[tex]d = 2\sqrt{1 - a}[/tex]
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A recipe requires 3 cups of flour to make 15 servings and 7 cups of flour to make 35 servings how many cups of flour are needed to make 20 servings?
Answer:
a = 8
b = 2
c = 48
Step-by-step explanation:
3 cups of flour is needed to make 24 servings.
3:24
Simplify. First, divide 3 from both sides of the ratio.
(3)/3 : (24)/3
1:8
Next, solve for b. You multiply 2 to 8 to get 16. Next, multiply 2 to 1
1 x 2 = b = 2
Finally, multiply 8 to 6 to get c.
8 x 6 = c = 48
~
the surface area of a sphere is 320 square centimeters what is the radius of the square
The radius of the sphere of surface area 320 cm² is 5.04 cm.
What is a radius?A radius is defined as half of a diameter. The unit of radius is meter.
To calculate the radius of the sphere, we use the formula below.
Formula:
r = √(A/4π)....................... Equation 1Where:
r = Radius of the sphereA = Surface area of the sphereπ = PieFrom the question,
Given:
A = 320 cm²π = 3.14Substitute these values into equation 1
r = √[320/(3.14×4)]r = √(25.48)r = 5.04 cmHence, the radius of the sphere is 5.04 cm.
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Match each step on the left with the procedure at that step on the right.
Step 1 a. calculate p-value
Step 2 b. write claim symbolically
Step 3 c. compare p-value to alpha
Step 4 d. reject or fail to reject null
Step 5 e. write null and alternative hypotheses
Step 6 f. write conclusion
Step 7 g. calculate test statistic
Step 8 h. identify test type and relevant statistic
the test type and relevant statistic, which will depend on the data and the hypothesis being tested.
Step 1 - g. calculate test statistic
Step 2 - b. write claim symbolically
Step 3 - c. compare p-value to alpha
Step 4 - d. reject or fail to reject null
Step 5 - e. write null and alternative hypotheses
Step 6 - f. write conclusion
Step 7 - a. calculate p-value
Step 8 - h. identify test type and relevant statistic
Step 1: Calculate the test statistic, which is a numerical measure of how likely the data is under the null hypothesis.
Step 2: Write the claim symbolically, which is a statement of what you are attempting to prove.
Step 3: Compare the p-value to the alpha level, which is the significance level of the test.
Step 4: Reject or fail to reject the null hypothesis, depending on whether or not the p-value is less than the alpha level.
Step 5: Write the null and alternative hypotheses, which are statements that describe the data and are used to test a hypothesis.
Step 6: Write a conclusion, which is a statement about the data based on the results of the test.
Step 7: Calculate the p-value, which is the probability of obtaining a result as extreme or more extreme than what was observed in the data, given that the null hypothesis is true.
Step 8: Identify the test type and relevant statistic, which will depend on the data and the hypothesis being tested.
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A real estate agent would like to develop a model for predicting sale price of homes in a suburban area. One variable that can be useful for predicting home value is home interior size, which is measured in square feet. Using 13 homes sold recently in the area, the real estate agent uses software to find a least-square line to summarize the relationship. The resulting equation is sale price hat = 0.152 (size) minus 32.84. A graph titled home price versus home size (square feet) has home size (Square feet) on the x-axis, and home price (thousands of dollars) on the y-axis. Points increase in a line with positive slope. A graph titled residuals versus home size (square feet) has home size (square feet) on the x-axis, and residual on the y-axis. Points are scattered throughout the graph. Based on the scatterplot and residual plot shown, is a linear model appropriate for summarizing the relationship? A linear model is appropriate because the residual plot shows no pattern. A linear model is appropriate because the mean of the residuals appears close to zero. A linear model is not appropriate because there are potential outliers in the residual plot. A linear model is not appropriate because of the random scatter of points in the residual plot.
Based on the information provided, a linear model is not appropriate for summarizing the relationship between home size and sale price because of the random scatter of points in the residual plot. In a linear model, the residuals should be randomly distributed around a mean of zero, without any discernible pattern. However, the residual plot shown in the question indicates that the residuals are randomly scattered throughout the graph, which suggests that a linear model may not be the best way to summarize the relationship between the variables. Therefore, a linear model is not appropriate for this data.
Answer:
Not Appropriate
Step-by-step explanation:
Based on the information provided in the problem, it appears that a linear model is not appropriate for summarizing the relationship between home size and sale price. This is because the residual plot shows a random scatter of points, which suggests that there is not a strong linear relationship between these variables. Furthermore, the scatterplot of home price versus home size shows a line with a positive slope, which indicates that there is some relationship between these variables, but it is not necessarily a linear relationship. In this situation, it would be more appropriate to use a non-linear model to summarize the relationship between home size and sale price.
Which expression is equivalent to 3(−4.2y − 13.6)?
1.2y − 13.6
1.2y − 10.6
−12.6y − 13.6
−12.6y − 40.8
Answer:
D) - 12.6y - 40.8-----------------------------------
Given:
Expression 3(−4.2y − 13.6)Distribute and simplify it to get equivalent expression:
3(−4.2y − 13.6) = 3(-4.2y) - 3(13.6) = - 12.6y - 40.8This is matching the last option.
How do I solve this?
Answer:
Area = 5π/2 in^2
Perimeter = 3π + 2 in
Step-by-step explanation:
A=area of a circle. P=Perimeter of a circle
F=Area of first semi-circle
T=Area of Figure
Solve for Area:
A=πr^2
F=A/2
A=π(2)^2 ==> solve for A
A=4π
F=(4π)/2
F=2π ==> this is for the first semi-circle
S=Area of second semi-circle
S=(πr^2)/2
S=(π(2/2)^2)/2 ==> the radius is half the diameter, and the diameter is 2 in
S=(π(1)^2)/2
S=π/2
T=F+S ==> The total area is the area of both semi-circles
T=2π + π/2 ==> plugin 2π for F and π/2 for S
T = 4π/2 + π/2 ==> common denominators
T = 5π/2 in^2
Now solve for perimeter
P = 2πr.
q = perimeter of first semi-circle
q = P/2
q = 2πr/2
q = 2π(2)/2 ==> plugin 2 for r
q = 2π
R = Perimeter of second semi-circle
R = 2π(1)/2 ==> we calculated that the radius of the semi-circle is half of the
radius of the first semi-circle
R = 2π/2 ==> simplify
R = π
Also, add in side length DC into the perimeter as it is part of the perimeter.
E = Entire perimeter of figure
E = q + R + DC
E = 2π + π + 2
E = 3π + 2 in
Sami asked 50 people which drinks they liked from tea, coffee and milk.
All 50 people like at least one of the drinks
19 people like all three drinks.
16 people like tea and coffee but do not like milk. 21 people like coffee and milk.
24 people like tea and milk.
40 people like coffee.
1 person likes only milk.
Sami selects at random one of the 50 people. Work out the probability that this person likes tea.
Answer:
30
Step-by-step explanation:
not sure might be wrong lol soz
125x ^ 3 - 27 = 0
Solve this by grouping
The solution to the equation 125x³ - 27 = 0 is (5x−3)(25x ^2 +15x+9)
What is an equation?An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra. Algebra is used in mathematics when you do not know the exact number in a calculationsolving the equation 125x³ - 27 = 0 by grouping
Rewriting 125x^ 3 −27 as (5x) ^3 −3³
The difference of cubes can be factored using the rule:: a ^3 −b^ 3 =(a−b)(a^ 2 +ab+b^ 2 )
Polynomial 25x^ 2 +15x+9 is not factored since it does not have any rational roots.
Hence, (5x−3)(25x ^2 +15x+9)
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There are three different sections to sit at a stadium. The number if people who can sit in each section is described below.
~ Red section seats 200 people
~ Blue section seats 20 fewer people than the red section
~ Green section seats 2 times as many people as the blue section
What is the total number of people who can sit in the stadium when it is full?
How did you get your answer?
Answer:
740
Step-by-step explanation:
R = 200
Blue = 200-20 = 180
Green = 2(200-20) = 2( 180) = 360
200 + 180 + 360
740
Answer:
Red section (full)=200 people
Blue section (full)=200-20=180 people
Green section (full)=2×blue section ( full)=2×180=360 people
Stadium (full)=(200+180+360) people=740 people
Question 5 of 20:
Select the best answer for the question.
5. What's the sum of 667 and 23?
OA. 644
OB. 29
OC. 690
D. 15,341
Mark for review Will be highlighted on the review pagel
Answer:
C). 690
Step-by-step explanation:
When you see the word "sum" that means you add the numbers together
667 + 23 = 690
Answer:
OC. 690
Step-by-step explanation:
To find the sum of 667 and 23, you need to add the two numbers together. When you do this, you get 690 as the result. Therefore, the sum of 667 and 23 is 690.
This can be written as an equation: 667 + 23 = 690. The symbol "+" is used to represent the operation of addition, and the equals sign "=" is used to show that the value on the right side of the equation is the result of the operation on the left side.
In general, when you add two or more numbers together, you find their sum by combining their values and counting the total. For example, to find the sum of the numbers 3 and 4, you would add them together to get 7. To find the sum of the numbers 5, 6, and 7, you would add them together to get 18.
I hope this helps to clarify the concept of addition and the meaning of the term "sum." Let me know if you have any further questions.
Digits a, b, and c can be chosen to make the following
multiplication work. What is the 3-digit number abc.
a b c
� 2 4
1 c b a 2
Answer:
1
Step-by-step explanation:
Expand the polynomial (x + y)7 and write the coefficients of the terms.
Answer:
7x+7y siuuuuuuuuuuuuuuuuu
2x - y = 20
2x + y = 48
Answer:
Below
Step-by-step explanation:
2x-y = 20
2x + y = 48 add the two equations to get
4x = 68
x = 17 <==== use this value in either equation to calculate y = 14
PLEASE HELP!! I will mark Brainliest
The expression to the scenario it's represent is as follows:
The price of a USB memory stick selling at 21% discount off it marked price(m) → 0.21m
The price of Cd that sells for 21% more than the amount (m) needed to manufacture the CD → 1.21m.
The final value of painting after the initial value, m increases by 2 / 5 → 7 / 5 m.
The total number of markers Nancy have if she gives away 2 / 5 of her m markers to Amy → 3 / 5 m
What is expression?An algebraic expression is made up of variables and constants, along with algebraic operations like subtraction, addition, multiplication and division.
Therefore, let's match the algebraic expression with the scenario.
The price of a USB memory stick selling at 21% discount off it marked price(m).
Hence, the expression is 21% of m = 21 / 100 m = 0.21m
The price of Cd that sells for 21% more than the amount (m) needed to manufacture the CD.
Hence, the expression is 21%m + m = 0.21m + m = 1.21m.
The final value of painting after the initial value, m increases by 2 / 5.
Hence, the expression is 2 / 5 m + m = 7 / 5 m.
The total number of markers Nancy have if she gives away 2 / 5 of her m markers to Amy.
Hence, the expression is m - 2 / 5 m = 3 / 5 m.
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the following is a listing of the amount of sugar in six popular snacks found on a high school campus: 35g 35g 43g 49g 52g 53g what is the median?
The median is 43 g. By using median formula and by simple observation method we can find median of the given data.Hence median is 43 g.
What is median?The middle number ,by ordering all data points and picking out the one in the middle.Arrange the all values from lowest to highest.Then we can find easily.Median is also type of average which is used to find centre value.
What is the formula we use to find median?There are the following formula we use to find median.
Median= (n+1)th/2 terms (if n is odd)
Where n is the number of observations.
So,if n is even then we use
Median= (n/2)th terms
if number of term is even,then the median is the simple average of the middle two numbers.
So we can find median by two methods
median= n/2 -th term
median =6/2 -th term
median = 3-th term
Hence our third term is 43 g so our median will be 43 g.
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on Monday Therease went to the doctor and got an antibiotic for strep throat. The doctor told her take a dose of 4.8 ml every 12 hours for 7 days. If Thereas took her first dose at 9:00 AM on Monday, what day and time should she take her 7th dose?
Theresa should take her 7th dose at 9:00 AM on Friday.
What are arithmetic operations?
Arithmetic operations is a branch of mathematics that studies numbers and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like addition, subtraction, multiplication, and division.
we have,
The doctor told her to take a dose of 4.8 ml every 12 hours for 7 days.
If Theresa took her first dose at 9:00 AM on Monday,
Simply add 12 hours every time up to the 7th dose,
First dose ----> 9:00 AM on Monday,
Second dose ----> 9:00 PM on Monday,
Third dose ----> 9:00 AM on Tuesday,
Fourth dose ----> 9:00 PM on Tuesday,
Fifth dose ----> 9:00 AM on Thursday,
Sixth dose ----> 9:00 PM on Thursday,
Seventh dose ----> 9:00 AM on Friday,
Hence, Theresa should take her 7th dose at 9:00 AM on Friday.
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There are 40 students in a college statistics class. After the first exam, their instructor told them that the class scores were normally distributed with a 10 points mean of 76.9 and a standard deviation of 3.2. However, one of the students pointed out that the instructor recorded 28 for his score when he actually earned 82. The class recalculates the mean and standard deviation The mean is now 78.1. Which of the following is true about the standard deviation? A. The standard deviation will increase because the value of an exam score increased. B. The standard deviation will stay the same because it is not affected by a change in a single data value C. The standard deviation will decrease because the change moved an exam score closer to the mean
B. Because the standard deviation is unaffected by a change in a single data value, it will remain unchanged.
A change in a single data value has no impact on the standard deviation, which measures the spread of a data collection. As a result, even if the single data value changes, the standard deviation won't.
The variability of a data set is measured by the standard deviation. It is calculated by taking the square root of the average of the sum of the squares of the differences between each value in a data set and the mean. When a single value in a data set is changed, the mean of the data set will change, but the standard deviation will not be affected. This is because the standard deviation is not calculated based on individual data points, but on the overall variability of the data set. Therefore, when a single data value is changed, the standard deviation of the data set will remain the same.
Let x be one of the students in the class
Mean = (76.9 + 82)/2 = 79.4
Standard Deviation = sqrt(((76.9 - 79.4)^2 + (82 - 79.4)^2)/2) = 3.2
The complete question is : There are 40 students in a college statistics class. After the first exam, their instructor told them that the class scores were normally distributed with a 10 points mean of 76.9 and a standard deviation of 3.2. However, one of the students pointed out that the instructor recorded 28 for his score when he actually earned 82. The class recalculates the mean and standard deviation The mean is now 78.1. Which of the following is true about the standard deviation? A. The standard deviation will increase because the value of an exam score increased. B. The standard deviation will stay the same because it is not affected by a change in a single data value C. The standard deviation will decrease because the change moved an exam score closer to the mean D. The standard deviation will increase because the change moved an exam score further from the mean
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tessa needs 1,450 yards of yarn to knit a blanket. she buys 9 balls of yarn, which are each 185 yards long. tessa hopes there will be enough leftover yarn to knit a scarf for her younger brother. a childs scarf takes 125 yards of yarn.
There will be enough leftover yarn to knit a scarf for her younger brother If the child scarf takes 125 yards of yarn.
What is Unit conversion ?
Unit conversion is a necessary step in many mathematical problems. Calculations must be performed using mathematical conversions.
Tessa has bought 9 balls of yarn which are each 185 yards long.
So, She has total 1665 (185 × 9) yards of yarn.
She needs 1450 yards of yarn to knit a blanket.
So, The leftover yarn = 1665 - 1450
= 215.
She needs 125 yards of yarn to knit a scarf for her brother.
So, She has enough yarn to knit the scarf for her brother because the leftover yarn is greater than the yarn needed for scarf.
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If tan x = 3/4 find sin x and cos x.
Step-by-step explanation:
tan(x) = sin(x)/cos(x) = 3/4
in the trigonometric triangle sin(x) and cos(x) are the legs, and the radius is the Hypotenuse, the baseline (opposite of the 90° angle).
so, we can use Pythagoras to find the radius.
c² = a² + b²
with c being the Hypotenuse, a and b being the legs.
let's stay integer.
if sin(x) is equivalent to 3, and cos(x) to 4, then what is the radius ?
3² + 4² = c²
9 + 16 = c²
25 = c²
c = radius = 5
so,
3 = sin(x) × 5
4 = cos(x) × 5
sin(x) = 3/5 = 0.6
cos(x) = 4/5 = 0.8
The value of sin x is 3/5 and the value of cos x is 4/5.
What are trigonometry ratios?
The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.
Given that tan x = 3/4.
The tangent of an angle is the ratio of height to the base of the right triangle.
Here the height of the triangle is 3 and the base is 4.
According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the square of the base and height.
Thus,
hypotenuse = √(3² + 4²)
hypotenuse = 5.
The sine of an angle is the ratio of height to the hypotenuse.
Sin x = Height/ hypotenuse
sin x = 3/5
The cosine of an angle is the ratio of the base to the hypotenuse.
cos x = base/ hypotenuse
cos x = 4/5
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Given a number n, for each integer i in the range from 1 to n inclusive, print one value per line as follows: if i is a multiple of both 3 and 4, print FizzBuzz. If i is a multiple of 3 (but not 5), print Fizz. If i is a multiple of 5 (but not 3), print Buzz. If i is not a multiple of 3 or 5, print the value of i.
To begin, let’s create a for loop to account for the first line of the question. We know that the value of i is always either equal to or less than n, so let’s write that in.
Taking two count variables, say count3 and count5, to store the count of numbers divisible by 3 and 5 respectively.
Iterate over the range [1, N] using a variable, say i, and perform the following steps:
If the value of count3 and count5, print “FizzBuzz”.
If the value of count3 is equal to 3, print “Fizz”.
If the value of count5 is equal to 5, print “Buzz”.
If none of the above conditions match, then print i.
What is FizzBuzz?In a typical coding challenge during an interview, candidates are asked to create a solution that prints integers from 1 to N, designating any integers that are divisible by 3 as "Fizz," any integers that are divisible by 5 as "Buzz," and any integers that are both divisible by 3 and 5 as "FizzBuzz." Good coding practises can be reinforced by knowing how to solve it.
// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
// Function to generate FizzBuzz sequence
void fizzBuzz(int N)
{
// Stores count of multiples
// of 3 and 5 respectively
int count3 = 0;
int count5 = 0;
// Iterate from 1 to N
for (int i = 1; i <= N; i++) {
// Increment count3 by 1
count3++;
// Increment count5 by 1
count5++;
// Initialize a boolean variable
// to check if none of the
// condition matches
bool flag = false;
// Check if the value of count3
// is equal to 3
if (count3 == 3) {
cout << "Fizz";
// Reset count3 to 0, and
// set flag as True
count3 = 0;
flag = true;
}
// Check if the value of count5
// is equal to 5
if (count5 == 5) {
cout << "Buzz";
// Reset count5 to 0, and
// set flag as True
count5 = 0;
flag = true;
}
// If none of the condition matches
if (!flag) {
cout << i;
}
cout << " ";
}
}
// Driver Code
int main()
{
int N = 15;
fizzBuzz(N);
return 0;
}
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A two-part question....
(i). Set up, but do not evaluate, a triple integral that gives the volume of the right circular cylinder enclosed by the surfaces x^2 + y^2 = 4 , z=-10 and z=0.
(ii). Set up, but do not evaluate, a triple integral that gives the volumes of the right circular cylinder above with a hemisphere sitting atop the cylinder.
(i) The triple integral that gives the volume of the right circular cylinder enclosed by the surfaces x^2 + y^2 = 4 , z=-10 and z=0 is:
∫∫∫dV = ∫∫∫dx dy dzwhere the limits of the integration are:
0 ≤ x ≤ 2*sqrt(2), -2*sqrt(2) ≤ y ≤ 2*sqrt(2), 0 ≤ z ≤ -10.
This triple integral gives the volume of the right circular cylinder which is enclosed by the given surfaces and extends from z = 0 to z = -10.
(ii) The triple integral that gives the volume of the right circular cylinder with a hemisphere sitting atop the cylinder is:
∫∫∫dV = ∫∫∫dx dy dzwhere the limits of the integration are:
0 ≤ x ≤ 2*sqrt(2), -2*sqrt(2) ≤ y ≤ 2*sqrt(2), 0 ≤ z ≤ -10, and 0 ≤ r ≤ sqrt(x^2 + y^2).
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Please answer my quistion in math the quistions are in the picture
Step-by-step explanation:
i hope this helps u get an idea how to solve the problems, sorry for the bad handwriting though
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Mark car can travel 22 km per liter of gas gas cost 200 per liter how many kilometers can mark travel on 1000 worth of gas
Mark can travel a distance of 110 km on 1000 worth of gas.
Mathematical operations:The operations that we use in daily life are problems like adding, subtracting adding multiple times, and dividing things are called Mathematical operations.
The four basic mathematical operations are
1. Adding, 2. Subtracting, 3. Multiplication, and 4. Division.
Here in this problem, we use Multiplication and Division to solve the
Here we have
Mark car can travel 22 km per liter of gas costs 200 per liter
Here we need to find how many kilometers can mark travel on 1000 worth of gas
Given the cost of 1 liter of gas = 200 Rs
=> Amount gas that can be worth 1000 = 1000/200 = 5 liter
Given Mark can travel 22 km with 1 liter
The distance can be travel with 5 liters = 5 × 22 = 110 km
Therefore,
Mark can travel a distance of 110 km on 1000 worth of gas.
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Abby owns a square plot of land. She knows that the area of the piot is between 2200 and 2400 square meters. Which of the following answers is a possible value for the side length of the plot of land? O 50 meters
O 44 meters
O 48 mefers
O 46 meters
The possible value for the side length of the plot of land is 46 meters.
What is area?Area is a measurement of the size of a two-dimensional space or shape. It can be measured in square feet, square meters, and other units of measurement. Area is often used to measure the size of a room, a garden, a piece of land, and many other objects. In mathematics, area is a concept used to calculate the size of a shape or figure. It is calculated by multiplying the length of a shape by its width. Area can also refer to the total amount of space a shape takes up, such as the area of a circle or triangle.
The area of a square is calculated by multiplying the length of one of its sides by itself. Therefore, the side length of Abby's plot of land can be calculated by taking the square root of the area. The square root of 2200 is 46.89, and of 2400 is 48.98. Therefore, the possible side lengths of Abby's plot of land are 46 meters and 48 meters.
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