Answer:
24.5
Step-by-step explanation:
we know that x=7
so 7x/2 (just a fancy way of saying x multiplied by 7/2)=
7*7/2= 24.5
Hope this helps! :)
USE SAS
Q4 - Import admission data and answer the following question. */
proc import datafile='/.../m3_admission_data.csv' /* update .../ with path containing m3_admission_data.csv*/
dbms=csv replace out=score;
run;
/*Q4.1, Using conditional logic, write code to create a categorical variable based on the variable 'GRE':
<305 LOW 305-325: MEDIUM > 325: HIGH */
***ANSWER: ; ********;
/*Q5(10 pts), Write a code to generate today's date such as '19FEB2023', then print out*/
The today is 19th February 2023, it will print '19FEB2023'.
Answer:In order to create a categorical variable based on the variable GRE using SAS, we will use conditional logic as mentioned in the question. Here's how the code will look like:proc import datafile='/.../m3_admission_data.csv' /* update .../ with path containing m3_admission_data.csv*/ dbms=csv replace out=score; run;data score; set score;if GRE < 305 then GRE_Category = 'LOW'; else if 305 <= GRE <= 325 then GRE_Category = 'MEDIUM'; else if GRE > 325 then GRE_Category = 'HIGH'; run;In order to generate today's date, we will make use of the date function which will return today's date. We will then use the PUT function to format the date in the desired format 'ddmonyyyy'. Here's how the code will look like: data _null_; today = date(); /* get today's date */ today_formatted = put(today, date9.); /* format the date */ put today_formatted; run; This will print today's date in the format 'ddmonyyyy'. For example, if today is 19th February 2023, it will print '19FEB2023'.
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what is the slope of the line?
Answer:
Slope = (-3/2)
Step-by-step explanation:
Slope(m) = (Y2 - Y1) / (X2 - X1)
= (0-3) / (2-0)
= (-3/2) Is the ans....
Find the rate of change of given functions. (a) [6pt] \( f(x)=-5 x^{2}+3 x-7 \) (a) (b) [8pt] \( g(x)=\frac{-5 x+7}{2 x-3} \) (b)
The rate of change of each given function are:
f(x) = 5x² + 3x - 7; f'(x) = 10x + 3g(x) = [tex]\frac{-5x + 7}{2x - 3}[/tex]; [tex]g'(x)=\( \frac{-10x+11}{(2x-3)^2} \)[/tex]To find the rate of change of given functions, we have to differentiate the given function w.r.t the variable provided. We will solve each part of the question and differentiate the functions step by step.
(a) f(x) = 5x² + 3x - 7The function is, f(x) = 5x² + 3x - 7
Differentiating the above function, we get;
f'(x) = (5x² + 3x - 7)/dx
f'(x) = 10x + 3
Therefore, the rate of change of function f(x) = 5x² + 3x - 7 is 10x + 3.
Now, let us solve the second part of the question.
(b)[tex]\( g(x)=\frac{-5 x+7}{2 x-3} \)[/tex]The function is,[tex]\( g(x)=\frac{-5 x+7}{2 x-3} \)[/tex]
Differentiating the above function using the quotient rule, we get;
[tex]\[\begin{aligned} g'(x)&=\frac{(2x-3)\cdot (-5)-(7)\cdot(2)}{(2x-3)^2}\\ &=\frac{-10x+11}{(2x-3)^2}\end{aligned}\][/tex]
Therefore, the rate of change of function [tex][tex]\( g(x)=\frac{-5 x+7}{2 x-3} \) is \( \frac{-10x+11}{(2x-3)^2} \).[/tex][/tex]
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The side length of a square is (√2-3√5) meters. Find the area of the square and write your answer in simplest radical form
Answer:
47 - 6√10
Step-by-step explanation:
Area of a square of side a = a²
Here a = √2 -3√5
Area A = a² = (√2 -3√5)²
We know that (a - b)² = a² -2ab +b²
So
A = (√2 -3√5)²
= (√2)² - 2(√2)(3√5) + (3√5)²
(√2)² = 2 because (√a)² = a
(3√5)² = 3² x (√5)² = 9 x 5 = 45
2(√2)(3√5) = 2 (√2 · 3 · √5)
= 2 x 3 √2 √5
√2√5 = √10
2 x 3 √2 √5 = 2 · 3 · √10 = 6√10
Therefore area = 2 - 6√10 + 45
= 47 - 6√10
The price of a box of pencils has been steadily increasing by $1.10 per year. The cost of a box of pencils is now $2.19. (3 pts) Write an equation to model the cost of pencils, g(x), in x years. g(x) =
An anthill has a volume of 8792 mm^3 of dirt. It’s radius is 20 mm.
Use 3.14 for pi and round your answer to the nearest mm if necessary.
The height of the cone is 11 mm and the slant height of the cone is 23 mm and the ant crawls 31 mm to get from the base of the cone to the top of the hill.
What is the volume of the right circular cone?
A right circular cone is a three-dimensional geometric shape that has a circular base and a vertex that is located directly above the center of the base. The axis of the cone is a line that passes through the vertex and the center of the base.
The volume of a right circular cone can be found using the formula:
[tex]V = (1/3)\pi r^2h[/tex]
where V is the volume of the cone, r is the radius of the circular base, and h is the height of the cone.
1) To find the height of the cone, we need to use the formula for the volume of a cone, which is [tex]V = (1/3)\pi r^2h[/tex]. Rearranging this formula, we get:
[tex]h = 3V / \pi r^2[/tex]
Substituting the given values, we get:
[tex]h = 3(8792) / (3.14)(20^2)[/tex]
h ≈ 11
Therefore, the height of the cone is approximately 11 mm.
2) To find the slant height of the cone, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In the case of the cone, the slant height is the hypotenuse of a right triangle formed by the height and the radius of the base. Therefore, we have:
[tex]s^2 = r^2 + h^2[/tex]
Substituting the values we found in part 1, we get:
[tex]s^2 = 20^2 + 11^2[/tex]
s ≈ 23
Therefore, the slant height of the cone is approximately 23 mm.
3) To find the distance the ant crawls to get from the base of the cone to the top of the hill, we can use the Pythagorean theorem again. This time, we need to find the distance along the slant height from the base of the cone to the top of the hill. This distance is the hypotenuse of a right triangle formed by the distance from the base to the apex (which is the height of the cone) and the radius of the base. Therefore, we have:
[tex]d^2 = r^2 + s^2[/tex]
Substituting the values we found in parts 1 and 2, we get:
[tex]d^2 = 20^2 + 23^2[/tex]
d ≈ 31
Therefore, the ant crawls approximately 31 mm to get from the base of the cone to the top of the hill.
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(write the standard form of the equation of each line)
helllp—-
Answer: 3x + 5y = -15
Which one isn’t a polynomial?
d is not a polynomial coz it has negative power
What is the equation of the line that has a slope of -3 and passes through the point (2, 2)? Select all that apply.
Answer: The equation of a line can be written in slope-intercept form as:
y = mx + b
where m is the slope and b is the y-intercept.
We are given that the line has a slope of -3 and passes through the point (2, 2). We can use the point-slope form of the equation of a line to find the equation of this line:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope.
Substituting the given values, we get:
y - 2 = -3(x - 2)
Expanding the right side:
y - 2 = -3x + 6
Adding 2 to both sides:
y = -3x + 8
Therefore, the equation of the line that has a slope of -3 and passes through the point (2, 2) is:
y = -3x + 8.
So the correct answer is:
y = -3x + 8
Step-by-step explanation:
Answer:
y=-3x+8
3x+y=8
y-2=-3(x-2)
u have a blessed day bru
Tell weather(3,20) is a solution of y=4x+8
Answer:
Step-by-step explanation:
To determine whether (3, 20) is a solution of y = 4x + 8, we need to substitute x = 3 and y = 20 into the equation and check whether the equation is true:
y = 4x + 8
20 = 4(3) + 8
20 = 12 + 8
20 = 20
Since the equation is true, we can say that (3, 20) is a solution of y = 4x + 8.
Answer:
Step-by-step explanation:
y= 4x+8
substituting x=3,
y= 4(3)+8
y= 12+8
y=20
∴ (3,20) is a solution of y= 4x+8
105 + what gives you 169?
Answer:
64
Step-by-step explanation:
When you have 105+x=169
x=64
If you do 169-105 you get 64
64+105=169
which of the following measurements does not express volume?
A. 4ft 2
B. 10in 3
C. 125cm 3
D. 9m 3
The measurements that does not express volume is (a) 4ft^2
How to determine the measurement that is not volumeFrom the question, we have the following parameters that can be used in our computation:
The list of options
The measure of volume is represented by cubic unit
Using the above as a guide, we have the following:
The measurement that does not express volume is 4ft^2.
4ft^2 is a measurement of area (square footage), whereas the other three options are measurements of volume.
This is so because:
10in^3 is cubic inches, which is a measurement of volume.125cm^3 is cubic centimeters, which is a measurement of volume.9m^3 is cubic meters, which is a measurement of volume.So, the unit is (a) 4ft^2
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Here is a map of a town.
It has a scale of 2 cm to 7 km.
A centimetre ruler is shown on the map.
What is the real-life distance between the ice rink and the theatre?
The real-life distance between the ice rink and the theater is given as follows:
14 km.
How to obtain the real-life distance?The real-life distance between the ice rink and the theater is obtained applying the proportions in the context of the problem.
The scale of 2 cm to 7 km means that each 2 cm drawn on the map represent a real distance of 7 cm.
The distance is of 4 cm on the map, hence the actual distance between the ice rink and the theater is obtained as follows:
4/2 x 7 = 14 km.
Missing Information
The distance is of 4 cm on the map.
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The table shows the party affiliation of the 100 senators of the 109th Congress. The ratio of Republicans to Democrats is 5:4. How many senators
are Democrats? Independents?
Complete the table. Enter your answers in the boxes.
Number of
Senators
Party
Affiliation
Republican
Democrat
55
Independent
There are 44 Democratic senators and no Independent senators based on ratio.
Since the ratio of Republicans to Democrats is 5:4, we can represent the number of Republican senators as 5x and the number of Democratic senators as 4x, where x is a positive integer. The total number of senators is given as 100, so we have:
5x + 4x + Independent = 100
Simplifying:
9x + Independent = 100
To find the values of x and Independent, we need to solve for these variables. We can start by subtracting Independent from both sides of the equation:
9x = 100 - Independent
Now, we need to find a value of x that makes the right-hand side of the equation divisible by 9. Since the sum of the digits of 100 is 1 + 0 + 0 = 1, which is not divisible by 9, we need to find a value of Independent that makes the sum of the digits of 100 - Independent divisible by 9. The only value that works is Independent = 1, which gives us:
9x = 99
x = 11
Now we can substitute this value of x back into the equation to find the number of Republican and Democratic senators:
Republican = 5x = 5(11) = 55
Democrat = 4x = 4(11) = 44
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A figure on a coordinate plane is dilated using the rule (6/5x, 6/5y). Tyson says the dilation was a reduction and tashi says the dilation was an enlargement who is correct
The dilation is an enlargement, and Tashi is correct.
How to determine the dilation?To determine whether the dilation (scaling) is a reduction or an enlargement, we need to compare the distances between corresponding points on the original figure and the dilated figure.
Suppose a point P(x,y) is on the original figure. After the dilation with the rule (6/5x, 6/5y), the corresponding point P'(x', y') will be:
P' = (6/5x, 6/5y)
The distance between point P and the origin is given by:
d(P) = √(x² + y²)
The distance between point P' and the origin is:
d(P') = √((6/5x)² + (6/5y)²)
= 6/5 * √(x² + y²)
Since the dilation multiplies each coordinate by a factor of 6/5, the distance between any point and the origin is multiplied by a factor of 6/5.
Therefore, if 6/5 < 1, then the distances between corresponding points are reduced, and the dilation is a reduction. If 6/5 > 1, then the distances are increased, and the dilation is an enlargement.
In this case, we have:
6/5 > 1
Therefore, the dilation is an enlargement, and Tashi is correct.
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Six small and four medium bottles of lotion give a combined total of 93 fluid ounces of lotion. Which of the following pieces of information could help you determine the number of fluid ounces of lotion in a small bottle and the number of fluid ounces in a medium bottle?
Please answer this question. Giving out BRAINLIEST.This is due today, please help.
Answer:
B
Step-by-step explanation:
In answer choice B, there is the same number of medium bottles as the number of medium bottles that you are given in the question.
Because you know that there are 93 fluid ounces in six small bottles and four medium bottles, you know that any different amount of fluid ounces with the answer choice would be because of the increase in small bottles.
By having a consistent change with only one variable (which is the small bottle) you can find the rate of change. Once you figure out how many fluid ounces are in the small bottles, you can find the total amount of fluid ounces that are in the small bottles. The amount that remains is the total fluid ounces for medium bottles.
Survey of 200 students at least 4 8 2 servings 7 3 servings 5 1 or less servings 5 what is the percent of students choose
2 or 3 servings ?
Around 76.5% of the 200 students polled said they would eat two or three servings, with 48.2% saying they would eat two and 28.3% saying they would eat three.
To get the percentage of students who select two or three servings, we must first add the 48 and 73 students who select two and three servings, respectively, for a total of 121 students.
The percentage is then calculated by dividing this sum by the total number of students polled (200), and multiplying the result by 100: (121/200) x 100 = 60.5%
As a result, 2. or 3. servings were selected by 60.5% of the students questioned. It's important to note that this estimate makes the assumption that each student will only select one option (2 servings or 3 servings), not both.
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4. Joey is trying to determine the volume of his toy box. He is able to
completely fill the base of the toy box with eight 1-inch cubes. After
creating 2 more layers, the entire toy box is filled. What is the volume of his
toy box?
The volume of Joey's toy box is 24 cubic inches.
If the base of the toy box is filled with 8 1-inch cubes, then the volume of the base is:
Volume of base = 8 cubes x [tex](1 inch/cube)^3[/tex] = 8 cubic inches
If the toy box has two more layers on top of the base, then it has a total of three layers. Let's call the height of each layer "h". Then the total height of the toy box is:
Total height = 3h
The volume of each layer is the same as the volume of the base, which is 8 cubic inches. Therefore, the volume of the entire toy box is:
Volume of toy box = volume of base + volume of 2 layers
Volume of toy box = 8 cubic inches + 2(8 cubic inches)
Volume of toy box = 8 cubic inches + 16 cubic inches
Volume of toy box = 24 cubic inches
Therefore, the volume of Joey's toy box is 24 cubic inches.
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If A and B are two mutually exclusive events with P(A)=0.45 and P(B)=0.45 , find the following probabilities: a) P(A and B)= b) P(A or B)= c) P(notA)= d) P(notB)= e) P(not(A or B))= f) P(A and ( not B))= Note: You can earn partial credit on this problem. You have attempted this problem 0 times. You have unlimited attempts remaining.
The probabilities of the events are:
a) P(A and B) = 0
b) P(A or B) = 0.9
c) P(notA) = 0.55
d) P(notB) = 0.55
e) P(not(A or B)) = 0.1
f) P(A and (not B)) = 0.45
How to find the probability of A and B?Probability is the measure of the likelihood or chance of an event occurring. It deals with the study of random events and the analysis of their outcomes.
Since A and B are mutually exclusive, they cannot happen at the same time. This means that P(A and B) = 0.
a) P(A and B) = 0
b) P(A or B) = P(A) + P(B)
P(A or B) = 0.45 + 0.45 = 0.9
c) P(notA) = 1 - P(A)
P(notA) = 1 - 0.45 = 0.55
d) P(notB) = 1 - P(B)
P(notB) = 1 - 0.45 = 0.55
e) P(not(A or B)) = 1 - P(A or B)
P(not(A or B)) = 1 - 0.9 = 0.1
f) P(A and (not B)) = P(A) - P(A and B)
P(A and (not B)) = 0.45 - 0 = 0.45
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You have 12 balloons to blow up for your party. You blow 1/3 of them, and your friend blows up 5 of them. What fraction of the balloons still need to blowing up?
Answer: One third
Step-by-step explanation: If you blow up a third of the balloons then you've blown 4 up because 12 divided by 3 is 4. Then you add the 5 balloons your friend blew up leaving you with 9 blown-up balloons in total. 9 blown-up balloons out of 12 is 2 thirds of the balloons leaving you with only one-third left to blow up.
Answer:
1/4
I hope this helps you <3
The stem and plot shows different lengths of oak wood available at the carpenters store. A customer purchased the two shortest lengths and the two longest lengths of the oak wood. how many feet of oak wood did the customer purchase
The total length of oak wood the customer purchase is 198 feet
How to determine the total length of oak wood the customer purchaseThe required stem and leaf plot is missing
So, I will make use of the attached plot to answer the question
From the question, we understand that the customer purchase are:
The two shortest lengths The two longest lengthsFrom the attached stem and leaf plot, we have the following readings:
The two shortest lengths = 21 and 23The two longest lengths = 61 and 93When these lengths are added, we have
Total = 21 + 23 + 61 + 93
Evaluate the sum
Total = 198
Hence, the length of purchase is 198 feet
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I need help with this problem please!
Answer: uh don't know
Step-by-step explanation: look it up
Answer: f(x,y)=e^(ax+by) with a^2+b^2=1. Prove that : f''(xx)+f''(yy)=1
Proved that if the function f(x,y)=e^(ax+by) with a^2+b^2=1, then f''(xx)+f''(yy)=1
To find the second partial derivatives of f(x, y), we differentiate f(x, y) twice with respect to x and y:
f'(x, y) = ae^(ax + by) and f''(xx) = a^2e^(ax + by)
f'(x, y) = be^(ax + by) and f''(yy) = b^2e^(ax + by)
Adding these second partial derivatives, we get:
f''(xx) + f''(yy) = a^2e^(ax + by) + b^2e^(ax + by)
Since a^2 + b^2 = 1, we have:
f''(xx) + f''(yy) = e^(ax+by)
But f(x, y) = e^(ax+by), so:
f''(xx) + f''(yy) = f(x, y)
Therefore, we have proved that f''(xx) + f''(yy) = 1.
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What is the value of m(7+9)/n, when m = 0.5 and n = 2?
a 4
b 6
c 8
d 10
Answer:
a.4
Step-by-step explanation: You first work on the parentheses( 7+9)=16. Then you multiply m and 16. Which is 0.5(16) or 16/2=8 now it’s 8/2 which is 4 .
The following table lists the number of unicyclists in Corvallis, OR. By age group.
Age Group Frequency
≤19 16
20-29 86
30-39 1
40-49 1
50-59 68
60-69 15
≥70 14
What is the probability that a randomly selected unicyclist from Corvallis, OR. Is not between 30 and 39?
The probability that an arbitrarily chosen Corvallis unicyclist is not between the ages of 30 and 39 is roughly 0.995, or 99.5%.
To find the probability that a randomly selected unicyclist from Corvallis is not between 30 and 39, we need to first determine the total number of unicyclists in Corvallis. We can find this by summing up the frequencies for all age groups:
Total number of unicyclists = 16 + 86 + 1 + 1 + 68 + 15 + 14 = 201
Next, we need to determine the frequency of unicyclists who are not between 30 and 39. We can do this by adding up the frequencies for all age groups that are not between 30 and 39:
Frequency of unicyclists not between 30 and 39 = 16 + 86 + 1 + 68 + 15 + 14 = 200
Finally, we can calculate the probability of selecting a unicyclist who is not between 30 and 39 by dividing the frequency of unicyclists not between 30 and 39 by the total number of unicyclists:
P(not between 30 and 39) = Frequency of unicyclists not between 30 and 39 / Total number of unicyclists
P(not between 30 and 39) = 200 / 201
P(not between 30 and 39) ≈ 0.995
Therefore, the probability that a randomly selected unicyclist from Corvallis is not between 30 and 39 is approximately 0.995 or 99.5%.
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The events A and B are independent. Suppose P(A) = 0.25 and P(B)
= 0.45. What is the probability of either A or B occurring
The probability of either A or B occurring is 0.55625.
The probability of either A or B occurring when given that events A and B are independent, and P(A) = 0.25 and P(B) = 0.45, can be calculated as follows: 0.25 + 0.45 - 0.25*0.45= 0.55625.:
When the events A and B are independent, then the probability of the two events occurring together is given as:P(A ∩ B) = P(A) × P(B)This is a formula for independent events, and when events A and B are independent, it implies that P(A ∩ B) = 0.
Therefore:P(A ∪ B) = P(A) + P(B) - P(A ∩ B)When the probability of A and B is given as P(A) = 0.25 and P(B) = 0.45, we can substitute these values in the above equation as:P(A ∪ B) = P(A) + P(B) - P(A) × P(B)Thus:P(A ∪ B) = 0.25 + 0.45 - 0.25*0.45= 0.55625Therefore, the probability of either A or B occurring is 0.55625.
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a_(1)=-54;a_(n)=a_(n-1)+7
The nth term of an AP with the first term a_1 and the common difference d is given by a_n = a_1 + (n-1)d. The nth term of the given AP is a_n = -54 + (n-1)7.
What is AP?Arithmetic Progression (AP) is a sequence of numbers in which the difference between the two consecutive numbers is always the same. Each number in the sequence is called a term of the progression. It is a type of sequence where the difference between consecutive terms is constant.
The given expression is an arithmetic progression (AP), in which the common difference between consecutive terms is 7. An AP is a sequence of numbers where each term after the first is formed by adding a fixed value to the preceding one.
The first term of the AP is given as a_1=-54 and the common difference (d) is 7. Thus, the nth term of the given AP can be found using the formula a_n = a_1 + (n-1)d. Substituting the values in this formula, we get a_n = -54 + (n-1)7.
Therefore, the nth term of the given AP is a_n = -54 + (n-1)7.
For example, if n = 10, then the 10th term of the given AP is a_10 = -54 + (10-1)7 = -54 + 63 = 9.
In general, the nth term of an AP with the first term a_1 and the common difference d is given by a_n = a_1 + (n-1)d.
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The nth term of the given AP is [tex]a_n[/tex] = -54 + (n-1)7. The nth term of an Arithmetic Progression with the first term [tex]a_1[/tex] and the common difference d is given by [tex]a_n[/tex] = [tex]a_1[/tex] + (n-1)d.
What is Arithmetic Progression?It is a sequence of numbers in which the difference between the two consecutive numbers is always the same. Each number in the sequence is called a term of the progression.
The given expression is an arithmetic progression (AP), in which the common difference between consecutive terms is 7.
The first term of the AP is given as [tex]a_1[/tex] =-54 and the common difference (d) is 7.
Thus, the nth term of the given AP can be found using the formula
[tex]a_n[/tex] = [tex]a_1[/tex] + (n-1)d.
Substituting the values in this formula, we get
[tex]a_n[/tex] = -54 + (n-1)7.
Therefore, the nth term of the given AP is
[tex]a_n[/tex] = -54 + (n-1)7.
In general, the nth term of an AP with the first term [tex]a_1[/tex] and the common difference d is given by [tex]a_n[/tex] = [tex]a_1[/tex] + (n-1)d.
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Question:
Find the nth term by using the given data.
[tex]a_1[/tex] =-54 ; [tex]a_n[/tex] = [tex]a_(n-1)[/tex] +7
Trevor's stack of books is 7 7/8 inches tall. Rick's stack is 3 times as tall. What is the difference in the heights of their stacks of books?
For rectangle type books, the difference in the heights of their stacks of books is 15 3/4 inches.
What exactly is a rectangle?
A rectangle is a type of quadrilateral (a four-sided polygon) that has four straight sides and four right angles. It is a two-dimensional shape, meaning it lies flat in a plane, and is defined by its two sets of parallel sides, each pair of which are equal in length.
In a rectangle, opposite sides are parallel and congruent (equal in length), and adjacent sides are perpendicular (meet at a right angle). The diagonals of a rectangle bisect each other (divide each other into two equal parts) and are congruent.
The area of a rectangle is calculated by multiplying its length and width, while its perimeter is found by adding the lengths of all its sides. The formula for the area of a rectangle is A = l x w, where A is the area, l is the length, and w is the width. The formula for the perimeter of a rectangle is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.
Now,
To solve this problem, we need to first find out the height of Rick's stack of books. We know that his stack is 3 times as tall as Trevor's stack, so:
Rick's stack = 3 x Trevor's stack
Rick's stack = 3 x 7 7/8 inches
Rick's stack = 23 5/8 inches
Now that we know the height of both stacks, we can find the difference between them:
Difference = Rick's stack - Trevor's stack
Difference = 23 5/8 inches - 7 7/8 inches
Difference = 15 6/8 inches
Difference = 15 3/4 inches
Therefore, the difference in the heights of their stacks of books is 15 3/4 inches.
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The area of the shape that includes squares will be 9 m² and perimeter will be 16m.
What are squares?
A square has four equal sides and four right angles. It is a special type of rectangle, and like rectangles, it is also a two-dimensional shape with all its sides lying in a plane.
A square has several important properties. Its sides are equal in length, and its diagonals are congruent (equal in length) and bisect each other at right angles. All angles in a square are also right angles, which means that it is a special type of rectangle where all angles measure 90 degrees.
The area of a square is calculated by squaring the side. For example, if a square has a side length of s, its area would be A = s². The perimeter of a square is found by adding up the lengths of all four sides, which is P = 4s.
Now,
The sides of the squares will be 2m, 2m and 1 m.
then area of the figure will be =2²+2²+1²
=4+4+1
=9 m²
and
Perimeter = sum of all sides
then Perimeter=5+2+2+2+2+1+1+1
=16 m
Hence,
The area of the shape that includes squares will be 9 m² and perimeter will be 16m.
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the ratio of the measure of angle PQR to the measure of angle PQS is 5:9 what is the measure of PQS A) 10 degrees B) 40 degrees C) 50 degrees D) 80 degrees
The measure of angle PQR is 50 degrees thus correct option is C) 50 degrees.
What is proportion?
A proportion is a statement that two ratios or fractions are equal. In proportion, the numerator of one fraction is proportional to the numerator of another fraction, and the denominator of one fraction is proportional to the denominator of another fraction. For example, if we have two ratios, a/b, and c/d, we can write them as a proportion as follows:
a/b = c/d
This means that the ratio of a to b is equal to the ratio of c to d. We can also write this as a fraction:
a/b = c/d = (a/b)/(c/d)
If the measure of angle PQR to the measure of angle PQS is in the ratio of 5:9, and the measure of angle PQS is 90 degrees, we can use this information to find the measure of angle PQR.
Let x be the measure of angle PQR in degrees. Then we can set up the following proportion:
5/9 = x/90
To solve for x, we can cross-multiply:
9x = 5 * 90
9x = 450
x = 50
Therefore, the measure of angle PQR is 50 degrees. Answer choice C) 50 degrees is the correct answer.
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Find the missing dimension of the cone. Round your answer to the nearest tenth.
Volume = 3.6 in.³
[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=3.6\\ h=4.2 \end{cases}\implies 3.6=\cfrac{\pi r^2(4.2)}{3}\implies 10.8=4.2\pi r^2 \\\\\\ \cfrac{10.8}{4.2\pi }=r^2\implies \sqrt{\cfrac{10.8}{4.2\pi }}=r\hspace{5em}\stackrel{\textit{diameter = 2r}}{2\sqrt{\cfrac{10.8}{4.2\pi }}} ~~ \approx ~~ \text{\LARGE 1.8}[/tex]