The required parameters of a smaller surface area and a smaller amount of metal per can are a radius of 3.05 cm and a height of 6.09 cm.
What is surface area?The measurement that indicates the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina. A three-dimensional shape's surface area is the sum of all of its faces. Finding the area of each face and adding them together gives us the surface area of a form.
Here,
V=πr²h
178=πr²h
πrh=178/r
S=2πr²+2πrh
S=2πr²+2*(178/r)
S=2πr²+356/r
S'=4πr-356/r²
S'=0
4πr=356/r²
r³=356/4π
r³=28.343
r=3.05 cm
h=178/πr²
h=178/(3.14*3.05*3.05)
h=178/29.23
h=6.09 cm
The dimensions needed for less surface area so each can uses less metal is radius as 3.05 cm and height as 6.09 cm.
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For the volume of soap in bottle, ryan determined the margin of error as 354. 85 mL to 354. 95 mL. What was the volume of soap the he measured
If the margin error of the volume of the soap is 354.85 ml to 354.95 ml, then the volume of the soap that he measured is 354.9 ml
The margin of error = 354.85 ml to 354.95 ml
The margin error is defined as the difference between the actual and projected results in a random survey sample. If the actual measurement is x, there is a chance of error in the measurement because of numerous reasons.
The margin of error in the measurement is 354.85 ml to 354.95 ml
In the given options the correct value is 354.9 ml, because it is the middle value of the given margin or error 354.85 ml to 354.95 ml
Therefore, the volume of soap that he measured is 354.9 ml
I have solved the question in general, as the given question is incomplete
The complete question is:
For the volume of soap in a bottle, Ryan determined the margin of error as 354.85 mL to 354.95 ml. What was the volume of soap that he measured? a) 354.8 mL b) 354.85 mL c) 354.9 mL d) 354.95 mL
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if a blood stain has a length of 3.0cm and a width of 1.5cm what is the angle of impact
If a blood stain has a length of 3.0cm and a width of 1.5cm, the angle of impact is 30 degrees
The length of the blood stain = 3 cm
The width of the blood stain = 1.5 cm
The equation for measuring the angle of impact is
sin (angle of impact) = The width of the blood stain / The length of the blood stain
Angle of impact = sin^-1 (The width of the blood stain / The length of the blood stain)
Substitute the values in the equation
Angle of impact = sin^-1(1.5 / 3)
= sin^-1(0.5)
= 30 degrees
Therefore, the angle of impact is 30 degrees
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11-14 are confusing can anyone help and tell me how to get the written answer
Answer:
11) KF = DB
12) DC=YZ
13) <C = <W
14) <S and <K
Step-by-step explanation:
11) For this question, we want to try and use SSS to prove the triangles are congruent. SSS stands for side-side-side postulate, so all sides have to be equivalent. We already have ED = FB as given, and DF = DF due to reflexive property. From this information, we already have two sides. Additional information that would be needed to figure out the third side is KF = DB, as it's the only side we are missing.
12) For this question, we want to use SAS postulate, which stands for side-angle-side. We already have one side congruent, which is BC=YX. We have one angle congruent which is <C = <Y. With this information, we have one side and one angle. This means that we need to find another side that is congruent. The side that we need to find here is DC=YZ, as it will help us prove the triangles are congruent with SAS.
13) For this question, we want to use AAS, which stands for angle-angle-side. We already have one angle congruent, which is <CDE = WDE. We have one side congruent as well, which is DE = DE due to reflexive property. With this given information, we have one angle and one side. We only need one more angle before the other angle to figure this out. The angles that are needed are <C = <W.
14) For this question, we want to use ASA, which stands for angle-side-angle. The one angle we have already is <KTM = <UTS, which is because of vertical angles are congruent. The one side that we have is ST=TK. With this, we have one angle and one side. We just need one more angle to prove this, which would be <S and <K.
Remember, for triangle congruency postulates, they have to be in order. They cannot just be out of order. For example, in question 14, we have to find the measures in order. First we need an angle, side, and then another angle. The first angle is <S and <K, then the side we have is ST=TK, and then our last angle, <KTM = <UTS.
f(x) = 3x³ + 4x² - 2x + 8 and g(x) = 2x³+3x²+5x+2. Find f(x) + g(x)
The value of f(x)+g(x) is 5x³+7x²+3x+10
Given that,
f(x)=3x³+4x²-2x+8
g(x)=2x³+3x²+5x+2
f(x)+g(x)=3x³+4x²-2x+8+2x³+3x²+5x+2
=3x³+2x³+4x²+3x²+5x-2x+8+2
=5x³+7x²+3x+10
Step-by-step explanation:
This question is a type of quadratic equation. To solve this type of question first, we have to put the values of f(x) and g(x). Then we have to put similar terms(which have similar coefficients with similar power)together. Then we add the similar term of f(x) with the similar term of g(x) like 3x³+2x³=5x³, 4x²+3x²=7x², 5x-2x=3x and 8+2=10
Therefore the value of f(x)+g(x) is 5x³+7x²+3x+10
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What are the domain and range of this graph? f(x)=x^5+x^2
Therefore ,the domain and range of this graph f(x)=x^5+x^2
Domain : (-∞,∞), {x|x ∈ R} Range:(-∞,∞), {y|y ∈} R
what is domain?A function's domain is the set of possible values that can be entered. This set reflects the values of x in a function like f. (x). Its range refers to the set of possible values that a function can accept. These are the values that are returned by the function when we enter an x value.
Here,
The domain is all values of x that make the expression defined.
Interval Notation:
(−∞,0)∪(0,∞)
=>(-∞,∞)
The Range is all values of y that make the expression defined.
Interval Notation:
(−∞,0)∪(0,∞)
=>(-∞,∞)
Therefore ,the domain and range of this graph f(x)=x^5+x^2 Domain : (-∞,∞), {x|x ∈ R} Range:(-∞,∞), {y|y ∈} R
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Select the correct answer.
Which expression is equivalent to this polynomial expression?
(82²y9z³y+9y) - (6x³y - zy² + 4y)
OA. 8-3x²y - zy² + 13y
OB.
82² 15z²y + zy² + 5y
O C. -7z²y - zy² + 13y
OD.
-72²y + zy² + 5y
Answer:
B. Just Minus expression with same one
simplify the expression 6²+4x3-18 divided by 6
Answer: The answer to this solution is 5.
If your school uses Desmos pls respond
20 points
Answer:
I use desmos; what do you need help with?
Answer:zegari6636 is king of brainlist
Step-by-step explanation:
My algebra teacher use Desmos and also thanks for the points have a good day do you need help
1) In the figure below Zy Zz and segment
AB I CD.
What is the length of AE?
F. 18
G. 20
H. 24
J. 30
Answer:
F
Step-by-step explanation:
15/10 = x+12/12
180=10x+120
x=6
x+12=18=AE
If f(x) and its inverse function, f–1(x), are both plotted on the same coordinate plane, what is their point of intersection?
On a coordinate plane, a curve opens down and to the right in quadrants 3 and 4 and then changes direction and curves up and to the left in quadrants 1 and 4. The curve crosses the y-axis at (0, negative 2), changes direction at (1, negative 1, and crosses the x-axis at (2, 0).
The point of intersection of f(x) and [tex]f^{-1}[/tex](x) is (3, 3)
What is a function?"It defines a relation between input and output values."
"In function, for each input there is exactly one output."
What is inverse function?"The inverse function of x = f(m) is m =[tex]f^{-1}[/tex] , where x, m are real values"
For given question,
A function f(x) and its inverse function [tex]f^{-1}(x)[/tex], are both plotted on the same coordinate plane.
We know that the inverse function [tex]f^{-1}(x)[/tex] is the mirror image of the function f(x.)
This means, both the functions must be symmetric about the line y = x.
The curve of inverse function [tex]f^{-1} (x)[/tex] would cross the Y-axis at (0, 2), changes direction at (-1, -1) and crosses the X-axis at (-2, 0)
And both the functions intersect each other only on y = x
The point which satisfy the line y = x is (3, 3)
Therefore, the point of intersection of f(x) and[tex]f^{-1} (x)[/tex] is (3, 3)
The complete question is : If f(x) and its inverse function, f–1(x), are both plotted on the same coordinate plane, what is their point of intersection?
On a coordinate plane, a curve opens down and to the right in quadrants 3 and 4 and then changes direction and curves up and to the left in quadrants 1 and 4. The curve crosses the y-axis at (0, negative 2), changes direction at (1, negative 1, and crosses the x-axis at (2, 0).
A.(0, –2)
B.(1, –1)
C.(2, 0)
D.(3, 3)
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Fred deposits $6,500 in a saving account that pays 0.5% interest, compounded quarterly. Round each answer to the nearest cent.
a. Find the first quarter's interest.
b. Find the first quarter's ending balance.
c. Find the second quarter's interest.
d. Find the second quarter's ending balance.
e. Find the third quarter's interest.
f. Find the third quarter's ending balance.
g. Find the fourth quarter's interest.
h. What is the balance at the end of one year?
i. How much interest does the account earn in the first year?
The amount of interest earned quarterly at 0.5% interest rate compounded quarterly are;
a. Interest for the first quarter = $8.125
b. First quarter ending balance = $6,508.125
c. Interest for the second quarter = $8.13515625
d. Second quarter ending balance = $6,516.26015625
e. Interest for the third quarter = $8.1432520325
f. Third quarter closing balance = $6,524.40548145
g. Interest for the fourth quarter = $8.15550685975
h. The amount of interest earned in a year is about $32.56
What is an interest earned on an amount?
An interest is the amount a borrower pays to a lenders as to make use of the lender's funds.
The amount Fred deposited, P = $6,500
The interest paid by the account, r = 0.5% compounded quarterly
a. The first quarter interest can be found by the formula;
C.I. = P[tex](1+ r/4)^{4 . 1/4}[/tex] - P
Therefore
C.I. = 6500 x (1 + [tex]\frac{0.5/100}{4}[/tex]) - 6500 = 8.125
b. The first quarter ending balance is therefore;
A = P + C.I.
A = $6,500 + $8.125 = $6,508.125
c. The second quarter's interest can be found from the formula;
C.I. = 6508.125 x (1 + [tex]\frac{0.5/100}{4}[/tex]) - 6508.125 = 8.13515625
The second quarter's interest is $8.13515625
d. The second quarter ending balance is therefore;
A = $6,508.125 + $8.13515625 = $6,516.26015625
The second quarter ending balance is $6,516.26015625
e. The third quarters interest is therefore;
C.I. = 6516.26015625 x (1 + [tex]\frac{0.5/100}{4}[/tex]) - 6516.26015625 = 8.1432520325
The third quarter's interest is about $8.1433
f. The third quarter's ending balance is therefore;
A ≈ $6516.26015625 + $8.1432520325 = $6,524.40548145
The third quarter's ending balance is $6,524.40548145
g. The fourth quarter's interest can be found as follows;
C.I. = 6524.40548145 x (1 + [tex]\frac{0.5/100}{4}[/tex]) - 6524.40548145 = 8.15550685975
The fourth quarter's interest is; $8.15550685975
h. The balance at the end of one year is therefore;
Balance = C.I. fourth quarter + Principal for the fourth quarter
Therefore;
Balance = $6,524.40548145 + $8.15550685975 = $6,532.56098831
i. The interest the account earns in a year is therefore;
$6,532.56098831 - $6,500 = $32.5609883
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The starting salary for a new employee is 25,000. The salary for this employee increases by 8% per year. what is the salary after 1 year?
Answer: $27,000
Step-by-step explanation:
Mrs. Smith is planning a field trip for all of the fourth grade students. There are 7 classes of
Fourth graders with 20 students in each class. If 30 students fit on a bus, how many buses will
Mrs. Smith need to reserve for the trip?
Answer:
5 buses
Step-by-step explanation:
Mrs. Smith will need to reserve buses for 7 classes of Fourth graders, with 20 students in each class, for a total of
7 * 20 = <<7*20=140>>140 students.
Since 30 students fit on a bus, Mrs. Smith will need to reserve
140 / 30 = <<140/30=4.67>>4.67 buses.
Since Mrs. Smith can't reserve a partial bus, she will need to reserve 5 buses for the trip.
Answer: 5 busses, you have to multiple the number of students by the amount of classes (7 x 20) to get a product of 140 students. If only 30 can fit on to each bus you have to divide 140 by 30 and you get 4.6666667 so you need to round up to get an answer of 5 busses
Step-by-step explanation:
the salaries of pharmacy techs are normally distributed with a mean of $32,000 and a standard deviation of $3,000. if 25 pharmacy techs are selected at random, what is the probability their average salary is less than $33,200? the answer should be typed as a decimal with 4 decimal places.
The probability their average salary is less than $33,200 is = 0.6554
Given that,
Mean = $32,000
Standard deviation = $3,000
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Standard deviation (SD) is a widely used measurement of variability used in statistics. It shows how much variation there is from the average (mean). A low SD indicates that the data points tend to be close to the mean, whereas a high SD indicates that the data are spread out over a large range of values.
The Z score is used to calculate how many standard deviations above or below the mean the raw score is. It comes from,
z = (x- μ) / σ (Equation-1)
Where,
x=raw score,
μ=mean,
σ=standard deviation
μ=32,000,
σ=3,000
Average salary is less than $33,200
x < 33,200
We can substitute values in Equation-1,
z = (33,200-32,000)/3000
z = 1200/3000
z = 0.4
Using the normal distribution table as a guide,
P(x < 33,200) = P(z < 0.4)
P(x < 33,200) = 1-P(z>0.4)
P(x < 33,200) = 0.6554
Therefore,
The probability their average salary is less than $33,200 is = 0.6554
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For linear function f.f(2)= 0 and f(4)=-6.
Write function f in slope-intercept
How do you find the slope of the line when you have 2 points?
Hence, when [tex]m=-3,b=6[/tex], so the equation of slope is [tex]y=-3x+6[/tex].
What is the slope of line?
The slope of a line gives the measure of its steepness and direction. The slope of a straight line between two points says [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] can be easily determined by finding the difference between the coordinates of the points.
The slope is usually represented by the letter [tex]m[/tex].
Here given that,
The linear function [tex]f(2)= 0[/tex] and [tex]f(4)=-6[/tex].
Let the linear function is
[tex]y=mx+b[/tex]
[tex]x=2,y=0[/tex]
Then
[tex]0=m(2)+b\\\\2m+b=0[/tex] .......[tex](1)[/tex]
And for
[tex]f(4)=-6\\x=4,y=-6[/tex]
[tex]-6=m(4)+b\\\\4m+b=-6[/tex] ......[tex](2)[/tex]
Solving equation [tex](1)[/tex] and [tex](2)[/tex], we get
In equation [tex](1)[/tex]
[tex]b=-2m[/tex] ........[tex](*)[/tex]
Substitute [tex]b=-2m[/tex] in equation [tex](2)[/tex]
[tex]4m-2m=-6\\\\2m=-6\\\\m==\frac{6}{2}\\\\m=-3[/tex]
Put [tex]m=-3[/tex] in [tex](*)[/tex] equation
[tex]b=2m\\\\b=-2(-3)\\\\b=6[/tex]
Hence, when [tex]m=-3,b=6[/tex], so the equation of slope is [tex]y=-3x+6[/tex].
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It costs £80.50 to buy 7 skirts. How much does it
cost to buy 10 skirts? Give your answer in pounds
(£).
Answer:
£115
Step-by-step explanation:
For the three-part question that follows, provide your answer to each question in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of your response as Part A, Part B, and Part C.
A bag contains three blue marbles, five red marbles, and four green marbles.
Part A: What is the probability of selecting three marbles where one is blue and two are green?
Part B: What is the probability of selecting one blue marble and then selecting three red marbles?
Part C: In your own words, write a short paragraph that explains your work for Parts A and B.
a) The probability of selecting three marbles where one is blue and two are green is of: 0.0818 = 8.18%.
b) The probability of selecting one blue marble and then selecting three red marbles is of: 0.0152 = 1.52%.
c) The probabilities were obtained dividing the number of desired outcomes by the number of total outcomes, and all the possible combinations were considered.
How to obtain the probabilities?The probabilities are obtained as the division of the number of desired outcomes by the number of total outcomes.
The outcomes with one blue and two green are given as follows:
Blue (3/12 probability) then two green, with 4/11 and 3/10 probabilities.Green then blue then green.Green, green then blue.Hence a multiplication for 3 is used for the probability, as follows:
p = 3 x 3/12 x 4/11 x 3/10 = 0.0818 = 8.18%.
For blue then three red, the outcomes are given as follows:
Blue (3/12 probability).Red: 5/11.Red: 4/10.Red: 3/9.Thus the probability is of:
p = 3/12 x 5/11 x 4/10 x 3/9 = 0.0152 = 1.52%.
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Evaluate the expression for a = 3, b = 2, and c = 4.
2a - b + c
Answer:
The expression is 2 * 3 - 2 + 4 = 8.
Step-by-step explanation:
In this expression, the variables a, b, and c are given specific values. Substituting these values into the expression, we have 2 * 3 - 2 + 4, which simplifies to 8.To evaluate an expression, we substitute the given values for the variables and carry out the operations according to the order of operations (i.e. parentheses, exponents, multiplication and division, addition and subtraction). In this case, the expression is already fully simplified, so we don't need to do any further calculations.
Roanne earned $5 for 1/2 of an hour of babyitting. How much would Roanne make in 1 hour
Using simple mathematical operations, we can conclude that Roanne will earn $10 in 1 hour.
What are mathematical operations?A mathematical "operation" is the process of calculating a value utilizing operands and a math operator.
There are predefined rules associated with the math operator's symbol that must be applied to the supplied operands or numbers.
The order of operations refers to the rules that govern how to solve an expression with several operations.
Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction are all referred to as PEMDAS (from left to right).
So, we know that:
Roanne earns $5 for 1/2 hour.
Roanne will earn in 1/2 * 2 = 1 hour:
5 * 2 = $10
Therefore, using simple mathematical operations, we can conclude that Roanne will earn $10 in 1 hour.
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10mm
5mm
13mm
Trapezium
The area of the trapezium will be = 90[tex]mm^{2}[/tex]
According to the figure of the trapezium =
Let us consider the length of base a = 5mm
length of base b = 13mm
height h of the trapezium = 10mm
According to the formula of the area of trapezium
= (1/2) x h x (a + b)
= (1/2) x 10 x (13 + 5)
= 5 x 18
= 90[tex]mm^{2}[/tex]
Therefore, the area of the trapezium will be = 90[tex]mm^{2}[/tex]
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The complete question here could be- Find the area of the trapezium given base a= 5mm, base b= 13mm and height h= 10mm
What is the vertex of this question
The vertex of the parabola y = x² - 16x + 24 will be at (8, -40). Then the correct option is D.
What is the equation of the parabola?Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
The equation is given below.
y = x² - 16x + 24
Convert the equation into vertex form, then we have
y = x² - 16x + 24
y = x² - 2·8·x + 8² - 8² + 24
y = (x - 8)² - 64 + 24
y = (x - 8)² - 40
The vertex of the parabola y = x² - 16x + 24 will be at (8, -40). Then the correct option is D.
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Reduce 45/99 to the standard form
Answer:
= 4.54545 × 10^-1
Step-by-step explanation:
[tex] \frac{45}{99} = \frac{5}{11} [/tex]
= 0.45454545
= 4.54545 × 10^-1
I hope this helped
Are x and y proportional?
Answer:
No
Step-by-step explanation:
If you look at the first numbers, 1 and 3, we can see that 1 is being multiplied by 3 to get 3.
But if you look at the second numbers, 2 and 4, then you can see that 2 is not being multiplied by 3 to get 4.
Therefore, it is not proportional.
Dennis Anderson purchased four gallons of milk for $11.67. Find the unit price per gallon rounded to the nearest cent.
Answer:
$2.92
Step-by-step explanation:
Divde $11.67 by the 4 gallons that Dennis bought.
11.67/4=2.9175
round to the nearst cent (or hundreths place)
since 7 is greater than 5, it rounds up
$2.92
If 9, 12, 15 is a Pythagorean Triple, which of the following could also be a Pythagorean Triple?
a) 5,7,9
b) 17, 20, 23
c) 36, 48, 60
d) 19, 22, 25
Answer:
c) 36, 48, 60
Step-by-step explanation:
A Pythagorean Triple is a set of positive integers (a, b, c) that follows the rule:
[tex]\boxed{a^2+b^2=c^2}[/tex]
where a < c and b < c.
It always consists of:
all even numbers, ortwo odd numbers and an even number.When a and b are both even, c is even.
When one of a and b is odd and the other is even, c is odd.
(5, 7, 9) cannot be a Pythagorean Triple since it consists of all odd numbers.
(17, 20, 23) is not a Pythagorean Triple since:
[tex]\implies 17^2+20^2=23^2[/tex]
[tex]\implies 289+400=529[/tex]
[tex]\implies 689 \neq 529[/tex]
(36, 48, 60) is a Pythagorean Triple since:
[tex]\implies 36^2+48^2=60^2[/tex]
[tex]\implies 1296+2304=3600[/tex]
[tex]\implies 3600=3600[/tex]
(19, 22, 25) is not a Pythagorean Triple since:
[tex]\implies 19^2+22^2=25^2[/tex]
[tex]\implies 361+484=625[/tex]
[tex]\implies 845\neq 625[/tex]
a new dictionary in the shape of a rectangular prism will have a thickness of 333 inches (\text{in})(in)(, start text, i, n, end text, ). the volume of the dictionary will be 216\,\text{in}^3216in 3 216, start text, i, n, end text, cubed. what must be the area of the front cover, a face perpendicular to the thickness, in square inches?
The area of the front cover a face perpendicular to the thickness is 72in²
What is a rectangular prism?
Having six faces, a rectangular prism is a three-dimensional shape (two at the top and bottom, and four are lateral faces). The prism's faces are all rectangular in shape. There are three sets of identical faces as a result. A rectangular prism is often referred to as a cuboid because of its shape.
Here, we have
Given:
A new dictionary in the shape of a rectangular prism will have a thickness of 3 inches.
The volume of the dictionary will be 216in².
Volume = W×L×H
Surface = volume/ height
= 216/3
= 72in²
Hence, the area of the front cover of a face perpendicular to the thickness is 72in².
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--7x-7y= 28
2x - 7y = 1
please solve this systems of eqautions
After solving the equation the linear equation is x = 27/5 , y = 7/5.
What do you mean by linear equation?
Equations with the highest degree of 1 are called linear equations. This means that the exponent of the variable in the linear equation is greater than 1. The graph of a linear equation is always a straight line.
A linear equation is an algebraic equation in which each term has exponent 1, and the graph of this equation is always a straight line. For this reason, it is called a "linear equation".
Given system of equation:
7x - 7y = 28 ..........(1)
2x - 7y = 1 .............(2)
Solve this system of linear equation. Find the value of 7y from equation (1) and substitute in equation(2)
7x - 7y = 28
7x - 28 =7y .............(3)
Substitute this value in equation (2)
2x - (7x - 28) = 1
2x - 7x + 28 = 1
-5x + 28 = 1
5x = 28 - 1
5x = 27
x = 27/5
Substitute this value in equation (3)
7y = 7(27/5) - 28
7y = 189/5 - 28
7y = 49/5
y = 7/5
Therefore, x = 27/5 , y = 7/5
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find using distributive property.{[7]\frac{x}{y}[/5]×([-3]\frac{x}{y}[/12])}±{[7]\frac{x}{y}[/5]×[5]\frac{x}{y}[/12]
The value of expression will be;
⇒ 7 / 30
⇒ - 14/15
What is Distributive property?
By the rule of distributive property, multiplying the sum of two or more addends by a number gives the same result as when each addend is multiplied individually by the number and the products are added together.
Given that;
The expression is,
⇒ [ 7/5 × - 3/12 ] ± [ 7/5 × 5/12 ]
Now,
Since, The expression is,
⇒ [ 7/5 × - 3/12 ] ± [ 7/5 × 5/12 ]
Solve the expression by using distributive property as;
⇒ [ 7/5 × - 3/12 ] ± [ 7/5 × 5/12 ]
⇒ [ 7/5 ] × [ - 3/12 ± 5/12 ]
It gives two solution as;
⇒ 7/5 × [ - 3/12 + 5/12 }
⇒ 7/5 × 2/12
⇒ 7/5 × 1/6
⇒ 7 / 30
And, 7/5 × [ - 3/12 - 5/12 }
⇒ 7/5 × - 8/12
⇒ 7/5 × - 2/3
⇒ - 14 / 15
Thus, The value of expression will be;
⇒ 7 / 30
⇒ - 14/15
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The area of a triangle is 474. Two of the side lengths are 87 and 19 and the included angle is acute. Find the measure of the included angle, to the nearest tenth of a degree.
Answer:
Let $x$ be the measure of the included angle. We can use the formula for the area of a triangle to find an equation in terms of $x$.
The area of a triangle is given by $\frac{1}{2}bh$, where $b$ is the length of the base and $h$ is the length of the altitude from the base to the opposite vertex. In this case, the base is 87 and the altitude is the length of the line segment from the vertex opposite the included angle to the base, which we can find using the Law of Sines:
$$\frac{h}{\sin x} = \frac{19}{\sin(180^\circ-x)}$$
$$h = \frac{19\sin x}{\sin(180^\circ-x)}$$
Substituting this expression for $h$ into the formula for the area of the triangle, we get
$$\frac{1}{2}bh = \frac{1}{2} \cdot 87 \cdot \frac{19\sin x}{\sin(180^\circ-x)} = 474$$
Solving this equation for $x$ is somewhat difficult, but we can use a calculator or computer to approximate the value of $x$. Using a calculator, we find that $x \approx 31.4^\circ$. Rounding to the nearest tenth of a degree, the measure of the included angle is $\boxed{31.4^\circ}$.
Step-by-step explanation:
A group of 10 students took tests in math, English, and chemistry.
The scatter plots compare the students’ scores on the tests
Complete the sentences to describe the data.
The math and English scores show
a positive correlation
a negative correlation
no correlation
The math and chemistry scores show
a positive correlation
a negative correlation
no correlation
The correlation of the scatterplots are defined as;
The math and English scores show; A positive correlation.
The math and chemistry scores show; A negative correlation
What is the correlation of the scatterplot?In correlation in statistics, it could either be positive correlation, negative correlation or no correlation at all.
A positive correlation is defined as a relationship between two variables that tend to move in the same direction. Thus, a positive correlation exists in the event that one variable tends to decrease while the other variable decreases, or one variable tends to increase while the other variable increases.
A negative correlation is defined as a relationship between two variables whereby one variable increases while the other decreases, and vice versa.
No correlation means there is no relationship between the two variables.
Now, for scatterplot of the math and English scores shown, we see that majority of the english scores increase as the maths scores increase and as sch it is a positive correlation.
Meanwhile, for the math and chemistry scores shown, majority of the maths score decreases with an increase in the chemistry score and as such this is a negative correlation.
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