To Find = Diameter, Area
Solution :
Diameter = 2 × Radius
Diameter = 2 × 6cm
Diameter = 12 cm
Area = 2πr
[tex]area \: = 2 \times \frac{22}{7} \times 6cm[/tex]
[tex]area \: = \frac{264}{7} [/tex]
[tex]area \: = 37.7 \: cm[/tex]
____________________________________2. Given : Diameter = 8 DM
( 1dm = 10 cm
8dm = 8 × 10 = 80cm )
To find : Radius , area
Solution :
[tex]raduis \: = \frac{1}{2} \times diameter[/tex]
[tex]radius \: = \frac{1}{2} \times 80cm[/tex]
[tex]radius \: = 40 \: cm \: or \: 4dm[/tex]
Area = 2πr
[tex]area \: = 2 \times \frac{22}{7} \times 40[/tex]
[tex]area \: = \frac{1760}{7} [/tex]
[tex]area \: = 251.4cm \: \: \: or \: 25.14dm[/tex]
____________________________________3. Given : Radius = 2.5m
To find : Diameter , Area
Solution :
Diameter = 2 × radius
Diameter = 2 × 2.5m
Diameter = 5m
Area = 2πr
Area = 2 × 22/7 × 5m
Area = 220/7
Area = 31.4m
Type the expression that results from the following series of steps:
Start with
y
, subtract 7, multiply by 3, then add 6.
Answer:
3y-15
Step-by-step explanation:
(y-7)3=3y-21
3y-21+6=3y-15
Solve for x: -24 = 6x
1/4
-4
4
- 1/4
Answer:
-4
Step-by-step explanation:
[tex]~~~~~-24 = 6x\\\\\\\implies -\dfrac{24} 6 = \dfrac{6x}6\\\\\\\implies x = -4[/tex]
The White Russian cocktail contains vodka, Tia Maria and milk in the ratio of 5:2:3. To make the cocktail for a party the barman used 180ml of milk. What was the total volume of the cocktail? If this was served in 60ml glasses, how many glasses would it serve?
Answer:
1) 600cm^3 2) 10 glasses
Step-by-step explanation:
x = total amount in ml
(3/10)x = 180ml (MILK)
x = 600ml
(2/10)600 = 120ml (TIA MARIA)
(1/2)600 = 300ml (VODKA)
1) 600cm^3
2) 600ml : 60ml = 10 (GLASSES)
1.
In AXYZ, |XZ| = 13 cm, XY = 12 cm and
ZXYZ = 90°. Find YZ if the area of the
triangle is 30 cm².
Step-by-step explanation:
I think you mean triangle XYZ. and angle XYZ.
so, the angle at Y is 90°.
that makes XZ the Hypotenuse (baseline opposite of the 90° angle) of the right-angled triangle.
so, we can actually use Pythagoras (we don't need the area of the triangle to solve) :
13² = 12² + YZ²
169 = 144 + YZ²
25 = YZ²
YZ = 5 cm
just to check - the area of this triangle is (remember, it is a right-angled triangle, so XY and YZ serve also as baseline and height) :
area = 12 × 5 / 2 = 60/2 = 30 cm²
correct, it fits.
Find the circumference of a circle that has a diameter of 2 ft. Use 3.14 for pi.
5.14 ft
6.28 ft
12.56 ft
7.14 ft
Answer:
6.28 ft
Step-by-step explanation:
using the formula [tex]\pi d[/tex] to find the circumference of the circle, you substitute the numbers. 3.14(2). 3.14 x 2 = 6.28 hence the answer
The total area of town C and town D is 120,000 square miles. The area of town C is 30,000 square miles more than that of town D. Find the area land of each town.
Answer:
Find the area land of each town.
Let x be the area of town D
then, x+ 30000 is the area of town C
we know that,
the total area of town C and town D is 120,000 square miles.
x+x+30000=120000
2x= 90000
x=45000
Area of town D= 45000 square miles
Area of town C= 45000+30000= 75000 square miles.
27
C
A
54
B
Based on the diagram, which expresses all possible
lengths of segment AB?
O AB = 25
O 27
OAB = 85
O AB< 27 or AB > 81
Answer:
B. 27 < AB < 81
Step-by-step explanation:
The triangle inequality requires that the length of any given side of a triangle be greater than the difference and less than the sum of the other two sides.
__
application54 -27 < AB < 54 +27
27 < AB < 81
_____
Additional comment
Some versions of the triangle inequality allow the "or equal to" case.
27 ≤ AB ≤ 81
Apparently, the one used here does not.
If the sum of the two short sides is equal to the long side, the "triangle" looks like a line segment. Its altitude and area are zero.
Find the value of x.
6
14
8
0
21
x = [ ? ]
3x-12
Answer: 7
Step-by-step explanation:
By the angle bisector theorem,
[tex]\frac{21}{14}=\frac{3x-12}{6}\\21(6)=14(3x-12)\\126=14(3x-12)\\9=3x-12\\21=3x\\x=\boxed{7}[/tex]
help please!!! i need to turn this in tomorrow
Answer:
$10955.6157151671
Step-by-step explanation:
Amount [A] = [tex]P(1+r)^{t}[/tex]
Here, P = principal (which is $5000)
r = rate of interest in decimal form(which is 0.04)
t = time in years (which is 20)
Substituting,
[tex]$5000(1+0.04)^{20}[/tex] = $10955.6157151671
Factor by grouping
5y^3(y-2)-15y(y-2)
5y³(y-2)-15y(y-2)
= (y-2)×(5y³-15y)
5 more than n is the quotient of n and 4
Simplify the expression
(2x^2y)3
Answer: Heyaa! ~
When simplifying (2x^2y)3 the answer will be... 6x²y
Step-by-step explanation:
Multiply the numbers:
2x²y · 3 6x²yHopefully this helps you! ^^
If one student is chosen at random, Find the probability that the student was NOT a female that got a "C"
--------- A // B // C // Total
Male: 10 // 8 // 15 // 33
Female: 7 // 9 // 17 // 33
Total: 17 // 17 // 32 //66
The probability that the student was NOT a female that got a "C" is 15 / 32.
What is the probability?
Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that the student was NOT a female that got a "C" = number of males that got a C / total number of people that got a C = 15 / 32.
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The graph of function g (x) predicts the profit of jimmy's famous Jer*y for a week. The x-axis represents the number of employees earning overtime for the week. The y-axis is the business's profit for the week in hundreds of dollars.
By identifying the maximums, we see that in each blank we need to write:
1) 2
2) 2
3) greater.
How to complete the given statement?
First, we need to find the maximum of the function g(x).
You can see that for x = 2 we have the maximum of the parabola, which gives y = 9.
Then the maximum profit is got when 2 employees earn overtime.
We also need to find the maximum for the table. Notice that the maximum value of the table also happens for x = 2, and this time the maximum is y = 16.
So we can see that the maximum of Cathy's cupcakes is larger than the maximum of Jimmy's.
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Can someone help me with this pls.
Answer:
a. 1/20, 1 out of twenty, or 5%
b. three out of ten, 3/10, 30%
c. 3/20 = 3/20 yes.
Step-by-step explanation:
a. It is a fraction. out of the 20 divisions there is only one 20. so there is 1 out of twenty which as a fraction is 1/20. this is equal to 1 divided by 20 wich eqauls 0.05. You move the decimal to the right twice to get 5%.
b. 6 out of twenty, 6/20. They are both even so it can be simplified.
6 ÷ 2 = 3
20 ÷ 2 = 10
It becomes 3/10, 0.3 or 30%
c. I decided that 3, 17, 2, 15, 10, and 9 are the lower right region.
the odds are 6/20 wich we know is 3/10
I only see 20 hits, but out of the 20, 6 are in the lower right region.
the odds from this is 6/20 which we know is 3/10.
We can see that the odds are equal.
Solve the following inequality algebraically:
-2 less-than x/3 + 1 less than 5
a.
Negative 9 greater-than x greater-than 12
b.
Negative 9 less-than x less-than 12
c.
Negative 2 less-than x less-than 5
d.
Negative 2 greater-than x greater-than 5
Answer:
d
Step-by-step explanation:
6. Janet spent $25, $30, $10, and $8 for
recreation in the last four weeks. What
was her average weekly expense for
recreation?
A. $12.50
B. $18.25
C. $25.25
D. $36.50
Answer:
B
Step-by-step explanation:
Total money spent = 25 + 30 + 10 + 8 = 73
Per week = 73 / 4 = 18.25
To determine how American college students feel about commuting, 100 students at a private
the university was chosen by selecting 50 men and 50 women to participate. They were asked
how far they commute each day (in minutes) to campus.
a. Is this an observational study or experiment?
b. What is the sample?
c. What is the target population?
d. What is the sampling method? (Simple random, stratified, convenient, …)
e. Is the data collected qualitative or quantitative?
f. Why is it unlikely that the results of this study will be valid?
The nature of the research is called Observational Study while the target Population is American Students.
How to find the sampling method?
1) In study, we survey members of a sample without trying to affect them while in experiment, we assign people or things to groups and apply some treatment to one of the groups, while the other group does not receive treatment. Thus, this is an observational study.
2) The sample is the 100 students made up of 50 boys and 50 girls.
3) The target Population are American College Students
4) The sampling method is; Simple random Sampling
5) The data is qualitative because it deals with description of feelings rather than dealing with numbers and figures.
6) It is unlikely that the results would be invalid because of sampling bias as it was only done in a private university.
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What is the solution to the trigonometric inequality sin^2(x) > cos(x) over the interval 0<= x <= 2pi radians?
The solutions to the trigonometric inequality in the interval is given by:
[tex]\frac{\pi}{6} \leq x \leq \frac{5\pi}{6}[/tex], or [tex]\frac{7\pi}{6} \leq x \leq \frac{11\pi}{6}[/tex]
What is the trigonometric inequality?It is given by:
[tex]\sin^{2}{x} > \cos{x}[/tex]
We have the following identity:
[tex]\sin^2{x} = 2\sin{x}\cos{x}[/tex]
Hence:
[tex]2\sin{x}\cos{x} > \cos{x}[/tex]
[tex]2\sin{x} > 1[/tex]
[tex]\sin{x} > \frac{1}{2}[/tex]
Between the first and second quadrant, the solution is:
[tex]\frac{\pi}{6} \leq x \leq \frac{5\pi}{6}[/tex]
Between the third and fourth quadrants, the solution is:
[tex]\frac{7\pi}{6} \leq x \leq \frac{11\pi}{6}[/tex]
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Jim is designing a seesaw for a children's park. The seesaw should make an angle of 30° with the ground, and the maximum height to which it should rise is 1 meter, as shown below:
A seesaw is shown with one end on the ground and the other in the air. The seesaw makes an angle of 30 degrees with the ground. The height of the seesaw from the ground, at the other end, is labeled 1 meter.
What is the maximum length of the seesaw?
Using the slope concept, it is found that the maximum length of the seesaw is of 1.73 meters.
What is a slope?The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
In this problem:
The vertical change is of 1 m.The horizontal change is the length l.The angle is of 30º.Hence:
tan(30º) = 1/l
l = 1/tan(30º)
l = 1.73.
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PLEASE GOD HELP ME!!!!
Another expression for the given rational function is [tex]x =r^\frac{1}{2}s^\frac{1}{2}[/tex]
Indices expressionGiven the rational function expressed as:
x = √rs
We can reconstruct the expression by writing it using exponents as shown;
[tex]x =\sqrt{rs}=(rs)^{\frac{1}{2} }[/tex]
Separate to have:
[tex]x =r^\frac{1}{2}s^\frac{1}{2}[/tex]
Hence another expression for the given rational function is [tex]x =r^\frac{1}{2}s^\frac{1}{2}[/tex]
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Which of the following fraction pairs is equivalent?
12/20 and 20/25 18/27 and 10/15 6/24 and 5/15 3/25 and 5/25
Answer:
b
Step-by-step explanation:
answer is b
This is super easy. Explanation, please!
The proposition given by definition of function "division" is false as [tex]\frac{f}{g} \ne {(1, 2)}[/tex] for the former function f = (9, 5) and the latter function g = (9, 0).
How to analyse a operation between two functions by propositional approach
In this question we have a definition of division between two functions, consisting in dividing each component of the ordered pair of the former function (f) by the component of the ordered pair of the latter function (g) such that resulting ordered pair is (1, 2).
We must check if the proposition is true for every ordered pair. Let analyze each case:
Case I
[tex]\frac{f}{g} = \left(\frac{1}{1}, \frac{6}{3} \right) = (1, 2)[/tex]
Case II
[tex]\frac{f}{g} = \left(\frac{9}{9}, \frac{5}{0} \right) = (1, NaN)[/tex]
Thus, the proposition is false.
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Solve the proportion: 35=x20
Answer:
either x = 1.75 or x = 700 , question wasn't clear
Step-by-step explanation:
Because you put the x in front of 20 , you might be meaning x/20 (second answer listed)? Or, you put the variable on the wrong side of 20. (first answer listed)
If you meant to type 20x
35 = 20x
÷20 ÷20 *
1.75 = x
*divide both sides by 20 to isolate x
x = 1.75
(x = [tex]\frac{35}{20}[/tex])
--------------------------------------------------------------------------
If you meant to type x/20
35 = [tex]\frac{x}{20}[/tex]
·20 ·20 *
700 = x
*multiply both sides by 20 to isolate x
700 = x
Write a doubles fact that can help you find the
sum. Write the sum.
3+4
Step-by-step explanation:
4 + 4 = 8 is one of the two closest double to 3 + 4
W.K.T(we know that )..
4 is 1 more than 3 this means ;
4 + 4 will be 1 more than 3 + 4
4 + 4 = 8 ,so finding 1 Less ;
3 + 4 = 7
here is the answer hope It helped U
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solve for y :
[tex]\longrightarrow \: \bold{3 + y = 18}[/tex]
ty! ~
Answer:
y = 15
Step-by-step explanation:
Given :
3 + y = 18
This a simple algebraic equation.
Subtract 3 from both sides :
⇒ 3 + y - 3 = 18 - 3
⇒ y = 15
Answer:
y = 15
Step-by-step explanation:
Given equation:
3+y=18To Find:
Value of ySolution:
We can rewrite this equation as:
y+3 = 8[This'll ain't change the answer]
Now we could solve on a easy way.
STEPS:
Transpose +3 to the RHS, make sure to change it's sign from “+” to “-”.
=> y = 18-3
Subtract the integers which's on the RHS:
=> y = 15
Hence,the value of y will be 15.
[tex] \rule{225pt}{2pt}[/tex]
If f(x) = 3x +3, which of the following is the inverse of f(x)?
O
A. f-1(x) = 3(x-3)
5
OB. f-1(x) = 3(x+3)
5
O C. f-1(x) = 5(x+3)
3
O D. f-1(x) = 5(x-3)
3
The inverse function of f(x) = 3x + 3 is f-1(x) = 1/3x - 1
How to determine the inverse?The equation is given as:
f(x) = 3x + 3
Express f(x) as y
y = 3x + 3
Swap the positions of y and x
x = 3y + 3
Make y the subject
3y = x - 3
Divide by 3
y = 1/3x - 1
Replace y with the inverse function
f-1(x) = 1/3x - 1
Hence, the inverse function of f(x) = 3x + 3 is f-1(x) = 1/3x - 1
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please help me!.. as fast as possible please help me at fastest possible
Which property justifies the following if angle A is congruent to angle B and angle b is congruent to angle C then angle a is congruent to angle c
Answer: Transitive property of congruence
the diagram shows a right angled triangle. 9cm 15cm x degrees. Find the size of angle x. Give your answer correct to 1 decimal place.
Answer:
31°
Step-by-step explanation:
As the opposing side and adjacent side of the angle x are given, we need to take the tan ratio of the angle.
=============================================================
Solving :
⇒ tan x° = 9/15
⇒ tan x° = 3/5
⇒ x = tan⁻¹ (0.6)
⇒ x = 31°
The size of the unknown angle "x"
Solution:We'll have to check which is the appropriate one from SOHCAHTOA.
In this question we'll have to use tan because opposite and adjacent is given.
[tex]\large\boxed{Formula: tan(A)= \frac{opp}{adj}}[/tex]
Substitute according to the formula.
[tex]tan \: x= \frac{9}{15}[/tex]
We'll have to use tan inverse.
[tex]x={tan}^{-1}(\frac{9}{15})[/tex]
[tex]x=30.96375653[/tex]
[tex]\large\boxed{x=31° }[/tex]
Hence, the size of the unknown angle "x" is 31°