Solution:
[tex]\searrow[/tex]
Detailed explanation:
Here we need to find both the circumference and the area of a circle whose diameter is 30 in.
///\\\///\\\///\\\///\\\///\\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\\////\\\\////\\\\///\\\///\\\///\\\///
⚜ Circumference ⚜
This is the formula that we use for the circumference. [tex]\large\texttt{$C=\pi d$}[/tex].
Here, C is the circumference,
[tex]\pi[/tex] is pi, *
d is the diameter
_____________
* The number pi is an irrational number. This means that no matter how hard we try, we cannot write this number as a fraction. The reason for that is: The number pi has never-ending digits after its decimal point.
To avoid getting never-ending numbers, we will use 3.14 for pi.
_____________
Alright, so now we just stick in the values.
[tex]\boldsymbol{C=3.14\cdot30}[/tex]
[tex]\boldsymbol{C=94.2\:inches}[/tex]
The circumference is successfully calculated.
///\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\////\\\\///\\\///\\\///\\\//\\//\/\/\/\//\///\\//
⚜ Area ⚜
This is the formula we will use to work out the area.
[tex]---\mapsto\boldsymbol{A=\pi r^2}[/tex]
Here,
A denotes the area
[tex]\pi[/tex] denotes pi
r denotes the radius (30/2=15, because the diameter is always two times the radius)
[tex]\large\boldsymbol{\therefore,\;the\;radius\;is\;15}[/tex]
Once again, it's just a matter of sticking in the values.
[tex]---\mapsto\boldsymbol{A=3.14\cdot15^2}[/tex]
NB:Remember the Order of Operations!
P.E.M.D.A.S.
P=Parentheses
This operation tells us to evaluate all expressions in the parentheses first, if any are present.
E=Exponents
This one tells us to evaluate all expressions with exponents, if any are present.
M=Multiplication | D=Division
Unlike the two operations above, these two are completely interchangeable.
A=Addition | S=Subtraction
Like M and D, A and S are interchangeable.
_________________
Now let's simplify... According to P.E.M.D.A.S., we should square 15 first.
[tex]---\mapsto\boldsymbol{A=3.14\cdot225}[/tex]
Now, we need to multiply.
[tex]---\mapsto\boldsymbol{A=706.5\;square\;inches}[/tex]
Question 3(Multiple Choice Worth 4 points)
Which expression is equivalent to 73.7-57
0 72
0 77
17
글
Answer: [tex]\frac{1}{7^{2}}[/tex]
Step-by-step explanation:
Using the exponent rule [tex]a^{b} \cdot a^{c}=a^{b+c}[/tex], we get that
[tex]7^{3} \cdot 7^{-5}=7^{-2}[/tex]
Then, using the exponent rule [tex]a^{-b}=\frac{1}{a^b}[/tex], we get that
[tex]7^{-2}=\boxed{\frac{1}{7^{2}}}[/tex]
If you drive 72 miles and use 6 gallons of gas, what is your rate
Answer:
Well, it depends if you are asking the rate per gallon it would be 12 miles per gallon.
The law of cosines is a² + b² - 2abcosC = c². Find the value of 2abcosC.
A. 20
B. 40
C. 37
D. -40
Answer:
C
Step-by-step explanation:
a = 4
b = 5
c = 2
C = arccos((a² + b² - c²) / 2ab)
C = arccos((16 + 25 - 4) / 2(4)(5))
C = arccos(37 / 40)
C = 22.33°
2abcosC
2(4)(5)cos(22.33)
40(0.925)
37
Option C is correct, if the law of cosines is a² + b² - 2abcosC = c² then the value of 2abcosC is 37.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
We have from law of cosines that a² + b² - 2abcosC = c²
We have to find the value of 2abcosC.
Now let us find the value of C
C = arccos((a² + b² - c²) / 2ab)
C = arccos((16 + 25 - 4) / 2(4)(5))
C = arccos(37 / 40)
C = 22.33°
Now plug in the value of C in 2abcosC.
2abcosC
=2(4)(5)cos(22.33)
=40(0.925)
=37
Hence, option C is correct, if the law of cosines is a² + b² - 2abcosC = c² then the value of 2abcosC is 37.
To learn more on trigonometry click:
https://brainly.com/question/25122835
#SPJ5
Find the area of the shaded portion of the
figure. All angles are right angles.
Dimensions are in inches.
3
8
5
======================================================
Explanation:
The white rectangle is 3 by 6 with area of 3*6 = 18 square inches.
The larger rectangle is 8 by 5 with area of 8*5 = 40 square inches.
The difference of these will get us the shaded area:
40 - 18 = 22 square inches
A water tank in the shape of an inverted circular cone has a base radius of 3 m and height of 7 m . If water is being pumped into the tank at a rate of 4.3 m^3 / min , find the rate at which the water level is rising when the water is 3.5 m deep. (Round your answer to three decimal places if required)
The water level increases by 0.608 meters per minute when the water is 3.5 m deep
How to determine the rate?The given parameters are:
Radius, r = 3Height, h = 7Rate in, V' = 4.3m^3/minThe relationship between the radius and height is:
r/h = 3/7
Make r the subject
r = 3h/7
The volume of a cone is;
[tex]V = \frac 13\pi r^2h[/tex]
This gives
[tex]V = \frac 13\pi (\frac{3h}{7})^2h[/tex]
Expand
[tex]V = \frac{3h^3}{49}\pi[/tex]
Differentiate
[tex]V' = \frac{9h^2}{49}\pi h'[/tex]
Make h' the subject
[tex]h' = \frac{49}{9\pi h^2}V'[/tex]
When the water level is 3.5.
We have:
[tex]h' = \frac{49}{9\pi * 3.5^2}V'[/tex]
Also, we have:
V' = 4.3
So, the equation becomes
[tex]h' = \frac{49}{9\pi * 3.5^2} * 4.3[/tex]
Evaluate the products
[tex]h' = \frac{210.7}{346.36}[/tex]
Evaluate the quotient
h' = 0.608
Hence, the water level increases by 0.608 meters per minute
Read more about volumes at:
https://brainly.com/question/10373132
#SPJ1
How many square feet of tile is needed for a room of 24 foot x 24 foot
Answer:576
Step-by-step explanation:
24 squared is 576
Look at the photo and answer it pls
Answer:
There isn't a photo
Step-by-step explanation:
There is no photo
What negative Z-score (standard score) would the area under the curve be 0.8621
z* = _______
What are the zeros of the quadratic function f(x)=6x^2+12x-7
Answer:
[tex]A) \ x=-1 \ ^ +_-\frac{\sqrt{13} }{\sqrt{6}}.[/tex]
Step-by-step explanation:
if to solve the given equation, then
D=6²+42=78;
[tex]\left[\begin{array}{ccc}x=\frac{-6-\sqrt{78}}{6} \\x=\frac{-6+\sqrt{78}}{6} \end{array} \ = > \ \left[\begin{array}{ccc}x=-1-\sqrt{\frac{13}{6} } \\x=-1+\sqrt{\frac{13}{6} } \end{array}[/tex]
Help me and i'll help you earn more points if the question is right
Use the property of real numbers to write the expression 2/5 x (-7)x 5/2
The simplified form of the expression 2/5 x (-7)x 5/2 would be -7.
How to solve the expression?When two fractions are multiplying each other, the numerator of both fractions multiplies each other, likewise the denominator of both fractions respectively.
Use the property of real numbers to write the expression
[tex]\dfrac{2}{5} \times (-7) \times \dfrac{ 5}{2}\\\\\dfrac{10}{10} \times (-7) \\\\-7 \times 1\\\\= -7[/tex]
Therefore, The simplified form of the expression would be -7.
Learn more about an expression here:
https://brainly.com/question/1249625
#SPJ1
Please help, will give the brainliest!
(J) 80 • 125
(K) (80+65) • 125
(L) (65 • 80) + (80 • 60)
M (65•80)+(80•60)
N (65•80)+ 1/2 (125 • 100)
Answer:
option N is the correct option, apply Formula of area of rectangle and triangle by splitting figure into 2 parts
How much of an alloy that is 30% copper should be mixed with 200 ounce of an alloy that is 70% copper in order to get an alloy that is 40% copper?
The alloy of copper will be 600 ounces.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Let us represent
Number of ounce of 30% copper = x
Hence, our Equation will be given below:-
x × 30% + 200 × 70% = (x + 200) × 40%
0.3x + 140 = (x + 200)0.4
0.3x + 140 = 0.4x + 80
Collect like terms
0.4x - 0.3x = 140 - 80
0.1x = 60
x = 60/0.1
x = 600 ounces
Therefore the alloy of copper will be 600 ounces.
To know more about expression follow
https://brainly.com/question/723406
#SPJ1
The credit remaining on a phone card (in dollors) is a linear function of the total calling trime made with the card ( in minutes). The remaining credit after 22 minutes is $36.70, and the remaining credit after 52 mintues is $32.20. What is the remaining credit after 85 mintues of calls?
After 85 minutes of calls, there are $27.25 left on the card.
What is the remaining credit after 85 minutes of calls?
A linear equation in slope-intercept form is:
y = a*x + b
Where a is the slope.
If the line passes through two points (x₁, y₁) and (x₂, y₂) the slope is:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
In this case, we know that the line passes through the points (22, 36.7) and (52, 32,20)
(points of the form (time, dollars)).
So the slope is:
[tex]a = \frac{32.2 - 36.7}{52 -22} = -0.15[/tex]
The linear equation is then:
y = -0.15*x + b
To find the value of b, we use the point (22. 36.7)
36.7 = -0.15*22 + b
36.7 + 0.15*22 = b = 40
Then the linear equation is:
y = -0.15*x +40
The amount remaining in the credit card after 85 minutes is given by evaluating the above equation in x = 85.
y = -0.15*85 + 40 = 27.25
This means that after 85 minutes of calls, there are $27.25 left on the card.
If you want to learn more about linear equations:
https://brainly.com/question/1884491
#SPJ1
Find the equation of the line parallel to y = 2x - 4 that runs through the point (-2, 4).
y = 1/2x + 4
y = 2x + 8
y = 2x + 4
y = -1/2x + 8
Answer:
y = 2x + 8
Explanation:
Equation: y = 2x - 4
Comparing it with slope intercept form "y = mx + b" where 'm' is slope and 'b' is y-intercept. This function has slope: 2 and y intercept of -4
Parallel lines has same slope.
Passes through (-2, 4)
[tex]\sf y - y_1 = m(x - x_1)[/tex]
[tex]\sf y - 4 = 2(x - (-2))[/tex]
[tex]\sf y - 4 = 2(x + 2)[/tex]
[tex]\sf y = 2x + 4 + 4[/tex]
[tex]\sf y = 2x + 8[/tex]
Answer: y = 2x + 8
Step-by-step explanation:
This is a fairly simple problem. I hope this helps!
So, to find a line parallel, it's simple, and it only requires that for the other line to have the same slope and a different y-intercept (or same "m" and different "b" in the equation y = mx + b).
To find a line parallel to a point is slightly harder, but don't worry, I'll teach you how.
To do this, we have to recognize the point. The point given is (-2, 4) where -2 is the x-value and 4 is the y-value. Remember, points always go by (x, y).
So, we set y to 4, and we set x to -2.
When testing out lines that are parallel to a point, you must always be careful that you end up with the same value. Such as 4 = 4 or 8 = 8, etcetera.
We get:
4 = 2 × (-2) + 8
Simplifying, we get:
4 = -4 + 8
Adding -4 to 8, we get 4:
4 = 4
Thus, y = 2x + 8 is parallel to the point (-2, 4)
In the 30-60-90 triangle below, side s has a length of.
length of
30
90⁰
S
10
60"
A. 5.2: 5.2
B. 5,10,3
and side q has a
Answer: C, 5, 5√3
Step-by-step explanation:
The short leg of a 30-60-90 triangle equal half the hypotenuse, 10/2 = 5. The long leg equals √3 times the short leg, 5*√3 = 5√3.
A motorboat moves across a lake at a constant speed. When it begins, it is 64 km from the shore. After 17 minutes, it is 30 km from the shore. Which function describes the motorboat's distance from the shore?
A. y=-17x+30
B. y=2x+64
C. y=-17x+64
D. y=-2x+64
Please solve fast!
I am giving a lot of points!
Answer:
y = -2x + 64
Explanation:
The x represents the time in minutes and y represents distance in km.
Determine coordinates: (0, 64), (17, 30)
Find slope:
[tex]\sf slope : \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
[tex]\rightarrow \sf slope \ (m) : \dfrac{30-64}{17-0} = -2[/tex]
Find equation:
[tex]\sf y- y_1 = m(x - x_1)[/tex]
[tex]\sf y - 64 = -2(x - 0)[/tex]
[tex]\sf y = -2x + 64[/tex]
What is the slope of the line that passes through the points (6, 2) and (4, 10)? −4 −14 14 4
Answer:
-4
Step-by-step explanation:
The equation for slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
m: Slope
(6, 2) = [tex](x_1, y_1)[/tex]
(4, 10) = [tex](x_2, y_2)[/tex]
Substitute these values into the equation:
[tex]m=\frac{10-2}{4-6}=\frac{8}{-2}=-4[/tex]
Therefore the slope is -4.
Learn more about slope here:
https://brainly.com/question/3493733
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
What is the slope of the line that passes through the points? 2 points given
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
The formula used here, is [tex]\bf{\dfrac{y2-y1}{x2-x1}}[/tex].
[tex]\rule{300}{1.7}[/tex]
[tex]\bf{\dfrac{10-2}{4-6}}[/tex] | subtract
[tex]\bf{\dfrac{8}{-2}}[/tex] | evaluate
[tex]\bf{-4}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=Slope\;-4}[/tex]
[tex]\boxed{\bf{aesthetic\not101}}[/tex]
Statement: "Three less than four times a number is greater
than or equal to 41."
Answer:
x≥11
Step-by-step explanation:
4x-3≥41
4x≥41+3 -44
x≥44/4 = 11
Find the inverse of the function y = 3x + 5 Find the inverse of the function y=3x+5
Answer:
First Inverse function= f^-1(x)=x/3-5/3
Second Inverse function=f^-1(x)=x/3-5/3
Step-by-step explanation:
the amount of money sue needs to pay (m) equals $30 to go to an apple orchard and pick apples plus $5 for every bushel of apples (b) she takes home
the elegante is aborto 3
NO LINKS!! Please help me with this problem
Answer:
23.1 years (nearest tenth)
Step-by-step explanation:
Compound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedGiven:
A = $1200P = $600r = 3% = 0.03n = 12 (as compounded monthly)t = yearsSubstitute the given values into the formula and solve for t:
[tex]\implies \sf 1200=600\left(1+\dfrac{0.03}{12}\right)^{12t}[/tex]
[tex]\implies \sf 1200=600\left(1.0025\right)^{12t}[/tex]
[tex]\implies \sf \dfrac{1200}{600}=\left(1.0025\right)^{12t}[/tex]
[tex]\implies \sf 2=\left(1.0025\right)^{12t}[/tex]
Take natural logs:
[tex]\implies \sf \ln 2=\ln \left(1.0025\right)^{12t}[/tex]
[tex]\implies \sf \ln 2=12t\ln \left(1.0025\right)[/tex]
[tex]\implies t=\dfrac{ \ln 2}{12 \ln (1.0025)}[/tex]
[tex]\implies t=23.13377513...[/tex]
[tex]\implies t=23.1\: \sf years \:\:(nearest\:tenth)[/tex]
The money will double in value in approximately [tex]\boxed{\sf 23.1}[/tex] years.
Used formula
[tex]\boxed{\sf A=P(1+\dfrac{r}{n})^{nt}}[/tex]
[tex]\\ \implies \sf 1200=600\left(1.0025\right)^{12t}[/tex]
[tex]\\ \implies \sf \dfrac{1200}{600}=\left(1.0025\right)^{12t}[/tex]
[tex]\\ \implies \sf 2=\left(1.0025\right)^{12t}[/tex]
Apply natural logarithm on both sides[tex]\implies \sf \ln 2=\ln \left(1.0025\right)^{12t}[/tex]
[tex]\\ \implies \sf \ln 2=12t\ln \left(1.0025\right)[/tex]
[tex]\\ \implies t=\dfrac{ \ln 2}{12 \ln (1.0025)}[/tex]
[tex]\\ \implies t=23.1years[/tex]
Transportation officials tell us that 60% of drivers wear seat belts while driving. Find the probability that more than 562 drivers in a sample of 900 drivers wear seat belts.
The probability that more than 562 drivers is 0.9328
What is probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given: p = 0.60
n = 900
Let X denote the number of drivers that wear a seat belt,
P(X > 562)
[tex]\mu[/tex] = n*p = 900(0.60) = 540
[tex]\sigma^{2}[/tex]= n*p*(1-p)
=900*0.60*0.40
=216
P(X >562) = Pr( Z > 1.4976)
= 0.9328
Hence, the probability that more than 562 drivers is 0.9328
Learn more about this concept here:
https://brainly.com/question/13853712
#SPJ1
If I=$312.50 R=25% T=0.25 what is P
Step-by-step explanation:
please mark me as brainlest
If you could please answer this that would be awesome!
Please graph it!
The graph is attached with the answer, This is looking like a horizontal staircase
What is a Step Function ?A step function is a piece wise function whose all pieces are horizontal line or a point.
It is given in the question to graph the interval
-2 ≤x≤2
for f(x) = |x+3|
-2 1
-1 2
0 3
1 4
2 5
The graph is attached with the answer.
This is looking like a horizontal staircase
To know more about Step Function
https://brainly.com/question/118594
#SPJ1
Your load is a container full of water. The container measures
1.0m x 1.25m x 1.1m and weighs 50kg when empty. Since 1 cubic
metre of water weighs 1 tonne, find the weight of the load
Answer:
1282kg
Step-by-step explanation:
1.0*1.12*1.1=1.232 tonnes
50kg + 1232kg = 1282kg
Hope this helps :)
Find the domain and range of the function graphed below. Write your answers in interval notation.
Answer:
Domain: [tex][1, \infty)[/tex]Range: [tex](-\infty, -2][/tex]Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
Value of x or y so that the line through the points has the given slope:
(X,9) and (9,-3), slope is -6/7
Sorry if it’s not worded great.
If we want the slope to be -6/7, then the value of x must be -5.
How to find the value of x?Remember that if a linear equation passes through (x₁, y₁) and (x₂, y₂), then the slope is:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here we have the points (x, 9) and (9, -3), and the slope must be -6/7, so we need to solve:
[tex]\frac{- 3 - 9}{9 - x} = \frac{-6}{7} \\\\\frac{-12}{9 - x} = \frac{-12}{14}[/tex]
Where on the second line we multiplied and divided the right fraction by 2.
Comparing the fractions, we see that we must have:
9 -x = 14
9 - 14 = x
-5 = x
So the value of x must be -5.
If you want to learn more about linear equations:
https://brainly.com/question/1884491
#SPJ1
The number of measles cases increased 36.5% to 193 cases this year. What was the number of cases prior to the increase? The number of measles cases increased 36.5 % to 193 cases this year . What was the number of cases prior to the increase ?
Answer:
70.445
Step-by-step explanation:
you have to subtract 36.5 by 193.
At school B, 108 year 8 students study French.
This is 60% of the year group.
How many students do not study French in year 8 in school B?
Step-by-step explanation:
108 = 60%
1% = 60%/60 = 108/60 = 1.8
100% = 1%×100 = 1.8×100 = 180
how many do not study French ?
the remainder of the students. that is 40% (100% - 60%) or 72 students (40×1.8 or simply 180-108).
Answer:
72 students do not study French.
Step-by-step explanation:
60% = 108 students
1. 108 ÷ 60 = 1.8 ( this is to find 1% of the students)
2. 1.8(1%) × 40 = 72
To check the answer:
108 + 72 = 180
180 × 60% = 108
