Answer: Radius = 5.33
Diameter = 10.66
Area = 89.3
Step-by-step explanation:
Circumference = 2πr
33.5 = 2πr
r = 33.5 / 2π
Diameter = 2r
Area = r²π
Area = 5.33²π
How many solutions does -14 + 6b + 7 - 2b = 1 + 5b have
The number of solutions that -14 + 6b + 7 - 2b = 1 + 5b has is 1 solution.
How to illustrate the information?It should be noted a equation is important to illustrate the relationship between the variables. In this case, the equation given is illustrated as:
-14 + 6b + 7 - 2b = 1 + 5b
Collect like terms
-8 + 6b - 2b = 5b
b = -8
Therefore, it has only one solution.
Learn more about equations on:
brainly.com/question/2972832
#SPJ1
Borrowed $30000 four year loan at 7% what’s monthly payment? And what’s the intrest I will pay on loan?
given:
There are given that the Borrowed is $30000.
Explanation:
To find the monthly amount, we need to use the formula:
[tex]R=\frac{P}{1-(i+1)^{-n}}[/tex]Where,
[tex]\begin{gathered} P=30000 \\ r=0.07 \\ m=12\text{ Thenn} \end{gathered}[/tex][tex]\begin{gathered} i=\frac{r}{m}=\frac{0.07}{12} \\ =0.0058 \end{gathered}[/tex]Ans,
[tex]\begin{gathered} n=mt=12(4) \\ =48 \end{gathered}[/tex]Then,
From the formula:
[tex]\begin{gathered} R=\frac{Pi}{1-(1+i)^{-n}} \\ R=\frac{30000(0.0058)}{1-(1+0.0058)^{-48}} \\ R=\frac{30,000(0.0058)}{1-(1.0058)^{-48}} \\ R=\frac{30000(0.0058)}{0.24} \\ R=725 \end{gathered}[/tex][tex]\begin{gathered} S.I=\frac{P\times r\times t}{100} \\ =\frac{30000\times7\times4}{100} \\ =4800 \end{gathered}[/tex]Final answer:
Hence, the monthly payment is $725 and the interest will be: $4800
Sue used 4 ounces of dark chocolate chips for every 3 ounces of white chocolate chips if she uses 21 ounces of chips altogether how many ounces of dark chocolate chips did she use
Answer: 12 oz
Step-by-step explanation:
Answer: 12
Step-by-step explanation:
A baker has a bag with 20 cups of flour. The baker plans to use the flour to make 4 loaves of bread. Each loaf of
bread uses 3 cups of flour.
How many cups of flour will remain in the bag when the baker has finished making the bread?
Enter your answer in the space provided.
Show all work for full credit.
Sketch the following curves, indicating all relative extreme points and inflection points. (10 pts)
a. y= x^3-6x^2+9x+3
For the given function, it is found that:
The extreme points are given by: (3,3) and (1,7).The inflection point is: (1,7).What are the extreme points of a function?The extreme points of a function happen at the values for x for which the first derivative is zero, that is:
y' = 0.
In this problem, the function is:
y = x³ - 6x² + 9x.
Hence the first derivative is:
3x² - 12x + 9.
The extreme values of x are:
3x² - 12x + 9 = 0.
3(x² - 4x + 3) = 0
x² - 4x + 3 = 0
(x - 3)(x - 1) = 0.
Then:
x - 3 = 0 -> x = 3.x - 1 = 0 -> x = 1.The numeric value of the function at these points is:
x = 3: y = 3³ - 6(3)² + 9(3) + 3 = 3.x = 1: y = 1³ - 6(1)² + 9(1) + 3 = 7.Hence the points are:
(3,3) and (1,7).
What are the inflection points of a function?The extreme points of a function happen at the values for x for which the second derivative is zero, that is:
y'' = 0.
For this problem, the second derivative is given by:
y'' = 6x - 12.
Hence the x-coordinate of the inflection point is:
6x - 12 = 0
6x = 12
x = 2.
The numeric value at x = 2 is:
2³ - 6(2)² + 9(2) + 3 = 5.
Then the inflection point is:
(2,5).
The graph with these points labeled is given at the end of the answer.
More can be learned about extreme and inflection points of a function at https://brainly.com/question/14338487
#SPJ1
Help with this problem
I₃ indifference curve represents the highest utility
What is an indifference curve?
An indifference curve is a graph that illustrates numerous pairings of two goods or commodities that leave the customer equally well off or satisfied—hence indifferent—when it comes to owning any pairing of the two items that is represented along the curve.
A consumer must give up more of one good in order to buy more of another, hence an indifference curve will always have a negative slope.
The given indifference map is a fast food meals per week vs movie tickets per week graph .
In which I₃ yields more than I₂ .
And I₂ yields more than I₁.
Thus, I₃ curve represents the highest utility.
To know more about indifference curve visit:
https://brainly.com/question/14514309
#SPJ13
What is the answer to m
the sum of the internal angles of a quadrilateral is 360, therefore:
[tex]\begin{gathered} m\angle A+m\angle B+m\angle C+m\angle D=360 \\ \text{and} \\ m\angle A+m\angle C=180 \\ m\angle B+m\angle D=180 \end{gathered}[/tex]so
[tex]\begin{gathered} a+5+a-25=180 \\ 2a-20=180 \\ 2a-20+20=180+20 \\ 2a=200 \\ \frac{2a}{2}=\frac{200}{2} \\ a=100 \end{gathered}[/tex]mm
mm
How could you correctly rewrite the equation 6(11-3) = 4(7 + 5) using the distributive property?
66-3 = 28 +35
Answer:
The formula for the distributive property is expressed as, a × (b + c) = (a × b) + (a × c );
Step-by-step explanation:
6(11-3) = 4(7 + 5)
(6×11)-(6×3)=(4×7)+(4×5)
66 - 18 = 28 + 20
Evaluate : limx→ tan2-sin2x x3
Given:
[tex]\lim _{x\to0}\frac{\tan 2x-\sin 2x}{x^3}[/tex]Solve:
[tex]\lim _{x\to0}\frac{\tan 2x-\sin 2x}{x^3}[/tex]Use l'hopital's rule:
[tex]\begin{gathered} =\lim _{x\to0}\frac{\frac{d}{dx}(-\sin 2x+\tan 2x)}{\frac{d}{dx}(x^3)} \\ =\lim _{x\to0}\frac{-2\cos (2x)+2\tan ^2(2x)+2}{3x^2} \end{gathered}[/tex]Simplify:
[tex]\begin{gathered} =\lim _{x\to0}\frac{-2\cos (2x)+2\tan ^2(2x)+2}{3x^2} \\ =\lim _{x\to0}\frac{2(-\cos (2x)+\tan ^2(2x)+1)}{3x^2} \end{gathered}[/tex]Apply the constant multiple rule:
[tex]\begin{gathered} \lim _{x\to0}cf(x)=c\lim _{x\to0}f(x) \\ \text{With c=}\frac{2}{3} \\ f(x)=\frac{-\cos (2x)+\tan ^2(2x)+1}{x^2} \end{gathered}[/tex][tex]\begin{gathered} =\frac{2\lim _{x\to0}\frac{-\cos (2x)+\tan ^2(2x)+1}{x^2}}{3} \\ =\frac{2\lim _{x\rightarrow0}\frac{(4\tan ^2(2x)+4)\tan (2x)+2\sin (2x)}{2x}}{3} \end{gathered}[/tex]Similary :
[tex]\begin{gathered} =\frac{2\lim _{x\to0}(2\cos (2x)+12\tan ^4(2x)+16\tan ^2(2x)+4)}{3} \\ =\frac{2(6)}{3} \\ =4 \end{gathered}[/tex]The measures of the angles of a triangle are shown in the figure below. Solve
for x.
62⁰
82⁰
(x+12)
Answer: 24
Step-by-step explanation:
The angles of a triangle add to 180 degrees, so:
[tex]62+82+x+12=180\\\\156+x=180\\\\x=24[/tex]
I need help
There are 3 consecutive even integers with a sum of 72. Which equation can be used to find such integers?
x + 2 = 24
x + 2 = 12
x + 1 = 12
x + 1 = 24
The equation used to find the 3 consecutive even integers with a sum of 72 is x + 2 = 24.
What is defined as the even integers?An even integer is one that is divisible by two, i.e. a multiple of two.For eg:- 2,4,6,... and −2,−4,−6,.... are divided by twoAs a result, the integers 2,4,6,... and −2,−4,−6,.... are all even integersThus, the integer of a form 2k is a even integer, in which k is an integer.For the given data in question.
Let the first even integer be 'x'.
Second even integer will be 'x + 2'.
Thirst even integer will be 'x + 4'.
The sum is 72
x + x + 2 + x + 4 = 72
Simplifying;
3x + 6 = 72
Divide whole equation by 3.
x + 2 = 24
Thus, the equation used to find the 3 consecutive even integers with a sum of 72 is x + 2 = 24.
To know more about the even integers, here
https://brainly.com/question/13723636
#SPJ13
Suppose a hospital would like to estimate the proportion of patients who feel that physicians who care for them always communicated effectively when discussing their medical care. A pilot sample of 40 patients found that 28 reported that their physician communicated effectively. Determine the additional number of patients that need to be sampled to construct a 90% confidence interval with a margin of error equal to 2% to estimate this proportion.
Part 1
The additional number of patients that need to be sampled is
(Round up to the nearest integer.)
174 more patients need to have their samples taken than were originally anticipated. This is further explained below.
What is a Marginal error?Generally, the equation for the margin of error is mathematically given as
[tex]{Margin\ of \ error } & \ amp;=Z_{o \text { it }} \text { at } 5 \% \text { lo.s } \times S E(p)[/tex]
Where
Z is the distributionSE is the standard deviationGiven that the margin of error should be 7%, or 0.07, the total number of extra patients is denoted by n.
sample proportion = 11/20 = 0.55
q =0.45
Margin of error = Zo at 5% lo.s * S E(p)
To solve for the 0.07amp
[tex]\\\\0.07 =1.96 \times \sqrt{\frac{p q}{n}}[/tex]
[tex]\\\\&0.07=1.96 \sqrt{\frac{0.55 \times 0.45}{20+n}} \\\\0.07 =\frac{0.97508}{\sqrt{20+n}} \\\\\sqrt{20+n} =\frac{0.97508}{0.07} \\\\\end{aligned}[/tex]
20+n =194.04
n =174.04
n=174
Read more about Marginal error
https://brainly.com/question/10501147
#SPJ1
The measures of the angles of a triangle are shown in the figure below. Solve for x.
50°
(6x-18)°
70°
Answer:
x=13
Step-by-step explanation:
We add all the numbers together, and all the variables
6x-78
We move all terms containing x to the left, and all other terms to the right
6x=78
x=78/6
which should equal 13
Use the point-slope formula to write an equation of the line that passes through (0,6) and (-2,0) write answer in slope intercept form
Equation using slope intercept form is 3y = x + 18
What is slope intercept form?An intercept in mathematics is a location on the y-axis through which the line's slope passes. It is a place on the y-axis where a straight line or a curve crosses. This is reflected in the equation for a line, which is written as y = mx + b, where m denotes slope and c denotes the y-intercept. Y = mx + b is the general formula for the slope-intercept form, where m stands for the line's slope and b for the y-value of the line's y-intercept. We may more easily determine a line's slope and its y-axis intersection using the slope-intercept form of a linear equation.
Given Data
Points(0,6) and (-2,0)
The slope formula = [tex]\frac{y_{2}-y_{1 } }{x_{2}-x_{1} }[/tex]
y₂= 0
y₁=6
x₂=-2
x₁=0
Slope = (-2-0)/(0-6)
Slope = -2/ -6
Slope = 1/3
Slope intercept form
y = mx + b
y = (1/3)x + 6
y = (x+18)/3
3y = x + 18
Equation using slope intercept form is 3y = x + 18
To learn more about slope intercept form, visit:
https://brainly.com/question/9682526
#SPJ10
Find the area of the circle A) 12.56 mm^2B) 25.12 mm^2C) 37.17 mm^2D) 50.24 mm^2
The formula in getting the area of the circle is:
[tex]A=\pi r^2[/tex]where r = the radius of the circle and the value of π = 3.14
In the diagram, the radius of the circle is 4 mm. Let's replace the "r" in the formula with 4 mm and "π" with 3.14
[tex]A=(3.14)(4mm)^2[/tex]Then, simplify.
[tex]\begin{gathered} A=(3.14)(16mm^2) \\ A=50.24\text{ }mm^2 \end{gathered}[/tex]Therefore, the area of the circle is 50.24 mm². (Option D)
We have π = 3.14 and the radius is 4 mm. Therefore we apply the following formula:
A = π * r²Replacing values in the equation.
A = 3.14 * (4 mm)²We calculate potentiation.
A = 3.14 * 16 mm²We multiply
A = 50.24 mm²
Answer: The circle area is 50.24 mm^2 (option D)✅ .
To learn: https://brainly.com/question/23422024To learn: https://brainly.com/question/16612428To learn: https://brainly.com/question/28570984To learn: https://brainly.com/question/24048237please quick I need this
Answer:
The remainder is [tex]4[/tex].
The quotient is [tex]3x^{2}+6x+1[/tex]
Step-by-step explanation:
Step 1: Do long division
To divide these expressions, we will have to make use of long division, which is shown in the picture.
Step 2: Identifying the remainder and quotient
The remainder is [tex]4[/tex].
The quotient is [tex]3x^{2}+6x+1[/tex]
help
fast 20 point
please
Answer:
A. 2
Step-by-step explanation:
Hope this helps
f(x)=x^2+6x+7
f(x+h)=?
f(x+h)-f(x)=?
f(x+h)-f(x)/h=?
The values are;
f (x + h) = x² + 2xh + h² + 6x + 6h + 7
f (x + h) - f (x) = h² + 2xh + 6h
f (x + h) - f (x) / h = h + 2x + 6
What is substitution method?
Find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
Given that;
The value of the function is;
f (x) = x² + 6x + 7
Now, Find the given values of f (x + h) , f (x + h) - f (x) and f (x + h) - f (x) / h by substitution method.
The value of the function is;
f (x) = x² + 6x + 7
Substitute x = x + h;
The value of the function is;
f (x + h) = (x + h)² + 6(x + h) + 7
= x² + 2xh + h² + 6x + 6h + 7
Thus, The value of f (x + h) = x² + 2xh + h² + 6x + 6h + 7.
Now,
f (x + h) - f (x) = (x² + 2xh + h² + 6x + 6h + 7) - (x² + 6x + 7)
= x² + 2xh + h² + 6x + 6h + 7 - x² - 6x - 7
= h² + 2xh + 6h
Thus, The value of f (x + h) - f (x) = h² + 2xh + 6h.
Now,
f (x + h) - f (x) / h = h² + 2xh + 6h / h
= h (h + 2x + 6) / h
= h + 2x + 6
Thus, The value of f (x + h) - f (x) / h = h + 2x + 6.
Therefore, The values are;
f (x + h) = x² + 2xh + h² + 6x + 6h + 7
f (x + h) - f (x) = h² + 2xh + 6h
f (x + h) - f (x) / h = h + 2x + 6
Learn more about the substitution method visit:
https://brainly.com/question/19256999
#SPJ1
Mary sold 192 worth of greeting cards if she received 25% Commission on all sales how much commission did she receive
25% of 192 = 192 * 25/100 = 192 * 0.25 = 48
Answer:
Mary received $48
the phone sells Jan a bicycle for $175 and a helmet for $17. The total cost for Jin is 160% of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally? How much money did he make by selling the bicycle and helmet to Jin
Jin
The bicycle selling price was : $175
The helmet was for : $17
Jin total cost was 160% of what Stefan spent originally to buy the two items
This means ; 160/100 * x = { 175+17} -----where x is the original amount stefan spent to buy the two items
1.6 x = 192
x = 192 /1.6
x=120
Stefan originally spent $120
The money he made after the sell is: $192-$120 =$72
Answer
a) $120
b) $72
If a 1/3 cup serving of cheese provides your fully daily value of calcium, then what percentage of your daily value of calcium is provided by 3/4 cup of the cheese?
If a 1/3 cup serving of cheese provides your full daily value of calcium, then 225% of your daily value of calcium is provided by ¾ cup of the cheese.
What are the ratios rules?Between amounts of the same sort, the ratio should exist. The units used to compare two items should be comparable.
Terms should be in a meaningful sequence. If two ratios are comparable to one another like fractions, they may be compared.
An easy ratio Is what?When both sides are whole numbers and cannot be split by another
whole number, a ratio is considered to be in its simplest form.
Think about full number ratios, such as 6:4. The fraction 64 can be used to represent it.
What proportion of your daily intake of calcium is delivered by 3/4 cup of the food if a serving of cheese that is 1/3 cup in size delivers your whole daily value of calcium?Daily value of calcium= (3/4)/(1/3) = 9/4
3/4 cup gives you 9/4 of your daily value of calcium.
We can convert fractions to percentages, we will get
9/4= 2.25
2.25*100=225%
Then the percentage of your daily value of calcium is 225%.
Learn more about the Ratio here:
https://brainly.com/question/2914376
#SPJ9.
Find 98.6% of 343.7. Round to the nearest thousandth.
Percentage, a relative value indicating hundredth parts of any quantity.
98.6% of 343.7 is in nearest thousandth 338.888
What is Percentage?Percentage, a relative value indicating hundredth parts of any quantity.
We need to find 98.6% of 343.7.
Ninty eight point six percentage of three hundred forty three point seven.
Ninty eight point six percentage we need to convert into decimal number this can be achieved by dividing with 100.
98.6% =98.6/100
When ninty eight point six is divided by hundred we get zero point nine eight six.
=0.986
We need to find what is 98.6% of 343.7.
To find ninty eight point six percentage of three hundred forty three point seven. we are required to multiply the converted value of 98.6% with three hundred forty three point seven.
Simply we need to multiply 0.986 with 343.7.
=0.986×343.7
=338.888
Hence 98.6% of 343.7 is 338.888
To learn more on Percentages click:
https://brainly.com/question/28269290
#SPJ1
3. Compute the derivatives of the following functions. Do not simplify.
a) f(x)=tanx/e^3
b) f(x)= tan -¹(x³)(x^5)(ln x) c) f(x)=^7√x^5+ 5^x d) g(x)=x^sec(x)
Answer:
A im sure
Example
hope itz helpppp
Mr. Connor's physics class has 105 students, classified by academic year and gender, as illustrated in the table. Mr. Connor randomly chooses one student to collect yesterday's work
Academic Year male female
Junior 8 11
senior 19 19
freshman 9 12
sophomore 19 8
The probability that he selects a Mel given that he chooses randomly from only the Juniors is 0.076.
How to calculate the probability?It should be noted that the probability is the likelihood that something will happen. The table shows that Connor's physics class has 105 students, classified by academic year and gender.
The probability will be:
Fraction of males that are junior / Fraction if Junior
= 8/105 / 19/105
= 0.076
The probability is 0.076.
The complete question is written below.
Learn more about probability on:
brainly.com/question/25870256
#SPJ1
What is the probability that he selects a Mel given that he chooses randomly from only the Juniors.
A DVD is available at a store for $16.99. The list price of this DVD was $18.75. What was the percent discount? % (Round to the nearest tenth as needed.)
The cost of DVD = $16.99
The list price of this DVD was $18.75
So, the discount =
[tex]18.75-16.99=1.76[/tex]And the percent discount =
[tex]\frac{1.76}{18.75}\cdot100=9.3866\%[/tex]Rounding the answer to the nearest tenth
So, the answer will be : the percent discount = 9.4%
write an equivalent expression for (925x to the 3rd times y to the negative 4th times z to the second) 0
Answer:
1
Step-by-step explanation:
Anything to the power of 0 is 1.
Ex:
[tex]x^{0} =1\\3643737737^{0} =1\\[/tex]
Gourmet in Italy has a policy of automatically adding an 18% tip to a restaurant bill. How much would a restaurant bill be if it had a tip of $3.20 added to it?
The restaurant charger a tip of the 18% of the bill
So the total amount charged is the money spent + 18%
The bill had a tip of $3.20 this is the 18% of the amount spent.
Using cross multiplication you can calculate the amount of the bill as:
Bill without tip: 100%
Tip: 18%
Total amount (bill + tip): 118%
If 18% ____ $3.20
Then 118%___$x
[tex]undefined[/tex]What can be concluded from the statement ∠1+∠2m∠1+m∠2 = 90°?
When two angles add to 90º they are called complementary angles.
Then, if in the given statement the sum of angles 1 and 2 is equal to 90º, angles 1 angle 2 are complementary.
Answer: <1 and <2 and <1and <2 are complementary
There are 500 fish in a pond, to 1sf. What is the least possible number of fish that could be taken from
the pond so that there are 400 fish in the pond to 1sf
Answer:
one
Step-by-step explanation:
The least number of fish COULD be 450 ....this would be 500 to 1 S.F.
if you take ONE fish away there are then 449 which would be 400 to 1 S.F
A test was given to a group of students. The grades and gender are summarized below A B C TotalMale4192043Female1116532Total15352575If one student is chosen at random from those who took the test,Find the probability that the student got a 'B' GIVEN they are male.