Answers
Given:
The diameter of the circle = d = 14 cm
The radius of the circle = r = d/2 = 7 cm
The circumference is given by the formula: 2πr
so, the exact value = 2π * 7 = 14π cm
The approximated value to the nearest hundredth = 43.98 cm
The area of the circle is given by the formula: πr²
The exact value of the area = π * 7² = 49π cm²
The approximated value to the nearest hundredth = 153.94 cm²
Related Questions
Rusell runs 9/10 mile in 5 minutes. at this rate, how many miles can he run in one minute?
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Answer:
in one minute, Rusell can run 9/50 mile.
[tex]\frac{9}{50}mile[/tex]Explanation:
Given that;
Rusell runs 9/10 mile in 5 minutes.
[tex]\begin{gathered} \frac{9}{10}\text{mile }\rightarrow\text{ 5 minutes} \\ \text{dividing both sides by 5;} \\ \frac{9}{10\times5}\text{mile }\rightarrow\text{ }\frac{5}{5}\text{ minutes} \\ \frac{9}{50}\text{mile }\rightarrow\text{ 1 minutes} \end{gathered}[/tex]Therefore, in one minute, Rusell can run 9/50 mile.
[tex]\frac{9}{50}mile[/tex]triangle A B C is translated 6 units to the left and 1 unit up to create A'B'C'.
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The correct answer is 6.1 square units.
The translation of triangle ABC to triangle A'B'C' will not change the dimensions of the original triangle.
Hence, the area of triangle ABC will not be affected by the translation.
[tex]\begin{gathered} \text{Area of }\Delta ABC=\frac{1}{2}bh \\ \text{where b=2, h=6.1} \\ \text{Area of}\Delta ABC=\frac{1}{2}\times2\times6.1 \\ \text{ = 6.1 square units} \end{gathered}[/tex]Hence, the correct answer is 6.1 square units
You can only use cross multiplication in solving rational equation if and only if you have one fraction equal to one fraction, that is, if the fractions are _______
Answers
Answer:
Proportional
Explanation:
The ratio of the cat's weight to the rabbit's weight is 7 to 4. Together, they weigh 22 pounds. How much does the rabbit weigh?
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cat's weight: rabbit's weight
7:4
[tex]undefined[/tex]I need help with graphing
Answers
to grpah a line, we need two points and join it
so, we give values for x and find the solution to find one point
[tex]y=-4+\frac{6}{5}x[/tex]x=0
[tex]\begin{gathered} y=-4+\frac{6}{5}(0) \\ \\ y=-4 \end{gathered}[/tex]First point (0,-4)
x=5
[tex]\begin{gathered} y=-4+\frac{6}{5}(5) \\ \\ y=-4+6 \\ y=2 \end{gathered}[/tex]second point (5,2)
now place on the graph and join
this is the line
Find the angle between the vectors u = i – 9j and v = 8i + 5j.
Answers
Answer:
[tex]\theta\text{ = 115.67}\degree[/tex]Explanation:
Here, we want to find the angle between the two vectors
Mathematically, we have that as:
[tex]cos\text{ }\theta\text{ = }\frac{a.b}{|a||b|}[/tex]The denominator represents the magnitude of each of the given vectors as a product while the numerator represents the dot product of the two vectors
We have the calculation as follows:
[tex]\begin{gathered} cos\text{ }\theta\text{ = }\frac{(1\times8)+(-9\times5)}{\sqrt{1^2+(-9)\placeholder{⬚}^2}\text{ }\times\sqrt{8^2+5^2}} \\ \\ cos\text{ }\theta\text{ = }\frac{8-45}{\sqrt{82}\text{ }\times\sqrt{89}} \\ \\ \end{gathered}[/tex][tex]\begin{gathered} cos\text{ }\theta\text{ = }\frac{-37}{\sqrt{82}\text{ }\times\sqrt{89}} \\ cos\text{ }\theta\text{ = -0.4331} \\ \theta\text{ = }\cos^{-1}(-0.4331) \\ \theta\text{ = 115.67}\degree \end{gathered}[/tex]3) = A store sells rope by the meter. The equation p = 0.8L represents the price p (in dollars) of a piece of nylon rope that is L meters long. a. How much does the nylon rope cost per meter? b. How long is a piece of nylon rope that costs $1.00?
Answers
(a) Since the equation is:
[tex]p=0.8L[/tex]And "L" is in meters, the cos per meter will be simply the slope of the line. Alternatively, we can just input L = 1 and check the corresponding cost:
[tex]\begin{gathered} p=0.8\cdot1 \\ p=0.8 \end{gathered}[/tex]So, the cost is $0.80 per meter.
(b) Now, we have to the the contrary, we input 1 input "p" and calculate "L":
[tex]\begin{gathered} p=0.8L \\ 1=0.8L \\ L=\frac{1}{0.8} \\ L=1.25 \end{gathered}[/tex]So, it will be 1.25 meters long.
What is the probability that the person has no high school diploma and earns more than $30,000?
Answers
Jessica currently has $180 dollars in her bank account and will add an additional $15 each week. Nate has $120dollars in his account and will add $20 each week.A. After how many weeks will they have the same amount of money in their accounts?B. What is the amount, in dollars, that each person will have after this many weeks?
Answers
Answer:
(a)12 weeks
(b)$360
Explanation:
Part A
Let the number of weeks when they have the same amount of money in their accounts be x.
[tex]\begin{gathered} \text{Jessica's amount after x weeks }=180+15x \\ \text{Nate's amount after x weeks }=120+20x \end{gathered}[/tex]If the amount of money is equal:
[tex]180+15x=120+20x[/tex]Solve for x:
[tex]\begin{gathered} 180-120=20x-15x \\ 60=5x \\ \frac{60}{5}=\frac{5x}{5} \\ x=12 \end{gathered}[/tex]Therefore, they will have the same amount of money after 12 weeks.
Part B
The amount that each person will have, (Using Jessica's Equation)
[tex]\begin{gathered} \text{Amount}=180+15x \\ =180+15(12) \\ =180+180 \\ =\$360 \end{gathered}[/tex]The amount, in dollars, that each person will have after 12 weeks is $360.
Simplify 4.3 1/2 x 2 1/2
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Start by making the mixed numbers as fractions
[tex]\begin{gathered} 3\frac{1}{2}=\frac{3\cdot2+1}{2}=\frac{7}{2} \\ 2\frac{1}{2}=\frac{2\cdot2+1}{2}=\frac{5}{2} \end{gathered}[/tex]then, find the product between them
[tex]\frac{7}{2}\times\frac{5}{2}=\frac{35}{4}[/tex]write the fraction as a mixed number
[tex]\frac{35}{4}=8\frac{3}{4}[/tex]Which function has the following domain and range? Domain: {-7,-3,0,4,12}Range: {-5,1,2}
Answers
The domain of a function is the values that x can assume, while the range is the values that the function assume.
So, we are looking for the function with points that have x equal to -7, -3, 0, 4 and 12 and y values equal to -5, 1 and 2.
"A" only has x equal to -7 and and -5, and y equal to 12 and 2.
"B" has an x value of -4, which can't exist if the domain is the wanted one.
"D" has x value of -5, which eliminates the alternative for the same reason.
"C" is the correct answer because have all the x and y values and no other than x = {-7, -3, 0, 4, 12} and y = {-5, 1, 2}.
So "C" is the corect answer.
numbers. у xt Y y page ted. 8 7+ 6- 5 above in every Good; Fair; 3 2+ 1+ + x -9-8-7-6-5-4-3-2 1 2 3 4 5 6 7 8 9 -2 -3 -5 -6 -77 -87 -9-
Answers
step 1
Find the slope
we need two points
we take
(-6,0) and (0,4)
m=(4-0)/(0+6)
m=4/6
m=2/3
step 2
Find the equation in slope intercept form
y=mx+b
we have
m=2/3
b=4
substitute
y=(2/3)x+4If x varies directly with y and x=6 when y=8, find x when y=18.Options:13.5122412.5
Answers
Given:
x varies directly with y, and x=6 when y=8
Required:
We need to find the value of x when y =18.
Explanation:
if x varies directly as y the equation of variation is expressed as follows.
[tex]y=kx[/tex]Substitute x =6 and y =8 in the equation to find teh value of k.
[tex]8=k(6)[/tex]Divide both sides by 6.
[tex]\frac{8}{6}=\frac{k(6)}{6}[/tex][tex]\frac{4}{3}=k[/tex]We get k =4/3.
The equation is
[tex]y=\frac{4}{3}x[/tex]Substitute y =18 in the equation to find the value of x.
[tex]18=\frac{4}{3}x[/tex]Divide both sides by 3/4.
[tex]18\times\frac{3}{4}=\frac{4}{3}x\times\frac{3}{4}[/tex][tex]13.5=x[/tex]We get x =13.5
Final answer:
[tex]x=13.5\text{ when y =18.}[/tex]
Find Q. round your final answer to the nearest tenth
Answers
To find Q, we use the SSS (side-side-side) theorem.
The law of cosine formula:
a^2 = b^2 + c^2 - 2bcCosA
using the letters in the diagram and since we looking for Q, it becomes:
q^2 = p^2 + r^2 -2prCosQ
Making Cos Q, the subject of formula:
q² - p² - r² = -2prCosQ
(q² - p² - r²)/-2pr = -2prCosQ/-2pr
(q² - p² - r²)/-2pr = CosQ
Cos Q = -(q² - p² - r²)/2pr
q =
Find each measure measurement indicated. Round your answers to the nearest tenth. Please show work. Answer number 1.
Answers
Let's redraw the given figure, to easily understood the problem:
The figure appears to be a triangle with the following given,
c = AB = 17 cm
a = BC = unknown
b = CA = 44 cm
θ = 125°
m∠B means it is the angle at vertex B of the triangle, it is also the only angle given in the figure.
Therefore, the measure of m∠B is 125°.
The GMAT scores of all examinees who took that test this year produced a distribution that is approximately normal with a mean of 430 and a standard deviation of 34.The probability that the score of a randomly selected examinee is between 400 and 480, rounded to three decimal places, is:
Answers
SOLUTION:
Case: Probability from a normal distribution
Given: Mean = 430, Standard deviation: 34
Required: To find the probability that the score of a randomly selected examinee is between 400 and 480
Method:
Steps
Step 1: Get the z-score with the lesser value:
[tex]undefined[/tex]Final answer:
Can you please help me and I have more questions
Answers
As given that P as profit and m as amount of money and h as hours:
[tex]P=m-(250+4h)[/tex]The equation to calculate the amount of money m when profit is $415:
Put the the value of P as 415 in given equation:
[tex]\begin{gathered} 415=m-(250+4h) \\ 415=m-250-4h \\ 415+250+4h=m \\ m=665+4h \end{gathered}[/tex]So the desired equation for calculate amount of money m is:
[tex]m=665+4h[/tex]Let f(x) = x2 - 9a and g(a) = 3 - x?.(f+g)(7) =- (f - 9)(7) =.· (f9)(7) =• (4) (7) -
Answers
Given the functions:
[tex]f(x)=x^2-9x[/tex][tex]g(x)=3-x^2[/tex]1) (f+g)(x) You have to calculate the sum between f(x) and g(x) for x=7
First, calculate the sum between both functions:
[tex]\begin{gathered} (f+g)=(x^2-9x)+(3-x^2) \\ (f+g)=x^2-9x+3-x^2 \end{gathered}[/tex]Order the like terms together and simplify:
[tex]\begin{gathered} (f+g)=x^2-x^2-9x+3 \\ (f+g)=-9x+3 \end{gathered}[/tex]Substitute the expression with x=7 and solve:
[tex]\begin{gathered} (f+g)(7)=-9x+3 \\ (f+g)(7)=-9\cdot7+3 \\ (f+g)(7)=-60 \end{gathered}[/tex]The result is (f+g)(7)= -60
2) (f-g)(7) You have to calculate the difference between f(x) and g(x) for x=7
First, calculate the difference between both functions:
[tex](f-g)=(x^2-9x)-(3-x^2)[/tex]First, erase the parentheses, the minus sign before (3-x²) indicates that you have to change the sign of both terms inside the parentheses, as if they were multiplied by -1, then:
[tex](f-g)=x^2-9x-3+x^2[/tex]Order the like terms and simplify:
[tex]\begin{gathered} (f-g)=x^2+x^2-9x-3 \\ (f-g)=2x^2-9x-3 \end{gathered}[/tex]Substitute the expression with x=7 and solve:
[tex]\begin{gathered} (f-g)(7)=2x^2-9x+3 \\ (f-g)(7)=2(7)^2-9\cdot7+3 \\ (f-g)(7)=2\cdot49-63-3 \\ (f-g)(7)=98-66 \\ (f-g)(7)=32 \end{gathered}[/tex]The result is (f-g)(7)= 32
3) (fg)(7) In this item you have to calculate the product of f(x) and g(x) for x=7
First, determine the product between both functions:
[tex](fg)=(x^2-9x)(3-x^2)[/tex]Multiply each term of the first parentheses with each term of the second parentheses:
[tex]\begin{gathered} (fg)=x^2\cdot3+x^2\cdot(-x^2)-9x\cdot3-9x\cdot(-x^2) \\ (fg)=3x^2-x^4-27x+9x^3 \\ (fg)=-x^4+9x^3+3x^2-27x \end{gathered}[/tex]Substitute with x=7 and solve:
[tex]\begin{gathered} (fg)(7)=-(7^4)+9\cdot(7^3)+3\cdot(7^2)-27\cdot7 \\ (fg)(7)=-2401+9\cdot343+3\cdot49-189 \\ (fg)(7)=-2401+3087+147-189 \\ (fg)(7)=644 \end{gathered}[/tex]The result is (fg)(7)=644
4) (f/g)(7) First, divide both functions:
[tex](\frac{f}{g})=\frac{x^2-9}{3-x^2}[/tex][tex]\begin{gathered} (\frac{f}{g})=\frac{(x-9)x}{3-x^2} \\ (\frac{f}{g})=\frac{(-1)(x-9)x}{(-1)(3-x^2)} \\ (\frac{f}{g})=\frac{(-x+9)x}{(-3+x^2)} \\ (\frac{f}{g})=\frac{(9-x)x}{(x^2-3)} \\ (\frac{f}{g})=\frac{9x-x^2}{x^2-3} \end{gathered}[/tex]Substitute with x=7 and solve:
[tex]\begin{gathered} (\frac{f}{g})(7)=\frac{9\cdot7-7^2}{7^2-3} \\ (\frac{f}{g})(7)=\frac{63-49}{49-3} \\ (\frac{f}{g})(7)=\frac{14}{46} \\ (\frac{f}{g})(7)=\frac{7}{23} \end{gathered}[/tex]The result is (f/g)(7)= 7/23
The total revenue from the sale of a poplar book is approximately by the rational function Where x us the number of years since publication and r(x) is the total revenue in millions of dollars. Use this function to complete parts a through dFind the total revenue at the of the first year ?
Answers
if M angle ABD equals 7X - 31 n m a angles c d b equals 4x + 5 find M angle ABD
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The quadrilateral is a rectangle, all of its corner angles are rigth angles.
5)
m∠DAC=2x+4
m∠BAC=3x+1
Both angles are complementary, which means that they add up to 90º
You can symbolize this as:
[tex]m\angle DAC+m\angle BAC=90º[/tex]Replace the expression with the given measures for both angles:
[tex](2x+4)+(3x+1)=90[/tex]Now you have established a one unknown equation.
Solve for x:
[tex]\begin{gathered} 2x+4+3x+1=90 \\ 2x+3x+4+1=90 \\ 5x+5=90 \\ 5x=90-5 \\ 5x=85 \\ \frac{5x}{5}=\frac{85}{5} \\ x=17 \end{gathered}[/tex]Next is to calculate the measure of m∠BAC, replace the given expression with x=17
m∠BAC=3x+1= 3*17+1=52º
6)
m∠BDC=7x+1
m∠ADB=9x-7
Angle m∠BDC is a corner angle of the rectangle, as mentioned before, all corner angles of a rectangle measure 90º, so there is no need to make any calculations.
Note: the diagonals of the rectangle bisect each corner angle, this means that it cuts the angle in half, so m∠BDC=2*(m∠ADB)
2) The shape of a playground is a parallelogram. The city is going to treat the asphalt with sealant this spring with cans that will cover 4 square yards each. The figure below is a drawing of the playground, For how many cans of sealant does the city need to budget for the treatment, if the playground has a perimeter of 34 yards and the height is 1.4 yards less than the diagonal side of the parallelogram? 10.6 yd 6.4 yd a. Write the equation in words. b. Find the unknown height. c. Calculate the area of playground. d. Choose a variable for the unknown quantity and write the equation with the substituted values. e. Solve the equation. Include appropriate units in your answer. f. How many cans of sealant are needed?
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In this situation, you have a parallelogram with lateral sides of L length and top and bottom sides of length D. The letter h represents the height of the parallelogram.
L=6.4 yd and D=10.6 yd. The perimeter is the sum of all 4 edges, so perimeter=2*L+2*D
a) If one can cover 4 square yards and you need to find how many cans you will need for the whole playground area, then you need to find the total area which is calculated by its height times its base (D), so it would be h*D=area. This area divided by 4 square yards will give you the number of cans you need.
b) If the height is 1.4 yards less than the diagonal side, then
[tex]h=L-1.4=6.4-1.4=5\text{ yards}[/tex]c)Then the area is given by:
[tex]h\cdot D=5\cdot10.6=53\text{ square yards}[/tex]d)The number of cans can be represented by a variable called n (n as in number), so:
[tex]n=\frac{area}{4}=\frac{53}{4}[/tex]e) Then, by calculating:
[tex]\frac{53}{4}=13.25\text{ cans}[/tex]f) You will need 14 cans of sealant, you will only use some of it from the last can
Find the area of the shaded region. Use 3.14 to represent pi. Hint: You need to find height of triangle.A: 329.04B: 164.52C: 221.04D: 272.52
Answers
The area of the shaded region is 164.52 inches squared
Here, we wan to calculate the area of the shape given
From what we have, there is a triangle and a semi-circle
So the area of the shape is the sum of the areas of the triangle and the semi-circle
Mathematically, we can have this as;
[tex]\begin{gathered} \text{Area of triangle = }\frac{1}{2}\text{ }\times\text{ b }\times\text{ h} \\ \\ \text{Area of semicircle = }\frac{\pi\text{ }\times r^2}{2} \end{gathered}[/tex]where b represents the base of the triangle which is the diameter of the semicircle
The radius of the semicircle is 6 inches and the diameter is 2 times of this which equals 2 * 6 = 12 inches
The height of the triangle is 18 inches
The radius of the semicircle is 6 inches as above
Thus, we have the area of the shape as follows;
[tex]\begin{gathered} (\frac{1}{2}\times\text{ 18 }\times\text{ 12) + (}\frac{3.14\text{ }\times6^2}{2}) \\ \\ =\text{ 108 + 56.52} \\ \\ =\text{ 164.52 inches squared} \end{gathered}[/tex]how much money should be deposited today in the account that are 7%, compounded and semi-annually so they will accumulate to 11,000 in 3 years
Answers
The rule of the compound interest is
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]A is the new amount
P is the initial amount
r is the rate in decimal
n is the number of the periods per year
t is the number of years
Since the rate is 7% compounded semi-annual, then
r = 7/100 = 0.07
n = 2
Since the amount after 3 years will be $11 000, then
A = 11 000
t = 3
Substitute them in the rule above to find P
[tex]\begin{gathered} 11000=p(1+\frac{0.07}{2})^{2(3)} \\ 11000=p(1.035)^6 \end{gathered}[/tex]Divide both sides by (1.035)^6 to find P
[tex]\begin{gathered} \frac{11000}{(1.035)^6}=P \\ 8948.507087=P \end{gathered}[/tex]Round it to the nearest cent (2 decimal places)
P = $8948.51
The amount invested was $8948.51
Amber rolls a 6-sided die. On her first roll, she gets a "6". She rolls again.(a) What is the probability that the second roll is also a "6".P(6 | 6) =(b) What is the probability that the second roll is a "4".P(46) =
Answers
Answer
Explanation
Given the word problem, we can deduce the following information:
1. Amber rolls a 6-sided die.
2. Amber gets a "6" on her first roll.
a)
To determine the probability that the second roll is also a "6", we note first that a 6-sided die has these values: 1,2,3,4,5,6
As we can see, there's only one 6 value on a 6-sided die while the total .So, the probability would be:
P(6 | 6) =1/6
b)
To determine that the second roll is a "4", we use the same reasoning above. Therefore, the probability is:
P(4 | 6) =1/6
1. BC = 16 ft2. PQ = 22 cm139RS1с3. JK = 3 mm4. GH = 13 ydGK126845. YZ = 9 in6. EF = 28 mEF11542ZCG
Answers
Let's begin by listing out the given information:
The area of a sector is calculated using the formula:
1.
[tex]\begin{gathered} Area=\frac{\theta}{360^{\circ}}\times\pi r^2 \\ \theta=51^{\circ} \\ r=BC=16ft \\ \pi=3.14 \\ Area=\frac{51^{\circ}}{360^{\circ}}\times3.14\times16^2 \\ Area=113.88\approx114 \\ Area=114ft^2 \end{gathered}[/tex]Please help I don’t know which to multiply or decide
Answers
a)
Answer:
Explanation:
From the information given, it costs $23 to rent a bike for 4 hours. Let x represent the number of hours that a customer gets per dollar. We have the following equations
4 = 23
x = 1
By cross multiplying,
x * 23 = 4 * 1
23x = 4
x = 4/23 = 0.17
A customer gets 0.17 hour per dollar
Hi, can you help me answer this question, please, thank you!
Answers
Answer
Standard deviation = 1.2083
Step-by-step explanation
[tex]\begin{gathered} \text{Mean = }\sum ^{}_{}xi\cdot\text{ p(xi)} \\ \text{Mean = }0\cdot\text{ 0.2 + 1 }\cdot\text{ }0.05\text{ + 2}\cdot\text{ }0.1\text{ + 3 }\cdot\text{ 0.65} \\ \text{Mean = 0 + 0.05 + 0.2 + 1.95} \\ \text{Mean = 2.2} \\ \text{Standard deviation = }\sqrt[]{\sum^{}_{}}(\text{ x - }\mu)^2\cdot\text{ p(xi)} \\ \text{let }\mu\text{ = 2.2} \\ \text{Standard deviation = }\sqrt[]{(0-2.2)^2\cdot0.2+(1-2.2)^2\cdot0.05+(2-2.2)^2\cdot0.1+(3-2.2)^2\cdot\text{ 0.65}} \\ \text{standard deviation = }\sqrt[]{0.968\text{ + 0.072 + 0.004 + 0.416}} \\ \text{Standard deviation = }\sqrt[]{1.46} \\ \text{Standard deviation = }1.2083 \\ \text{Hence, standard deviation is 1.2083} \end{gathered}[/tex]How do you know if a sequence is a geometric sequence. A It has a common difference. B It has a common ratio.
Answers
A geometric sequence in which each next term is found by multiplying the previous term by a constant; therefore, every adjacent pair on entires in a geometric sequence have a common ratio. Hence, if any two consecutive entries in a sequence have a common ratio, it is a geometric series; therefore, choice B is the correct one to choose.
Divide 22 stars to represent the ratio 4:7.
Answers
Answer
Dividing 22 stars into the ratio 4:7 will give
8 stars : 14 stars
Explanation
We need to divide 22 stars into the ratio 4:7
Divide the ratio through by 11 (the sum of the two numbers in the ratio)
4:7 = (4/11) : (7/11)
Multiplying through by 22
(4/11) : (7/11)
= (4 × 22/11) : (7 × 22/11)
= 8 : 14
Hope this Helps!!!
find the circumference to the nearest whole number the whole number is 14
Answers
Answer:
The circumference is 88 in
Explanation:
The circumference of a circle can be determined, using the formula:
[tex]C=2\pi r[/tex]Where r is the radius of the circle.
Given a radius of 14 in, then
[tex]\begin{gathered} C=2(14)\pi \\ =28\pi \\ =28\times3.14 \\ =87.92 \\ \approx88in \end{gathered}[/tex]