The circumference of circle with diameter 6 feet will be 6π feet.
According to the question,
We have the following information:
Diameter of the circle = 6 feet
Now, we will find the radius of the circle. We know that the radius of the circle is half that of its diameter.
Radius of the circle = Diameter/2
Radius of the circle = 6/2 feet
Radius of the circle = 3 feet
We know that the following formula is used to find the circumference of the circle:
Circumference of the circle = 2πr
Circumference of the circle = 2π*3
Circumference of the circle = 6π feet
Hence, the circumference of the circle is 6π feet.
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A number between 280 and 380 when rounded to the nearest hundred is 45 less than the original number what number is the original number
If the unknown number is an integer between 280 and 349;
When rounded to the nearest hundred, the unknown number is 300.
If the unknown number is an integer from 350-380;
When rounded to the nearest hundred, the unknown number is 400.
If the approximation is 45 less than the original number, thus it cant be in the range of 350-380.
But;
[tex]300+45=345[/tex]When 345 is rounded to the nearest hundred, it is 300.
And the difference between the approximated value and the original value is 45.
Hence, 345 is the original number.
CORRECT ANSWER: 345
A flower bed is in the shape of a rectangle. It measures7 yd long and 4 yd wide. Chris wants to use mulch tocover the flower bed. The mulch is sold by the squarefoot. Use the facts to find the area of the flower bed insquare feet.2ftX 5?Conversion facts for length1 foot (ft)1 yard (yd)1 yard (yd)===12 inches (in)3 feet (ft)36 inches (in) i need help with this math problem.
Answer
252 ft²
Step-by-step explanation
1 yard is equivalent to 3 feet. Using this conversion factor, the equivalence of 7 yd is:
[tex]\begin{gathered} 7\text{ yd =}7\text{ yd}\cdot\frac{3\text{ ft}}{1\text{ yd}} \\ \text{ Simplifying the units:} \\ 7\text{ yd =}\frac{7\cdot3}{1}\text{ ft} \\ 7\text{ yd }=21\text{ ft} \end{gathered}[/tex]Similarly, the equivalence of 4 yards is:
[tex]\begin{gathered} 4\text{ yd }=4\text{ yd}{}\cdot\frac{3\text{ ft}}{1\text{ yd}} \\ 4\text{ yd }=4\cdot3\text{ ft} \\ 4\text{ yd}=12\text{ ft} \end{gathered}[/tex]Therefore, the length of the bed is 21 ft and the width is 12 ft.
Finally, the area of the bed (a rectangle) is calculated as follows:
[tex]\begin{gathered} A=legnth\cdot width \\ A=21\cdot12 \\ A=252\text{ ft}^2 \end{gathered}[/tex]solve the inequality for 5x + 9 ≤ 24
From the problem, we have an inequality of :
[tex]5x+9\le24[/tex]Subtract 9 to both sides of the inequality :
[tex]\begin{gathered} 5x+9-9\le24-9 \\ 5x\le15 \end{gathered}[/tex]Divide both sides by 5 :
[tex]\begin{gathered} \frac{5x}{5}\le\frac{15}{5} \\ x\le3 \end{gathered}[/tex]The answer is x ≤ 3
Please help me no other tutor could or understand it
We must find the equation that models the amount of medication in the bloodstream as a function of the days passed from the initial dose. The initial dose is a and we are going to use x for the number of days and M for the amount of mediaction in the bloodstream. We are going to model this using an exponential function which means that the variable x must be in the exponent of a power:
[tex]M(x)=a\cdot b^x[/tex]We are told that the half-life of the medication is 6 hours. This means that after 6 hours the amount of medication in the bloodstream is reduced to a half. If the initial dose was a then the amount after 6 hours has to be a/2. We are going to use this to find the parameter b but first we must convert 6 hours into days since our equation works with days.
Remember that a day is composed of 24 hours so 6 hours is equivalent to 6/24=1/4 day. This means that the amount of medication after 1/4 days is the half of the initial dose. In mathematical terms this means M(1/4)=M(0)/2:
[tex]\begin{gathered} \frac{M(0)}{2}=M(\frac{1}{4}) \\ \frac{a\cdot b^0}{2}=a\cdot b^{\frac{1}{4}} \\ \frac{a}{2}=a\cdot b^{\frac{1}{4}} \end{gathered}[/tex]We can divide both sides of this equation by a:
[tex]\begin{gathered} \frac{\frac{a}{2}}{a}=\frac{a\cdot b^{\frac{1}{4}}}{a} \\ \frac{1}{2}=b^{\frac{1}{4}} \end{gathered}[/tex]Now let's raised both sides of this equation to 4:
[tex]\begin{gathered} (\frac{1}{2})^4=(b^{\frac{1}{4}})^4 \\ \frac{1}{2^4}=b^{\frac{1}{4}\cdot4} \\ b=\frac{1}{16} \end{gathered}[/tex]Which can also be written as:
[tex]b=16^{-1}[/tex]Then the equation that models how much medication will be in the bloodstream after x days is:
[tex]M(x)=a\cdot16^{-x}[/tex]Using this we must find how much medication will be in the bloodstream after 4 days for an initial dose of 500mg. This basically means that a=500mg, x=4 and we have to find M(4):
[tex]M(4)=500mg\cdot16^{-4}=0.00763mg[/tex]So after 4 days there are 0.00763 mg of medication in the bloodstream.
Now we have to indicate how much more medication will be if the initial dose is 750mg instead of 500mg. So we take a=750mg and x=4:
[tex]M(4)=750mg\cdot16^{-4}=0.01144mg[/tex]If we substract the first value we found from this one we obtained the required difference:
[tex]0.01144mg-0.00763mg=0.00381mg[/tex]So the answer to the third question is 0.00381mg.
Daphne rolls two 6-sided number cubes. What is the probability that she rollsa sum equal to 3? Use the diagram of the sample space to help you. please help me
From the sample space, there are 2 results equal to 3, and there are 36 total results. Then the probability that she rolls a sum equal to 3 is: 2/36 or 1/18
(8-4) mulitiply (3-2)=
what is its base of the parallelogram is72 meters²
The area of a parallelogram is computed using the formula base x height.
Here we have a parallelogram with an area of 72 square meters and a height of 9 meters. Using the formula, we can solve for the base.
[tex]\begin{gathered} A=bh \\ 72=b(9) \\ \\ \frac{72}{9}=\frac{b(9)}{9} \\ \\ 8=b \end{gathered}[/tex]The base is 8 meters long.
The cost of a laptop computer decreased from $600 to $480. By what percentage did the cost of the computer decrease?
Initial value= $600
new value = $ 480
[tex]\begin{gathered} =\frac{600-480}{480}\times100 \\ =\text{ }\frac{120}{480}\times100 \\ =\text{ 25\%} \end{gathered}[/tex]25% decrease is the answer
I inserted a picture of the question can you please hurry
Given:
[tex](-2,-5)\text{ and (}1,4)\text{ are given points.}[/tex][tex]\begin{gathered} \text{Slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{Slope}=\frac{4+5}{1+2} \\ \text{Slope}=\frac{9}{3} \\ \text{Slope}=3 \end{gathered}[/tex]In the following expression, place a decimal point in the divisor and the dividend that is 4368÷6208 to create a new problem with the same answer as in question 11 that is 7 meters / 7
---------------------------------
436.8m -------------------> 62.08s
xm -------------------------->1s
Using cross multiplication:
[tex]\begin{gathered} \frac{436.8}{x}=\frac{62.08}{1} \\ \text{solve for x:} \\ x=\frac{436.8}{62.08} \\ x=7.036082474m \\ \end{gathered}[/tex](1 point) For each trigonometric expression A,B,C,D, E, choose the expression from 1,2,3,4,5 that completes a fundamental identity. Enter the appropriate letter (A,B,C,D, or E) in each blank.
Answer:
Step-by-step explanation:
I would recommend looking up the magic trig hexagon, it has all of these identities and more within it.
1 - this corresponds with C as sin^2(x)+cos^2(x)=1
1-cos^2(x) - this corresponds with A, using the identity from number 1, we can rewrite it in the form sin^2(x)=1-cos^2(x)
cot(x) - for this it is important to know that cotangent is the inverse of tangent. Since tan(x)=sin(x)/cos(x), cot=cos(x)/sin(x) which is B.
sec^2(x) - much like the cos and sin pythagorean identity, sec and tan are related. sec^2(x)=tan^2(x)+1 which is answer choice E.
tan(x) - this is sin(x)/cos(x), choice D.
Answer the questions about the figures below. 4 ft Figure A 6 ft 6 ft 4 ft (a) Which figures are parallelograms? Mark all that apply. Figure A O Figure B (b) Which figures are squares? Mark all that apply. Figure A Figure B (c) Which figures are rectangles? Mark all that apply. Figure A Figure B O Figure C Figure C Figure C 6 ft Figure B 4 ft 4 ft 6 ft None of the figures None of the figures None of the figures 6 ft X Figure C 6 ft 6 ft Ś 6 ft ?
A parallelogram is a 4 sided figures that has the opposite sides parallel.
Figure A has right angles so the opposite sides are parallel
Figure B has the opposite sides of equal length, so the opposite sides are parallel
Figure C has right angles so the opposite sides are parallel
For Question A, Figure A, B C are parallelograms
Squares have opposites sides parallel and all 4 sides of equal length and all angles right angles
The only figure with all 4 sides of equal length, all 4 angles right angles is Figure C ( opposites sides are parallel because 4 sides are equal length and all 4 angles are right angles)
The figure that is a square is Figure C
Rectangles are shapes that have opposite sides parallel and all 4 angles are right angles. Squares are special rectangles
Figure A has opposite sides parallel and all 4 angles equal length. Figure C is a square, which is a special rectangle
The rectangles are figures A and C
based on the data provided what was the rent expenses each month
From the table it can be observed that rate expense for a month is -$1,120.00. The negative value means that amount is reduced.
So rent expense is -$1,120.00, where negative sign is for decrease in amount.
what do you do when you solve for X.
Using the property vertically opposite angles and the corresponding angles, the value of x can be determine as,
[tex]\begin{gathered} 19x-4=110 \\ 19x=114 \\ x=6 \end{gathered}[/tex]Thus, the required value of x is 6.
Trey's chocolate bar is 52% cocoa. If the weight of the chocolate bar is 66 grams, how many grams of cocoa does it contain? Round your answer to the nearest
tenth.
Trey's chocolate bar is 52% cocoa and if the weight of the chocolate bar is 66 grams, it contains 34.32 grams of cocoa using the concept of percentage.
What is percent?A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" is also used, the percent sign, "%," is frequently used to indicate it. A percentage is a number without dimensions and without a standard measurement.What is a fraction?
Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many parts of a particular size there are when spoken in everyday English.Here, 52% of 66 grams:
=(52/100)*66=0.52*66=34.32 grams of cocoa52% cocoa makes up Trey's chocolate bar.
Using the concept of percentage, a 66-gram chocolate bar would contain 34.32 grams of cocoa.
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The probability that the degree is not a bachelor's given that thr recipient Is male is
Answer
Probability that the degree is not a bachelor's given that thr recipient Is male = 0.36
Explanation
The probability of an event is calculated as the number of elements in the event divided by the total number of elements in the sample space.
For this question,
Number of degrees that are not bachelor's degree given to a male = Number of associate's degree given to a male = 239
Total number of males = 239 + 427 = 666
Probability that the degree is not a bachelor's given that thr recipient Is male = (239/666)
= 0.36
Hope this Helps!!!
Adina sets up a taste test of 3 different waters: tap, bottled in glass, and bottled in plastic. She puts these waters in identical cups and has a friend taste them one by one. The friend then tries to identify which water was in each cup. Assume that Adina's friend can't taste any difference and is randomly guessing. What is the probability that Adina's friend correctly identifies each of the 3 cups of water
Given
3 different waters: tap, bottled in glass, and bottled in plastic.
Find
probability that Adina's friend correctly identifies each of the 3 cups of water
Explanation
As we have given three different waters : tap , bottled in glass and bottled in plastic.
number of ways in which the person can make guesses about the 3 cups of water =
[tex]\begin{gathered} ^3P_3 \\ \frac{3!}{0!} \\ 6 \end{gathered}[/tex]number of ways in which person identifies correctly the 3 cups of water = 1
so , probability that Adina's friend correctly identifies each of the 3 cups of water =
[tex]P\text{ = }\frac{number\text{ of ways in which person identifies correctly the 3 cups of water}}{number\text{ of ways in which the person can make guesses about the 3 cups of water }}[/tex]so , P = 1/6
Final Answer
Therefore , the probability that adina's friend correctly identifies each of the cup of water = 1/6
In which graph does the height difference between Winter Hill and Frozen Field equal the height of BlizzardRun?Choose 1 answer:605040Height (in meters)30.©20100Blizzard RunSnow SlopeWinter HillFrozen FieldSledding hill
In graph A, you can see that:
• The height of Frozen Field is 50 meters
,• The height of Winter Hill is 15 meters
,• The height of Blizzard Run is 35 meters
Now, we can write the equation that describes the height difference between Winter Hill and Frozen Field.
[tex]\text{ Height of Frozen Field }-\text{ Height of Winter Hill }=50m-15m=35m_{}=\text{ Height of Blizzard Run }[/tex]In graph B, you can see that:
• The height of Frozen Field is 45 meters
• The height of Winter Hill is 10 meters
• The height of Blizzard Run is 55 meters
Now, we can write the equation that describes the height difference between Winter Hill and Frozen Field.
[tex]\text{ Height of Frozen Field }-\text{ Height of Winter Hill }=45m-10m=35m\ne55m_{}=\text{ Height of Blizzard Run }[/tex]Therefore, the graph where the height difference between Winter Hill and Frozen Field is equal to the height of Blizzard Run is graph A.
24) The radius of a circle is 6 inches. What is the area of a sector that has a central angle of 100 degrees 
Answer
Area of the sector = 31.42 square inches
Explanation
The area of a sector that has a central angle, θ, in a circle of radius r, is given as
[tex]\begin{gathered} \text{Area of a sector = }\frac{\theta}{360\degree}\times(Area\text{ of a circle)} \\ \text{Area of a circle =}\pi\times r^2 \\ \text{Area of a sector = }\frac{θ}{360°}\times\pi\times r^2 \end{gathered}[/tex]For this question,
θ = central angle = 100°
π = pi = 3.142
r = radius = 6 inches
[tex]\begin{gathered} \text{Area of a sector = }\frac{θ}{360°}\times\pi\times r^2 \\ \text{Area of a sector = }\frac{100\degree}{360\degree}\times3.142\times6^2=31.42\text{ square inches} \end{gathered}[/tex]Hope this Helps!!!
Ramon has assets that sum up to $253,000. He has liabilities that sum up to $216,345. what is his net worth?
Net worth is equal to total assets minus total liabilities (debt).
So,
Total Assets = 253000
Total Liabilities = 216345
Hence,
Net Worth = 253000 - 216345 = $36,655
My name is Nika and I need help in math I’m 73 and done with school but still don’t under algebra
The given equation is
[tex]2x-3=9[/tex]To solve this equation we have to isolate x on one side and put the numbers on the other side
To do that we will add 3 to each side to move 3 from the left side to the right side
[tex]2x-3+3=9+3[/tex]Simplify it
[tex]\begin{gathered} 2x+0=12 \\ 2x=12 \end{gathered}[/tex]Now we need to move 2 from the left side to the right side, then
Divide both sides by 2
[tex]\begin{gathered} \frac{2x}{2}=\frac{12}{2} \\ x=6 \end{gathered}[/tex]Then the solution of the equation is
x = 6
Production has indicated that they can produce widgets at a cost of $16.00 each if they lease new equipment at a cost of $40,000. Marketing has estimated the number of units they can sell at a number of prices (shown below). Which price/volume option will allow the firm to avoid losing money on this project?
The price/volume option that will allow the firm to avoid losing money on this project is C. 2,300 units at $34.00 each.
How is this option determined?To determine the correct option, we use the cost-volume-profit analysis tool.
The cost-volume-profit (CVP) analysis involves determining how the volume of sales drives profitability.
The CVP technique classifies costs into their variable and fixed cost elements for the purpose of this analysis.
Variable cost per unit = $16
Fixed cost = $40,000
Option A Option B Option C Option D Option E
Sales units 3,000 1,900 2,300 2,500 1,700
Unit selling price $29 $36.50 $34 $31.50 $39
Sales revenue $87,000 $69,350 $78,200 $78,750 $66,300
Variable costs 48,000 30,400 36,800 40,000 27,200
Fixed cost 40,000 40,000 40,000 40,000 40,000
Total costs 88,000 70,400 76,800 80,000 67,200
Thus, the price/volume option that meets the firm's goal is Option C because the sales revenue exceeds the total costs.
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Question Completion with Price/Volume Options:A. 3,000 units at $29.00 each.
B. 1,900 units at $36.50 each.
C. 2,300 units at $34.00 each.
D. 2,500 units at $31.50 each.
E. 1,700 units at $39.00 each.
solve the following system of inequalities graphically on the set of axes below?witch of the coordinates points would be in the solution set
Convert the binary number ( 365.24 ) into decimal number.
Given:
The given deciaml number is 365.24.
Required:
We need to convert the given decimal number into a binary number.
Explanation:
Consider the integer part of the given number.
[tex]365[/tex]Divide the number 365.
Consider the fraction part of the given number.
[tex]0.24[/tex]Multiply the number 0.24 by 2.
The binary number of the decimal number is
[tex]365.24_{10}=101101101.0011110101_2[/tex]Final answer:
[tex]101101101.0011110101[/tex]What is the most specific name for each type of special quadrilateral
From the given quadilaterals, let's determine the specific name for each based on the property marked.
• 1a. ,All four sides are marked equal.
Since all four sides are equal, we can say the specific name for the quadilateral is a Square.
A square is a quadilateral with four equal sides.
• 1b. In this quadilateral, we have one pair of parallel sides.
Given that the quadilateral is NOT drawn to scale, the quadilatral here can be said to be a Trapezoid.
A trapezoid is a quadilateral with one pair of parallel side.
• 1c. In this quadilateral, all four angles are marked as right angles.
Given that all four angles are right angles, the specific name for the quadilateral is a Rectangle.
A rectangle is a quadilateral with four interior right angles.
ANSWER:
• 1a. Square
,• 1b. Trapezoid
,• 1c. Rectangle.
After every score in a sample is multiplied by 5,the mean is found to be M = 40.What was the value for the original mean?
Since each of the data value is multiplied by 5, the new mean will be 5 times the original mean.
To get the original mean, we need to divide by 5.
Therefore the original mean is given by:
[tex]\frac{40}{5}=8[/tex]Answer: 8
Picture of question linked. The choices for the answer are -infinity, infinity, and 0
The behavior of any polynomial function is determined by the exponent and the signal of the first term of the function.
In the case of f(x), the leading term is negative, and its expoent is odd. Therefore, when x is negative, the leading term will be positive and, when x is positive, the leading term is negative.
Therefore, we have:
[tex]\begin{gathered} As\text{ }x\rightarrow-\infty,\text{ }f(x)\rightarrow\infty \\ As\text{ }x\rightarrow\infty,\text{ }f(x)\rightarrow-\infty \end{gathered}[/tex]46) The hundreds digit of the smallest six-digit number divisible by 12, 13,
14, 15 and 16 is
Answer: 2
Step-by-step explanation:
[tex]12=2^2 \times 3\\\\13=13\\\\14=2 \times 7\\\\15=3 \times 5\\\\16 =2^4\\\\\therefore \lcm(12, 13, 14, 15, 16)=2^4 \times 3 \times 5 \times 7 \times 13=21840[/tex]
Multiplying this by 5 to make it the smallest possible six-digit number, we get 109200, meaning the hundreds digit is 2.
QUESTION 6Emily has enrolled in a first year math class. The course has 5 assignments each worth 2%, 3 tests worth 20% and 2 tests worth 15%. Emily thus far has completed 3 assignments scoring: 72%, 84%, and 58%. In addition to the assignments, Emily has completed 2 tests: Test 1 (worth 20%) she scored 85% and Test 2 she scored 68% (worth 15%). What is Emily's current grade? Keep the answer in percent and round to the tenth if necessary. Do not input the percent (%) into the answer.
ANSWER:
76.8
STEP-BY-STEP EXPLANATION:
Given:
3 Assignments (2%)
1. 72%
2. 84%
3. 58%
1 Test (20%)
85%
1 Test (15%)
68%
We can calculate Emily's current grade using the weighted average principle, just like this:
[tex]p=\frac{\sum ^{}_{}x_i\cdot w_i}{\sum ^{}_{}w_i}[/tex]In this case, the value of x are the scores and w are the percentages associated with that value, we replace:
[tex]\begin{gathered} g=g=\frac{72\cdot2\%+84\cdot2\%+58\cdot2\%+85\cdot20\%+68\cdot15\%}{2\%+2\%+2\%+20\%+15\%} \\ g=\frac{72\cdot0.02+84\cdot0.02+58\cdot0.02+85\cdot0.2+68\cdot0.15}{0.02+0.02+0.02+0.2+0.15} \\ g=\frac{31.48}{0.41} \\ g=76.78 \\ g\cong76.8\% \end{gathered}[/tex]Therefore, Emily's current grade is 76.8%.
If $2,000 is invested at 6% compounded monthly, what is the amount after 5 years?
Remember that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is the number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
P=$2,000
t=5 years
r=6%=6/100=0.06
n=12
substitute the given values in the above formula
[tex]\begin{gathered} A=2,000(1+\frac{0.06}{12})^{12*5} \\ \\ A=\$2,697.70 \end{gathered}[/tex]therefore
The answer is $2,697.70