considering the distance between the center of the circle and the chord is perpendicular, pythagorean theorem can be applied to calculate the radius of the circle.
[tex]r^2=a^2+b^2[/tex] , r=radius, a=half of the chord length, b the distance between the center of the circle and the center of the chord
[tex]r^2=(4.5cm)^2+(5cm)^2\\r^2=20.25cm^2+25cm^2\\r^2=45.25cm^2\\r=\sqrt{45.25cm^2}\\r=6.7268cm[/tex]
What is the solution set of this inequality?
-8-1> 3z + 14
Answer:
z>7.67
Step-by-step explanation:
-9>3z+14
3z<-14-9
3z<-23
3z>23
z>(23÷3)
z>7.67
Michael is using a number line to evaluate the expression –8 – 3.
After locating –8 on the number line, which step could Michael complete to evaluate the expression?
The next step that Michael could use to evaluate the expression is count 3 units to the left of -8
Which step could Michael complete to evaluate the expression?The expression is given as
-8 - 3
The first step is given as
Locating –8 on the number line
The other term of the expression is a negative number i.e. -3
This means that Michael needs to count 3 units to the left of the first number
Hence, the next step that Michael could use to evaluate the expression is count 3 units to the left of -8
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Alonzo is playing a role playing game with his friends. He will roll dice to determine if his character casts a spell. The odds in favor of his character casting a spell are 13/6. Find the probability of his character casting a spell.
A child has a box full of colored building blocks. If he chooses one block without looking, the probability of choosing a green block is 7/9. What are the odds against choosing a green block?
A. The probability of his character casting a spell will be 1/6.
B. The odds against choosing a green block is 2/9.
How to calculate the probability?A. It should be noted that probability has to do with the chance of a particular thing happening.
In this case, the odds in favor of his character casting a spell are 1/6, therefore the probability of his character casting a spell is 1/6.
B. When a child has a box full of colored building blocks and he chooses one block without looking, the probability of choosing a green block is 7/9, therefore, the odds against choosing a green block will be:
= 1 - P(green block)
= 1 - 7/9
= 2/9
Therefore, the odds against choosing a green block will be 2/9.
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How long does it take to ride a bicycle 100 miles at each of the following speeds: 5 mph, 10 mph, 15 mph, 20 mph, 25 mph? What is always true about the product speed x time?
Answer:
5 mph ⇒ 20 h10 mph ⇒ 10 h15 mph ⇒ 6 2/3 h20 mph ⇒ 5 h25 mph ⇒ 4 hspeed × time = 100 miles
Step-by-step explanation:
The graph shows an inverse relation between speed and time. You want to know what is true about the product of speed and time.
Inversely proportionalTwo quantities are inversely proportional when one is proportional to the inverse of the other. A constant of proportionality will be involved. The relation can be written ...
y = k(1/x)
where x and y are the quantities inversely related, and k is the constant of proportionality.
ApplicationIn the present case, we have a graph of the relation ...
time = distance/speed
where the distance is 100 miles.
Comparing this to the above inverse proportion relation, we see that "distance" is the constant of proportionality (k):
time = (100 miles)/speed
The times at various speeds are ...
5 mph ⇒ 20 h10 mph ⇒ 10 h15 mph ⇒ 6 2/3 h20 mph ⇒ 5 h25 mph ⇒ 4 hMultiplying both sides of this equation by speed, we get ...
speed × time = speed × (100 miles)/speed
speed × time = 100 miles
The product of speed and time is always 100 miles in this scenario.
How do I do this? A tennis tournament starts with 117 players. If a player is eliminated after losing three matches, what is the least possible number of matches played when four players are left?
When only 4 players remain, the fewest number of matches that can be played is 37.
What do we mean by algebra?Algebra is one of the many branches of mathematics. Algebra, in broad terms, is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a thread that runs through almost all of mathematics.Given information:
The total number of players in the tournament is 117.number of players to be eliminated after losing three matches = 1, number of matches played when only four players remain = nWhen only four players remain, the smallest number of matches that can be played is calculated as follows:
117 - 1(3n) = 4117 - 3n = 43n = 117 - 43n = 113Now, divide both sides by 3 as follows:
n = 113/3n = 37.67n ≈ 37 matchesTherefore, when only 4 players remain, the fewest number of matches that can be played is 37.
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The largest fish ever caught in lake a Weighed 651 pounds. This is 95.4 pounds less than six times the weight of the largest fish ever caught in lake B find the weight of the largest fish caught in lake b?
Answer:
124.4 pounds
Step-by-step explanation:
We have:
651 + 95.4 = 6.B
=> 746.4 = 6.B
=> B = 746.4/6
=> B = 124.4
What is the LCM of 10 and four
The least common multiple of 10 and 4 is 20.
L.C.M is defined as Least Common multiple. The Least Common multiple of two numbers is the least possible number that can be divisible by both the numbers. Or, in simple words, the least common multiple of two or more numbers is the smallest number among all common multiples of the given numbers.
We need to find the L.C.M of two numbers which are 10 and 4
First we will find out few multiples of 10 and 4which are:
multiples of 10 : 10,20,30,40,50,60,70,80.....
multiples of 4 : 4,8,12,16,20,24,28,32,36,40,......
Then we will filter out the common multiple.
common are : 20 and 40
From these two number the least number is 20.
Hence the least common multiple of 10 and 4 is 20.
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Find two factors of the first number such that their product is the first and the sum is the second for 51,20
The factors are 17 and 3.
The given conditions are two factors of the first number, 51 such that their product is 51 and the sum is the second number 20.
let say, the factors are x and y.
therefore, we can write, x.y = 51 ... (1) and x + y = 20 .... (2)
Putting the value of x from equation (2) in equation (1) we get,
(20 - y).y = 51
or, 20y - y² = 51
or, y² - 20y + 51 = 0
or, y = 17, 3
then x = 3,17
Therefore, The factors are 17 and 3.
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QUESTION 6
A product costing 60 cents per unit to produce had been selling at the average rate of 1,200,000 units per month. After the product was improved, sales increased to an average of 2,000,000 units per month. However, the new product cost five percent more to produce. If the manufacturer's selling price in each instance was 75 cents per unit, what was the manufacturer's added profit per month with the newer product?
O, a. $20,000
O b. $240,000
• c. One cannot tell from the information given.
O d. $60,000
O e. $200,000
Thus the profit of the manufacturer is 240000$ per month
It is given that a product costing 60 cents per unit to produce had been selling at the average rate of 1,200,000 units per month.
After the product was improved, sales increased to an average of 2,000,000 units per month.
It is also given that the new product cost five percent more to produce.
If the manufacturer's selling price in each instance was 75 cents per unit, We are required to find what was the manufacturer's added profit per month with the newer product.
Cost price is the price which the manufacturer pays for each unit
It is given that the cost price of new version is 5 percent more than the previous one.
Thus, the cost price of each unit of product = 60 cents +5 percent of 60 cents = 60+5/100*60=63 cents
It is also given that selling price of each unit is 75 cents
Profit=selling price- cost price
= 75-63= 12 cents
Thus, total profit on selling the 2000000 products= 2000000x12cents
Now we know that 100 cents = 1 dollar
Thus the profit in dollars will be = 2000000*12/100=240000
Thus the profit of the manufacturer is 240000$ per month
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A bag with 10 marbles has 3 blue marbles, 2 red marbles, and marbles, and 5 yellow marbles A marble is chosen from the bag at random.what is the probability that it is blue
Answer:
10 Probability of blue is 2/10%
Step-by-step explanation:
lim x 3^ + |6-2x|/ sqrt x-3
Answer: maybe this will help. try searching this
Lim x 3^ + |6-2x|/ sqrt x-3 Evaluate the expression. to watch this video that I have screenshot down below.
Step-by-step explanation:
Brayden is saving up to buy a new video game. He already has $25 and can save an
additional $5 per week using money from his after school job. How much total money
would Brayden have after 4 weeks of saving? Also, write an expression that represents the amount of money Brayden would have saved in w weeks.
Total savings after 4 weeks:
Total savings after w weeks:
Answer:
After 4 weeks: $45, After w weeks: 5w + 25
Step-by-step explanation:
5 per week is 20 for 4 weeks. $25 + $20 = $45.
5w is 5 times the week. +25 because he had 25 to begin with. 5w+25.
What is the value of the function at x=−2?
Answer:
See below
Step-by-step explanation:
Look for where the vertical line x = -2 crosses the graph.....the value is shown below.....
Su mei is looking at online classified ads. she finds a used cell phone for US$99 plus US$30 for shipping. The same cell phone cost C$199 new at a local store. a) what is the total cost of the used cell phone in canadian dollars. b) Do you think Su Mei should buy the cell phone online why
The total cost of the used cell phone in Canadian dollars is C$130.16.
Su Mei should buy the used cell phone because it is cheaper than the new cell phone.
Which phone should Su Mei buy?
The exchange rate is the rate at which one unit of a currency is exchanged for another currency. For example, if the exchange rate of the US dollar and the Canadian dollars is 1.00903. It means that 1 unit of the US dollar would buy 1.00903 of the Canadian dollars.
The first step is to determine the total cost of the used cell phone in US dollar. The total cost would be the sum of the used cell phone and the shipping cost.
Total cost of the used cell phone = $99 + $30 = $129
The next step is to convert the cost of the used cell phone that is priced in the US dollar to Canadian dollars.
129 x 1.00903 = $130.16
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Find the equation of the line with slope 4 which goes through the point (8,5).
Give your answer in slope-intercept form y=mx+b.
Answer:
y = 4x - 27
Step-by-step explanation:
The point (8,5) contains and x and y on the line. The x is 8 and the y is 5. Using this and the slope given we can write the equation. We need to solve for b.
y = mx + b
5 = 4(8) + b
5 = 32 + b Subtract 32 from both sides of the equation
-27 = b
y = mx + b
y = 4x - 27
Answer:
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Step-by-step explanation:
y-y1=m(x-x1)
where y1=5,x1=8 and m=4
y-5=4(x-8)
y-5=4x-16
y=4x-16+5
y=4x-11
Find the circumference and area of circle X if each unit on the graph measures 1 centimeter. Round answers to the
nearest tenth, if necessary.
The circumference and area of the circle are 13cm and 13cm^2 respectively
How to determine the valuesThe formula for circumference of a circle is expressed as:
Circumference = 2πr
From the graph shown, we have the radius of the circle as 2 cm
Substitute the value into the formula
Circumference = 2 × 3. 142 × 2
Multiply through
Circumference = 12. 568
Circumference = 13cm
The formula for area of a circle is expressed as:
Area = πr^2
Substitute the value into the formula
Area = 3. 142 × (2)^2
Area = 3. 142 × 4
Area = 12. 568
Area = 13cm^2
Thus, the circumference and area of the circle are 13cm and 13cm^2 respectively.
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If AC = 31 and BC = 6, then AB
The measure of segment AB from the given question is 25
Addition postulate
In line geometry, a line is the distance between two points while an angle is the point where two lines intersect.
Given the following parameters
AC = 31
BC = 6
Required
AB
Using the addition postulate
AB + BC = AC
Substitute
AB = AC - BC
AB = 31 - 6
AB = 25
Hence the measure of segment AB from the given question is 25
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12. When Bruce started bowling, he won
7
of the games he played. Within six months,
he was winning of his games. If he
improves at the same rate, what fraction
16
of his games should he expect to win after
another six months?
Answer:
I think the answer is 7/16 hope it's correct
Solve the absolute value equation or indicate that the equation has no solution. |x-5|=4
Step-by-step explanation:
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How to turn a decimal number into a fraction
For an example-
(1.5)
Answer: 3/2 for improper fraction and 1 1/2 for a mixed number
Step-by-step explanation:
Represent the values of x in interval notation:
x can be any real number between 5 and
I
Points possible: 10
This is attempt 1 of 1.
Submit
-
3 or any real number greater than or equal to 22.
Use "oo" for infinity.
License
Interval notation
(-5,-3) U [22,00)
• Interval notation in mathematics is a method to represent an interval of a number on the number line. In simpler words, interval notation is a way of writing subsets of the real number line .
• An interval comprises of the numbers lying between two specific given numbers. For example a set of numbers lying between 0 and 3 is an interval that contains 1,2.The way to represent interval notation is by using square bracket or round brackets, square brackets for both value included and round brackets for both value not included.
We are given that x is a real number which lies between -3 and -5 or any real number greater than or equal to 22
Firstly, x lies between -3 and -5
-5< x <-3
x = (-5,-3)
Secondly, x is greater than 22
x>=22
x = [22,00)
Interval notation
(-5,-3) U [22,00)
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if 8/9 is multiplied by 3/7 will the product be greater than either of the 2 factors
If 8/9 is multiplied by 3/7 then the product will not be greater than either of the two factors.
According to the question
on multiplying 8/9 by 3/7 we get
=8/9*3/7
=(8*3)/(9*7)
=24/63
=0.38095 ...(i)
On comparing it with two factors,
8/9 = 0.88888 .....(ii)
and
3/7 = 0.42857 ......(iii)
As we can see that on comparing equation (i) with equation (ii) and
equation (i) with equation (iii) , we get that the product of 8/9 and 3/7 is less than both 8/9 and 3/7 .
Therefore , if 8/9 is multiplied by 3/7 then the product will not be greater than either of the two factors.
The given question is incomplete , the complete question is
If 8/9 is multiplied by 3/7 , will the product be greater than either of the 2 factors ?
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f(x) = 3x + 2
f(4) = ?
Answer:
3x+2 = 14.12
f(4) = 0
Answer: EVALUATE
3x+8f
f(x)=3x+2f(4)=
Multiply 2 and 4 to get 8.
3x+8f
DIFFERENTIATE W.R.T. X
3
Step-by-step explanation:
A traffic cone with a height of 20 in. is ideal for traffic control. Find the lateral area of a cone with a height of 20 in. and a diameter of 12 in. Round the answer to the nearest whole number.
The lateral area of the cone is 394 square inches
How to determine the lateral areaThe formula for lateral area of a cone is expressed as;
Lateral area = πr √h² + r²
Given that;
height = 20 inDiameter = 12 in, radius = 12/ 2 = 6 inSubstitute the values into the formula
Lateral area = 3. 142(6) √20² + 6²
Lateral area = 18. 85 √436
Lateral area = 18. 85 × 20. 8
Lateral area = 394 square inches
Thus, the lateral area of the traffic cone is 394 square inches
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Random simple service of voters were taken in three different regions of a county that has a voter population of 55,000. On average 42 out of 100 voters supported issue seven and 58 oppose it estimated number of voters in the county who support the issue.
Answer: 23100 voters
Step-by-step explanation:
42*55000=2310000
2310000/100=23100 voters
A bottle of Vitamin E contains 100 soft gels, each containing 15 mg of vitamin E. How many total
grams of vitamin E are in this bottle?
Answer:
1.5 g are in that bottle.
Step-by-step explanation:
100 soft gels × 15 mg each = 1500 mg of vit. E
1500 mg = 1.5 g
What two variables are involved in this problem? Which variable can best be designated as the dependent variable? As the independent variable? a. Independent variable - amount of depreciation per year; Dependent variable - number of years you own the truck. b. Independent variable - value of the truck; Dependent variable - amount of depreciation per year. c. Independent variable - number of years you own the truck; Dependent variable - value of the truck. d. Independent variable - value of the truck; Dependent variable - number of years you own the truck.
The designation of the dependent variable and the independent variable can be d. Independent variable - value of the truck; and Dependent variable - number of years you own the truck.
How to determine the designation of the dependent variable and the independent variable?In most cases, dependent variables are used to represent discrete values
Take for instance:
Number of yearsNumber of hoursNumber of peopleWhile independent variables are used to represent continuous values
Take for instance:
AmountCostUsing the above as a hint, the designation of the dependent variable and the independent variable can be d. Independent variable - value of the truck; and Dependent variable - number of years you own the truck.
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determine how many different possibilities for two-digit numbers 1,5,3,6,9
Answer:
Step-by-step explanation:
unit place can be selected in ways=5
ten's place can be selected in ways=5
total numbers=5×5=25
but if the numbers at two places is different then number of ways=5×4=20
6. Describe the shape of the distribution
shown in the histogram which displays
the light output, in lumens, of various light
sources. (Lesson 1-4)
20
18
16
14
12
10
8+
6+
4
2-
200
400
600
800 1,000
Lumens
1,200
Answer:1200
Step-by-step explanation: