Answer: $117
Step-by-step explanation: 1st subtract 3 then divide by 2 then subtract 3 again and divide by 2 again
In a circle, an angle measuring 7.1 radians intercepts an arc of length 2.4. Find the radius of the circle to the nearest 10th.
The radius of the circle with arc length of 2.4 and subtended angle at the center, 7.1 radians is 0.3
What is an arc of a circle?The arc of a circle is defined as the part or segment of the circumference of a circle. A straight line that could be drawn by connecting the two ends of the arc is known as a chord of a circle. If the length of an arc is exactly half of the circle, it is known as a semicircular arc.
length of arc = 2.4
if 7.1 rad is the angle subtended by the intercepts of the arc
But [tex]\pi[/tex] rad = 180°
so 7.1 rad in degree = [tex]\frac{7.1}{\pi }[/tex] x 180 which is [tex](\frac{1278}{\pi } )^{} }[/tex] degree which is [tex]\alpha[/tex]
Length of an arc = [tex]\frac{\alpha }{360} * 2\pi r[/tex]
2.4 = [tex](\frac{1278}{\pi } )^{} }[/tex] x [tex]\frac{1}{360}[/tex] x 2 x [tex]\pi[/tex] x r
The equation reduces to
2.4 = 7.1r
r = 2.4 ÷ 7.1
r = 0.334 which is 0.3
In conclusion the radius of the circle is 0.3
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a farmer wants to fence an area of 3750 square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. what should the lengths of the sides of the rectangular field be so as to minimize the amount of fencing needed?
The lengths of the sides of the rectangular field so as to minimize the amount of fencing needed is 30 feet by 20 feet
Let x represent the length of the fence and y represent the width of the fence.
Since the area is 3750, hence:
Area = length * width = x * y
3750 = xy
y = 3750/x
A fence divide the field in half and is parallel to one of the sides of the rectangle. Hence:
Amount of fencing needed (P) = x + x + y + y + y = 2x + 3y
Amount of fencing needed (P) = 2x + 3(3750/x) = 2x + 1800/x
To minimize the amount of fencing needed, dP/dx = 0, hence:
dP/dx = 2 - 1800/x²
2 - 1800/x² = 0
2 = 1800/x²
2x² = 1800
x² = 900
x = 30 feet
y = 600/x = 600/30 = 20 feet
Hence, the lengths of the sides of the rectangular field so as to minimize the amount of fencing needed is 30 feet by 20 feet
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How can the triangles be proven similar by the SAS similarity theorem? I give brainiest
Answer:
Show that the ratios UV/XY and WV/ZY are equivalent, and ∠V ≅ ∠Y.
An urn has 4 green balls and 6 red balls. A experiment consists of selecting 5 balls from the urn without replacement. Find the expected number of red balls chosen, and its variance.
The expected variance of red balls chosen is 2/3 from the urn.
Define the term variance?Variability is measured by the variance. The average of the squared variance is used to calculate it. The degree of dispersion within your data set is indicated by variance. The variance is greater in respect to the mean the more dispersed the data.Six red balls and four green balls are in an urn.
Till a urn is empty, we take balls out of it one at a time without replacing them and noting their order of the colors.
Let X represent the proportion of red balls in the initial five drawings.Y represent the proportion in the next five draws.The, the variance is found as-
Variance(X,Y) = E(XY) - E(X).E(Y).E(XY)
E(XY) = 25×(6/10)(4/9)
E(X) = 5×(6/10)
E(Y) = 5×(4/10)
Thus,
Variance(X,Y) = 25(6/10)(4/9) - 25(6/10)(4/10)
Variance(X,Y) = 2/3
Thus, the variance for choosing red balls is 2/3.
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donnell is doing market research for a major brand by surveying customers at a local mall the probability of a customer agreeing to take the survey is 22% what is the probability that one of the first five sustomers agrees to take the survey
The probability that one of the first five customers agrees to take the survey is 71%
Here we have to use binomial distribution.
What is binomial distribution?
A common probability distribution known as the binomial distribution simulates the likelihood of getting one of two outcomes given a set of parameters. It provides a summary of the number of trials when each trial has an equal chance of producing a particular result.
A binomial distribution with the following formula could be used to represent the proportion of clients who agree to participate in the survey out of 5:
X ~ Bin (n = 5, p = 0.22)
Thus the probability is computed as:
P(X >= 1) = 1 - P(X = 0) = [tex]1 - (1-0.22)^5[/tex]
= 0.71
The required probability in this case is therefore 71%.
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Write the word sentence as an equation. Then solve the equation.
5 more than a number x is 9.
An equation that represents this word sentence is
The solution is x =
Find the slope of the line that passes through (6, 6) and (3, 13). Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer: -3/7
Step-by-step explanation:
So the fomula for slope is m=x2-x1/y2-y1
if (6,6) is our first coordinate and (3,13) is our second that means 6 is x1 and 3 is x2. 6 will be y1 and 13 will be y2. now we plug in the numbers
m=3-6/13-6
m= -3/7
The hydrogen ion concentration, [H+], in a certain cleaning compound is [H+]=3.3x10^-12. Use the formula pH=-log [H+] to find the pH of the cleaning compound.
The pH of the cleaning compound is 2.51.
What is pH?pH, quantitative measure of the acidity or basicity of aqueous or other liquid solutions.
Given that, The hydrogen ion concentration, [H+], in a certain cleaning compound is [H+]=3.3x10^-12.
[OH-] = 1.0*10^-14/3.3*10^-12 = 0.303*10^-12
pH = -log0.303*10^-12 = 2.51
Hence, The pH of the cleaning compound is 2.51.
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B. If I go to be early, then I sleep well.
Converse:
Inverse:
Contrapositive:
The converse, inverse and contrapositive statements for the given conditional statement are :
Converse: if I sleep well, then I go to be early
Inverse: if I don't go to be early, then I don't sleep well
Contrapositive: if I don't sleep well, then I don't go to be early.
What is conditional statement?A conditional statement is a part of mathematical reasoning which is a critical skill that enables students to analyze a given hypothesis without any reference to a particular context or meaning.
Given is a conditional statement, "If I go to be early, then I sleep well", we need to form its converse, inverse and contrapositive statements,
The rules for the given conditional statement are ;
Let p and q be the parts of the statement,
1) Converse statement = if p then q, converse = if q then p.
Therefore,
Converse: if I sleep well, then I go to be early.
2) Inverse statement = if p then q, inverse = if not p then not q.
Therefore,
Inverse: if I don't go to be early, then I don't sleep well.
3) Contrapositive statement = if p then q, Contrapositive = if not q then not p.
Therefore,
Contrapositive: if I don't sleep well, then I don't go to be early.
Hence, the converse, inverse and contrapositive statements for the given conditional statement are :
Converse: if I sleep well, then I go to be early
Inverse: if I don't go to be early, then I don't sleep well
Contrapositive: if I don't sleep well, then I don't go to be early.
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help help help help help me
What grade is that?
Step-by-step explanation:
A person casts a shadow that aligns with the shadow of a tree. The person is 5.5 feet tall, and casts a shadow of 8.25 feet long. The tree's shadow measures 22.5 feet long.
How tall is the tree? How far is the person standing from the tree?
Part a: Height of tree; 15 feet.
Part b: distance of tree from person; 14.25 feet.
What characteristics do related triangles share?When the ratio of two triangles' respective sides is equal in magnitude while their corresponding angles are congruent, two triangles are said to be comparable in geometry.Furthermore, two geometric forms are only regarded as congruent when their associated side lengths and angle magnitudes are congruent.We can now create an equation which can be used to calculate the height of the tree.Part a: Height of the tree;
We get the following mathematical formula (equation) since the ratio of a corresponding sides of similar triangles is equal in magnitude:
22.5/8.25 = x/5.5
In which
x is the height of the tree.
Then,
22.5/8.25 = x/5.5
Further simplifying;
8.25x = 22.5 × 5.5
8.25x = 123.75
x = 123.75/8.25
x = 15 feet. (height of the tree)
Part b: distance of tree from person;
These calculations can be used to determine how far away from the tree this individual is:
Distance equals the product of a person's shadow and a tree's shadow
Distance = 22.5 - 8.25
Distance = 14.25 feet.
Thus, distance of tree from person is 14.25 ft.
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Given the inequality 3(n − 6) < 2(n 12), determine which integer make the inequality fale. S:{−5}
S:{3}
S:{12}
S:{42}
The FALSE condition for the given inequality 3(n−6)<2(n+12) is (D) S:{42}.
What is inequality?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.
The majority of the time, size comparisons between two numbers on the number line are made.
So, we have the inequality: 3(n − 6) < 2(n + 12)
Now, verify the false inequality as follows:
(A) S:{−5}
3(n − 6) < 2(n + 12)
3(-5 − 6) < 2(-5 + 12)
3(-11) < 2(7)
-33 < 14: TRUE
(B) S:{3}
3(n − 6) < 2(n + 12)
3(3 − 6) < 2(3 + 12)
3(-3) < 2(15)
-9 < 30: TRUE
(C) S:{12}
3(n − 6) < 2(n + 12)
3(12 − 6) < 2(12 + 12)
3(6) < 2(24)
18 < 48: TRUE
(D) S:{42}
3(n − 6) < 2(n + 12)
3(42 − 6) < 2(42 + 12)
3(36) < 2(54)
108 + 108: FALSE
Therefore, the FALSE condition for the given inequality 3(n−6)<2(n+12) is (D) S:{42}.
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Correct question:
Given the inequality 3(n − 6) < 2(n + 12), determine which integer makes the inequality false.
a. S:{−5}
b. S:{3}
c. S:{12}
d. S:{42}
Simplify the following expression completely. 3(2x-1)+5(2x-1)
Answer:
= 16x - 8
Step-by-step explanation:
3(2x - 1) + 5(2x - 1)
8(2x - 1)
16x - 8
Answer:
16x - 8
Step-by-step explanation:
Given expression,
→ 3(2x - 1) + 5(2x - 1)
Simplifying the expression,
→ 3(2x - 1) + 5(2x - 1)
→ 6x - 3 + 10x - 5
→ (6x + 10x) + (-3 - 5)
→ 16x +(-8)
→ 16x - 8
Hence, solution is 16x - 8.
help answer right answers only
Answer:
3. 70 degrees
4. 110 degrees
Step-by-step explanation:
3. The angles are mirrored on both sides
4. A straight line is equal to 180 degrees so if <AED is 70 degrees then you would do 180-70 to get 110 degrees
Hurry please i have 24 hours to do this. The area of the triangle below is 29.25 square feet. What is the length of the base?
6.5 ft
Answer:
length of base = 9 feet
Step-by-step explanation:
b= base A= area h= height
[tex]b=2*\frac{A}{h} = 2*\frac{29.25}{6.5} = 9[/tex]
Three cups of baking soda are poured into 9 mixing bowls so that each bowl holds the same amount of baking soda.
This visual model represents the situation, with each letter representing one of the bowls.
Three equally sized rectangles. Each rectangle is divided into 9 equal parts. Longer lines separate every 3 parts. The first 3 parts of the first rectangle are each labeled A. The second 3 parts of the first rectangle are each labeled B. The third 3 parts of the first rectangle are each labeled C. The first 3 parts of the second rectangle are each labeled D. The second 3 parts of the second rectangle are each labeled E. The third 3 parts of the second rectangle are each labeled F. The first 3 parts of the third rectangle are each labeled G. The second 3 parts of the third rectangle are each labeled H. The third 3 parts of the third rectangle are each labeled I.
How much baking soda does each mixing bowl hold?
Responses
19 cup
1 over 9, cup
16 cup
1 over 6, cup
14 cup
1 fourth, cup
13 cup
Answer:
Answer: 3 or 2 1/2 ethier is right
Step-by-step explanation:
Function g can be thought of as a translated (shifted) version of f(x) = x2.
++
-7-6-5-4-3-2
ल
1
उक्त
-2-
-3-
-5-
-6-
Write the equation for g(x).
9 (x) = [
9
+2
2 3 4 5 6 7
Answer: 3
Step-by-step explanation:
In winter, apple prices suddenly increase by €0.75 per kilogram. Sam bought 3 kilograms of apples for the new price of €5.88.
Answer:
p represents the original per pound price
3p represents the cost of three pounds
3p + 3(0.75) = 5.88 multiply
3p + 2.25 = 5.88 subtract 2.55 from both sides
3p = 3.63 divide both sidesby 3
p = 1.21
The original price was $1.21 per pound.
1.21 = 0.75
1.96
3(1.96)
5.88
question if r and s are positive integers, is r over s less than one third ? (1) r is less than 20. (2) s is greater than 65.
The correct option e. Statements (1) and (2) TOGETHER are NOT sufficient.
(1) r is less than 20: NOT sufficient.(2) s is greater than 65: NOT sufficient.Define the term positive integers?The counting numbers or natural numbers, which are also known as the positive integers, are the numbers 1, 2, 3,... Any figure higher than zero is considered positive.For the stated question-
1. R is less than 20: insufficient since s is unknown.
2. Because there is no date for r, statement 2 is insufficient because S is bigger than 65.
We now have two conditions when combined. s>0 and s>65, r 20 and r>0.
Using the maximum possible value of r as an example and the least possible value of s as an example, the value is greater than 1/3.
Therefore, every values for r would only decrease, while s will rise.
Therefore, simply stating that it won't be below 1/3 will do.
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The complete question is-
If r and s are positive integers, is r/s less than 1/3 ?
(1) r is less than 20.
(2) s is greater than 65.
a. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
b. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
c. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
d. EACH statement ALONE is sufficient.
e. Statements (1) and (2) TOGETHER are NOT sufficient.
Which side is the longest
Answer:
PR
Step-by-step explanation:
The longest side is opposite the largest angle.
Answer: There are two equal sides
Step-by-step explanation:
Considering P and R are both 48 degrees and the only different angle is Q that would mean there are two equal sides.
Help me please
Use the line information to determine the slope and y-intercept
The slope and y-intercept of the given equations of line are shown below.
What is the slope intercept form of an equation ?When any equation is represented in the y = mx +c form, it is called the slope intercept from of the equation.
Here m is slope and c is constant.
(1)
y = 3x + 3
Slope m = 3
y intercept, at x =0,
y = 3
(2)
y = 3x - 3
Slope m = 3
y intercept, at x =0,
y = - 3
(3)
y = (1/3)x + 3
Slope m = 1/3
y intercept, at x =0,
y = 3
(4)
y = -(1/3)x + 3
Slope m = -1/3
y intercept, at x =0,
y = 3
(5)
y = (1/3)x - 3
Slope m = 1/3
y intercept, at x =0,
y = -3
(6)
y = -(1/3)x - 3
Slope m = -1/3
y intercept, at x =0,
y = -3
(7)
y = -3x + 3
Slope m = -3
y intercept, at x =0,
y = 3
(8)
y = -3x - 3
Slope m = -3
y intercept, at x =0,
y = - 3
The slope and y-intercept are shown above.
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out of 240 racers who started the marathon, 209 completed the race, 22 gave up, and 9 were disqualified. what percentage did not complete the marathon?
The percentage of racers that did not complete the marathon is 12.9 %
What is arithmetic?
Arithmetic is an elementary a part of mathematics that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, involution, and extraction of roots
Main Body:
Total racers = 240
racers that completed race = 209
so racers that did not complete the marathon = 240 - 209
= 31
percentage of racers that did not complete the marathon = (31/240)*100
= 12.9 %
Hence percentage of racers that did not complete the marathon is 12.9%
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what is the answer i need an answer pls
Answer: The first option
Step-by-step explanation: Once you multiply all the denominators to make them the same, the numerators (in the original order they are given in) become 63, 16, and 44.
16<44<63, which is the first option.
a ladder reaches a maximum length of about 23 m. for any ladder to be safe, the angle it makes with the ground should be between 65° and 70°. one storey of a building is about 4 m. a fire breaks out on the fifth storey of a building. will the extension ladder reach the fifth storey safely?
Answer:
Given,
Let's assume the maximum safe height of wall = h
angle formed between ladder and ground = 70°
length of ladder = 16 ft
From the given data, it can be seen that ladder will form a right angle triangle structure with the wall
So,from the concept of trigonometry,
Sin70^o\ =\ \dfrac{\textrm{maximum safe height of wall}}{\textrm{length of ladder}}Sin70
o
=
length of ladder
maximum safe height of wall
= > Sin70^o\ =\ \dfrac{h}{16\ ft}=>Sin70
o
=
16 ft
h
= > \ h\ =\ 16\times Sin70^o=> h = 16×Sin70
o
=> h = 16 x 0.9396
=> h = 15.03 ft
So, the maximum safe height that can be reached by the ladder will be 15.03 ft.
Sorry I put the wrong answer.
find the mean, median and mode of these numbers: 9, 10, 9, 9, 11, 9, 10, 9, 9, 10 round all answers to the hundreth place.
The mean median mode of the data 9,10,9,9,11,9,10,9,9,10 is
Mean =9.5
Median = 11 or 9
Mode is 9
Given that,
The data is 9,10,9,9,11,9,10,9,9,10
The data's mean, median, and mode must be determined.
We know that,
The arithmetic mean of the provided data is another name for mean. If the data are grouped and sorted in ascending order, the median is the value that falls in the middle of the set of grouped data. The value that dominates the data is known as the mode. The Mean, Median, and Mode formulas are described independently for the group of data in the sections that follow.
The data is 9,10,9,9,11,9,10,9,9,10
Mean = 9+10+9+9+11+9+10+9+9+10/10 =95/10=9.5
Median = 11 or 9
Mode is 9
Therefore, The mean median mode of the data 9,10,9,9,11,9,10,9,9,10 is
Mean =9.5
Median = 11 or 9
Mode is 9
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the sum of the height and radius of a right cylinder is 12 inches. what is the maximum volume of this cylinder
The maximum volume of this cylinder = 256π cubic inches
What is volume?
In three-dimensional space, volume is the area occupied by an object within its borders. Another name for it is an object's capacity.
Let h be the height and r be the radius.
Then, h+r = 12
=> h=12-r
Volume of the cylinder (V):
V=πr²h
=> h= πr² ( 12-r )
=> h= π ( 12r² - r³ )
Differentiate with respect to r , we get
dv/dr = 24 πr - 3πr²
Find r by taking dv/dr=0
24 πr - 3πr² = 0
3π ( 8r - r² ) = 0
8r = r²
r=8
Again differentiating, we get
d²V/dr² = 24π - 6 π r
When r=8, 24π - 48 π <0
So, V is maximum at r= 8 inches
And h= 12-8= 4 inches
Hence, the required volume of the cylinder = π8²*4 = 256π cubic inches
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Please help :') ty ty ty ty ty. Show your work too! :)
Please answer asap!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
I would be C
Step-by-step explanation:
lookup here
some stickers were divided among avea, brianna, and carson in the ratio 1:3:4. brianna recieved 21 stickers. how many stickers did ava receive?
Avea received 28 stickers when brianna, and carson in the ratio 1:3:4 and brianna received 21 stickers.
What is a ratio?The ratio is defined as the comparison of two or more quantities of the same units, which shows how much bigger one quantity is than another.
Equating the ratios :Given,The ratio of the distribution of stickers among Avea, Brianna and Carson is 1:3:4
The number of stickers Briana received is 21
Let us consider x as the common factor of the given ratio then, The number of stickers received by the girls are
Avea = xBriana = 3x
Carson = 4x
As we know 3x = 21 x
= 21/3
= 7
then,4x
= 4×7
= 28
The number of stickers that Avea received is 28. Hence, the answer is 28
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a farmer needs to enclose three sides of a garden with a fence (the fourth side is a river). the farmer has 47 meters of fence and wants the garden to have an area of 266 sq-meters. what should the dimensions of the garden be?
The dimensions of the garden would be length = 28 meters and width = 9.5 meters.
What are quadratic equations?
A quadratic equation in math is a second-degree equation of the form ax² + bx + c = 0. Here a, and b, are the coefficients, c is the constant term, and x is the variable. Since the variable x is of the second degree, there are two roots or answers for this quadratic equation.
Let the width be = w
Let the length be = L
enclose three side ( 2w+L) = 47 meter
L = 47-2w
Area of field = w*L
Area = w(47 - 2w)
266 = 47w - 2w²
2w² - 47w + 266 = 0
Solving this, we get
w = 14 or w = 9.5
The width should be less than the length so w = 9.5
Length = 47 - 2(9.5)
= 47 - 19
= 28 meters.
Hence, the dimensions of the garden would be length = 28 meters and width = 9.5 meters.
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