The perimeter of the circle formed by bending the rectangular wire will be equal to the length of the wire.
Perimeter of the circle = Length of the wire
2πr = 2(l+b) where r is the radius of the circle, l is the length of the wire, and b is the breadth of the wire.
Substituting the given values, we get:
2 x 3.14 x r = 2(32 + 12)
6.28r = 88
r = 14 cm
Therefore, the radius of the circle is 14 cm.
Answer:
14.01 cm
Step-by-step explanation:
The length of the wire is equal to the perimeter of the rectangle. So, the length of the wire is:
2 × (32 + 12) = 88 cmWhen this wire is bent into a circle, its length becomes equal to the circumference of the circle. The formula for the circumference of a circle is:
(let r = radius)
2 × π × rSo, we can write:
2 × π × r = 88Solving for r, we get:
r = 88 ÷ (2 × π) = 14.01 cmSo, the exact value of the radius of the circle formed by bending this rectangular wire is 14.01 cm.
Find the value of z such that 0.6318 of the area lies between −z and z. Round your answer to two decimal places.
A standard normal distribution table or a calculator again, we can find that the z-score that corresponds to this area is approximately 0.42.
Describe Standard Normal Distribution?The standard normal distribution is useful because it allows us to calculate probabilities for any normal distribution by converting the distribution to a standard normal distribution using a process called standardization. Standardization involves subtracting the mean of the distribution from each observation and then dividing by the standard deviation. The resulting values are called z-scores, and they represent the number of standard deviations that an observation is from the mean of the distribution.
Assuming a standard normal distribution, we know that 0.5 of the area lies between -z and z, since the normal distribution is symmetric around the mean. Therefore, we need to find the value of z such that the area between -z and z is 0.6318 - 0.5 = 0.1318.
Using a standard normal distribution table or a calculator, we can find that the area between the mean and z is 0.5 + 0.1318/2 = 0.5659. Therefore, the z-score that corresponds to this area is approximately 0.18.
Since the distribution is symmetric, the area between -z and z is twice the area between the mean and z, so we can solve for z:
0.1318/2 = 0.0659 of the area lies between the mean and z
Using a standard normal distribution table or a calculator again, we can find that the z-score that corresponds to this area is approximately 0.42.
Therefore, z = 0.42 rounded to two decimal places.
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82. Write an expression that represents the number that
(a) is 7 more than X;
(d) exceeds X by 7;
(b) is 7 less than X;
(e) is X less than 7;
(c) is X more than 7
(f) exceeds 7 by X
Answer:
dont understand 14+14=π
Decompose the composite figure to find its total area.
Answer:
152 in²
Step-by-step explanation:
Area of rectangle = L x W
1st rectangle area
10 x 8 = 80 in²
2nd rectangle area
Length = 20 - 8 = 12 in
12 x 6 = 72 in²
Total area
80 + 72 = 152 sq. in
So, the answer is 152 in²
The temperature in Chicago was 7 degrees Celsius. It was dropping at a steady rate of 3 degrees per hour. How many hours did it take for the temperature to drop below -5 degrees Celsius?
Write an inequality that represents the situation.
Answer:
-3x+7 < -5
Step-by-step explanation:
Lets set x as the number of hours since the time it was 7 degrees.
This means that the expression 7-3x would represent the temperature after x hours.
To find the inequality that represents when it would be below -5 degrees, we just set this less than -5:
-5 > 7-3x.
If you want, you can also rearrange this to -3x+7 < -5.
Answer:
4 hours
Step-by-step explanation:
Inequality:
[tex]7-3x < -5[/tex]
[tex]7-7-3x < -5-7[/tex]
[tex]-3x < -12[/tex]
[tex]\frac{-3x}{-3} < \frac{-12}{-3}[/tex]
[tex]x > 4[/tex]
Hope this helps
The drop down options are “greater than”, “less than”, and “equal to”
The length of FG is equal to the length of F'G'.
The perimeter of pentagon CDEFG is equal to the perimeter of pentagon C'D'E'F'G.
What are the properties of a translated shape?The properties of a translated shape are the shape and size of the translated shape are the same as that of the original shape. The orientation of the translated shape is the same as that of the original shape. The distance between the corresponding points of the translated shape and the original shape is constant.
The area and perimeter of the translated shape are the same as that of the original shape. The interior angles of the translated shape are the same as that of the original shape. The coordinates of the vertices of the translated shape are obtained by adding a constant value to the corresponding coordinates of the vertices of the original shape.
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Image transcribed:
Pentagon CDEFG is translated 7 units up and 5 units left, resulting in pentagon C'D'E'F'G' (not shown).
Part A
Select from the drop-down menu to correctly complete this sentence:
The length of FG is ___ the length of F'G'.
Part B
The perimeter of pentagon CDEFG is ____ the perimeter of pentagon C'D'EF'G.
The quadratic regression corresponding to the number of birds f(x) in a park relative to the number of people x in the same park is given by f(x) = -0.1536x² + 3.3915x +88.738. Use the quadratic regression to estimate the number of people in the park when there are 80 birds. Round your answer to the nearest whole number. en is Provide your answer below: people An
The quadratic regression function f(x) = -0.1536x² + 3.3915x + 88.738, then estimate value for the number of people in the park when there are 80 birds is equals to the 24.
A quadratic regression is the process of finding the equation of the parabola that best fits a set of data. An equation of the form, y = ax² + bx + c where a≠0. We have a quadratic regression function is defined by f(x) = -0.1536x² + 3.3915x +88.738 --(1), where, f(x) = the number of birds in a park relative to the number of people x in the same park. We have to determine quadratic regression to estimate the number of people in the park when there are 80 birds. Now, f(x) = 80, substitute the known value in equation (1),
=> 80 = -0.1536x² + 3.3915x +88.738
=>0.1536x²- 3.3915x -88.738 + 80 = 0
=> 0.1536x²- 3.3915x - 8.738 = 0
=> x² - 22.08x - 56.88 = 0 --(2)
Using the quadratic formula for solution of (2), x = (-b ±√b² - 4ac)/2a, for ax² + bx + c = 0. So, [tex]x =\frac{ -(-22.08) ± \sqrt{(22.08)² + 4× 56.88}}{2}[/tex]
=> x = 24.41 or - 2.3331
but number of people can't be negative hence, the required value is 24.41 ~ 24.
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It was incorrect. A=80-B, C=70-B.
(80-b) +b+(70-b)=100. Therefore:
80-70-b=100
B= - 90. Negative number,
So, A=170
C=160. Correct answer
The values of A, B, and C are 30, 50, and 20, respectively.
What is the sum?
The sum is the result of adding two or more numbers together. The sum is found by performing the operation of addition, which involves combining the values of two or more quantities to find the total or the sum.
If A = 80 - B and C = 70 - B, and the sum of A, B, and C is 100, then we can write:
A + B + C = 100
Substituting A and C with their given values, we get:
(80 - B) + B + (70 - B) = 100
Simplifying and combining like terms, we get:
150 - B = 100
Subtracting 150 from both sides, we get:
-B = -50
Dividing both sides by -1, we get:
B = 50
Now that we know B = 50, we can substitute this value back into the equations for A and C:
A = 80 - B = 80 - 50 = 30
C = 70 - B = 70 - 50 = 20
Therefore, the values of A, B, and C are 30, 50, and 20, respectively.
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Homework Progress 19 / 22 Marks Four different sized jerry cans are shown below. A holds 30 litres Write the missing fractions as simply as possible. The first one is done for you. Can D holds of the amount can C holds. Can C holds of the amount can A holds. Can D holds B holds 18 litres of the amount can B holds. Can B holds C holds 6 litres holds 3 litre of the amount can A holds. Answer
The fraction shows that can d holds 1/2 of the amount can c holds.
Can c holds 1/5 of the amount can a holds.
Can d holds 1/6 of the amount can b holds.
Can b holds 1/5 of the amount can a holds.
How to explain the fractionCan d holds 1/2 of the amount can c holds. This is because can d holds 3 litres and can c holds 6 litres, so if you divide the volume of can d (3 litres) by the volume of can c (6 litres), you get 3/6 or 1/2.
Can c holds 1/5 of the amount can a holds. Can c holds 6 litres and can a holds 30 litres, so if you divide the volume of can c (6 litres) by the volume of can a (30 litres), you get 6/30 or 1/5.
Can d holds 1/6 of the amount can b holds: This is because can d holds 3 litres and can b holds 18 litres, so if you divide the volume of can d (3 litres) by the volume of can b (18 litres), you get 3/18 or 1/6.
Can b holds 1/5 of the amount can a holds: This is because can b holds 18 litres and can a holds 30 litres, so if you divide the volume of can b (18 litres) by the volume of can a (30 litres), you get 18/30 which can be simplified as 3/5 or 1/5.
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What is the area, in square inches, of the shaded part of the rectangle below?
72 points <3
Answer:
Step-by-step explanation:
16 × 19 = 304
1/2(19×9)=85.5
304-85.5= 218.5
1. Given the function f(x)=x^2+1, copy and complete the following table
A
,
B
and
C
form a triangle where
∠
B
A
C
=
90
∘
.
A
B
=
14.7
mm and
B
C
=
25.9
mm.
Find the length of
A
C
, giving your answer rounded to 1 decimal place.
To find the length of AC, we can use the Pythagorean theorem, which states that in a right triangle. the length of AC is approximately [tex]29.8 mm[/tex].
What is the square of the length of the hypotenuse?the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, we can use AC as the hypotenuse, so:
[tex]AC^2 = AB^2 + BC^2[/tex]
[tex]AC^2 = (14.7 mm)^2 + (25.9 mm)^2[/tex]
[tex]AC^2 = 216.09 mm^2 + 671.61 mm^2[/tex]
[tex]AC^2 = 887.7 mm^2[/tex]
Taking the square root of both sides, we get:
[tex]AC = \sqrt887.7 mm[/tex]
[tex]AC \approx 29.8 mm[/tex] (rounded to 1 decimal place)
Therefore, the length of AC is approximately [tex]29.8 mm[/tex].
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Rajan baut a book for Rs 180 and sold it to sajan at a profit of 20%. Sajan sold that book to nirajan at a lost 20%. At what price nirajan should sell the book to receive 5% profit ?
Solution,
CP for rajan=180 rs
Sp for rajan=(20%+1)×180
=216
Cp for niranjan=216
And, Sp=.8×216
=172.8
Cp for niranjan=172.8
For 5% profit,
Sp for Niranjan=(5%+1)×172.8
=181.44
Hence, for Niranjan to gain 5% profit, he must sell it for 181.44 rs
Answer - 181.44
Explanation - For Rajan,
Cost Price = Rs 180
Profit Percent = 20%
Profit Percent = (S.P - C.P/C.P)*100
20 = (S.P - 180/180) *100
S.P = Rs 216
For Sajan,
C.P = Rs 216
Loss Percent= 20%
Loss = (C.P - S.P/C.P)*100
20 = (216-S.P/216)*100
S.P = Rs 172.8
For Niranjan to Sell Book and get 5% profit,
C.P = Rs 172.8
Profit Percent = (S.P - C.P/C.P)*100
5 = (S.P-172.8/172.8)*100
S.P = 181.44
Help please, view attachment below
Which graph represents the function over the interval [−3, 3]?
f(x)=⌈x⌉−3
The correct graph is Option D - the bottom left graph.
What is the explanation for the above?Given function is f(x)=ceil(x+1)
To plot graph of f(x) in interval of(-3,3) :
ceil(x+1) is ceiling function
The output of ceil(x) is least integer greater than x
for example ceil(5.5)=6
For an interval of (-3,-2):
Take x=(-2.4)
x+1=(-1.4)
y=f(x)=ceil(x+1)=(-1)
Similarly,
For an interval of (-2,-1):
Take x=(-1.4)
x+1=(-0.4)
y=f(x)=ceil(x+1)=(0)
For an interval of (-1,0)
y=f(x)=1
For an interval of (0,1)
y=f(x)=2
For an interval of (1,2)
y=f(x)=3
For an interval of (2,3)
y=f(x)=4
Thus, The correct graph is the bottom left graph.
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Pls help! I don't know what to do!!
14. The length of AB for the given right-angled triangle is [tex]$24{\sqrt{2}}$[/tex].
15. The value of base GF is √247 or 15.716234
What are Heights and Distances in trigonometry?The ideas of angles, right triangles, and the trigonometric functions of sine, cosine, and tangent are used in trigonometry to calculate heights and distances.
It is possible to determine the height of an object or the distance between two objects by measuring the angle of elevation or depression between the observer's line of sight and the object being observed and the distance between them. These ideas are frequently applied in the engineering, navigation, and surveying industries.
14. In a right-angled triangle, if one angle is 45 degrees, then the other acute angle is also 45 degrees and hence,
Let AB = x
Using the trigonometric ratio for the 45 degree angle in the triangle:
tan(45) = opposite/adjacent
We know that the opposite side is BC = [tex]$24{\sqrt{2}}$[/tex] and the adjacent side is AB = x.
tan(45) = BC/AB
1 = [tex]$24{\sqrt{2}}/x$[/tex]
x = [tex]$24{\sqrt{2}}$[/tex]
15. Using Pythagoras theorem:
HF² = HG² + GF²
16² = 3² + GF²
GF² = 16² - 3²
GF² = 256 − 9
GF² = 247
GF = √247
GF = 15.716234
Thus, The value of base GF is √247 or 15.716234
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50 POINTS!!!!! PLEASE HELP ASAP
Example of the Disjunctive Syllogism?
Premise:
Premise:
Conclusion:
disjunctive syllogism = p v q, ~ p / q
example: he wants to be on either the football or wrestling team. he's not on the wrestling team. therefore, he's on the football team.
A student mows lawns on the weekends. It takes him 120 min to mow 4 lawns. What prediction can you make about the time he will spend this weekend if he has 12 lawns to mow?
It will take him 30 hours to mow 12 lawns.
It will take him 9 hours to mow 12 lawns.
It will take him 6 hours to mow 12 lawns.
It will take him 3 hours to mow 12 lawns.
Answer: It will take him 6 hours
Step-by-step explanation: 4 lawns = 120 min
1 lawn = 30 min
12 lawn = 360 min = 6 hours
To mow 12 lawns, the student will spend 6 hours.
Explanation:To predict the time the student will spend mowing 12 lawns, we can use the information given in the question. The student takes 120 minutes to mow 4 lawns. We can calculate the time the student will take to mow 1 lawn by dividing 120 minutes by 4, which equals 30 minutes per lawn. Since the student has 12 lawns to mow, we multiply 30 minutes by 12 to get the total time. The student will spend 360 minutes, or 6 hours, mowing 12 lawns.
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4 feet 4 inch into inch.
Answer:
52 inches
Step-by-step explanation:
1 foot=12 inches
4(12)=48 inches
Then you add the other 4 inches.
48+4=52
52 inches
If f(x) = -4x + 4, what is f(x) when x = 3?
f(3) = what is it
Answer:
-8
Step-by-step explanation:
f(3) = -4(3) + 4 = -12 + 4 = -8
Answer:
f(x) = -8Step-by-step explanation:
[tex]\boxed{\sf f(x) = -4x + 4 \;\: when \;\; x=3}[/tex]
For f(x) -4x+4 substitute x with 3:-
[tex]\sf f\left(3\right)\:=\:-4(3)\:+\:4[/tex]
[tex]\sf f\left(3\right)\:=\:-4\times 3\:+\:4[/tex]
[tex]\sf f(3)=-12+4[/tex]
[tex]\sf f(3)=-8[/tex]
Therefore, f(x) = -8.
______________________
Hope this helps!
. Sam is 8 ft man and the length of his shadow is 10 feet. Find the height of the building casting a shadow of 200 feet. (Draw a diagram , and label, set up a proportions and solve)
The height of the building is 160 ft
Proportion is an equation that defines that the two given ratios are equivalent to each other. In other words, the proportion states the equality of the two fractions or the ratios.
Types of proportion :
Direct Proportion
Inverse Proportion
Continued Proportion
Comparing the heights and shadows using ratio proportions
Sam Height = 8 ft
Sam Shadow = 10 ft
Building Height = x ft
Building Shadow = 200 ft
Sam Height/Sam Shadow = Building Height/Building Shadow
AB/BC = PQ/QR
8/10 = x/200
8*200 = 10*x
1600/10 = x
x = 160 ft
The height of the building is 160 ft
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Part C
Now you will attempt to copy your original triangle using only two of its sides and the included angle:
Using point E as the center, draw a circle with a radius equal to the length of
, which you calculated in part B.
Using point E as the vertex and
as one side of the angle, create an angle that is equal to the measure of
. Draw ray
.
Locate the intersection of the ray and the circle, and label the point F.
Complete
by drawing a polygon through points D, E, and F.
Take a screenshot of your results, save it, and insert the image below.
Here no figure just go through the definition.
What is a polygon?A polygon is a two-dimensional geometric shape that is defined as a closed figure with straight sides. It is made up of line segments that connect at endpoints called vertices. The term polygon comes from the Greek words "poly" meaning many and "gonia" meaning angle, indicating that polygons have many angles.
Polygons can have different numbers of sides, with the most basic being a triangle, which has three sides and three angles. Other examples of polygons include squares, rectangles, pentagons, hexagons, and octagons. The sides of a polygon do not have to be equal in length or the angles between them do not have to be the same, but they must be straight lines and the polygon must be closed.
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After responding to the prompt, we can deduce that in order to circle and finish the copied triangle, a polygon should be drawn through the coordinates D, E, and F.
What is a polygon?The definition of a polygon, a two-dimensional geometric form, is a closed figure with straight sides. It consists of line segments joined at ends known as vertices. The word "polygon," which means "many angles," is derived from the Greek terms "poly," which means "many," and "gonia," which means "angle."
A triangle is the most basic polygon because it has three edges and three angles. Polygons can have various amounts of sides. Squares, rectangles, pentagons, hexagons, and octagons are additional instances of polygons. In order for a polygon to be considered closed, all of its sides must be straight lines, regardless of whether their lengths or angles are equivalent.
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What’s the value of a?
An airline can sell no more than 155 tickets for a flight. So far 97 tickets
have been sold. Denzel made this number line to show the number of
tickets the airline is still able to sell.
Answer:
Step-by-step explanation:
I need to find the maximum revenue!
The revenue is maximized for a value p = 100, and the maximum revenue is:
R = 23,500
How to maximize the revenue?We know that the number of items sold for a prize p is:
-2.35p + 470
Then the revenue will be:
R = (-2.35p + 470)*p
So we need to find the value of p that maximizes that quadratic equation, we can see that the maximum will be at the vertex, then let's write:
R = -2.35p² + 470p
The vertex is at:
p = -470/(2*2.35)
p = 100
Finally, the maximum revenue is:
R = -2.35*100² + 470*100
R = 23,500
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True or False. A hypothesis is a speculation.
Justify your answer.
A contestant on a game show has a 1 in 6 chance of winning for each try at a certain game. Which probability models can be used to simulate the contestant’s chances of winning??
Select ALL of the models that can be used to simulate this event.
A) a fair six-sided number cube
B) a fair coin
C) a spinner with 7 equal sections
D) a spinner with 6 equal sections.
E) a bag of 12 black chips and 60 red chips.
The probability models that represents a probability of winning of 1/6 are given as follows:
A) a fair six-sided number cube.
D) a spinner with 6 equal sections.
E) a bag of 12 black chips and 60 red chips.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
For this problem, we want a probability of 1/6 of winning each trial, hence the events are given as follows:
A) a fair six-sided number cube. -> One out of the six numbers is equivalent to winning.
D) a spinner with 6 equal sections. -> One out of the six regions is equivalent to winning.
E) a bag of 12 black chips and 60 red chips. -> 12/(12 + 60) = 12/72 = 1/6.
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wholesale 575.00
marked up 40%
List price?
How many 4-letter code symbols can be formed with the letters P, D, Q, X
without repetition?
Algebra 2
After answering the presented question, we can conclude that As an expression result, there are 24 4-letter code symbols that may be constructed without duplication using the letters P, D, Q, and X.
what is expression ?
An expression in mathematics is a collection of representations, digits, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a combination of the two can be used as an expression. Mathematical operators include addition, subtraction, rapid spread, division, and exponentiation. Expressions are often used in arithmetic, mathematics, and form. They are employed in the representation of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.
We may use the method for permutations of n items taken r at a time to compute the number of 4-letter code symbols that can be created with the letters P, D, Q, X without repetition:
n! / (n-r)! P(n,r) = n!
where n denotes the number of items (in this example, four letters) and r the number of things taken at once (in this case, 4).
Thus far, we have:
P(4,4) = 4! / (4-4)! = 4! / 0! = 4 x 3 x 2 x 1 / 1 = 24
Hence, As a result, there are 24 4-letter code symbols that may be constructed without duplication using the letters P, D, Q, and X.
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Complete question:
How many 4-letter code symbols can be formed with the letters P, D, Q, and X without repetition?
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answer:
Step-by-step explanation:
[tex]y=\frac{1}{2} x+2[/tex]
[tex]y=(x-h)^2+k[/tex]
[tex]y=(x+3)^2-2=x^2+6x+7[/tex]
Decompose the composite figure to find its total area.
Answer: 36 m^2
Step-by-step explanation: I got it correct trust btw can i get brsainliest
PLEASE GUYS HELP!!
Solve 2(x + 3) = 18
Answer:
[tex]\mathrm{x=6}[/tex]Step-by-step explanation:
[tex]\mathrm{2\left(x+3\right)=18}[/tex]
Divide both sides by 2:-
[tex]\mathrm{\cfrac{2\left(x+3\right)}{2}=\cfrac{18}{2}}[/tex]
Simplify:-
[tex]\mathrm{x+3=\cfrac{18}{2} }[/tex]
[tex]\mathrm{x+3=9}[/tex]
Subtract 3 from both sides:-
[tex]\mathrm{x+3-3=9-3}[/tex]
[tex]\mathrm{x=6}[/tex]
_____________________
Hope this helps!