The range for the length of the third side is it must be greater than 10 feet and less than 30 feet.
What is the condition for the sides of triangles?The triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater than or equal to the length of the third side. That sum can equal the length of the third side only in the case of a degenerate triangle, one with collinear vertices.
The length of the third side had to be greater than the difference between the two given sides and less than the sum of the two given sides.
(20 – 10) < S <(20+ 10) ; 10< S < 30
Therefore, the range for the length of the third side is it must be greater than 10 feet and less than 30 feet.
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A scientist claims that 9% of viruses are airborne. If the scientist is accurate, what is the probability that the proportion of airborne viruses in a sample of 533 viruses would differ from the population proportion by less than 3%
The probability that the sample proportion of airborne viruses in differ from the population proportion by greater than 3% is 0.006.
According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
μρ=ρ
The standard deviation of this sampling distribution of sample proportion is:
σρ=[tex]\sqrt \frac{p(1-p)}{n}[/tex]
The information provided is:
n = 533
p = 0.09
As the sample size is quite large, i.e. n = 533 > 30, the central limit theorem can be used to approximate the sampling distribution of sample proportion by a Normal distribution.
The mean and standard deviation are:
μρ=ρ=0.09
σρ=[tex]\sqrt \frac{p(1-p)}{n}[/tex]=[tex]\sqrt\frac{0.09(1-0.09)}{533}=0.01239[/tex]
Compute the probability that the sample proportion of airborne viruses in differ from the population proportion by greater than 3% as follows:
[tex]p(p^-p > 0.03)=P(p^ > 0.12) \\=P(z > \frac{0.12-0.9}{0.012}) \\= P(Z > 2.5) \\= 1-P(Z > 2.5) \\ = 1- 0.993 \\ = 0.00621[/tex]
Thus, the probability that the sample proportion of airborne viruses in differ from the population proportion by greater than 3% is 0.006.
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Each of the performers at a circus convention is either a unicyclist, a mime or an aerial artist. The ratio of unicyclists to mimes is 3: 14 The ratio of unicyclists to aerial artists is 9 : 11 There are 88 aerial artists. What percentage of the performers are unicyclists? Give your answer to 2 d.p.
Answer:
14.52% are unicyclists
Step-by-step explanation:
First, we can use proportions to find the number of unicyclists at the convention. Since we know that the ratio of unicyclists to aerial artists is 9:11, and there are 88 aerial artists, we can set up the following equation:
[tex]\frac{9}{11}=\frac{x}{88}[/tex]
If we cross multiply, we get that 11x = (88)(9). After we divide through by 11 to isolate x, we get that x = (8)(9) = 72
Second, we have to figure out the number of mimes at the convention to figure out the total number of people there. We know that the ratio of unicyclists to mimes is 3:14, and the number of unicyclists is 72. So, we can set up the following proportion:
[tex]\frac{3}{14}=\frac{72}{y}[/tex]
If we cross multiply, we get that 3y = 1008, or y = 336 mimes
The total number of people at the convention is 336 mimes + 72 unicyclists + 88 unicyclists = 496. Now we have to figure out what percent of 496 is 72 (the number of unicyclists). If we let z = the percentage, we can simply set up an equation that says that 72 is z% of 496:
[tex]72=0.01z*496\\0.01z=0.14516\\z=14.52[/tex]
This means that approximately 14.52% of the performers are unicyclists.
Answer:
14.52%
Step-by-step explanation:
U/A = 9/11 and A = 88 multiply by 8/8 ( to get A=88 as given)
9/11 * 8/8 = 72/88 = U / A so U = 72
Then U/M = 3/14 multiply by 24/24 ( to get U = 72 as found above)
then U/M= 72 / 336 M = 336
U / ( A + U + M ) x 100% = 14.52 %
At what input value will the function
f(x) = -x - 2 + 2 begin to have real
outputs?
The function will begin to have real output when the input value is 2
How to determine the input value?The function is given as:
[tex]f(x) = -\sqrt{x - 2} + 2[/tex]
Set the radical greater than or equal to 0
[tex]x - 2 \ge 0[/tex]
Add 2 to both sides
[tex]x \ge 2[/tex]
This represents the domian
Hence, the function will begin to have real output when the input value is 2
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Complete question
At what input value will the function [tex]f(x) = -\sqrt{x - 2} + 2[/tex] begin to have real outputs?
If g stands for a whole number, find the first three possible values of g2 + 3.
3, 4, 7
1, 4, 7
3, 5, 7
0, 4, 7
So the first three possible values of g^2 + 3 are:
3, 4, 7
The first option is the correct one.
Which ones are the first three possible values?
The set of the whole numbers is {0, 1, 2, 3...}
Then the first possible value is when g = 0.
0^2 + 3 = 3
The second possible value is when g = 1
1^2 + 3 = 4
The third possible value is when g = 2.
2^2 + 3 = 7
So the first three possible values of g^2 + 3 are:
3, 4, 7
The first option is the correct one.
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Answer:
3,4,7
Step-by-step explanation:
jus took the test
Pls, help me work this out!
Geometry) Find the value of x
Answers are
A. 108^o
B. 36^o
C. 136^o
D. 54^o
(The picture is below) THANK YOU!
The correct answer is 108° i.e Option A.
.
.
.
HOPE IT HELPS! :)
Directions: Find the product and simplify
(3m+n)(3m-n)
ty <3
Answer:
9m²-n²
Step-by-step explanation:
(3m+n)(3m-n)
This is so easy algebraic expression.
Just rewrite as,
[tex](3m) {}^{2} - n {}^{2} [/tex]Simplifying,
[tex]9m {}^{2} - n {}^{2} [/tex][Alternate method is there]
A sprinkler rotates 360 degrees the total are watered is 204yds squared
what is the raduius
The radius of the area the sprinkler has watered is 8.06 yards.
What is Rotation ?Rotation is spinning around a fixed point with a fixed radius in circular motions.
It is given that a sprinkler rotates 360 degree
The area watered is 204 sq. yards
Radius = ?
A sprinkler rotates in circle
Therefore the area of the circle = π r²
204 = π r²
204 * 7 /22 = r²
r² = 64.91
r = 8.06 yards
Therefore the radius of the area the sprinkler has watered is 8.06 yards.
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Calculate the force acting on a body of mass 0.8kg (g=9.8*-2; F=mg)
The force acting on a body of mass 0.8 kg is F = 7.84 kg-m-s⁻² or F = 7.84 N
What is mass?A tangible body's mass is the amount of matter it possesses. It's also a metric of inertial or the resistance to velocity when a net force is exerted.
We have:
The mass of the body m = 0.8 kg
As we know,
F = mg
F is the force acting on the body and g is the acceleration due to gravity.
g = 9.8 m-s⁻²
F = (0.8)(9.8)
F = 7.84 kg-m-s⁻²
or
F = 7.84 N
Thus, the force acting on a body of mass 0.8 kg is F = 7.84 kg-m-s⁻² or F = 7.84 N
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Work out quickly will give brainiest
Sara has rs. 836 with her. she gives 9/11 of this to her sister. out of the remaining money, she gives rs. 38 to her brother. she now has a fraction of the original amount is left with her?
The original amount Sara has left is 172/209
The calculation can be done as follows
Let y represent the amount left
9/11 × 836
= 7524/11
= 110
Y can be calculated as follows
Y + 38 +110= 836
148 + Y= 836
Y= 836 - 148
Y= 688
Therefore the fraction is
688/836
= 172/209
Hence the fraction of the original amount left is 172/209
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A system of three linear equations in three variables is inconsistent. how many solutions to the system exist? none one three infinitely many
No solutions exist to this system of equations
A system of equations is said to be inconsistent if the two equations do not agree, meaning that there is no set of values that can simultaneously satisfy each equation. For example, the most basic inconsistent system of equations could be x = 4 a nd x = 5 at same time which is not possible.
A single equation in three unknowns can be interpreted geometrically in 3-dimensional space. If we look at a system of such linear equations, the solution set is the set of all points lying in all of the corresponding planes.
Systems of equations in three variables that are inconsistent could result from three parallel planes, two parallel planes and one intersecting plane, or three planes that intersect the other two but not at the same location.
Hence, No solutions exist to this system of equations
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Answer:
a
Step-by-step explanation:
At times, latitudes with values higher than ________ degrees can have ~ 24 hours of continuous sunshine.
At times, latitudes with values higher than 66.5 degrees can have ~ 24 hours of continuous sunshine.
Locations above the Arctic Circle (north of latitude 66.5 degrees, 90 degrees minus the tilt of the Earth's axis) are exposed to 24-hour sunlight. Below the Arctic Circle (latitude 66.5 degrees south), there is 24-hour darkness.
When at the equator, the sun is directly above – at the poles, the sun is on the horizon. However, regardless of the current location (from the pole to the equator), all parallels are bisected, so we have 12 hours a day and 12 hours a night in all locations.
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what is
x. 10-x 3 D N C X = [?]
Equations are written by equating the expressions to each other. The value of x is 7
Equations and expressionsEquations are written by Equating the expressions to each other.
Given the equation below:
10 - x = 3
Subtract 10 from both sides
10 - x - 10 = 3 - 10
-x = -7
Multiply both sides by -1
-(-x) = -(-7)
x = 7
Hence the value of x is 7
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Which segment is a perpendicular bisector of triangle ABC?
helpp due 20 mins..
Answer:
SR and RZ
Step-by-step explanation:
A perpendicular bisector is a line segment that passes through the midpoint of a side of a triangle. In other words, If it goes through a side, it should split the segment in half perfectly. Furthermore, it must be perpendicular to the side it passes through (it should form a ninety-degree angle with the side). Given these two rules, one can say that one of the perpendicular bisectors is SR. SR forms a right angle with (and is thus perpendicular to) side AB. Furthermore, AS is congruent to (has the same length as) SB, which means SR cuts AB in half exactly. Another bisector would be RZ (for similar reasoning). Let me know if that doesn't make sense.
isosceles triangle has a base that measures 14 units.
A triangle has a base length of 14. The other 2 sides have a length of y.
The value of y, the length of each leg, must be
equal to 7.
between 7 and 14.
greater than 7.
between 14 and 28.
The value of y, the length of each leg, must be greater than 7.
What is Isosceles triangle?
This is a type of triangle with two equal sides.
Rules for side length of trianglesThe sum of any two sides of a triangle must be greater than the third side.Let the first, second and third side = a, b and c respectively
(b - a) < c < (a + b)
For an isosceles triangle with base of 14 units, the two other sides must be equal.
c < (a + b)
c = 14
a = b = y
14 < (y + y)
14 < 2y
7 < y
Thus, the value of y, the length of each leg, must be greater than 7.
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Answer: C. greater than 7.
Step-by-step explanation: Trust Me!
Did it on Edge got the answer correct! :)
In a school of 100 students School Population By Gender
Males Females Total
Freshman 8 17 25
Sophomores 15 10 25
Juniors 12 13 25
Seniors 15 10 25
Total 50 50 100
In a school of 100 students, what is the probability of randomly selecting a student that is either a
female or a senior?
The probability of randomly selecting a student that is either a female or a senior is 3/4.
What is probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
Males Females Total
Freshman 8 17 25
Sophomores 15 10 25
Juniors 12 13 25
Seniors 15 10 25
Total 50 50 100
Now, the probability of randomly selecting a student that is either a
female or a senior
= 50/100 + 25/100
= 75/100
= 3/4
Hence, the probability of randomly selecting a student that is either a female or a senior is 3/4.
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Copy the figure below onto a separate sheet of paper. Find the image of the figure under reflections in line m and then line t. In the box below, describe the rotation equivalent to the composition of reflections with respect to lines m and t.
The reflection of the quadrilateral DEFG will be given in the figure.
What is a transformation of geometry?A spatial transformation is each mapping of feature shapes to itself, and it maintains some spatial correlation between figures.
Reflection does not change the size and shape of the geometry.
The image of the figure under reflections in line m and then line t.
The reflection of the quadrilateral DEFG will be given in the figure.
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Rashaad leans a 22-foot ladder against a wall so that it forms an angle of 65° with the ground. How high up the wall does the ladder reach? Round vour answer to the nearest hundredth of a foot if necessary.
The ladder reaches 19.938 foot high from the ground on the wall.
What is a Right Angled Triangle ?A right angled triangle is a triangle that has one of its angle measure as 90 degree.
It is given that
Ladder Length = 22 foot
The angle between the ladder and the ground is 65 degree.
When the ladder leans on a wall , the wall makes 90 degree with the ground and the ladder is the hypotenuse of the right angled triangle formed.
The figure is attached with the answer.
sin 65 = Height of the wall / Hypotenuse
0.9063 = Height of the wall / 22
Height of the wall = 19.938 foot
Therefore the ladder reaches 19.938 foot high from the ground on the wall.
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Answer:
19.94
Step-by-step explanation:
Please help!!! Very much appreciated!! Natalie has a budget of $15,000 dollars to spend on tracking devices to study bison. A radio tracker costs $650 and a GPS tracker costs $1400. Natalie wants to buy at least 9 radio trackers and more than 3 GPS trackers.
The following system of inequalities represents this situation, where x is the number of radio trackers and y is the number of GPS trackers.
x ≥ 9
y > 3
650x + 1400y ≤ 15000
Which yellow shaded region corresponds to Natalie's possible choices?
Answer:
d.)
Plot these inequalities:
x ≥ 9y > 3650x + 1400y ≤ 15000Graphed below (shaded yellow region):
where all the inequalities meet or touches each other.
Please explain this.
Angles EBA and DBC are congruent. The three angles EBA, EBD, and DBC are together supplementary, so their measures sum to 180°. This means
x + (4x + 11°) + x = 180°
6x + 11° = 180°
6x = 169°
x = (169/6)°
Then the measure of angle D is
2x + 8° = 2 (169/6)° + 8° = (193/3)°
The interior angles of any triangle sum to 180°, so if y is the measure of angle C, we have
(169/6)° + (193/3)° + y = 180°
y = (175/2)° = 87.5°
Given f(x) and g(x) = f(k x), use the graph to determine the value of k. Please explain how to get the answer
A) 5
B) 1/5
C) -1/5
D) -5
Using translation concepts, the value of k is given as follows:
B) 1/5.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this graph, we have that g(x) = f(kx), hence since g(-2) = f(-10):
-2 = -10k
k = 2/10
k = 1/5.
Hence option B is correct.
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Solve 6(2)x = 384.
will mark brainliest !
Answer:
6(2)x = 384
12x = 384
12x/12 = 384/12
x = 32
Step-by-step explanation:
Question 7 of 8
Which of the following are equal to 25 miles per gallon? Check all that apply.
A. 125 miles per 5 gallons
B. 525 miles per 15 gallons
C. 725 miles per 25 gallons
D. 625 miles per 25 gallons
E. 50 miles per 3 gallons
SUBMIT
Answer:A
Step-by-step explanation:125 miles divided by 5 gallons would equal 25, meaning 25 gallons per mile
If the two triangles are congruent, state how you know. If not, state "not congruent."
1.AAS
2.ASA
3.SSS
4.SAS
5.not congruent
Select the two values of x that are roots of this equation. 2x2 + 7x + 6 = 0
Answer:
x = -3/2, -2
Step-by-step explanation:
2x^2 + 7x + 6 = 0
(2x + 3)(x + 2) = 0
(2x + 3)
2x = -3
x = -3/2
(x + 2)
x = -2
Answer:
[tex]\large {\textsf{A and C}}\ \implies x_1=-2,\ x_2=-\dfrac{3}{2}}[/tex]
Step-by-step explanation:
In this problem, we can use two methods to solve for the values of x (roots) of the given equation. Those methods are: using the quadratic formula and factoring.
Standard Form of a Quadratic Equation: ax² + bx + c = 0, where a ≠ 0
Given equation: 2x² + 7x + 6 = 0
⇒ a = 2, b = 7, c = 6
Method 1: Using the Quadratic Formula
Quadratic Formula: [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Step 1: Substitute the values of a, b, and c into the quadratic formula.
[tex]\implies x=\dfrac{-7\pm\sqrt{7^2-4(2)(6)}}{2(2)}\\\\[/tex]
Step 2: Simplify
[tex]\implies x=\dfrac{-7\pm\sqrt{\bold{7^2}-4(2)(6)}}{\bold{2(2)}}\\\\\implies x=\dfrac{-7\pm\sqrt{49-4\bold{(2)(6)}}}{4}\\\\\implies x=\dfrac{-7\pm\sqrt{49\bold{-4(12)}}}{4}\\\\\implies x=\dfrac{-7\pm\sqrt{\bold{49-48}}}{4}\\\\\implies x=\dfrac{-7\pm\sqrt{\bold{1}}}{4}\\\\\implies x=\dfrac{-7\pm1}{4}[/tex]
Step 3: Separate into two possible cases and solve for the values of x.
[tex]\implies x_1=\dfrac{-7-1}{4}\implies \dfrac{-8}{4}\implies \boxed{-2}\\\\\implies x_2=\dfrac{-7+1}{4}\implies \dfrac{-6}{4}\implies\boxed{-\dfrac{3}{2}}[/tex]
Method 2: Solve by Factoring
In order to be able to solve this equation by factoring, let's rewrite the middle term by finding the factors that give a product of the first and last terms (a • c = 12) and give us the sum of the middle term (b = 7).
Factors that give a product of a • c: 4 • 3 = 12
Factors that give a sum of b: 4 + 3 = 7
Step 1: Rewrite the given equation with those factors.
2x² + 7x + 6 = 0
⇒ 2x² + 4x + 3x + 6 = 0
Step 2: Factor out 2x and 3.
(2x² + 4x) + (3x + 6) = 0
⇒ 2x(x + 2) + 3(x + 2) = 0 [ Factor out the the common factor. ]
⇒ (2x + 3)(x + 2) = 0
Step 3: Apply the Zero-Product Property (if m•n = 0, then m = 0 or n = 0).
a) 2x + 3 = 0 ⇒ 2x = -3 ⇒ x = -³⁄₂
b) x + 2 = 0 ⇒ x = -2
Therefore, the two roots of this equation are x = -³⁄₂ and x = -2.
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HEELLLPPMEEEEEEEE PLS 30 pointss
Suppose that x≠0 and y≠0. We know from our work in this section that 1/x∙1/y is equivalent to 1/xy. Is it also true that 1/x+1/y is equivalent to 1/(x+y)? Provide evidence to support your answer.
Answer:
No
Step-by-step explanation:
Let's assume that x=2 and y=3.
1/2+1/3≠1/5
Also, when adding fractions, you cannot simply add the denominator. You have to make the denominators of all fractions the same and then add.
So, if you are given 1/x +1/y, you should get (y+x)/xy, not 1/(x+y)
Simplify 2(a + 3b) + 3(4a + b).
(A) 6a+6b
(B) 14a + 9b
(C) 14a + 4b
(D) 6a+ 7b
Answer: = 14a + 9b
Step-by-step explanation:
distribute:
2(a+3b) + 3(4a+b)
2a + 6b + 12a + 3b
combine like terms:
2a + 6b + 12a + 3b
14a + 6b + 3b
14a + 6b + 3b
= 14a + 9b
Matt and Ming are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Matt sold 3 small boxes of oranges and 14 large boxes of oranges for a total of $203. Ming sold 11 small boxes of oranges and 11 large boxes of oranges for a total of $220. Find the cost each of one small box of oranges and one large box of oranges.
help :((
Juan wants to change the shape of his vegetable garden from a square to a rectangle, but keep the same area so he can grow the same amount of vegetables. The rectangular garden will have a length that is 2 times the length of the square garden, and the width of the new garden will be 16 feet shorter than the old garden. The square garden is x feet by x feet.
Old garden area = New garden area
x2 = (2x)(x – 16)
x2 = 2x2 – 32x
0 = x2 – 32x
What is the value of x that makes sense in this context?
What are the dimensions of the new garden?
The value of x that makes sense in this context is; 32.
The dimensions of the new garden is; 64 by 16.
How to find the real dimensions of the rectangle?The expression that represents the problem statement is;
x² = (2x)(x – 16)
Expanding the bracket gives us;
x² = 2x² – 32x
x² - 32x = 0
x(x - 32) = 0
Thus; x = 0 or x = 32
x can't be 0 and as such the value of x is 32.
Thus;
The length of the new garden is; l = 2x = 64.
The width of the new garden is; w = x - 16 = 32 - 16 = 16
The dimensions of the new garden are therefore; 64 by 16
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