We can solve this problem by using the formula:
s = σ / sqrt(n)
where,
s = standard deviation of the sample
σ = standard deviation of the population = 3 years
n = number of samples = 100
Substituting:
s = 3 years / sqrt (100)
s = 0.3 years (ANSWER)
Which point satisfies both f(x)=2^x and g(x)=3^x (0,1) (0,-1) (1,0) (-1,0)
A cold front moved in last weekend. In 8 hours overnight, the temperature outside dropped from 14 degrees to -10. What was the average temperature change for each hour?
I need the answer as quick as I can and I put it at max points!
Answer:
Step-by-step explanation:
The difference between 14 and 0 is 14, and the difference between 0 and -10 is 10. 14+10=24 for total change. For the average over 8 hours, we have 24/8=3 degrees
Explain how you would use a number line to find the absolute value of –12.
PLEASE HELP IMAGE ATTACHED! These triangles are similar. Find the area of the smaller triangle to the nearest whole number.
The area of smaller triangle is 59 square feet
What are the similar triangles?Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.
What is the formula for the area of triangle?The formula for the area of triangle is
[tex]Area = \frac{1}{2} \times base \times \ height[/tex]
According to the given question.
The area of the larger triangle is 105 square feet.
And the one side of the larger triangle and the smaller traingle is 16 and 12 feet respectively.
Suppose the height of thesmaller triangle be x feet and the height of the larger triangle be y feet.
Since, the corresponding edges of similar triangles are proportional.
Therefore,
[tex]\frac{y}{x} = \frac{16}{12}[/tex]
[tex]\implies y = \frac{4}{3} x[/tex]
Also, the area of larger triangle is 105 square feet.
[tex]\implies \frac{1}{2} \times \frac{4}{3} x \times 16 = 105[/tex]
The above euqtaion can be written as
[tex]\implies \frac{1}{2}\times \frac{4}{3} x \times \frac{4}{3} \times 12 = 105[/tex]
[tex]\implies \frac{1}{2} \times (\frac{4}{3} )^{2} \times x \times 12 = 105[/tex]
[tex]\implies \frac{1}{2} \times x \times 12 = 105 \times \frac{9}{16}[/tex]
[tex]\implies \frac{1}{2} \times x \times 12 = 59[/tex]
⇒ Area of smaller triangle = 59 square feet
Hence, the area of smaller triangle is 59 square feet.
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The following is a geometric sequence 5,3,1,-1
Math help needed. Thank you
Given: The coordinates of iscosceles trapezoid JKLM are J(-b, c), K(b,c), L(a,0), and M(-a,0).
Prove: The diagonals of an isosceles trapezoid are congruent.
As part of the proof, find the length of KM
A) a2+b2+c2
B) (-a+b)2+c2
C) (a+b)2+c2
Answer with explanation:
It is given that, coordinates of Isosceles trapezoid J K L M are J(-b, c), K(b,c), L(a,0), and M(-a,0).
To Prove: The diagonals of an isosceles trapezoid are congruent.
Proof:
Distance formula , that is distance between two points in x y plane is given by
[tex]=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex]
Where, [tex](x_{1},y_{1}),(x_{2},y_{2})}[/tex] are coordinates of two points in the plane.
Length of Diagonal J L
[tex]=\sqrt{(a+b)^2+(0-c)^2}\\\\=\sqrt{(a+b)^2+c^2}[/tex]
Length of Diagonal K M
[tex]=\sqrt{(a+b)^2+(0-c)^2}\\\\=\sqrt{(a+b)^2+c^2}[/tex]
So, we can see that,
J L = KM [tex]=\sqrt{(a+b)^2+(c)^2}[/tex]
Hence,The diagonals of an isosceles trapezoid are congruent.
So ,
[tex]KM=\sqrt{(a+b)^2+c^2}[/tex]
Option C
Which of the following equations have graphs that are parallel to the graph of the equation y=-3/2x+8?
I. 3x + 2y = 10
II. 2x − 3y = 9
III. 6x + 4y = 28
IV. 3x − 2y = 8
I and III only
II and III only
IV only
III only
Which Graph correctly represents x+2y≤4?
Answer with Step-by-step explanation:
We are given an inequality:
x+2y≤4
We have to determine its correct graph
In graph A and graph C (0,4) lies in shaded region but (0,4) does not satisfy the inequality(since, 0+2×4=8 which is not less than or equal to 4)
Hence, A and C are not the graph of this inequality
In graph D (0,2) does not lie in shaded area but it satisfies the inequalityHence, D is also not the graph of this inequality
Hence, correct graph of x+2y≤4 is:
Graph B
(6.3 × 1011) ÷ (7 × 105)
can someone help me please
Julio just bought a $267,900 house. He had a 20 year mortgage with a fixed rate of 5.875%. Julio's monthly payments are $1558.09. What percent of the purchase price was Julio's down payment?
Answer: c
Step-by-step explanation:
On monday eliza read her book. on tuesday she read three times as long as she read on monday. on wednesday she read 20 minutes less than tuesday. on thursday she read for 20 minutes which was half as long as she read on wednesday. how many minutes did eliza read over the 4-day period
How many sixteenth notes would be needed to have the same duration as 3 quarter notes? Represent this as a fraction
Find all values of $x$ such that $6= \dfrac{35}{x} -\dfrac{49}{x^2}$. If you find more than one value, then list your solutions in increasing order, separated by commas.
Answer:
[tex]x=\frac{7}{3} , \frac{7}{2}[/tex]
Step-by-step explanation:
[tex]6= \frac{35}{x} - \frac{49}{x^2}[/tex]
Now we need to solve for x
To get 'x' alone we make the denominators same
LCD = x^2
WE multiply the whole equation by x^2
[tex]6x^2 = 35x - 49[/tex]
Now we the equation =0, move all the terms to left hand side
[tex]6x^2-35x + 49=0[/tex]
Now we apply quadratic formula to solve for x
a= 6, b= -35 , c= 49
[tex]x= \frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x= \frac{-(-35)+-\sqrt{(-35)^2-4(6)(49)}}{2*6}[/tex]
[tex]x= \frac{35+-\sqrt{49}}{12}[/tex]
[tex]x= \frac{35+-7}{12}[/tex]
Now frame two equations , one with + and another with -
[tex]x= \frac{35+7}{12}[/tex] [tex]x= \frac{35-7}{12}[/tex]
[tex]x= \frac{42}{12}[/tex] [tex]x= \frac{28}{12}[/tex]
[tex]x= \frac{7}{2}[/tex] [tex]x= \frac{7}{3}[/tex]
So value of x= {7/3, 7/2}
how much would $500 invested at 6% interest compounded annually be worth after 4 years
Find the y-intercept and x-intercept of the line.
5x - 4y = 15
y-intercept: __
x-intercept: __
which statement is true about angles 1 and 2
Answer:
Option a) They are adjacent angles
Step-by-step explanation:
Given is a picture of a graph with angles 1 to 6 around it.
Out of these angle 2 and 5 are right angles.
1 and 2 are adjacent to each other.
They are not complementary because 1+2 not equals 90
They are neither supplementary since sum does not equal 180
They cannot be vertical because they are not formed by intersection of two lines.
Hence only option a is right
Option a) They are adjacent angles
∠EFG and ∠GFH are a linear pair, m∠EFG=3n+19, and m∠GFH=55+33 What are m∠EFG and m∠GFH?
16x^2=100
How many solutions will there be to the following equation?
Answer:
There are two solutions [tex]x=\frac{5}{2},-\frac{5}{2}[/tex]
Step-by-step explanation:
Given : Equation [tex]16x^2=100[/tex]
To find : How many solutions will there be to the following equation?
Solution :
Equation [tex]16x^2=100[/tex]
Solve the equation,
Divide by 16 both side,
[tex]\frac{16x^2}{16}=\frac{100}{16}[/tex]
[tex]x^2=\frac{100}{16}[/tex]
Taking root both side,
[tex]x=\sqrt{\frac{100}{16}}[/tex]
[tex]x=\sqrt{\frac{10^2}{4^2}}[/tex]
[tex]x=\pm\frac{10}{4}}[/tex]
[tex]x=\pm\frac{5}{2}}[/tex]
Therefore, There are two solutions [tex]x=\frac{5}{2},-\frac{5}{2}[/tex]
Kara has 90 lollipops, 36 chocolate bars, and 72 gumballs to put in goody bags for her party. What is the largest number of goody bags that Kara can make so that each goody bag has the same number of lollipops, the same number of chocolate bars, and the same number of gumballs?
The largest number of goody bags that Kara can make are [tex]18[/tex] .
What is Highest Common Factor ?Highest or greatest Common Factor is the largest common factor that all the numbers have in common.
We have,
Number of Lollipops [tex]=90[/tex]
Number of chocolate bars [tex]=36[/tex]
Number of gumballs [tex]=72[/tex]
So,
To find the number of bags;
First find out the Highest Common Factor of [tex]90,36,72[/tex];
[tex]90=2*3*3*5[/tex]
[tex]36=2*2*3*3[/tex]
[tex]72=2*2*2*3*3[/tex]
So, from the factors of all numbers we have,
Highest Common Factor [tex]=18[/tex]
Now,
Lollipops [tex]=\frac{90}{18} =5[/tex]
Chocolate bars [tex]=\frac{36}{18} =2[/tex]
Gumballs [tex]=\frac{72}{18} =4[/tex]
So, the largest number of goody bags that Kara can make are [tex]18[/tex] so that each goody bag has [tex]5[/tex] number of lollipops, [tex]2[/tex] number of chocolate bars, and [tex]4[/tex] number of gumballs.
Hence, we can say that the largest number of goody bags that Kara can make are [tex]18[/tex] .
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Mr. calloway is an algebra teacher. every class period he draws a piece of paper out of a hat without looking to determine the number of homework problems he will assign. each different color of paper represents a different number of homework problems. the hat contains 2 blue, 6 red, 10 yellow, and 7 purple pieces of paper.what is the probability that mr. calloway draws a purple piece of paper during the first class period and a blue piece of paper during the second class period if he replaces all pieces of paper before each drawing?
The probability that Mr. Calloway will draw a purple piece of paper during the first class period and a blue piece during the second class period with replacement is [tex]\frac{14}{25}[/tex].
The question involves calculating the probability of drawing a purple piece of paper during the first class period and a blue piece of paper during the second class period with replacement. To find this probability, we first calculate the probability of each event separately since the events are independent. Mr. Calloway's hat contains a total of 25 pieces of paper (2 blue, 6 red, 10 yellow, and 7 purple).
The probability of drawing a purple piece of paper in the first class period is the number of purple papers divided by the total number of papers:
P(purple) = Number of purple pieces / Total pieces = [tex]\frac{7}{25}[/tex]
Since the pieces are replaced, the probabilities in the second class period are the same as in the first. Thus, the probability of drawing a blue piece of paper in the second class is:
P(blue) = Number of blue pieces / Total pieces = [tex]\frac{2}{25}[/tex]
Because these events are independent, we multiply the probabilities of each event happening:
Total probability = P(purple) times P(blue) = ([tex]\frac{7}{25}[/tex]) times ([tex]\frac{2}{25}[/tex]) = [tex]\frac{14}{25}[/tex].
Therefore, the probability that Mr. Calloway draws a purple piece of paper during the first class period and a blue piece of paper during the second class period with replacement is [tex]\frac{14}{25}[/tex].
Use ABC to find the value of sin A. See picture below. Thanks!
type the slope-intercept equation of the line that passes through the points (0,2) and (2,0) y={?]x+{ }
In triangle ABC, angle B = 30°, a = 210, and b = 164. The measure of angle A to the nearest degree is a0
The length of the third side of the triangle would be 106.5 units approx.
What is a triangle?A triangle is a two - dimensional figure with three sides and three angles.
The sum of the angles of the triangle is equal to 180 degrees.
∠A + ∠B + ∠C = 180°
Given is that in triangle ABC, angle B = 30°, a = 210, and b = 164.
The cosine formula is given as follows -
c² = a² + b² + 2abcos(α)
c = √(a² + b² + 2abcos(α))
c = √(210)² + (164)² + 2(210)(164)cos(30°)
c = 106.5 units approx.
Therefore, the length of the third side of the triangle would be 106.5 units approx.
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What is the correct name for this circle?
A rectangle has a base of 3 inches and a height of 9 inches. If the dimensions are doubled, what will happen to the area of the rectangle?
Answer:
Area will increase by 4 times
Step-by-step explanation:
Given: A rectangle has a base of 3 inches and a height of 9 inches.
To find: If the dimensions are doubled, what will happen to the area of the rectangle?
Solution:
It is given that a rectangle has a base of 3 inches and a height of 9 inches.
Now, to find if the dimensions are doubled what will happen to the area, first we need to find the original area.
Original area of rectangle, when base is 3 inches and height 9 inches is
[tex]9\times3=27[/tex] square inches
Now, when dimensions are doubled , the base becomes 6 inches and height becomes 18 inches
So, new area becomes [tex]6\times18=108[/tex] square inches.
Now,
[tex]\frac{\text{new area}}{\text{original area} }=\frac{108}{27}[/tex]
[tex]\implies\frac{\text{new area}}{\text{original area} }=\frac{4}{1}[/tex]
Hence, the area will increase by 4 times.
The Pyramid of Giza is one of the largest pyramid structures still standing in Egypt. It is a right pyramid with a square base, a base length of 230 m, and height of 150 m. The area of the base is __________ The volume is ________
Answer:- The area of base is 52900 square meters. The volume is 2654000 cubic meters.
Explanation:-
Base length of right pyramid (square) a =230m
Height of right pyramid = 150m
Area of base of right pyramid[tex]=a^2=(230)^2=52900\ m^2[/tex]
Volume of right pyramid with square base[tex]=\frac{1}{3}a^2h\\=\frac{1}{3}\times52900\times150=2645000\ m^3[/tex]
Thus, the area of base is 52900 square meters and the volume is 2654000 cubic meters.
The area of the base of the pyramid is 52900 m²
The volume of the square base pyramid of Giza is 2645000 m³
The pyramid is a square base pyramid. Therefore,
volume of a square base pyramid;v = 1 / 3 Bhwhere
B = base area
h = height
h = 150 m
Therefore,
area of the base = l²
where
l = length of side
area of the base = 230² = 52900 m²
Volume = 1 / 3 × 52900 × 150
volume = 7935000 / 3
volume = 2645000 m³
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Perform the operation(s) and write the answer in simplest form.
( 1/2 + 1/3) / 15/4
A.) 3 1/8
B.) 53/90
C.) 2/9
D.) 8/75
Find the product of (x − 2i)^2.
The product of (x-2i)²=x²-4+i4x
What is the process of multiplication of complex numbers?The product or multiplication of two complex numbers is also a complex number. The formula for multiplying complex numbers is: (a + ib) (c + id) = (ac - bd) + i(ad + bc).
Given here (x-2i)² =(x-2i) (x-2i)
=x²-4+i4x
Hence, the product is x²-4+i4x
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