The greatest common multiple of 10 and 40 is 10.
What is meant by greatest common multiple?The greatest common divisor (GCD) of two or more integers, where at least one of them is not zero, is the largest positive integer that is a divisor of both numbers. For example, the GCD of 8 and 12 equals 4.
In the divisibility preorder relation, the GCD of a and b is their greatest positive common divisor. This signifies that a and b's common divisors are the same as their GCD divisors. The Euclidean algorithm or Euclid's lemma are widely used to establish this. This is the definition of "greatest" in the context of GCD generalizations.
Foe calculating the GCD of 10 and 40, we have to find the factors of 10 and 40.
Factors of 10:
1, 2, 5, 10
Factors of 40:
1, 2, 4, 5, 10, 20, 40
From all these factors we have to choose the greatest factor that is exactly divisible by both 10 and 40 are 1, 2, 10, and 5.
So, the greatest common multiple of 10 and 40 is 10.
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Maria made two batche of fruit punch. The equation =. Repreent the relationhip between the amount of apple juice, x, and the amount of grape juice, y, in the fruit punch. Complete the table that how thi relationhip and verify the contant of proportionality
The constant of proportionality is, 8/5. And the equation that represents this relationship is, [tex]y = \frac{8}{5}x[/tex].
What is constant of proportionality?
The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality.
Let, the equation [tex]\frac{Grape juice (x)}{Apple Juice(y)}[/tex] represent the relationship between the amount of apple juice, x, and the amount of grape juice, y, in the fruit punch.
From table we can write as,
[tex]\frac{Grape Juice (x)}{(Apple Juice(y)} = \frac{8}{5} =\frac{16}{10} = \frac{8}{5} = \frac{y}{x}[/tex]
⇒ y / x = 8 / 5
From above equation,
y = ( 8 / 5 ) x
This is the equation that represent the relationship between the amount of apple juice, x, and the amount of grape juice, y, in the fruit punch.
Hence, the constant of proportionality is, 8/5.
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Which of the following best describes the sequence 18,6,-6,-18
A. Arithmetic
B. Geometric
C. Harmonic sequence
D. Fibonacci sequence
The sequence 18 , 6 , -6 , -18 is Arithmetic sequence.
An arithmetic progression is a sequence where the differences between every two consecutive terms are the same.
In general an arithmetic sequence can be written like: {a, a+d, a+2d, a+3d, ... }.For the first term 'a' of an AP and common difference 'd'
Common difference of an AP: d = a₂ - a₁ = a₃ - a₂ = a₄ - a₃= ... = aₙ - aₙ₋₁
Given in the question,
The sequence 18 , 6 , -6 , -18
a₁ = 18 , a₂ = 6 , a₃ = -6 and a₄ = -18
Common difference : d = a₂ - a₁
=> d = 6 - 18
=> -12
For a₃ - a₂
=> -6 - 6 = 12
Therefore , the common difference is same i.e. 12
Hence, the sequence is Arithmetic sequence
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Suppose that random variable X is uniformly distributed between 8 and 25. Draw a graph of the density function, and then use it to help find the following probabilities: a. P(X > 25) = b. P(X < 14.9) = C. P(10 < X < 23) = d. P(18 < X < 27) =
A) Probability = 0
B) Probability = 0.4059
C) Probability = 0.7647
D) Probability = 0.4118
A probability simple definition is what?
Probability is a metric used to express the possibility or chance that a particular event will occur. Probabilities can be expressed as fractions from 0 to 1, as well as percentages from 0% to 100%.
where a = 8 and b = 25 are the uniform distribution parameters.
A)
probability = P(X>25)= 1-P(X<25)= 1-(25-8)/(25-8)= 0.0000
B)
probability = P(X<14.9)= (14.9-8)/(25-8)= 0.4059
C)
probability = P(10<X<23)= (23-10)/(25-8)= 0.7647
D)
probability = P(18<X<27)= (25-18)/(25-8)= 0.4118
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x+3 -12 need help ASAP 100POINTS!!!
Answer:
x-9
Step-by-step explanation:
I didn't know if you wanted it graphed or simplified so I gave ya both, hope it helps!!!
Answer: x - 9
Step-by-step explanation:
= x + 3 - 12
= x + (3 - 12)
= x-9
Megan creates a four-digit code for her debit card. The first digit is 2. The 4-digit code is odd. How many possible codes are there?
The total number of possible codes is 500.
What is the fundamental principle of counting?According to the fundamental counting principle, if there are n ways to do one thing and m ways to do another, then there are n×m methods to accomplish both things.
Given that, the first digit of the four-digit code is 2 and the number is odd.
The first digit of the number is 2, therefore, there is only one possible number for the first digit.
Since the number is odd, the last digit of the number must be an odd number.
Therefore, there are 5 possible numbers, 1,3,5,7, and 9, for the last digit.
Now, for the second and the third digit there are 10 possible numbers, from 1 to 10.
Therefore, as per the principle of counting, the total number of possible codes is:
1 × 10 × 10 × 5
= 500
Hence, the total number of possible codes is 500.
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Rewrite the expression with a rational exponent as a radical expression. Four to the two fifths power all raised the one fourth power.
The following are the offered rational exponents in expression form:
• (A) the fourth root's tenth root = [tex]\sqrt[10]{4}[/tex]
A mathematical expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations. This mathematical operation enables the multiplication, division, addition, or subtraction of numbers. The following is the structure of an expression: Expression: The following rational exponents are expressed in the expression form (Math Operator, Number/Variable, Math Operator): (A) the tenth root of four= [tex]\sqrt[10]{4}[/tex]
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An open box is to be made from a eighteen-inch by eighteen-inch square piece of material by cutting equal squares from the corners and turning up the sides (see figure). Find the volume of the largest box that can be made. 18-2x
v=............ in^3
The volume of the largest box that can be made is V=x(18-2x)² inches³
What is meant by volume?Volume is expressed in cubic units like m3, cm3, in3, and so on. At times, volume is also referred to as capacity.
Volume is a measurement of the amount of three-dimensional space that is occupied. It is typically quantified numerically with SI-derived units or different imperial or US customary units. The definitions of length and volume are inextricably related.
Consider the open box's height to be x inches.
The length of the box is then (18-2x) inches.
Because it is a square box, its length and width are the same.
As a result, the box's width becomes (18-2x) inches.
The volume of the open box (V)= (length)(breadth)(height)
V=(18-2x)(18-2x)(x)
V=x(18-2x)²
V=x(18-2x)² cubic inches.
Therefore, the volume of the box is V=x(18-2x)² inches³
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The area of the Earth covered by water is 361 million km² The area of the Earth not covered by water is 149 million km² Work out the total area of the Earth. Give your answer in standard form.
The area of the Earth in standard form can be expressed as [tex]5*10^8[/tex] km².
What is the area of any geometrical shape?
The area of the shape on the paper is referred to as its Area. Consider your square to be made up of smaller unit squares. The area of a figure is calculated as the number of unit squares required to cover the entire shape.
Given data:
The area of the Earth covered by water = 361 million km²
The area of the Earth not covered by water = 149 million km²
The total area of the Earth = Area of the Earth covered by water + Area of the Earth not covered by water
= 361 + 149
= 510 million km²
= [tex]510*10^6[/tex] km²
= [tex]510*10^8[/tex] km².
Hence, the area of the Earth in standard form can be expressed as [tex]5*10^8[/tex] km².
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How do you find the Y intercept of a system of equations?.
Set x = 0 and solve for y to find the y-intercept. The main point will be (0,y).
The point on the line where it intersects the y axis is known as the y intercept.
In analytic geometry, a y-intercept or vertical intercept is a point where the graph of a function or relation intertwines the y-axis of the coordinate system, with the horizontal axis representing a variable x and the vertical axis representing a variable y. As a result, these points satisfy the x = 0 condition.
An intercept is a point on the y-axis through which the slope of a line passes. It is the y-coordinate of a y-axis point at which a straight line or a curve interferes. This is represented by the straight line equation,
y = mx+c,
where m denotes the slope and c is the y-intercept
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evaluate the line integral, where c is the given curve. (x 9y) dx x2 dy, Evaluate the line integral, where C is the given curve, Integral c (x+2y)dx+x^2dy, C consists of line segments from (0, 0) to (9, 1) and from (9, 1) to (10, 0)
the integral of the line, where c is the specified curve. The line integral is (x 9y) dx x2 dy, where C is the provided curve. The line segments from (0, 0) to (9, 1) and from (9, 1) to (10, 0), respectively, make up the integral c (x+2y)dx+x2dy, C. is 95/3
[tex]\int\limits^a_c {(x+9y,x^{2} )} \, dr_{2} = \int\limits^1_0{9+t+9-9t, (9+t )^2} .(1, -1)\, dt[/tex]
it is possible to parameterize the first line segment by
[tex]r_{1} (t) = (0,0)(1-t) + (9,1)t = (9t,t)[/tex] with 0 ≤ t ≤ 1 indicate this first section with [tex]C_{1}[/tex] then
[tex]\int\limits^a_c {(x}+9y,x^2 ) \, dr_{1} = \int\limits^1_0 {(9t+9t,81t^2) . (9,1)} \, dt\\ \\= \int\limits^1_0 {(162t + 81t^2) } \, dt\\\\= 108[/tex]
secondly the line segment [tex]C_{2}[/tex] can be characterised as
[tex]r_{2} (t) = (9,1)(1-t) + (10,0)t = (9+t,1-t)[/tex] again using interval 0 ≤ t ≤ 1 then
[tex]\int\limits^a_c {(x+9y,x^{2} )} \, dr_{2} = \int\limits^1_0{9+t+9-9t, (9+t )^2} .(1, -1)\, dt[/tex]
= -229/3
finally ,
= 108-229/3
= 95/3
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What is in the form a bi?.
In complex number a+ib a is real and ib is the imaginary part.
What is complex number?Complex numbers are the numbers that are communicated as a+ib where, a,b are genuine numbers and 'I' is a fanciful number called "particle". The worth of I = (√-1). For instance, 2+3i is a complicated number, where 2 is a genuine number (Re) and 3i is a imaginary number (Im).
According to question:We have, a + ib is a complex number in mathematics
where a is the real part and ib is the imaginary part of the complex number.
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You are designing a rectangular swimming pool that is to be sent into the ground. The width of the pool is 5 feet more than the depth, and the length is 35 feet more than the depth. The pond holds 2000 cubic feet of water, What are the dimensions of the pool?
Answer: depth = 5 ft
width = 10 ft
length = 40 ft
Step-by-step explanation:
d = depth
width = d + 5
length = d + 36
Volume = length x width x depth = 2000 cf
d(d+35)(d+5) = 2000
d([tex]d^{2}[/tex] + 40d + 175) = 2000
d^3 + 40d^2 + 175d = 2000
rewrite in standard cubic polynomial form : ax3 + bx2 + cx + d = 0
d^3 + 40(d^2) + 175d - 2000 = 0
Find the roots of the cubic polynomial:
factors of 2000 are 1, 5, 10 15, 20, etc.
Try the factor 5 first by plugging it in the equation:
5^3 + 40(5^2) + 175(5) - 2000 = 0
Lucky break! No need to find the other roots because they will be negative, and you can't have a negative value for a pool depth.
So, depth = 5 ft
width = 5 + 5 = 10 ft
length = 5 + 35 = 40 ft
Angle b has a measure of 135 degrees. A circle is centered at the vertex of angle b and 1/360th of the circumference of the circle is 0. 15 cm. How long is the arc subtended by angle b?.
there are 360 degrees of angle in a circle, when it reads 1/360th of the circumference is 0.58 cm, it is informing you that 1 degree equals 0.58 cm.
The question then becomes, how many 0.58 cm there are in 87 cm. This is a division problem, therefore 87 cm divided by 0.58 cm equals 150, which we would translate to 150 degrees.The ratio of the second one's arc to circumference will be the same as the ratio of its angle to the circle's total 360 degrees. This is equivalent to 334.6 cm / 504 cm = x / 360 in mathematics. The result of solving for x is 239 degrees.
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Which pair of triangles can be proven congruent by SAS?.
Similar triangles may or may not be congruent.
The pair of triangles that can be proved by SAS is (a) the first pair
What is congruent triangles?
Congruence of triangles: 2 triangles are same to be congruent if all 3 corresponding sides square measure equal and every one the 3 corresponding angles square measure equal in measure.
Main body:
From the attached figures, we have the following observations
Figure 1
Two sides of both triangles are congruent
The angles between the sides are corresponding
The two congruent sides represent SS
The corresponding angles imply: SAS
This means that, the first pair of triangles are congruent by SAS postulate
Figure 2
Two angles of both triangles are congruent
The triangle share a common side
The two congruent angles represent AA
The common side imply: ASA
This means that, the second pair of triangles are congruent by ASA postulate
Figure 3 and 4
All sides of both triangles are congruent
This means that, the third and the fourth pairs of triangles are congruent by SSS postulate
Hence, the pair of triangles that can be proved by SAS is (a) the first pair
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preston, an official for a state's department of safety, wants to show that the population mean speed of passenger vehicles traveling on a certain expressway is greater than the posted speed limit of 65mph. preston collects a random sample of 59 passenger vehicles traveling on the expressway and finds that the sample mean speed is 67.1mph with a sample standard deviation of 7.5mph.
The null hypothesis rejects as the significance level α= 0.10.
What is z test?
If the data is distributed normally, a z test can be used to determine whether the means of two populations differ from one another. The z test statistic's value must be determined, together with the null hypothesis and alternative hypothesis setups, for this reason. On the z critical value, the decision criterion is based. The distribution graph is divided into acceptance and rejection zones during hypothesis testing by the z critical value. The null hypothesis can be rejected if the test statistic lies inside the rejection region; otherwise, it cannot.
First off, because the sample size is greater than 30, this is a z test rather than a t test (i.e., 59 > 30).
Z = 2.15
Currently, the p value for the given value of Z is 0.0158.
That comes out to 0.01 0.0158 0.025.
Because the significance level, alpha = 0.10, is less than 0.01 p-value 0.025, the null hypothesis should be rejected.
Hence, The null hypothesis rejects as the significance level α= 0.10.
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What is the 2003rd term of the sequence of odd numbers 1, 3, 5, 7, 9,.........
The 2003rd term of the sequence of odd numbers 1, 3, 5, 7, 9,.. is 4005.
How to calculate the sequence?It should be noted that this is an arithmetic sequence and the formula will be written as:
a + (n - 1)d
a = first term = 1
n = number of terms = 2003
d = common difference = 3 - 1 = 2
Therefore, the 2003rd term will be:
= a + (n - 1)d
= 1 + (2003 - 1) × 2
= 1 + (2002 × 2)
= 1 + 4004
= 4005
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there are 16 animals in the field. some are buffalo and some are ducks. there are 56 legs in all. how many of each animal are in the field?
(System of equations, solve algebraically, number of buffalos, number of ducks)
Answer:
There would be 12 buffalos and 4 ducks.
Step-by-step explanation:
Formula:
Buffalos = 4 legs
Ducks = 2 legs
16 animals in total.
56 legs in total.
_________________
So, in order to find this answer, we need to multiply/divide (whichever way is easier for you) the buffalos as high as possible to 56, without actually getting to 56.
56 divided by 4 = 14.
Now, this is too close, so we need to go down 1 more than this because it has too many legs:
52 divided by 4 = 13.
(52 because 56 - 4 = 52).
Now, we have 13 buffalos with 4 more legs to choose from. Which does not work because ducks have 2 legs, which 13 + 2 = 15, which is not 16. Let's go down 4 more:
48 divided by 4 = 12
Now, we have 12 buffalos with 48 legs.
56 - 48 = 8. So, we need 8 more legs, in which we need to use ducks:
8 divided by 2 = 4 ducks
12 buffalos + 4 ducks = 16 animals!!!!
We did it!
There would be 12 buffalos and 4 ducks.
Check your answer:
12 x 4 = 48.
4 x 2 = 8
48 + 8 = 56.
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
geometry check the photo!!!
The first is a polyhedron but the second one is not
What is polyhedron?
A polyhedron is a three-dimensional structure in geometry that has flat, polygonal faces, edges that are straight, and sharp vertices. A convex polyhedron is made up of finitely many points that are not all on the same plane and has a convex hull. Convex polyhedra include shapes like cubes and pyramids.
1. The solid is formed by polygonal faces, so it is a polyhedron. This solid has two congruent pentagonal bases, so it is a pentagonal prism.
Face: Each flat surface is called face.
Edges: The line segments where the faces intersect are called edges.
Vertex: The point where three or more edges intersect is called a vertex.
Bases: HIJKL, PQMNO
Faces: HIJKL, PQMNO
Edges: IJ , IN , IH , MH , JO , JK , ON, OP , MQ , QP , QL , LH , KL , KJ , KP
Vertices : H,I,J,K,L,M,N,O,P,Q
2. A solid called a polyhedron is composed of flat surfaces that enclose a single area of space. This object is not a polyhedron since its surfaces are curved. The presented figure is a solid with parallel bases that are congruently spaced apart and are joined by a curved surface. It is therefore a cylinder.
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Is it possible to construct a triangle whose sides measure 6 cm 5 cm and 10 cm?.
Yes, It is possible to construct a triangle whose sides measure 6 cm 5 cm and 10 cm Because the total of a triangle's two sides is bigger than the third side.
Define sides of triangle.The three vertices of a triangle connect the straight lines that make up its sides. In other terms, we can state that a triangle's sides are line segments that converge at the triangle's vertices. A right triangle's hypotenuse is its longest side, its "opposite" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question.
Given,
Sides 6 cm 5 cm and 10 cm
Sum = 6 + 5
Sum = 11
Because the total of a triangle's two sides is bigger than the third side, it is conceivable to construct a triangle with sides that measure 10 cm, 5 cm, and 6 cm.
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Is it possible to construct a triangle whose sides are 3. 5 cm 9. 2 cm and 5. 3 cm Why or why not?.
No, it is not possible to construct a triangle whose sides are 3. 5 cm 9. 2 cm and 5. 3 cm. Because the sum of the triangle's two sides, 3.5 cm and 5.3 cm, is not greater than the third side, 9.2 cm, the triangle cannot exist.
Define sides of triangle.A triangle has three vertices, which connect the triangle's sides, which are all straight lines. The sides of a triangle are, in other words, line segments that converge at the triangle's vertices. An "opposite" side in a right triangle is the one that is across from a specific angle, and an "adjacent" side is the one that is next to a specific angle. The hypotenuse is the longest side in a right triangle.
Given,
Sides 3.5cm, 5.3 cm and 9.2 cm
Sum = 3.5 + 5.3
Sum = 8.8
There are three sides offered, with dimensions of 3.5 cm, 5.3 cm, and 9.2 cm. The third side is always greater than the sum of any two triangle sides, as we are all aware of. Because the sum of the triangle's two sides, 3 cm and 5 cm, is not greater than the third side, 8 cm, the triangle cannot exist.
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* 7) If 100 J of work is required to stretch a spring 50cm beyond its natural length, how much
work is required to stretch the spring 80 cm beyond its natural length?
Hooke's law is generalized in modern elasticity theory to say that the strain (deformation) of an elastic object or material is proportional to the stress...
Which low is used for find the answer ?When a spring is stretched 0.4 m beyond its natural length, it exerts a force of 150 N. How much effort is required to extend the spring's natural length by 0.9 m?
Hooke's law expresses the amount of force required to stretch a spring beyond its natural length (x=0).
Newtons Fs(x)=kx
Experiment is used to determine the value of the spring constant k. The query demonstrates an experimental stretching. A 150 N force extended the spring's natural length by 0.4 m.
Fs=150=k0.4k=1500.4 Nm Fs=150=k0.4k=1500.4 Nm
How much effort is required to extend the spring's natural length by 0.9 m?
Work is defined as force multiplied by distance. Hooke's Law, on the other hand, describes a variable force that depends on how much it is stretched, x. To solve this, an integral is required.
W=∫xf0Fs(x)dx
W=∫0.90kxdx=k2x2|0.90
W=1500.412x2|0.90
W=15008x2|0.90=15008(0.9)2
Answer
W equals 151.875 joules
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let w be a subspace of rn, and let w ? be the set of all vectors orthogonal to w . show that w ? is a subspace of rn using the following steps. a. take z in w ?, and let u represent any element of w . then zu d 0. take any scalar c and show that cz is orthogonal to u. (since u was an arbitrary element of w , this will show that cz is in w ?.) b. take z1 and z2 in w ?, and let u be any element of w . show that z1 c z2 is orthogonal to u. what can you conclude about z1 c z2? why? c. finish the proof that w ? is a subspace of rn.
The three properties of a subspace must be demonstrated for the set of all vectors orthogonal to w, indicated as w?, in order to demonstrate that it is a subspace of Rn.
What is the vector?In mathematics, objects with both magnitude and direction are called vectors. The vector's size is determined by the magnitude. It is shown as a line with an arrow, where the length of the line indicates the vector's magnitude and the arrow points in the desired direction. In addition, it goes by the names Euclidean vector, Geometric vector, Spatial vector, or just "vector."
What is the vectors are orthogonal?The term "orthogonal" in mathematics denotes a direction at a 90° angle. If two vectors are perpendicular to one another and the result of the dot product analysis is zero, then the vectors are said to be orthogonal.
a) Let u be any component of w and choose any z in w. Since z and w are orthogonal to one another, zu = 0. Now, let cz be the result of c and z for any scalar c. The equation (cz)u = c(zu) = c * 0 = 0 is known. As u was an arbitrary element of w, this demonstrates that cz is orthogonal to u and therefore cz is in w?
b) Let u be any component of w and consider z1 and z2 in w. Both z1u and z2u are known to be zero. Given that the first argument of the dot product is linear, we know that (z1 + z2)u = z1u + z2u = 0 + 0 = 0. As u was an arbitrary member of w, this demonstrates that z1 + z2 is orthogonal to u and that z1 + z2 is in w?
c) We have demonstrated that w? is closed under addition and scalar multiplication from a and b. We observe that the zero vector is obviously orthogonal to any vector in w and is thus in w? to demonstrate that it contains the zero vector. This demonstrates that w? is a subspace of Rn since it satisfies all three characteristics of a subspace.
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In a large set of data that are approximately normally distributed,
r is the value in the data set that has a z-score of -1.00
s is the value of the first quartile, and
t is the value of the 20th percentile.
Which of the following is the correct order from least to greatest for the values of r, s, and t?
A: r, s, t
B: r, t, s
C: s, t, r
D: t, r, s
E: t, s, r
The correct order from least to greatest for the values of r, s, and t is given by:
B. r, t, s.
How to order the values?The values are ordered considering the normal distribution, in which each z-score has an equivalent p-value, which gives the percentile of the score.
The values are given as follows:
r is the value in the data set that has a z-score of -1.00 -> 16th percentile, as z = -1.00 has a p-value that is rounded to 0.16.s is the value of the first quartile, hence it is the 25th percentile.t is the value of the 20th percentile.The greater the percentile, the higher the measures, hence the measures are ordered from least to greatest as follows:
r, t and s.
Meaning that option B gives the correct option.
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based on observations of his own children, jean piaget formed a theory about the cognitive development of all children. this is an example of _______reasoning.
based on observations of his own children, jean piaget formed a theory about the cognitive development of all children. this is an example of inductive reasoning reasoning.
Inductive reasoning :
Inductive reasoning is a method of reasoning by proceeding from the specific to the general. Inductive reasoning or inductive logic is a type of reasoning in which a general conclusion is drawn from a set of specific observations.
It contrasts with deductive reasoning, which usually moves from general information to specific conclusions. Inductive reasoning is also known as inductive logic or bottom-up reasoning because it involves extending certain premises to broader generalizations.
Examples of Inductive Reasoning:
Here is the basic form of inductive reasoning, with premises and generalized conclusions based on concrete data:
1. All the swans I have seen are white. (Premise)
2. Therefore, all swans are white. (Conclusion)
In this example the conclusion is actually wrong
- There is also a black swan. This is the so-called "weak" argument. However, it is easy to strengthen the conclusion by increasing the likelihood.
1. All the swans I have seen are white. (Assumption)
2. Therefore, most swans are probably white. (Conclusion)
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Cari ay if a triangle ha the ide length of 3, 3 , and 9, then the triangle i a 30-60-90 triangle. Dana ay if a triangle ha the ide length of 2, 2 3 , and 4, then the triangle i a 30-60-90 triangle. Who i correct and why?
In both cases, i.e. Cari and Dana, Dana is correct because the triangle follows the 30-60-90 triangle rule.
What is the 30-60-90 Triangle?
The 30-60-90 triangle is referred to as a special right triangle because its angles have a particular ratio of 1:2:3. A right triangle in this context refers to any triangle with a 90° angle. A unique kind of right triangle called a 30-60-90 triangle always has angles that measure 30, 60, and 90 degrees.
Given, for Cari, the triangle has a length of 3, 3, and 9
And, for Dana, the triangle has a length of 2, 2[tex]\sqrt{3}[/tex], and 4
For a 30-60-90 triangle, sides are distributed in the form of x, x[tex]\sqrt{3}[/tex] , and 2x.
So, in Dana's case, triangle sides have sides in the form of x, x[tex]\sqrt{3}[/tex] , and 2x i.e. 2, 2[tex]\sqrt{3}[/tex], and 4 respectively.
Therefore, Dana is correct.
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Use continuity theorem to show that, as n → 00, a. if X, is bin(n, 1/n) then the distribution of X, converges to a Poisson distribution, b. if Yn is geometric with parameter p = a/n then the distribution of Yn converges to an exponential distribution.
The continuity theorem, also known as the intermediate value theorem, asserts that if a function is continuous on a closed interval, then it takes on every value inside the interval between the function's minimum and maximum values.
a. Using the continuity theorem, we know that as n→∞, the distribution of Xn converges to a Poisson distribution if the probability mass function of Xn converges to the probability mass function of a Poisson distribution.
This is true because the probability mass function of Xn, which is bin(n, 1/n), converges to the probability mass function of a Poisson distribution as n→∞.
b. Similarly, using the continuity theorem, we know that as n→∞, the distribution of Yn converges to an exponential distribution if the probability mass function of Yn converges to the probability mass function of an exponential distribution.
This is true because the probability mass function of Yn, which is geometric with parameter p = a/n, converges to the probability mass function of an exponential distribution as n→∞.
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The National Sleep Foundation recommends that teenagers aged 14 to 17 years old get at least 8 hours of sleep per night for proper health and wellness. A statistics class at a large high school suspects that students at their school are getting less than 8 hours of sleep on average. To test their theory, they randomly sample 42 of these students and ask them how many hours of sleep they get per night. The mean from the sample is x-bar=7.5 hours.
Here's their alternative hypothesis:
"The average amount of sleep students at their school get per night is...
What is an appropriate ending to their alternative hypothesis?
answer choices
less than 7.5 hours
less than 8 hours
more than 7.5 hours
more than 8 hours
An appropriate ending to the alternative hypothesis is less than 8 hours. The alternative hypothesis would be: The average amount of sleep students at their school get per night is less than 8 hours.
What is alternative hypothesis?The alternative hypothesis is a statement used in statistical inference experiment which is contradictory to the null hypothesis and denoted by Ha or H1. In hypothesis testing, an alternative hypothesis is a statement that a researcher is testing.
The alternative hypothesis could take one of three forms, depending on the context of the test:
Ha: parameter > value.Ha: parameter < value.Ha: parameter ≠ value.Which alternative hypothesis we use (< or > or ≠) is sometimes called the direction of the test. Which direction we choose depends on the context of the test.
In this case, it is suspected that students at the school are getting less than 8 hours of sleep on average, so that is the alternative hypothesis.
Ha: The average amount of sleep students at their school get per night is less than 8 hours.
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What value of x is in the solution set of 4x 12 ≤ 16 8x 10?.
The value of x is in the solution set of 4x - 12 ≤ 16+8x is x ≥ -7.
Given inequality:
⇒ 4x - 12 ≤ 16+8x
rearranging the like terms
4x - 8x - 12 ≤ 16
4x - 8x ≤ 16+12
-4x ≤ 16+12
-4x ≤ 28
divide by 4 on both sides
-4x/4 ≤ 28/4
-x ≤ 28/4
-x ≤ 7
x ≥ -7.
Therefore the value of x is in the solution set of 4x - 12 ≤ 16+8x is x ≥ -7.
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Give the slope of the line that passes
through the given points.
(-18, 5), (-45, 7)
Give only the number in fraction form
Answer:
[tex]m=-\frac{2}{27}[/tex]
Step-by-step explanation:
[tex]Slope (m) =\frac{y_2-y_1}{x_2-x_1}\\(x_1,y_1)=(-18,5)\\(x_2,y_2)=(-45,7)\\m=\frac{7-5}{-45-(-18)}\\m=\frac{2}{-45+18}\\m=\frac{2}{-27}\\m=-\frac{2}{27}[/tex]
How do you tell if a function table is linear or not?.
If the function is on a graph and it's a straight line then its linear.
What is a linear function?A linear function is modeled by the following rule: y = mx + b
In which m is the slope, which is the rate of change, that is, the change in y divided by the change in x.
Here b is the y-intercept, which is the the value of y when the function crosses the x-axis, that is, when x = 0.
If the function is on a graph and it's a straight line then its linear.
If the function is not on a graph, it will fall under a few different formulas, but as a general rule if it does not have an exponent on the x or y then it'll be linear.
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