The range of the accidents reported from the grouped frequency table is 22.
What is a range in a set of data?The range is the difference between the highest value and the lowest value of a given set of data.
We have,
The number of accidents reported from the grouped frequency table.
The largest number of accidents = (19 - 25)
The smallest number of accident = (3 - 7)
Now,
Range.
= 25 - 3
= 22
Thus,
The range of the reported accidents is 22.
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A university just acquired more land which is shown by the triangle in the diagram. What is the area of the land that the university just aquired?
Therefore , the solution of the given problem of area comes out to be the land acquired by university is of 3 miles square area.
Define area.The term "area" describes the amount of space occupied by a 2D form or surface. We use cm2 or m2 as our units for measuring area. A shape's area is determined by dividing its length by its breadth.
Area = length x breadth.
Here,
Given : A triangle land which has
height = 2miles
and base = 1.5+ 1.5 = 3 miles
Thus,
To find the area of triangle :
=> Area = 1/2*b*h
=>Area = 3*2/2
=> Area = 3 miles square
Therefore , the solution of the given problem of area comes out to be the land acquired by university is of 3 miles square area.
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Greg has 14 as many songs on his computer as Mark. Raj has 6 fewer than 60% of the songs that Mark has. Mark has 720 songs on his computer.
Using percentage and equations, Greg has 734 songs, Raj has 426 songs and Mark has 720 songs
What is PercentagePercentage is a way of expressing a number as a fraction of 100. It is often denoted using the percent symbol, "%". For example, 45% (read as "forty-five percent") is equal to 45/100, or 0.45. Percentages have no dimension, which it's why they are dimensionless number. for example 60% of a number, then it means 60 per cent of its whole.
In this problem, we can write an equations and solve to determine the number of songs Greg has on his computer.
Let;
x = number of songs Greg hasy = Number of songs Raj hasSince Mark has 720 songs in his computer;
x = 14 + 720
x = 734
Greg has 734 songs
We can calculate the number of songs Raj has by;
y = 60%(720) - 6
y = [(0.6) * 720] - 6
y = 426
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A line passes through the points (-2,8) and (5,-20)
The linear equation that passes through these two points is:
y = -4x
How to find the equation for the line?A general linear equation can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If we know that the line passes through two known points (x₁, y₁) and (x₂, y₂), then we can write the slope as:
a = (y₂ - y₁)/(x₂ - x₁)
Here we know the two points (-2, 8) and (5, -20), so the slope is:
a = (-20 - 8)/(5 + 2) = -28/7 = -4
So the line is:
y = -4*x + b
To find the value of b, we can replace the values of the point (-2, 8), so we will get:
8 = -4*(-2) + b
Now we can solve this for b.
8 = -4*(-2) + b
8 = 4*2 + b
8 = 8 + b
8 - 8 = b
0 = b
Then the linear equation is:
y = -4*x
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SHOW YOUR WORK 256 divided by 6400
Each of the students in class writes a different 2 digit number on the whiteboard. The teacher claims that no matter what the students write there will be at least three numbers on the white board whose digits have the same sum what is the smallest number of students in the calls for the teacher to be correct?
Answer: The teacher's claim is that there will be at least three numbers on the whiteboard whose digits have the same sum, no matter what the students write. To see if this claim is true, we can consider different cases for the number of students in the class.
If there are only two students in the class, the teacher's claim is not true. The two students can write any two different two-digit numbers, and it's not guaranteed that the digits in those numbers will have the same sum.
If there are three students in the class, the teacher's claim is true. The three students can write any three different two-digit numbers, and at least one of those numbers is guaranteed to have digits that have the same sum as one of the other numbers.
If there are more than three students in the class, the teacher's claim is true. No matter what numbers the students write, there will always be at least three numbers whose digits have the same sum.
Therefore, the smallest number of students for the teacher's claim to be true is three students.
It's worth mentioning that the teacher's claim is not necessarily true for all cases, it's only true that any three numbers picked out of the two-digit numbers set, will have digits with the same sum.
Step-by-step explanation:
How do you represent a number line on a class 7?
Draw a line and locate the origin '0', mark the positive numbers on the right and the negative number on the left of '0' at an equal distance.
A number line is a horizontal straight line in which the integers are placed in equal intervals. All the numbers can be represented in a number line. This line can be extended indefinitely at both ends.
A number line is a graphical representation of numbers on a straight line. It is used for comparing and ordering numbers. It can be used for representing any real number that includes every whole number and natural number.
Draw a line and locate the point ‘0’. This point is known as the origin. If the given number is positive, draw it on the right side of the origin. If it is a negative number, draw it on the left side of zero. Divide each unit into the values equal to the denominator of the given fraction.
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How do you solve a 3 by 3 system of equations using matrices?
The solutions can be read off of the diagonal entries in the reduced matrix.
To solve a 3 x 3 system of equations using matrices, first we need to create the augmented matrix for the system of equations. The augmented matrix contains the coefficients of the variables and the constants for each equation on each row. Then we can use row operations to reduce the augmented matrix to reduced row-echelon form. This can be done by adding or subtracting rows to each other, multiplying or dividing a row by a non-zero number, and swapping two rows. After reducing the matrix to row-echelon form, we can back-substitute the solutions to the system of equations. The solutions can be read off of the diagonal entries in the reduced matrix. For example, if the matrix is reduced to the form [a b c d e f g h i] then the solution to the system of equations is x = d/a, y = e/b, and z = f/c.
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Solve for x in this triangle. Round your answer to the nearest tenth. 18 Xº 23
Answer:
51.50004959055205
Step-by-step explanation:
[tex]sin (x) = \frac{18}{23}[/tex]
hi, can someone please help me
this is your proper answer
hii, how are you
Answer:
15
Step-by-step explanation:
Let the total number of beads be x[tex]\because\: \frac{3}{8}[/tex] of the beads are blue.& Total number of blue beads = 9[tex]\rightarrow\: \frac{3}{8}\times x= 9[/tex][tex]\rightarrow\: x= \cancel{9}\times\frac{8}{\cancel{3}}[/tex][tex]\rightarrow\: x=3\times 8[/tex][tex]\rightarrow\: x=24[/tex]Number of purple beads = 24 - 9 = 15What is the area of this parallelogram?
Answer: B
Step-by-step explanation:
Area = 4 x 5
= 20 cm^2
Remember that area of parallelogram is the base x perpendicular height. is The perpendicular height is not 6cm but 5cm. (right angle labelled on diagram)
Answer: 20 cm²
Step-by-step explanation:
area parallelogram = base x height
=> 4 x 5 = 20
How do you write log in e form?
Log to exponential form is very useful to easily perform complicated numeric calculations. The logarithmic form
loga N=x
can be easily transformed into the exponential form as:
ax=N
Normally, large astronomical and scientific calculations are written in exponential form, and here we can use the log to exponential form of transformation.
Logarithms are occasionally transformed using antilog tables to normal form, rather than transforming into exponential form.
Log to exponential form required specific formulas of logarithms and exponents. Logarithms help in easily transforming the multiplication and division across numbers into addition and subtraction.
And exponentials help in working across numbers with different bases and different powers.
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Find the value of x in the following equation:
3.5(5x + 4) = 17.5x + 14
No solution
Infinite solutions
x = 0
x = 1.3
The system of equations .5(5x + 4) = 17.5x + 14 have Infinite solutions.
What are simultaneous equations?We know two simultaneous equations have a unique solution when they intersect at a point,
when they are parallel they have no solution and when they are coinciding they have an infinite no. of solutions.
Given, A system of equation 3.5(5x + 4) = 17.5x + 14.
17.5x + 14 = 17.5x + 14.
As the LSH and RHS are equal the equation of the two lines is the same and hence they coincide and have an infinite number of solutions.
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Can someone please explain how to do inequalities in math.
please add an example too.
What are the 11 identities?
Trigonometric identities are categorized as various identities out of which 11 are ,
Sin θ = 1/Coc θCos θ = 1/Sec θ Tan θ = 1/Cot θTan θ = Sin θ/Cos θCot θ = Cos θ/Sin θSin (90 – θ) = Cos θCos (90 – θ) = Sin θTan (90 – θ) = Cot θCot ( 90 – θ) = Tan θSec (90 – θ) = Cos θCos (90 – θ) = Sec θSin (-θ) = – Sin θTrigonometric Identities are used when trigonometric functions are given in an expression. Geometrically, these identities include one or more trigonometric functions
These are the sine , cosine or the tangent functions.
There are numerous trigonometric identities relating the side length and angle of a triangle. Only the right-angle triangle has the trigonometric identities.
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Angle AOB is a central angle with a measure of 110 degrees.
What is the measure of its arc AB?
The measure of the ACB arc is 250° when in the picture we have a circle with an angle AOB is a central angle with a measure of 110°.
Given that,
In the picture we have a circle with an angle AOB is a central angle with a measure of 110°.
We have to find the measure of the ACB arc.
We know that,
Suppose that AB is the minor arc that is m(arc AB) = 110°
We know that measure of the major arc is 360°- measure of minor arc.
m(arc ACB)= 360- m(arc AB)
m(arc ACB)= 360-110
m(arc ACB)= 250°
Therefore, The measure of the ACB arc is 250° when in the picture we have a circle with an angle AOB is a central angle with a measure of 110°.
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What is the interval of zero?
If the confidence interval for a difference between groups includes zero, that means that if you run your experiment again you have a good chance of finding no difference between groups.
If the confidence interval for a difference between groups includes zero, that means that if you run your experiment again you have a good chance of finding no difference between groups.
If the confidence interval for a correlation or regression includes zero, that means that if you run the experiment again there is a good chance of finding no correlation in the data.
In both of these cases, you will also find a high p-value when you run the statistical test, meaning that the results could have occurred under the null hypothesis of no relationship between variables or no difference between groups.
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help im no good at this
Answer:
8.2 × 10⁻³
Step-by-step explanation:
1.64 × 10⁰ 1.64 × 1 1.64
-------------- = -------------- = ---------- = 0.0082
2.0 × 10² 2 × 100 200
Scientific notation: 8.2 × 10⁻³
I hope this helps!
5. Measure the length of each leg and the hypotenuse of this triangle: a.f = units ag units fg = units
To find the length of the side opposite the angle, multiply the hypotenuse by sin(). Alternatively, to obtain the side next to the angle, multiply the hypotenuse by cos()
What is Hypotenuse triangle?The term "hypotenuse" refers to a right-angled triangle's longest side as compared to the base and perpendicular lengths. The right angle, the largest angle of the three angles in a right triangle, is opposite the hypotenuse side. In essence, only the right triangle possesses the hypotenuse feature, not any other triangles. When we study the right-angled theorem, Pythagoras Theorem, or Pythagorean Theorem, this is better understood.
Hypotenuse TheoramPythagoras theorem defines the hypotenuse theorem. This theorem states that the square of a right-angled triangle's hypotenuse side is equal to the sum of its base and perpendicular squares, so that;
Hypotenuse2 = Base2 + Perpendicular2
The square root of the sum of the base and perpendicular squares of a right-angled triangle provides the formula to get the hypotenuse. The hypotenuse formula is represented as follows:
Hypotenuse = √[Base2 + Perpendicular2]
Length of the hypotenuse:Hypotenuse length: In the scenario where the square root is not a perfect square, we take an approximation of the root here in order for the solution to appear.Additionally, the squares of the base and the height should always be added to establish the value, however this does not provide a perfect square.Due to the imperfect square-root number, we must therefore approximation the solution.To know more about Hypotenuse Triangle refer to:
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What is the 3 triangular number?
A triangular number succession is the representation of numbers as just an ordered set of equilateral triangles. The order of these numbers is 1, 3, and 6.
What exactly is meant by triangular numbers?A triangular number is one that may be written as the sum of a initial n positive integers.
A good example of a triangular number is 6, which may be written as 1+2+3 when the first three positive integers are added together.Triangular numbers make up a sequence if one considers the sum of the first positive integer as the initial element, the sum of the first two positive integers as the second element, and so on.If a number equals that sum of such initial n positive integers, then n denotes the position of that particular triangular number with in the series.Triangular numbers can be used to create equilateral triangles.The first 3 triangular numbers are therefore 1, 3, and 6.
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IS this statement true. When two conjugates are multiplied, the product is a
difference of two squares
Therefore the product of two conjugates is a difference of two squares.
What are conjugates?When two binomials have the same terms but different arithmetic operators in the center of these related words, they are said to be conjugate. For instance, the conjugate of p + q is p - q.
Define binomial numbers.An integer known as a binomial number is produced by evaluating a homogeneous polynomial with two terms, also known as a binomial.
This statement is true.
The conjugates of a complex number are two complex numbers that differ only in their signs. They are of the form a + bi and a - bi.
When two conjugates are multiplied, the product is (a + bi)(a - bi) = a^2 + (bi)^2 = a^2 - b^2 + (2abi) = (a^2 - b^2) + (2ab)i.
which is in the form (a^2 - b^2) + (2ab)i = (a^2 - b^2) + (2ab)i = (a+b)(a-b)
So the product of two conjugates is a difference of two squares.
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how to get the Y intercept when you don't have a 0 X coordinate?
Answer: You plug in y as 0 into your equation.
Step-by-step explanation:
Do the above thing OK.
6 x/11 ➕1
What does x equal
X is 55 after rearranging the equation given
Is Avogadro's number equal to one mole?
One mole consists of 6.02214076×10²³ units which is Avogadro's number. Thus one mole is known as Avogadro's number.
What is one mole?
A mole is 6.02214076×10²³ of any chemical unit, including atoms, molecules, ions, and others. Due to the large number of atoms, molecules, or other components that make up any substance, the mole is a useful measure to utilize. The mole was initially defined as the quantity of atoms contained in 12 grammes of carbon-12, but the General Conference on Weights and Measures declared in 2018 that the mole will only contain 6.02214076×10²³ of some chemical unit as of May 20, 2019.
In chemistry, a mole, sometimes spelled mol, is a common scientific measurement unit for significant amounts of very small objects like atoms, molecules, or other predetermined particles.
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Rewrite 14x4y3 − 42x3y4 using a common factor.
The expression 14x⁴y³ - 42x³y⁴ is rewritten to 14x³y³(x - y)
What is an algebraic expression?
An algebraic expression can be described as a mathematical expression that is made up of terms, coefficients, variables, factors and constants.
They are also made up of some arithmetic operations, such as;
SubtractionMultiplicationDivisionBracketParenthesesAddition, etcFrom the information given, we have the algebraic expression;
14x⁴y³ - 42x³y⁴
Now, factor the common numbers, we have;
14(x⁴y³ - 3x³y⁴)
Factor the common variables, we get;
14x³y³(x - y)
Hence, the expression is 14x³y³(x - y)
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What are the 3 possible solutions for any quadratic?
There are three basic methods for solving quadratic equations: factoring, using the quadratic formula, and completing the square.
quadratic equations
Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax^2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient and 'c' is called the absolute term of f (x).
factoring
factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.
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7
A scientist is investigating the weight of 50 tigers.
Here is some information about these tigers.
Number of tigers
Mean weight of tigers (kg)
Siberian
22
260
Type of tiger
The mean weight of all 50 tigers is 218 kg
Work out the mean weight of the Bengal tigers.
Bengal
28
Consequently, there is a 0.89736 percent chance or probability that he weighs fewer than 258 kilograms.
What is probability?Probability fundamentals. A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
Here,
we use the z-score algorithm to answer this query.
Score Z = x - μ/σ
x = the raw score
population mean= μ
Population standard deviation is σ
Hence,
x = 258, μ = 220, σ = 30
Z = 258 - 220/30
=1.26667
Probability based on the Z-Table:
P(x<258) = 0.89736
Consequently, there is a 0.89736 percent chance that he weighs fewer than 258 kilograms.
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Will give you brainlist
What are the two equations to set up to solve the equation?
|3x-2|=19
3x-2=
~QUESTION 2~
3|x+2|-7=14
x=_______
_____
~QUESTION 3~
-2|2x+3|+14(greater than and equal to symbol) -16
= < with line * < with line
The two equation to set up to solve the equation |3x - 2| = 19 are
3x - 2 = 193x - 2 = -19Question 2
x = 5 OR -9
Question 3
x ≥ 6 OR x ≥ -9
What is absolute value?Without taking direction into account, absolute value describes how far away from zero a certain number is on the number line.
A number can never have a negative absolute value.
How to write the absolute value equationThe equation is written in the form below
|3x - 2| = 19
removing the absolute value sign
3x - 2 = ± 19
the two equations are
3x - 2 = 19
3x - 2 = -19
Question 2
solving for x
3|x + 2| - 7 = 14
3|x + 2| = 14 + 7
3|x + 2| = 21
divide through by 3
|x + 2| = 7
removing the absolute value sign
x + 2 = ±7
solving for x for positive value
x + 2 = 7
x = 5
solving for the negative sign
x + 2 = -7
x = -9
Question 3
-2|2x+3| + 14 ≥ -16
-2|2x+3| ≥ -30
dividing through by -2
|2x+3| ≥ 15
2x+3 ≥ ±15
solving for the positive sign
2x+3 ≥ 15
x ≥ 6
solving for the negative sign
2x+3 ≤ -15
x ≥ -9
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Factor the expression completely.
x^4-15x^2+54
Answer:
x^2(x^2 - 15) + 9(x-6)(x+1)
Step-by-step explanation:
To factor the expression x^4 - 15x^2 + 54 completely, we need to find the common factors in each term. In this case, we can see that the terms x^4 and -15x^2 share a common factor of x^2. To factor this out, we can use the difference of squares factorization:
x^4 - 15x^2 + 54 = x^4 - 15x^2 + (9x^2 - 9x^2) + 54
= x^2(x^2 - 15) + 9(x^2 - 6)
= x^2(x^2 - 15) + 9(x-6)(x+1)
Since x^2-15 can't be factored further. The expression is fully factored.
We can check this by multiplying it back and it should be the same as original expression.
1. What is the unit of measurement for speed using the metric system?
Answer:
meter per second(m/s)
Answer:
Hey there! The metric system has a unit called meters per second for measuring speed. It's abbreviated as m/s and it's used to measure how far something travels in a certain amount of time. For example, if something goes 50 meters in 10 seconds, its speed would be 50 m/s / 10 s = 5 m/s. There are other units for measuring speed too, like kilometers per hour (km/h) and centimeters per second (cm/s). It just depends on what you're measuring and how precise you need to be.
________________________________________________________
How do things like distance and time affect the speed of an object?Well, speed is all about how far something goes in a certain amount of time. So if you increase the distance traveled or decrease the time it takes to travel that distance, the speed will increase. On the other hand, if you decrease the distance traveled or increase the time it takes to travel that distance, the speed will decrease.
Why is it important to measure and calculate speed in certain situations?There are all sorts of situations where knowing the speed of something is important. For example, if you're driving a car, it's important to know how fast you're going so you can stay safe and follow the speed limits. In sports, measuring speed can help coaches and players improve their performance. And in science, measuring the speed of light or other phenomena can help us better understand the world around us. So as you can see, speed is a pretty important concept!
How do you find the area of the pre image and the image?
Coordinates for the pre-image are X(3,18) Y(18,18) and Z(18,9) and the image coordinates are X’(1,6) Y’(6,6) Z’ (6,3)
and what is the relationship between the two areas?
Answer: To find the area of the pre-image and the image, you can use the coordinates of the vertices of the shapes to calculate the lengths of the sides and use the formula for the area of a triangle:
Area = (base * height)/2
For the pre-image, the coordinates are X(3,18) Y(18,18) and Z(18,9). The base of the triangle is the distance between X and Z, which is 18 - 3 = 15. The height of the triangle is the distance between Y and Z, which is 18 - 9 = 9. The area of the pre-image is therefore:
Area = (15 * 9)/2 = 67.5
For the image, the coordinates are X’(1,6) Y’(6,6) Z’ (6,3). The base of the triangle is the distance between X’ and Z’, which is 6 - 1 = 5. The height of the triangle is the distance between Y’ and Z’, which is 6 - 3 = 3. The area of the image is therefore:
Area = (5 * 3)/2 = 7.5
The relationship between the two areas is that the area of the image is smaller than the area of the pre-image. This is because the image has been scaled down in size relative to the pre-image. The amount by which the image has been scaled down can be calculated by dividing the area of the image by the area of the pre-image:
Scale factor = area of image / area of pre-image = 7.5 / 67.5 = 0.11
This means that the image has been scaled down by a factor of 0.11 relative to the pre-image.
Step-by-step explanation:
Answer:
preimage area: 67.5 square unitsimage area: 7.5 square unitsimage area is 1/9 of preimage area, the square of the scale factorStep-by-step explanation:
You want to know the areas and their relationship of the preimage with coordinates X(3,18), Y(18,18), and Z(18,9), and the image with coordinates X’(1,6), Y’(6,6), Z’ (6,3).
TrianglesWhen you plot the points on a graph, you see they define right triangles. Each has sides aligned with the x- and y-axes, so it is easy to find their dimensions by counting grid squares or subtracting coordinates.
The preimage triangle is 18-3 = 15 units in the x-direction, and 18-9 = 9 units in the y-direction.
The image triangle is 6-1 = 5 units in the x-direction, and 6-3 = 3 units in the y-direction.
We notice that both the coordinates and the dimensions of the image triangle are 1/3 those of the preimage triangle.
AreasThe area of each triangle is given by the formula ...
A = 1/2bh
Using the dimensions we found above, the areas are ...
preimage area: 1/2(15)(9) = 135/2 = 67.5 . . . . square units
image area: 1/2(5)(3) = 15/2 = 7.5 . . . . square units
Relationship
We have observed that the image dimensions are 1/3 those of the preimage. The image area is 7.5/67.5 = 1/9 of that of the preimage. This value is the square of the scale factor of the dimensions,