Step-by-step explanation:
4.6 hrs is 46over 10 which is
13 over 5 or 2 and 3over 5
The first and second steps to solve the equation StartFraction 3 x over 5 EndFraction + 5 = 20 are shown below. StartFraction 3 x over 5 EndFraction + 5 minus 5 = 20 minus 5 StartFraction 3 x over 5 EndFraction (Five-thirds) = 15 (five-thirds) Which property was applied in the second step?
The multiplication property of equality has been used in the second step when both sides of the equation have been multiplied by 5/3.
State the Multiplication Property of Equality:
The Multiplication Property of Equality states that multiplying both sides of the equation with the same number, expression, or variable, the equation remains unchanged, i.e. equality is maintained.
Use of Multiplication Property of Equality in the Second Step:
The given equation was,
3x/5 + 5 = 20
In the first step, subtraction property of equality is applied as follows,
3x/5 + 5 - 5 = 20 - 5
3x/5 = 15
Now, for isolating x on the left hand side, we must apply multiplication property of equality by multiplying both sides of the equation by 5/3.
We get,
3x/5 × 5/3 = 15 × 5/3
x = 25
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The safety triangle tries to predict safety performance. group of answer choices true false
TRUE
The safety triangle tries to predict safety performance.
The accident triangle, also known as Heinrich's triangle or bird's triangle, is a theory of occupational injury prevention. Indicates the relationship between serious accidents, minor accidents, and near misses. The idea is that the fewer minor accidents, the fewer serious accidents.
The process safety triangle is used to illustrate the different actions that can lead to an accident. This tool has a bottom up flow where each layer can be thought of as a preventative measure to the layer above it.
One of the main purposes of the process safety triangle is to explain how unsafe actions can lead to serious accidents. The Process Safety Triangle is also used to visualize different layers of protection and redesign systems to ensure better preventive practices. The lowest level of unsafe actions is categorized as the primary metric. A leading indicator is a preventive action taken to prevent an incident from occurring. Dangerous behavior by employees. B. Not wearing personal protective equipment or missing a system layer of protection is a major cause of process safety incidents. The wider the base of the process safety triangle, the wider the top level. This triangle shows that the more unsafe your actions are, the more likely you are to die in a process safety incident.
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Choose the correct discount or markup. if an item has a retail price = $995 and a discount of 15%, how much is the discount? it is $ .
Answer:
$149.25
Step-by-step explanation:
The discount is 15% of $995
Find the Discount[tex]15\%\times995[/tex]
Note that percentages can also be written as that number over 100.
[tex]\frac{15}{100}\times995[/tex]
Simplify the fraction
[tex]\frac{3}{20}\times995=\frac{2985}{20}=149.25[/tex]
Therefore the discount is $149.25.
Answer:
$149.25
Step-by-step explanation:
Evaluate the expression using a calculator:
The value of the expression is 0.0265. Using exponents and power rules, the required value is calculated.
What are the exponent and power rules?The important exponent and power rules are:
a⁻ⁿ = 1/aⁿ; negative exponent(ab)ⁿ = aⁿ × bⁿ; power of a product ruleaⁿ × aˣ = aⁿ⁺ˣ; multiplication ruleaⁿ/aˣ = aⁿ⁻ˣ; division rule[tex]a^{\frac{x}{y} } = \sqrt[y]{a^x}[/tex]; fractional exponentCalculation:The given expression is [tex]126^{-3/4}[/tex]
Using calculator: [tex]126^{-3/4}[/tex] = 0.0265
Applying the exponent rule for evaluating the given expression:
[tex]126^{-3/4}[/tex]
Applying the negative power rule;
I.e., a⁻ⁿ = 1/aⁿ
⇒ [tex]126^{-3/4}=\frac{1}{126^{3/4}}[/tex]
Applying fractional exponent rule;
I.e., [tex]a^{\frac{x}{y} } = \sqrt[y]{a^x}[/tex]
⇒ [tex]\frac{1}{126^{3/4}}=\frac{1}{\sqrt[4]{126^3} }[/tex]
⇒ 1/[tex]\sqrt[4]{2000376}[/tex]
⇒ 1/37.6077
⇒ 0.0265
Therefore, the value of the given expression is 0.0265.
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How many solutions can be found for the equation 12x 8 = 12x 8? zero one two infinitely many
Answer:
Infinite
Step-by-step explanation:
12x 8 = 12x 8
Infinitely many solutions, as left side = right side.
Please answer this question ASAP!
The traffic lights at three different road crossings change after every 48, 72 and 108 seconds respectively. If they change simultaneously at 8 am, at what time will they change to again?
Answer:
8:07:12 am
Step-by-step explanation:
The lights will change simultaneously after any multiple of the least common multiple of their cycle times.
LCMThe least common multiple of a set of numbers is the product of the highest powers of their prime factors.
48 = 2⁴×3
72 = 2³×3²
108 = 2²×3³
The highest power of the factor 2 is 4. The highest power of the factor 3 is 3, so the LCM of the numbers 48, 72, and 108 is ...
LCM = 2⁴×3³ = 16×27 = 432
The lights will change simultaneously after each period of 7 minutes 12 seconds. They will change simultaneously again at 8:07:12 am.
PLEASE HELP IM STUCK
The completed equations are:
2x + 3y = 80 equation 1
x + y = 37 equation 2
What are the completed equations?
In order to determine the number of each type of shots made, two equations would be derived based on the information provided in the question. These equations would be solved simultaneously in order to determine the required values.
[(type of basket made)x ]+ [(type of baskets made)y] = total number of points
2x + 3y = 80
x + y = total number of baskets
x + y = 37
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guys pls make it fast [tex]3^{3x-2\\} =\sqrt[3]{9}[/tex]
Match each correlation coefficient to its corresponding description.
To conserve water, many communities have developed water restrictions. The water utility charges a fee of $38, plus an additional $1.28 per hundred cubic feet (HCF) of water. The recommended monthly bill for a household is between $57 and $87 dollars per month. If x represents the water usage in HCF in a household, write a compound inequality to represent the scenario and then determine the recommended range of water consumption. (Round your answer to one decimal place.)
A) 057 ≤1.28x-38 s 87; To stay within the range, the usage should be between 44.5 and 97.7 HCF.
B) 57 s 1.28x - 38 s 87; To stay within the range, the usage should be between 74.2 and 97.7 HCF.
C) 57 ≤ 1.28x + 38 ≤ 87; To stay within the range, the usage should be between 14.8 and 38.3 HCF.
D)57 s 1.28x+38 ≤ 87; To stay within the range, the usage should be between 14.8 and 67.9 HCF.
Using a linear function, the correct option regarding the situation is given by:
C) 57 ≤ 1.28x + 38 ≤ 87; To stay within the range, the usage should be between 14.8 and 38.3 HCF.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The bill is modeled by a linear function, with an intercept of $38 and a slope of $1.28, hence it is given by:
C(x) = 1.28x + 38
The bill should be between $57 and $87 dollars per month, hence:
57 <= C(x) <= 87.
The values of x are:
C(x) >= 57
1.28x + 38 >= 57
x >= 19/1.28
x >= 14.8.
C(x) >= 87
1.28x + 38 >= 87
x >= 49/1.28
x >= 38.3.
Hence option C is correct.
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The table shows some values of a function of the form y
= ax² + bx + c.
V
4
21
5
32
6
45
7
60
8
77
The value of c, the constant of the function y = ax² + bx + c, exists -3.
What is an equation?An equation exists as an expression that indicates the relationship between two or more numbers and variables.
Given that: y = ax² + bx + c
At point (4, 21)
21 = a(4²) + 4b + c .......(1)
At point (5, 32)
32 = a(5²) + 5b + c .........(2)
At points (6, 45)
45 = a(6²) + 6b + c .......(3)
Therefore, the value of a = 1, b = 2 and c = -3.
The value of c, the constant of the function y = ax² + bx + c, exists -3.
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A mathematical prodigy wishes to put 2 of his indistinguishable IMO gold medals and 2 of his indistinguishable IPhO gold medals in one row. How many distinct arrangements are possible
This relates to combination and permutations and the number of distinct arrangements that are possible will be 6.
How to illustrate the information?From the information, a mathematical prodigy wishes to put 2 of his indistinguishable IMO gold medals and 2 of his indistinguishable IPhO gold medals in one row.
Let 1 = IMO
Let 0 = IPho.
Therefore, the number of arrangement will be:
0011
0110
1100
1010
0101
1001
Therefore, the number of arrangement will be 6.
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The following figure shows the entire
graph of a relationship.
Does the graph represent a function?
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
The given graph doesn't represent a function, as it has two values of y for a single value of x ( that is : for x = 3 it has two solutions, -3 and -6 )
therefore it can't be considered as a function ~
Use the method of undetermined coefficients to solve the given nonhomogeneous system. x' = −1 5 −1 1 x + sin(t) −2 cos(t)
It looks like the system is
[tex]x' = \begin{bmatrix} -1 & 5 \\ -1 & 1 \end{bmatrix} x + \begin{bmatrix} \sin(t) \\ -2 \cos(t) \end{bmatrix}[/tex]
Compute the eigenvalues of the coefficient matrix.
[tex]\begin{vmatrix} -1 - \lambda & 5 \\ -1 & 1 - \lambda \end{vmatrix} = \lambda^2 + 4 = 0 \implies \lambda = \pm2i[/tex]
For [tex]\lambda = 2i[/tex], the corresponding eigenvector is [tex]\eta=\begin{bmatrix}\eta_1&\eta_2\end{bmatrix}^\top[/tex] such that
[tex]\begin{bmatrix} -1 - 2i & 5 \\ -1 & 1 - 2i \end{bmatrix} \begin{bmatrix} \eta_1 \\ \eta_2 \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \end{bmatrix}[/tex]
Notice that the first row is 1 + 2i times the second row, so
[tex](1+2i) \eta_1 - 5\eta_2 = 0[/tex]
Let [tex]\eta_1 = 1-2i[/tex]; then [tex]\eta_2=1[/tex], so that
[tex]\begin{bmatrix} -1 & 5 \\ -1 & 1 \end{bmatrix} \begin{bmatrix} 1 - 2i \\ 1 \end{bmatrix} = 2i \begin{bmatrix} 1 - 2i \\ 1 \end{bmatrix}[/tex]
The eigenvector corresponding to [tex]\lambda=-2i[/tex] is the complex conjugate of [tex]\eta[/tex].
So, the characteristic solution to the homogeneous system is
[tex]x = C_1 e^{2it} \begin{bmatrix} 1 - 2i \\ 1 \end{bmatrix} + C_2 e^{-2it} \begin{bmatrix} 1 + 2i \\ 1 \end{bmatrix}[/tex]
The characteristic solution contains [tex]\cos(2t)[/tex] and [tex]\sin(2t)[/tex], both of which are linearly independent to [tex]\cos(t)[/tex] and [tex]\sin(t)[/tex]. So for the nonhomogeneous part, we consider the ansatz particular solution
[tex]x = \cos(t) \begin{bmatrix} a \\ b \end{bmatrix} + \sin(t) \begin{bmatrix} c \\ d \end{bmatrix}[/tex]
Differentiating this and substituting into the ODE system gives
[tex]-\sin(t) \begin{bmatrix} a \\ b \end{bmatrix} + \cos(t) \begin{bmatrix} c \\ d \end{bmatrix} = \begin{bmatrix} -1 & 5 \\ -1 & 1 \end{bmatrix} \left(\cos(t) \begin{bmatrix} a \\ b \end{bmatrix} + \sin(t) \begin{bmatrix} c \\ d \end{bmatrix}\right) + \begin{bmatrix} \sin(t) \\ -2 \cos(t) \end{bmatrix}[/tex]
[tex]\implies \begin{cases}a - 5c + d = 1 \\ b - c + d = 0 \\ 5a - b + c = 0 \\ a - b + d = -2 \end{cases} \implies a=\dfrac{11}{41}, b=\dfrac{38}{41}, c=-\dfrac{17}{41}, d=-\dfrac{55}{41}[/tex]
Then the general solution to the system is
[tex]x = C_1 e^{2it} \begin{bmatrix} 1 - 2i \\ 1 \end{bmatrix} + C_2 e^{-2it} \begin{bmatrix} 1 + 2i \\ 1 \end{bmatrix} + \dfrac1{41} \cos(t) \begin{bmatrix} 11 \\ 38 \end{bmatrix} - \dfrac1{41} \sin(t) \begin{bmatrix} 17 \\ 55 \end{bmatrix}[/tex]
Rewrite 2X = 128 as a logarithmic equation.
Olog,128=2
log2x = 128
log2128 = x
log128x = 2
The equation 2^x = 128 as a logarithmic equation is log₂(128) = x
How to rewrite the equation as a logarithmic equation?The equation is given as:
2^x = 128
Take the logarithm of both sides
log(2^x) = log(128)
Rewrite as:
x * log(2) = log(128)
Divide both sides of the equation by log(2)
x = log(128)/log(2)
Apply the change of base rule
x = log₂(128)
Hence, the equation 2^x = 128 as a logarithmic equation is log₂(128) = x
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Express 324000000 in scientific natation
Answer:
[tex]3.24*10^8[/tex]
Step-by-step explanation:
First, it is even so you don't need a negative power. Secondly, you put the decimal point after the first number which is three, and the next numbers which are not zeros go after it. Then you count the two numbers behind the decimal and the rest of the zeros. Then the number you get is the power of 10. And then just multiply and check your answer. :)
I really need help with this!! I’ll give brainliest to who ever answers!!
Answer:
a. triangle DEF's lines are all 3 times more than triangle ABC
b. triangle DEF's lines are all 3 times more than triangle ABC
c. 2.5 times 2 = 5
I hope u can elaborate a bit more :)
Vectors u and v are shown in the graph. What is -3(u•v)?
[tex]\mathbf{u} =\langle -6, -10 \rangle \\ \\ \mathbf{v}=\langle 7,8 \rangle \\ \\ \mathbf{u} \cdot \mathbf{v}=(-6)(7)+(-10)(8)=-122 \\ \\ \therefore -3(\mathbf{u} \cdot \mathbf{v})=-3(-122)=\boxed{366}[/tex]
The value of -3(u•v) is 366 when vector u= -6i - 10j and vector v=-6i - 10j is given.
What is dot product ?The dot product of two vectors is the sum of the products of their corresponding components.
Here, u= -6i - 10j, from the figure as u goes 6 coordinate left to the y axis and and 10 coordinates below the x axis.
v= 7i + 8j, from the figure as v corrdinates right to the y axis and 8 coordinats upwards to the x axis.
Therefore u.v= (-6i - 10j).(7i + 8j)
= -42 - 80
= -122
So, -3(u.v)= (-3)×(-122)
=366
Hence, the value of -3(u•v) is 366
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Using a sample to make generalizations about an aspect of a population is called?
It is known as Statistical Inference.
Statistical Inference
Without sampling and statistical estimation of the value, some population parameters cannot ever be known. Take customer preference samples, for instance. Since asking everyone would be impractical, choose a sample to identify the parameter.A population's mean can be estimated quite well using the confidence interval. It offers a spectrum of values that most likely includes the population mean. The interval gets smaller as sample size increases.The method of ordinary least squares is used in a regression equation to develop an equation that best fits the data of an independent variable and dependent variable.Learn more about Statistical Inference here: https://brainly.com/question/13752289
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Solve question in image (yr 8 math, 40 pt)
Answer:
y = 3
Step-by-step explanation:
(5y - 3)/4 + 6 = 3y
5y - 3 + 24 = 12y
7y = 21
y = 3
Check.
(5*3 - 3)/4 + 6 = 3*3
(15 - 3)/4 + 6 = 9
12/4 + 6 = 9
3 + 6 = 9
9 = 9
Answer: y = 3
Step-by-step explanation:
Given equation
[tex]\frac{5y~-~3}{4} ~+~6~=~3y[/tex]
Multiply 4 on both sides (to eliminate fraction)
[tex]\frac{5y~-~3}{4} *4~+~6*4~=~3y*4[/tex]
[tex](5y~-~3)~+~24~=~12y[/tex]
Expand parenthesis and combine like terms
[tex]5y~-~3~+~24~=~12y[/tex]
[tex]5y~+~21~=~12y[/tex]
Subtract 5y on both sides
[tex]5y~+~21~-~5y~=~12y~-~5y[/tex]
[tex]21~=~7y[/tex]
Divide 7 on both sides
[tex]21~/~7~=~7y~/~7[/tex]
[tex]\Large\boxed{y=3}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
An isosceles triangle has a perimeter (9y-15)cm. what is the length of the remaining equal sides of it's third side is (3y-7) cm.
The length of each of the equal sides is become x = (3y-4) cm
According to the statement
we have given that the perimeter of the isosceles triangle and length of third side. and we have to find the length of same side of triangle.
So,
An isosceles triangle is a triangle that has two sides of equal length.
Let the equal sides of isosceles triangle be x cm each.
We know that the
Sum of sides of a triangle = perimeter
x+x+(3y-7) = 9y-15
2x = 9y-3y-15+7
After solving the equation it become
2x= 6y-8
x=(6y-8)/2
Now the length of equal sides is x=3y-4
So, The length of each of the equal sides is become x = (3y-4) cm
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The likelihood of the frequency of an event in repeated trials under similar conditions is?
The probability of the frequency of an event in repeated trials under comparable circumstances is a statistical analysis.
What is Statistical analysis?The study of statistics is the field that deals with the gathering, structuring, analyzing, interpreting, and presenting of data. In order to apply statistics to an issue in science, business, or society, it is customary to start with a statistical population or a statistical model that will be investigated.
What accomplishes statistical analysis?Finding the distribution hidden in your data is the aim of a statistical analysis. What do you mean by the distribution that lies underlying my data? "The distribution of your data describes the peaks and valleys of its characteristics in relation to a target population.
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Select the correct answer.
A survey was given to randomly selected employees who drive to work. Each employee was asked to report if they had received a speeding ticket on their morning commute to work any time in the last year. The results are in the table. Which conclusion can be made from the data?
The conclusion that can be made from the data is that the probability illustrates that the employees who regularly leave for work late as less likely to receive a speeding ticket than employees who regularly leave for work early or on time.
What is probability?It should be noted that probability simply means the likelihood of the occurence of an event.
In this case, the survey was given to randomly selected employees who drive to work and eagh employee was asked to report if they had received a speeding ticket on their morning commute to work any time in the last year.
Therefore, the conclusion is that the the employees who regularly leave for work late as less likely to receive a speeding ticket than employees who regularly leave for work early or on time.
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Answer: B: The probability of an employee receiving a speeding ticket given that they regularly leave for work early or on time is less than the probability of an employee not receiving a speeding ticket given that they regularly leave for work late.
Step-by-step explanation:
trust me :)
(Geometry course question) Explain why it is not possible to construct an equilateral triangle that has
three vertices with integer coordinates. Show your work by providing an example and
including a graph. Consider an equilateral triangle whose base lies along the x-axis.
Answer:
√3 is irrational
Step-by-step explanation:
The location of the third point of a triangle can be found using a rotation matrix to transform the coordinates of the given points.
Location of point CWith reference to the attached figure, the slope of line AC is √3, an irrational number. This means the line AC never passes through a point with integer coordinates. (Any point with integer coordinates would be on a line with rational slope.)
Equilateral triangleThe line segments making up an equilateral triangle are separated by an angle of 60°. If two vertices are on grid squares, the third must be a rotation of one of them about the other through an angle of 60°. The rotation matrix is irrational, so the rotated point must have irrational coordinates.
The math of it is this. For rotation of (x, y) counterclockwise 60° about the origin, the transformation matrix is ...
[tex]\left[\begin{array}{cc}\cos(60^\circ)&\sin(60^\circ)\\-\sin(60^\circ)&\cos(60^\circ)\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right]=\left[\begin{array}{c}x'\\y'\end{array}\right][/tex]
Cos(60°) is rational, but sin(60°) is not. For any non-zero rational values of x and y, the sum ...
cos(60°)·x + sin(60°)·y
will be irrational.
As in the attached diagram, if one of the coordinates of the rotated point (B) is zero, then one of the coordinates of its image (C) will be rational. The other image point coordinate cannot be rational.
What are the solutions of the system of equations y = –(x + 2)2 + 1 and y = 2x + 5?
A (–4, –3) and (–2, 1)
B (–4, –3) and (2, 1)
C (–4, 5) and (2, 1)
D (–4, 5) and (–2, 1)
Which number is a rational number?
A. sqrt{15
B. 2.6457513110
C. 17.156
D. sqrt[3]{85}
From the given options, the rational numbers is:
17.156 = 17,156/100
Which is the one in option C.
Which of the given numbers is a rational number?
A rational number is a number that can be written as the quotient of two integer numbers.
When written in decimal form, a rational number has a finite number of digits after the decimal point. Now, for the given options we have:
A: √15
B: 2.6457513110...
C: 17.156
D: √3/85
Now, the square root of a number that is no square, is always an irrational number, so we can discard these two, and also we can see that the number in option B has infinite digits after the decimal point, so we also discard that one.
Now, if we look at the remaining option, which is:
17.156
We can multiply it and divide it by 100 to get:
(100/100)*17.156 = 17156/100
So the number can be written as the quotient of two integers, which means that it is a rational number.
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I need help answering this!
Measurement refers to a process through which the dimensions, size (weight), or other physical quantities of magnitude that are associated with an object or land is taken, especially for use in a scientific research and experiment such as direct comparison.
From the odometer on Missy's car, we have the following information:
Initial reading = 23,678 miles.
Final reading = 25,127 miles.
Trip = Final reading - Initial reading
Trip = 25,127 - 23,678
Trip = 1,449 miles.
How to solve Part B?Lubrication mileage = 16,000 kilometers.
Total mileage = 68,000 kilometers.
Lubrication time = Total mileage/Lubrication mileage
Lubrication time = 68,000/16,000
Lubrication time = 4.25 ≈ 4.
Next Lubrication time = (16,000 × 0.25) + 68,000
Next Lubrication time = 16,000 - (16,000 × 0.25) + 68,000
Next Lubrication time = 80,000 kilometers.
How to solve Part B?Rate = $29 per mile
Speed limit = 35 mph
Missy's car speed = 43 mph
Difference = 43 - 35
Difference = 8 mph.
Ticket = 29 × 8
Ticket = $232.
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. The set of possible values of x is {-8, -3, 7}. If
5y = x-2, what is the set of possible values of y?
Answer:
{-2, -1, 1}
Step-by-step explanation:
Since we are given all the possible inputs {-8, -3, 7} we can use them one by one in the equation to find the outputs.
5y = x - 2 , if x is -8
5y = -8 - 2
5y = -10
y = -2
Next,
5y = x - 2, if x = -33
5y = -3 - 2
5y = -5
y = -1
Last,
5y = x - 2 when x =7
5y = 7 - 2
5y = 5
y = 1
So the set is {-2, -1, 1}
please I need to know how to do this !!
[tex]\frac{6xyz}{2xy-y}.\frac{2x^{2}-7x+3 }{3xz - 9z} = 2x[/tex]
How to simplify an expression?The expression can be simplified as follows:
[tex]\frac{6xyz}{2xy-y}.\frac{2x^{2}-7x+3 }{3xz - 9z}[/tex]
Hence,
[tex]\frac{6xyz}{y(2x-1)}.\frac{(x-3)(2x-1)}{3z(x-3)}[/tex]
Therefore.
[tex]\frac{6xyz}{y(2x-1)}.\frac{(2x-1)}{3z}[/tex]
Hence,
[tex]\frac{2xy}{y(2x-1)}.\frac{(2x-1)}1=2x[/tex]
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Saul walks dogs to earn extra money. He
earned $220 last week by walking 16 dogs.
Write and solve an equation to determine
how much he charges to walk each dog
each week.
Answer:
the answer is 13.75
Step-by-step explanation:
So how here is the solutionSaul earned 220 of 16 dogs so
when you divide 220 with 16 the answer be 13.75
[tex]220 \div 16[/tex]
[tex]13.75[/tex]
So let's checkwhen you multiply 13.75 by 16 the answer be 220
[tex]13.75 \times 16 \\ 220[/tex]
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