The required fraction that makes the equation true is 3/15.
What is a fraction?
Fractions represent parts of a whole or group of objects. A fraction is made up of two parts. The number at the top of the line is referred to as the numerator. It specifies the number of equal parts of the whole or collection that are taken. The denominator is the number below the line. It displays the total number of equal parts into which the whole is divided or the total number of identical objects in a collection.
Let x be the required fraction.
Blank divided by 3/7 = 7/15
Then, [tex]\frac{x}{3/7} = \frac{7}{15}[/tex]
or, [tex]\frac{7x}{3} = \frac{7}{15}[/tex]
or, 7x = 21/15
or, x = 3/15
Hence the required fraction that makes the equation true is 3/15.
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Evaluate the verbal expression below where x = 3 and y = 4.
The quantity of 6 less than y, raised to the power of x
A. 8
B. 58
C. -58
D. -8
The evaluated expression the quantity of 6 less than y, raised to the power of x is - 8. Therefore, the correct option is D.
How to evaluate an expression?The quantity of 6 less than y, raised to the power of x can be expressed as follows:
The verbal expression can be converted to a mathematical expression as follows:
(y - 6)ˣ
when
y = 4
x = 3
Therefore,
(y - 6)ˣ = (4 - 6)³
Therefore,
(4 - 6)³ = (-2)³
(-2)³ = -8
Therefore, the evaluated expression is -8.
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Write equation of hyperbola from key features
Check the picture below, so the hyperbola looks more or less like so.
the center of the hyperbola is half-way between the foci, so namely at (-2 , -1) as you see there, since we know the covertices, half that distance is the "b" component, so all we're really missing is the "a" component, but we know what "c", since it's just the distance from a foci to the center, so
[tex]\textit{hyperbolas, horizontal traverse axis } \\\\ \cfrac{(x- h)^2}{ a^2}-\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=-2\\ k=-1\\ b=15 \end{cases}\implies \cfrac{( ~~ x- (-2) ~~ )^2}{ a^2}-\cfrac{( ~~ y- (-1) ~~ )^2}{ 15^2}=1[/tex]
[tex]\stackrel{\textit{we know that}}{c=17}\qquad 17=\sqrt{a^2+15^2}\implies 17^2=a^2+15^2\implies 17^2-15^2=a^2 \\\\\\ \sqrt{17^2-15^2}=a\implies \sqrt{64}=a\implies 8=a \\\\[-0.35em] ~\dotfill\\\\ \cfrac{( ~~ x- (-2) ~~ )^2}{ 8^2}-\cfrac{( ~~ y- (-1) ~~ )^2}{ 15^2}=1\implies {\Large \begin{array}{llll} \cfrac{(x+2)^2}{64}-\cfrac{(y+1)^2}{225}=1 \end{array}}[/tex]
The quadrilateral below, JKLM, is a rhombus.
If MN=15 and JL=24, what is the length of JK ?
Note: Write your answer in simplest radical form. In the first blank put the coefficient in front of the V. And in the second blank, put the coefficient that is inside the v.
"* If there is no coefficient in front of the V, enter a 1 in the blank **
JK=
Maricopa's Success scholarship fund receives a gift of $ 160000. The money is invested in stocks, bonds, and CDs. CDs pay 4 % interest, bonds pay 3.6 % interest, and stocks pay 8 % interest. Maricopa Success invests $ 15000 more in bonds than in CDs. If the annual income from the investments is $ 7520 , how much was invested in each account?
Maricopa Success invested $ ______ in stocks.
Maricopa Success invested $ ______ in bonds.
Maricopa Success invested $ ______ in CDs.
The amount that was invested in each account is:
Maricopa Success invested $47,858 in stocks.
Maricopa Success invested $63,571 in bonds.
Maricopa Success invested $47,571 in CDs.
How to find the amount invested?Let c represent Cds
Let b represent bonds
Let s represent stocks
Equations:
b = c + 15000
s = 160000 - b - c = 160000 - c - 15000 - c = -2c + 145,000
0.08(-2c + 145000) + 0.036(c + 15000) + 0.04c = 7520
-0.16c + 11600 + 0.036c + 540 + 0.04c = 7520
-0.084c = -4,080
Divide both side by -0.084
c = -4,080 / 0.084
c= $48,571 (CDs)
b = 48,571+ 15000
b=$63,571 (bonds)
s = 160,000 - $63,571- 48,571
s= $47,858 (stock)
Therefore Maricopa Success invested $47,858 in stocks,Maricopa Success invested $63,571 in bonds and Maricopa Success invested $47,571 in CDs.
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Need help with this question.
580 lb to kg
(Round to the nearest hundredth as needed)
Answer:
264 kg.
Step-by-step explanation:
To convert from pounds to kilograms, divide the number of pounds by 2.20462. In this case, we have:
580 lb / 2.20462 = 263.74 kg
So, rounded to the nearest hundredth, the answer is 264 kg.
Please help! Need an answer quickly!
The quadratic equation 3 / x - [x / x + 6] = 18 / (x² + 6) have roots at 0 and 3
Quadratic EquationsQuadratics can be defined as a polynomial equation of a second degree, which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations. The general form of the quadratic equation is given as ax² + bx + c = 0
In the given equation, we are to solve for the value of x
3 / x - [x / x + 6] = 18 / (x² + 6)
On the left hand side of the equation, we can find the LCM and simplify
3(x + 6) - x² = 18
3x + 18 - x² = 18
x = 3 or x = 0
The solutions to the equation are 0 and 3
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Use quadratic regression to find a model for the following data set. (Round the terms to four decimal places.) f(x)=___________________________________x 1 3 5 6 8f(x) 2.1 7.4 28.4 34.9 64.4
Use quadratic regression a model for the following data set is [tex]y=1.96 x^2-5.2 x+5.33[/tex].
What is quadratic regression?
A statistical method called quadratic regression is used to identify the parabola equation that best fits a given collection of data. Finding the equation of the straight line that most closely fits a collection of data is the goal of this sort of regression, which is an extension of simple linear regression.
The equation of the parabola that best fits a collection of data is the process of a quadratic regression. As a consequence, we arrive at the equation y=ax2+bx+c where a≠0. The least squares approach is the most effective way to manually locate this equation.
[tex]$$\begin{aligned}& x=1, f(x)=2.1 \\& x=3 \quad f(x)=7.4 \\& x=5 \quad f(x)=20 \cdot 4 \\& y=a x^2+b x+c \\& \text { Print (1) } \\& 2 \cdot 1=a(1)^2+b \times 1+c \\& 2.1=a+b+c \\& \text { Point(2) } \\& 7.4=a(3)^2+b \times 3+c \\& 7.4=9 a+3 b+c \\& \text { Poin (3) } \\& 28.4=a(5)^2+b \times 5+c \\& 28 \cdot 4=25 a+5 b+c \\& \text { by solving (4) (5) (6) } \\& a=1.96 \\& b=-5.2 \\& c=5.33 \\&\end{aligned}$$[/tex]
so, quadratic equation -
[tex]y=1.96 x^2-5.2 x+5.33[/tex]
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can anyone explain these 3 questions to me in detail and how the answer is found
The solution to the first and the second equation are 28.648 and 183.5 respectively.
What is a radical expression?A radical expression is an expression consisting of a square root or nth root.
(1) The given equation is [tex]-5\sqrt[4]{x-1}=12[/tex].
Solve the equation as follows:
[tex]-5\sqrt[4]{x-1}=12\\\\\sqrt[4]{x-1}= -\frac{12}{5}\\\\(x-1) = (-\frac{12}{5})^4\\x-1 = 27.648\\x = 28.648[/tex]
(2) The given equation is [tex]-2\sqrt[6]{4x-5}+9 =3[/tex].
Solve the equation as follows:
[tex]-2\sqrt[6]{4x-5}+9 =3\\ \\2\sqrt[6]{4x-5}= 9-3\\\\\sqrt[6]{4x-5}=3\\\\4x-5=3^6\\\\4x=729+5\\\\x=734/4\\\\x=183.5[/tex]
The third equation is the same as the first equation.
Hence, the solution to the first and the second equation are 28.648 and 183.5 respectively.
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Find the solution to the following system by substitution
y=2 x-1
y=5 x-7
A. (2,3)
B. (6/7), (5/7)
C. (-2,-5)
D. (1,1)
the correct answer is a=(2,3)
Use the Distributive property to solve the equation 2(x-3)+3=6x-5
Answer:
x = -2
Step-by-step explanation:
Isolate the variable by dividing each side b factors that don't contain the variable.
2-[(8×2)+(8×2)]+2=A
The value of A is -28 according to arithmetic
What is BODMAS?
BODMAS is associate descriptor and it stands for Bracket, Order, Division, Multiplication, Addition, and Subtraction. In sure regions, PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction) is employed, that is that the word of BODMAS.
Main body:
According to question:
2-[(8×2)+(8×2)]+2=A
to find: value of A
firstly we need to remove brackets according to rule
⇒2-[(8×2)+(8×2)]+2
⇒2-[16+16]+2
⇒2- 32 +2
⇒-28
hence value of A is -28
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Sammy used his past health history and information about his doctor visits to create this table to compare health costs with and without insurance.
Probability of
Needing the
Service
100%
30%
18%
6%
Description of
Service
annual premium
single doctor visit
two doctor visits
medication
What is the expected value of each option?
Cost with
Insurance Plan
$1,580
$25
$50
$24
The expected value of health care without insurance is $
The expected value of health care with insurance is $
Cost Without
Insurance Plan
$0
$350
$700
$75
Answer:
W/O insurance: 235.50
with insurance: 1597.94
Step-by-step explanation:
Weighted Average:
annual premium 1 $1,580.00 $0
single doctor visit 0.3 $7.50 $105
two doctor visits 0.18 $9.00 $126
medication 0.06 $1.44 $5
$1,597.94 $235.50
"Match the expression and its value to the value of x that gives the expression its value by filling in the box in the correct column.
Evaluate the expression 4 n-5 r for n=-2 and r=3
(A) 23
(C) 7
(B) -7
(D) -23
The surface area for a rectangular prism with a square base is given the expression 2 s²+4 s h, where s is the side length of the square h is the height of the prism. What is the surface area in square feet rectangular prism when s=4 feet and h=6feet?"
Value of the expression 4n - 5r when n = -2 and r = 3 is -23.
The surface area in square feet rectangular prism when s=4 feet and h=6feet is 128 square feet.
What do you mean by algebraic expression?
The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.
Given expression:
4n - 5r
When n = -2 and r = 3
The value of the expression become,
4(-2) - 5(3)
= -8 - 15
= -23
Hence, option D is correct.
Now, it is given that the surface area for a rectangular prism with a square base is given by the expression 2s²+4sh, where s is the side length of the square h is the height of the prism.
The surface area in square feet rectangular prism when s=4 feet and h=6feet is
2[tex](4)^{2}[/tex] + 4(4)(6)
= 2(16) + 96
= 32 + 96
= 128 square feet
therefore, the surface area in square feet rectangular prism when s=4 feet and h=6feet is 128 square feet.
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Liam spent $5.76 on 12 pounds of potatoes. How much did he spend per pound? How to solve this step by step
He spend 0.48 per pounds
What is division ?
Division in mathematics is the process of dividing an amount into equal parts. For instance, we may split a group of 20 people into four groups of 5, five groups of 4, and so on.
One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.
A group is divided into equal portions. Division can be used to divide a class into equal groups for a game or activity, or even to divide a pizza among a group of friends in equal quantities. Partitive division and quotative division are the two types of division.
As it is $5.76 for 12 pounds
∴ for one pound
5.76 / 12
= 0.48 pounds
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I’ll mark you BRAINLIST please help!!
I'm sorry i don't know :(
Services provided by public service companies are also known as
OA. housing expenses
OB. bills
C. cost of living
D. utilities
Services provided by public service companies are also known as utilities.
What are public utilities, housing expenses, cost of living and bills?
The term "public utilities" describes a group of particular services offered by entities and organisations that are both public and private and make up the public services sector.
The sum of a homeowner's monthly mortgage principal and interest payments and any additional costs related to their home constitutes their total housing expense.
The cost of living is the sum of money required in a certain location and time frame to meet necessities including housing, food, taxes, and medical care.
A declaration of money owed for products or services provided is referred to as a bill.
Based on the above definition,
Hence, services provided by public service companies are also known as utilities.
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Two questions show work
1. What is 0.00526 in scientific notation?
2. What is 0.00639 in scientific notation?
1. To convert 0.00526 into scientific notation, follow these steps:
Move the decimal 3 times to right in the number so that the resulting number, m = 5.26, is greater than or equal to 1 but less than 10
Since we moved the decimal to the right the exponent n is negative
n = -3
Write in the scientific notation form, m × 10n
= 5.26 × 10-3
Therefore, the decimal number 0.00526 written in scientific notation is 5.26 × 10-3 and it has 3 significant figures.
2. To convert 0.00639 into scientific notation also known as standard form, follow these steps:
Move the decimal 3 times to right in the number so that the resulting number, m = 6.39, is greater than or equal to 1 but less than 10
Since we moved the decimal to the right the exponent n is negative
n = -3
Write in the scientific notation form, m × 10n
= 6.39 × 10-3
Therefore, 0.00639 in scientific notation is 6.39 × 10-3 and It has 3 significant figures. In scientific e-notation it is written as 6.39e-3.
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Kyle buys last years best selling hardcover for $19.50 . This is with a 25% discount from the original price. What was the original price of the novel ,
Use variable x to set up an equation to solve the given problem. DONT TAKE STEPS TO SOLVE
The answer to your problem is $26
Consider the system of equations
4 x+4 y=-12
3 x-4 y=-23
Part A: Solve the system. Show your work.
Part B: Use the solution to your equation to find the value of x-y. Show your work.
x-y=___
The value of x and y is x = -5 and y = 2
x - y = -7
What is an equation ?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."
The three main types of linear equations are the slope-intercept form, standard form, and point-slope form.
Solving the equation
4x + 4y = -12 ⇒(1)
3x - 4y = -23 ⇒(2)
eq (1)*3 eq (2)*4
12x + 12y = -36 ⇒ (3)
12x - 16y = -92 ⇒ (4)
Solving eq (3) and eq (4)
28 y = 56
y = 2
substituting the value of y in eq (1)
4x + 4(2) = -12
4x + 8 = -12
4x = -12 - 8
4x = -20
x = -5
x - y = -5 -2
= -7
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Which ordered pair is a solution of the inequality?
y ≥ 4x - 5
O (3,0)
O (1, 1)
O (2, 1)
O (3, 4)
Answer:
3_0
Step-by-step explanation:
Drag the equation or type of function to the corresponding graph. Drag the items on the left to the correct location on the right.
Options F and A=[tex]y=\frac{1}{2}^{x}[/tex] match the fourth graph (exponential decay.)
Options G and B=[tex]y=\log_{10}x[/tex] match the second graph (logarithmic growth).
Options E and C=[tex]y=e^{x}[/tex] match the first graph (exponential growth).
Options H and D=[tex]y=\log_{0.5}x[/tex] matches the third graph (logarithmic decay).
What are growth curves?
An illustration of changes in similar circumstances is referred to as a growth curve. It exemplifies how things vary through time, including population, consumer preferences, demand or supply, etc.
What are decay curves?
The decay curve, basically, is a way to depict the rate or specifically exponential rate at which disintegration occurs in a radioactive sample
If we equate the curves and the graphs, we see that both options A and F merge up to the exponential decay model.
Similarly, both options B and G merge up to the logarithmic growth graph model.
Options C and E merge up to the exponential growth model.
Options D and H merge up to the logarithmic decay model.
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What is the left cv and the right cv?
The critical values and shecht the rejection reglues for a theo-tall tent, in a Z procedure with significance level isterse is (-1.812,1.812).
[tex]$\alpha=0.07$[/tex] This is two tailed lest
critical values are [tex]$\pm 1.812$[/tex]
What is critical values ?
A critical value is a value used as a cut-off to indicate the beginning of a zone where the test statistic from a hypothesis test is unlikely to decrease. In hypothesis testing, the crucial value and the resulting test statistic are compared to decide whether or not the null hypothesis has to be rejected.
For hypothesis testing, the crucial value graphically separates the graph into the acceptance region and the rejection zone. A test statistic's statistical significance should be verified. We will learn more about the critical value in this article, including its types, formula, and calculation method.
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Determine the product
(2x+5)(x²-x+2)
Answer:
2x³ + 3x² - x + 10
Step-by-step explanation:
2x³ - 2x² + 4x + 5x² - 5x + 10
2x³ + 3x² - x + 10
For every $45 she earns Emily puts $18 into saving what percent of her pay does she put into her saving?
Using the concept of ratio, the percentage Emily saved is 40%
What is Percentage?Percentage can be defined as a ratio or a number which can be expressed as a fraction of 100. When we need to calculate percent of a number, divide the number by the whole and multiply by 100. The percentage in this can be said to be a part per hundred.
Data;
Total amount earned = 45Amount saved = 18The percentage saved = (amount saved / total amount earned) * 100
Substituting the values into the equation above;
The percentage saved = (18 / 45) * 100
The percentage saved = 0.4 * 100
The percentage saved = 40%
The percentage saved is 40%
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Write an equation for the parabola that:
Has a y-intercept of (0,8), an a value of 6 , and passes through the point (-1,8)
The equation of the required parabola is y = [tex]6x^2+6x+ 8[/tex]
What is a parabola?
Parabola is a curve where all the point on the curve maintains a fixed distance from a point called the focus and a line called the directrix.
Let the equation of the parabola be y = [tex]ax^2+bx+c[/tex]
Here, a = 6
So equation of parabola is y = [tex]6x^2+bx+c[/tex]
The parabola passes through (0, 8) and (-1, 8)
Putting x = 0 and y = 8 in the equation
c = 8
y = [tex]6x^2+bx+8[/tex]
Putting x = -1 and y = 8
[tex]8 = 6(-1)^2 + b(-1) + 8\\ b = 6[/tex]
So equation of the parabola is y = [tex]6x^2+6x+ 8[/tex]
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Imagine that a school recently issued requests that all students change their login passwords to improve security and prevent unauthorized access to student accounts.
One of your friends claims that the best password (from a purely probabilistic perspective) is one that is short but highly complex. They decide to create a randomly generated 7-character password that contains both upper- and lower-case letters (A – Z and a – z) and numbers (0 to 9). What is the probability of guessing their password based on these conditions?
Answer:
The probability of guessing this password is 1 in 62^7, or approximately 1 in 5.4 trillion.
Step-by-step explanation:
Based on the information you provided, your friend's password is a randomly generated 7-character password that contains both upper- and lower-case letters and numbers. This means that the password could be any combination of the 62 possible characters (26 upper-case letters, 26 lower-case letters, and 10 digits).The probability of guessing this password is 1 in 62^7, or approximately 1 in 5.4 trillion. This means that, in theory, it would take someone a very long time to guess your friend's password by randomly trying different combinations of characters.However, it's important to note that there are other factors that can affect the security of a password, such as whether the password is easy to guess or has been used before by the user or someone else. It's generally recommended to use a long, complex password that is unique and not easily guessable to maximize security.
Answer: 1/(3,521,614,606,208)
Explanation:
There are 26 letters in the English alphabet. This doubles to 52 when considering upper and lowercase letters. Then add on 10 more because of the digits 0 through 9.
In total, there are 2*26+10 = 52+10 = 62 different characters to pick from for any given slot of the 7-character password.
Assuming repeated characters are allowed, this then gives us
62^7 = 3,521,614,606,208
different passwords possible. This massive number is a little over 3.5 trillion. In scientific notation, it is approximately equal to 3.522 * 10^12
The probability of randomly guessing the correct password is 1 over that massive number, since there's only one way to get the correct password. We get the fraction 1/(3,521,614,606,208)
We can say the odds of guessing the correct password are roughly 1 in 3.5 trillion.
If A = {3, 5, 7, 8, 9, 10} and B= {1,4,7,9,11,12}
Find
a) ANB=
b) AUB=
Answer:
pls mark as brainliest
Step-by-step explanation:
If A = {3, 5, 7, 8, 9, 10} and B= {1,4,7,9,11,12}
a) ANB= { 7 , 9 }
b.)AUB= { 1 , 3 , 4 , 5 , 7 , 8 , 9 , 10 , 11 , 12 }
Write and graph the inverse of y=-x²+9
Write the inverse of y=-x²+9
y=
(Simplify your answer. Use a comma to separate answers as needed.)
The inverse of y=-x²+9 is [tex]x=\sqrt{9-y}[/tex]
What is Inverse of a Function ?
A function takes in values, applies specific operations to them, and produces an output. The inverse function acts, agrees with the outcome, and returns to the initial function.
The output of a function is returned by the inverse function, which also returns the initial value.
If f and g are inverse functions, then f(g(x)) = g(f(x)) = x. The initial value is fetched via a function that is its inverse.
For instance, f(x) = 2x + 5 = y
Therefore, the inverse of f is g(y) = (y-5)/2 = x. (x).
The relationship that results from swapping out an independent variable with a variable that depends on a given equation; the inverse may or may not be a function.
A function is said to be an inverse function if its own inverse is represented by the symbol f-1.
[tex]x^2=9-y\\\\\x=(9-y)^\frac{1}{2}\\\\ x=\sqrt{9-y}[/tex] is the inverse of y=-x²+9
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Use the number line to explain why 2 is 10 times the value of 2.0
on the number line, 2.0 is to the right of 2, and multiplying 2.0 by 10 moves it 10 times as far to the right as 2.0 is from 2. This is why 2 is 10 times the value of 2.0.
What is the number line?
The number line is a visual representation of the set of all real numbers, which are the numbers that can represent any value on the continuous number scale, including fractions and decimals. On the number line, each point corresponds to a specific real number.
The number 2 is represented by a point on the number line, as is the number 2.0. These two numbers are different because 2.0 is a decimal number, while 2 is a whole number.
2 is 10 times the value of 2.0 if you multiply 2.0 by 10. This is because multiplying a number by 10 shifts its decimal point one place to the left, which increases its value by a factor of 10. For example, if you multiply 2.0 by 10, you get 20.0, which is 10 times the value of 2.0.
Hence, on the number line, 2.0 is to the right of 2, and multiplying 2.0 by 10 moves it 10 times as far to the right as 2.0 is from 2. This is why 2 is 10 times the value of 2.0.
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Justyne is valued by her organization as a high-utility employee who can answer the phones, greet customers, handle billing questions, operate the manufacturing equipment, and be a quality checker. Because she is competent in so many areas, Justyne is frequently moved around the company to wherever she is needed that day. It is likely that Justyne has high emotional stability. generalized self-efficacy. self-esteem.
Justyne is frequently moved around the company to wherever she is needed as it is likely that she has high generalised self-efficacy.
Justyne is valued by her organization as a high-utility employee who can answer the phones, greet customers, handle billing questions, operate the manufacturing equipment, and be a quality checker. This proves her capacity that she can act in the ways necessary to reach specific goals that she is meant to achieve.
As she is competent in so many areas, she is frequently moved around the company wherever needed.
Hence, it is likely that Justyne has high generalized self-efficacy.
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