Answer:By adding a constant value to every salary amount, the measures of
central tendency are increased by the amount, while the measures of
dispersion, remains the same
The correct responses are;
(a) The shape of the data remains the same
(b) The mean and median are increased by $1,000
(c) The standard deviation and interquartile range remain the same
Reasons:
The given parameters are;
Present teachers salary = Between $38,000 and $70,000
Amount of raise given to every teacher = $1,000
Required:
Effect of the raise on the following characteristics of the data
(a) Effect on the shape of distribution
The outline shape of the distribution will the same but higher by $1,000
(b) The mean of the data is given as follows;
Therefore, following an increase of $1,000, we have;
Therefore, the new mean, is equal to the initial mean increased by 1,000
Median;
Given that all salaries, , are increased by $1,000, the median salary, , is also increased by $1,000
Therefore;
The correct response is that the median is increased by $1,000
(c) The standard deviation, σ, is given by ;
Where;
n = The number of teaches;
Given that, we have both a salary, , and the mean, , increased by $1,000, we can write;
Therefore;
; The standard deviation stays the same
Interquartile range;
The interquartile range, IQR = Q₃ - Q₁
New interquartile range, IQR = (Q₃ + 1000) - (Q₁ + 1000) = Q₃ - Q₁ = IQR
Therefore;
The interquartile range stays the same
Step-by-step explanation:
Find the point t=4pi/3
The point t on the unit circle is ( -1/2, √3 /2 ).
The intersection of the x-axis (the horizontal number line) and the y-axis in the cartesian system divides the coordinate plane into four equal pieces. Because each of these four areas occupies a quarter of the entire coordinate plane, they are collectively referred to as quadrants.
Consider the point t = - 4π/3 on the circle.
Now, the reference angle is π / 3.
- 4π / 3 is in quadrant 2 where the value of cosine is negative and sine is positive.
Therefore, the point t(x,y) will be:
( x, y ) = ( - cos ( π / 3 ), sin ( π / 3 ) )
( x, y ) = ( - 1/ 2 , (√3 )/ 2 )
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Which table best shows the average speed of the toy car at different time intervals?
Answer:
Table A
Step-by-step explanation:
Note that the curve flattens out between 4 and 6 s
So the average speed is 0( the train is standing still) in the time interval 4-6 s
From the tables we can see that (A) and (D) are the only two tables that have average speed of 0 for 4-6 second interval. So let's eliminate the other two(B and C) and focus on these two
Looking at tables A and D we can see that the average speed in the 0-2 interval is 1.0 for both
So let's focus on the only entry where the tables show different values ie the interval 2-4 = 2s)
Looking at the graph we can see that in the interval 2-4, the train travels from distance of 2m to distance of 3m. In other words it covers a distance of 1 meter ( 3 - 2 ) in 2 seconds
Therefore average speed at this time interval = 1m/2sec = 0.5 m/s
So table A shows the correct average speed
Subtract.
(2x² + 5) - ( − 3x² + 5)
Answer:
Step-by-step explanation:
1) distribute the signs to the brackets
2x^2 + 5 + 3x^2 - 5
2) solve
5x^2 + 0
Hopefully, it's correct and helpful
5 + 2[(4 + 2)^2 – (3^3 + 2)]
Answer:
19
Step-by-step explanation:
PEMDAS is your bff here:
5 + 2[(4 + 2)^2 – (3^3 + 2)]
Do the parenthesis first (yes i do solve for 3^3 and add the 2 to it, it makes it quicker)
5 + 2[(6)^2 - 29)]
now do exponents
5 + 2 (36 - 29)
subtraction
5 + 2(7)
multiple cation
5 + 14
And add those together to get 19
I need to know how how to do these please.
The scatter plot shows negative correlation because as the plotted values of x increase, the values of y generally decrease.
What is negative correlation?When two variables are said to have negative correlation, it means that they move in the opposite direction from each other. When one variable is increasing, the other variable is decreasing.
The values of x and y in order of x are:
x 3 4 5 6 7 8 9
y 6 7 5 4 3 4 2
As shown above, when x increases, y generally decreases and when x decreases, y generally increases. This is therefore a negative correlation relationship.
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What is 48,100,000,000,000 in scientific notation? 4.81 x 10^-11, 4.81 x 10^-13, 4.81 x 10¹¹, 4.81 x 10¹³
Check the picture below.
dose the base have to be flat when finding base x height?
for finding the parallegram for height dose the height have to touch and make a 90 degree angle?
(Cosec a -cot a)^2=1-cos\1+cos
Answer:
Step-by-step explanation:
[tex]\displaystyle\\(cosec \alpha -cot\alpha )^2=\\\\(\frac{1}{sin\alpha } -\frac{cos\alpha }{sin\alpha })^2 =\\\\(\frac{1-cos\alpha }{sin\alpha } )^2=\\\\\frac{(1-cos\alpha)^2 }{sin^2\alpha }=\\\\ \frac{(1-cos\alpha )^2}{1-cos^2\alpha } =\\\\\frac{(1-cos\alpha )^2}{(1+cos\alpha )(1-cos\alpha )} =\\\\\frac{1-cos\alpha }{1+cos\alpha }[/tex]
NEED SOLUTION
Give the quotient of the following:
Need solution
1.168 ÷ 8
2.246÷12
3.4328÷4
4.729÷9
5.8415÷5
Answer
1.168 ÷ 8= 0.146
2.246÷12= 0.1871
3.4328÷4=0.8582
4.729÷9=0.5254
5.8415÷5=1.168
Step-by-step explanation:
Choose the equation that represents the graph below (1point) graph of a line passing threw points negative 2 comma 0 and 0 comma negative 4 y =-2x- 4y=2x+4y=-2x+4y=2x-4
The equation of line is,
⇒ y = -2x - 4
What is equation of line?
The equation of line with slope m is given by;
⇒ y = mx + b
Now, The points are;
(-2, 0) and (0, -4)
Hence, slope = (-4 - 0) / (0 - (-2) = -4 / 2 = -2
Since, Equation of line with slope (m) is;
y = mx + b
Here, Slope (m) = -2
To find the value of b we use either of the points;
Take point (0,-4)
x = 0 and y = -4
We get after substitute;
-4 = -2(0) + b
-4 = b
Hence, The equation of line is,
⇒ y = -2x - 4
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Jeremiah finished 3/4 of his timed math quiz. Of those he attempted, he correctly answered 5/9
The fractional part of the quiz that he get correct will be 5/12.
How to calculate the value?From the information, Jeremiah finished 3/4 of his timed math quiz. Of those he attempted, he correctly answered 5/9.
The fractional part of the quiz that he get correct will be
= 3/4 × 5/9
= 5/12
Therefore, the fractional part of the quiz that he get correct will be 5/12.
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Jeremiah finished 3/4 of his timed math quiz. Of those he attempted, he correctly answered 5/9. What fractional part of the quiz did he get correct?
PLEASE HELP ILL GIVE BRAINELST
Answer:
1) 8
2) 3
3) 4
4) 5
5) 6
6) 2
7) 1
8) 18
Step-by-step explanation:
whenever you see a letter, just change that letter with whatever the guide says, for example, 6+c would be 6+2, which is 8. Another example is ab, which would be 6 times 3 because a is 6 and b is three
Lucretia who works part time as a substance abuse counselor ,earns $18.15 per hour and works 20 hours per week. she is single and claims one withholding allowance. she lives in a state with no income tax
Answer:
$363
Step-by-step explanation:
i mean with what your given it 18.15 x 20 x could be . for others
Frances left a 22% tip on a meal. Including the tip, its cost was 21.96 what was the cost of the meal before the tip
Hence we would conclude that If Frances left the tip of 22 percent on a meal, the cost of the meal before the tip would be 18 dollars.
How to solve for the cost of the tipLet us define x to be the cost of the meal
such that we would have
x + 22%x = 21.96
= x + 0.22x = 21.96
1.22x = 21.96
We would have to divide through the equation that we have by 1.22
x = 21.96 / 1.22
x = 18
X is the cost for the meal that that Frances ate before she gave the tip that she did to the waiter.
Hence we would conclude that If Frances left the tip of 22 percent on a meal, the cost of the meal before the tip would be 18 dollars.
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Zendaya has $540 to spend at a bicycle store for some new gear
and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $269.88.
She buys 4 bicycle reflectors for $10.57 each and a pair of a
bike gloves for $17.76.
She plans to spend some or all of the money she has left to
buy new biking outfits for $65.65 each.
Write and solve an inequality which can be used to determine
x, the number of outfits Zendaya can purchase while staying
within her budget.
The inequality that can be used to determine x, the number of outfits Zendaya can purchase is 329.92 + 65.65x <= 540
How to write and solve an inequality which can be used to determine x, the number of outfits Zendaya can purchase while staying within her budget?The given parameters are:
Budget = $540
New bicycle = $269.88.
4 bicycle reflectors = $10.57 each
Pair of a bike gloves = $17.76.
New biking outfits = $65.65 each.
Let the number of new biking outfits be x
So, we have
New bicycle + 4 * price of bicycle reflectors + Pair of a bike gloves + New biking outfits <= Budget
This gives
269.88 + 4 * 10.57+ 17.76 + 65.65x <= 540
This gives
329.92 + 65.65x <= 540
Solve the inequality
65.65x <= 210.08
Divide by 65.65
x <= 3.2
Hence, the inequality that can be used to determine x, the number of outfits Zendaya can purchase is 329.92 + 65.65x <= 540
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y = -2x - 4
y= 3x + 1
What is the solution to the system of equations?
Answer:
x = -1
y = -2
Step-by-step explanation:
We are given the following equations:
[tex]y = -2x - 4[/tex]
[tex]y = 3x + 1[/tex]
As we can see, the expressions [tex]{-2x - 4}[/tex] and [tex]3x + 1[/tex] are both equal to [tex]y[/tex]. Therefore, we can equate them:
[tex]-2x - 4 = 3x + 1[/tex]
Now we can solve for [tex]x[/tex] by making [tex]x[/tex] the subject of the equation:
⇒ [tex]-2x - 4 -3x = 3x + 1 - 3x[/tex] [Subtracting [tex]3x[/tex] from both sides]
⇒ [tex]-5x - 4 = 1[/tex]
⇒ [tex]-5x - 4 + 4 = 1 + 4[/tex] [Adding 4 to both sides of equation]
⇒ [tex]-5x = 5[/tex]
⇒ [tex]\frac{-5}{-5}x = \frac{5}{-5}[/tex] [Dividing both sides by -5]
⇒ [tex]x = \bf -1[/tex]
Now that we know the value of [tex]x[/tex], we can calculate the value of [tex]y[/tex] by replacing the [tex]x[/tex] with -1 in any of the equations for [tex]y[/tex] given above:
[tex]y = 3x + 1[/tex]
⇒ [tex]y = 3(-1) + 1[/tex]
⇒ [tex]y = -3 + 1[/tex]
⇒ [tex]y = \bf -2[/tex]
Therefore, the solution to the system of equations is : x = -1, y = -2.
Answer:
x = -1
y = -2
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}y = -2x - 4\\y= 3x + 1\end{cases}[/tex]
Use the method of substitution to solve for x:
[tex]\begin{aligned}& \textsf{Substitute}: & 3x+1 & = -2x-4\\& \textsf{Add $2x$ to both sides}: & 3x+1+2x & = -2x-4+2x\\& \textsf{Combine like terms}: & 5x+1 & = -4\\& \textsf{Subtract $1$ from both sides}: & 5x+1 -1& = -4-1\\& \textsf{Simplify}: & 5x & = -5\\& \textsf{Divide both sides by $5$}: & \dfrac{5x}{5} & = \dfrac{-5}{5}\\& \textsf{Simplify}: & x & = -1\end{aligned}[/tex]
Substitute the found value of x into one of the equations and solve for y:
[tex]\begin{aligned}& \textsf{Equation}: & y& = 3x+1\\& \textsf{Substitute in $x=-1$}: & y & = 3(-1)+1\\& \textsf{Multiply the numbers}: \quad & y & = -3+1\\& \textsf{Simplify}: & y & = -2\\\end{aligned}[/tex]
Therefore, the solution to the given systems of equations is (-1, -2).
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Katya is making rectangular table that is
3/4.The table has an area of
1 1/5 m2.How long is the table?
Answer:
which step by step
rectangular table
Calculate the required rate of return for Mercury Inc., assuming that investors expect a 5% rate of inflation in the future. The real risk-free rate is equal to 3% and the market risk premium is 5%. Mercury has a beta of 2.0, and its realized rate of return has averaged 15% per year over the last 5 years.
The required rate of return for Mercury Inc., assuming that investors expect a 5% rate of inflation in the future is 18%.
How to calculate the rate if return?Real risk free rate = 3%
Inflation Premium = 5%
Nominal risk free rate Rf = Real risk free rate + Inflation Premium = 3% + 5% = 8%
Market risk premium (Rm –Rf) = 5%
Beta = 2
As per CAPM, required rate of return:
= Rf + beta * (Rm – Rf)
= 8% + 2 * 5%
= 8% + 10%
= 18%
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help me please please please!!!!
Which graph represents the inequality 0.5 is greater than the product of −2.5 and a number?
number line with open circle on point 0.2 and arrow shaded to the left
number line with open circle on point negative 5 and arrow shaded to the left
number line with open circle on point negative 0.2 and arrow shaded to the right
number line with open circle on point negative 5 and arrow shaded to the right
The correct graph representation of the given inequality is,
⇒ Number line with open circle on point negative 0.2 and arrow shaded to the right.
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
The written expression is given as,
0.5 is greater than the product of −2.5 and a number.
Let a number is x.
Then, The given expression is written as;
0.5 > -2.5x
Now, We can solve as;
0.5 > -2.5x
Multiply by -1 we get;
- 0.5 < 2.5x
-0.2 < x
Hence, The graph of inequality is;
⇒ Number line with Open circle on point negative 0.2 and arrow shaded to the right.
So, The correct graph representation of the given inequality is,
⇒ Number line with open circle on point negative 0.2 and arrow shaded to the right.
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Answer:
A
Step-by-step explanation:
Question 3(Multiple Choice Worth 2 points)
(Solving Equations Using Square and Cube Roots LC)
Solve y³ = -8.
Pre-algebra 8th grade pls help thx!!
The cubic equation y³ = -8 has the value of y = -2 which is first option.
The cubic equation given to us is y³ = -8
We can shift the power from left hand side to right hand side but the cubic power would turn cube root of -8
We know that square root of any negative number is not a real number but in case of Cube roots , This is possible and the root with negative sign and simple root
Also, when we square root any number we add ± sign but in case of cube root we only add the sign of number whose cube root is taken
y³ = -8
y = ∛-8
y = ∛(-2)(-2)(-2)
y = ∛(-2)³
y = -2
So, The cubic equation y³ = -8 has the value of y = -2 which is first option.
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On April 1, Mr. Olson’s meter read 7,329 kw-hr. On may 1, the meter read 8,284 kw-hr. At $.08 per kw-hr, what was his electric bill for the month of April?
His electric bill for the month of April is $76.4
How to determine his electric bill for the month of April?The given parameters are
April 1 = 7,329 kw-hr.
May 1 = 8,284 kw-hr
Rate = $.08 per kw-hr
His electric bill for the month of April is calculated as
Bill = (May 1 - April 1) * Rate
So, we have
Bill = (8,284 - 7,329) * .08
Evaluate
Bill = 76.4
Hence, his electric bill for the month of April is $76.4
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What is the arena of the circle for model 3
The area of the circle is approximately 78.5 square meters
What are areas?The area of a shape is the amount of space on the shape
How to determine the area of the circle?The given parameters are:
Radius = 5
The area of a circle is calculated using
A = pi r^2
In this case
pi = 3.14
So, we have:
A = 3.14 * 5^2
Evaluate the product
A = 78.5
Hence, the area of the circle is approximately 78.5 square meters
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Possible question
What is the area of a circle for model 3 where the radius is 5 meters.
Use pi approx3.14 . The area of the circle is approximately square meters
Enter only the number.
Help solve the perimeter of this shape.
The perimeter CDE of the triangle is solved to be 9.66 (to the nearest hundredth)
How to find the perimeter of CDE
Given data
C ( 4, -1 )
D ( 4, -5)
E ( 2, -3 )
perimeter of CDE = CD + CE + DE
length = √(x2 - x1)^2 + (y2 - y1)^2
using C ( 4, -1 ) and D ( 2, -3 )
CD = √(4 - 4)^2 + (-1+5)^2
CD = √(4)^2
CD = 4
using C ( 4, -1 ) and E ( 2, -3 )
CE = √(4 - 2)^2 + (-1+3)^2
CE = √(2)^2 + (2)^2
CE = √8
using D ( 4, -5) and E ( 2, -3 )
CD = √(4 - 2)^2 + (-5 + 3)^2
CD = √(2)^2 + (-2)^2
CD = √8
the perimeter = 4 + √8 + √8
the perimeter = 4 + √8 + √8
the perimeter = 9.6568
the perimeter = 9.66 (to the nearest hundredth)
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How many natural numbers below 2021 have exactly 15 positive integer factors
Answer:
ITO PO ANSWER:PA BRAINLEST NALANG PO HEHE
factor 3a^2b^2+15ab^3 please show work
Answer:
3ab²(a + 5b)
Step-by-step explanation:
3a²b² + 15ab³ ← factor out 3ab² from each term )
= 3ab²(a + 5b)
PLEASE PLEASE HELP ME!!
which one do you need answered look it up
is making a Rice Krispie cakes.
Timothy
A recipe uses 240g of chocolate and 160g of Rice Krispies to make 24 cakes.
(a) Write down the ratio of chocolate to Rice Krispies in its simplest form.
(b) How much Rice Krispies should Timothy use to make 30 cakes?
Sarah is making shortbread biscuits.
Answers to both the subparts are as follows:
(A) Ratio of chocolate to Rice Krispies in its simplest form: 3:2(B) Rice Krispies Timothy should use to make 30 cakes: 200gWhat are ratios?A ratio in mathematics indicates how many times one number contains another. For example, if a bowl of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six. Similarly, the lemon to orange ratio is 6:8, and the orange to total fruit ratio is 8:14. Ratios are used to compare two numbers by dividing them. If you want to compare one data point (A) to another (B), your formula would be A/B. This means that you are dividing data A by data B. If A is five and B is ten, your ratio will be 5/10.So, (A) ratio of chocolate to Rice Krispies:
240g : 160g240/160 ⇒ 24/16 ⇒12/8 ⇒ 6/4 ⇒ 3/23 : 2Now, (B) Rice Krispies should Timothy use to make 30 cakes:
Rice Krispies used in 24 cakes: 160g
Then, Rice Krispies used on 1 cake:
160/24 ⇒ 80/12 ⇒ 40/6 ⇒ 20/3 ⇒ 6.67So, Rice Krispies used in 30 cakes:
6.67 × 30 = 200gTherefore, answers to both the subparts are as follows:
(A) Ratio of chocolate to Rice Krispies in its simplest form: 3:2(B) Rice Krispies Timothy should use to make 30 cakes: 200gKnow more about ratios here:
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Select all the correct answers.
Consider the circle represented by this equation.
X^2+4x+y^2-2y-4=0
Which features are features of the circle?
center at (-2, 1)
radius of 1
radius of 3
radius of 9
center at (2,-1)
center at (-4, 2)
Answer ASPA
Based on the calculations, the features which are features of the circle include the following:
center at (-2, 1).radius of 9.What is a circle?A circle can be defined as a closed, two-dimensional curved geometric shape with no edges or corners. Also, a circle refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).
The equation of a circle.Mathematically, the standard form of the equation of a circle is given by;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center.r represents the radius of a circle.Given the following equation:
x² + 4x + y² - 2y - 4 = 0
x² + 4x + y² - 2y = 4
Next, we would evaluate the equation by using completing the square method:
x² + 4x + 4 + y² - 2y + 1 = 4 + 5
(x² + 2x + 2x + 4) + (y² - y - y + 1) = 9
(x + 2)² + (y - 1)² = 3²
By comparing the above equation with the standard form of the equation of a circle, we have:
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Simplify a raised to the negative two power over quantity 3 times b raised to the fourth power end quantity all cubed.
A: 1 over quantity 9 times a raised to the sixth power times b raised to the twelfth power end quantity
B: 1 over quantity 27 times a raised to the sixth power times b raised to the twelfth power end quantity
C: 27b12a6
D: quantity 27 times b raised to the twelfth power end quantity over a raised to the sixth power
The solution to simplifying the given expression using laws of exponents is; B: 1 over quantity 27 times a raised to the sixth power times b raised to the twelfth power end quantity
How to use laws of exponents?
Some of the Laws of Exponents are;
When multiplying similar bases, retain the base as same and add the exponents. When raising a base with a power raised to another one, retain the base the same and multiply the exponents. When dividing like bases, keep the base the same and subtract the denominator exponent from the numerator exponent.We want to simplify a raised to the negative two power over quantity 3 times b raised to the fourth power end quantity all cubed. This is expressed as;
(a⁻²/3b⁴)³
Using the second law of exponent quoted above, we have;
(a⁻²*³)/(3³b⁴*³) = a⁻⁶/27b¹² = 1/a⁶27b¹²
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