Answer: Option C
A data set with less variation will have a smaller __ interquartile range__.
Step-by-step explanation:
The datasets that have less variation are those that have smaller dispersion or variation measures.
Some of these measures of variance are variance, standard deviation, mean absolute deviation, range and interquartile range. Among the options shown, the only one that is used as a measure of variation is the interquartile range. The interquartile range is the difference between the third quartile and the first quartile of a data distribution. In other words, the interquartile range measures the range between the central 50% of the data.
Then the answer is the option C
Write the equation of the line shown in the graph. Please help.
On this line, for all y-values, the x-value will always be -3.
Since it is a vertical line it has no run, only a rise. This makes the slope undefined.
This said, the equation for this line is x = -3
Hope this helped!
~Just a girl in love with Shawn Mendes
What is the value of k?
Answer:
i thought its -9
Step-by-step explanation:
x / x-2=x-k / x-4x /x=x-k/x-4+2cut x/x of first side
k=x/x-6now cut x/x
k=-63=-6-6-3-9find the radius of a circle with a diameter of 40 in
Answer:
20 in
Step-by-step explanation:
The radius is half the diameter.
You are given the diamter is 40 in.
So the radius is half of 40 in.
Half of 40 in means what is 40 in divided by 2.
Half of 40 in or 40 in ÷ 2 is 20 in.
The radius is 20 in.
Answer: 20 inches
Step-by-step explanation: A radius is half of the circle, and a diameter is a whole circle. 2 radius are equal to one diameter. So divide the diameter by 2 to get the radius.
40/2 = 20
The radius of the circle is 20 inches.
Which function describes this graph?
—
10
А. y = (х – 4 )(х - 4)
В. у = х2 - 2x +6
оооо
ос. у = х2 + 8х +12
D. у = (х-2)(х – 6).
Answer:
C. y = x2 + 8x + 12
Step-by-step explanation:
To find x intercept/zero, substitute y = 0
0 = x^2 + 8x + 12
x^2 += 8x + 12 = 0
x^2 + 8x + 12 = 0
Solve the quadratic equation
ax^2 + bx + c = 0 using x = -b±[tex]\sqrt{b^2 -4ac[/tex] / 2ax = -8±[tex]\sqrt{8^2 -4(1)(12)[/tex] / 2(1)x = -8±[tex]\sqrt{8^2 -4(12)[/tex] / 2(1)
any expression multiplied by 1 remains the same
x= -8±[tex]\sqrt{8^2 - 4(12)[/tex] / 2(1)
Evaluate the power
8^2
write the exponentiation as a multiplication
8(8)
multiply the numbers
64
x = -8±[tex]\sqrt{64 - 4(12)[/tex] / 2(1)
multiply the numbers
x = -8±[tex]\sqrt{64 - 48[/tex] / 2(1)
any expression multiplied by q remains the same
x = -8±[tex]\sqrt{64-48[/tex] /2
subtract the numbers
x = -8±[tex]\sqrt{16[/tex] / 2
calculate the square root
x= -8± 4 / 2
x= -8 + 4 / 2
x= -8 - 4 / 2
simplify the expression
x = -2
x = -8 - 4 / 2
x = -2
x = -6
final solutions are
x1 = -6, x 2 = -2
Which power raised to a power expression are equivalent to 8 to the power of 12? Check all that apply
Answer:
[tex]\tt{(8^{-3})}^{-4}; \ \ \ {(8^{1})}^{12}; \ \ \ {(8^{6})}^{2}[/tex]
Step-by-step explanation:
[tex]\boxed{\tt {(a^m)}^n=a^{m\cdot n}}\\\\\\ \tt{(8^{-3})}^{-4}=8^{-3\cdot(-4)}=8^{12}\\\\{(8^{1})}^{12}=8^{1\cdot12}=8^{12}\\\\{(8^{6})}^{2}=8^{6\cdot2}=8^{12}\\\\[/tex]
Answer:A,D,F
Step-by-step explanation:
7 days left until the launch of our new product and we have $668.00 left in our promotion budget we need to spend 85.00 on the last day how many dollars can we spend on the remaining days
Answer:
$97.16 per day
Step-by-step explanation:
Total amount you have = $668.00
You have to spent $85.00 on the last day.
$668.00-85.00
=$583
It means you have $583 for the remaining 6 days in the week.
If you spend equal amount of money each day , you can calculate it by dividing remaining amount and number of days
=583/6
=$97.16
It means you can spend $97.16 per day....
what is the range of y=log_8 x
The answer is:
Range: All the real numbers or (-∞,+∞)
Why?To solve the problem, we need to rewrite the variable "x" as "y" and the variable "y" as "x", and then, isolate "y". Then, we need to look if there is any restriction to the resulting value of "y".
We are given the function:
[tex]y=log_8(x)[/tex]
Now, rewriting we have:
[tex]x=log_8(y)[/tex]
Then, isolating we have:
[tex]8^{x} =8^{(log_8(y))}\\\\8^{x}=y[/tex]
Therefore, we can see that the resultant function is a quadratic or polynomial function, we need to remember that there is no restriction for this type of functions, it means that the range of the function is equal to the Real numbers where the values of "x" exist.
Hence, the answer is:
Range: All the real numbers or (-∞,+∞)
Have a nice day!
Note: I have attached a picture for better understanding.
A Large school wants to put a clock in each of its 224 classrooms
The clocks are sold in packs of 14.
How many packs of clocks should the school buy?
Answer:
16 packs
Step-by-step explanation:
u just have to divide 224 by 14 to get 16
the school wants to get 224 clocks, they clocks come in packs of 14, so each pack has 14 clocks, how many packs are needed?
well, how many times does 14 go into 224? 224 ÷ 14, and you know what that is.
Dimensions for an office floor plan is 15ft. By 15ft and 28ft. By 28ft. Tile runs $1 per square foot and carpeting $5 per square foot. What is the estimated total cost for the floor coverings installed
Answer:
$2520
Step-by-step explanation:
Taking the dimensions of the office floor from the plan to be;
[tex]15ft*28ft[/tex]
Area of the floor to be covered will be the product of the sides dimensions
[tex]=15*28=420ft^{2}[/tex]
Cost of putting tile on the floor
1ft²=$1
420ft²=?
=[tex]\frac{420*1}{1} =420[/tex]
=$420
Cost of putting a carpet on the floor
1ft²=$5
420ft²=?
[tex]=\frac{420*5}{1} =2100[/tex]
=$2100
Estimated cost
Total estimated cost =cost for putting tiles+cost for putting carpet
=$420+$2100=$2520
What does it mean to simplify?
Answer:
To make something as small as possible or easier for something in particular.
Hope I helped!
Two consecutive positive integers have a
product of 6. What are the integer?
Answer:
They are 2 and 3.
Step-by-step explanation:
2 * 3 = 6
Samir is trying to decide between two checking account plans. After researching plans at two banks, he finds that Unity Bank offers a monthly compounded interest rate of 0.14%, while Sunrise Banking offers 1.6% interest compounded annually. Which is the better plan? Explain.
(SHOW WORK)
Answer:
The monthly compounded interest rate of 0.14% of Unity Bank is a better plan.
Step-by-step explanation:
Step 1 : Write the formula for calculating a monthly compound interest rate and for calculating an annually compounded interest rate.
Monthly compound interest rate = P(1+r/n)^nxt
n=12 (number of months in a year)
t=1 (number of years)
Annually compound interest rate = P(1+r/n)^nxt
n=1 (because it is for 1 year only)
t=1 (number of years=1)
Step 2 : Lets assume that P is $100 in both banks and time is 1 year.
Step 3 : Lets substitute the values to find out which one is better.
Monthly compound interest rate = P(1+r/n)^nxt
Monthly compound interest rate = 100(1+0.14/12)^12x1
Monthly compound interest rate = 114.93
114.93 - 100 = $14.93 per month
14.93 x 12 = $179.16 for 12 months or 1 year
Annually compound interest rate = P(1+r/n)^nxt
Annually compound interest rate = 100(1+1.6/1)^1x1
Annually compound interest rate = 260
260-100 = $160 for 1 year
Therefore, the monthly compounded interest rate of 0.14% of Unity Bank is a better plan.
!!
Answer:
The Unity Bank is offering a good plan.
Step-by-step explanation:
Unity Bank offers a monthly compounded interest rate of 0.14%
So, yearly rate will be = [tex]0.14\times12=1.68[/tex]% or 0.0168
Sunrise Banking offers 1.6% or 0.016 interest compounded annually.
Lets check an example with these two rates.
The compound interest formula is = [tex]A=P(1+r/n)^{nt}[/tex]
Lets take P = $1000 and t = 1 year
Case 1: when r = 1.68% and n = 12
Putting the values in formula we get
A = [tex]1000(1+0.0168/12)^{12}[/tex]
= [tex]1000(1.0014)^{12}[/tex]
A = $1016.92
Case 2: when r = 1.6% and n = 1
Putting the values in formula we get
A = [tex]1000(1+0.016/1)^{1}[/tex]
= [tex]1000(1.016)^{1}[/tex]
A = $1016.00
So, we can see that the first case gives more return than second one.
Therefore, the Unity Bank is offering a good plan.
14. Solve this system of equations:
4x + 2y = 22
3x – 2y = 13
Answer:
(x,y)= (5,1)
Step-by-step explanation:
4x+2y=22
3x-2y=13
2y=22-4x
3x-2y=13
3x-(22-4x)=13
x=5
3·5-2y=13
y=1
(x,y)= (5,1)
Answer:
(5, 1); x = 5 and y = 1.
Step-by-step explanation:
Step 1: Add the system of equations
4x + 2y = 22
3x - 2y = 13
-----------------------------
7x = 35
Step 2: Solve for x
x = 5
Step 3: Substitute the value of x in one of the original equations
4(5) + 2y = 22
Step 4: Solve for y
20 + 2y = 22
2y = 2
y = 1
Step 5: Write your answer as an ordered pair
(5, 1)
A classroom floor has an area of
(30x3 + 8x2) ft, with a width of 2x feet.
What is the length of the floor?
Answer:
The length of the floor is [tex](15x^{2}+4x)\ ft[/tex]
Step-by-step explanation:
we know that
The area of a rectangle ( classroom floor) is equal to
[tex]A=LW[/tex]
in this problem we have
[tex]A=(30x^{3}+8x^{2})\ ft^{2}[/tex]
[tex]W=2x\ ft[/tex]
substitute in the formula and solve for L
[tex](30x^{3}+8x^{2})=2x(L)[/tex]
Divide by 2x both sides
[tex]L=(15x^{2}+4x)\ ft[/tex]
In the number 2010, the value represented by the digit 1 is what fraction of the value represented by the digit 2?
Answer:
Step-by-step explanation:
The two represents 2000
The one represents 10
The fraction you want is 10/2000 = 1/200 or 0.005
The value represented by the digit 1 in the number 2010 is 1/200 of the value represented by the digit 2. This is determined by comparing their place values, with 1 in the tens place and 2 in the thousands place.
To determine the value represented by the digit 1 in the number 2010, we need to understand place value.
→ The digit 1 is in the tens place, so its value is 10 (1 × 10).
→ The digit 2 is in the thousands place, so its value is 2000 (2 × 1000).
The fraction of the value represented by the digit 1 to the value represented by the digit 2 is calculated as follows:
→ Fraction = Value of digit 1 / Value of digit 2
= 10 / 2000
= 1/200
Therefore, the value represented by the digit 1 is 1/200 of the value represented by the digit 2 in the number 2010.
Factor completely
abb + abc
Idek how to factor letters
Answer:
ab( b+c)
Step-by-step explanation:
abb +abc
There is an a and b in each term
What remains goes inside the parentheses
ab( b+c)
Answer:
ab(b+c)
Step-by-step explanation:
Take out each variable like you would any other number
abb+abc
ab(b+c), This is the answer, with the distributive property, you can convert it back to its original form.
ab*b+ab*c=ab^2+abc
Mellisa is an expert scuba diver.she's down in the Pacific Ocean, looking for a rare type of sunfish. At one point, she is 29 meters below the surface of the water.
A. As she swims around for the fish, she swims for 12 mins and rises upward by 15 meters. What is her final depth at the end of the 12 minutes?
B. Later in her dive, Mellisa is at a depth of 40 meters. She decides to rise toward the surface very slowly. Every minute, she rises 2 meters. If she does this for eight minutes, what is her depth?
Answer:
A. 14 meters
B. 24 meters
Step-by-step explanation:
A. Mellisa starts at 29 meters deep, then rises 15 meters. So her final depth is 29 − 15 = 14 meters.
B. Melissa starts at 40 meters deep, then rises 2 m/min for 8 minutes. That means she rises a total distance of 2 × 8 = 16 meters. So her final depth is 40 − 16 = 24 meters.
Answer:
At one point, Mellisa is 29 meters below the surface of the water.
A.
As she swims around for the fish, she swims for 12 mins and rises upward by 15 meters.
So, her final depth at the end of the 12 minutes = [tex]29-15=14[/tex] meters
B.
Mellisa is at a depth of 40 meters. Every minute, she rises 2 meters.
So, in 8 minutes she will rise [tex]2\times8=16[/tex] meters
Her depth will be = [tex]40-16=24[/tex] meters
For 1-Z; the local craft store charges a
registration fee of $10 and $5.50 per
class.
1. Which expression can be used to
determine the total charge, in
dollars, to participate inx number
of classes?
[tex]\huge{\boxed{5.5x+10}}[/tex]
We multiply the class fee by the number of classes. [tex]\bf{5.5x}[/tex]
A registration is a one-time fee, so it is simply added. [tex]5.5x \bf{+10}[/tex]
Divide (10m^8+4m^6+10m^5) / 2m^2
Answer:
5m^6 + 2m^4 + 5m^3
hope this works!!!!
To divide (10m⁸ + 4m⁶ + 10m⁵) by 2m², simplify each term by subtracting 2 from the exponents. The result is 5m⁶ + 2m⁴ + 5m³. The correct answer is D).
To divide (10m⁸ + 4m⁶ + 10m⁵) by 2m², follow these steps
Write the given expression: (10m⁸ + 4m⁶ + 10m⁵) / 2m².
Divide each term in the numerator by 2m² separately:
(10m⁸ / 2m²) + (4m⁶ / 2m²) + (10m⁵ / 2m²).
Simplify each term:
5m⁶ + 2m⁴ + 5m³.
The final result is 5m⁶ + 2m⁴ + 5m³.
The correct option is D).
In this division, we use the rule of exponents: when dividing terms with the same base, subtract the exponents.
The division by 2m² reduces the power of 'm' in each term by 2. So, 10m⁸ becomes 10m⁶, 4m⁶ becomes 2m⁴, and 10m⁵ becomes 5m³. The constants 10 and 4 remain unchanged. The simplified expression is the final result.
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Simplyify t^12/t^6 *PLEASE HELP*
Answer:
C
Step-by-step explanation:
In division when bases are same you do top exponent minus bottom exponent.
So here you do t^(12-6) which is t^6.
Which of the following describes a triangle?
A. One-dimensional
B. Two-dimensional
C. Zero-dimensional
D. Three-dimensional
Answer:
B
Step-by-step explanation:
A triangle has both x and y values making it 2D. A 1D object is a point, a 3D object is a cube or something, and a 0D object is nothing.
help can’t find the answer
Answer:
Volume= 82.4in³
Step-by-step explanation:
Volume is the measure of the amount of space inside of a solid figure, like a cube, ball, cylinder or pyramid. It's units are always "cubic"
To find the volume of sphere, we will use the following formula of Volume:
Volume = 4/3 πr³
Put the values in the formula:
As we know that the value of π is 22/7 or 3.14
Radius = 2.7
According to the formula:
Volume = 4/3 * 3.14 *(2.7)³
Volume= 4/3* 3.14(19.683)
Volume=4/3(61.80462)
Volume=247.21848/3
Volume= 82.4in³....
6. Solve the following equation for x. Show each step.
5x + 2 = 3x + 4(2x - 1)
Answer:
x=1
Step-by-step explanation:
5x + 2 = 3x + 4(2x - 1)
Distribute the 4
5x + 2 = 3x + 8x - 4
Combine like terms
5x + 2 = 11x - 4
Subtract 5x from each side
5x -5x + 2 = 11x - 5x - 4
2 = 6x-4
Add 4 to each side
2+4 = 6x-4+4
6 = 6x
Divide each side by 6
6/6 =6x/6
1= x
The value of x is 1 for equation 5x + 2 = 3x + 4(2x - 1).
A statement that affirms the equivalence of two expressions joined by the equals symbol "=" is known as an equation.
Given,
[tex]5x+2=3x+4(2x-1)\\[/tex]
[tex]5x+2=3x+8x-4[/tex]
On transposing like terms on one side of the equation.
[tex]5x-3x-8x=-4-2\\-6x=-6[/tex]
On multiplying -1 on both sides,
[tex]-6x\times(-1)=-6(-1)\\6x=6[/tex]
On dividing by 6 on both sides,
[tex]\frac{6x}{6}=\frac{6}{6}\\x=1[/tex]
Hence, the value of x is 1.
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What is the value of "c" in the quadratic equation 3x 2 + 5x + 7 = 0?
Answer:
7
Step-by-step explanation:
The quadratic equation looks like:
ax + by + c = 0
"c" is the variable that stands for the "constant", or the number that does not have an extra variable attached, and so is "unchanging". In this case, your answer is 7, which is the constant of the equation. Once defined, the number cannot be changed.
~
A 15-foot board rests against a wall. The angle that the board makes with the
ground is 60°. How far is the base of the board away from the wall?
Select the correct trig ratio and distance from wall.
Answer:
Step-by-step explanation:
Let the base of the board is x feet away from the wall .
And the hypotenuse, which is represented by the length of the board be 15 foot .
So here we have adjacent represented by the base and the hypotenuse .
And cosine function relates adjacent and hypotenuse , which is cos 60=15/x
And the value of cos 60 is half .
Performing cross multiplication
1/2=15/x
Dividing both sides by 2
x=7.5ft
Answer:
7.5 feet.
Step-by-step explanation:
The boardgame resting against the wall is creating a triangle rectangle and as it is forming a 60º angle with the ground that would be solve with the cosine of 60, which is the value of the division of the hypotenuse by the adjacent side, which would be the distance from the base of the board game to the wall:
Cos60= .5
cos60=adjacent side/hypotenuse
.5= adjacent side/15
adjacent side= 15x.5
Adjacent side=7.5 feet
Jane and Jill want their mom to ride the rollercoaster with them, but she thinks it will be too fast. She asks the girls to find out how fast the rollercoaster will be travelling. They find out that the speed of the rollercoaster, in miles per hour, is modeled by the function g(x) = x4 - 4x2 + 7x - 8, where x is time measured in
seconds. How fast is the rollercoaster travelling at 2 seconds?
6 miles per hour
22 miles per hour
26 miles per hour
54 miles per hour
Answer:
Given that the function is a model of miles per hour with x being representative of time in seconds, you simply have to plug 2 into the equation for each x.
Therefore,
g(x) = x^4 - 4x^2 + 7x - 8
becomes
g(x) = 16 - 16 + 14 - 8 = 6 miles per hour.
So, 6 mph is your answer!!
At rate of 6 miles per hour the rollercoaster travelling at 2 seconds.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
g(x) = [tex]x^4[/tex] - 4x² + 7x - 8
where x is time measured in seconds.
Now, the speed of roller-coaster for t= 2 seconds
g(2) = [tex]x^4[/tex] - 4x² + 7x - 8
g(2) = [tex]2^4[/tex] - 4(2)² + 7(2) - 8
g(2)= 16 - 16 + 14 - 8
g(2) = 6 miles per hour.
Hence, the speed 6 miles per hour.
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In the graph, the area below f(x) is shaded and labeled A, the area below g(x) is shaded and labeled B, and the area where f(x) and g(x) have shading in common labeled AB.
A
[tex]y \leqslant - 2 + 3 \\ y \leqslant x + 3[/tex]
B
[tex]y \geqslant - 2x + 3 \\ y \geqslant x + 3[/tex]
C
[tex]y \leqslant - 3x + 2 \\ y \leqslant - x + 2[/tex]
D
[tex]y > - 2x + 3 \\ y > x + 3[/tex]
Answer:
[tex]\large\boxed{A.\ y\leq-2x+3,\ y\leq x+3}[/tex]
Step-by-step explanation:
<, > - dotted line
≤, ≥ - solid line
<, ≤ - shaded region below the line
>, ≥ - shaded region above the line
=============================================
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept → (0, b)
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
From the graph we have the points:
(0, 3) - y-intercept → b = 3 (for both lines)
f(x)
(0, 3), (1, 1)
[tex]m=\dfrac{1-3}{1-0}=\dfrac{-2}{1}=-2[/tex]
Substitute:
[tex]f(x):\ y=-2x+3[/tex]
The shaded region is below the solid line. Therefore: [tex]y\leq-2x+3[/tex]
g(x):
(0, 3), (2, 5)
[tex]m=\dfrac{5-3}{2-0}=\dfrac{2}{2}=1[/tex]
Substitute:
[tex]g(x):\ y=1x+3=x+3[/tex]
The shaded region is below the solid line. Therefore: [tex]y\leq x+3[/tex]
Answer:
b
Step-by-step explanation:
Which expression can be used to determine the slope of the line that passes through the points (–7, 3) and (1, –9)?
Answer:
-9-3/1-(-7)
Step-by-step explanation:
Answer:
The slope of given line = -3/2
Step-by-step explanation:
Points to remember
slope of the line with end points (x1, y1) and (x2, y2) is given by,
Slope = (y2 - y1)/(x2 - x1)
To find the slope of the line
Here (x1, y1) = (-7, 3) and (x2, y2) = (1, -9)
Slope = (y2 - y1)/(x2 - x1)
= (-9 - 3)/(1 - -7)
= (-12)/8
= -3/2
Therefore the slope of given line = -3/2
The radius of a cylinder construction pipe is 1.5ft . If the pipe is 13ft long what is it’s volume? Use value 3.14 for pi
Answer:
V =91.845 ft^3
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h where r is the radius and h is the height
V = pi (1.5)^2 *13
Letting pi = 3.14
V = 3.14 (1.5)^2 * 13
V =91.845 ft^3
Answer:
V=91.89
Step-by-step explanation:
Given:
radius, r= 1.5 ft
height, h=13 ft
volume of cylinder= pi *r^2 *h
V=3.14 *(1.5)^2 *13
V=91.89 ft^3 !
How do you divide something like this?
Answer:
So [tex]\frac{x^2-12x+8}{x-5}=(x-7)+\frac{-27}{x-5}[/tex]
Step-by-step explanation:
Since we are dividing by a linear factor, I'm going to use synthetic division.
Since the linear factor that we are dividing by is (x-5), I'm going to put 5 on the outside:
5 | 1 -12 8
| 5 -35
|--------------------------
1 -7 -27
So the quotient x-7 while the remainder is -27.
So [tex]\frac{x^2-12x+8}{x-5}=(x-7)+\frac{-27}{x-5}[/tex]
You could do long division if you prefer:
x-7
------------------------
(x-5) | x^2-12x+8
- (x^2-5x)
--------------------------
-7x+8
-(-7x+35)
---------------------
-27
You still get the same thing that the quotient is x-7 and the remainder is -27.