Answer:
819
Step-by-step explanation:
Givens
a = -1r = - 4n = 6Formula
Sum = a(1 - r^n) / ( 1 - r)
Sum = -1(1 - (-4)^6 / (1 - -4)
Sum = -1 (1 - 4096) / 5
Sum = -1 (- 4095 ) / 5
Sum = 819
Twenty students in Class A and 20 students in Class B were asked how many hours they took to prepare for an exam. The data sets represent their answers. Class A: {2, 5, 7, 6, 4, 3, 8, 7, 4, 5, 7, 6, 3, 5, 4, 2, 4, 6, 3, 5} Class B: {3, 7, 6, 4, 3, 2, 4, 5, 6, 7, 2, 2, 2, 3, 4, 5, 2, 2, 5, 6} Which statement is true for the data sets? A. The mean study time of students in Class A is less than students in Class B. B. The mean study time of students in Class B is less than students in Class A. C. The median study time of students in Class B is greater than students in Class A. D. The range of study time of students in Class A is less than students in Class B. E. The mean and median study time of students in Class A and Class B is equal.
Answer:
Option B
Step-by-step explanation:
Given
Two Data sets
Class A :{ 2, 5, 7, 6, 4, 3, 8, 7, 4, 5, 7, 6, 3, 5, 4, 2, 4, 6, 3, 5}
Class B : {3, 7, 6, 4, 3, 2, 4, 5, 6, 7, 2, 2, 2, 3, 4, 5, 2, 2, 5, 6}
In order to check the options we will have to find the mean and median of both data sets.
So for Class A:
Mean= x =(Sum of values)/(Number of values)
=96/20
=4.8
For median the data has to be arranged in ascending order, so
2, 2,3,3,3,4,4,4,4,5,5,5,5,6,6,6,7,7,7,8
Median will be the average of middle two values as the number of items are odd.
Median=(5+5)/2
=10/2
=5
Range = 8-2 = 6
For Class B:
Mean= x =(Sum of values)/(Number of values)
=80/20
=4
For median, arranging the values
2,2,2,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,7
Median=(4+4)/2
=8/2
=4
Range = 7-2 = 5
We get,
Mean of class A > Mean of Class B
Median of Class A > Median of Class B
Range of Class A > Range of Class B
We observe that only option B is correct for the given data sets..
Use complete sentences to explain how to use linear factors to determine the equation of a polynomial function
Answer: p(x) = a (x-b)(x-c)(x-d)
Step-by-step explanation:
The first step is to determine the degree of the polynomial.
It shall depend totally on the linear factors given for the polynomial.
If there is one, it is a linear polynomial.
If there are 2, then it is a quadratic polynomial.
If there are three then it shall be a cubic polynomial.
Now let us assume that there are three linear factors.
We multiply those factors and write the polynomial.
If x-b, x-c & x-d are the factors we write
p(x) = (x-b)(x-c)(x-d)
But as we may have a leading coefficient so we write the polynomial as
Then we go on to expand this to get the polynomial in the standard form.
Answer with Step-by-step explanation:
First we find the degree of polynomial.
Consider two linear factors
(x-a) and (x-b)
Multiplying these two factors to get the polynomial.
[tex]p(x)=(x-a)(x-b)=x^2-(a+b)x+ab[/tex]
There are two linear factors .
Therefore, the degree of polynomial is 2 and the polynomial is quadratic.
Degree of polynomial=Number of linear factors
If the linear factors are three then the polynomial formed by multiplying theses factors .
Then, we get the polynomial of degree 3 and the polynomial is cubic polynomial.
It we have four linear factors.
After multiplying these four factors, we get a polynomial of degree 4.
The polynomial is bi quadratic.
Find the volume of the cone.
Either enter an exact answer in terms of π or use 3.14 for π and round your final answer to the nearest hundred
V≈301.59
I think this is the answer.
Hope this helps!
The answer is 96pi units^3
to the nearest hundredth what is the length of A
Answer:
13.6
Step-by-step explanation:
Use the a^2 + b^2 = c^2 formula.
Answer:
A = 7.55
Step-by-step explanation:
A^2 + B^2 = C^2A^2 = C^2 - B^2A = square root (C^2 - B^2)A = square root (11^2 - 8^2)A = square root (121 - 64)A = square root (57)A = 7.55The test grades of 10 different students were used to create the box plot above. Which of the following is the median of the set of grades?
A. 62
B. 80
C. 71
D. 70
Answer:
the answer is 71
Step-by-step explanation:
On a box and Quaker plot the median is the middle dot is the median so 71
help me please
-4.5+4.4+_____=0
To find the missing value in the equation, we add -4.5 and 4.4 first, then solve for the missing value.
Explanation:To find the missing value, we need to solve the equation. Start by adding -4.5 and 4.4. (-4.5 + 4.4 = -0.1)
Now we have: -0.1 + ___ = 0
To solve for the missing value, subtract -0.1 from both sides of the equation: ____ = 0 + 0.1 = 0.1
The missing value is 0.1.
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Final answer:
The missing value is 0.1.
Explanation:
This expression is a quadratic equation of the form at² + bt + c = 0, where the constants are a = 4.90, b = -14.3, and c = -20.0.
To solve for the missing value, we can rearrange the equation:
-4.5 + 4.4 + ____ = 0
Simplifying the equation, we get:
-4.5 + 4.4 + ____ = 0
-0.1 + ____ = 0
By adding 0.1 to both sides of the equation, we can isolate the missing value:
____ = 0.1
Therefore, the missing value is 0.1.
Someone please help me with this math problem, and please show the work
To solve this math problem, calculate the expression, write a linear equation, and round the result. Include units in your final answer.
Explanation:To solve this math problem, you need to calculate the given expression, write a linear equation, and round the result to four decimal places. Let's break it down:
Enter the given data into a calculator or computer.Perform the necessary calculations to find the value of the expression.Write the linear equation based on the given expression. For example, if the expression is y = mx + b, find the values of m and b.Round the result to four decimal places, keeping in mind the rules for significant figures.Remember to include the appropriate units in your final answer.
Tyler goes to a school dance. He arrives at 8:12 pm and leaves at 10:45 pm. How long was he at the dance?
Answer:
2 hours 33 mins
Step-by-step explanation:
Arrives = 8.12 pm
Leaves = 10.45 pm
8.12 pm to 10.12 pm = 2 hours
10.12 pm tp 10.45 pm = 33 minutes
Total
= 2 hours + 33 mins
= 2 hours 33 mins
Answer:
2:33
Step-by-step explanation:
For 8:00 to get to 10:00 add two which means two hours then subtract :45 by :12 which gives you 33 so tyler stayed there for 2 hours and 33 minutes.
The current (I) in an electrical conductor varies inversely as the resistance (R) of the conductor. The current is 6 amperes when the resistance is 722 ohms. What is the current when the resistance is 768 ohms? Round your answer to two decimal places if necessary.
a.
5.6 amps
b.
0.16 amps
c.
6.4 amps
d.
0.18 amps
Hence, the correct answer is:
Option : a
a. 5.6 amps
Step-by-step explanation:It is given that:
The current (I) in an electrical conductor varies inversely as the resistance (R) of the conductor.
This means that:
[tex]I\propto \dfrac{1}{R}[/tex]
Hence, we get the relation as:
[tex]\dfrac{I_1}{I_2}=\dfrac{R_2}{R_1}[/tex]
where [tex]R_1[/tex] is the resistance corresponding to the current [tex]I_1[/tex]
and [tex]R_2[/tex] is the resistance corresponding to the current [tex]I_2[/tex]
We have:
[tex]I_1=6\ ,\ R_1=722\ ,\ R_2=768[/tex]
Hence, we get:
[tex]\dfrac{6}{I_2}=\dfrac{768}{722}\\\\\\i.e.\\\\\\I_2=\dfrac{722\times 6}{768}\\\\\\I_2=5.6406\ amperes[/tex]
Hence, the answer is:
Option : a
How many feet per minute
Answer:
3.5 feet / per minute
Step-by-step explanation:
3 1/2 feet / minute = 3.5 feet / minute
hope this helps :)
Remy recorded the favorite sport of students at his school. He surveyed 500 students. How many students chose Baseball?
(Chart)
Football 45%
Baseball 15%
Basketball 20%
Tennis 20%
Answer: 75 students
Step-by-step explanation:
15% of 500= 75
Help Please!!!!!!
The equation of a circle is x² + y² - 4x + 2y - 31 = 0. What is the center and the radius of the circle? Show your work.
Answer:
centre = (2, - 1), radius = 6
Step-by-step explanation:
Rearrange the equation by placing the x and y terms together and adding 31 to both sides
Given
x² + y² - 4x + 2y - 31 = 0, then
x² - 4x + y² + 2y = 31
Use the method of completing the square
add ( half the coefficient of the x/y term )² to both sides
x² + 2(- 2)x + 4 + y² + 2(1)y + 1 = 31 + 4 + 1
(x - 2)² + (y + 1)² = 36
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r the radius
compare to (x - 2)² + (y + 1)² = 36, then
centre = (2, - 1) and r = [tex]\sqrt{36}[/tex] = 6
The center of the circle is (2, - 1) and the radius is 6 units.
What are the types of equations of a circle?The equation for a circle has the generic form x² + y² + 2gx + 2fy + c = 0.
The standard equation of a circle is x² + y² = r².
The polar form of the equation of the circle is (rcosθ)² + (rsinθ)² = p².
Given, The equation of a circle is x² + y² - 4x + 2y - 31 = 0.
We know, In x² + y² + 2gx + 2fy + c = 0, The center of the circle is,
(- g, - f) and radius is [tex]\sqrt{g^2 + f^2 - c[/tex].
Therefore, 2gx = - 4x and 2fy = 2y.
2g = - 4 and 2f = 2.
g = - 2 and f = 1.
- g = 2 and - f = - 1.
So, The center is (2, - 1).
And the radius is, [tex]\sqrt{2^2 + -1^2 + 31[/tex].
= [tex]\sqrt{4 + 1 + 31[/tex].
= [tex]\sqrt{36[/tex].
= 6 units.
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A circle with radius x is shown below. The diagram is not drawn to scale.
ANSWER
[tex]11 .6[/tex]
EXPLANATION
x is the radius of the circle.
It is equal to the hypotenuse of the right triangle created by connecting the center and the end of the chord with a straight line.
[tex] {x}^{2} = {5}^{2} + {( \frac{21}{2} )}^{2} [/tex]
[tex]{x}^{2} = 25 + 110.25[/tex]
[tex] {x}^{2} = 135.25[/tex]
[tex]x = \sqrt{135.25} [/tex]
[tex]x = 11.6[/tex]
Of the students at Milton Middle School 126 are girls.35% of the students are girls, how many total students are there at Milton Middle school?
Answer:360
Step-by-step explanation:
35% of of 100% with 126 being as the part and the whole is missing.You multiply 126 by 100 which equals 12600 divided by 35 which is equals 360.
Answer:
C)
Step-by-step explanation:
If you multiply twice, you will get 70%. If you multiply by three, you will get 378. That is higher than 360. So it's 360(c)
a scatter plot containing the point(12,12) has the regression equation^y=1/4x+1. what is the residual e when x equals 12
Answer:
8, substitute 12 into the equation and then subtract it from 12
Step-by-step explanation:
Determine the area of the yellow sector
The area of the yellow sector is 15/8 π in² in pi form.
One carton of eggs contains 12 eggs. Make a table to find the number of eggs in 5, 6, 7, and 8 cartons.
Given : One carton of eggs contains 12 eggs.
By unitary method we can find the number of eggs in following cartoons :
1 cartoon = 12 eggs
5 cartoons = 12 × 5 = 60 eggs
6 cartoons = 12 × 6 = 72 eggs
7 cartoons = 12 × 7 = 84 eggs
8 cartoons = 12 × 8 = 96 eggs
Answer:
D
Step-by-step explanation:
what is the equation of the line that is parallel to the line x=-2 and passes through the point (-5,4)
Answer:
x = - 5
Step-by-step explanation:
The line with equation x = - 2 is a vertical line parallel to the y- axis
The equation of a vertical line is
x = c
where c is the value of the x- coordinates the line passes through
The line passes through (- 5, 4) with x- coordinate - 5, thus
equation of parallel line is x = - 5
Please help I need to pass this class pls pls pls
Answer:
it is the first one
Step-by-step explanation:
There are some black and white buttons in a container.
7/10 of the buttons are black.
The difference between the number of black and white buttons is 24.
How many buttons are there in the container?
ANSWER
60 buttons.
EXPLANATION
Let the number of buttons in the container be x.
Then the number of buttons that are black are:
[tex] \frac{7}{10} x[/tex]
The number of buttons that are white
[tex] \frac{3}{10} x[/tex]
The difference between the white and the black buttons
[tex] \frac{4x}{10} = 24[/tex]
Solve for x.
[tex]4x = 240[/tex]
[tex]x = \frac{240}{4} [/tex]
[tex]x = 60[/tex]
Hence there are 60 buttons in the container.
The library sponsors a chess club for members of all ages and skill levels. Currently, the ages of the members are 7, 9, 10, 11, 13, 14, 15, 16, 18, 19, 20, 21, and 22. The librarian uses a histogram to track the number of members in different age groups. For this situation, which is the appropriate way to label the age intervals on the x-axis? A) 7−11; 11−14; 15−19; 20−22 B) 7−10; 11−14; 15−18; 19−22 C) 7−10; 10−15; 15−19; 19−22 D) 7−13; 15−19; 20−22
Answer:
I would do answer B if not A.
Step-by-step explanation:
I would do this because then they would be relatively closer in skill set.
The appropriate way to label the age intervals on the x-axis is: Option: B
B) 7−10; 11−14; 15−18; 19−22
Step-by-step explanation:The rule for determining the number of intervals is:
Take the square root of the number of observations to the nearest whole number.Here we have 13 observations
and √(13)=3.6055≈4
Hence, we have a total of four intervals.
The width of each interval is calculated as:
The ratio of range to the total number of intervals.i.e. (22-7)/4=15/4=3.75≈4
We know that for classifying a class interval in a histogram the width of each of the interval must be equal.
A) 7−11; 11−14; 15−19; 20−22
In option: A--
the width of first interval is: 4
width of second interval is: 3
Width of third interval is: 4
Width of fourth interval is: 2
Hence, the width of each interval is not equal.
Hence, option: A is discarded.
C) 7−10; 10−15; 15−19; 19−22
In option: C--
the width of first interval is: 3
width of second interval is: 5
Width of third interval is: 4
Width of fourth interval is: 3
Hence, the width of each interval is not equal.
Hence, option: C is discarded.
D) 7−13; 15−19; 20−22
In option: D--
the width of first interval is: 6
width of second interval is: 4
Width of third interval is: 2
Hence, the width of each interval is not equal.
Hence, option: D is discarded.
B) 7−10; 11−14; 15−18; 19−22
There are a total of 4 intervals and also width of each interval is equal and equal to 4.
Hence, option: B is the correct answer.
Brainliest + Points?
Please answer and explain
Answer:
see explanation
Step-by-step explanation:
For 2 similar figures
linear ratio = a : b, then
area ratio = a² : b²
volume ratio = a³ : b³
Given linear ratio = [tex]\frac{2}{5}[/tex], then
(a)
perimeter is a linear ratio = [tex]\frac{2}{5}[/tex]
(b)
surface area ratio = [tex]\frac{2^2}{5^2}[/tex] = [tex]\frac{4}{25}[/tex]
(c)
volume ratio = [tex]\frac{2^3}{5^3}[/tex] = [tex]\frac{8}{125}[/tex]
Ashley ran from home to school in 10 minutes. What is her average speed, if the distance between her house and her school is 1.5 miles?
(.15 miles / 1 minute) * (60 minutes / 1 hour) = 9 miles / hour
7 lb in 12 oz equals blank ounces
7lb in 12 oz equals blank ounces = 124 ounces
The number of children who attended the fair on opening day is 351 more than the value of 4 thousands. How many children attended the fair
To find the total number of children who attended the fair on opening day, add 351 to 4000, giving a result of 4351 children.
Explanation:The number of children who attended the fair on opening day is calculated by adding 351 to the value of 4 thousands. To find the answer, we follow these steps:
Identify the value of 4 thousands, which is 4000.Add 351 to 4000 to get the total number of children who attended the fair.Perform the addition: 4000 + 351 = 4351.Therefore, 4351 children attended the fair on the opening day.
HELP PLZ!!
At what points are the equations equal
Answer:
Step-by-step explanation:
f,d,e
Answer:
F, C, B
Step-by-step explanation:
Just look at where the two graphs intersect and then correspond that point with the color and letter.
Leah flips a coin, and then she spins the pointer on a spinner with equal sections of red, green, and blue. Which of the following is a compound event? Select all that apply. A. 00:00 The coin lands heads up. B. 00:00 The coin lands heads up, and the pointer lands on red. C. 00:00 The coin lands tails up, and the pointer lands on green. D. 00:00 The pointer lands on blue. E. 00:00
Answer:
B. is your answer because its compounded
Step-by-step explanation:
Answer:
Step-by-step explanation:
Given that Leah flips a coin, and then she spins the pointer on a spinner with equal sections of red, green, and blue.
Both flipping a coin and spins the pointer on a spinner is the compound event.
A is not compound since only coin is flipped
B is compound because it contains two events together
C is compound
D is not compound as this is single event.
Mrs. Benton prepares a 7 cup green bean casserole. She divides the casserole into equal 1/2 cup servings. If she eats one serving each day, how many days of servings are available? A) 10 days B) 14 days c) 18 days D) 24 days
Answer:
B
Step-by-step explanation:
7 serving multiplied by 2 is equal to 14
Answer:
the answer is prob B i am i on usatest prep and it is correct
Step-by-step explanation:
What is the volume of a rectangular solid, the width of which is equal to a cm, the length is twice the width and the height is twice the length?
the width is equal to a cm.
the length is twice the width, therefore the length is equal to 2a cm.
the height is twice the length, therefore the height is equal to 4a cm.
the volume is equal to width times length times height which is equal to a * 2a * 4a which is equal to 8a^3 cubic cm.
For Example:
let a = 5
then 2a = 10
then 4a = 20
a is the width
2a is the length
4a is the height.
the length is twice the width.
the height is twice the length
the volume is equal to a * 2a * 4a which is equal to 8a^3 cubic cm.
this is equivalent to 8 * 5^3 which is equal to 8 * 125 which is equal to 1000 cubic cm.
5 * 10 * 20 = 50 * 20 = 1000 cubic cm.
formula works and so is considered to be good.
the volume is equal to 8a^3 cubic cm.
* hope you understand*
The volume of a rectangular solid where width equals a cm, length equals twice the width, and the height is twice the length is calculated to be 8a³ cubic cm.
Explanation:Based on the question, we know that the width of the rectangular solid is a cm. Where the length equals twice the width, so it is 2a cm; likewise, the height, which is twice the length, turns out to be 4a cm. The equation for calculating the volume of a rectangular solid is width * length * height. Therefore, if we substitute the given values, we have a cm * 2a cm * 4a cm, which equals 8a³ cubic cm. As a result, the volume of this given rectangular solid is 8a³ cubic cm.
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Which number sentence is NOT true?
A. |-6.7| = 6.7
B. |0| < |-45|
C. |45| > 0
D. |6.7| > |-45|
Answer: D. |6.7| > |-45|
Step-by-step explanation:
When in these | | then any negative number becomes positive. 6.7 is NOT grater than 45.