Answer: D. 8.25
Step-by-step explanation: A data set can be divided into 4 equal parts, called Quartile. A quartile divides the data into three points:
Lower quartile: Q1;Median: Q2;Upper quartile: Q3;Interquartile Range (IQR) is a measure of variability based on data divided into quartiles or the measure of where the bulk of the values are.
To calculate interquartile range:
IQR = Q3 - Q1
The table shows Q1 = 27.825 and Q3 = 36.075, then
IQR = 36.075 - 27.825
IQR = 8.25
The value of interquartile range is 8.25.
Factor.
x2 – 5x - 36
(x - 9)(x + 4)
(x - 12)(x + 3)
(x + 9)(x - 4)
(x + 12)(x - 3)
Answer:
The answer is option AStep-by-step explanation:
x² - 5x - 36
To factor the expression rewrite -5x as a difference
That's
x² + 4x - 9x - 36
Factor out x from the expression
x( x + 4) - 9x - 36
Factor out -9 from the expression
x( x + 4) - 9( x+ 4)
Factor out x + 4 from the expression
The final answer is
( x - 9)( x + 4)Hope this helps you
Answer:
[tex] \boxed{(x - 9) \: (x + 4) }[/tex]
Option A is the correct option.-
Step-by-step explanation:
( See the attached picture )
Hope I helped!
Best regards!
find the dimension of the swimming pool if the sum must be 50 feet and the length must be 3 times the depth.
Answer:
depth 5 8.3 ft, length 5 24.9 ft, width 5 16.8 ft
Consider the following sample data: 12, 13, 7, 5, 15, 18. Which one of the following represents the value of the standard deviation?
A. 11.67
B. 4.89
C. 2.52
D. 23.87
Answer:
Standard deviation= 4.46
B) 4.89 is the nearest answer
Step-by-step explanation:
Standard deviation √variance
Variance= (summation (x-mean)²)/n
Mean= summation of numbers/total
Mean =( 12+13+ 7+5+15 18)/6
Mean= 70/6
Mean= 11.67
Variance=(( 12-11.67)²+(13-11.67)²+ (7-11.67)²+(5-11.67)²+(15-11.67)²+ (18-11.67)²)/6
Variance= (0.1089+1.7689+21.8089+44.4889+11.0889+40.0689)/6
Variance= 119.3334/6
Variance= 19.8889
Standard deviation= √variance
Standard deviation= √19.8889
Standard deviation= 4.46
The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 6 to 5 . If there were 4545 no votes, what was the total number of votes?
Answer:
The total number of votes= 9999
Step-by-step explanation:
The ratio of vote specifically the ratio of yes to no vote in a city vote is 6 to 5.
There is a total of 4545 no votes.
Yes/no = 6/5
Yes= no(6/5)
Yes= 4545(6/5)
Yes= 5454
The total number of yes votes are 5454.
The total number of votes= yes votes+ no votes
The total number of votes= 5454+4545
The total number of votes= 9999
Given v(x) = g(x) (3/2*x^4 + 4x – 1), find v'(2).
Answer:
Step-by-step explanation:
Given that v(x) = g(x)×(3/2*x^4+4x-1)
Let's find V'(2)
V(x) is a product of two functions
● V'(x) = g'(x)×(3/2*x^4+4x-1)+ g(x) ×(3/2*x^4+4x-1)
We are interested in V'(2) so we will replace x by 2 in the expression above.
g'(2) can be deduced from the graph.
● g'(2) is equal to the slope of the tangent line in 2.
● let m be that slope .
● g'(2) = m =>g'(2) = rise /run
● g'(2) = 2/1 =2
We've run 1 square to the right and rised 2 squares up to reach g(2)
g(2) is -1 as shown in the graph.
■■■■■■■■■■■■■■■■■■■■■■■■■■
Let's derivate the second function.
Let h(x) be that function
● h(x) = 3/2*x^4 +4x-1
● h'(x) = 3/2*4*x^3 + 4
● h'(x) = 6x^3 +4
Let's calculate h'(2)
● h'(2) = 6 × 2^3 + 4
● h'(2) = 52
Let's calculate h(2)
●h(2) = 3/2*2^4 + 4×2 -1
●h(2)= 31
■■■■■■■■■■■■■■■■■■■■■■■■■■
Replace now everything with its value to find V'(2)
● V'(2) = g'(2)×h(2) + g(2)× h'(2)
● V'(2)= 2×31 + (-1)×52
●V'(2) = 61 -52
●V'(2)= 9
find the derivative of f(x)=3x^2✓x
Answer:
[tex]f'(x)=\dfrac{15x\sqrt{x}}{2}[/tex]
Step-by-step explanation:
The power rule applies.
d(x^n)/dx = nx^(n-1)
__
[tex]f(x)=3x^2\sqrt{x}=3x^{\frac{5}{2}}\\\\f'(x)=3(\frac{5}{2})x^{\frac{3}{2}}\\\\\boxed{f'(x)=\dfrac{15x\sqrt{x}}{2}}[/tex]
On a coordinate plane, line P Q goes through (negative 6, 4) and (4, negative 4). Point R On a coordinate plane, a line goes through (negative 4, 0) and (4, negative 4). A point is at (2, 3). What is the equation of the line that is parallel to the given line and passes through the point (2, 3)? x + 2y = 4 x + 2y = 8 2x + y = 4 2x + y = 8
Answer:
x + 2y = 8.
Step-by-step explanation:
Line goes through (-4, 0) and (4, -4).
The slope is (-4 - 0) / (4 - -4) = -4 / (4 + 4) = -4 / 8 = -1/2.
Since we are looking for the equation of the line parallel to that line, the slope will be the same.
We have an equation of y = -1/2x + b. We have a point at (2, 3). We can then say that y = 3 when x = 2.
3 = (-1/2) * 2 + b
b - 1 = 3
b = 4.
So, we have y = -1/2x + 4.
1/2x + y = 4
x + 2y = 8.
Hope this helps!
ANSWEAr
x + 2y = 8
because it is
Michael records the height of 1000 people. This data is a normal distribution and the sample mean was 0.75. Identify the margin of error for this data set.
Answer:
0.0284Step-by-step explanation:
The formula for calculating the Margin of error of a dataset is expressed as;
Margin of error = [tex]Z*\sqrt{\frac{p(1-p)}{n} } \\\\[/tex] where;
Z is the z-score of 95% confidence interval = 1.96
p is the sample proportion/mean = 0.75
n is the sample size = total number of people = 1000
Note that when the confidence interval is not given, it is always safe to use 95% confidence.
Substituting this values into the formula we have;
[tex]ME = 1.96*\sqrt{\frac{0.7(1-0.7)}{1000} } \\\\ME = 1.96*\sqrt{\frac{0.7(0.3)}{1000} } \\\\ME = 1.96*\sqrt{0.00021} } \\\\ME = 1.96*0.01449\\\\ME = 0.0284[/tex]
Hence the margin error for the dataset is 0.0284
What Number is equivalent to 4^3
A. 7
B. 12
O C. 64
D. 81
Answer:
C
Step-by-step explanation:
4³ means 4 multiplied by itself 3 times, that is
4 × 4 × 4
= 16 × 4
= 64 → C
Find the sum of (5x3 + 3x2 - 5x + 4) and (8x3 -5x2 + 8x + 9)
Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. n^2+5/2n
Answer: [tex]\bigg(n+\dfrac{5}{4}\bigg)^2[/tex]
Step-by-step explanation:
[tex]n^2+\dfrac{5}{2}n+\underline{\qquad}\\\\\\n^2+\dfrac{5}{2}n+\bigg(\dfrac{5}{2\cdot 2}\bigg)^2\\\\\\n^2+\dfrac{5}{2}n+\bigg(\dfrac{5}{4}\bigg)^2\\\\\\=\bigg(n+\dfrac{5}{4}\bigg)^2[/tex]
Is the quotient of two rational numbers always a rational number? Explain.
Answer:
Yes,
Step-by-step explananation
The quotient of two rational numbers is always rational, and the reason for this lies in the fact that the product of two integers is always an rational number.
The Quotient of two Rational Numbers is a Rational Number if and only if Numerator and Denominator are Multiples.
From Algebra, we know that a Rational Number is a Real Number of the form:
[tex]x = \frac{a}{b}[/tex], [tex]a, b\in \mathbb{N}[/tex], [tex]x \in \mathbb{R}[/tex] (1)
Where:
[tex]a[/tex] - Numerator.[tex]b[/tex] - Denominator.[tex]x[/tex] - Quotient.The Quotient can be an Integer or not. In the first case, all Quotients have their equivalent Rational Numbers.
Now, if we divide a Rational Number by another Rational Number, then we have the following expression:
[tex]x' = \frac{x_{1}}{x_{2}}[/tex]
If [tex]x'[/tex] is a Rational Number, then it must also an Integer and if [tex]x'[/tex] is an Integer, then [tex]x_{1}[/tex] and [tex]x_{2}[/tex] must be Multiples of each other.
The Quotient of two Rational Numbers is a Rational Number if and only if Numerator and Denominator are Multiples.
Please see this question related to Rational Numbers: https://brainly.com/question/24398433
What is the rate of change from x = 0 to x = pi over 2 ? (6 points) trig graph with points at: (0, negative 4) and (pi over 2, 0) and (pi, 4) and (3 pi over 2, 0) and (2 pi, negative 4)
Answer:
Rate of Change : 8 / π
Step-by-step explanation:
To determine this rate of change, we have to first consider the points at x = 0 and x = π / 2.
When x = 0, f( x ) = - 4,
When x = π / 2, f( x ) = 0
Remember that rate of change is represented by a change in y / change in x. Therefore,
( 0 - ( - 4 ) ) / ( π / 2 - 0 ),
( 0 + 4 ) / ( π / 2 ),
4 / π / 2 = 8 / π
Therefore the rate of change from x = 0 ➡ x = π / 2 will be 8 / π.
An artifact was found and tested for its carbon-14 content. If 72% of the original carbon-14 was still present, what is its probable age (to the nearest 100 years)? (Carbon-14 has a half-life of 5,730 years).
Answer:
2700 years
Step-by-step explanation:
The exponential function for the fraction remaining is ...
r(t) = (1/2)^(t/5730)
where r is the remaining fraction and t is the time in years. We can solve for t to get ...
log(r) = (t/5730)log(1/2)
t = 5730·log(r)/log(1/2)
For the given r=0.72, the age of the artifact is estimated to be ...
t = 5730·log(0.72)/log(0.5) ≈ 2700 . . . years
Which is the solution to the inequality?
2 3/5 <b-8/15
Answer:
3 2/15 <b
Step-by-step explanation:
2 3/5 <b-8/15
Add 8/ 15 to each side
2 3/5 + 8/ 15 <b-8/15 + 8/15
2 3/5 + 8 /15 <b
Get a common denominator
2 3/5 *3/3 + 8/15
2 9/15 + 8/15 < b
2 17/15 < b
2 + 15/15 + 2 /15 < b
3 2/15 <b
Answer:
B > 3 2/15
Step-by-step explanation:
What are the solution(s) of the quadratic equation 98 - x2 = 0?
x = +27
Ox= +63
x = +7/2
no real solution
Answer:
±7 sqrt(2) = x
Step-by-step explanation:
98 - x^2 = 0
Add x^2 to each side
98 =x^2
Take the square root of each side
±sqrt(98) = sqrt(x^2)
±sqrt(49*2) = x
±7 sqrt(2) = x
Answer:
[tex]\huge \boxed{{x = \pm 7\sqrt{2} }}[/tex]
Step-by-step explanation:
[tex]98-x^2 =0[/tex]
[tex]\sf Add \ x^2 \ to \ both \ sides.[/tex]
[tex]98=x^2[/tex]
[tex]\sf Take \ the \ square \ root \ of \ both \ sides.[/tex]
[tex]\pm \sqrt{98} =x[/tex]
[tex]\sf Simplify \ radical.[/tex]
[tex]\pm \sqrt{49} \sqrt{2} =x[/tex]
[tex]\pm 7\sqrt{2} =x[/tex]
[tex]\sf Switch \ sides.[/tex]
[tex]x= \pm 7\sqrt{2}[/tex]
Please answer this correctly without making mistakes
Answer:
105/4 or 26.25 mi
Step-by-step explanation:
hillsdale to fairfax 8 7/8 = 71/8
fairfax to yardley = 17 3/8 = 139/8
71/8 + 139/8 = 105/4 or 26 2/8
F
13
5
H
12
G
se
Find mZH to the nearest degree.
67
O 18
O 45
O 23
Answer:
∠ H ≈ 23°
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan H = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{FG}{HG}[/tex] = [tex]\frac{5}{12}[/tex] , thus
∠ H = [tex]tan^{-1}[/tex] ( [tex]\frac{5}{12}[/tex] ) ≈ 23° ( to the nearest degree )
Combine like terms to simplify the expression: 2/5k - 3/5 +1/10k
━━━━━━━☆☆━━━━━━━
▹ Answer
1/2k - 3/5
▹ Step-by-Step Explanation
2/5k - 3/5 + 1/10k
Collect like terms:
2/5k + 1/10k = 1/2
Final Answer:
1/2k - 3/5
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Answer:
1/2k - 3/5
Step-by-step explanation:
Hey there!
Well the only fraction needed to combine are,
2/5 and 1/10.
To add them we need to make 2/5 have a denominator of 10.
To do that we multiply 5 by 2.
5*2 = 10
What happens to the denominator happens to the denominator.
2*2 = 4
Fraction - 4/10
4/10 + 1/10 = 5/10
5/10
simplified
1/2
1/2k - 3/5
Hope this helps :)
Write the equation of the line that passes through (−2, 6) and (2, 14) in slope-intercept form. (2 points)
Answer:
[tex]y = 4x + 14[/tex]
Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation we must first find the slope of the line
Slope of the line using points (−2, 6) and (2, 14) is
[tex]m = \frac{14 - 6}{2 + 2} = \frac{8}{2} = 4[/tex]
Now we use the slope and any of the points to find the equation of the line.
Equation of the line using point ( - 2, 6) and slope 4 is
[tex]y - 6 = 4(x + 2) \\ y - 6 = 4x + 8 \\ y = 4x + 8 + 6[/tex]
We have the final answer as
[tex]y = 4x + 14[/tex]
Hope this helps you
a is less than or equal to 10
Lmk
Answer:
[tex]a \leqslant 10[/tex]
Step-by-step explanation:
a is less than or equal to 10
less than: <
equal: =
less than or equal to: ≤
Hope this helps ;) ❤❤❤
hope it helps you
imp=draw dark shaded point in thqt line and point towards left
1. Transform the polar equation to a Cartesian (rectangular) equation: 2. Transform the Cartesian (rectangular) equation to a polar equation: y^2 = 4x
Answer:
Attachment 1 : 5x + 6y = 5, Attachment 2 : 4cotθcscθ
Step-by-step explanation:
Remember that we have three key points in solving these types of problems,
• x = r cos(θ)
• y = r sin(θ)
• x² + y² = r²
a ) For this first problem we need not apply the third equation.
( Multiply either side by 5 cos(θ) + 6 sin(θ) )
r [tex]*[/tex] ( 5 cos(θ) + 6 sin(θ) ) = 5,
( Distribute r )
5r cos(θ) + 6r sin(θ) = 5
( Substitute )
5x + 6y = 5 - the correct solution is option c
b ) We know that y² = 4x ⇒
r²sin²(θ) = 4r cos(θ),
r = 4cos(θ) / sin²(θ) = 4 cot(θ) csc(θ) = 4cotθcscθ - again the correct solution is option c
Solving a word problem with three unknowns using a linear...
Rachel, Trey, and Deshaun sent a total of 98 text messages during the weekend. Trey sent 4 times as many messages as Deshaun. Rachel sent 10 fewer
messages than Deshaun. How many messages did they each send?
Number of text messages Rachel sent:
221
Х
?
Answer:If Rachel texted 221 text messages, then Deshaun texted 231 text messages, and Trey texted 924 text messages.
Step-by-step explanation:
221+10=231, 321 times 4 equal 924
What is 1/3 of 675 is left
I need some help with simplifying expressions, please. 8y - 9y =
As your first step to this problem, change the minus sign to plus a negative.
So we have 8y + -9y.
8y + -9y simplifies to -1y which is our final answer.
Note that if you wrote -y instead, it means the same thing.
However, use the 1 to help avoid confusion if you need it.
Manuel says that he can solve the equation 3n = 21 by multiplying both sides by ⅓. Explain why this is correct.
Step-by-step explanation:
はい、両側を削除して、3を掛けて7にします
Step-by-step explanation:
Given:
3n = 21
if we multiply both sides by 1/3, we will get:
3n = 21
3n x (1/3)= 21 x (1/3)
3n/3 = 21/3
n = 21/3
n = 7
Hence we can indeed solve for n by multiplying both sides by (1/3)
A polling company reported that 53% of 1018 surveyed adults said that secondhand smoke issecondhand smoke is "very harmful.""very harmful." Complete parts (a) through (d) below.
a. What is the exact value that is 53% of 1018?
b. Could the result from part (a) be the actual number of adults who said that secondhand smoke issecondhand smoke is "very harmful" question mark "very harmful"? Why or why not?
c. What could be the actual number of adults who said that secondhand smoke issecondhand smoke is "very harmful" question mark "very harmful"?
d. Among the 10181018 respondents, 260260 said that secondhand smoke issecondhand smoke is "not at all harmful.""not at all harmful." What percentage of respondents said that secondhand smoke issecondhand smoke is "not at all harmful" question mark "not at all harmful"?
Answer:
a. 539.54
b. No, the result from part (a) could not be the actual number of adult who said that secondhand smoke are very harmful because a count of people must result into a whole number.
c. 540
d. 25.54%
Step-by-step explanation:
Given that:
A polling company reported that 53% of 1018 surveyed adults said that secondhand smoke is "very harmful."
Complete parts (a) through (d) below.
a. What is the exact value that is 53% of 1018?
The 53% of 1018 is :
=[tex]\dfrac{53}{100} \times 1018[/tex]
= 0.53 × 1018
= 539.54
b. Could the result from part (a) be the actual number of adults who said that secondhand smoke is ''very harmful"? Why or why not?
No, the result from part (a) could not be the actual number of adult who said that secondhand smoke are very harmful because a count of people must result into a whole number.
c. What could be the actual number of adults who said that secondhand smoke is secondhand smoke "very harmful"?
Since, a count of people must result into a whole number, the actual number of adults who said that secondhand smoke is secondhand smoke "very harmful" can be determined from the approximation of the exact value into whole number which is 539.54 [tex]\approx[/tex] 540.
d. Among the 1018 respondents, 260 said that secondhand smoke is is "not at all harmful.'' What percentage of respondents said that secondhand smoke is "not at all harmful"?
Since 260 respondents out of 1018 respondents said that the second hand smoke is not harmful, then the percentage of the 260 respondents is :
= [tex]\dfrac{260}{1018} \times 100 \%[/tex]
= 25.54%
A random sample of 10 single mothers was drawn from a Obstetrics Clinic. Their ages are as follows: 22 17 27 20 23 19 24 18 19 24 We want to determine at the 5% significance level that the population mean is not equal to 20. What is the rejection region?
Answer:
0.09
Step-by-step explanation:
Let x = ages of mother
x : 22 17 27 20 23 19 24 18 19 24
N = 10
Mean = ∑x/N = 218/10 = 21.8
Difference in mean = 21.8 - 20 = 1.8
If significance level = 5% or 0.05
∴ Rejection region = 1.8 X 0.05 = 0.09
Given that
[tex]\sqrt{2p-7}=3[/tex]
and
[tex]7\sqrt{3q-1}=2[/tex]
Evaluate
[tex]p + {q}^{2} [/tex]
Answer:
Below
Step-by-step explanation:
The two given expressions are:
● √(2p-7) = 3
● 7√(3q-1) = 2
We are told to evaluate p+q^2
To do that let's find the values of p and q^2
■■■■■■■■■■■■■■■■■■■■■■■■■■
Let's start with p.
● √(2p-7) = 3
Square both sides
● (2p-7) = 3^2
● 2p-7 = 9
Add 7 to both sides
● 2p-7+7 = 9+7
● 2p = 16
Divide both sides by 2
● 2p/2 = 16/2
● p = 8
So the value of p is 8
■■■■■■■■■■■■■■■■■■■■■■■■■■
Let's find the value of q^2
● 7√(3q-1) = 2
Square both sides
● 7^2 × (3q-1) = 2^2
● 49 × (3q-1) = 4
● 49 × 3q - 49 × 1 = 4
● 147q - 49 = 4
Add 49 to both sides
● 147q -49 +49 = 4+49
● 147q = 53
Divide both sides by 147
● 147q/147 = 53/147
● q = 53/ 147
Square both sides
● q^2 = 53^2 / 147^2
● q^2 = 2809/21609
■■■■■■■■■■■■■■■■■■■■■■■■■
● p+q^2 = 8 +(2809/21609)
● p+q^2 = (2809 + 8×21609)/21609
● p+q^2 = 175681 / 21609
● p + q^2 = 8.129
Round it to the nearest unit
● p+ q^2 = 8
There are $400$ pages in Sheila's favorite book. The average number of words per page in the book is $300$. If she types at an average rate of $40$ words per minute, how many hours will it take to type the $400$ pages of the book?
Answer:
50hours
Step-by-step explanation:
Given that there are 400 pages in Sheila's favorite book.
The average number of words per page in the book is 300
She types an average rate of 40words per minute.
So to type 400pages of the book
Total number of words in the pages = 400×300 = 120000 words
Typing rate : 40words ------- 1minute
120000 words ----------- x minutes
Hence we have 40 × X mins = 120000 × 1min
Make X the subject
40X = 120000minutes
X = 120000/40
X = 3000minutes
Since 60minutes = 1hour
3000minutes = 3000minutes/60
= 50hours
Hence it took her 50hours to type 400pages
Solution:
The total number of words in the book is 400 x 300. Sheila types at a rate of 40 words per minute, or 40 x 60 words per hour. The number of hours it takes her is equal to the number of words divided by her rate of typing, or 400x300/40x60 = 50 hours.
