The following table shows scores obtained in an examination by B.Ed JHS Specialism students. Use the information to answer the questions that follow: Score 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 Frequency 10 4 10 20 30 15 3 2 1 5.a. Construct a cumulative frequency curve for the data. b. Find the; i. inter-quartile range. ii. 70th percentile class scores. iii. probability that a student scored at most 50 on the examination
Please is urgent .can I get help
Answers
Answer:
(a) The cumulative frequency curve for the data is attached below.
(b) (i) The inter-quartile range is 10.08.
(b) (ii) The 70th percentile class scores is 0.
(b) (iii) the probability that a student scored at most 50 on the examination is 0.89.
Step-by-step explanation:
(a)
To make a cumulative frequency curve for the data first convert the class interval into continuous.
The cumulative frequencies are computed by summing the previous frequencies.
The cumulative frequency curve for the data is attached below.
(b)
(i)
The inter-quartile range is the difference between the third and the first quartile.
Compute the values of Q₁ and Q₃ as follows:
Q₁ is at the position:
[tex]\frac{\sum f}{4}=\frac{100}{4}=25[/tex]
The class interval is: 34.5 - 39.5.
The formula of first quartile is:
[tex]Q_{1}=l+[\frac{(\sum f/4)-(CF)_{p}}{f}]\times h[/tex]
Here,
l = lower limit of the class consisting value 25 = 34.5
(CF)[tex]_{p}[/tex] = cumulative frequency of the previous class = 24
f = frequency of the class interval = 20
h = width = 39.5 - 34.5 = 5
Then the value of first quartile is:
[tex]Q_{1}=l+[\frac{(\sum f/4)-(CF)_{p}}{f}]\times h[/tex]
[tex]=34.5+[\frac{25-24}{20}]\times5\\\\=34.5+0.25\\=34.75[/tex]
The value of first quartile is 34.75.
Q₃ is at the position:
[tex]\frac{3\sum f}{4}=\frac{3\times100}{4}=75[/tex]
The class interval is: 44.5 - 49.5.
The formula of third quartile is:
[tex]Q_{3}=l+[\frac{(3\sum f/4)-(CF)_{p}}{f}]\times h[/tex]
Here,
l = lower limit of the class consisting value 75 = 44.5
(CF)[tex]_{p}[/tex] = cumulative frequency of the previous class = 74
f = frequency of the class interval = 15
h = width = 49.5 - 44.5 = 5
Then the value of third quartile is:
[tex]Q_{3}=l+[\frac{(3\sum f/4)-(CF)_{p}}{f}]\times h[/tex]
[tex]=44.5+[\frac{75-74}{15}]\times5\\\\=44.5+0.33\\=44.83[/tex]
The value of third quartile is 44.83.
Then the inter-quartile range is:
[tex]IQR = Q_{3}-Q_{1}[/tex]
[tex]=44.83-34.75\\=10.08[/tex]
Thus, the inter-quartile range is 10.08.
(ii)
The maximum upper limit of the class intervals is 69.5.
That is the maximum percentile class score is 69.5th percentile.
So, the 70th percentile class scores is 0.
(iii)
Compute the probability that a student scored at most 50 on the examination as follows:
[tex]P(\text{Score At most 50})=\frac{\text{Favorable number of cases}}{\text{Total number of cases}}[/tex]
[tex]=\frac{10+4+10+20+30+15}{100}\\\\=\frac{89}{100}\\\\=0.89[/tex]
Thus, the probability that a student scored at most 50 on the examination is 0.89.
Related Questions
what is simplifying?
what is simplifying in math?
Answers
Answer:
Simplifying means making (something) simpler or easier to do or understand.
Simplification in math is the process of replacing a mathematical expression by resolving it or making it shorter.
Step-by-step explanation:
hope it will help :)
Can Someone please help me with this?
Answers
Answer:
9^18
Step-by-step explanation:
The applicable rule of exponents is ...
(a^b)^c = a^(bc)
__
[tex](9^3)^6=9^{3\cdot 6}=\boxed{9^{18}}[/tex]
In a multiplicative model, if the seasonal factor is 1.15 for a particular season, then we expect that the time series in that season would be (other things being equal
Answers
Answer:
15% above the trend.
Step-by-step explanation:
A time series represented by Y comprises of dataset observed over a particular period of time. Time series is handy in determining the future of a particular business.
In a multiplicative model, if the seasonal factor is 1.15 for a particular season, then we expect that the time series in that season would be
Y = T × C × S × 1
where;
Seasonal S = 1.15
As such Y would increase by 15% above the trend if all other things are being equal.
Can someone help me!!!
Answers
Answer:
Step-by-step explanation:
[tex]a.\\sin \theta =\frac{12}{13}\\\theta=sin ^{-1}(\frac{12}{13}) \approx 67^\circ\\b.\\cos75=\frac{x}{13}\\x=13 cos ~75 \approx 7.5 ~ft[/tex]
it forms a right angled triangle.
ladder=hypotenuse.
side of house=perpendicular.
from the base of house to the foot of ladder on the ground=base
Which value of x makes the equation true?
X + 7 = -9
A.-16
B.-2
C. 2
D.16
Answers
the answer is:
A. -16
Part 1: Use the transformations to prove congruency
Answers
Answer:
See Explanation
Step-by-step explanation:
[tex] \overline{CB} ||\overline {ED}... (GIVEN) \\
\& BD\:\&\: CE \: are \: transversals\\
\angle CBF\cong \angle EDF.. (alternate \: \angle 's) \\
\overline{CB} \cong \overline {ED}..... (GIVEN) \\
\angle BCF \cong \angle FED.. (alternate \: \angle 's) \\
\therefore \triangle CBF \cong \triangle EDF.. (By \: ASA\: Postulate) [/tex]
Answer: see proof below
Step-by-step explanation:
Statement Reason
1. CB || ED 1. Given
2. ∠E ≅ ∠C 2. Alternate Interior Angle Postulate
3. ∠D ≅ ∠B 3. Alternate Interior Angle Postulate
4. CB ≅ ED 4. Given
5. ΔCBF ≅ ΔEDF 5. ASA Congruency Theorem
PLZ HELP ME OUT Is 1.3 rational or irrational? Is 36 rational or irrational Is 3.14 or pi rational or irrational Is 2/3 rational or irrational
Answers
A rational number can be made by dividing two integers.
An irrational number cannot be made by dividing two integers.
1.3 is rational
36 is rational
2/3 is rational
Pi is not rational
Hey Jean’s grandmother is teaching him how to make a salsa recipe each batch of salsa requires one for 12 cup of red onions if they have one and a half cup of red onions how many batches of salsa can they make
Answers
Answer:
Number of salsa batches produced = 18 batches
Step-by-step explanation:
Given:
1 red onion = 12 batch of salsa
Amount of red onion = one and half (1.5)
Find:
Number of salsa batches produced
Computation:
Number of salsa batches produced = 1.5 × 12
Number of salsa batches produced = 18 batches
) A basketball court is 94 feet by 50 feet. Eight fans can
fit next to each other in a 3 ft. by 3 ft. area. How
many kids would you estimate can fit side by side
over the entire floor?
Answers
Answer:
4178kidsStep-by-step explanation:
Area of the basket ball court = Length * Breadth (since it is rectangular in nature)
Area of the basket ball court = 94 feet * 50 feet
Area of the basket ball court = 4700ft²
Area of the space covered by 8 kids = 3ft * 3ft = 9ft²
To know the number of kids that would fit the entire floor, we will use the expression;
Number of kids in the floor = 8*Area of the basket ball court /Area of the space covered by 8 kids = 8*4700/9
= 8*4700/9
= 8*522.22
≈ 4,178 kids
Hence approximately 4,178 kids can fit side by side over the entire floor
It is known that the birth weights of full-term newborn infants in the U.S. have an approximately normal distribution with a mean weight of 6.8 lbs and a standard deviation of 1.7. Approximately what proportion of newborn babies will have a birth weight between 6 lbs and 8 lbs? Provide all four decimal places in your answer.
Answers
Answer: 0.4419
Step-by-step explanation:
Given: The birth weights of full-term newborn infants in the U.S. have an approximately normal distribution with a mean weight of 6.8 lbs and a standard deviation of 1.7.
i.e. [tex]\mu=6.8\ \ \ \text{ and }\sigma= 1.7[/tex]
Let X denotes the birth weight.
Then, the proportion of newborn babies will have a birth weight between 6 lbs and 8 lbs is given by :-
[tex]P(6<X<8)=P(\dfrac{6-6.8}{1.7}<\dfrac{X-\mu}{\sigma}<\dfrac{8-6.8}{1.7})\\\\=P(-0.47<Z<0.71)\ \ \ [Z=\dfrac{X-\mu}{\sigma}] \\\\=P(Z<0.71)-(1-P(Z-0.47))\\\\=0.7611-(1-0.6808)\ \ \ [\text{By z-table}]\\\\= 0.4419[/tex]
Hence, the proportion of newborn babies will have a birth weight between 6 lbs and 8 lbs is 0.4419 .
what is the probability that the card drawn from a stack of 52 cards is a face card or a black card?
Answers
Answer: 8/13
Step-by-step explanation:
There are 52 cards in a deck.
26 cards are black --> P(Black) = 26/52
Face cards are J, Q, K. There are 12 face cards --> P(Face) = 12/52
6 Face cards are black --> P(both) = 6/52
Face card or Black card - both Face card & Black
[tex]\dfrac{26}{52}[/tex] + [tex]\dfrac{12}{52}[/tex] - [tex]\dfrac{6}{52}[/tex] [tex]=\dfrac{32}{52}[/tex]
[tex]\dfrac{32}{52}\div \dfrac{4}{4}=\dfrac{8}{13}[/tex]
What does a “3-mile” radius mean? What does it look like, and how large is it?
Answers
Answer:
the radius is halfway across the circle, while diameter is all the way across. for reference, a three mile radius would be equivalent to 52.8 football fields
Step-by-step explanation:
Perform the calculations and determine the absolute and percent relative uncertainty. Express each answer with the correct number of significant figures. To avoid rounding errors, do not round your answers until the very end of your calculations. [8.47(±0.06)]1/3=[8.47(±0.06)]1/3= absolute uncertainty: ±± percent relative uncertainty: ±± %% log[6.56(±0.05)]=log[6.56(±0.05)]= absolute uncertainty: ±± percent relative uncertainty ±± %%
Answers
Answer: (a). 0.2% (b). 0.4%
Step-by-step explanation:
This is quite straightforward, so let us follow this carefully.
(a) let us consider the expression that was given in the question;
(8.47 + 0.06)1/3 from the binomial expression,
⇒ (x + ∆x)n = xn + nxn-1∆x
So using the stated formula above
(8.47 + 0.06)1/3 = (8.47)1/3+ 1/3(8.47)1-(1/3) (0.06) = 2.038 + 1/3(8.47)(2/3) (0.06)
= 2.038 + 0.005
This gives us the algebric value as x = 2.038
Also, the uncertainity is ∆x = 0.005
Let us calculate the percentage of relative uncertainity;
Relative uncertainity percent is given thus;
⇒ (∆x / x) * 100
= (0.005 / 2.038) * 100 = 0.2%
We have that the relative uncertainity percent is 0.2%
(b). Also we will consider the expression;
log(6.56 + 0.05)
Let us apply the binomial expression to this;
log(6.56 + 0.05) = log(6.56) + ((0.05)2 / 6.56) = 0.817 + 0.003
This makes the algebric value of x = 0.817
and the uncertainity is ∆x = 0.003
Therefore the Relative uncertainity percent is = (∆x / x) * 100
= (0.003 / 0.817) * 100 = 0.4%
We have the relative uncertainity percent as 0.4%
cheers I hope this helped !!
If a=8 and b=5 and x=4 and y=6m -2 what is the value of m ?
Answers
Answer:
m = 2
Step-by-step explanation:
Given:
x = 4
y = 6m - 2
a = 8
b = 5
Required:
Value of m
SOLUTION:
x and y are segments of a chord divided when it intersects another chord that also has segments a and b.
According to the Intersecting chords theorem, [tex] a*b = x*y [/tex]
Thus:
[tex] 8*5 = 4*(6m - 2) [/tex]
Solve for m
[tex] 40 = 24m - 8 [/tex]
[tex] 40 + 8 = 24m - 8 + 8 [/tex]
[tex] 48 = 24m [/tex]
[tex] \frac{48}{24} = \frac{24m}{24} [/tex]
[tex] 2 = m [/tex]
The value of m = 2
Y=4x-3; A(5,17) Use substitution to determine whether the point is on the line.
Answers
Answer:
the point is on the line
Step-by-step explanation:
The ordered pair gives the values of (x, y). Put those values in the equation and see if it is true:
y = 4x -3
17 = 4(5) -3 = 20 -3 . . . . . . for (x, y) = (5, 17)
17 = 17 . . . . true, the point is on the line
a ladder 10 m long,leans against a vertical wall at an angle of 70° to the ground.if the ladder slips down the wall 4m,find,correct to 2 significant figure
(a) the new angle which the ladder makes with the ground
(b) the distance the ladder slipped back on the ground from it's original position
Answers
Answer:
(a) The new angle the ladder makes with the ground = 32.66°
(b) The distance the ladder slipped back on the ground from it's original position = 5 m
Step-by-step explanation:
The given parameters are;
The length of the ladder = 10 m
Angle of inclination of the ladder = 70°
Length to which the ladder slips down the wall = 4 m
(a) The height of the wall adjacent to the ladder = 10×sin(70°) ≈ 9.4 m
The new height of the wall adjacent to the ladder after the ladder slips down 4 m = 9.4 - 4 = 5.4 m
Therefore, the new angle of inclination of the ladder = sin⁻¹(5.4/10) = 32.66°
The new angle the ladder makes with the ground = 32.66°
(b) The distance the ladder slipped back on the ground from its original position is found as follows
The initial distance of the base of the ladder from the wall = 10 × cos(70°) = 3.42 m
The distance of the base of the ladder from the wall after slipping 4 m down the wall = 10 × cos(32.66°) ≈ 8.42 m.
Therefore, the amount by which the ladder slip back on the ground from its original position = 8.42 - 3.42 = 5 m.
The distance the ladder slipped back on the ground from it's original position = 5 m.
Johanna rode her bike 7 miles to a lake . She rode 3/4 of distance to the lake before lunch. How many miles did johanna ride before lunch?
Answers
Answer:
5.25 miles
Step-by-step explanation:
Total distance = 7 miles
Distance she rode before lunch = 3/4 of the total distance
=> 3/4 of 7
=> 21/4
=> 5.25 miles
So, she drove 5.25 miles before lunch.
What mixed
number represents thirty-eighths?
Answers
Answer:
............... 3 6/8
30/8
= 3.75
0.75=6/8
3 6/8
It can be simplified to 3 3/4
Translate into a variable expression.
the product of a number n and four more than the number
Answers
Reason: product is multiplication
Answer:
(x)n+4
Step-by-step explanation:
x=quantity multiplied by n for a product
n=a number
+4=4 more than the number
HOPE THIS HELPS!!!!!! :)
<3333333333
A temperature recorded in Antarctica was - 122°F. The temperature recorded in the Sahara Desert was 130°F. How many degrees warmer is 130°F than - 122°F?
ebook
Answers
Answer:
252* warmer
Step-by-step explanation:
130 -(-122) = 130 + 122 = 252
9 6/1 − 5 3/1 is equal to what?
Answers
Answer:
7
Step-by-step explanation:
Convert the mixed numbers to improper fractions, then find the LCD and combine.
Which of the following is an odd function?
f(x) = x3 + 5x2 + x
f (x) = StartRoot x EndRoot
f(x) = x2 + x
f(x) = –x
Answers
Answer: [tex]f(x)=-x[/tex]
Step-by-step explanation:
When f(-x)= -f(x), then it is known as an odd function.
i) [tex]f(x) = x^3 + 5x^2 + x[/tex]
Then, [tex]f(-x)=(-x)^3+5(-x)^2+(-x)=-x^3+5x^2-x\neq -x^3-5x^2-x[/tex]
i.e. [tex]f(-x)\neq-f(x)[/tex]
ii) [tex]f(x)=\sqrt{x}[/tex]
[tex]f(-x)=\sqrt{-x}\neq-\sqrt{x}[/tex]
i.e. [tex]f(-x)\neq-f(x)[/tex]
iii) [tex]f(x)=x^2+x[/tex]
[tex]f(-x)=(-x)^2+(-x)=x^2-x\neq-x^2-x[/tex]
i.e. [tex]f(-x)\neq-f(x)[/tex]
iv) [tex]f(x)=-x[/tex]
[tex]f(-x)=-(-x)=x[/tex]
[tex]-f(x)=-(-x)=x[/tex]
i.e. [tex]f(-x)=-f(x)[/tex]
Hence, f(x) is an odd function.
Answer:
D
Step-by-step explanation:
if you don't want to read
Geometry: Find the value of x.
X = [?]°
Answers
Answer:
x = 25°
Step-by-step explanation:
The secant- secant angle DGB is half the difference of the intercepted arcs, that is
[tex]\frac{1}{2}[/tex] ( BD - FE) = 55
[tex]\frac{1}{2}[/tex](135 - x) = 55 ( multiply both sides by 2 )
135 - x = 110 ( subtract 135 from both sides )
- x = -25 ( multiply both sides by - 1 )
x = 25°
Find the value of 4!.
Answers
☺ Hi ☺
Find the value of 4!.
• Let's find the value of 4! :
[tex]4! = 4 × 3 × 2 × 1 = {24}[/tex]
What is the value of 4 in the number 45?
Answers
Answer:
40
Step-by-step explanation:
4 is in "Ten's place".
So, the number is multiplied with 10.
=> 4 x 10
=> 40
The value of 4 in 45 = 40
Solve equation x-9= -12
Answers
Answer: x=-3
Step-by-step explanation:
move -9 over to -12 and the 9 becomes positive and then add -12+9 and your answer will be negative
+9=+9
————
X=46
What is the prime factorization of 315?
Answers
In triangle abc, the length of side and is 10 inches and the length of side be is 17 inches . Which of the following could be the length of side ac
Answers
Answer:
a^2=b^2+c^2.
a^2=10^2+17^2.
a^2=100+289.
a^2=389.
a=√389.
a=19.72~20cm.
Determine if ΔABC and ΔFHG are similar. If so, write the similarity statement.
options:
A) The triangles are not similar
B) ΔABC ∼ ΔHFG
C) Impossible to determine.
D) ΔABC ∼ ΔFHG
Answers
Answer:
[tex]\Large \boxed{\mathrm{D) \ \triangle ABC \sim \triangle FHG }}[/tex]
Step-by-step explanation:
The two triangles are similar.
The corresponding sides are proportional.
AB ∼ FH
[tex]\displaystyle \frac{72}{12} =6[/tex]
AC ∼ FG
[tex]\displaystyle \frac{48}{8} =6[/tex]
BC ∼ GH
[tex]\displaystyle \frac{84}{14} =6[/tex]
Convert 330 meters per second (m/s) to kilometers per minute (km/min). A) 1.98 x 10^1 km/min B) 1.98 x 10^-1 km/min C) 1.98 x 10^2 km/min D) 1.98 x 10^-2 km/min
Answers
Answer:
A
Step-by-step explanation:
330 m/s=330×60 m/min=19800/1000 km/min=198 km/min=1.98×10^1 km/min