Professor Hopkins is grading the final exam. She notices that the
mean test score is 71, and the standard deviation is 6. The test
scores were normally distributed.
If there were 300 students in the data sample, how many would
have a test score between 71 and 83?*
*Round your answer to the nearest whole value.
students
Answers
Answer:
143
Step-by-step explanation:
The interval of interest extends from the mean score (71) to 2 standard deviations above the mean (71+2(6) = 83). The area under the normal distribution curve in this interval can be found using a suitable table, probability app, spreadsheet, or web site. It can also be found using the "empirical rule", which tells you that the 95% of the area is within 2 standard deviations of the mean.
__
Since the curve is symmetrical, and we're only interested in the area above the mean, the empirical rule tells us that 95%/2 = 47.5% of the sample will be in the range of interest.
0.475 × 300 = 142.5 ≈ 143
143 students will have a score between 71 and 83.
__
The attachment shows a calculator output for the same calculation. You will notice it is slightly different from the "empirical rule," which is only an approximation. Either way, we find 143 students have scores in the range.
Related Questions
Help pls!
Which rational function has zeros at x = -1 and x = 6 ?
Answers
Answer:
[tex]f(x) = \frac{x^{2} -5x-6}{x^{2} -4}[/tex]
Step-by-step explanation:
Let's factorize the 1st option :
⇒ [tex]f(x) = \frac{x^{2} -5x-6}{x^{2} -4}[/tex]
⇒ [tex]f(x) = \frac{x^{2}+x-6x-6 }{(x+2)(x-2)}[/tex]
⇒ [tex]f(x) = \frac{(x+1)(x-6)}{(x+2)(x-2)}[/tex]
===============================================================
Finding the zeros :
⇒ Factors of numerator should be equated to 0
x + 1 = 0 ⇒ x = -1x - 6 = 0 ⇒ x = 6=============================================================
Solution :
[tex]f(x) = \frac{x^{2} -5x-6}{x^{2} -4}[/tex]
Answer:
first option
Step-by-step explanation:
the zeros are determined by the numerator of the rational function.
given that the zeros are x = - 1 and x = 6 , then the corresponding factors are
(x + 1) and (x - 6) , that is
(x + 1)(x - 6) ← expand using FOIL
= x² - 5x - 6
the rational function is then
f(x) = [tex]\frac{x^2-5x-6}{x^2-4}[/tex]
PLEASE HELP!
The chart shows the relationship between the cost of internet service per month and degree of customer satisfaction.
Based on a linear model, what would you expect a customer to rate their satisfaction for an internet plan that costs $10 per month. Give your answer to 2 decimal places
Answers
A customer that uses an internet plan that costs $10 per month is expected to give a customer rating of 6
How to determine the customer rating?We start by calculating the regression equation of the table of values using a graphing calculator.
Using the graphing calculator, we have:
y = 0.04x + 5.75
When the cost is $10 per month, it means that
x = 10
So, we have:
y = 0.04 * 10 + 5.75
Evaluate
y = 6.15
Approximate
y = 6
Hence, a customer that uses an internet plan that costs $10 per month is expected to give a customer rating of 6
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a fruit vendor bought 75 Kg of bananas she gave 10kg of the bananas to a poor family she sold the remainder at $28 per kg if she make a loss of $55 on the transaction calculate the cost price of the bananas
Answers
Answer:
$25
Step-by-step explanation:
the fruit vendor sold 75-10 = 65 kg of bananas. 65*28 = 1820 dollars. so the fruit vendor earned 1820 dollars.
since she lost 55 dollars, 75 * cost = 1875, divide by 75 to get cost = 25
Is not a polygon because ???
Answers
Answer:
The shape includes a curve; all polygons are supposed to have straight sides, which this shape does not.
Answer: The shape includes a curve
Step-by-step explanation:
Polygons are closed shapes with at least three straight sides.
This shape is closed, but it includes a curve. This means the answer to our question is the second option from the top,
"The shape includes a curve"
What figure is graphed from the following points? Graph the figure. (0, 2) (2, 7) (4, 2) (6, 7)
Answers
Answer:
Rhombus
Step-by-step explanation:
The first and third points have the same y-coordinate along with the second and fourth. None have the same x-coordinate. This figure has two sets of parallel sides but no right angles.
What table represents a linear function
Answers
Considering the constant rate of change, it is found that table 1 represents a linear function.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.From the concept of the slope, we have that the rate of change of a linear function is constant, that is, when x changes by 1, y has to change always by the same amount, which happens in table 1, with a constant rate of change of 1/2 = 0.5.
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Donna is making a cookie recipe that calls for 1 ¾ cups of sugar. However, when she
goes to take out the measuring cups she can only find the one-half cup measuring cup. How many one-half cups will she need to fill to get the correct amount of sugar for her cookie recipe?
Answers
Answer:
3 and 1/2 half-cups
Step-by-step explanation:
We are asked to find the number of half-cups that will equal 1 3/4 cups.
__
Let the desired number be represented by n. Then we require ...
n × 1/2 = 1 3/4 . . . . some number of 1/2-cups will give 1 3/4 cups
Using a common denominator, we have ...
n × 2/4 = 7/4
Multiplying by the inverse of the coefficient of n gives ...
n × 2/4 × 4/2 = 7/4 × 4/2
n = 7/2 = 3 1/2 . . . . . simplify
That is, Donna can measure 1 3/4 cups of sugar by using her 1/2-cup measure 3 times, and filling it half-full for the final 1/4 cup she needs.
She needs 3 1/2 half-cups to get the correct amount.
Through a regular hexagon whose base edge is 8cm and whose height ii 12cma hole in the shape of the right prism with ots end being rhombus with diagonals of 6cm and 8cm is drilled find the total surface area and volume of the remaining soild?
Answers
The total surface area of the remaining solid is 48(4+✓3) centimeters square.
How to calculate the surface area?Through a regular hexagonal prism whose base edge is 8 cm and the height is 12 cm, a hole in the shape of a right prism.
The formula for the total surface area will be:
= Total surface area=2(area of the base)+ parameter of base × height
where,
Height= 8cm
Parameter of base=12(2) = 24
Area of the base= 6×✓3/4×4² = 64✓3/4
The surface area of the remaining solid will be:
= 2(64✓3/4) + 24 × 8
= 2(64✓3/4 + 192
With the hole is a rhombus prism with the following parameters:
diagonal 1 = 6, diagonal 2 = 8, height = 12
The volume is:
V1 =0.5 × d1 × d2 × h
V1 = 0.5 × 6 × 8 × 12
V1 = 96
The dimensions of the hexagonal prism are:
Base edge (a) = 8
Height (h) = 12
The volume is
V2 = (3✓(3)/2)a²h
V2 = (3✓3)/2) × 8² × 12
V2 = 1152✓3
The remaining volume is
V = V2 -V1
V = 1152✓3 - 96
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Please help
Francine has a picture with a length its width. She wants to enlarge the picture to have an area of 375 in2. What will the dimensions of the enlarged picture be? Model the scenario and solve. Then, explain in at least one sentence your solution and include the reasonableness of your solution.
Answers
Answer:
25 in x 15 in
Step-by-step explanation:
Given:
Length = 3/5 the widthArea = 375 in²Let width = [tex]x[/tex]
Therefore, length = 3/5 [tex]x[/tex]
First create an equation for the area of the picture based on the given information for its width and length:
[tex]\begin{aligned} \implies \textsf{Area of original picture} & = \sf width \times length\\& = x\left(\dfrac{3}{5}x\right)\\& = \dfrac{3}{5}x^2\end{aligned}[/tex]
We are told the area of the enlarged picture is 375 in². Therefore, substitute this into the equation and solve for [tex]x[/tex] to find the width of the enlarged picture:
[tex]\begin{aligned}\textsf{Area} & = 375\\ \implies \dfrac{3}{5}x^2 & = 375\\ x^2 & =375 \cdot \dfrac{5}{3}\\ x^2 & =625\\ x & = \sqrt{625}\\ x& = 25\end{aligned}[/tex]
Therefore, the width of the enlarged picture is 25 in.
Substitute the found value of [tex]x[/tex] into the expression for length to find the length of the enlarged picture:
[tex]\begin{aligned}\sf Length & = \dfrac{3}{5}x\\\\\implies \sf Length & = \dfrac{3}{5}(25)\\\\& = 15\: \sf in\end{aligned}[/tex]
Therefore, the dimensions of the enlarged picture are 25 in x 15 in. The width is 25 in and the length is 15 in, as the length is 3/5 of the width.
Answer:
correct
Step-by-step explanation:
use the probability model listing all 6 possible outcomes when rolling a six-sided number cube. what is the probability of rolling 5 or greater
Answers
Answer:
The probability of it rolling 5 or above is 45%
Step-by-step explanation:
I have passed the test of it
You have two sticks. each stick has one blue side and one pink side. you throw the sticks 10 times and record the results. use the table to find the experimental probability of the event.
1. tossing 2 pink
2. tossing 1 blue and 1 pink
3. not tossing all pink
outcome | frecuency
2 blue | 1
2 pink | 3
1 blue, 1 pink | 6
Answers
Answer:
1. 30%, 2. 60%, 3. 70%Step-by-step explanation:
According to table the total frequencies is:
1 + 3 + 6 = 10Probability = Favorable outcome frequency / total frequency
Find each probability according to equation above:
1. P(2 pink) = 3/10 = 30%2. P(blue and pink) = 6/10 = 60%3. P(not all pink) = (10 - 3)/10 = 7/10 = 70%The experimental probability of the event are: 3/10; 3/5; 7/10.
Experimental probabilityFrequencies=1 + 3 + 6
Frequencies = 10
Hence:
Tossing 2 pink:
P(2 P) = 3/10
P(2 P) =30%
Tossing 1 blue and 1 pink:
P(B and P) = 6/10
P(B and P)=60% or 3/5
Not tossing all pink:
P(not all P) = (10 - 3)/10
P(not all P)= 7/10
P(not all P)=70%
Therefore the experimental probability of the event are: 3/10; 3/5; 7/10.
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On Monday the temperature was -7 degrees Fahrenheit in Akron Ohio on Tuesday the temperature was colder than Monday what is a possible temperature in degrees Fahrenheit for Tuesday
Answers
the degrees Fahrenheit is -9
I need help to this equation Ive been stuck for awhile
Answers
Answer:
try 1500 in the top slot and 5 in the bottom slot
Step-by-step explanation:
Please help soon!!!!!!
Answers
Solving the exponential function, it is found that the times that will take to have the desired measures are given by:
a) 3.6 hours.
b) 38.51 hours.
c) 56.98 hours.
What is the exponential function for the amount of Carbon-10 after t hours?The function is given by:
[tex]A(t) = 140(0.5)^{\frac{t}{19.255}}[/tex]
Solving for t, we have that:
[tex](0.5)^{\frac{t}{19.255}} = \frac{A(t)}{140}[/tex]
[tex]\log{(0.5)^{\frac{t}{19.255}}} = \log{\frac{A(t)}{140}}[/tex]
[tex]\frac{t}{19.255} = \frac{\log{\frac{A(t)}{140}}}{\log{0.5}}[/tex]
[tex]t = 19.255\frac{\log{\frac{A(t)}{140}}}{\log{0.5}}[/tex]
In item A, we have that A(t) = 123, hence:
[tex]t = 19.255\frac{\log{\frac{123}{140}}}{\log{0.5}}[/tex]
t = 3.6 hours.
In item B, we have that A(t) = 35, hence:
[tex]t = 19.255\frac{\log{\frac{35}{140}}}{\log{0.5}}[/tex]
t = 38.51 hours.
In item C, we have that A(t) = 18, hence:
[tex]t = 19.255\frac{\log{\frac{18}{140}}}{\log{0.5}}[/tex]
t = 56.98 hours.
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Find the width of the rectangle shown with an area of 18 mm2 and a length of 6 mm.
Answers
Area = 18
Length = 8
Width = ?
Area = length * width
(Substitute the values)
18 = 6 * width
Width = 18 / 6
Width = 3mm
Therefore, width of the rectangle is 3mm
To check if the answer is correct
Area = length * width
Area = 6 * 3
Area = 18 mm2
solve
[tex] \frac{2x - 3}{4} = 3x[/tex]
with working out pls
Answers
[tex]~~~~~~\dfrac{2x-3}{4} = 3x\\\\\implies 2x-3 = (3x)(4)\\\\\implies 2x -3 = 12x \\\\\implies 12x -2x = -3\\\\\implies 10x = -3\\\\\implies x = -\dfrac{3}{10}[/tex]
Answer:
x = -3/10
Step-by-step explanation:
Given :
[tex]\frac{2x-3}{4} = 3x[/tex]
============================================================
Multiply both sides with 4 :
⇒ [tex]4 \times \frac{2x-3}{4} = 4 \times 3x[/tex]
⇒ 2x - 3 = 12x
============================================================
Subtract 2x from both sides :
⇒ 2x - 3 - 2x = 12x - 2x
⇒ -3 = 10x
⇒ x = -3/10
Which piece of additional information can be used to prove CEA CDB
Answers
Based on the angle-angle similarity theorem, the piece of additional information can be used to prove ΔCEA ≅ ΔCDB is: A. ∠BDC and ∠AED are right angles.
What is the Angle-angle Similarity Theorem?Based on the angle-angle similarity theorem, if two triangles have two pairs of corresponding angles that are congruent, then both triangles are similar.
In the diagram given, we can establish that the two triangles have one pair of congruent angles, ∠CEA ≅ ∠CDB.
Thus, an additional information that is needed to prove that both triangles are similar is: A. ∠BDC and ∠AED are right angles.
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Answer: A. ∠BDC and ∠AED are right angles
Step-by-step explanation:
Please helpp!!!!!! Quick
Answers
The area of the parallelogram in the given diagram is 103.68 cm²
Calculating area of ParallelogramFrom the question, we are to determine the area of the given parallelogram
The area of a parallelogram can be calculated by using the formula,
A = bh
Where A is the area
b is the base
and h is the perpendicular height
From the given diagram,
b = 14.4 cm
h = 7.2 cm
Putting the parameters into the equation, we get
A = 14.4 × 7.2
A = 103.68 cm²
Hence, the area of the parallelogram in the given diagram is 103.68 cm²
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On a coordinate plane, triangle B C D is rotated 180 degrees clockwise to form triangle B prime C prime D prime. Identify the angle of rotation that maps triangle BCD to triangle B’C’D’. What is the angle of rotation? 90° 180° 270° 360°
Answers
Answer:
180
Step-by-step explanation:
2. At the sale, Jessica bought 4 pairs
sunglasses. How much did she
of
spend?
8.78176.60
A $51.58
B $51.80
C$55.80
D$54.80
Answers
Please help I don't Understand!
Answers
Answer: SAS similarity theorem
Proportional relationship:
[tex]\sf \dfrac{AB}{AC} = \dfrac{AM}{AN}[/tex]
insert values
[tex]\rightarrow \sf \dfrac{21+9}{14+6} = \dfrac{21}{14}[/tex]
simplify
[tex]\rightarrow \sf 1 = 1[/tex]
L.H.S = R.H.S
The triangles are congruent and follows the rule SAS similarity theorem.
The triangles has/starts from the same angle, corner (A).
Which statement is true about angles 3 and 6?
A. They Are adjacent angeles
B. They Are complementary angles
C. They are supplementary angles
D. They are vertical angles
Answers
Answer: They are vertical angles
Step-by-step explanation:
Intersecting lines form vertical angles.
On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 7) and (0, 2). Everything to the left of the line is shaded.
Which is the graph of the linear inequality y < 3x + 1?
On a coordinate plane, a solid straight line has a positive slope and goes through (negative 1, negative 2) and (0, 1). Everything to the left of the line is shaded.
On a coordinate plane, a solid straight line has a positive slope and goes through (negative 1, negative 2) and (0, 1). Everything to the right of the line is shaded.
On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 1, negative 2) and (0, 1). Everything to the left of the line is shaded.
On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 1, negative 2) and (0, 1). Everything to the right of the line is shaded.
Answers
The attached graph represents the graph of the inequality
How to determine the graph of the inequality?The points on the line are given as:
(-3,-7) and (0,2)
Start by calculating the linear equation using:
[tex]y = \frac{y_2 -y_1}{x_2 -x_1}(x -x_1) + y_1[/tex]
This gives
[tex]y = \frac{2 + 7}{0 + 3}(x -0) + 2[/tex]
Evaluate the fraction expression
y = 3(x -0) + 2
Evaluate the difference
y = 3x + 2
From the question, we understand that the line of the inequality is a dashed line and the left of the line is shaded.
This means that the inequality is greater than i.e. >
So, we have:
y > 3x + 2
See attachment for the graph of the inequality
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pls help!!!! i have eight more minutes to answer
eeeeeeeeee
Answers
Step-by-Step Explanation:
As we can observe from the graph,
Length (l) = 5 units
Breadth (b) = 3 units
Perimeter = 2(l + b)
Therefore,
= 2(l + b)
= 2(5 + 3)
= 2(8)
= 2 * 8
=> 16
Perimeter = 16 units
What is the value of the expression below when y=2 6y^2 +8y-9
Answers
Answer:
6y^2+7
Step-by-step explanation:
when you put in the two for y you get tour answer. i tried to simplify it down to the simplest form.
The value of the expression 6y² + 8y - 9 at y = 2 is 31.
What is substitution?Substitution in mathematics is when we replace some specific numerical values with variables according to our wants or given in the problem.
Given, An expression 6y² + 8y - 9.
Now, The value of the expression at y = 2, can be obtained by replacing
y = 2.
Therefore, 6(2)² + 8(2) - 9.
= 6(4) + 16 - 9.
= 24 + 16 - 9.
= 40 - 9.
= 31.
So, The value of the expression at y = 2 is 31.
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!!! PLEASE HELP FAST !!!!
The school that Nicole goes to is selling tickets to a play. On the first day of
ticket sales the school sold 7 adult tickets and 5 student tickets for a total of
$105. The school took in $84 on the second day by selling 7 adult tickets and 2
student tickets. What is the price each of one adult ticket and one student
ticket?
A) adult ticket: $7, student ticket: $10
C) adult ticket: $11, student ticket: $6
B) adult ticket: $5, student ticket: $10
D) adult ticket: $10, student ticket: $7
Answers
Answer:
the answer is d
Step-by-step explanation:
1st day : 7 × 10 = 70
5 × 7 = 35 70+ 35= 105
2nd day : 7 × 10 = 70
2 × 7 = 14 70+14 = 84
Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.
y = 4200 (1.07)
Answers
For the given exponential function there will be an exponential growth of 7%.
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and independent variable.
we have
[tex]f(x) = 4200(1.07)^x[/tex]
This is an exponential function of the form
[tex]f(x)=ab^x[/tex]
where
a - is the initial value
b - is the base
If b > 1 ----> is a exponential growth
0 < b < 1 ----> is a exponential decay
r is the per cent rate
b = 1 + r
In this problem we have
a = 4200
b = 1.07
We can see that 1.07 > 1 -----> is a exponential growth
Find out the per cent rate
b = 1 + r
r = 1.07 - 1
r = 0.07
r = 7 x 100 = 7%
Therefore the given exponential function there will be an exponential growth of 7%.
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4.5:2.25 in n:1 how would i solve this
Answers
The required ratio is 2:1.
We have given that,
4.5:2.25
Since we have given that
We need to find the ratio in the form of n:1.
What is the ratio?
A ratio indicates how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six. Similarly, the ratio of lemons to oranges is 6:8 and the ratio of oranges to the total amount of fruit is 8:14.
so, it becomes,
[tex]=\frac{4.5}{2.25}:1\\\\=2:1[/tex]
Hence, the required ratio is 2:1.
Express the ratio in the simple form
4.5:3 1/2.
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can i have help with this
Answers
Answer:
6^a+v
Step-by-step explanation:
a^m * a^n = a^(m+n)
so, 6^a * 6^v = 6^a+v
Answer:
[tex] {6}^{a+v} [/tex]
Step-by-step explanation:
We want to find the value of
[tex]{6}^{a} \times 6 ^{v} [/tex]
We can do so by using basic exponent laws.
Multiplying exponents with the same base law:
(note that the base is the number under the exponent, in this case both bases have a value of 6 so we use this law)
[tex]a ^{m} \times {a}^{n} = {a}^{m+n} [/tex]
Explanation of law : We simply keep the bases the same and add the exponents.
Applying this law to 6^a * 6^v
We acquire
6^a * 6^v
==> keep the bases the same and add the exponents
6^a+v
You deposit $150 into an account that yields 2% interest compounded quarterly. how much money will you have after 5 years?
Answers
Answer:
2 divided by 100 multiply 150