SAT verbal scores are normally distributed with a mean of 433 and a standard deviation of 90. Use the Empirical Rule to determine what percent of the scores lie between 433 and 523.
Answers
34% of the scores lie between 433 and 523.
Solution:
Given data:
Mean (μ) = 433
Standard deviation (σ) = 90
Empirical rule to determine the percent:
(1) About 68% of all the values lie within 1 standard deviation of the mean.
(2) About 95% of all the values lie within 2 standard deviations of the mean.
(3) About 99.7% of all the values lie within 3 standard deviations of the mean.
[tex]$Z(X)=\frac{x-\mu}{\sigma}[/tex]
[tex]$Z(433)=\frac{433-\ 433}{90}=0[/tex]
[tex]$Z(523)=\frac{523-\ 433}{90}=1[/tex]
Z lies between o and 1.
P(433 < x < 523) = P(0 < Z < 1)
μ = 433 and μ + σ = 433 + 90 = 523
Using empirical rule, about 68% of all the values lie within 1 standard deviation of the mean.
i. e. [tex]((\mu-\sigma) \ \text{to} \ (\mu+\sigma))=68\%[/tex]
Here μ to μ + σ = [tex]\frac{68\%}{2} =34\%[/tex]
Hence 34% of the scores lie between 433 and 523.
Using the Empirical Rule for normally distributed scores, about 34% of SAT verbal scores lie between 433 (mean) and 523 (mean plus one standard deviation).
Explanation:The Empirical Rule, also known as the 68-95-99.7 rule, applies to a normally distributed set, as we have here with SAT verbal scores. This rule states that approximately 68% of the data falls within one standard deviation from the mean in a normal distribution.
In this scenario, the mean (average) SAT verbal score is 433, the standard deviation is 90. We're going to find what percent of the scores lie between 433 (mean) and 523 (mean plus one standard deviation).
According to the Empirical Rule, approximately 68% of the scores fall within one standard deviation of the mean (both above and below). So about 34% of the scores fall between the mean and one standard deviation above the mean. Thus, about 34% of the students scored between 433 and 523 on the SAT verbal section.
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Related Questions
A family ordered some candy bars and bags of chips for snacking. The number of candy bars was twice as much as the number of bags of chips. If the family spent a total of $5.50, how many bags of chips did the family buy?
Answers
Answer:
The family bought approximately 2 bags of chips.
Step-by-step explanation:
Given:
Total spent by family = $5.50
We need to find bags of chips did the family buy.
Solution:
Let number of bags of chips bought be 'x'.
Also Given:
The number of candy bars was twice as much as the number of bags of chips.
number of candy bars = [tex]2x[/tex]
Now we can say that;
Total spent by family is equal to sum of the number of bags of chips bought and number of candy bars.
framing in equation form we get;
[tex]x+2x=5.5\\\\3x=5.5[/tex]
Dividing both side by 3 we get;
[tex]\frac{3x}{3}=\frac{5.5}{3}\\\\x=1.83\approx2[/tex]
Hence the family bought approximately 2 bags of chips.
An Investment of $2,000 is earning interest at the rate of 6.2% compounded quarterly over 5 years. Approximately how much
interest is earned on the investment?
Answers
Answer: $720.37
Step-by-step explanation:
interest = 2000(1.0155)^20 - 2000
= 720.37
Hope this helps!!! Good luck!!! :)
30 divided by 18 into improper fraction
Answers
Answer:
5/3
Step-by-step explanation:
30/18
you can easily simplify a large improper fraction by finding a common number.
in this case the number is 6.
6x5=30 & 6x3=18
therefore, if you divide each number by 6 you get 5/3
decimal: 1.66667 or 1.67 or 1.7
improper fraction: 5/3
proper fraction 1 2/3
Final answer:
30 divided by 18 as an improper fraction is ⅓, or 5/3, obtained by converting the division result into a mixed number and then back into an improper fraction.
Explanation:
To convert 30 divided by 18 into an improper fraction, you first divide 30 by 18 to get the decimal form, which is approximately 1.666. To express this as an improper fraction, we recognize that 1.666 is 1 and 2/3 in mixed number form.
Since 2/3 is already a fraction, we can convert the mixed number back into an improper fraction by multiplying the whole number 1 by the denominator 3 and then adding the numerator 2. This gives us 3 + 2 = 5, so the improper fraction is 5/3.
Mark buys 6 notebooks for $9.Steven buys 4 notebooks of the same time for $6.Which of the following points is not on the graph of the relationship between notebooks and price?
Please help as soon as you can
Answer Choices:
F(3,4.50)
G(8,12)
H(7,10.50)
J(12,16)
Answers
Answer:
F, G, H
Step-by-step explanation:
$9/6 = $1.5
$6/4 = $1.5
The price is $1.50 per notebook.
Every point on the graph must have a y-coordinate that is 1.5 times the x-coordinate.
The function is y = 1.5x
F(3,4.50) 3 * 1.5 = 4.5 Yes
G(8,12) 8 * 1.5 = 12 Yes
H(7,10.50) 7 * 1.5 = 10.5 Yes
J(12,16) 12 * 1.5 = 18 No
What is 2/15+8/15 in simplest form
Answers
Answer:2/3
Step-by-step explanation:
So you add 8 plus 2 And keep the denominator the same and then simplify with 5
The student council is planning the school carnival. Each ticket costs $2.50. Explain how to write an equation that represents this scenario. Let x represent the number of tickets sold, and y represent the total amount of money raised.
Answers
Answer:
Step-by-step explanation:
Let x represent the number of tickets sold, and y represent the total amount of money raised. Since each ticket is $2.50, the total amount of money raised is equal to $2.50 times the number of tickets. The equation would be y = 2.50x.
Answer:
y=2.5x
The total amount of money raised(y) = how many tickets are sold(x) x the price per ticket(2.5)
Hypothetically, if 24 tickets were sold, we could substitute 24 into x...
y=2.5(24)
y=60
Let x represent the number of tickets sold, and y represent the total amount of money raised. Since each ticket is $2.50, the total amount of money raised is equal to $2.50 times the number of tickets. The equation would be y = 2.50x.
The x variable represents the number of tickets sold.
The y variable represents the total amount of money raised from ticket sales.
The equation for the scenario is y = 2.50x.
Solve for y. y + 1.05 = 7.26 y = -6.21 y = -8.31 y = 6.21 y = 8.31
Answers
To solve for 'y' in the equation 'y + 1.05 = 7.26', subtract 1.05 from both sides of the equation, the answer is 'y = 6.21'.
Explanation:In mathematics, solving for 'y' involves rearranging the equation to isolate the 'y' variable. In this case, the equation is 'y + 1.05 = 7.26'.
To solve for y, begin by performing the inverse operation of addition on both sides of the equation. This means subtracting 1.05 from both sides.
After doing so, the equation would look like this:
So the solution for y in this equation is 6.21.
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xavier sells homemade necklaces for a profit of $22 per necklace. he is considering switching to a new type of pendant that will increase his profit, as expressed by the function y=29x, where x is the number sold and y is the amount of profit. how many more dollars will xavier earn on each necklace if he switches to the new material?
Answers
Answer:
29 dollars each
Answer:
$7 more
Step-by-step explanation:
According to the question, Xavier sells homemade necklaces for a profit of $22 per necklace .
Now, he’s considering switching to a new type of pendant that will increase his profit as expressed by
y = 29x
Where x = number sold and
y = amount of profit
From the expression, if he sells one necklace made with the new type of pendant ,
y = 29 x 1
= $29
Remember he makes $22 per necklace already .
$ earns if he switches to the new pendant = $29 - $22
= $7
He’ll earn $7 more if he switches to the new material
What is the slope of (0,1) and (5,4)
Answers
Answer:
3/5
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(4-1)/(5-0)
m=3/5
What is the value of X: X^2=9/144
Answers
Answer:
3/12
Step-by-step explanation:
To solve this problem, we can use square roots. Due to x being squared, we can square root both the top and the bottom. The square root of 9 is 3 with 144 being 12. In the end, x equals 3/12
[tex]\text{Hey there!}[/tex]
[tex]\mathsf{What\ is\ the\ value\ of\ x: x^2=\dfrac{9}{144}\ ?}[/tex]
[tex]\mathsf{First,\ you\ have\ to\ simplify\ both\ sides\ of\ your\ equation!}[/tex]
[tex]\mathsf{\dfrac{9}{144}= \dfrac{9\div9}{144\div9} = \boxed{\dfrac{1}{16}}}[/tex]
[tex]\mathsf{New\ equation\ (for\ now): x^2=\dfrac{1}{16}}[/tex]
[tex]\mathsf{Take\ your\ square\ root!}[/tex]
[tex]\mathsf{x=\pm\sqrt{\dfrac{1}{16}}}[/tex]
[tex]\boxed{\boxed{\mathsf{Thus,\ your\ answer\ is: x =0.25\ or\ x = -0.25}}}[/tex][tex]\boxed{\boxed{\checkmark}}[/tex]
[tex]\boxed{\boxed{\boxed{\mathsf{You\ could\ also\ say\ x= \dfrac{3}{12}\ or\ x=-\dfrac{3}{12}}}}}[/tex][tex]\boxed{\boxed{\boxed{\checkmark}}}[/tex]
[tex]\mathsf{Side\ note: that's\ when\ the\ plus\ or\ minus\ sign\ (\pm)\ came\ in\ handy!}[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
What is the area of a triangle with A = 15°, B= 113', and b = 7?
a. 3.8 units
c. 5.4 units
b. 4.2 units
d. 4.4 units
Answers
Answer:
The answer is C, 5.4 units
Step-by-step explanation:
: Kara works at a fine jewelry store and earns commission on her total sales for the week. Her weekly paycheck was in the amount of $6,500, including her salary of $1,000. Her sales for the week totaled $25,000. Express her rate of commission as a percent. Round to the nearest whole number.
Answers
Answer:
[tex]Rate\ of\ commission=22\%[/tex]
Step-by-step explanation:
Let her rate of commission[tex]=x\%[/tex]
Salary[tex]=\$ 1000[/tex]
Weekly Amount[tex]=\$ 6500[/tex]
So earning from commission=Weekly Amount-Salary
Earning from the commission[tex]=6500-1000[/tex]
Earning from the commission[tex]=\$ 5500[/tex]
Total Sales[tex]=\$ 25000[/tex]
Commission is[tex]=x\%\ of\ 25000[/tex]
[tex]x\%\ of\ 25000=5500\\\\\frac{x}{100}\times 25000=5500\\\\x\times 250=5500\\\\x=\frac{5500}{250}\\\\x=22\%[/tex]
[tex]Rate\ of\ commission=22\%[/tex]
I have 60 coins both quarters and dimes. The combined total is 9.45. What are two equations I can use to solve this problem?
Answers
Answer:
q+d = 60.25q +.10d = 9.45Step-by-step explanation:
Assuming the problem you want to solve is finding the number of each coin, you can let variables represent those numbers. I like to use mnemonic variables, such as q for the number of quarters, and d for the number of dimes.
The two equations you can write are based on the given information:
q + d = 60 . . . . . . you have 60 coins
.25q +.10d = 9.45 . . . . . their value is 9.45
_____
You have 23 quarters and 37 dimes.
_____
I like to solve these by substitution, using an expression to replace the variable representing the lowest-value coin.
d = 60 -q . . . . . . . expression for the number of dimes
.25q +.10(60 -q) = 9.45
.15q +6.00 = 9.45 . . . . . eliminate parentheses, collect terms
.15q = 3.45 . . . . . . . . . . .subtract 6.00
q = 23 . . . . . . . . . . . . . . . divide by 0.15
d = 60 -q = 37
write an equation in slope - intercept form, and then find the slope and y- intercept 3x-y=14
Answers
Answer:
slope-intercept form: y = 3x - 14
slope: 3
y-intercept: -14
Step-by-step explanation:
To find the equation in slope-intercept form, isolate the "y" variable by moving everything to the other side. Slope-intercept form looks like y = mx + b.
"x" and "y" mean points that are on the line.
"m" is the slope.
"b" is the y-intercept.
Rearrange the equation to isolate "y"
3x - y = 14
3x - 3x - y = 14 - 3x Subtract 3x from both sides
-y = 14 - 3x Multiply both sides by -1.
y = -14 + 3x Put "3x" in front of "-14" because it has the 'x'
y = 3x - 14 Looks like y = mx + b
State the "m" and "b".
m = 3 (Slope of the line)
b = -14 (y-intercept of the line)
Therefore the equation of the line in slope-intercept form is y = 3x - 14. The slope is 3 and the y-intercept is -14.
Suppose a pizza is removed from an oven at 400°F into a kitchen whose temperature is a constant 76°F. Three minutes later the temperature of the pizza is found to be 267°F. (Round your answers to two decimal places.)
(a) What is the temperature
T(t)
of the pizza after 5 minutes?
T(5) =
(b) Determine the time when the temperature of the pizza is 150°F.
min
(c) After a very long period of time, what is the approximate temperature of the pizza?
°F
Answers
Answer:
A. 178.35°F
B. ≅ 5.64 minutes or 5 minutes 38 seconds approximately
C. 76°F.
Step-by-step explanation:
1. Let's review the information given to us to answer the questions correctly:
Temperature of the pizza in the oven = 400°F
Temperature of the kitchen = 76°F constantly
Temperature of the pizza after 3 minutes = 267°F
2. A. What is the temperature T(t) of the pizza after 5 minutes?
We will use the ratio of how much degrees the temperature of the pizza decreases per minute, this way:
Ratio = (Temperature of the pizza in the oven - Temperature of the pizza after 3 minutes)/ Minutes
Ratio = (400 - 267)/3 = 133/3 = 44.33 (Rounding to two decimal´places)
It means that the temperature of the pizza diminishes 44.33°F per minute.
Therefore, the temperature T(t) of the pizza after 5 minutes, will be:
T(5) = 400 - (44.33 * 5) = 400 - 221.65 = 178.35°F
B. Determine the time when the temperature of the pizza is 150°F.
min.
Time when the pizza is 150°F = (400 - 150)/44.33 = 250/44.33 = 5.64 minutes or 5 minutes 38 seconds approximately
C. After a very long period of time, what is the approximate temperature of the pizza? It will be the temperature of the kitchen, 76°F.
The sum of two numbers is 18. Three times the greater number exceeds four times the smaller number by 5. Find the numbers
Answers
Answer:
6 1/8 and 11 7/8
Step-by-step explanation:
Just use algebra. x+y is equal to 18. 3x=4y+5. Then you substitute the value x for y by dividing by three. From there it is just computation
Answer:
The numbers are 11 and 7
Step-by-step explanation:
Let the numbers be P and V
Let P be the greater number and V be the smaller number.
From the question, the sum of the numbers equals 18 i.e
P + V = 18
Also from the question,
We were told that three times the greater number exceeds four times the smaller number by 5 i.e
3P = 4V + 5
P = (4V + 5) / 3
Substituting the value of P into equation (1), we obtain:
P + V = 18.
(4V + 5) / 3 + V = 18
Multiply through by 3 to express in linear form, we have:
4V + 5 + 3V = 54
Collect like terms
4V + 3V = 54 - 5
7V = 49
Divide both side by the coefficient of V i.e 7
V = 49/7
V = 7
P + V = 18
P = 18 - V
P = 18 - 7
P = 11
The numbers are 11 and 7
Passing through (-6, -1) and PARALLEL 2x + 3y = 3
Answers
Answer:5
Step-by-step explanation:
If 1 1/4 kg sugar cost 2.25, find the cost of 3 1/4 kg of sugar
Answers
Step-by-step explanation:
because 1 kg is worth 2 is 1/4 is worth .25
so multiply 2 by 3 and add 1/4
good luck hope this helps.
Answer:
cost of [tex]3\frac{1}{4}[/tex] kg sugar is [tex]5.80[/tex]
Step-by-step explanation:
Converting the quantity of sugar from mixed fraction to proper fraction
[tex]1\frac{1}{4} =\frac{(1*4)+1}{4} =\frac{5}{4}[/tex]
Cost of [tex]\frac{5}{4}[/tex] kg of sugar= 2.25
Cost of 1 kg of sugar [tex]2.25*\frac{4}{5} \\=0.45*4\\=1.80[/tex]
similarly, [tex]3\frac{1}{4} =\frac{(3*4)+1}{4}=\frac{13}{4}[/tex]
So, the cost of [tex]\frac{13}{4}[/tex] kg of sugar is
[tex]\frac{13}{4}*1.80 \\=5.80[/tex]
cost of [tex]3\frac{1}{4}[/tex] kg sugar is [tex]5.80[/tex]
A vertical wheel with a string around it
Answers
answer key for middle school math with pizzazz! book d d-47
Answers
Answer:
hola
Step-by-step explanation:
What is the area of the triangle below
Answers
The area of a triangle is 1/2*base*height
If h=8, b=15, then we have 1/2*8*15 which is 1/2*120 which is 60
So the right choice is B
Hope this helped!
Which expression is equivalent to (x3 · x2)5? x10
Answers
Step-by-step explanation:
The given expression is
[tex]x^3.x^2[/tex]
To write the given expression is equivalent = ?
The given expression is
[tex]x^3.x^2[/tex]
We know that,
The exponential identity,
[tex]a^{m}.a^{n}=a^{m+n}[/tex]
= [tex]x^{3+2}[/tex]
= [tex]x^{5}[/tex]
∴ The given expression is equivalent = [tex]x^{5}[/tex]
Thus, the given expression is equivalent to [tex]x^{5}[/tex].
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Answer:
The answer to (x3*x2)5 is x25
Step-by-step explanation:
Rewrite the following as a mix numbers 17/3
Answers
answer is 5 2/3.............
Answer:
5 2/3
Step-by-step explanation:
What is 0.00072 written in scientific notation
Answers
Answer: 7.2 * 10 to the negative four
Step-by-step explanation:
The expression 210,000\left(1.02\right)^x210,000(1.02)
x
models the estimated home value after x years. Which statement is the correct representation of the 1.02 in the expression?
The house has a starting value of 1.02.
The house is decreasing in value by 2% each year.
The house is increasing in value by 2% each year.
The value of the house is changing by 0.02% each year.
Answers
Answer:
The house is increasing in value by 2% each year.
Correct the increase is 1.02 per year the value of b>0 and the percentage of increase each year is:
[tex] \frac{1.02-1}{1} *100 = 2\%[/tex]
Step-by-step explanation:
For this case if we have this expression
[tex] 210000(1.02)^x[/tex]
We have the same functional forma like the exponential model given by:
[tex] y = a b^x[/tex]
Where a = 210000 represent the constant or initial value and b = 1.02 represent the base.
So let's analyze the possible options:
The house has a starting value of 1.02.
False the starting value for this case is 210000 since if x=0 then we see that the value is 210000
The house is decreasing in value by 2% each year.
False the increase is 1.02 each year so then in % we have
[tex] \frac{1.02-1}{1} *100 = 2\%[/tex]
We have an increase of 2% each year
The house is increasing in value by 2% each year.
Correct the increase is 1.02 per year the value of b>0 and the percentage of increase each year is:
[tex] \frac{1.02-1}{1} *100 = 2\%[/tex]
The value of the house is changing by 0.02% each year.
False the increase is 2% per year
Bag A contains 9 red marbles and 3 green marbles. Bag B contains 9 black marbles and 6 orange marbles, Find the probability of selecting one green marble from bag A and one black marble from bag B.
Answers
Answer:
3/20
Step-by-step explanation:
Prob. (For green (Bag A)) = 3/12
Prob. (For Black (Bag B)) = 9/15
3/12 x 9/15 = 3/20
The probability of selecting one green marble from bag A and one black marble from bag B is 0.15
There are 3 green marbles in bag A out of a total of 12 marbles (i.e. 3 green and 9 red).
So, the probability of selecting a green marble from bag A is:
[tex]Pr = \frac 3{12}[/tex]
There are 9 black marbles in bag B out of a total of 15 marbles (i.e. 9 black and 6 orange).
So, the probability of selecting a black marble from bag B is:
[tex]Pr = \frac 9{15}[/tex]
The required probability is then calculated as:
[tex]P = \frac 3{12} * \frac 9{15}[/tex]
Multiply
[tex]P = 0.15[/tex]
Hence, the probability of selecting one green marble from bag A and one black marble from bag B is 0.15
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Choose one of the theorems about chords of a circle and state it using your own words.
Create a problem about chords that uses the theorem that you explained.
Answers
See the explanation
Explanation:Theorem:
A perpendicular dropped from the center of the circle to a chord bisects it. It means that both the halves of the chords are equal in length.
In my own words, I'd explain this by drawing a circle and the diameter of the circle drawn in red. Also, we have a chord of the circle drawn in blue. The theorem says that the diameter bisects the chord in a right angle, so we will have two halves that measure the same so that's why we drew two hash marks on each half of the chord.
A problem about this is indicated in figure 2. Suppose you have a perpendicular dropped from the center of the circle to a chord and you know that the left half measures 2 cm, so we want to know the x-value of the right half. Since the diameter bisects the chord, then it is true that [tex]x=2cm[/tex] as well.
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You volunteer at an animal shelter on the weekends and today is adoption day! At the beginning of the event, you start with 44
44
cats/kittens.
x
number of cats/kittens get adopted. But then, at the end of the day, someone drops off twice as many new cats/kittens as were adopted. You now have 50
50
cats/kittens.
How many
cats/kittens were adopted.
Answers
6 cats/kittens were adopted.
Step-by-step explanation:
Given,
Number of cats/kittens at the event = 44
Number of cats/kittens adopted = x
Number of cats/kittens returned = Twice returned as adopted = 2x
New total = 50
We will subtract the adopted and add the returned cats/kittens.
Total cats/kittens at event - adopted + returned = New total
[tex]44-x+2x=50\\44+x=50\\x=50-44\\x=6[/tex]
6 cats/kittens were adopted.
Keywords: expression, variables
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100 increased by 3.1%
Answers
Answer:
103,1
Step-by-step explanation:
Use this formula: 100*(1+3.1%)
After traveling 345 miles, the
Johnston family stopped at a
rest stop for lunch. Looking at
the map, they realized they had
completed of the trip. If d
represents the total distance in
miles, which equation can be
used to find d ?
Answers
Answer:
3/5 x d = 345
Step-by-step explanation:
got the question right on the quiz