The proportion of people with IQs above 130 is 2.3%.
How to calculate the value?Normal distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.
Here the mean is 100 and a standard deviation of 15.
µ = 100, σ = 15
P(X > 130) =
= P( (X-µ)/σ > (130-100)/15)
= P(z > 2)
= 1 - P(z < 2)
Using excel function:
= 1 - NORM.S.DIST(2, 1)
= 0.023 = 2.3%
The value is 2.3%.
Learn more about proportion on:
https://brainly.com/question/19994681
#SPJ1
What is an equation of the line that passes through the points (6, 4) and(6,−6)?
Answer:
Step-by-step explanation:
One angle of a triangle measures twice the smallest angle. The third angle measures five more than twice the smallest angle. Find the measure of the smallest angle.
Answer: The smallest angle is 35°
Step-by-step explanation:
1 angle: 2x
smallest angle: x
third angle: 2x + 5
all angles in a triangle add up to 180 degrees. Therefore,
2x+x+2x+5 = 180
5x+5=180
5x+5(-5)=180(-5)
5x = 175
5x/5 = 175/5
x = 35
The smallest angle is 35°
Determine whether AB and CD are parallel, perpendicular, or neither. A(-3, 2), B(5, 1), C(2, 7), D(1, -1)
Answer:
perpendicular
Step-by-step explanation:
We'll find the slope of both lines and see what it tells us.
If the slopes are the same, the lines are parallel. If the slopes are opposite sign and flipped (negative reciprocals) then they are perpendicular.
The slope is y-Y on top of a fraction and x-X on the bottom.
Slope of AB:
m = 2-1 / -3 -5
= 1/-8 = -1/8
Slope of CD:
m = 7- -1 / 2-1
= 8/1 = 8
Since the slopes are -1/8 and 8, the lines are perpendicular, because they are opposite sign and flipped (negative reciprocals)
Select all of the following that are quadratic equations.
5x-1=3x+8
5 x- 3 = 0
x²-2x = 4x+1
2x²+12 x = 0
x³-6x² + 8 = 0
9x²+6x-3=0
The quadratic equations among all the options given are [tex]x^{2} -2x=4x+1[/tex],[tex]2x^{2} +12x=0[/tex] and [tex]9x^{2} +6x-3=0[/tex].
Given six equations as under:
5x-1=3x+85 x- 3 = 0x²-2x = 4x+12x²+12 x = 0x³-6x² + 8 = 09x²+6x-3=0We are required to find the quadratic equations among the above equations.
Quadratic equations are those equations in which the highest power of the variable present in the equation is 2.
It is in form of [tex]ax^{2} +bx+c=0[/tex].
In our options quadratic equations are [tex]x^{2} -2x=4x+1[/tex],[tex]2x^{2} +12x=0[/tex] and [tex]9x^{2} +6x-3=0[/tex].
5x-1=3x+8: It is not a quadratic equation as the highest power is 1.
5 x- 3 = 0:It is also a linear equation not quadratic equation.
x³-6x² + 8 = 0:It is a cubic equation not a quadratic equation.
Hence the quadratic equations among all the options given are [tex]x^{2} -2x=4x+1[/tex],[tex]2x^{2} +12x=0[/tex] and [tex]9x^{2} +6x-3=0[/tex].
Learn more about equations at https://brainly.com/question/2972832
#SPJ1
Solve equation -1/9 / (-1/3)
Answer: 1/3
Step-by-step explanation:
-1/9 / -1/3 = ?
Keep: -1/9
Change: *
Flip: -3/1
Solve: -1/9 * -3/1 = 3/9
Simplify: 1/3
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathsf{-\dfrac{1}{9}\div - \dfrac{1}{3}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{-\dfrac{1}{9}\div - \dfrac{1}{3}}[/tex]
[tex]\huge\textsf{Convert:}[/tex]
[tex]\mathsf{= -\dfrac{1}{9} \times -\dfrac{3}{1}}[/tex]
[tex]\huge\textsf{Multiply:}[/tex]
[tex]\mathsf{= \dfrac{-1\times3}{9\times -1}}[/tex]
[tex]\mathsf{= \dfrac{-3}{-9}}[/tex]
[tex]\mathsf{= \dfrac{-3 \div -3}{-9\div-3}}[/tex]
[tex]\mathsf{= \dfrac{1}{3}}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{\dfrac{1}{3}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
If n = 140 and X = 112, construct a 95% confidence interval for the population proportion, p.
Give your answers to three decimals
The confidence interval for the population proportion, p is (0.766, 0.833)
Confidence intervalThe formula for calculating the confidence interval for proportion is expressed as:
CI = p±√pq/n
Given the following
p = 112/140 = 0.8
q = 1-p = 0.2
Substitute
CI = 0.8±√(0.8)(0.2)/140
CI = 0.8±0.0338
CI = (0.766, 0.833)
Hence the confidence interval for the population proportion, p is (0.766, 0.833)
learn more on confidence interval here: https://brainly.com/question/2141785
#SPJ1
Find the unit rate for each brand. Round to the nearest cent (hundredth).
The unit rate of each of the brands are:
Brand A's unit rate = 37 cents per ounce.
Brand B's unit rate = 31 cents per ounce.
How to Find the Unit Rate?The unit rate of each brand is simply how much a brand of tomatoes will cost per ounce.
To find the unit rate of each brand, do the following:
Brand A's unit rate = 2.99/8 = $0.37 per ounce = 37 cents per ounce.
Brand B's unit rate = 4.99/16 = $0.31 per ounce = 31 cents per ounce.
Learn more about unit rate on:
https://brainly.com/question/19493296
#SPJ1
Theodore invests $20,000 at 6% simple interest for 1 year. How much is in the account at the end of the 1
year period?
Answer:
Answer:
$21200
Step-by-step explanation:
6% × 20000 = 1200.
20000 + 1200 = 21200
basically yout find 6% of 20000 then add it the original 20000
Given b(x)=|x+41|, what is b(-10)?
Answer:
31
Step-by-step explanation:
Substitute -10 for x in b(x)=|x+41|, obtaining f(-10) = |-10 + 41|. This result simplifies to f(-10) = |31| = 31
everythings in the image
Answer:
t= d/r t=5
Step-by-step explanation:
divide each side by d to isolate t
Use the distance formula to find the length of the segment C(2, 1) to
D(5,6). Round your answer to two decimal places.
Answer: 5.83
Step-by-step explanation:
[tex]\sqrt{(2-5)^2 + (1-6)^2}=\sqrt{34} \approx 5.83[/tex]
1. How much percent more than the cost price should a shopkeeper mark his goods so that after allowing a discount of 25% on the marked price, he gains 20% ?
2. When a bicycle is sold at marked price, a profit of 20% is earned by the seller. If a discount of 5% is allowed, the profit is only Rs. 180 earned by the seller. How much did the seller pay for the bicycle?
Answer:
1. 60%
2. He paid Rs. 1285.71
Step-by-step explanation:
1.
He buys an item for x.
He sells the item with a 25% of the marked price, and he still makes a 20% profit over his cost x.
He must sell for x + 20% of x which is the same as 1.2x.
Let the markup be y%.
Since he gives a 25% discount over the marked price, he sells for 75% of the marked price.
0.75(x + y% of x) = 1.2x
0.75(x + xy/100) = 1.2x
x + xy/100 = 1.6x
Divide both sides by x.
1 + y/100 = 1.6
Multiply both sides by 100.
100 + y = 160
y = 60
Remember that y is in percent, so the markup must be 60%.
Check:
He buys an item for $10.
He applies a markup of 60%. 1.6 × $10 = $16.
He has a price of $16 for this item.
Now he gives a 25% discount. That means the discounted price is 75% of the marked price.
75% of $16 = $12
He sells at a 25% discount for $12.
Compare the actual selling price after the 25% discount with this cost.
$12 compared to $10.
$12/$10 = 1.2 = 120%
Since he sells for 120% of the original price, the markup is 20% which is what he wanted.
2.
The cost to the seller is x.
If he sells it at a 20% profit, then he sells it for 1.2x
Now he gives a discount of 5%, so the final selling price after discount is
0.95(1.2x)
The profit is the difference between what he sold it for, 0.95(1.2x), and what he bought is for, x, and it is Rs. 180.
0.95(1.2x) - x = 180
1.14x - x = 180
0.14x = 180
x = 1285.71
Answer: He paid Rs. 1285.71
The sum of two numbers is 42. The greater number is equal to 5 times the smaller number. Find the numbers.
Answer:
35 and 7
Step-by-step explanation:
5x + 1x =42
6x=42
x=7
Answer:
Greater number: 35
Smaller number: 7
Step-by-step explanation:
1) Set up system of equations.
Let x = greater number
Let y = smaller number
----------------------------------------------
x + y = 42
x = 5y
2) Solve them using elimination or substitution.
x + y = 42
x - 5y = 0
----------------
6y = 42
y = 42/6
y = 7
3) Substitute the found answer into one of the two equations to find the value of x.
x = 5(7)
x = 35
Therefore, the greater number is 35, and the smaller number is 7.
What is the value of the expression below when y = 4?
Answer:
6y²-7y+9
Submit Answer
In a recent year, the scores for the reading portion of a test were normally distributed, with a mean of 22.4 and a standard deviation of 5.1. Complete parts (a) through (d) below.
(a) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is less than 19.
The probability of a student scoring less than 19 is.
(Round to four decimal places as needed.)
(b) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is between 17.7 and 27.1.
The probability of a student scoring between 17.7 and 27.1 is.
(Round to four decimal places as needed.)
(c) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is more than 33.1.
The probability of a student scoring more than 33.1 is
3.1
is.
(Round to four decimal places as needed.)
(d) Identify any unusual events. Explain your reasoning. Choose the correct answer below.
OA. None of the events are unusual because all the probabilities are greater than 0.05.
B. The event in part (c) is unusual because its probability is less than 0.05.
C. The events in parts (a) and (b) are unusual because its probabilities are less than 0.05.
D. The event in part (a) is unusual because its probability is less than 0.05.
Help me solve this
Using the normal distribution, we have that:
a) The probability of a student scoring less than 19 is 0.2709 = 27.09%.
b) The probability of a student scoring between 17.7 and 27.1 is 0.6424 = 64.24%.
c) The probability of a student scoring more than 33.1 is 0.0179 = 1.79%.
d) The correct option is: B. The event in part (c) is unusual because its probability is less than 0.05.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 22.4, \sigma = 5.1[/tex]
Item a:
The probability is the p-value of Z when X = 19, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{19 - 22.4}{5.1}[/tex]
Z = -0.67.
Z = -0.67 has a p-value of 0.2709.
The probability of a student scoring less than 19 is 0.2709 = 27.09%.
Item b:
The probability is the p-value of Z when X = 27.1 subtracted by the p-value of Z when X = 17.7, hence:
X = 27.1:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{27.1 - 22.4}{5.1}[/tex]
Z = 0.92.
Z = 0.92 has a p-value of 0.8212.
X = 17.7:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{17.7 - 22.4}{5.1}[/tex]
Z = -0.92.
Z = -0.92 has a p-value of 0.1788.
0.8212 - 0.1788 = 0.6424.
The probability of a student scoring between 17.7 and 27.1 is 0.6424 = 64.24%.
Item c:
The probability is one subtracted by the p-value of Z when X = 33.1, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{33.1 - 22.4}{5.1}[/tex]
Z = 2.1.
Z = 2.1 has a p-value of 0.9821.
1 - 0.9821 = 0.0179.
The probability of a student scoring more than 33.1 is 0.0179 = 1.79%.
Item d:
Probabilities less than 0.05 are unusual, hence the correct option is:
B. The event in part (c) is unusual because its probability is less than 0.05.
More can be learned about the normal distribution at https://brainly.com/question/28135235
#SPJ1
Identify the next number in the following sequence and tell how:
25 - 49 - 97 - ?
a) 124 b) 171 c) 139 d)193
Answer:
d
Step-by-step explanation:
multiply by 2 then subtract 1
2(25)-1=49
2(49)-1=97
2(97)-1=193
Which choice is equivalent to the quotient shown here for acceptable
values of X?
√25(x-1) + √5(x-1)²
OA. √25(x-1)-5(x-1)²
OB.
5
1(x-1)
OC. √125(x-1)3³
OD. √5(x-1)
The equivalent to the quotient shown in the task content for acceptable values of x is; √(5/(x-1)).
What is the equivalent of the quotient?It follows from the task content that the expression given is; √(25(x-1)) ÷ √(5(x-1)²).
It therefore follows from the the laws of indices that the evaluation is thus;
= √{(25/5) ×(x-1)/(x-1)²}.
Ultimately, upon evaluation we have;
= √(5/(x-1))
Read more on equivalent expressions;
https://brainly.com/question/11258067
#SPJ1
Fill in the blank 57.59 - ___=1.29
Answer: 57.59- 56.3=1.29
Step-by-step explanation:
57.59-x = 1.29
-x= 1.29-57.59
(—) -x= - 56.3
x=56.3
Which of the following inequalities matches the graph?
Ox=-7
Oxs-7
Oys-7
Oyz-7
Answer:
Second option
Step-by-step explanation:
As its a solid line, it indicates the inequality contains equal to in it. As the line crosses the x - axis it must be an option whereby x > or x < . Now read the value which is 7 therefore x ≤ 7
does this represent quntitites that are proportional
Answer:
B
Step-by-step explanation:
Not all of the pairs represent the same ratio
For csc 330:
a) state value of the ratio exactly
b) find one equivalent expression
c) draw a diagram to illustarte.
The value of the ratio based on the angle illustrated is 1:12.
How to illustrate the information?From the information given, it should be noted that the angle in a circle is 360°. Therefore, the value of theta will be:
= 360° - 330°
= 30°
The equivalent expression based on the angle will be:
= 30/360
= 1/12
= 1:12
Learn more about ratio on:
brainly.com/question/2328454
#SPJ1
Identify the vertices of the feasible region for the given linear programming constraints.
System of Linear Programming:
z=−3x+5y
x+y≥−20
x−2y≥−2
x−y≤2
Fill in the vertices of the feasible region:
(−14, )
( ,−11)
(6, )
The vertices of the feasible region are as follows,
(-14, -11), (9, -11) and (6, 4)
What is a Feasible Region?
The area of the graph where all constraints are satisfied is the feasible solution zone or feasible region. It might also be thought of as the point where each constraint line's valid regions intersect. Any decision in this region would lead to a workable resolution for our objective function.
Vertices of the Feasible Region
As it can be seen in the graph, the vertices of the feasible region surrounded by the given constraints are:
(-14, -11), (9, -11) and (6, 4)
Learn more about feasible region here:
https://brainly.com/question/7243840
#SPJ1
pls can solve this question . thanks
if x was 4, what is the value of 4x + 3
Answer:
19
Step-by-step explanation:
4(4)+3
16+3=19
Answer:
19
Step-by-step explanation:
4x+3
4(4)+3
16+3
19
hope it helps
The games have been sorted into video games and board games. The number of video games is 28 less than 6 times the number of board games. The games are 80% video games. How many board games are there?
8
10
13
14
The number of board game sorted is 14
How to find the number of games?The games have been sorted into video games and board games.
The number of video games is 28 less than 6 times the number of board games.
Therefore,
the number of board games = x
number of video game = 6x - 28
The games are 80% video games. Hence,
80 / 100 × x + 6x - 28 = 6x - 28
4 / 5 × 7x - 28 = 6x - 28
4 / 5 (7x - 28) = 6x -28
28 / 5 x - 112 / 5 = 6x - 28
28 / 5 x - 6x = -28 + 112 / 5
28x - 30x / 5 = - 28 + 112 / 5
-2x / 5 = -28 / 5
-10x = -140
x = 14
Therefore, the number of board game sorted is 14.
learn more on numbers here: https://brainly.com/question/13456434
#SPJ1
Answer:
14
Step-by-step explanation:
80 / 100 × x + 6x - 28 = 6x - 28
4 / 5 × 7x - 28 = 6x - 28
4 / 5 (7x - 28) = 6x -28
28 / 5 x - 112 / 5 = 6x - 28
28 / 5 x - 6x = -28 + 112 / 5
28x - 30x / 5 = - 28 + 112 / 5
-2x / 5 = -28 / 5
-10x = -140
x = 14
please help me!! i don’t understand this like at all this is algebra btw
The length and width of the fence should be made 76.25 feet and 23.75 feet respectively. Also, the expression for the length is L = 3W + 5 and the perimeter is P = 2(4W + 5).
How to determine the fence's dimension?Mathematically, the perimeter of a rectangle can be calculated by using this formula;
P = 2(L + W)
Where:
P is the perimeter of a rectangle.L is the length of a rectangle.W is the width of a rectangle.Since the length of this fence is 5 more than 3 times the width, we have:
L = 3W + 5
Substituting the given parameters into the formula, we have;
200 = 2(3W + 5 + W)
200 = 2(4W + 5)
200 = 8W + 10
8W = 190
W = 190/8
W = 23.75 feet.
For the length, we have:
L = 3W + 5
L = 3(23.75) + 5
L = 76.25 feet.
Read more on perimeter of a rectangle here: https://brainly.com/question/17107023
#SPJ1
A ladder 8 m long is leaning against a building. How high on the building will the ladder reach when the bottom of the ladder is x = 1m from the building?
Answer:
7.9
Step-by-step explanation:
this would just be sqrt (8^2 - 1^2) or sqrt 63 or about 7.9
The ladder reaches 7.9 meters when the bottom of the ladder is x = 1m from the building.
What is the Pythagoras theorem?The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.
It is given that:
A ladder 8 m long is leaning against a building.
From the data given, a right angle triangle is formed:
Applying the Pythagoras theorem:
Building high² = 8² - 1²
Building high² = 63
Building high = 7.9 meters
Thus, the ladder reaches 7.9 meters when the bottom of the ladder is x = 1m from the building.
Learn more about Pythagoras' theorem here:
https://brainly.com/question/21511305
#SPJ2
Can someone answer this for me
The linear equation graphed is given by:
y - 5 = 3(x - 1).
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.In point-slope form, considering a point [tex](x_0, y_0)[/tex], the equation is:
[tex]y - y_0 = m(x - x_0)[/tex]
The line goes through points (0,2) and (1,5), hence the slope is:
m = (5 - 2)/(1 - 0) = 3.
Since the line goes through point (1,5), the equation is:
y - 5 = 3(x - 1).
More can be learned about linear equations at https://brainly.com/question/24808124
#SPJ1
Write the following powers of 6 exponential form: 6 x 6
The exponential form of 6 × 6, is written as: 6².
How to Write an Expression in Exponential Form?Repeated multiplication involving base exponents and base can be written in exponential form, such as: a × a × a = a³.
Given the expression, 6 × 6, the number 6 will be the base while 2 will be the exponent if we want to express it in exponential form. Therefore:
6 × 6 = 6².
Learn more about exponential form on:
https://brainly.com/question/23275698
#SPJ1
Consider the following 8 numbers, where one labelled
x
is unknown.
34
,
31
,
15
,
x
,
17
,
4
,
20
,
25
Given that the range of the numbers is 69, work out 2 values of
x
.
x
=
x
=
Answer:
x = 73
x = -35
Step-by-step explanation:
Here are the 8 numbers:
34, 31, 15, x, 17, 4, 20, 25
Here are the 8 numbers in ascending order with x as the greatest number:
4, 15, 17, 20, 25, 31, 34, x
x - 4 = 69
x = 73
Here are the 8 numbers in ascending order with x as the smallest number:
x, 4, 15, 17, 20, 25, 31, 34
34 - x = 69
-x = 69 - 34
-x = -35
x = -35
Answer:
x = 73
x = -35