iq scores have a bell shape distribution with a mean of 100 and standard deviation of 15. 81.855% of the population has an iq score between 70 and 115
What is z-score?
The z score, also referred to as the standard score, serves to calculate how far each data point place is from its mean. In other words, it calculates x's (data point's) deviation in terms of standard deviations.
Using z tables, you may calculate the proportion of the population that is either below or above the score.
Now, according to the question;
IQ scores follow a normal distribution, with a mean of 100 as well as a standard deviation = 15.
A z score is determined as follows:
z = (x - μ)/σ
μ = mean of the distribution
σ = standard distribution of the sampling.
Calculation for the z score for x = 70 and 115
z= (70-100)/15
= -30/15
=-2
and x=115
z = (115 - 100)/15
= 15/15
z = 1.0
Use z-score table, then likelihood that a randomly chosen person's IQ is more than 115 is,
P( -2 < z < 1)= P(z<1) - P(z< -2)
= 0.8413 - 0.02275
= 0.81855
Therefore, the percent of the population has an iq between 70and 115 is 81.855%.
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need help on this, thanks
Answer:
x=15, y=7
Step-by-step explanation:
Angles that form a linear pair are supplementary, so:
[tex]2(5x-5)+3x-5=180 \\ \\ 10x-10+3x-5=180 \\ \\ 13x-15=180 \\ \\ 13x=195 \\ \\ x=15 \\ \\ \\ \\ 5y+5+20y=180 \\ \\ 25y+5=180 \\ \\ 25y=175 \\ \\ y=7[/tex]
Answer:
[tex]x=\boxed{15}\\\\y=\boxed{7}[/tex]
Step-by-step explanation:
Angles on a Straight Line Theorem
The sum of angles on a straight line is equal to 180°.
Solving for x:
[tex]\boxed{\begin{aligned}2(5x-5)^{\circ}+(3x-5)^{\circ}&=180^{\circ}\\2(5x-5)+(3x-5)&=180\\10x-10+3x-5&=180\\13x-15&=180\\13x-15+15&=180+15\\13x&=195\\13x \div 13 &=195\div 13 \\x&=15\end{aligned}}[/tex]
Solving for y:
[tex]\boxed{\begin{aligned}(5y+5)^{\circ}+20y^{\circ}&=180^{\circ}\\(5y+5)+20y&=180\\5y+5+20y&=180\\25y+5&=180\\25y+5-5&=180-5\\25y&=175\\25y \div 25 &=175\div 25 \\y&=7\end{aligned}}[/tex]
Therefore:
[tex]x=\boxed{15}\\\\y=\boxed{7}[/tex]
Gigi makes a scale drawing of a patio the drawing below shows the two scales she used to plan two patios of different sizes
Gigi makes a scale drawing of a patio the drawing, The two scales are
Scale 1 is defined as 35ft by 25ft Scale 2 is defined as 56 ft by 40 ftThis is further explained below.
What are dimensions?Generally, In mathematics, a dimension is a measurement that may be taken in one direction to determine the size or distance of an item, area, or space.
To put it another way, it is the process of determining the dimensions of anything by calculating its length, breadth, and height.
Actual ratio measurements with a scale of 1
For the Lenght
Length=7 cm
Length =7*5
Lenght=35 ft
Width=5 cm
Width=5*5
Width=25 ft
Therefore
The dimensions are 35 ft by 25 ft
Find the actual dimensions of a ratio with the scale 2
A scale of 2 is equal to
1 cm/8 ft
For Length=7 cm
L=7*8
L=56 ft
For Width=5 cm
W=5*8
W=40 ft
In conclusion, The dimensions are 56ft by 40f
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What is the value of -3 + |-17|?
Please helppp
Create a table of data for two different linear functions. The table should use the same values of x for both functions. Based on your table, will the graphs of these two functions intersect? Explain your answer
These two functions' graphs do indeed intersect:
Formula 1: F(X)=2X+5
The formula 2=H(X)=3X+2
INTERSECT=(3,11)
Describe function:a mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).Everywhere in mathematics are functions, which are essential for building physical connections in the sciences.
According to the given data:The first step is to generate two linear functions. I created the linear functions f(x)=2x+5 and h(x)=3x+2 (without a quadratic term). Then
You substitute a number for the x:
F(X)=2X+5 in Table 1 (H(X)=3X+2) Table 2
X=1——->Y=2+5=7 X=1------> Y=3·1+2=5
X=2---->
Y=2·2+5=9 X=2-----> Y=3·2+2=8
X=3---->
Y=3·3+5=11 X=3-----> Y=3·3+2=11
The two - dimensional functions will intersect at the X=3/Y=11 location, as demonstrated by both data tables, which is the answer.
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A man earned wages of 41,500 received 1900 and interest from a savings account and contributed 2900 to a tax deferred retirement plan he was entitled to a personal exemption of $4050 and had deductions totally $6660 find his gross income adjusted gross income and taxable income
Answer:
Gross Income = $ 43400
Adjusted Gross Income=$40500
Taxable Income = $33840
Step-by-step explanation:
given that-
Income paid to man
Wages = $41,500
Savings Interest = $1900
Tax Def Contribution=$2900
Deductions= $6660
personal exemption =$4050
Gross Income = Income paid to man = 41500 + 1900 = $ 43400
Adjusted Gross Income = Income - Tax Def Contribution = $43400-$2900=$40500
Taxable Income = AGI - Deductions = 40500 - 6660 = $33840
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-2x + absoulute value of y
x= -1/2
y= 6/5
Answer:
please rate as brainliest
the question is in the picture
Given
[tex]S=\mleft\lbrace1,2,3,4,5,6,7,8,9\mright\rbrace[/tex]by selecting two numbers from S, the number of possible outcomes is
[tex]n(S)=9\times9=81[/tex]Let E be the event that selecting two numbers randomly and their sum is 12 with replacement.
[tex]E=\lbrack(3,9),(4,8),(5,7),(6,6),(7,5),(8,4),(9,3)\}[/tex][tex]n(E)=7[/tex]The probability is
[tex]P(E)=\frac{n(E)}{n(S)}[/tex]Substitute values, we get
h is
[tex]P(E)=\frac{7}{81}[/tex]b)without replacement
Areplacementout
[tex]A=\mleft\lbrace(3,9\mright),(4,8),(5,7),(7,5),(8,4),(9,3)\}[/tex][tex]n(A)=6[/tex][tex]P(A)=\frac{n(A)}{n(S)}[/tex]Substitute the values, we get
[tex]P(A)=\frac{6}{81}=\frac{2}{27}[/tex]The probability that the sum is 12 if selecting two numbers without replacement
[tex]P(A)=\frac{2}{27}[/tex]Segment BD bisects ZABC. Solve for 2. Round to the nearest tenth, if necessary.
(Image not necessarily to scale.)
Answer:
x = 10.5 units=================================
Angle bisector theorem:
An angle bisector of a triangle divides the opposite side into two proportional parts as the two sides of same angle.Applying to the given triangle:
AB / BC = AD / DC, orx / 14 = 6 / 8Solve it for x:
x = 14*6/8x = 10.5
If ACDE were reflected across the line y = x, what would be the coordinates of AC'D'E?
Answer: D
Step-by-step explanation:
Reflecting over the line y=x means [tex](x,y) \longrightarrow (y,x)[/tex].
[tex]C(1, -5) \longrightarrow C'(-5, 1)\\\\D(8, -2) \longrightarrow D'(-2, 8)\\\\E(7, -6) \longrightarrow E'(-6, 7)[/tex]
Chose the inequality shown by this diagram
Answer: C
Step-by-step explanation:
Open Circle: [tex]< , >[/tex]
Closed Circle: [tex]\leq ,\geq[/tex]
What is
the circumference of
a circle with a radius of 9.7 inches?
Use 3.14 for
pi.
Enter your answer as a decimal in the box.
The circumference of circle with radius 9.7inch is 60.916 inch.
What is circumference of circle ?The perimeter of a circle is known as its circumference. It is the length of the circle's whole perimeter. The diameter of a circle and the constant are multiplied to get the circumference of the circle. This measurement of a circle's circumference is necessary for someone to cross a circular park or for a circle-shaped table to have a border. The units of the circumference are the same as the units of length and it is a linear value.
A circle is a closed round object whose border points are all equally spaced apart from the center, which is a fixed point.
Given that :the circle with a radius of 9.7 inches
Circumference of a circle is [tex]2\pi r[/tex]
2 ×3.14×9.7 = 60.916
The circumference of circle with radius 9.7inch is 60.916 inch.
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Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verify the real zeros and the given function value. N=3; -3 and 4+4i are the zeros; f(-1)=82
The polynomial function is f(x) = x³ - 5x² + 8x + 96.
We have to find a polynomial of degree 3.We are given that the polynomial has -3, 4-4i, and 4+4i as its roots.We are also given that f(-1) equals 82.If x = -3 is a root, then:(x+3) is a factor of the polynomial.If x = 4-4i is a root, then:(x-4+4i) is a factor of the polynomial.If x = 4+4i is a root, then:(x-4-4i) is a factor of the polynomial.All the three roots are of the same polynomial.So, the polynomial is the product of these factors.f(x) = k(x+3)(x-4+4i)(x-4-4i)f(x) = k(x+3)[(x-4)² - (4i)²]f(x) = k(x+3)[x² + 16 - 8x + 16]f(x) = k(x+3)[x² - 8x + 32]f(x) = k[x³ - 8x² + 32x + 3x² - 24x + 96]f(x) = k[x³ - 5x² + 8x + 96]To find "k", we know that f(-1) = 82.f(-1) = k[(-1)³ - 5(-1)² + 8(-1) + 96]82 = k[-1 - 5 - 8 + 96]82 = k*82k = 1Thus, the polynomial is f(x) = x³ - 5x² + 8x + 96.To learn more about polynomials, visit :
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5 to the second power x [7 - 3] divided by 5
Answer:
Answer is 20 :).........
Pls help with this question
Answer:
3
Step-by-step explanation:
[tex]4x^6 y^3 - 3x^6 y^3 + 2x^2 y^2 - x^6 y^3 - x^2 y^2 +y \\ \\ =x^2 y^2+y \\ \\ =(-2)^2 (-1)^2 -1 \\ \\ =4-1 \\ \\ =3[/tex]
a researcher conducts a study and finds that the difference between the population mean (μ) and the sample mean (m) is 4, the sample size (n) is 36, and the standard deviation of the population (σ) is 3.5. what is the value of cohen's d?
The value of cohen's d based on the population and the deviation given is 1.14.
How to calculate the value?It should be noted that based on the information, the researcher conducts a study and finds that the difference between the population mean (μ) and the sample mean (m) is 4, the sample size (n) is 36, and the standard deviation of the population (σ) is 3.5.
Sample mean = 4
Sample size = 36
Standard deviation = 3.5
Cohen D = Sample mean / Standard deviation
= 4 / 3.5
= 1.14
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HELP ASAP DUE IN AN HOUR
What are the similarities and differences between number 1 and 3?
What are the similarities and differences do you see between 3 and 4
For example:
Similar: both arithmetic/linear/common difference
Different: #1 is discrete #3 is continuous
WILL GIVE BRAIN
Arithmetic sequences, often known as the common difference, are patterns of numbers that rise or fall at a consistent rate.
What is the formula for calculating the average difference between two arithmetic sequences?
D is equal to a(n) - a(n - 1), where a(n) is the last term and a(n - 1) is the term before it in the series.
Answer and justification ,A common difference exists in every arithmetic sequence. We can enter the values of an, a1, and n into the arithmetic sequence formula and find the common difference if a problem offers us an, a1, and n but not the common difference.
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David traveled 4/5 of his trip by bicycle and the rest of the distance by foot. If the whole trip was 160km, how many kilometres dad he travel by foot?
Answer:
Step-by-step explanation:
I will explain it in a screenshot. That all the way is divided into 5 parts. And 4 of them were by bicycle, and 1 part is by walk. So we divide all the way to 5 and multiply to leftover 1 piece.
pls help me solve these questions, i have no clue where to start
For given proof the missing statements are:
14 : NA + AL = NA + BM
15 : NL = NM
16 : Addition postulate of equality
In this question, we have been given a proof.
We need to write missing statements or reasons of the given proof.
We have been given NL ≅ NM and AL ≅ BM
We need to prove NA ≅ NB
1) NL ≅ NM; AL ≅ BM ................(Given)
2) NL = NA + AL and
NM = NB + BM ...........(Segment Addition Postulate)
3) NA + AL = NA + BM ...........(Subatitution)
4) NA + BM = NB + BM ..............(NL = NM)
5) NA = NB ............(Addition postulate of equality)
Therefore, for given proof the missing statements are:
14 : NA + AL = NA + BM
15 : NL = NM
16 : Addition postulate of equality
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Is the relation in this graph a function?
Is the relation in this graph a function?
Answer:
the first is a function and the parabola is not a function
Step-by-step explanation:
A simple way to know why is the vertical line test.
Draw a vertical line and see whether if there are more than one point in the vertical line. If there's more than one point in the line then it's not a function, but if only one point on the vertical line it IS a function.
In the first graph, you'll notice that any vertical line you'll draw won't pass through two points ever. On the other hand, second graph will have two points found in the vertical line drawn by you, for example: (-2, 3);(-2, -3)
Wish you've enjoyed my answer because the more you enjoy maths, taste it, love it, and understand it, the more you will be successful in it. Good luck
Simplify 4.5p(2 − 0.2p).
9p − 0.9p2
9p − 0.2p2
9 − 0.2p2
9 − 0.9p2
Answer:
9p-0.9p^2
Step-by-step explanation:
If F, G, and H are the midpoints of the sides of AJKL, FG = 37, KL = 48, and GH = 30, find each of the following measures. FH= JL= KJ= FJ=
For the given, F, G and H are the midpoints of the sides of ΔJKL, FG = 37, KL = 48, and GH = 30, then measure of FH = 24, measure of JL = 74, measure of KJ = 60 and measure of FJ = 30.
As given in the question,
F, G, and H are the midpoints of the sides of ΔJKL.
F is the midpoint of KJ, G is the midpoint KL, H is the midpoint of JL
Measure of the required sides are as follow:
FH = (KL / 2) (by midpoint theorem)
= (48/2)
= 24
JL = 2 x FG (by midpoint theorem)
= 2 x 37
= 74
KJ = 2 x GH (by midpoint theorem)
= 2 x 30
= 60
FJ = GH = 30 (by midpoint theorem)
Therefore, for the given, F, G and H are the midpoints of the sides of ΔJKL, FG = 37, KL = 48, and GH = 30, then measure of FH = 24, measure of JL = 74, measure of KJ = 60 and measure of FJ = 30.
The complete question is:
If F, G, and H are the midpoints of the sides KJ, KL, and JL respectively of ΔJKL, FG = 37, KL = 48, and GH = 30, find each of the following measures. FH= JL= KJ= FJ=
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18 ÷ 6 = 3, therefore 18 ÷ 0.6 = 0.3.
True
False
Answer:
True but I could be wrong!
Step-by-step explanation:
When we divide 18 by 0.6 we get 30 not 0.3. However, 30 as a decimal is 0.3.
Rational or Irrational
Answer:
rational : improper fractions,
mixed numbers
decimals that either ternimate or repeat,
irrational : decimals that do not terminate or repeat,
negative integers
A(2h, h), B(p, t), and C(2p, 3t) are three points on a straight line. B divides AC internally in the ratio 2 : 3. Express p in terms of t.
p expressed in terms of t is -2t.
What is the section formula?The formula used to calculate the coordinates of a point on a line segment that divides it into two segments is referred to as the section formula. Let's imagine that the line segment marked with the coordinates A (x₁,y₁) and B(x₂,y₂) has a point P(x,y) that splits it in the ratio m:n. We employ the section formula, which is mathematically defined to determine the coordinates of P.[tex]P(x,y) = (\frac{mx_{2} + nx_{1} }{m+n} ),(\frac{my_{2} + ny_{1}}{m+n} )[/tex]
Given points on the straight line are A(2h, h), B(p, t), and C(2p, 3t).
B divides AC internally in the ratio 2 : 3.
Using the section formula, we determine the coordinates of B
[tex]B(p,t) =(\frac{2*2p + 3*2h}{2+3} ),(\frac{2*3t+ 3h}{2+3} )[/tex]
[tex]B(p,t) =(\frac{4p + 6h}{5} ),(\frac{6t+ 3h}{5} )[/tex]
Equate the points,
[tex]p =\frac{4p+6h}{5}[/tex]
[tex]5p = 4p +6h[/tex]
[tex]p =6h[/tex]
[tex]t= (\frac{6t+ 3h}{5} )[/tex]
[tex]5t = 6t +3h[/tex]
[tex]t = -3h[/tex]
[tex]h =\frac{t}{-3}[/tex]
So, [tex]p =6h = \frac{6t}{-3} = -2t[/tex]
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can someone help me outt plsss
Answer: 4.91(6)7
Step-by-step explanation:
divide 59/12 to get decimal form, also the 6 inside the brackets just mean the 6 repeats
What is the equation of the line that passes through the point (-1, 5) and
has a slope of -3?
Answer:
Equation of line is given as y = mx + c, where m is the slope and c is the y-intercept.
Since slope is -3, equation is y = -3x + c.
Substitute point (-1,5) into equation to find c.
5 = -3(-1) + c
c = 2
Hence, equation of line is y = -3x + 2
3 5/11 s a decimal exspansion
By rational number algebra, the mixed number 3 5 / 11 is equivalent to the decimal expansion 3.[tex]\overline {45}[/tex].
How to transform a mixed number into a decimal number
According to the statement, we find a mixed number, that is, a notation to represent rational numbers that combines both integers and fractions. The procedure to obtain the decimal form of a mixed number is:
Transform the mixed number into a single rational number by using the following formula:Then, the decimal expansion of the mixed number 3 5 / 11 is:
3 5 / 11 = (3 · 11) / 11 + 5 / 11 = 33 / 11 + 5 / 11 = 38 / 11 = 3.[tex]\overline {45}[/tex]
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if f(x)=x^2, what is g(x)? the graph shows the points: (1, -1), (-1,3), (-3,-1)?
IMAGE OF QUESTION
ANSWER
[tex]g(x)=-(x+1)^2+3[/tex]EXPLANATION
We have that the function graphed g(x) is a transformation of:
[tex]f(x)=x^2[/tex]When the parent quadratic function f(x) is transformed, it takes the following form:
[tex]g(x)=a(x-h)^2+k[/tex]This form also represents the vertex form of a quadratic equation, where (h, k) is the vertex of the function.
This means that we can find the function by using the vertex of the function.
The vertex of a function is the maximum or minimum value of the function; from the given graph, it is a maximum value and it is located at:
[tex](h,k)=(-1,3)[/tex]Therefore, we can input this into the vertex form of the function:
[tex]\begin{gathered} g(x)=a(x-(-1))^2+3 \\ g(x)=a(x+1)^2+3 \end{gathered}[/tex]Now, we have to find the value of a. To do this, pick any coordinate point from the graph and input it into the function above.
Let us pick:
[tex](0,2)[/tex]Therefore, we have:
[tex]\begin{gathered} 2=a(0+1)^2+3 \\ 2=a\cdot1+3 \\ 2=a+3 \\ \Rightarrow a=2-3 \\ a=-1 \end{gathered}[/tex]Therefore, the function graphed above is:
[tex]g(x)=-(x+1)^2+3[/tex]the line passing through (8,7) and (6,5)
has the steepest possible slope. How do you know for
sure?
Answer:
find gradient:
5-7/6-8
=-2/-2
=1
1 is the steepest possible slope which is not undefined
Allen decides to make 3 cups of dark orange paint and 3 cups of light orange paint. How many ounces of yellow paint does he need