The z - score of the normal deviation will be 0.8.
What is Standard deviation?
Standard deviation is the measure of dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
Given that;
A normal distribution has the mean = 62
Standard deviation = 20
Since, The formula for the z - score will be;
z = (x - μ) / σ
Where, σ is the standard deviation and μ is the mean of normal distribution.
Substitute all the values in above equation, we get;
z = (x - μ) / σ
z = (46 - 62) / 20
z = - 16 / 20
z = - 0.8
Therefore,
The z - score of the normal deviation will be 0.8.
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Could you help me with this please is from apex
Answer:
Completing the table we have;
Explanation:
Given the table in the attached image, we want to complete the table;
[tex]\text{Interest is 1\% compounded monthly}[/tex]For period 1;
simple interest;
[tex]i_1=Prt=100\times0.01\times1=\text{ \$1.00}[/tex]Compound interest;
[tex]\begin{gathered} f_1=P(1+\frac{r}{n})^{nt}=100(1+\frac{1}{12})^{1(12)}=\text{ \$}101.00 \\ \text{ Interest = }101.00-100=\text{ \$1.00} \end{gathered}[/tex]For period 2;
simple interest;
[tex]i_2=Prt=100\times0.01\times1=\text{ \$1.00}[/tex]compound interest;
[tex]\begin{gathered} f_2=P(1+\frac{r}{n})^{nt} \\ P=f_1=101.00 \\ =101(1+\frac{1}{12})^{1(12)}=\text{ \$}102.01 \\ \text{Interest}=102.01-101=\text{ \$}1.01 \end{gathered}[/tex]Total interest
simple interest;
[tex]i_t=i_1+i_2=1+1=\text{ \$2.00}[/tex]Compound Interest;
[tex]\text{ Total interest}=1.00+1.01=\text{ \$2.01}[/tex]Therefore, completing the table we have;
Factor 12x² + 19x - 21.O (6x + 7)(2x − 3)—O (4x - 3)(3x + 7)O(6x-7)(2x + 3)(4x + 3)(3x7)
given the expression
[tex]12x^2+19x-21[/tex]we are loking 2 numbers whose multiplication is equal to 12
and other 2 number whose multiplication is equal to 21
the sum of the cross multiplication is equal of 19, as follows
[tex](4x*3x)+((4x*7)+(3x*-3))+(-3*7)[/tex]factor is
[tex]\left(4x-3\right)\left(3x+7\right)[/tex]correct answer option B
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In a test of a sex-selection technique, results consisted of 284 female babies and 15 male babies. Based on this result, what is the probability of a female being born to
a couple using this technique? Does it appear that the technique is effective in increasing the likelihood that a baby will be a female?
The probability that a female will be born using this technique is approximately
(Type an integer or decimal rounded to three decimal places as needed.)
Does the technique appear effective in improving the likelihood of having a female baby?
O No
O Yes
The probability of the girl being born to a couple is 0.949. Yes, it is effective in increasing the likelihood that the baby will be a girl as the number of girls is more than the number of boys.
What is probability?
Probability means possibility. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
Given
In a test of sex-selection technique, results consisted of 284 female babies and 15 baby boys.
Total children = 284 + 15 = 299
The probability of the girl being born to a couple will be
[tex]P = \frac{284}{299}[/tex]
P = 0.9498
Thus, the probability of the girl being born to a couple is 0.9498.
Yes, it is effective in increasing the likelihood that the baby will be a girl as the number of girls is more than the number of boys.
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HELP PLS A line includes the points (9,10) and (6,9). What is its equation in point-slope form?
Use one of the specified points in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
Answer:
[tex]y-10=\dfrac{1}{3}(x-9)[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4.4cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\\\end{minipage}}[/tex]
To find the equation of a line that passes through two given points, first find its slope by substituting the given points into the slope formula.
Define the points:
(x₁, y₁) = (9, 10)(x₂, y₂) = (6, 9)Substitute the points into the slope formula:
[tex]\implies m=\dfrac{9-10}{6-9}=\dfrac{-1}{-3}=\dfrac{1}{3}[/tex]
Therefore, the slope of the line is ¹/₃.
[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]
To find the equation in point-slope form, simply substitute the found slope and one of the given points into the point-slope formula:
[tex]\implies y-10=\dfrac{1}{3}(x-9)[/tex]
4j+2=h solve for j please help
To solve for j'
4j + 2 = h
subtract 2 from both-side of the equation
4j + 2-2 = h -2
4j = h-2
divide both-side of the equation by 4
4j/4 = h-2/4
[tex]j=\frac{h-2}{4}[/tex]Calculate the area of the circle. Round decimal answer to the nearest tenth.
Give the radius of a circle, r, we can find its area by using:
[tex]A=\pi r^2[/tex]In the picture, the 30 ft segment passes from on side of the circle to the other passing thourhg tht center, so it is the diameter. The radius is half the diameter, so:
[tex]r=\frac{30}{2}=15[/tex]Now, we can use the formula for the area to find it:
[tex]A=\pi(15)^2=3.14159\ldots\cdot225=706.8583\ldots\cong706.9[/tex]So, the area is approximately 706.9 ft².
Picture explains it all
Answer: .1$ so 10cents
Step-by-step explanation:
BK has endpoints B(1,4) and K(4, -3). Rotate BK clockwise 270 degrees about the ongin. Part A: Write an algebraic description of the transformation of BK. Part B: What are the endpoints of the new line segmente
B ( 1, 4)
K (4, -3)
We plot the points and after that, calculate their angles, then we measure 270 clockwise to calculate the new points.
The endpoints of the new segment are
B' = (-4.5, 1)
K' = (3, 4)
These are the points of the new segment
ZA and ZB are supplementary angles. If mZA= (8x – 27) and m ZB = (4x + 3), then find the measure of ZA.
Supplementary angles sum up to 180 degrees.
Since mZA and mZB are given to be (8x - 27) and (4x + 3) respectively, we need to know the value of x to be able to find
Supplementary angles sum up to 180 degrees.
Since mZA and mZB are given to be (8x - 27) and (4x + 3) respectively, we need to know the value of x to be able to find
What are all the factors of 54?
To find the factors of a number, we can look for factors to divide it by subsequently.
It is easier to start with lower factors.
Let's start by "2".
Since "54" is even, it is divisable by "2":
[tex]\frac{54}{2}=27[/tex]So "2" is one of the factors.
Now, we have got 27. It is not even anymore, but it is divisable by "3":
[tex]\frac{27}{3}=9[/tex]So "3" is another factor.
Now we have got "9" and it is also divisable by "3":
[tex]\frac{9}{3}=3[/tex]So there is another "3" factor.
And since we have got now another "3", we know it is divisable by "3":
[tex]\frac{3}{3}=1[/tex]Now we have got to "1", so we found all the prime factors:
[tex]54=2\cdot3\cdot3\cdot3[/tex]Now,, we need to combine them to find all possible combinations.
We will start from low to high.
"1" is always a factor.
There is "2" there, so it is also a factor.
Then we have "3" as another factor.
There is no need to combine "1" with another factor, so we will start b combining 2 and 3:
[tex]2\cdot3=6[/tex]So, "6" is another factor.
We can combine 3 with 3:
[tex]3\cdot3=9[/tex]"9" is another factor.
Now we start combining three of them:
[tex]\begin{gathered} 2\cdot3\cdot3=6\cdot3=18 \\ 3\cdot3\cdot3=9\cdot3=27 \end{gathered}[/tex]So, "18" and "27" are factors.
And now we combine 4 of them, but this is get us back to "54" which is the last factor.
So, the factors of 54 are: 1, 2, 3, 6, 9, 18, 27, 54.
Answer:
Step-by-step explanation:
1 × 54 = 54, (1, 54) is a pair factor of 54.
2 × 27 = 54, (2, 27) is a pair factor of 54
3 × 18 = 54, (3, 18) is a pair factor of 54
6 × 9 = 54, (6, 9) is a pair factor of 54
Therefore, the positive pair factors are (1, 54), (2, 27),(3, 18) and (6, 9).
Basically, the question is asking to solve a problem about rectangular prisms. It says the the shape of one box, with (h) height in feet, has a volume defined by the function:V(h) = h (h-5)(h-6)It says to graph the function. What is the maximum volume for the domain 0
The function representing the volume of the rectangular prism is given to be:
[tex]V(h)=h(h-5)(h-6)[/tex]Since we are expected to find the volume using the graph, we can prepare a table of values for the function using values of h as integers from 1 - 5, such that:
[tex]\begin{gathered} At\text{ }h=1 \\ V(1)=1(1-5)(1-6)=-4\times-5=20 \end{gathered}[/tex]The completed table is shown below:
Hence, we can plot these points on a graph using a graphing calculator for ease of work. This is shown below:
The maximum volume of the prism is represented by the highest point on the graph. The graph's highest point is at:
[tex]h=1.811[/tex]The corresponding value for the volume as can be seen on the graph is:
[tex]V=24.193[/tex]This is the maximum volume of the prism.
To the nearest cubic foot, the maximum volume of the rectangular prism is 24 cubic feet.
Which graph represents an exponential function
This is algebra two graphing exponential functions
Answer: The Curved Line on Top
Step-by-step explanation: A positive-valued function of a real variable. So the top one
Just learned about this in Algebra 1 about 4 days ago.
(06.03 MC) Use the expression 5(6 + 4x) to answer the following: Part A: Describe the two factors in this expression. (4 points) Part B: How many terms are in each factor of this expression? Part C: What is the coefficient of the variable term? (2 points)
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Expression:
5(6 + 4x)
Step 02:
5(6 + 4x)
A.
5 = factor 1
(6 + 4x) = factor 2
B.
5 = factor 1 ( 1 term)
(6 + 4x) = factor 2 (2 terms)
C.
variable term: 4x
coefficient = 4
That is the full solution.
To the nearest whole foot, how many feet would it be to walk diagonally across this field? A. 42B. 50C. 65D. None of the above
Find the perimeter of LMNPQ if the perimeter of ABCDE = 25.2 cm and ABCDE = LMNPQ
If two polygons are similar with the lengths of corresponding sides, we need to find the ratio between both figures:
Then:
[tex]\frac{SIDE\text{ PQ}}{\text{SIDE DE}}=\frac{25}{15}=\frac{5}{3}=\text{ 1,666}[/tex]So, the ratio is 5:3
The perimeter of LMNPQ is the same to say :
P of ABCDE = 25.2cm
Use the ratio
P of LMNPQ = 25.2 (5/3) cm
Then P = 42 cm
lana 15:02If two events A and B are independent and you know that P(A) = 0.3, what is the value of P(A|B)?
Since the events are independent, we have the following property:
[tex]P(A)=P(A|B)[/tex]That is, the probability of A is the same as the probability of A given B (since the events are independent, event B does not affect event A).
So, if P(A) = 0.3, therefore P(A|B) is also equal to 0.3.
ill send a pic of the question :) plsss help me
We have the next information
4 cups of water
1 cup lemon concentrate
in total, we have 5 cups of lemonade
5 ----- 100%
1 ------ x
x is the percentage of lemon concentrate
[tex]x=\frac{100}{5}=20[/tex]the percentage of lemon concentrate in the lemonade is 20%
I need help answering this question The other values of x are 8 and 13
Given the modulus function expressed as:
[tex]y=|x-8|[/tex]Since the function is a modulus function, the dependent variables "y" will all be a positive value
Using the values of x to be -5, 8, and 13 to determine the ordered pairs
When x = -5
y = |-5 - 8|
y = |-13|
y = 13
The first ordered pair will be (-5, 13)
If x = 8
y = |8 - 8|
y = |0|
y = 0
The second ordered pair will be (8, 0)
If x = 13
y = |13 - 8|
y = |5|
y = 5
The third ordered pair will be at (13, 5)
The graph of the function is as shown below:
Does the relation in the table represent direct variation, inverse variation, or neither? If it is direct or inverse variation, write an equation to represent the relation. Explain your answer.See image
Statement Problem: Does the relation in the table represent direct variation, inverse variation, or neither? If it is direct or inverse variation, write an equation to represent the relation. Explain your answer.
Solution;
We observe that as the value of x is increasing, the value of y is decreasing. Hence, it has a feature of an inverse variation.
When two variables are inversely related;
[tex]\begin{gathered} x\propto\frac{1}{y} \\ x=\frac{k}{y} \end{gathered}[/tex]But;
[tex]x=5,y=2[/tex]Thus, we have;
[tex]\begin{gathered} x=\frac{k}{y} \\ 5=\frac{k}{2} \\ k=5\times2 \\ k=10 \end{gathered}[/tex]Thus, the equation to represent the information is;
[tex]\begin{gathered} x=\frac{k}{y} \\ \text{Put the value of k in the equation;} \\ x=\frac{10}{y} \end{gathered}[/tex]The equation to represent the information is;
[tex]x=\frac{10}{y}[/tex]it snowed 20 inches in 10 days in Montreal. Find the unit rate.
the expression is
[tex]\frac{20}{10}[/tex]We must divide each value by the value of the denominator to obtain the unit ratio
so
[tex]\frac{\frac{20}{10}}{\frac{10}{10}}=\frac{2}{1}=2[/tex]the unit ratio is 2 inches per day
This relation map is the musician to the instrument they play. is this relation a function?
Finding a final amount in a word problem on exponential growth or decay
Answer:
19g
Explanation:
Given the starting amount as 155grams, the below amount will be left after the 1st half life;
[tex]\frac{155g}{2}=77.5g[/tex]After the 2nd half-life, the below amount will remain;
[tex]\frac{77.5g}{2}=38.75g[/tex]After the 3rd half-life, the below amount will remain;
[tex]\begin{gathered} \frac{38.75}{2}=19.375g\approx19g\text{ (rounding to the nearest gram)} \\ \end{gathered}[/tex]on a horizontal line segment, point A is located at 21, point b is located at 66. point p is a point that divides segment ab in a ratio of 3:2 from a to b where is point p located
We have a one-dimensional horizontal line segment. Three points are indicated on the line as follows:
In the above sketch we have first denoted a reference point at the extreme left hand as ( Ref = 0 ). This is classified as the origin. The point ( A ) is located on the same line and is at a distance of ( 21 units ) from Reference ( Ref ). The point ( B ) is located on the same line and is at a distance of ( 66 units ) from Reference ( Ref ).
The point is located on the line segment ( AB ) in such a way that it given as ratio of length of line segment ( AB ). The ratio of point ( P ) from point ( A ) and from ( P ) to ( B ) is given as:
[tex]\textcolor{#FF7968}{\frac{AP}{PB}}\text{\textcolor{#FF7968}{ = }}\textcolor{#FF7968}{\frac{3}{2}\ldots}\text{\textcolor{#FF7968}{ Eq1}}[/tex]The length of line segment ( AB ) can be calculated as follows:
[tex]\begin{gathered} AB\text{ = OB - OA } \\ AB\text{ = ( 66 ) - ( 21 ) } \\ \textcolor{#FF7968}{AB}\text{\textcolor{#FF7968}{ = 45 units}} \end{gathered}[/tex]We can form a relation for the line segment ( AB ) in terms of segments related to point ( P ) as follows:
[tex]\begin{gathered} \textcolor{#FF7968}{AB}\text{\textcolor{#FF7968}{ = AP + PB }}\textcolor{#FF7968}{\ldots}\text{\textcolor{#FF7968}{ Eq2}} \\ \end{gathered}[/tex]We were given a ratio of line segments as ( Eq1 ) and we developed an equation relating the entire line segment ( AB ) in terms two smaller line segments as ( Eq2 ).
We have two equation that we can solve simultaneously:
[tex]\begin{gathered} \textcolor{#FF7968}{\frac{AP}{PB}}\text{\textcolor{#FF7968}{ = }}\textcolor{#FF7968}{\frac{3}{2\text{ }}\ldots}\text{\textcolor{#FF7968}{ Eq1}} \\ \textcolor{#FF7968}{AB}\text{\textcolor{#FF7968}{ = AP + PB }}\textcolor{#FF7968}{\ldots Eq2} \end{gathered}[/tex]Step 1: Use Eq1 and express AP in terms of PB.
[tex]AP\text{ = }\frac{3}{2}\cdot PB[/tex]Step 2: Substitute ( AP ) in terms of ( PB ) into Eq2
[tex]AB\text{ = }\frac{3}{2}\cdot PB\text{ + PB}[/tex]We already determined the length of the line segment ( AB ). Substitute the value in the above expression and solve for ( PB ).
Step 3: Solve for PB
[tex]\begin{gathered} 45\text{ = }\frac{5}{2}\cdot PB \\ \textcolor{#FF7968}{PB}\text{\textcolor{#FF7968}{ = 18 units}} \end{gathered}[/tex]Step 4: Solve for AP
[tex]\begin{gathered} AP\text{ = }\frac{3}{2}\cdot\text{ ( 18 )} \\ \textcolor{#FF7968}{AP}\text{\textcolor{#FF7968}{ = 27 units}} \end{gathered}[/tex]Step 5: Locate the point ( P )
All the points on the line segment are located with respect to the Reference of origin ( Ref = 0 ). We will also express the position of point ( P ).
Taking a look at point ( P ) in the diagram given initially we can augment two line segments ( OA and AP ) as follows:
[tex]\begin{gathered} OP\text{ = OA + AP} \\ OP\text{ = 21 + 27} \\ \textcolor{#FF7968}{OP}\text{\textcolor{#FF7968}{ = 48 units}} \end{gathered}[/tex]The point ( P ) is located at.
Answer:
[tex]\textcolor{#FF7968}{48}\text{\textcolor{#FF7968}{ }}[/tex]
The Wong family and the Nguyen family each used their sprinklers last summer. The water output rate for the Wong familys sprinkler was 35 L per hour. The water output for the Nguyen familys sprinkler was 20 L per hour. The families used their spirit for a combined total of 75 hours, resulting in a total water output of 2100 L. How long was each sprinkler used?
Let W be the time of the wong family and N the time of the Nguyen family. We are told that the output rate of the Wong family is 35 L/h and the output for the Nguyen family is 20 L/h, if the total water output is 2100 L, then we can write this mathematically as:
[tex]35W+20N=2100,(1)[/tex]Where "35W" is the total water output of the wong family and "20N" is the total water output of the Nguyen family. The two outputs combined must be 2100. We are also told that the total time is 75 hours, therefore we have:
[tex]W+N=75,(2)[/tex]We get a system of two equations and two variables. We can solve for "W" in equation (2), by subtracting "N" from both sides:
[tex]W=75-N[/tex]Now we can replace this value in equation (1):
[tex]35(75-N)+20N=2100[/tex]Now we apply the distributive property:
[tex]2625-35N+20N=2100[/tex]Now we add like terms;
[tex]2625-15N=2100[/tex]Now we subtract 2625 from both sides:
[tex]\begin{gathered} -15N=2100-2625 \\ -15N=-525 \end{gathered}[/tex]Now we divide both sides by 15:
[tex]N=-\frac{525}{-15}=35[/tex]Now we replace this value in equation (2) where we already solved for W:
[tex]\begin{gathered} W=75-35 \\ W=40 \end{gathered}[/tex]Therefore, the time for the Wong family is 40 hours and the Nguyen family is 35 hours.
2(3 + v) =
Please help solve this problem and thank you
Answer:
6 +2v
Step-by-step explanation:
This is distributive property. That means you will multiply each term inside the parentheses by the term on the outside of the parentheses.
2(3 + v)
2(3) + 2(v)
6 +2v
If triangular pyramid P and triangular pyramid D are similar, which of the following statements must be true?
When two figures are similar, the relation or proportion between same measures is the same. So answer is option d.
geometry extra credit- 25 questions
Given that the triangles are similar, then their corresponding sides are in proportion, that is,
[tex]\frac{AB}{JK}=\frac{BX}{KY}[/tex]Substituting with data and solving for BX:
[tex]\begin{gathered} \frac{32}{10}=\frac{BX}{6} \\ 3.2=\frac{BX}{6} \\ \text{3}.2\cdot6=BX \\ 19.2=BX \end{gathered}[/tex]Which graph represents the table below?
Answer:
The answer will be D because you have to look very close and make sure the 1 is on the x-intercept and not the y-intercept.
The following triangles are not similar. Determine the ratio between AMCD and AOLN. Howcould you change the measurement(s) to make them similar?
The ratio between MD and DC IS
[tex]\frac{MD}{DC}=\frac{14}{6}=\frac{7}{3}[/tex]The ratio of ON to LN
[tex]\frac{ON}{LN}=\frac{49}{21}=\frac{7}{3}[/tex]The ratio CM to CD
[tex]\frac{CM}{CD}=\frac{12}{6}=\frac{2}{1}[/tex]The ratio of OL to LN
[tex]\frac{OL}{LN}=\frac{40}{21}[/tex]To make the
How would you use the Pythagorean Theorem to find the missing length in the triangle shown? Find the missing length.
The given triangle is a right angle triangle. The pythagorean theorem is expressed as
hypotenuse^2 = one leg^2 + other leg^2
From the diagram,
hypotenuse = AB = c
one leg = BC = 9
other leg = AC = 12
By applying the pythagorean theorem, we have
[tex]\begin{gathered} c^2=9^2+12^2\text{ = 81 + 144} \\ c^2\text{ = 225} \\ c\text{ = }\sqrt[]{225} \\ c\text{ = 15} \end{gathered}[/tex]The missing length is 15 cm