Answer:
The answer is below
Step-by-step explanation:
Given that mean (μ) = $32500, standard deviation (σ) = $2500.
a) The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
For x < 36000:
[tex]z=\frac{36000-32500}{2500}=1.4[/tex]
From the normal distribution table, P(x < 36000) = P(z < 1.4) = 0.9192 = 91.92%
b) One standard deviation of mean = μ ± σ = (32500 ± 2500) = (30000, 35000)
Two standard deviation of mean = μ ± 2σ = (32500 ± 2*2500) = (27500, 37500)
Empirical rule states that 68% of data falls within one standard deviation from the mean, 95% falls within two standard deviation from the mean and 99.7% falls within one standard deviation from the mean.
Hence 95% of salaries is between $27,500 and $37,500.
c) 95% of salaries is between $27,500 and $37,500.
P(x < 27500) = (100% - 95%) / 2 = 2.5%
d) If the z score is less than -3 or greater than 3, it is considered an outlier.
For x < 42000:
[tex]z=\frac{42000-32500}{2500}=3.8[/tex]
Hence $42000 is an outlier
-2/3×3/5+5/2-3/5×1/6
Answer:
2
Step-by-step explanation:
Answer:
Step-by-step explanation:
[tex]\frac{-2}{3}*\frac{3}{5}+\frac{5}{2}-\frac{3}{5}*\frac{1}{6}=\frac{-2}{5}+\frac{5}{2}-\frac{1}{5*2}\\\\= \frac{-2}{5}+\frac{5}{2}-\frac{1}{10}\\\\=\frac{-2*2}{5*2}+\frac{5*5}{2*5}-\frac{1}{10}\\\\=\frac{-4}{10}+\frac{25}{10}-\frac{1}{10}\\\\=\frac{-4+25-1}{10}\\\\=\frac{20}{10}\\\\= 2[/tex]
2. What is the equation of a line that has a slope of 3 and a y-intercept of
-2?
y=-3x + 2
y = 3x + 2
y = 3x - 2
3x - 2y = 6
Answer:
y=3x-2
Step-by-step explanation:
y = mx + b
m = slope
b=yint
y=3(slope)x+ -2(y int)
Need help if anyone can help me that’ll be nice
Answer:
times up the outside bc we know the outside is the area
please help me asappppppp!
9514 1404 393
Answer:
a) ADC
b) ABC
c) ACB
d) CAD, DAB
e) CDm, BDA
f) ABD
Step-by-step explanation:
a) Any of the letters on lines going through point D could be used to name an angle with DC as one side. (Letters s and C would name an angle of measure zero, so might not be of interest.)
∠ADC has side DC
__
b) Any angle name with B in the middle will have B as its vertex.
∠ABD is an angle with vertex B
__
c) Ray CE is coincident with ray CD, so ...
∠ACE is another name for ∠ACD
__
d) Adjacent angles share a side, typically between the two angles. A linear pair of angles will be adjacent angles.
∠BAD and ∠CAD are adjacent angles
__
e) In order to properly name a pair of vertical angles, we need to be able to name two sets of opposite rays that share end points. Opposite rays emanate from points C and D, but no named points are seen outboard of those intersections. If we use 'm' as the name of a point on line m, then we can say a pair of vertical angles is ...
CDm and BDA are two vertically opposite angles
__
f) The supplement to EBD will be the other angle that makes a linear pair with angle EBD. It is defined using point A on the ray opposite ray BE.
∠ABD is the supplement of ∠EBD
Use the zeros and the labeled point to write the quadratic function represented by the graph.
Answer:
The quadratic function represented by the graph is [tex]y = x^{2}-6\cdot x + 8[/tex].
Step-by-step explanation:
Parabolae are defined by second order polynomials, that is, a polynomial of the form:
[tex]y = a\cdot x^{2} + b\cdot x + c[/tex] (1)
Where:
[tex]x[/tex] - Independent variable.
[tex]y[/tex] - Dependent variable.
[tex]a, b, c[/tex] - Coefficients.
By Algebra, we know can calculate the set of all coefficients based on the knowledge of three distinct points. According to the graph, we have the following points: [tex](x_{1}, y_{1}) = (2, 0)[/tex], [tex](x_{2}, y_{2}) = (4, 0)[/tex] and [tex](x_{3}, y_{3}) = (6, 8)[/tex], and the resulting system of linear equations is:
[tex]4\cdot a + 2\cdot b + c = 0[/tex] (2)
[tex]16\cdot a + 4\cdot b + c = 0[/tex] (3)
[tex]36\cdot a + 6\cdot b + c = 8[/tex] (4)
The solution of the system of linear equations is:
[tex]a = 1, b = -6, c = 8[/tex]
Hence, the quadratic function represented by the graph is [tex]y = x^{2}-6\cdot x + 8[/tex].
Granite has a specific heat of 800 J/g oC. What mass of granite is needed to store 150,000 J of heat if the temperature of the granite changes from 80 oC to 95 oC? (12.5 g)
Answer:
12.5g
Step-by-step explanation:
Given data
Shc= 800 J/g oC
Q=150000J
T1= 80
T2= 95
Q=mc(T2-T1)
150000= m*800(95-80)
150000= m*800*15
150000= 12000m
m= 150000/12000
m= 12.5g
Answer ASAP! Please answer! please answer (NOT HARD)
Answer:
221
Step-by-step explanation:
5(3)2-4
Answer:
221
Step-by-step explanation:
Help me out please???
9514 1404 393
Answer:
x = 5
Step-by-step explanation:
DE being a midsegment means that D is a midpoint. Then BD = DA, or x = 5.
pls help me do this question but pls don't get it wrong this is my attempt
Answer: (c)
Step-by-step explanation:
Given
The function is [tex]y=-x^2+6x-4[/tex]
Range of a function describes the values y can take
from the graph it is clear that the maximum value of y is 5
[tex]\therefore y\leq5[/tex]
Hence. option (c) is correct.
Please help me I don’t understand this at all
Answer:
you see on the right where the ( - ) are put the dot at -3 which is on the line because y } -x (which means your on the negative side) + 3 is -6 so put the dot on 6
The fencing William chooses costs $29.53 per foot, including installation. What will the fencing cost? Show your work.
Answer:
[tex]C = 29.53x[/tex]
Step-by-step explanation:
Given
[tex]Unit\ cost = \$29.53[/tex]
Required
The cost of fencing (C)
The cost is calculated as:
[tex]C = Unit\ Cost * Perimeter\ of fencing[/tex]
Let:
[tex]x \to Perimeter\ of fencing[/tex]
So, we have:
[tex]C = Unit\ Cost * x[/tex]
[tex]C = 29.53 * x[/tex]
[tex]C = 29.53x[/tex]
The question cannot be solved further since the dimension of the fence is not given
If you know the dimension, calculate the fence perimeter and substitute the value for x
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Mar
Solve for b.
- 32 + 106 = -22
Answer:
-30+10b=-22
32-22=10b
10b=10
-32+10=-22
hope it helps
A farm categorizes its chickens into 3 classes according to the weight: small, medium, andbig. For any chicken in this farm, the distribution of the weight (denoted byW) follows a GaussianPDF with mean 3.8 lb and standard deviation 0.6 lb. The categories follow the following rule
small: W <= 3.5lb
medium: 3.5 <= 4.9lb
Large: W > 4.9lb
Required:
a. What are the probabilities that a chicken is in the classes of small, medium, and large, respectively?
b. Find c such that PW < c = 0.6.
c. Suppose that 5 chickens are selected at random. What is the probability that 3 out of the 5 will be small?
Answer:
A) P ( chicken is small ) = 0.3085, P ( chicken is medium ) = 0.6621
P (chicken is large ) = 0.0294
B) C = 3.9233
C) 0.1404
Step-by-step explanation:
A) Probabilities
i) P ( chicken is small )
P( w ≤ 3.5 ) = Fw ( 3 .5 )
= F ( 3.5 - 3.8 / 0.6 )
= F ( -0.5 ) = 1 - F( 0.5 ) [∵ F(-x) 1 - F(x) ]
= 1 - 0.6915 ( from Table )
= 0.3085
ii) P ( chicken is medium )
P ( 3.5 < w < 4.9 )
P ( w < 4.9 ) - P ( w < 3.5 )
= Fw ( 4.9 ) - Fw ( 3.5 )
= F ( 4.9 - 3.8 / 0.6 ) - 0.3085
= 0.9706 - 0.3085 = 0.6621
iii) P (chicken is large )
= P ( w > 4.9 )
= 1 - P ( w < 4.9 )
= 1 - Fw ( 4.9 ) = 1 - 0.9706 = 0.0294
B) Find c
Given: P( w < c ) = 0.6
Fw ( c ) = 0.6
F ( c - 3.8 / 0.6 ) = 0.6
c - 3.8 / 0.6 = 0.2055 ( from table )
∴C = 3.9233
C) P ( 3 out of 5 = small )
P ( 3 of 5 = small ) = 0.1404
attached below is a detailed solution
12
There are 81 counters in a bag.
32 of the counters are green.
The rest of the counters are orange.
One of the counters is taken at random.
Find the probability that the counter is orange.
helpppp pls
Answer:
49
81
Step-by-step explanation:
Probability = number of possible outcome.
number of total outcome.
= orange counters = 81 - 32 = 49
49
81
Express it in slope-intercept form.
Answer:
y = 1/4x - 4
Step-by-step explanation:
The slope is four points behind the origin, so we subtract -4 from the equation:
y = 1/4x - 4
use two points on the line to find the slope:
(0,-4) (4,2)
Slope = change in y over change in x
Slope = (2 - -4) / (4-0) = 6/4 = 3/2
Y-intercept is the y value when x is 0, the line goes through y=2 at x = 0, so the t intercept is 2
The equation is:
Y = 3/2x + 2
Which expression represents the probability of choosing an item from the intersection of A and B
OPTION A is the correct answer
The intersection of event A and B is given by P( A∩B) , Option A is the correct answer.
What is Probability ?Probability is the likeliness of an event to happen.
It is given that the Probability of two independent event A and B is given by
P(A) and P(B)
The intersection of event A and B is given by
P( A∩B)
Therefore Option A is the correct answer.
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Using the quadratic formula to solve x2 35-x, what are the values of x?
-12-121
-12-11
54.
12/19
51 21
2
Answer:
x = (-1 ± √21) / 2
The first choice
Step-by-step explanation:
x² = 5 - x
Put in standard form
x² + x - 5 = 0
Use quadratic equation
x = ( -b ± √( b² - 4ac) ) / (2a)
Plug in a = 1, b = 1 , c = -5
x = (-1 ± √( 1² - 4*1*(-5)) ) / 2
evaluate
x = (-1 ± √21) / 2
Помогите пожалуйста
y= sinx/cosx ; y=?
Answer:
[tex]\frac{1}{cos^2x}[/tex]
Step-by-step explanation:
[tex]y'=\frac{(sinx)'*cosx-(cosx)'*sinx}{cos^2x}=\frac{1}{cos^2x}.[/tex]
WILL MARK BRAINLIEST PLEASE HELP
36 apples cost $6. how many apples can you buy for $1?
Answer:
16 cents
Step-by-step explanation:
6 divided by 36 = 0.16666667
9/50 percents and decimals
Answer:
18% and 0.18
Step-by-step explanation:
converting fraction 9/50 as a percent leaves u with 18%
Please help me I am stressed out
Answer:
a) 0.3 liters
b) 3 ÷ 10 = 0.3 liters
Step-by-step explanation:
3 ÷ 10
3 × 1/10
0.3
Which type of correlation does the scatter plot show
Answer:
D
Step-by-step explanation:
From the given scatter plot, it is positive correlation.
What is scatter plot?Scatter plots are used to observe and plot relationships between two numeric variables graphically with the help of dots. The dots in a scatter plot shows the values of individual data points.
Interpretation of correlation
A scatter plot with increasing values of both variables can be said to have a positive correlation. A scatter plot with an increasing value of one variable and a decreasing value for another variable can be said to have a negative correlation.From the given graph,
The coordinates points are in increasing order.
Therefore, the correlation is positive.
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How many lines of symmetry does the symbol for a state capital have?
The solution is:
The figure has 4 lines of symmetry.
- A vertical line through the middle of the figure.
- A horizontal line through the middle of the figure.
- The two diagonals through the figure are lines of symmetry too.
What is line of symmetry?In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry. In 2D there is a line/axis of symmetry, in 3D a plane of symmetry.
here, we have,
Explanation
Lines of symmetry refer to lines that can be drawn on figures and the figure on either sides of the line will be mirror images of each other.
For example, for this figure given, if a vertical line is drawn straight through the middle of the figure, the two resulting figures on either sides of the vertical line will be mirror images of each other.
So, the other lines of symmetry for this include
- A horizontal line through the middle of the figure
- The two diagonals through the figure are lines of symmetry too.
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A local hamburger shop sold a combined total of 617 hamburgers and cheeseburgers on Wednesday. There were 67 more cheeseburgers sold than hamburgers.
How many hamburgers were sold on Wednesday?
Answer:
check the picture
Step-by-step explanation:
I hope you get it
what is the slope of the line that passes through these two points?
Answer:
The answer seems to be 3/1.
Step-by-step explanation:
Use the equation:
(y2-y1)/(x2-x1)
-4n(2n-7)=0
Simplif your answer
Answer:
n=3.5, n=0
Step-by-step explanation:
Open the parenthesis
2n(-4n)-7(-4n)=0
-8n^2+28n=0
Factor:
n(-8n+28)=0
Solve:
n=0, or -8n+28=0
-8n=-28
8n=28
n=28/8
n=3.5
n can be either 3.5 or 0
Answer:
0, 7/2
Step-by-step explanation:
See image below:)
PLEASEEE HELPPP
A cone-shaped mold is filled with cake batter. The height of the mold is 15 inches, and the base diameter is 5.5 inches. What is the volume of the mold? Round to the nearest tenth.
Answer:
118.8 cubic inches
Step-by-step explanation:
volume of a cone is
[tex]vol \: = \frac{1}{3} \times \pi \times \frac{ {d}^{2} }{4} \times h[/tex]
where d is base diameter and
h is cone height.
hence
[tex]vol \: = \frac{1}{3} \times \pi \times \frac{ {5.5}^{2} }{4} \times 15 \\ = \pi \times \frac{30.25}{4} \times 5 \\ = 118.8 \: cu \: in[/tex]
The volume of the cone-shaped mold is 118.73 in³
What is volume?Volume is the measure of the capacity that an object holds. For example, if a cup can hold 100 ml of water up to the brim, its volume is said to be 100 ml.
Given that a cone shaped mold is filled with the cake batter, the height of the mold is 15 inches, and the base diameter is 5.5,
We need to find the volume of the mold,
Volume of the cone = π × radius² × height / 3
= 3.14 × 2.75² × 15 / 3
= 118.73
Hence, the volume of the cone-shaped mold is 118.73 in³
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A bookmark is shaped like a rectangle with a semicircle attached at both ends. The rectangle is 10 cm long and 4 cm wide. The diameter of each circle is the width of the rectangle. What is the area of the bookmark? Use 3.14 for π.
The area of the bookmark is cm2.
Plzz help me
Answer:
Area of the bookmark = 52.56 cm²
Step-by-step explanation:
The two semicircles attached at both end of the rectangle will give us a full circle.
Therefore,
Area of the bookmark = area of rectangle + Area of a circle
Area of the bookmark = L × W + πr²
Length (L) = 10 cm
Width (W) = 4 cm
radius (r) = ½(4) = 2 cm
π = 3.14
Plug in the values into the equation
Area of bookmark = 10 × 4 + 3.14 × 2²
= 40 + 12.56
= 52.56 cm²
