Answer:$375
Step-by-step explanation: To find the average, we need to add all of the numbers up and divide by the number of numbers in the set. Since there are 4 deposits, to get an average of #365, Jen needs to have deposited 365x4 = $1460 in total. Now, it is pretty easy to find the answer. We add up her 3 deposits: 325+280+480 = $1085 and see that it is still $375(1460 - 1085) short. So, Jen needs to deposit $375 on her fourth deposit to have an average of $365.
An account begins the year with a
$4000.00 balance. If the account
earns 3% simple interest, what is the
balance at the end of one year?
A. $4,120.00
C. $4,300.00
B. $4,003.00
D. $4,012.00
[tex]s = c(1 + in) \\ s = 4000(1 + 0.03 \times 1) [/tex]
[tex]s = 4120.00[/tex]
Option: AA movie theater has a seating capacity of 331. The theater charges $5.00 for children, $7.00 for students, and $12.00 for adults. There are half as many adults as there are children. If the total ticket sales was $ 2404, How many children, students, and adults attended?
Answer:
87 adults
174 children
70 students
Step-by-step explanation:
Using a spreadsheet program, create an amortization schedule for a 30-year mortgage of $500,000 at an annual interest rate of 4.23%.
(a)
In which month does the amount of principal in a monthly payment first exceed the amount of interest?
(b)
How much interest is repaid for the term of the loan? (Round your answer to the nearest cent.)
$
(c)
If the loan amount was $750,000 instead of $500,000, would the month in which the amount of principal in a monthly payment first exceeded the amount of interest change?
Yes
No
This exercise requires the ability to create Amortization Schedules Using a Spreadsheet program. Based on the information given about the Amortization of the loan, the principal payable per month became greater than the interest payable per month on the 159th month (given that the loan amount is $500,000.
In which month does the amount of principal in a monthly payment first exceed the amount of interest?The amount of principal in a monthly payment first exceeds the interest payment In 159th Month. The interest on this month is $1, 248.39 while the principal on this month is $1, 205.46.
It is to be noted that when a loan is taken, the constituents of the amounts being paid back is the Principal and part of the interest on the loan.
How do you Calculate Amortization of Loans?The yearly interest rate must be divided by 12.
Your monthly interest rate, for instance, will be 0.3525 percent if your annual interest rate is 4.23 percent (0.0423 annual interest rate x 12 months).
Additionally, you'll add 12 to the number of years remaining on your loan term.
How much interest is repaid for the term of the loan?The total amount of interest that is paid for the term loan is $383,385.54
If the loan amount was $750,000 instead of $500,000, would the month in which the amount of principal in a monthly payment first exceeded the amount of interest change?Yes it would change. It would change to the 165th month. In this month, the interest paid is $1, 834.00 while the principal paid back is $1,846.77. See the attached image for answer C.
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Write the following number in scientific notation.
788,000
Answer:
788,000 =
788 x 10^3
78.8 x 10^4
7.88 x 10^5
.788 x 10^6
and so on
Sports clubs have increasingly been acknowledged as important settings for health promotion. The term sport club is synonymous with organized sport and both are considered to consist of environments that support the healthy behaviors of its athletic members. One of the member Sanjaya pays rupees 500 in advance on his account at a sports club ,each time he visits the club 10 rupees is deducted from his account. Q6. Which of the following equation represent the left balance of sanjaya’s y after visiting x number of days? * A) y=500+10x B) y=10+500x C) x=500-10y D) y=500-10x NO RESPONSE
The linear equation that represent the left balance of sanjaya’s y after visiting x number of days is:
y = 10x + 500.
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.From the data given, we have that:
The y-intercept is of 500.The slope is of 10.Hence the balance is given as follows:
y = 10x + 500.
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The Mogul Runners ski club planned a trip to Park City. Of the total number of club members, 11 signed up to go. If this is 25% of the club, how many members does the ski club have?
Answer: 44
Step-by-step explanation: Since 11 members are equal to 25% of the club, 11 members is 1/4 of the club because 25% = 1/4. There are four-fourths in a whole so 11x4 = 44 members. The ski club has 44 members.
help pleaseeeee
tysm
Answer: Either Rohmbus or Parallelogram...
Step-by-step explanation: Your picture is a bit small, sry
Use identities to find the values of the sine and cosine functions for the following angle measure.
θ, given that cos 20 =12/13 and θ terminates in quadrant I. Find sin θ and cos θ. Can you explain how do it and what is the answer?
Using the cosine double angle formula,
[tex]\cos 2\theta=2\cos^2 \theta-1=\frac{12}{13}\\\\2\cos^{2} \theta=\frac{25}{13}\\\\\cos^{2} \theta=\frac{25}{26}\\\\\boxed{\cos \theta=\frac{5}{\sqrt{26}}}[/tex]
(Note I took the positive case since [tex]\theta[/tex] terminates in the first quadrant)
Using the Pythagorean identity,
[tex]\sin^2 \theta+\cos^2 \theta=1\\\\\sin^2 \theta+\frac{25}{26}=1\\\\sin^2 \theta=\frac{1}{26}\\\\\boxed{\sin \theta=\frac{1}{\sqrt{26}}}[/tex]
(Note I took the positive case since [tex]\theta[/tex] terminates in the first quadrant)
Target Costing
Instant Image Inc. manufactures color laser printers. Model J20 presently sells for $460 and has a product cost of $230, as follows:
Direct materials $175
Direct labor 40
Factory overhead 15
Total $230
It is estimated that the competitive selling price for color laser printers of this type will drop to $400 next year. Instant Image has established a target cost to maintain its historical markup percentage on product cost. Engineers have provided the following cost-reduction ideas:
Purchase a plastic printer cover with snap-on assembly, rather than with screws. This will reduce the amount of direct labor by 15 minutes per unit.
Add an inspection step that will add six minutes per unit of direct labor but reduce the materials cost by $20 per unit.
Decrease the cycle time of the injection molding machine from four minutes to three minutes per part. Forty percent of the direct labor and 48% of the factory overhead are related to running injection molding machines.
The direct labor rate is $30 per hour.
a. Determine the target cost for Model J20, assuming that the historical markup on product cost and selling price are maintained.
$fill in the blank 1
per unit
b. Determine the required cost reduction.
$fill in the blank 2
per unit
c. Evaluate the three engineering improvements together to determine if the required cost reduction (drift) can be achieved. Do not round interim calculations but round your final answers to two decimal places.
1. Direct labor reduction $fill in the blank 3
per unit
2. Additional inspection $fill in the blank 4
per unit
3. Injection molding productivity improvement $fill in the blank 5
per unit
Total savings $fill in the blank 6
per unit
The target cost for Model J20 is $2000.
The required cost reduction is $30.
The total saving will be $30.3.
How to compute the cost?The target cost will be:
= Sales price - (100% × Target cost)
= 400 - (100% × Y)
Y + Y = 400
2Y = 400
Y = 400/2 = 200
Target cost = $200
Therefore, the target cost is $200.
The required cost reduction will be:
= $230 - $200
= $30
The required cost reduction is $30.
The three engineering improvements together will be:
Direct labor reduction = 7.5
Additional inspection = 17
Injection molding = 5.8
Total savings = 30.3
The total savings is $30.3.
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Identify the lateral area and the surface area of a cube with edge length 15 in.
The Lateral area of the cube = 900 in.²
The Surface area of the cube = 1,350 in.².
What is the Lateral Area of a Cube?A cube's lateral area is the area covered by the lateral surfaces of the cube shape. The formula for the lateral area of a cube is given as: LA = 4a², where:
a = edge length of cube.
What is the Surface Area of a Cube?The surface area of a cube is the total area of all its 6 surfaces. The formula for finding the surface area of a cube is: 6a², where:
a = edge length of cube.
Edge length of cube (a) = 15 in.
Lateral area = 4a² = 4(15²)
Lateral area = 4(225)
Lateral area of the cube = 900 in.²
Surface area = 6a² = 6(15²)
Surface area = 6(225)
Surface area of the cube = 1,350 in.².
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The length of a rectangle is 3 m longer than its width.
If the perimeter of the rectangle is 34 m, find its area.
Step-by-step explanation:
With this question ,
The length of the rectangle is 3m longer than it's width=3 +w
then the width =w
therefore perimeter= 2L +2w
34= 2(3+w) +2w
34= 6+2w +2w
34-6 = 4w
28=4w
7= w
Area= Length x breadth
Area = (7+3) x7
Area= 10 x7
Area= 70cm square
If the lengths of two sides of a triangle measure 8 and 13, the length of the third side is:
Answer:
A
Step-by-step explanation:
Triangle side length rule says any two sides added together must be greater than third side .... '6' is the only side length that will work
A troupe of 12 dancers is going to line up on stage. Of these dancers, 6 are wearing green and 6 are wearing blue. A dancer wearing green must be in the first position and they must alternate between colors. In how many ways can the dancers line up?
The number of ways that the dancers can line up is; 518400 ways
What is the Fundamental Counting Theorem?The fundamental counting theorem is a theorem that states that if there are n things, each with ways to be done, each thing independent of the other, the number of ways they can be done is:
N = n1 * n2 * n3.....*nₙ
Total = 12
Dancers on Green = 6
Dancers on blue = 6
Number of ways for those wearing green = 6!
Dancers wearing green must be in the first position and so 6 places are left for the blue dancers.
Number of ways to arrange those wearing blue = 6!
Thus;
Number of ways that the dancers can line up = 6! * 6! = 518400 ways
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A bicyclist traveled with a speed of 12 km/h from a camping ground to a station, located 60 km away. Write a formula expressing the dependence of the variable s on t, where s is the distance between the bicyclist and the station in km, t - the duration (time) of his travel in hours. Using the formula, find: d for t=3.5
1. The formula expressing the dependence of the variable s on t is: s = 60 - 12t
2. the distance travelled at time t = 3.5 h is 18 Km
What is speed?Speed is the distance travelled per unit. Mathematically, it can be expressed as:
Speed = distance / time
1. How to determine the formula expressing the dependence of the variable s on tFrom the question given, bicyclist traveled with a speed of 12 km/h from a camping ground to a station, located 60 km.
Thus, we shall determine the distance travel in time t as follow
Speed = 12 Km/hTime = tDistance in time t = ?Speed = distance / time
12 = distance / t
Cross multiply
Distance = 12 × t
Distance in time t = 12t
But the total distance travelled is 60 Km. Thus, the remaining distance (s) from the bicyclist to the station at time (t) will be given as:
s = 60 - 12t
Thus, the formula expressing the dependence of the variable s on t is: s = 60 - 12t
2. How to determine the distance at t = 3.5 hoursThe distance at t = 3.5 hours can be obtained as illustrated below:
Time (t) = 3.5 hoursDistance (s) = ?s = 60 - 12t
s = 60 - (12 × 3.5)
s = 60 - 42
s = 18 Km
Thus, the distance travelled at t = 3.5 hours is 18 km
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Question 24: [1 + 1 + 1 + 1= 4 points]
Let X be a discrete random variable with the following
x 0.2 0.4 0.5 0.8 1
P(x) 0.1 0.2 0.2 0.3 0.2 (a) Find () , the range of the random variable X
Considering the given discrete probability distribution, the range of the variable X is given by:
Range(X) = {0.2, 0.4, 0.5, 0.8, 1}.
What is the range of a random variable?The range of a random variable is the set of all values that the variable can assume.
From the table, we have that X can assume the values of 0.2, 0.4, 0.5, 0.8 and 1, hence the range of the variable X is given by:
Range(X) = {0.2, 0.4, 0.5, 0.8, 1}.
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Find the value of u -8 given that -7u-5=2
Answer: u - 8 = -9
Step-by-step explanation:
Given equation
-7u - 5 = 2
Add 5 on both sides
-7u - 5 + 5 = 2 + 5
-7u = 7
Divide -7 on both sides
-7u / (-7) = 7 / (-7)
u = -1
Substitute values into the goal expression
u - 8 = (-1) - 8 = [tex]\Large\boxed{-9}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
The answer is -9.
First, let's find the value of u.
-7u - 5 = 2-7u = 7u = -1Now, substitute in the expression.
u - 8(-1) - 8-9Maricopa's Success scholarship fund receives a gift of $ 215000. The money is invested in stocks, bonds, and CDs. CDs pay 2.25 % interest, bonds pay 2 % interest, and stocks pay 9.2 % interest. Maricopa Success invests $ 15000 more in bonds than in CDs. If the annual income from the investments is $ 8087.5 , how much was invested in each account?
The amount of money invested in stocks was $50000, $90000 was invested in bonds and $75000 was invested in CDs
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.
Let x represent the amount of money invested in stocks, y represent bonds and z represent CDs, hence:
x + y + z = 215000 (1)
Also:
0.0225z + 0.02y + 0.092x = 8087.5 (2)
And:
y = 15000 + z (3)
The solution of the equation is:
x = 50000, y = 90000 and z = 75000
The amount of money invested in stocks was $50000, $90000 was invested in bonds and $75000 was invested in CDs
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Find the difference. Enter your answer in lowest terms in the box below as a
fraction, using the slash mark (/) for the fraction bar. 8/11 - 4/15
Answer:
76/165
Step-by-step explanation:
The difference of fractions can be found using the formula ...
a/b -c/d = (ad -bc)/(bd)
DifferenceUsing the given values in the formula, we have ...
[tex]\dfrac{8}{11}-\dfrac{4}{15}=\dfrac{8(15)-11(4)}{11\cdot15}=\dfrac{120-44}{165}=\boxed{\dfrac{76}{165}}[/tex]
Here, the difference fraction does not need to be reduced. Many calculators and spreadsheets can do this arithmetic for you.
The above formula can also be used for sums of fractions. In that case, the sign changes from minus to plus.
Answer:
Step-by-step explanation:
76/165 is the answer
QUESTION IS DOW BELOW 5 POINTS EACH PLEASE HELP PLEASE HELP PLEASE HELP
WILL GIVE BRAINLIEST FOR ACCURATE ANWSER
The central angle in the circle is ∠DAC,major arc is BED, minor arc is ADC and BC=(5π*BD)/18.
Given that BD is diameter of the circle and angle BAC is 100°.
We are required to find the central angle, major arc, minor arc, m BEC, BC.
Angle is basically finding out the intensity of inclination of something on the surface.
In the circle central angles are many like BAC and CAD. We can write CAD as DAC also.
Major arc of a circle is that arc whose length is larger than all other arcs in the circle.
In our circle the major arc is arc BED.
Minor arc of a circle is that arc whose length is smaller.
In our circle the minor arc is arc ADC.
We know that arc's length is 2πr(Θ/360)
In this way BC=2π*(BD/2)*100/360
=(5π*BD)/18
We cannot find angle BEC.
Hence the central angle in the circle is ∠DAC,major arc is BED, minor arc is ADC and BC=(5π*BA)/18.
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6. Dacă a + 2b = 18 şi b+3c=17, calculaţi 3a+8b+6c.
Answer:
Răspuns: 88=>rezultatul
Explicație pas cu pas:
a+2b =18/×3
b+3c=17/×2
3a+6b =54 ^
2b+6c=34 | +
3a+(6b+2b)+6c=54+34
3a+8b+6c=88
Step-by-step explanation:
If we draw lines to join each given point to the origin identify the points whose corresponding line has a slope that is an integer value
The slopes of OA, OB and OC are integer values.
According to the statement
we have given that the some points on the graph and we have to find that the slopes of these points have integer value or not.
So, For this we know that the
If a line passing through two points then the slope of the line is
So, [tex]m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
Then
The slope of line OA is 4 because 8/2 = 4.
And
The slope of line OB is 3 because 9/3 = 3.
And
The slope of line OC is 2 because 8/4 is 2.
And
The slope of line OD is 8/5 because it is 8/5.
And
The slope of line OE is 7/6 because it is 7/6.
And
The slope of line OE is 6/7 because it is 6/7.
From all this it is clear that
So,The slopes of OA, OB and OC are integer values.
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Question 25: [1 + 2 + 2 + 2 + 2 + 1= 10 points]
Given student of classified as belonging to three colleges and gender males and Females in the following table.
Eng (E) Life (L) Sci (S) sum F 60 40 30 130
M 40 20 10 70 sum 100 60 40 200
a) [1 points] Find the probabilities whole events. () , (), (), () , and ()
b) [2 points] Find the probabilities of Intersection (AND) Events:
( ∩ ) = ( ∩ ) ( ∩ ) = ( ∩ ) ( ∩ ) = ( ∩ )
( ∩ ) = ( ∩ ) ( ∩ ) = ( ∩ ) ( ∩ ) = ( ∩ )
c) [2 points] Find the probabilities of Union (OR) disjoint Events:
( ∪ ) = ( ∪ ) ( ∪ ) = ( ∪ )
( ∪ ∪ ) = ( ∪ ∪ ) ( ∪ ) = ( ∪ )
d) [2 points] Find the probabilities of Union (OR) joint events: ( ∪ )
( ∪ )
e) [2 points] Find the probabilities of Conditional Probabilities
(/) (/)
(/) (/)
(/) (/)
(/) (/)
f) [1 points] Use The multiplication low for dependent events to find the Conditional probability. ( ∩ ) = () (/)
See below for the values of the probabilities
How to determine the probabilities?The probabilities of the whole events
For event A, the probability of the whole event is calculated using
P(A) = n(A)/Total
Using the table of values, we have:
P(F) = 130/200 = 0.65
P(M) = 70/200 = 0.35
P(L) = 60/200 = 0.30
P(S) = 40/200 = 0.20
The probabilities of the intersection events
For events A and B, the probability of the intersection events is calculated using
P(A n B) = n(A n B)/Total
Using the table of values, we have:
P(F n E) = P(E n F) = 60/200 = 0.30
P(F n L) = P(L n F) = 40/200 = 0.20
P(F n S) = P(S n F) = 30/200 = 0.15
P(M n E) = P(E n M) = 40/200 = 0.20
P(M n L) = P(L n M) = 20/200 = 0.10
P(M n S) = P(S n M) = 10/200 = 0.05
The probabilities of the Union (OR) disjoint events
For events A and B, the probability of the union (OR) disjoint events is calculated using
P(A u B) = P(A) + P(B)
Using the table of values, we have:
P(E u S) = P(E) + P(S) = 100/200 + 40/200 = 0.70
P(E u L) = P(E) + P(L) = 100/200 + 60/200 = 0.80
P(E u L u S) = P(E) + P(L) + P(S) = 100/200 + 60/200 + 40/100 = 1
P(F u M) = P(F) + P(M) = 130/200 + 70/200 = 1
The probabilities of the Union (OR) joint events
For events A and B, the probability of the union (OR) joint events is calculated using
P(A u B) = P(A) + P(B) - P(A n B)
Using the table of values, we have:
P(E u F) = P(E) + P(F) - P(E n F) = 100/200 + 130/200 - 60/100 = 0.85
P(L u M) = P(L) + P(M) - P(L n M) = 60/200 + 70/200 - 20/100 = 0.55
The probabilities of the conditional probabilities
For events A and B, the conditional probability is calculated using
P(A/B) = P(A n B)/P(B)
Using the table of values, we have:
P(F/S) = P(F n S)/P(S) = 0.15/0.20 = 0.75
P(F/E) = P(F n E)/P(E) = 0.30/0.50 = 0.60
P(M/S) = P(M n S)/P(S) = 0.05/0.20 = 0.25
P(M/L) = P(M n L)/P(L) = 0.10/0.30 = 0.33
P(S/F) = P(F n S)/P(F) = 0.15/0.65 = 0.23
P(E/F) = P(F n E)/P(F) = 0.30/0.65 = 0.46
P(S/M) = P(M n S)/P(M) = 0.05/0.35 = 0.14
P(L/M) = P(M n L)/P(M) = 0.10/0.35 = 0.29
The multiplication of dependent events
For events A and B, the conditional probability is calculated using
P(A n B) = P(A) * P(B/A)
Using the table of values, we have:
P(F n L) = P(F) * P(L/F)
This gives
P(F n L) = 0.65 * (0.20/0.30)
Evaluate
P(F n L) = 0.43
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What is the value of y?
OA. 30°
OB. 120°
OC. 60°
60
Answer:
60
Step-by-step explanation:
60 + y + y = 180
2y = 120
y = 60
X is 30% of Y and Y is 45% of 600. What is the value of X?
Answer:
X = 81
Step-by-step explanation:
600 × 0.45 = 270
270 × 0.3 = 81
X = 81
(SAT Prep) If the lengths of two sides of a triangle are 5 and 9 which would be length of the third side?
The length of third side of triangle is 4 or 14.
According to the statement
we have given that the two sides of the triangle which are 5 and 9 and we have to find the length of the third side of triangle.
So, For this purpose, we know that the
If we had a triangle with sides a, b and c, then we can say
b-a < c < b+a
where b is larger than 'a'. This is the triangle inequality theorem
In this case, a = 5 and b = 9 so,
b-a < c < b+a
9-5 < c < 9+5
4 < c < 14
Telling us that c is some number between 4 and 14, not including either endpoint. If c is a whole number, then c could be any value from this set.
And
We see that the numbers 4 and 14 are in this set. The values 2 and 7 are not in the set.
So, The length of third side of triangle is 4 or 14.
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An agricultural company called Phatsima Pty. Ltd. owns an rectangular fuel tank that measures 75 cm by 65 cm by 30 cm.
How many millilitres of fuel are needed to fill their tank?
If the fuel price is R20.35 per liter. How much will it cost to fill half of their tank?
Choose an option below that has both answers correct.
a.
1. 146 250.00 ml and 2. R 1 488.10
b.
1. 150 000.00 ml and 2. R 2 976.19
c.
1. 73 125.00 ml and 2. R 1 488.10
d.
1. 146 250.00 ml and 2. R 2 000.00
Multiply -2x^-3 y(5yx^5+8xy-4y^2x^2).
Answer:
[tex]\textsf{Option 3}: \quad -10 x^2y^2-16x^{-2}y^2+8x^{-1}y^3[/tex]
Step-by-step explanation:
Given expression:
[tex]-2x^{-3}y(5yx^5+8xy-4y^2x^2)[/tex]
Distribute:
[tex]\implies -2x^{-3}y(5yx^5) -2x^{-3}y(8xy)-2x^{-3}y(-4y^2x^2)[/tex]
Multiply the constants and collect like terms:
[tex]\implies -10 x^{-3}x^5yy-16x^{-3}xyy+8x^{-3}x^2yy^2[/tex]
Remember that a = a¹.
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies -10 x^{(-3+5)}y^{(1+1)}-16x^{(-3+1)}y^{(1+1)}+8x^{(-3+2)}y^{(1+2)}[/tex]
[tex]\implies -10 x^2y^2-16x^{-2}y^2+8x^{-1}y^3[/tex]
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Question 26: [4 points]
1% of a population have a certain disease and the remaining 99% are free from this disease. A test is used to detect this disease. This test is positive in 95% of the people with the disease and is also (falsely) positive in 2% of the people free from the disease.
If a person, selected at random from this population, has tested positive, what is the probability that she/he has the disease?
Let D be the event "have the disease" and FD be the event "free from the disease" Let the event TP be the event that the "test is positive".
A diagram with all the above information is shown.
[tex]P(D/TP) = \frac{P(D \: n \: TP)}{P(TP)} [/tex]
[tex]P(TP) = P(TP \: n \: D)+P(TP \: n \: FD) \\ P(TP) = 0.95×0.99 + 0.02×0.01 = 0.9407[/tex]
[tex]P(D/TP) = \frac{0.9405}{0.9407} = \frac{9405}{9407} [/tex]≈0.999787
The graph shows a system of inequalities.
Graph of two inequalities. One is a solid line increasing from left to right passing through negative 3 comma 0 and 0 comma 3, and it has shading below the line. The second is a solid upward opening parabola with a vertex at 1 comma negative 4 and x-intercepts at negative 1 comma 0 and 3 comma 0. This parabola is shaded inside the curve.
Which system is represented in the graph?
A. y > x2 –2x – 3
y > x + 3
B. y < x2 – 2x – 3
y < x + 3
C. y ≥ x2 – 2x – 3
y ≤ x + 3
D. y > x2 – 2x – 3
y < x + 3
The graphed system of inequalities is:
y ≥ x^2 - 2x - 3y ≤ x + 3So the correct option is the third one.
Which system is represented by the graph?On the graph we can see that the two lines are solid, so we need to use the symbols ≤ and ≥. (If instead, we had dashed lines, then we would need to use the symbols > and <).
We also can see that the region above the parabola is shaded (the shaded region represents the region of solutions for each inequality), and the region below the line is shaded, then the system of inequalities is of the form:
y ≥ parabola.y ≤ line.Only with that, we conclude that the correct option is the third option:
y ≥ x^2 - 2x - 3y ≤ x + 3If you want to learn more about systems of inequalities:
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Find the critical value zα/2 that corresponds to the confidence level 84%.
The critical value z_α/2 that corresponds to the confidence level 84% is; 1.41
How to find the critical value?We want to find the two tail critical values.
This means that at an 84% confidence level, we want to get the probability of not rejecting the null value to be equal to a = 100% - 84% = 16%.
Now, z - scores refers to a numerical measurement that describes a value's relationship to the mean of a group of values and is gotten from normal distribution. Z-score is measured in terms of standard deviations from the mean.
However, under a normal distribution, we want a/2% = 16%/2 = 8% to be located right in the higher tail and lower tail.
From the above, it denotes that the critical value closest to 0.92 will give you the two tail 84% confidence interval. Utilizing a normal distribution table figure online to find the z score gives;
z = 1.41
Thus, we can conclude from this calculation that he critical value z_α/2 that corresponds to the confidence level 84% is; 1.41
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