Answer:
Where are the followings
Step-by-step explanation:
A valid FICO credit score ranges from 300 to 850. A score outside this range is not valid. Key components of a FICO score include credit mix and the impact of new credit, both accounting for 10% of the score respectively.
When it comes to determining what is not a valid FICO credit score, it's important to understand that FICO scores range from 300 to 850. Any score that is not within this range would be considered invalid. Components that make up a FICO score include payment history, amounts owed, length of credit history, new credit, and credit mix. Credit mix refers to the variety of credit types you have, such as credit cards, retail accounts, installment loans, finance company accounts, and mortgage loans, and makes up 10% of your FICO score. Regarding new credit, opening a new account can temporarily lower your score because it reduces the average age of your accounts, which also accounts for 10% of your FICO score.
Two common myths are that opening a new retail credit card is always good for your credit score and that it hurts your score to comparison shop for loans. In reality, opening a retail credit card can lower your score initially, though responsibly managing your new credit can eventually have a positive effect. When it comes to loan comparison shopping, FICO provides a grace period for hard inquiries that are related, bundling them into a single inquiry if they occur within a 14 to 45-day span, depending on the type of credit. This is designed to not penalize consumers who are responsibly shopping for the best rates.
find mABC
*please help asap
Answer:
10 degrees
Step-by-step explanation:
What are the solutions of the equation 2x² = 18? Use a graph of the related function.
The solutions of the equation 2x² = 18 are x = 3 and x = -3.
Explanation:To find the solutions of the equation 2x² = 18, we need to solve for x.
We can start by dividing both sides of the equation by 2, which gives us x² = 9.
Next, we can take the square root of both sides to find the solutions. The square root of 9 is 3, so the solutions are x = 3 and x = -3.
Learn more about Quadratic Equations here:https://brainly.com/question/30098550
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The equation 2x² = 18 has two solutions, x = 3 and x = -3, which can be determined both algebraically and graphically by observing the points where the parabola f(x) = 2x² - 18 intersects the x-axis.
The solutions of the equation 2x² = 18 can be found by first dividing both sides of the equation by 2, which simplifies to x² = 9. This is a standard quadratic equation which can be further solved by taking the square root of both sides. The solutions are x = 3 and x = -3. If we graph the related function, which is f(x) = 2x² - 18, we will see a parabola opening upwards with its vertex at the origin (0,0), and it will intersect the x-axis at the points (3,0) and (-3,0), representing our solutions.
To use a graph of the related function, we can plot the equation 2x² - 18 = 0 on a graph and find the x-values where the graph intersects the x-axis. These x-values correspond to the solutions of the equation.
If the zeros of the quadratic equation x^2+25=0 are +-5 (plus-minus 5), what is the correct factored form?
(x+5)(x-5)=0
(x+5i)(x-5i)=0
(x+12.5i)(x-12.5i)=0
(x+12.5)(x-12.5)=0
ANSWER
[tex](x + 5i)(x - 5i) = 0 [/tex]
EXPLANATION
The given function is
[tex] {x}^{2} + 25 = 0[/tex]
The zeros of this function are;
[tex]x = \pm5i[/tex]
Or
[tex]x = - 5i \: and \: x = 5i[/tex]
[tex]x + 5i = 0\: and \: x - 5i = 0[/tex]
Hence the factored form is:
[tex](x + 5i)(x - 5i) = 0 [/tex]
If the equation were:
[tex] {x}^{2} - 25 = 0[/tex]
Then the factored form is
[tex](x + 5)(x - 5) = 0 [/tex]
Please help! ASAP!!!
Answer:
[tex]\large\boxed{r=\dfrac{1}{4}}[/tex]
Step-by-step explanation:
[tex]y=rx\to r=\dfrac{y}{x}\\\\\text{From the table:}\\\\x=8,\ y=2\to r=\dfrac{2}{8}=\dfrac{1}{4}\\\\x=16,\ y=4\to r=\dfrac{4}{16}=\dfrac{1}{4}\\\\x=32,\ y=8\to r=\dfrac{8}{32}=\dfrac{1}{4}[/tex]
What solid will be produced if rectangle ABCD is rotated around line m? Assume that the line bisects both sides it intersects. What will the dimensions of the three-dimensional solid be?
rectangular prism; length = 12 in.; width = 6 in.; height = 5 in.
triangular prism; length = 12 in.; width = 6 in.;
height = 5 in.
cylinder; radius = 12 in.; height = 5 in.
cylinder; radius = 6 in.; height = 5 in.
Answer:
D) cylinder; radius = 6in.; height = 5 in.
The solid produced if rectangle ABCD is rotated around line m is a cylinder with radius of 6 in and height of 5 in.
What is a solid figure?
A solid figure is a three dimensional shape having length, width and height. Examples of three dimensional figures are prism, pyramid, cone, cylinder and so on.
The solid produced if rectangle ABCD is rotated around line m is a cylinder with radius of 6 in and height of 5 in.
Find out more on solid figure at: https://brainly.com/question/12663789
Find interest earned and the future value of an annuity with monthly payments of $150 for two years into an account that pays 4% interest per year compounded monthly.
Answer:
interest earned= 12.47
the future value of an annuity= 162.47
Step-by-step explanation:
Given Data:
Interest rate,r= 4%
time,t = 2 years
monthly payment, P= 150
n= 12 as monthly
At the end of 2 years, final investment A= ?
As per the interest formula for compounded interest
A= P(1+r/n)^nt
Putting the values in above equation
= 150(1+0.04/12)^24
= 162.47
Interest earned = A-P
= 162.47-150
= 12.47 !
Consider the function y= x^2 +4x-4.
a) what is the vertex of this function? Show your work.
b) what is the equation of the axis of symmetry? Explain how you know.
c) What is the y- intercept?
d) Graph the line of symmetry. Plot the vertex and the point containing the y-intercept. Then plot another point on the graph and use the plotted points and the axis of symmetry to plot two more points. Draw the graph of the function through the points.
Answer:
Part a) The vertex is the point (-2,-8)
Part b) The equation of the axis of symmetry is x=-2
Part c) The y-intercept is the point (0,-4)
Part d) The graph in the attached figure
Step-by-step explanation:
we know that
The equation of a vertical parabola in vertex form is equal to
[tex]y=a(x-h)^{2} +k[/tex]
where
(h,k) is the vertex of the parabola
if a> 0 then the parabola open upward (vertex is a minimum)
if a<0 then the parabola open downward (vertex is a maximum)
The axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex
so
x=h ----> equation of the axis of symmetry
In this problem we have
[tex]y=x^{2}+4x-4[/tex]
This is the equation of a vertical parabola open upward
The vertex is a minimum
Part a)
what is the vertex of this function?
Convert the function into vertex form
[tex]y=x^{2}+4x-4[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]y+4=x^{2}+4x[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side.
[tex]y+4+4=(x^{2}+4x+4)[/tex]
[tex]y+8=(x^{2}+4x+4)[/tex]
Rewrite as perfect squares
[tex]y+8=(x+2)^{2}[/tex]
[tex]y=(x+2)^{2}-8[/tex] ----> equation in vertex form
The vertex is the point (-2,-8)
Part b) what is the equation of the axis of symmetry?
we know that
The axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex
so
x=h ----> equation of the axis of symmetry
The vertex is the point (-2,-8)
The x-coordinate of the vertex is -2
therefore
The equation of the axis of symmetry is x=-2
Part c) What is the y- intercept?
we know that
The y-intercept is the value of y when the value of x is equal to zero
so
For x=0
[tex]y=(0)^{2}+4(0)-4[/tex]
[tex]y=-4[/tex]
The y-intercept is the point (0,-4)
Part d) Graph the line of symmetry. Plot the vertex and the point containing the y-intercept. Then plot another point on the graph and use the plotted points and the axis of symmetry to plot two more points. Draw the graph of the function through the points
To plot the function find the x-intercepts
we know that
The x-intercept is the value of x when the value of y is equal to zero
For y=0
[tex]0=(x+2)^{2}-8[/tex]
[tex](x+2)^{2}=8[/tex]
square root both sides
[tex]x+2=(+/-)2\sqrt{2}[/tex]
[tex]x=-2(+/-)2\sqrt{2}[/tex]
[tex]x1=-2(+)2\sqrt{2}=0.828[/tex]
[tex]x2=-2(-)2\sqrt{2}=-4.828[/tex]
the graph in the attached figure
Which amount should be entered for the balance after Anna transfers money from savings on 6/3/18?
A) $1416.42
B) $1516.42
C)$1660.32
D) $1670.52
B is the correct answer
What is the value of y?
3/3 units
53 units
9 3 units
12/3 units
Answer:
[tex]y=6\sqrt{3}[/tex]
Step-by-step explanation:
Using the Pythagoras theorem for triangle MTU,
[tex]TU^2+3^2=6^2[/tex]
[tex]TU^2+9=36[/tex]
[tex]TU^2=36-9[/tex]
[tex]TU^2=27[/tex]
[tex]TU^2=27[/tex]
From, triangle NTU,
[tex]y^2=TU^2+NU^2[/tex]
This implies that:
[tex]y^2=27+9^2[/tex]
[tex]y^2=27+81[/tex]
[tex]y^2=108[/tex]
[tex]y=\sqrt{108}[/tex]
[tex]y=6\sqrt{3}[/tex] units.
Answer:
The value of y=6√3 units.
Step-by-step explanation:
edge2020
Given: BD is a diameter
m 1 = 100°
m BC= 30°
m 3 =
30
60
100
Answer:
30°
Step-by-step explanation:
Given
BC=30°
Central abgle is equal to its arc
so <3=30°
Answer:
The answer is 30
Step-by-step explanation:
Simplify the expression.
For this case we must simplify the following expression:[tex](x ^ {\frac {3} {2}}) ^ 6[/tex]
We have that by definition of properties of powers that is fulfilled:
[tex](a ^ n) ^ m = a ^ {n * m}[/tex]
Then, rewriting the expression:
[tex]x ^ {\frac {3 * 6} {2}} =\\x ^ {\frac {18} {2}} =\\x ^ 9[/tex]
ANswer:
Option D
13 metres long and 8 metres wide what is the area
13 x 8= 104
hope this helps!
Kellianna drives 118 miles each day how many does she drive in 31 days?
Answer: 3,658 miles
Step-by-step explanation:
118 x 31 = 3,658 miles
Multiply the daily value by the number of days to find the total.
Answer:
3,658
Step-by-step explanation:
So if Kellianna drives 118 Miles each day you would simply multiply the 118 x 31 (Days) = 3,658
To help solve the trigonometric inequality 2sin(x)=>-1, which two equations can be graphed?
A. y=sin(x) and y=-1
B. y=sin(x) and y=-1/2
C. y=sin(x) and y=1/2
D. y=sin(x) and y=1
Answer:
B. y=sin(x) and y=-1/2
Step-by-step explanation:
We have been given the following trigonometric inequality;
2sin(x)=>-1
The above inequality can be re-written as;
sin(x)=>-1/2
after dividing both sides by 2.
We can then formulate two separate equations, one containing the expression on the right hand side and the other containing the expression on the left hand side;
From the left hand side we form the following equation;
y = sin(x)
From the right hand side we form the following equation;
y = -1/2
Therefore, the above two equations can be graphed to help solve the given trigonometric inequality
Answer: B
y=sin(x) and y=-1/2
Step-by-step explanation:
A number is multiplied by the number 3less than itself. The result is 54. The number is...
Answer:
• positive answer: 9
• negative answer: -6
Step-by-step explanation:
Since you know your multiplication tables, you are familiar with the fact 6·9 = 54. One of these factors is 3 larger than the other, so is the answer you seek.
The number is 9.
___
These multiplication problems often have negative solutions as well. Usually, the negative solution is the other factor of the pair, but with a minus sign. Here, that is -6:
(-6)(-9) = 54 . . . . . where -9 is 3 less than -6.
Answer:
9
Step-by-step explanation:
Let's break it down
" A number is multiplied "
Okay so we know that a number is being multiplied
" by the number 3 less than itself"
So whatever number it is, (lets use x) is being multiplied by a number (lets use y) 3 less then itself. So x - 3 = y and x·y = 54
So I started dividing all the numbers 1 - 9
54 ÷ 9 = 6
54 ÷ 8 = 6.75
54 ÷ 7 = 7.71~
54 ÷ 6 = 9
Then I stopped
Read the question again
"A number is multiplied by the number 3 less than itself. The result is 54."
A number - 9
Multiplied by the number 3 LESS then itself - 6
The result is 54 - 9 × 6 = 54
Hope that helps ^^
How do you explain ratios?
A ratio is the part divided by the whole. Johnny took 3 pieces of pizza when the whole pizza had 8. Johnny has 3/8 (3 out of 8) pieces of pizza, or .375 parts. To find that number, literally divide your part from your whole to get the decimal form.
How many square feet of outdoor carpet will we need for this hole?
Answer:
6 ft^2 and 2ft^2
Step-by-step explanation:
Multiply the height and length of each hole to get the answers. Not sure if you wanted both or not.
Answer:
im on the same question but i think u just have to multiply length times width for all of them then u subtract. hope it helps
Step-by-step explanation:
What is the solution to the equation?
A. h=11/3
B.h=5
C.h=21/2
D. h=7
Answer:
D. h=7
Step-by-step explanation:
1 2 16
------ + ------------ = ----------
h-5 h+5 (h^2 -25)
1 2 16
------ + ------------ = ----------
h-5 h+5 (h-5)(h+5)
Since h^2 -25 factors in (h-5) (h+5) ( it is the difference of squares)
We will multiply both sides by (h-5) (h+5) to clear the fractions
(h-5) (h+5) 2 (h-5) (h+5) 16 (h-5) (h+5)
------ + ------------ = ----------
h-5 h+5 (h-5)(h+5)
Canceling like terms
(h+5) 2 (h-5) 16
------ + ------------ = ----------
1 1 1
h+5 + 2(h-5) = 16
Distribute
h+5 + 2h -10 = 16
Combine like terms
3h-5=16
Add 5 to each side
3h-5+5 =16+5
3h =21
Divide each side by 3
3h/3 = 21/3
h = 7
Determine the number of real solutions of -2x^2+5x-3=0
Answer:
Two distinct real solutions.
Step-by-step explanation:
Given the equation in the form [tex]ax^2+bx+c=0[/tex], you need to find the Discriminant with this formula:
[tex]D=b^2-4ac[/tex]
For the equation [tex]-2x^2+5x-3=0[/tex] you can identify that:
[tex]a=-2\\b=5\\c=-3[/tex]
Then, substituting these values into the formula, you get that the Discriminant is:
[tex]D=5^2-4(-2)(-3)[/tex]
[tex]D=1[/tex]
Since [tex]D>0[/tex], then [tex]-2x^2+5x-3=0[/tex] has two distinct real solutions.
Which statements about the box plot are correct? Check all that apply.
Fifty percent of the data values lies between 34 and 46.
Seventy-five percent of the data values lies between 42 and 70.
It is unlikely that there are any outliers.
The interquartile range'is 24.
The range is 36
Answer:
The correct options are 1 and 3.
Step-by-step explanation:
From the given box plot it is clear that
[tex]\text{Minimum values}=34[/tex]
[tex]Q_1=42[/tex]
Q₁ is 25% of a data.
[tex]Median=46[/tex]
Median is 50% of a data.
[tex]Q_3=70[/tex]
Q₃ is 75% of a data.
[tex]\text{Maximum values}=76[/tex]
34 is minimum value of the data and 46 is median it means 50% of the data values lies between 34 and 46. Therefore option 1 is correct.
42 is first quartile and and 70 is third quartile. it means 50% of the data values lies between 42 and 70. Therefore option 2 is incorrect.
The difference between Minimum value and first quartile, Maximum value and third quartile is less than 1.5×(IQR), therefore it is unlikely to have any outliers in the data.
Hence option 3 is correct.
The interquartile range of the data is
[tex]IQR=Q_3-Q_1[/tex]
[tex]IQR=70-42=28[/tex]
The interquartile range is 28. Therefore option 4 is incorrect.
Range of the data is
[tex]Range=Maximum-Minimum[/tex]
[tex]Range=76-34=42[/tex]
The range is 42. Therefore option 5 is incorrect.
Answer:
A,C
Step-by-step explanation:
got it right on edge 2021
have a wonderful day
Find the circumference of a circle with an area of 615.75 square inches
Answer:
C ≈ 87.96in
Step-by-step explanation:
PLEASE ANSWER THIS ONE QUESTION WITH CHOICES! ! BRAINLIEST!!! Number 10
What the test is looking for is obviously x<=5 (the second one), but I'd actually say 0 is equal or less than x that is equal or less than 5, where x is a natural number.
You cannot have a negative quantity of books, nor can you have 4.3627272828 ones.
Answer: The correct option is (B) [tex]x\leq 5.[/tex]
Step-by-step explanation: We are given to write an inequality for the following situation :
"No more than 5 books are in your backpack".
Let the number of books in the backpack be x.
The given situation implies that there will be either less than or equal to 5 books in the backpack.
Therefore, the required situation can be written as
[tex]x\leq 5.[/tex]
Thus, (B) is the correct option.
Brainliest + Points
Can someone please help? Kind of struggling. Would you please explain
In 2008, Adam Lopez set a world record by singing the highest note ever recorded, a C8. That is four octaves above middle C and not on a normal piano keyboard. What is the frequency to the nearest hertz of this musical note if its period is 0.00024?
A.
1,873 hertz
B.
2,631 hertz
C.
3,845 hertz
D.
4,167 hertz
Answer:
ok friend so the answer is :) D
Step-by-step explanation:
because
Freq = 1 / Period
Freq = 1 / 0.00024 = 4166.66 Hz = 4167 Hz
:)
The frequency of the C8 note set by Adam Lopez is the inverse of its period of 0.00024 seconds. Calculating 1/0.00024 gives a frequency of 4166.67 Hz, which rounds to d) 4167 Hz.
The frequency of a musical note is the inverse of its period. The period is the amount of time it takes for one complete cycle of the sound wave. If Adam Lopez's record-setting C8 has a period of 0.00024 seconds, we can calculate the frequency as follows:
FrequencyTo the nearest hertz, the frequency of the C8 note is 4167 hertz.
The correct answer is D. 4167 hertz.
Find the value of y. Please help
4y-7=2y-1
Subtract 2y from both sides
2y-7=-1
Add 7 to both sides
2y=6
Y=3
The Bucio family wants to buy a new car which has a list price of $18,000. The salesperson is offering a discount of $3,000. What is the rate of the discount? ( rounded to the nearest whole percent)
Answer:
Discount Rate=17%
Step-by-step explanation:
We know the price and discount of the car. The formula for calculating the discount when rate is given is:
[tex]Discount=Listed\ price*discount\ rate[/tex]
We know two quantities out of three, so putting in the known values:
[tex]3000=18000*rate\\rate=\frac{3000}{18000}\\Rate=16.67%[/tex]
The rate rounded off to nearest percent will give us:
17 percent.
So the discount rate is 17% ..
When rounded to the nearest whole percent, the discount rate is 17%.
To calculate the rate of the discount for the Bucio family's new car purchase, we will use the formula for finding the percentage rate of a discount, which is:
Discount Rate = (Discount Amount / Original Price) x 100.
In their case, the car has an original list price of $18,000, and they are offered a discount of $3,000. Plugging these values into the formula gives us:
Discount Rate = ($3,000 / $18,000) x 100
Discount Rate = 0.1667 x 100
Discount Rate = 16.67%
When rounded to the nearest whole percent, the discount rate is 17%.
Help ASAP WILL GIVE BRAINLIEST AND 10 POINTS
Answer: She Is Not Correct The Answer Is 24
Step-by-step explanation: The answer is 24. This is because when you have order of operations, you always do parentheses first. (27-9) equals 18. Then multiply it by 3 so do 20 times 3 and then subtract 6 and you get 54. Then divide 54 by 9 and you get 6. 6+18 does not equal 42 so it would be the third one.
-HAVE A GREAT DAY-
Answer:
the answer is C.
Step-by-step explanation:
using pemdas you start with parenthesis,
(27-9)*3÷9+18=42
18*3÷9+18=42 . use rules of multiplication and division
54÷9+18=42 divide again
6+18=42 add
24=42
this is false because the numbers don't match up on the left and right side, so 24 is the real answer.
Find The mass of a solid cone of platinum with a height of 21 cm and a diameter of 8 cm.
For this case we have that by definition, the density is given by:
ρ =[tex]\frac {M} {V}[/tex]
Where:
M: It's the mass
V: It's the volume
The volume of a solid cone is given by:
[tex]V = \frac {1} {3} \pi * r ^ 2 * h[/tex]
Where:
A: It's the radio
h: It's the height
Substituting the data we have:
[tex]V = \frac {1} {3} \pi * (4) ^ 2 * 21\\V = \frac {1} {3} \pi * 16 * 21\\V = 401.92 \ cm ^ 3[/tex]
On the other hand, we have that by definition, the density of the platini is given by:
[tex]21.45 \frac {g} {cm ^ 3}[/tex]
Substituting in the initial formula, we look for the mass:
[tex]M = 401.92 \ cm ^ 3 * 21.45 \frac {g} {cm ^ 3}\\M = 8621.184 \ g[/tex]
ANswer:
The mass of the platinum cone is 8621.2 grams.
To find the mass of a solid platinum cone with a height of 21 cm and a diameter of 8 cm, calculate the volume using the formula for a cone (⅓πr²h) and then multiply by platinum's density (21,450 kg/m³) to get approximately 30.342 kg.
Explanation:Calculate the Mass of a Platinum Cone
To determine the mass of a solid cone made of platinum with a given height and diameter, we must first calculate its volume and then use the density of platinum to find its mass. The density of platinum is approximately 21,450 kg/m³. The volume of a cone is given by the formula ⅓πr²h, where r is the radius and h is the height. For our cone with a height (h) of 21 cm and a diameter of 8 cm, the radius (r) would be half of the diameter, so r = 4 cm = 0.04 m. Plugging the values into the formula, we get:
Volume (V) = ⅓π(0.04 m)²×21 cm = ⅓π(0.0016 m²)× 0.21 m = 0.0014136 m³.
To find the mass (m), we multiply the volume by the density of platinum (ρ):
Mass (m) = Density (ρ) × Volume (V) = 21,450 kg/m³ × 0.0014136 m³ = 30.342 kg.
Therefore, the mass of the solid platinum cone is approximately 30.342 kilograms.
how can rebecca divide 3/4 of a cake into 9 pieces. What fraction of the whole cake will each piece be?
Answer:
each slice will be 1/36
Step-by-step explanation:
1/4 • 1/9 equals 3/36
Final answer:
Rebecca can divide ¾ of a cake into 9 pieces by finding the fraction of each piece relative to the whole cake, which is ⅛ or one-twelfth of the whole cake.
Explanation:
How to Divide a Cake into Equal Pieces
To divide ¾ of a cake into 9 equal pieces, Rebecca must consider how many pieces the whole cake can be divided into first. Since she has three-quarters of a cake, and she wants to make 9 pieces out of it, each piece will be one-ninth of the three-quarters of a cake. To find out the size of each piece relative to the whole cake, she divides ¾ by 9. This can be calculated as ¾ × ⅟, which simplifies to ⅛. This means that each piece of cake will be one-twelfth of the whole cake.
Understanding fractions such as halves, thirds, and quarters is useful in daily life and in solving problems like these. Knowing that a quarter is 25 cents makes it easier to grasp a quarter of a pie or cake. If you can visualize that two-thirds of a pie is more than half a pie, it helps when dividing portions or budgeting resources.
Sarah rolled a number cube numbered 1 to 6. The table below shows the results of rolling the cube 50 times. Use the results in the table to find the experimental probability.
Answer “P(3)”
If P(3) stands for the probability of the number 3 getting rolled, since 3 was rolled 5 times (as shown on the graph) out of 50 (as mentioned in the question), the experimental probability would be: 5/50, which when simplified, is 1/10
The student is asked to calculate the experimental probability of rolling a 3, but the specific frequency Sarah rolled a 3 is not provided. Without this, we cannot compute the experimental probability. Generally, the method involves dividing the number of times a 3 was rolled by the total number of rolls.
Explanation:The question asks for the experimental probability of rolling a 3 on a six-sided die based on the results Sarah obtained from her 50 rolls. However, the provided information does not include the actual frequency of rolling a 3 in her experiment. If we had that data, the experimental probability P(3) would be the number of times a 3 was rolled divided by the total number of rolls (50 in Sarah's case).
For example, if Sarah rolled a 3 ten times out of 50, then the experimental probability of rolling a 3 would be calculated as follows: P(3) = 10/50 = 1/5. Without the specific results of Sarah's rolls, we cannot determine the experimental probability from the information given in the question.
The graph shows the feasible region for the system with constraints:
y ≤ 15 x + y ≤ 25 x + 2y ≥ 30
What are the vertices of the feasible region? Check all of the boxes that apply.
(0, 25)
(0, 15)
(10, 15)
(20, 5)
(25, 0)
(30, 0)
What is the minimum value of the objective function C = 4x + 9y?
C =
Answer:
The vertices feasible region are (0 , 15) , (10 , 15) , (20 , 5)
The minimum value of the objective function C is 125
Step-by-step explanation:
* Lets look to the graph to answer the question
- There are 3 inequalities
# y ≤ 15 represented by horizontal line (purple line) and cut the
y-axis at point (0 , 15)
# x + y ≤ 25 represented by a line (green line) and intersected the
x-axis at point (25 , 0) and the y- axis at point (0 , 25)
# x + 2y ≥ 30 represented by a line (blue line) and intersected the
x-axis at point (30 , 0) and the y-axis at point (0 , 15)
- The three lines intersect each other in three points
# The blue and purple lines intersected in point (0 , 15)
# The green and the purple lines intersected in point (10 , 15)
# The green and the blue lines intersected in point (20 , 5)
- The three lines bounded the feasible region
∴ The vertices feasible region are (0 , 15) , (10 , 15) , (20 , 5)
- To find the minimum value of the objective function C = 4x + 9y,
substitute the three vertices of the feasible region in C and chose
the least answer
∵ C = 4x + 9y
- Use point (0 , 15)
∴ C = 4(0) + 9(15) = 0 + 135 = 135
- Use point (10 , 15)
∴ C = 4(10) + 9(15) = 40 + 135 = 175
- Use point (20 , 5)
∴ C = 4(40) + 9(5) = 80 + 45 = 125
- From all answers the least value is 125
∴ The minimum value of the objective function C is 125
The vertices of the feasible region are (0, 15), (10, 15), and (20, 5). The minimum value of the objective function C = 4x + 9y is 190 at the vertex (10, 15).
The feasible region is the area on a graph where all the constraints of a system of inequalities are satisfied. To find the vertices of the feasible region, we need to find the intersection points of the lines formed by the given constraints. By solving the system of equations, we find that the vertices of the feasible region are (0, 15), (10, 15), and (20, 5).
To find the minimum value of the objective function C = 4x + 9y, we substitute the x and y values of each vertex into the objective function and determine which vertex gives the smallest value. By evaluating the objective function at each vertex, we find that the minimum value is obtained at the vertex (10, 15) with a value of 4(10) + 9(15) = 190.
Learn more about Feasible Region here:https://brainly.com/question/31686791
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