Answer:
[tex] x = \frac{12 \pm \sqrt{(-12)^2 -4(5)(-7)}}{2(5)}[/tex]
And we got for the solution:
[tex] x_1= 2.885 , x_2 = -0.485[/tex]
And the value sof y are using the function y =2x-3:
[tex] y_1=2.77, y_2=-3.97[/tex]
Step-by-step explanation:
For this case we have this function given:
[tex] y = 2x-3[/tex] (1)
And the circle with center the origin and radius 4 is given by;
[tex] x^2 +y^2 = 16[/tex] (2)
We can solve fro y from the last equation and we got:
[tex] y = \pm \sqrt{16-x^2}[/tex] (3)
Now we can set equal equations (3) and (1) and we got:
[tex] 2x-3 = \sqrt{16-x^2}[/tex]
[tex] (2x-3)^2=16-x^2[/tex]
[tex] 4x^2 -12x +9 = 16-x^2[/tex]
[tex] 5x^2 -12x -7=0[/tex]
And using the quadratic equation we got:
[tex] x = \frac{12 \pm \sqrt{(-12)^2 -4(5)(-7)}}{2(5)}[/tex]
And we got for the solution:
[tex] x_1= 2.885 , x_2 = -0.485[/tex]
And the value sof y are using the function y =2x-3:
[tex] y_1=2.77, y_2=-3.97[/tex]
Find the present value of $10,000 received at the start of every year for 20 years if the interest rate is J1 = 12% p.a. and if the first payment of $10,000 is received at the end of 10 years.
Answer:
Step-by-step explanation:
The person receives 10000 every month
for one year total principal 10000 * 12 = 120000
r= 12%p.a and t is 1yr
simple interest= 120000*12*1/100 = 14400
total money received in present year 120000 + 14400 = 134400
for 20 yrs principal becomes 10000*12*20= $2400000
simple interest = 2400000*12*20/100= $5760000
total amount received for 20 yrs = 2400000+ 5760000=8160000.
present value of principal as money receive 10000 for 10 yrs = 10000*10 = 100000
si = 100000*10*12/100= 120000
amount = $220000
solve 2x-4÷ 5 = 4
really need help fast
Step-by-step explanation:
here is the answer u can get help from it.....
The solution to the equation (2x-4)/5 = 4 is x = 12.
What is the solution of the equation?To solve the equation (2x-4)/5 = 4, we will use the following steps.
Multiply both sides of the equation by 5 to eliminate the denominator as;
5[(2x-4)/5] = 5 x 4
This simplifies to:
2x - 4 = 20
Add 4 to both sides of the equation to isolate the term with x:
2x - 4 + 4 = 20 + 4
This simplifies to:
2x = 24
Divide both sides of the equation by 2 to solve for x:
(2x)/2 = 24/2
This simplifies to:
x = 12
Thus, the solution to the equation (2x-4)/5 = 4 is x = 12.
Learn more about simplification here: https://brainly.com/question/28008382
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sector with a radius of \maroonD{10\,\text{cmd}}10cm start color #ca337c, 10, start text, c, m, end text, end color #ca337c has a central angle measure of \purpleD{252\degree}252°start color #7854ab, 252, degree, end color #7854ab. \theta=252\degreeθ=252°r=10\,\text{cm}r=10cm
Answer:
219.91cm²
Step-by-step explanation:
The question is not properly structured. Here is the complete question.
A sector with a radius of 10cm and has a central angle of 252°. Calculate the area of the sector.
Area of a sector = theta/360 × πr²
theta is the angle substended by the circle
r is the radius of the circle.
Given radius = 10cm
theta = 252°
Area of a sector = 252°/360° × π(10)²
Area of a sector = 252/360 × 100π
Area of a sector = 79168.13.360
Answer:
Step-by-step explanation:
The question is not properly structured. Here is the complete question.
A sector with a radius of 10cm and has a central angle of 252°. Calculate the area of the sector.
Area of a sector = theta/360 × πr²
theta is the angle substended by the circle
r is the radius of the circle.
Given radius = 10cm
theta = 252°
Area of a sector = 252°/360° × π(10)²
Area of a sector = 252/360 × 100π
Area of the sector = 219.91cm²
Answer:
70pi
Step-by-step explanation:
That is the answer on khan academy
2.
The Parkside Packing Company needs a rectangular shipping box. The box must have a length
of 11 inches and a width of 8 inches. Find, to the nearest tenth of an inch, the minimum height
of the box such that the volume is at least 800 cubic inches.
(3 points)
Answer:
9.1 Inches
Step-by-step explanation:
Length of the proposed box=11 Inches
Width of the proposed box=8 Inches
Required Volume, [tex]V \geq 800 $ cubic inches.[/tex]
Volume of a Rectangular Prism =Length X Width X Height
Therefore:
[tex]800\\11*8*Height\geq 800\\88*Height \geq 800\\$Divide both sides by 88\\Height \geq 800 \div 88\\Height \geq 9.\overline{09}$ inches[/tex]
Therefore, the minimum height to the nearest tenth of an inch is 9.1 Inches.
can some work out 1/(2x10^5)+(5x10^4)
Solve.
y = x – 8
2x + 3y = 1
Use the substitution method.
Substitute [tex]y=x-8[/tex] into the second equation to get [tex]2x+3(x-8)=1,[/tex] which simplifies to [tex]5x=25,[/tex] so [tex]\boxed{x=5}.[/tex] It easily follows that [tex]\boxed{y=-3}.[/tex]
Answer:
x=5, y=-3
Step-by-step explanation:
What would be the arc length of 1/5 of a circle with a radius of 4 ft?
Answer:
5.029ft
Step-by-step explanation:
[tex](titer \div 360) \times \pi \times diameter[/tex]
[tex](75degrees \div 360) \times \pi \times 8[/tex][tex] = 5.029[/tex]Divide these polynomials (8x^3+2x^2-7x+2)/(2x-1)
Answer:
[tex]4x^2+3x-2[/tex]
Step-by-step explanation:
We are given that
[tex]\frac{8x^3+2x^2-7x+2}{2x-1}[/tex]
We have to divide the polynomials.
We have
Divisor polynomial=[tex]2x-1[/tex]
Dividend polynomial=[tex]8x^3+2x^2-7x+2[/tex]
[tex]\frac{8x^3+2x^2-7x+2}{2x-1}=4x^2+3x-2[/tex]
Quotient=[tex]4x^2+3x-2[/tex]
Remainder=0
What is the value of the expression?
458+56−134
Enter your answer as a mixed number in simplest form
Answer:
Step-by-step explanation:
Apply the priority rule,
(458+56)-134=514-134=380
Several employees have submitted different methods of assembling a subassembly. Sample data for each method are: Minutes Required for Assembly Sample Number Lind's Method Szabo's Method Carl's Method Manley's Method 1 16.6 22.4 31.4 18.4 2 17.0 21.5 33.4 19.6 3 16.9 22.6 30.1 17.6 How many treatments are there?
Answer:
There are 4 treatments
Step-by-step explanation:
In this study, there are four treatments. Each sample from 1 to 3 was subjected to each treatments which in this case are the methods; Lind's Method, Szabo's Method, Carl's Method and Manley's Method.
Thus, the methods in this study are the treatments the samples are subjected to.
What is (-3)x(5-7)-9(39/3)
Answer:-111
Step-by-step explanation:
0.09 is smaller than 0.001
Answer:
no
Step-by-step explanation:
The degree of the polynomial f (x) is 3, and the degree of the polynomial g(x) is 4. Find the degree of the polynomial f (x) + g(x).
Answer:
The degree would be 4
Step-by-step explanation:
When you add polynomials without multiplying bases, you cannot add or subtract the degree. So the highest degree would be 4 in this case.
(+20) + (-4) [(+3) 2 - (+6)]
Suppose that 80% of all trucks undergoing a brake inspection at a certain inspection facility pass the inspection. Consider groups of 17 trucks and let X be the number of trucks in a group that have passed the inspection. What is the probability that at least 10 but fewer than 13 trucks pass the inspection
Answer:
0.2308 = 23.08% probability that at least 10 but fewer than 13 trucks pass the inspection
Step-by-step explanation:
For each truck, there are only two possible outcomes. Either they pass the inspection, or they do not. The probability of a truck passing the inspection is independent of other trucks. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
80% of all trucks undergoing a brake inspection at a certain inspection facility pass the inspection.
This means that [tex]p = 0.8[/tex]
17 trucks:
This means that [tex]n = 17[/tex]
What is the probability that at least 10 but fewer than 13 trucks pass the inspection
[tex]P(10 \leq X < 13) = P(X = 10) + P(X = 11) + P(X = 12)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 10) = C_{17,10}.(0.8)^{10}.(0.2)^{7} = 0.0267[/tex]
[tex]P(X = 11) = C_{17,11}.(0.8)^{11}.(0.2)^{6} = 0.0680[/tex]
[tex]P(X = 12) = C_{17,12}.(0.8)^{12}.(0.2)^{5} = 0.1361[/tex]
[tex]P(10 \leq X < 13) = P(X = 10) + P(X = 11) + P(X = 12) = 0.0267 + 0.0680 + 0.1361 = 0.2308[/tex]
0.2308 = 23.08% probability that at least 10 but fewer than 13 trucks pass the inspection
18. Which inequality is equivalent to
3x + 2 > 5?
A) x <1
B) x>-1
C) x 1
D) X > 3
Answer:
C)
Step-by-step explanation:
3x+2>5
3x>3
x>1
I believe that you mistyped C so I think its C
The midpoint of (-2,1) and (-1,1)
Answer:
The midpoint of (-2,1) is -1. The midpoint for (-1,1) is 0.
Step-by-step explanation:
To find the midpoint you will have to add x+y then divide by 2.
can someone please help me!
Answer:
D
Step-by-step explanation:
Let's derive the equations for the two graphs;
For the graph towards the right,
The slope = y2-y1/x2-x1; so we choose two corresponding points (x1,y1); (x2,y2)
Let's choose points;
(2,1) and (3,2)
The slope = 2-1/ 3-2 = 1/1 = 1
From the general equation of a line
y = mx + c = 1× x + (-1) = x-1
y = x-1
Similarly for that towards the left we have;
The slope = y2-y1/x2-x1; so we choose two corresponding points (x1,y1); (x2,y2)
Let's choose points;
(2,1) and (3,2)
The slope = 2-1/ 3-2 = 1/1 = 1
From the general equation of a line
y = mx + c = 1× x + (-1) = x-1
y = x-1
Similarly for that towards the left we have;
The slope = y2-y1/x2-x1; so we choose two corresponding points (x1,y1); (x2,y2)
Let's choose points;
(-7,0) and (-4,-3)
Slope = -3-0/ -4-(-7) = -3/ 3 = -1
From the general equation of a line
y = mx + c = -1× x + c = -x + c
Since c is not obvious we can find the equation by picking just a point along the graph along side an arbitrary (x,y) point hence we have for slope;
If we pick (-7,0)
y-0 / x-(-7) = -1
y / x+7 = -1
y = -x -7
The equations of the graphed lines are;
y=x-1
y=-x-7
Look at option D you we see it's the same as the equation of the graph towards the right y=x-1
For the records
y=[x+3]-4 = x+3-4 = x-1
n a survey of 331 customers, 66 say that service is poor. You select two customers without replacement to get more information on their satisfaction. What is the probability that both say service is poor?
Answer:
3.93% probability that both say service is poor
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The customers are chosen without replacement, and the order in which they are chosen is not important. So we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
What is the probability that both say service is poor?
Desired outcomes:
Two saying it is poor, from a set of 66. So
[tex]D = C_{66,2} = \frac{66!}{2!(66-2)!} = 2145[/tex]
Total outcomes:
Two customers from a set of 331. So
[tex]T = C_{331,2} = \frac{331!}{2!(331-2)!} = 54615[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{2145}{54615} = 0.0393[/tex]
3.93% probability that both say service is poor
There are 13 comma 17913,179 eligible voters in one town. In a poll of 834834 eligible voters from this town, the proportion who say that they plan to vote in the next mayoral election is 0.470.47. Based on that sample statistic, what is the best estimate of the proportion for all eligible voters in the town? Round to two decimal places as needed.
Answer:
The best estimate of the proportion for all eligible voters in the town, that is, the best estimate for the population, is 0.47.
Step-by-step explanation:
Since the sample is large enough, the proportion from the sample is the best estimate for the proportion of the population.
In this question, we have that:
For the sample, the proportion who say that they plan to vote in the next mayoral election is 0.47
So the best estimate of the proportion for all eligible voters in the town, that is, the best estimate for the population, is 0.47.
A homeowner is designing a rectangular pool for her backyard. Due to the size of the yard, the width of the pool will be one-third its length, and the pool will have a uniform depth of 5 feet. Which of the following equations can be used to describe l, the length of the pool, in terms of its volume, V?
Answer:
Step-by-step explanation:
Does Anyone know how to do this It’s very difficult for me
Answer: D
Step-by-step explanation: y int is when x=0, thus when there are no chirps.
Y=(1/6)x + 50
put in 0
Y=(1/6)*0 + 50
Y=50
Slope is the rate at which x changes, in this case, 1/6
The temperatures at several times of the day are shown in the coordinate plane below. The x-axis represents the number of hours before or after noon. For example, -1 would represent 11 a.m. The y-axis represents the temperature in degrees Celsius. At 5 p.m.5, start text, space, p, point, m, point, end text, the temperature is halfway between the temperature at 2 \text{ p.m.}2 p.m.2, start text, space, p, point, m, point, end text and the temperature at 8 \text{ p.m.}8 p.m.8, start text, space, p, point, m, point, end text What coordinates represent the temperature at 5pm?
Question:
The temperatures at several times of the day are shown in the coordinate plane below. The x-axis represents the number of hours before or afternoon. For example, -1 would represent 11 a.m. The y-axis represents the temperature in degrees Celsius.At 5 p.m, the temperature is halfway between the temperature at 2 p.m. and the temperature at 8 p.m.
What coordinates represent the temperature at 5 p.m.?
Answer:
(5, 2)
=> At 5pm, the temperature is at 2⁰C
Step-by-step Explanation:
Coordinates of any point on a cartesian/coordinate plane is represented by (x, y). Where x is the number at the point on z-axis, while y is the number at the same point on the y-axis.
From the diagram of the coordinate plane attached below, we can simply find out what coordinates represent the temperature at 5pm.
==> Given that the temperature at 5pm is half way between the temperature at 2pm (y=7) and temperature at 8pm (y=-3), the point that is being referred to = [7+(-3)] ÷ 2 = ⁴/2 = 2 (i.e. 2 on the y axis representing temperature)
*The position of the point is indicated in the second picture that is attached below.
At that position of the point, we have 2 as the coordinate for the y axis representing temperature, and at that same position, we have 5 on the x-axis representing the number of hours.
Therefore, coordinates of the point (x, y) representing 5p.m = (5, 2)
==> At 5pm, the temperature is at 2⁰C
Answer:
Look above for a good answer!
Step-by-step explanation:
The coordinates are 5,2
A goal is to get at least 10% of daily calories from polyunsaturated fats as are found in various nuts, oils, and fish. One serving of walnuts (about 15 pieces) has about 20 g of polyunsaturated fat. Each fat gram has 9 calories. About what percent of daily calories does one serving of walnuts provide, assuming a 2,000-calorie diet?
The percent of daily calories does one serving of walnuts provide is 9%.
This question is solved using proportions.
We have:
A diet of 2,000 calories.To find the percentage of daily calories provided by one walnut, we have to find the amount of calories in the walnut, and find it's percentage relative to 2,000.-----------------
Walnut:
Has 20 grams of polyunsaturated fat.Each gram has 9 calories.Thus, the amount of calories of fat is:
[tex]A = 20 \times 9 = 180[/tex]
-----------------
Percentage:
180 calories out of a daily diet of 2000 calories, so:
180*100%/2000 = 9%
The percent of daily calories does one serving of walnuts provide is 9%.
A similar question is found at https://brainly.com/question/10491646
In a spelling test the scores are 15,8,11,16,10,5and 10. what is the range
Solution,
Given data=15,8,11,16,10,5,10
Highest score= 16
lowest score= 5
Range=highest score- lowest score
=16-5
=11
Answer:
[tex]10[/tex]
Step-by-step explanation:
Given data =
[tex]15 \: \: 8 \: \: 11 \: \: 16 \: \: 10 \: \: 5 \: \: 10[/tex]
[tex]range = height \: \: - \: lowest \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: score \: \: \: \: \: \: \: \: \: \: \: \: \: score \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 15 \: \: \: \: \: - \: \: \: \: 5 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 10[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
A drink is a mixture of three parts water to 1 part orange concentrate. How much water should be added to 100ml of orange concentrate? *
Answer:
300 mL
Step-by-step explanation:
If one part is 100 mL, then 3 parts will be 300 mL.
300 mL of water should be added.
uppose that Mary's utility function is U(W) = W0.5, where W is wealth. She has an initial wealth of $100. How much of a risk premium would she want to participate in a gamble that has a 50% probability of raising her wealth to $115 and a 50% probability of lowering her wealth to $77? Mary's risk premium is $ nothing. (round your answer to two decimal places)
Note that [tex]U(W) = W^{0.5}[/tex]
Answer:
Mary's risk premium is $0.9375
Step-by-step explanation:
Mary's utility function, [tex]U(W) = W^{0.5}[/tex]
Mary's initial wealth = $100
The gamble has a 50% probability of raising her wealth to $115 and a 50% probability of lowering it to $77
Expected wealth of Mary, [tex]E_w[/tex]
[tex]E_{w}[/tex] = (0.5 * $115) + (0.5 * $77)
[tex]E_{w}[/tex] = 57.5 + 38.5
[tex]E_{w}[/tex] = $96
The expected value of Mary's wealth is $96
Calculate the expected utility (EU) of Mary:-
[tex]E_u = [0.5 * U(115)] + [0.5 * U(77)]\\E_u = [0.5 * 115^{0.5}] + [0.5 * 77^{0.5}]\\E_u = 5.36 + 4.39\\E_u = \$ 9.75[/tex]
The expected utility of Mary is $9.75
Mary will be willing to pay an amount P as risk premium to avoid taking the risk, where
U(EW - P) is equal to Mary's expected utility from the risky gamble.
U(EW - P) = EU
U(94 - P) = 9.63
Square root (94 - P) = 9.63
If Mary's risk premium is P, the expected utility will be given by the formula:
[tex]E_{u} = U(E_{w} - P)\\E_{u} = U(96 - P)\\E_u = (96 - P)^{0.5}\\(E_u)^2 = 96 - P\\ 9.75^2 = 96 - P\\95.0625 = 96 - P\\P = 96 - 95.0625\\P = 0.9375[/tex]
Mary's risk premium is $0.9375
A student walk 60m on a bearing of 028 degree and then 180m due east. How is she from her starting point, correct to the nearest whole number?
Answer:
She is 215 m from the starting point
Step-by-step explanation:
Let's begin by constructing a figurative representation of the information given (figure attached)
We know 2 sides of the triangle and the inner angle, we can therefore use the Cosine Rule
Mathematically represented as:
b² = a² + c² - 2ac(CosB)
b = ?, a = 60 m, c = 180, B = 118° (the sum of the 90° right angle at B + the interior angle of 28° from A)
b² = 60² + 180² - 2(60)(180)Cos 118°
b² = 3600 + 32400 - (- 10140.586)
b² = 46140.586 ⇒ b = [tex]\sqrt{46140.586}[/tex]
b = 214.8 m ≈ 215 m
b = 215 m (to the nearest whole number)
∴ the student is 215 m from the starting point
Which of the following is an arithmetic sequence?
Answer: choice D
Step-by-step explanation:
An arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence.
in this exampke the constant(d) is -3
Answer:
D is the correct answer.
Step-by-step explanation:
because the numbers are decreased by -3
Defination: in arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence.
"According to a 2018 Gallup poll, 5% of U.S. adults consider themselves to be vegetarian. Nonwhite Americans (9%) are three times as likely as white Americans (3%) to describe themselves as vegetarian." This statement is based on a random sample of 1033 American adults interviewed in July 2018, in which 270 respondents identified as "nonwhite" and 742 as "white.
The cited value 5% is part of the:
a. Experimental
b. Conditional
c. Observational
d. Anecdotal
e. Marginal
and distribution of the:
a. Ethnicity, given diet choice
b. Diet choice, given ethnicity
c. Ethnicity, D. Diet
Answer:
(c) Observational Distribution
(d) Diet Choice
Step-by-step explanation:
Out of 1033 American adults interviewed in July 2018, 5% consider themselves to be vegetarian.
Since the poll observes the diet habit of the respondents, the cited 5% is part of the Observational distribution of whether the respondent is a vegetarian or not (which is the Diet Choice).
If on the other hand, the poll seeks to manipulate the conditions of the study, it would have been an experimental distribution.