Answer:
[tex](x-14)^2 +(y-22)^2 = (\sqrt{65})^2[/tex]
Step-by-step explanation:
If the two given points are the extremes of the diameter, the center of the circle has to be its middle point - that we can find by taking the average of the coordinates. The center thus sits in
[tex](\frac{22+6}2; \frac{21+23}2)[/tex] or [tex](14; 22)[/tex]. At this point we either find the length of the diameter and halve it, or the distance between the center and either point. Let's go for the diameter.
[tex]r=\sqrt{(22-6)^2+(21-23)^2}=\sqrt{16^2+2^2} = \sqrt {260}=2\sqrt{65}[/tex]. That makes our radius half of that. We can easily write the equation of the circle now:
[tex](x-14)^2 +(y-22)^2 = (\sqrt{65})^2[/tex]
Now, in theory you can improve it by multiplying it out and taking every term to the LHS, but I think it's good enough like that.
What is the total repayment made, including principal and interest, on a loan of $1,100 at 3.5% interest compounded annually over four years?
The total repayment made, including principal and interest is $1262.27
Compound interestThe formula for calculating the compound interest is calculated as shown below;
A = P(1+r)^t
where
P is the principal = $1100
rate = 3.5% = 0.035
time "t" =4 years
Substitute
A. = 1100(1+0.035)^4
A = 1100(1.035)^4
A = 1100(1.14752)
A = 1262.27
Hence the total repayment made, including principal and interest is $1262.27
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A recipe for a cake instructs you to bake it at 220° C for 45 minutes. How many degrees Fahrenheit is this?
This is an exercise on Thermometric scales.
We have as data:
T = 220 °CT = °F ??We apply the following formula:
[tex]\large\displaystyle\text{$\begin{gathered}\sf ^{\circ}F=\frac{9}{5}\ ^{\circ}C+32 \end{gathered}$}[/tex]
We substitute data in the formula:
[tex]\large\displaystyle\text{$\begin{gathered}\sf ^{\circ}F=\frac{9}{5}\times220+32 \end{gathered}$}[/tex]
First multiply 9 x 220, then the result of this division is divided by 5.
[tex]\large\displaystyle\text{$\begin{gathered}\sf =396+32 \ \ \to \ \ [Add] \end{gathered}$}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf =428 \ ^{\circ}F \end{gathered}$}}[/tex]
Therefore the cake recipe that should be baked at 220 °C for 45 minutes, on the Fahrenteir scale is 428 °F. Which indicates that it will be very hot.
9 cos(sin¯¹(x)) = √81 – 81x²
The equation 9cos(sin¯¹(x)) = √(81 – 81x²) is true since L.H.S = R.H.S
To answer the question, we need to know what an equation is
What is an equation?An equation is a mathematical expression that show the relationship between two variables.
Given 9cos(sin¯¹(x)) = √(81 – 81x²), we need to show L.H.S = R.H.S
So, L.H.S = 9cos(sin¯¹(x))
= 9[√{1 - sin²(sin¯¹(x)}] (Since sin²y + cos²y = 1 ⇒ cosy = √[1 - sin²y])
9[√{1 - sin²(sin¯¹(x)}] = √9² × √{1 - sin²(sin¯¹(x)}]
= √[9² × {1 - sin²(sin¯¹(x)}]
= √[81 × {1 - sin²(sin¯¹(x)}]
= √[81 × {1 - x²}] (since sin²(sin¯¹(x) = [sin(sin¯¹(x)]² = x²)
= √(81 – 81x²)
= R.H.S
So, the equation 9cos(sin¯¹(x)) = √(81 – 81x²) is true since L.H.S = R.H.S
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Find the Diameter of the Circle with the following equation. Round to the nearest tenth.
(x - 2)2 + (y + 6)2 = 35
The diameter of the circle is 11.8 units
How to determine the diameter of the circle?The circle equation is given as:
(x - 2)^2 + (y + 6)^2 = 35
A circle equation is represented as:
(x - a)^2 + (y - b)^2 = r^2
Where
Diameter = 2r
By comparing both equations, we have
r^2 = 35
Take the square root of both sides
r = 5.9
Multiply by 2
2r = 11.8
Hence, the diameter of the circle is 11.8 units
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how much must be deposited today to have $45,000 in 5 years with a quarterly compounding and an APR of 7.3%
Answer:
$31,341.81
Step-by-step explanation:
The compound amount equation is A = P(1 + r/n)^(nt), where P is the unknown principal, r is the annual interest rate, n is the number of compounding periods per year and t is the number of years. We want to solve this for P:
A
------------------- = P
(1 + r/n)^(nt)
Substituting the given numerical values;
$45,000
--------------------------- = P
(1+0.073/4)^(4*5)
Using a calculator, we evaluate this expression, obtaining: $31,341.81
Evaluate 8xy+16y/5x
if x = 4 and y=-5.
A-42
B-7
C-23
D-12
Answer:
D
Step-by-step explanation:
substitute x = 4 , y = - 5 into the expression
[tex]\frac{8(4)(-5)+16(-5)}{5(4)}[/tex]
= [tex]\frac{-160-80}{20}[/tex]
= [tex]\frac{-240}{20}[/tex]
= - 12
The table gives a partial set of values of a polynomial h(x), which has a leading coefficient of 1.
x –3 –2 0 1 2
h(x) 0 –23 –12 0 0
If every x-intercept of h(x) is shown in the table and has a multiplicity of one, what is the equation of the polynomial function?
h(x) = x3 + 6x2 + 11x – 6
h(x) = x3 – 7x + 6
h(x) = x3 – 7x – 6
h(x) = x4 + 2x3 – 7x2 – 8x + 12
The equation of the polynomial function from the given table is; Option B: h(x) = x³ - 7x + 6
How to find the equation of a Polynomial?
From the given table, we see that the x-intercepts are;
(-3, 0), (1, 0) and (2, 0)
Now, we are told the the x-intercepts have a multiplicity of one which means they occur as roots only once. Thus, we can say that the roots in factor form are;
(x + 3), (x - 1), (x - 2)
Then, the polynomial will be;
h(x) = (x + 3) * (x - 1) * (x - 2)
h(x) = (x + 3)(x² - 3x + 2)
h(x) = x³ + 3x² - 3x² - 9x + 2x + 6
h(x) = x³ - 7x + 6
Thus, the equation of the polynomial function from the given table is; Option B: h(x) = x³ - 7x + 6
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Nan is 20 year old. In 8 years,she will be twice as old as Clarisse.how old is clarisse now?
Answer:
6
Step-by-step explanation:
The equation for this problem would be c = (20 + 8) / 2 - 8. Add 20 and 8 to get 28, divide 28 by 2 to get 14, then subtract 8 to get 6.
Consider the function f denoted by:
[tex]f(x) = ln(x) [/tex]
Find the nth derivative of f(x) denoted by:
[tex]f {}^{(n)} (x ) [/tex]
Irrelevant answers will be reported immediately.
Step-by-step explanation:
Let take the first derivative
[tex] \frac{d}{dx} ln(x)) = x {}^{ - 1} [/tex]
The second derivative
[tex] - {x}^{ - 2} [/tex]
The third derivative
[tex]2 {x}^{ - 3} [/tex]
The fourth derivative
[tex] - 6 {x}^{ - 4} [/tex]
The fifth derivative
[tex]24 {x}^{ - 5} [/tex]
Let create a pattern,
The values always have x in it so
our nth derivative will have x in it.
The nth derivative matches the negative nth power so the nth derivative so far is
[tex] {x}^{ - n} [/tex]
Next, lok at the constants. They follow a pattern of 1,2,6,24,120). This is a factorial pattern because
1!=1
2!=2
3!=6
4!=24
5!=120 and so on. Notice how the nth derivative has the constant of the factorial of the precessor
so our constant are
[tex](n - 1)[/tex]
So far, our nth derivative is
[tex](n - 1)!x {}^{ - n} [/tex]
Finally, notice for the odd derivatives we are Positve and for the even ones, we are negative, this means we are raised -1^(n-1)
[tex] - 1 {}^{n -1} (n - 1) ! {x}^{-n} [/tex]
That is our nth derivative
Which of the following inequalities matches the graph?
Ox=-7
Oxs-7
Oys-7
Oyz-7
Answer:
Second option
Step-by-step explanation:
As its a solid line, it indicates the inequality contains equal to in it. As the line crosses the x - axis it must be an option whereby x > or x < . Now read the value which is 7 therefore x ≤ 7
I need answers please help me
Answer:
the ansqer is g(x) = 4^x-4 + 2
Find the measure of the ndicaited angle to the nearest degree 35 and 38
The measure of the indicated angle to the nearest degrees is 23 degrees.
How to find angle of a right angle triangle?The angle of a right angle triangle can be found as follows:
Therefore, the angle can be found using trigonometric ratios as follows;
cos ∅ = adjacent / hypotenuse
Therefore,
adjacent side = 35 units
hypotenuse side = 38 units
Hence,
cos ∅ = 35 / 38
∅ = cos⁻¹ 0.92105263157
∅ = 22.9272842944
∅ ≈ 23 degrees.
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PLEASE NEED HELP
The lifespans of crocodiles have an approximately Normal distribution, with a mean of 18 years and a standard deviation of 2.6 years. What proportion of crocodiles live between 17.5 and 20.5 years?
Find the z-table here.
0.3147
0.4068
0.5932
0.6853
Using the normal distribution, it is found that 0.4068 of crocodiles live between 17.5 and 20.5 years.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given as follows:
[tex]\mu = 18, \sigma = 2.6[/tex]
The proportion of crocodiles live between 17.5 and 20.5 years is the p-value of Z when X = 20.5 subtracted by the p-value of Z when X = 17.5, hence:
X = 20.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{20.5 - 18}{2.6}[/tex]
Z = 0.96
Z = 0.96 has a p-value of 0.8315.
X = 17.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{17.5 - 18}{2.6}[/tex]
Z = -0.19
Z = -0.19 has a p-value of 0.4247.
0.8315 - 0.4247 = 0.4068
0.4068 of crocodiles live between 17.5 and 20.5 years.
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During a recent poll with a travel agency, 24 customers were surveyed to determine the most popular cities in the US to visit.
The Venn diagram shows this information for the three most popular cities: New York, Los Angeles, and Orlando.
a. Which customers chose Orlando but not New York or Los Angeles?
b. How many customers chose New York and Los Angeles, but not Orlando ?
c. Which customers liked Orlando and New York only?
Based on the Venn diagram with results from the travel agency and the popular cities to visit, the following are true:
5 people.1 person.2 people.What cities were the most popular in the U.S.?The Venn diagram shows that the number of people who chose Orlando alone are 5 people namely: John, Michael, Angel, Andrew, and Sally.
Only one customer in the person of Jordan preferred New York and Los Angeles.
2 people liked Orlando and New York only and they were Luke and Robert.
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where a=8a=8a, equals, 8 is a solution.
Answer:
a=0
Step-by-step explanation:
If this is what you are asking, and if I understand it correctly, 8*8=64 and not 8, but 8*0=0, therefore 0 is a solution.
4)48 Ans: The average height of a group of boys was 145 cm. When 2 boys joined the group, the average height became 148 cm. Given that the average height of the 2 additional boys was 160 cm, find the number of boys in the group at first.
Answer:
8
Step-by-step explanation:
The definition of an average can be used with the given values to write an equation for the number of boys.
SetupThe average is the total divided by the number. If there were n original boys, the total was T, where ...
T/n = 145 ⇒ T = 145n
Adding two boys with an average of 160 cm height, the new total became (T +2(160)) and the new average became ...
(T +2(160))/(n +2) = 148 ⇒ T = 148(n +2) -320
Equating the values of T, we have ...
T = 145n = 148(n +2) -320
SolutionSolving for n, we find ...
0 = 3n -24 . . . . . . . . . . . . subtract 145n and simplify
0 = n -8 . . . . . . . . . . . divide by 3
8 = n . . . . . . . . . . . add 8
The number of boys in the group at first was 8.
Compute the monthly payments for each add-on interest loan. The amount of the loan is $1150. The annual interest rate is 6%. The term of the loan is 4 years
The monthly payments for each add-on interest loan is $29.7.
What is interest?Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.
According to the question,
Principal (P) = $1150
Rate of Interest(R) = 6%
Time (T) = 4 years
The interest is calculated as follows:
SI = (P × R × T)/100
SI = (1150 × 6 × 4)/100
SI=$ 276
Amount (A) = P + SI
A = $(1150 +276)
A = $1426
Monthly payment with interest = A/(4×12)
= $ 1426/48
= $29.7
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A building contractor is to dig a foundation 30 feet long, 12 feet wide, and 6 feet deep. The contractor pays $20 per load for trucks to remove the dirt. Each truck holds 8 cubic yards. What is the cost to the contractor to have all the dirt hauled away?
Answer:
$1800
Step-by-step explanation:
Volume of the foundation: 30*12*6 = 2160 cubic feet
we need to convert this into yards because a truckload is 8 cubic yards, 2160/3 = 720 cubic yd
One truckload is 8 cubic yards
# of truckloads needed: 720/8 = 90 truckloads
Cost: $20*90 = $1800
1. The mean urine sodium concentrationof18caseswas120mmol/L with standard deviation of 15 mmo/L. assume the urine sodium is normally distributed, what is the 95%confidence interval within which the mean of the total population of such cases is expected lie
Using the t-distribution, the 95% confidence interval within which the mean of the total population of such cases is expected lie is:
(112.5, 127.5).
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 18 - 1 = 17 df, is t = 2.1098.
The parameters for this problem are:
[tex]\overline{x} = 120, s = 15, n = 18[/tex].
Hence the bounds of the interval are:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 120 - 2.1098\frac{15}{\sqrt{18}} = 112.5[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 120 + 2.1098\frac{15}{\sqrt{18}} = 127.5[/tex]
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a) Out of all items sent for refurbishing, %40 had mechanical defects, %50 had electrical
defects, and %25 had both. Denoting defectmechanicalahasitemanA and
defectmechanicalahasitemanB . Fill the probabilities into the Venn diagram and
determine the quantities listed below.
(i) AP [2 Marks]
(ii) BAP [1 Mark]
(iii) BAP c
i. P(A) = 0. 4
ii. P(AB) = 0. 9
iii. P(A∩B) =0. 25
How to determine the probability
From the information given,
Universal set = 40% + 50% + 25% = 0.40 + 0. 50 + 0. 25
A = Mechanical defects = 40%
B = Electrical defects = 50%
A∩B =25%
i. Probability of A , P(A)
= [tex]\frac{40}{100}[/tex]
= [tex]0. 4[/tex]
ii. Probability of B, P(AB)
= [tex]\frac{40}{100} + \frac{50}{100}[/tex]
= [tex]0. 4 + 0. 5[/tex]
= [tex]0. 9[/tex]
iii. Probability of A∩B entails the common factor between A and B
P(A∩B) = [tex]\frac{25}{100}[/tex] = [tex]0. 25[/tex]
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A group of people were asked if they had run a red light in the last year. 150 responded yes and 185 responded no. Find the probability that if a person is chosen at random, they have run a red light in the past year
The probability that a person chosen at random have run a red light in the past year is 0.45.
Given that 150 people have responded yes and 185 have responded no in a group of people when they asked whether they have run a red light.
Probability lies between 0 and 1. The value of probability can be find by :
Probability= Number items/total items.
Number of people who said that they have run red light=150
Number of people who said that they have not run red light=185
Total people=150+185
=335 people
Probability that a person chosen at random have run red light in the past year=
=Number of people who said that they have run red lights / total people
=150/335
=0.447
After rounding off it will be 0.45.
Hence the probability that a person chosen at random have run a red light in the past year is 0.45.
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Find the equation of the line passing through the points (3,7) and (-2,5)
Answer:
The equation of the line passing through the points (3,7) and (-2,5) is y=⅖x+29/5
Step-by-step explanation:
Greetings !
[tex]first \: find \: the \: slope \: m \\ m = \frac{(Y₂-Y₁)}{(X₂-X₁)} ..substitute \: vlues \\ m = \frac{(5 - 7)}{( - 2 - 3)} = \frac{ - 2}{ - 5} = \frac{2}{5} \\ y = mx + b \: to \: find \: equation \: of \: aline \\ between \: two \: poins and \: use \: \\ one \: of \: the \: two \: points \: lets \: take( - 2.5) \\ y = mx + b \\ 5 = \frac{ - 2}{5} ( - 2) + b \\ 5 = \frac{ - 4}{5} + b \\ 5 + { - 4}^{5} = b \\ \frac{25 + 4}{5} = b \\ b = \frac{29}{5} \\ finally \: equation \: of \: the \: line \: will \: be \\ y = \frac{2}{5} x + \frac{29}{5} [/tex]
The table below shows some inputs and outputs of the invertible function f with domain all real numbers.
The values of f⁻¹(f(6.022)) is 6.022 and f⁻¹(10) + f(-6) is 4
How to evaluate the function?As a general rule;
f⁻¹(f(x)) = x
This means that:
f⁻¹(f(6.022)) = 6.022
Also, we have:
f⁻¹(10) + f(-6)
From the table of values, we have:
f⁻¹(10) = -6 and f(-6) =10
So, we have:
f⁻¹(10) + f(-6) = -6 + 10
Evaluate
f⁻¹(10) + f(-6) = 4
Hence, the values of f⁻¹(f(6.022)) is 6.022 and f⁻¹(10) + f(-6) is 4
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The temperature was 56 degrees this morning, but dropped one degree per hour through the rest of the day. The equation is y=-x+56. You may usey=56-x . They are the same equation. Use x-values: 0, 5, and 10.
At x=0
y=56-0y=56°CAt x=5
y=56-5y=51°CAt x=10
y=56-10y=46°Csimplify 5x(3x^2+2x-3)
Answer:
[tex]15x^3 +10x^2 - 15x[/tex]
Step-by-step explanation:
Hello!
Use the distributive property and multiply like terms.
Simplify[tex]5x(3x^2 + 3x - 3)[/tex][tex]5x(3x^2) + 5x(2x) + 5x(-3)[/tex][tex]15x^3 +10x^2 - 15x[/tex]The simplified form is [tex]15x^3 +10x^2 - 15x[/tex].
what is the value of x 44 inches and 55 inches triangle
Answer: I don't know what you are talking about, but if x is the area, then the answer is 1,210.
Step-by-step explanation: 44 x 55 x 1/2 = 1,210. The formula for the area of a triangle is 1/2 times length times height. Therefore, x = 1,210
Hope this helps.
at a party 5/9 of the persons were men and the rest were women.if there was total 1260 persons find the number of women in the present
SOLUTION :
let total people in the party be x i.e. 1260
then , number of men = 5/9 of x
= 5/9 of 1260 = 5 × 140 = 700 men
now ,
number of women = Total person - (number of total men)
= ( 1260 - 700 ) women
= 560 women
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Q.3 Write the factors of 28 in circle A and the factors of 32 in circle B. Write
heir common factors in the common part of both. Which is the biggest
common factor of 28 &32?
Answer: The largest common factor of 28 and 32 is 4.
Step-by-step explanation:
The factors of 28 are 1, 2, 4, 7, 14, 28
The factors of 32 are 1, 2, 4, 8, 16, 32
Which of the following inequalities has no solutions?
Ox>3 and x < 2
Ox>3 and x < -2
Ox>3 and x < 2
Ox>3 and x > - 2
Answer:
A) x > 3 and x < 2 has no solutions
Step-by-step explanation:
Given inequalities below and we are looking for a pair with no solution.
Let's verify:
A) x > 3 and x < 2,
It has no solutions since the two inequalities have no common interval.B) x > - 3 and x < - 2,
Its solution is -3 < x < - 2, the interval between two given endpoints.C) x > - 3 and x < 2,
Similar to option B, the interval is between two endpoints:- 3 < x < 2D) x > - 3 and x > - 2,
Its solution is x > - 2, the two inequalities cover almost same interval.Find the values of the variables in the parallelogram.
please help asap
tysm
Answer:
Step-by-step explanation: