Answer:
x = 12.29
Step-by-step explanation:
present value of the claim = x² / (1 + 2%)¹⁵ = 0.743x²
present value of the 10 premiums:
x + x/1.02 + x/1.02² + x/1.02³ + x/1.02⁴ + x/1.02⁵ + x/1.02⁶ + x/1.02⁷ + x/1.02⁸ + x/1.02⁹ = x + 0.9504x + 0.9612x + 0.9423x + 0.9238x + 0.9057x + 0.888x + 0.8706x + 0.8535x + 0.8368x = 9.1323x
0.743x² = 9.1323x
x² / x = 9.1323 / 0.743
x = 12.29
Answer
x = 12.29
Step-by-step explanation:
Given that the policy claims x² in 15 years, at 2% = 0.02, the present value of the claim is given as:
x²/(1 + 0.02)^15
= x²(1/1.02)^15
= 0.743x²
The present value of the 10 premiums:
x + x/1.02 + x/1.02² + x/1.02^3 + x/1.02^4 + x/1.02^5 + x/1.02^6 + x/1.02^7 + x/1.02^8 + x/1.02^9
= x + 0.9504x + 0.9612x + 0.9423x + 0.9238x + 0.9057x + 0.888x + 0.8706x + 0.8535x + 0.8368x
= 9.1323x
Now,
0.743x² = 9.1323x
x²/x = 9.1323/0.743
x = 12.29
This is what we are looking for.
Solve and type in a different form by using the given theorems of logarithms.
log10 Mk =
Answer: log1= 1
not sure about Mk
Answer:
k*log_10M
Step-by-step explanation:
take the k and put it in front of the equation and it cannot be further simplified.
What is the value of x?
Answer:
5.6
Step-by-step explanation:
We want to find the value of x, which is part of the segment that includes the length 10.
We need to use Power of Points, one property of which essentially says that if we have two intersecting chords such that they are each cut into two parts to make a and b, and c and d, then ab = cd (see attachment).
Here, we can say that a = 10, b = x, c = 7, and d = 8. Plug these in:
ab = cd
10 * x = 7 * 8
10x = 56
x = 56/10 = 5.6
The answer is 5.6.
Each diagonal has two parts (a, b, c, and d).
The formula is ab = cd
We have the values:
a = 10
b = x
c = 8
d = 7
Put these in the formula:
10x = (8)(7)
Solve for x.
10x = (8)(7)
10x = 56
10x/10 = 56/10
x = 5.6
Therefore, the answer is x = 5.6
Best of Luck!
y+1 y+8 y+2 y+7
----- + ----- = ----- + -----
y+2 y+9 y+3 y+8
find y
plssssss help this is fraction
[tex]\dfrac{y+1}{y+2}+\dfrac{y+8}{y+9}=\dfrac{y+2}{y+3}+\dfrac{y+7}{y+8}[/tex]
Write all fractions in terms of a common denominator:
[tex]\dfrac{y+1}{y+2}=\dfrac{(y+1)(y+9)(y+3)(y+8)}{(y+2)(y+9)(y+3)(y+8)}[/tex]
[tex]\dfrac{y+8}{y+9}=\dfrac{(y+8)^2(y+2)(y+3)}{(y+2)(y+9)(y+3)(y+8)}[/tex]
[tex]\dfrac{y+2}{y+3}=\dfrac{(y+2)^2(y+9)(y+8)}{(y+2)(y+9)(y+3)(y+8)}[/tex]
[tex]\dfrac{y+7}{y+8}=\dfrac{(y+7)(y+2)(y+9)(y+3)}{(y+2)(y+9)(y+3)(y+8)}[/tex]
Then move all fractions to one side and simplify the numerator:
[tex]\dfrac{(y+1)(y+9)(y+3)(y+8)+(y+8)^2(y+2)(y+3)-(y+2)^2(y+9)(y+8)-(y+7)(y+2)(y+9)(y+3)}{(y+2)(y+9)(y+3)(y+8)}=0[/tex]
The numerator dictates when the fraction reduces to 0. The denominator can never be 0, so we know that y cannot take any of the values -2, -9, -3, nor -8.
So the equation reduces to
[tex](y+1)(y+9)(y+3)(y+8)+(y+8)^2(y+2)(y+3)-(y+2)^2(y+9)(y+8)-(y+7)(y+2)(y+9)(y+3)=0[/tex]
Expand the left side; you would end up with
[tex]-6(2y+11)=0[/tex]
[tex]2y+11=0[/tex]
[tex]2y=-11[/tex]
[tex]\implies\boxed{y=-\dfrac{11}2}[/tex]
Explain how you could use paperfolding to divide a line segment into four segments of equal length
16 less than a number is 49. Find the number.
Answer:
the number is 65.
Step-by-step explanation:
n-16=49
n=65
Therefore, the number is 65.
If Mario puts $12,000 in a bank account that pays 4% interest quarterly, how much will he have after 3 years?
Answer:
[tex] P=12000, r= 0.04, t=3[/tex]
And n=4 since the rate is compounded quarterly, so then replacing this info we got:
[tex] A = 12000 (1+ \frac{0.04}{4})^{4*3} = 13521.9[/tex]
So then Mario will have about $13521.9 after the 3 years with the rate of interest used.
Step-by-step explanation:
For this case we can use the formula for future value based on a compound interest given by:
[tex] A= P (1+ \frac{r}{n})^{nt}[/tex]
Where A represent the future value, P the present value or the inversion r is the rate of interest on fraction, n the number of times that the rate of interest is compounded in a year and t the number of years.
For this case we know this:
[tex] P=12000, r= 0.04, t=3[/tex]
And n=4 since the rate is compounded quarterly, so then replacing this info we got:
[tex] A = 12000 (1+ \frac{0.04}{4})^{4*3} = 13521.9[/tex]
So then Mario will have about $13521.9 after the 3 years with the rate of interest used.
42% of jacksons halloween candy from last year was chocolate. what fraction of his candy's chocolate
Answer:
21/50
Step-by-step explanation:
Given that Jackson's sweets from last Halloween from last year was 42% chocolate, we can assume he had a total of 100 sweets.
Out of 100 sweets, 42 pieces are chocolate, so:
42/100
When simplifying this fraction into its simplest form, the most you can do is divide the numerator(top) and denominator(bottom) by 2.
Your result would be 21/50
Hope this helps!
A study showed that 14 of 180 publicly traded business services companies failed a test for compliance with Sarbanes-Oxley requirements for financial records and fraud protection. Assuming that these are a random sample of all publicly traded companies, construct a 95% confidence interval for the overall noncompliance proportion. (Round your answers to 4 decimal places.)
Answer:
The 95% confidence interval for the overall noncompliance proportion is (0.0387, 0.1169).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 180, \pi = \frac{14}{180} = 0.0778[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.0778 - 1.96\sqrt{\frac{0.0778*0.9222}{180}} = 0.0387[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.0778 + 1.96\sqrt{\frac{0.0778*0.9222}{180}} = 0.1169[/tex]
The 95% confidence interval for the overall noncompliance proportion is (0.0387, 0.1169).
Which measurement is most accurate to describe the weight of an apple
Answer: (BRAINLIEST PLEASE)
120 g.
Step-by-step explanation:
Answer:
1/4 of a pound
Step-by-step explanation:
What integer can be represented by 22 positive tiles and 21 negative tiles?
A. 1
B. 6
C. -1
D. 43
Answer:
option A is your answer in my opinion.
Sry i am not sure
plzzzzzzzzzzzzzzzz Help Marshmello i wasn't born yesterday.
Answer:
82.45
Step-by-step explanation:
The price of the purse is 75.99 and tax is 8.5%
Tax = price time tax rate
tax = 75.99*.085
tax =6.45915
Rounding to the nearest cent
tax = 6.46
Add this to the price of the purse
total cost = 75.99+6.46
82.45
Most U.S. households spend about 5% of their income on entertainment. Which of the following are equivalent to 5%? Choose all equivalent expressions.
A. 120
B. 15
C. 12
D. 0.05
E. 0.005
Answer:
1/20 and 0.05 :)
Step-by-step explanation:
(50 POINTS) Complete the square to find the center and radius of each circle.
Answer:
Rewrite in standard form to find the center (h,k) and radius r.
Center: (−1,−2)
Radius: √6
Rewrite in standard form to find the center (h,k) and radius r.
Center: (3/2,6)
Radius: 11/2
Rewrite in standard form to find the center (h,k) and radius r.
Center: (3,−7)
Radius: 8
Rewrite in standard form to find the center (h,k) and radius r.
Center: (0,10)
Radius: 9
Rewrite in standard form to find the center (h,k) and radius r.
Center: (−4,−4)
Radius: 4√2
What is the volume of this rectangular prism 5/2 cm 4 cm 1/2
Answer:
[tex]5cm ^{3} [/tex]
Step-by-step explanation:
[tex]v = whl \\ = \frac{5}{2} \times \frac{4}{1} \times \frac{1}{2} \\ = \frac{20}{4} \\ = 5 {cm}^{3} [/tex]
x and y are supplementary angles. y measures 108
What is the measure of x?
Answer:
126
Step-by-step explanation:
this is because you have 3 angles so its a triangle you have 360 degrees so 360 - 108 = 252 you need to divide it by 2 as there are 3 angles so you get 126 i hope it helps
Rachel is making nachos for a party the recipe calls for 2/3 cup of cheese for each plate of nachos how many full plate of nachos can Rachel make with 5 cups of cheese how many more cups of cheese would Rachel need to make 9 plates of nachos
Answer:
7 plates1 cupStep-by-step explanation:
If we let c and p represent the cups of cheese and plates of nachos, we have ...
c = 2/3p . . . . . each plate of nachos requires 2/3 cups of cheese
Solving for p, we find ...
(3/2)c = p . . . . . multiply by 3/2
Then for 5 cups of cheese, we have ...
(3/2)(5) = p = 15/2 = 7 1/2 . . . . plates of nachos
5 cups of cheese will make 7 full plates of nachos.
__
For 9 plates of nachos, we need ...
c = 2/3(9) = 6 . . . . . . cups of cheese
Since we have 5 cups of cheese, we need 1 more cup of cheese to make 9 plates of nachos.
John drives 257 miles and uses 9 gallons of gas. How many miles per gallon did he get?
Answer:
29 miles were used per gallon
Step-by-step explanation:
257 / 9 = 28.555..
We can round 28.555 to about 29.
So John got 29 miles per gallon.
find the term to term rules for the following sequences 28, 25 ,22, 19, 16
Answer:
-3n+31
Step-by-step explanation:
ok
The nth term of the sequence 28, 25 ,22, 19, 16 is aₙ=31-3n.
What is Sequence?Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
The given sequence is 28, 25 ,22, 19, 16
Twenty eight comma twenty five comma twenty two comma nineteen comma sixteen.
The sequence is an arithmetic sequence as there is a common difference between consecutive terms.
The first term is a=28
Common difference =25-28=-3
aₙ=28+(n-1)(-3)
aₙ=28-(n-1)(3)
aₙ=28-3n+3
aₙ=31-3n
Hence the nth term of the sequence 28, 25 ,22, 19, 16 is aₙ=31-3n.
To learn more on Sequence click:
https://brainly.com/question/21961097
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What’s the answers
Answer:
Look below
Step-by-step explanation:
Since the opposite sides are congruent then the figure is a parallelogram.
About 24% of flights departing from New York’s John F. Kennedy International Airport were delayed in 2009. Assuming that the chance of a flight being delayed has stayed constant at 24%, we are interested in finding the probability of 10 out of the next 100 departing flights being delayed. Noting that if one flight is delayed, the next flight is more likely to be delayed, which of the following statements is correct? Group of answer choices
Answer:
Step-by-step explanation:
The question is incomplete. The missing part is:
(A) We can use the geometric distribution with n = 100, k = 10, and p = 0.24 to calculate this probability. (B) We can use the binomial distribution with n = 10, k = 100, and p = 0.24 to calculate this probability. (C) We cannot calculate this probability using the binomial distribution since whether or not one flight is delayed is not independent of another. (D) We can use the binomial distribution with n = 100, k = 10, and p = 0.24 to calculate this probability
Solution:
In binomial probability, the assumption is that there is only one outcome for each trial. This is because the probability of success or failure is constant. Each trial is also independent of the other trial. This means that the probability of event A happening does not depend on the outcome of event B.
In the given scenario, the probability of a flight being delayed depends on the probability of the previous flight being delayed. It means that the outcomes are not independent. In geometric probability, a trial is repeated until success is achieved. The outcomes are also independent. Therefore, the correct option is
(C) We cannot calculate this probability using the binomial distribution since whether or not one flight is delayed is not independent of another.
The statement that is correct would be:
C). We cannot calculate this probability using the binomial distribution since whether or not one flight is delayed is not independent of another.
Binomial probabilityIn the case of binomial probability, it is assumed that the outcome occurring for every trial would remain 1 only because there is consistency in terms of success or defeat.
This implies that the outcome of one will not impact the other's result.
Since the third statement shows that there is no possibility of estimating the probability by employing the method of binomial distribution as one flight's taking off or delay will not impact the other and they remain independent.
Thus, option C is the correct answer.
Learn more about "Probability" here:
brainly.com/question/795909
The options are missing in the question. They are provided as follows:
(A) We can use the geometric distribution with n = 100, k = 10, and p = 0.24 to calculate this probability.
(B) We can use the binomial distribution with n = 10, k = 100, and p = 0.24 to calculate this probability.
(C) We cannot calculate this probability using the binomial distribution since whether or not one flight is delayed is not independent of another. (D) We can use the binomial distribution with n = 100, k = 10, and p = 0.24 to calculate this probability
United Express, a nationwide package delivery service, charges a base price for overnight delivery of packages weighing 1 pound or less and a surcharge for each additional pound (or fraction thereof). A customer is billed $ 25 $25 for shipping a 7 7-pound package and $ 55 $55 for shipping a 22 22-pound package. Find the base price and the surcharge for each additional pound. Round answers to the nearest thousandth (to three decimal places).
Answer:
Base price: $13.
Surcharge: $2 per additional pound.
Step-by-step explanation:
The base price can be considered a constant, while the surcharge is a function of the additional weight of the package, over 1 pound.
Then, we can model this as a linear function, with additional weight as the independent variable.
[tex]f(x)=b+sx[/tex]
being b: base price, and s: surcharge for each additional pound.
The 7-pound package cost $25. The additional weigth in this case is 7-1=6 pounds.
The 22-pound package cost $55. The additional weigth is 21 pounds.
So we have the first point (6, 25):
[tex]f(6)=b+s(6)=25\\\\b=25-6s[/tex]
Then, for the second point (21, 55) we have:
[tex]b=25-6s\\\\f(21)=(25-6s)+s(21)=55\\\\25+(21-6)s=55\\\\15s=55-25=30\\\\s=30/15=2\\\\\\b=25-6(2)=25-12=13[/tex]
Then, the prices are:
Base price: $13.
Surcharge: $2 per additional pound.
Write the number 2.4 in the form a/b using integers
Answer:
[tex]2\frac{4}{10}=\frac{24}{10}=\frac{12}{5}[/tex]
Step-by-step explanation:
Here we have a number in the ones place, 2, and a number in the tenths place, 4.
Any number in front of the decimal becomes the whole number in front of the mixed number fractionThe numerator will be any number after the decimalThe denominator will be the value of the place the number after the decimal is inHere our whole number is 2, the numerator is 4, and it is in the tenths place, so our denominator will be 10
Our fraction becomes [tex]2\frac{4}{10}[/tex] which then turns into the improper fraction [tex]\frac{24}{10}[/tex] and then simplifying if needed becomes [tex]\frac{12}{5}[/tex] after dividing the fraction by 2
Complete the equation with a number that makes the expression on the right side of the equal sign equivalent to the expression on the left side 5x - 2.5 + 6x - 3 = ______ (2x - 1)
Answer:
5.5
Step-by-step explanation:
5x-2.5+6x-3=_____(2x-1)
11x-5.5=5.5(2x-1)
11x-5.5=11x-5.5
Answer:
5.5
Step-by-step explanation:
Determine if the function f is an exponential function. If so, identify the base. If not, why not? f(x) = 3^x + 1
Answer:
3
Step-by-step explanation:
f(x) has the variable in the exponent, so is an exponential function.
The base is 3.
__
The base is what is being raised to the power of x.
What’s the correct answer for this?
Answer:
Option 4.
Step-by-step explanation:
The information is that the points G and H are the midpoints of ED and EF.
For example G will be (5 + (-2))/ 2 , (4 - 0) / 2 which is (1.5, 2).
If we calculate H it is (6.5, -3).
The answer is option 4.
What is the length of arc AB? 6π cm 12π cm 18π cm 36π cm
Answer:
6π cm
Attached is the missing image
Step-by-step explanation:
The circumference of a circle can be expressed as;
C = 2πr
The length of an arc with angle ∅ (in radian) can be expressed as;
Arc Length = radius × radian angle
L = r∅
Given; from the attached image
Radius r = 18 cm
Radian angle ∅ = π/3 radians
Substituting the values;
Arc length L = 18cm × π/3 = 18/3 π cm
Arc length L = 6π cm
Answer:
its A
Step-by-step explanation:
6 CM
Vanessa is skiing along a circular ski trail that has a radius of 2.5 km. She starts at the 3-o'clock position and travels in the CCW direction. Vanessa stops skiing when she is 1.244 km to the right and 2.169 km above the center of the ski trail. Imagine an angle with its vertex at the center of the circular ski trail that subtends Vanessa's path.
How many radians has the angle swept out since Vanessa started skiing?
Answer:
1.05 radians
Step-by-step explanation:
Given that Vanessa is skiing along a circular ski trail that has a radius of 2.5 km. She starts at the 3-o'clock position and travels in the Counter Clockwise direction.
She stops skiing when she is 1.244 km to the right and 2.169 km above the center of the ski trail.
This can be represented as (1.244, 2.169) on a circle of radius 2.5 km.
From the coordinate point (1.244, 2.169) derived, x=1.244 and y=2.169.
By the definition of tangent,
[tex]\tan \theta =\frac{y}{x} \\\\\tan \theta =\dfrac{2.169}{1.244}\\\\ \theta=\arctan \dfrac{2.169}{1.244}\\\\\\ \theta=1.05006[/tex]
Vanessa swept out approximately 1.05 radians since she started skiing.
4. Would a 51-foot ladder be long enough to climb a 50-foot wall? Sketch a graph and find your answer using a trigonometric ratio.
Answer:
It is
Step-by-step explanation:
Using Pythagoras 51^2 = 50^2 + b^2
b=10.0499
Write the equation of the line that passes through (7,-4) and (-1,2) in slope-intercept form.
Answer:
slope intercept form y = m x +C
[tex]y = \frac{4x}{3} -\frac{40}{3}[/tex]
Step-by-step explanation:
step(i):-
Given two points are A (7,-4) and B(-1,2)
Slope of two lines formula
[tex]m= \frac{y_{2} -y_{1} }{x_{2} -x_{1} } = \frac{-1-7}{2-(-4)} =\frac{-8}{6} = \frac{4}{3}[/tex]
Step(ii):-
The equation of the straight line passing through the two points
y-y₁ = m(x-x₁)
Let (x₁ , y₁) = (7,-4)
y - (-4) =[tex]\frac{4}{3}[/tex] (x-7)
On cross multiplication , we get
3(y+4) = 4(x-7)
3 y +12 = 4 x -28
subtract '12' on both sides , we get
3 y = 4 x -28 -12
3 y = 4 x - 40
Dividing '3' on both sides, we get
Now slope intercept form y = m x +C
[tex]y = \frac{4x}{3} -\frac{40}{3}[/tex]
Final answer:-
slope intercept form y = m x +C
[tex]y = \frac{4x}{3} -\frac{40}{3}[/tex]
will give brainliest! :)
Answer:
Step-by-step explanation: