The value of the missing length is 20
Let the missing length be x
From Parallel lines and transversal theorem, we have that
If three or more parallel lines intersect two transversals, then they cut off the transversals proportionally.
Then, we can write that
\(\frac{x}{15} =\frac{16}{12}\)
∴ \(x = \frac{15\times 16}{12}\)
x = 20
Hence, the value of the missing length is 20
Learn more here: https://brainly.com/question/24258397
Marianna finds an annuity that pays 8% annual interest, compounded quarterly. She invests in this annuity and contributes $10,000 each quarter for 6 years. How much money will be in her annuity after 6 years? Enter your answer rounded to the nearest hundred dollars.
The amount of money in Marianna's annuity after 6 years will be approximately $300,516.
To calculate the amount of money in Marianna's annuity after 6 years, we can use the formula for compound interest on an annuity:
A = P * ((1 + r/n)^(n*t) - 1) / (r/n)
Where:
A = the final amount in the annuity
P = the regular contribution (each quarter) = $10,000
r = annual interest rate = 8% = 0.08
n = number of compounding periods per year = 4 (since it's compounded quarterly)
t = number of years = 6
Plugging in the values:
A = 10000 * ((1 + 0.08/4)^(4*6) - 1) / (0.08/4)
Calculating this expression:
A ≈ 10000 * ((1.02)^24 - 1) / 0.02
A ≈ 10000 * (1.601032449136241 - 1) / 0.02
A ≈ 10000 * 0.601032449136241 / 0.02
A ≈ 10000 * 30.05162245681205
A ≈ 300,516.22
For more such questions on annuity,click on
https://brainly.com/question/25792915
#SPJ8
Answer:
304200
Step-by-step explanation:
To find the value of P6, use the savings annuity formula
PN=d((1+r/k)N k−1)r/k.
From the question, we know that r=0.08, d=$10,000, k=4 compounding periods per year, and N=6 years. Substitute these values into the formula gives
P6=$10,000 ((1+0.08/4)6⋅4−1)/(0.08/4).
Simplifying further gives P6=$10,000 ((1.02)24−1)/(0.02) and thus P6=$304,218.62.
Rounding as requested, our answer is 304200.
Please help asap! The question is below!
Based on the information, the hedgehogs have made the better offer
How to know who made the better offerThe Turkeys are offering a yearly salary of S(t) = 90000t over the course of eight years. To calculate the present value of each payment, an equation is used:
PV = S(t) * e^(-rt)
The variable "r" denotes a continuous interest rate of 0.03. "t" equals the years from t=0 to the time of payment. By this method, the current value of the Turkeys' offer can be assessed as follows:
PV(Turkeys) = ∫[0,8] 90000t * e^(-0.03t) dt
= 736,918.63
Comparatively, the Hedgehogs propose a yearly salary of S(t) = 80000t for nine years. Utilizing the formula employed in the previous scenario, the following result is derived:
PV(Hedgehogs) = ∫[0,9] 80000t * e^(-0.03t) dt
= 753,472.49
Given these calculations and the presumption that Rogelio may earn a continuous interest rate of 3% on his funds, it would best serve him to accept the Hedgehogs’ item offer since they have offered him a more favorable contract based on the accumulated present value of both contracts.
Learn more about present value on
https://brainly.com/question/30390056
#SPJ1
12. Shanti's sister Uri is Shanti's age plus 3 years. Uri is 7 years old. Write an
equation to find Shanti's age.
The equation to find Shanti's age is y = x - 3 where y is Shanti's age.
Given,
Shanti's sister Uri is Shanti's age plus 3 years.
Uri is 7 years old.
We need to write an equation to find Shanti's age.
We have,
Uri age = Shanti age + 3______(1)
Uri = 7 years old
Putting in (1)
We get,
Uri age = Shanti age + 3
7 = Shanti age + 3
Subtracting 3 on both sides.
7 - 3 = Shanti age + 3 - 3
4 = Shanti age
We see that Shanti's age is 4 years old.
If we have to write an equation then,
Consider Uri's age to be x and Shanti's age to be y.
Now,
Uri age = Shanti age + 3
x = y + 3
Subtracting 3 on both sides
x -3 = y
y = x - 3 is our equation.
Thus the equation to find Shanti's age is y = x - 3.
Learn more about finding the age of a person's here:
https://brainly.com/question/12046558
#SPJ1
Can you help with these vocabulary word
Answer:
is more than 90 degrees right angles are 90 degrees
Determine how long it will take for a principal amount of $1,500 to become double its initial value when deposited into an account paying interest at a rate of 13%, continuously compounded.
A.
5.33 years
B.
6.32 years
C.
11.25 years
D.
14.33 years
c is incorrect
Heather planted 4 times as many tulips as Sarah planted. If Heather planted 64 tulips, how many tulips (s) did Sarah plant?
Step-by-step explanation:
let, the tulips be 'x'
According to the question,
heather=4x
& sarah=x
but heather planted 64 so,
4x=64
or, x=64/4
x=16
hence, sarah planted 16 tulips
Heather planted 4x Sarah's tulips. On the off chance that Heather has 64 tulips, Sarah has 16 tulips (64/4 = 16).
How to determine how many tulips (s) Sarah planted using algebraLet's utilize algebra to illuminate this issue. Let s speak to the number of tulips Sarah planted.
Concurring to the data given, Heather planted 4 times as numerous tulips as Sarah, so we will compose this as:
Heather's tulips = 4 * Sarah's tulips
64 = 4s
Presently, ready to fathom for s:
s = 64 / 4
s = 16
Sarah planted 16 tulips.
Learn more about algebra here:
https://brainly.com/question/4344214
#SPJ2
N
m
4
5
4
U
-
3-
Cu v
-5-4-3-2-1
2
-2
1 w
60
r
2345x
What is the domain of the function on the graph?
O all real numbers
O all real numbers greater than or equal to-2
O all real numbers greater than or equal to-5
O all real numbers greater than or equal to 0
Help please
Answer:
Step-by-step explanation:
Question
N
m
4
5
4
U
-
3-
Cu v
-5-4-3-2-1
2
-2
1 w
60
r
2345x
What is the domain of the function on the graph?
O all real numbers
O all real numbers greater than or equal to-2
O all real numbers greater than or equal to-5
O all real numbers greater than or equal to 0
Help please
Given a mortgage of $48,000 for 15 years with a rate of 11% , what are the total finance charges?
Answer:
$54,576
Step-by-step explanation:
The difference between eleven and the number d
experimento aleatorio con orden,remplazo y sin repeticion
A randomized experiment with order, replacement, and no repetition is one in which the order of the outcomes matters, the same outcome can occur multiple times, and no outcome can occur more than once.
How to explain the information.For example, drawing a card from a deck and then flipping a coin would be a random experiment with order, replacement, and no repetition. The order of the results is important because the outcome of the coin toss will depend on the outcome of the card draw.
The same result can occur multiple times because the same card can be drawn twice, and no result can occur more than once because the coin can only land heads or tails once.
Learn more about the experiments at
brainly.com/question/17274244
#SPJ1
Random experiment with order, replacement and without repetition
Find the midpoint of the segment with the given endpoints.
(-7,10) and (6.-10)
Answer:
c
Step-by-step explanation:
cc
1.43 x -20/39 is close to -.075. Is this estimate reasonable? The product is negative and half of ?
Answer:
yes, that is correct
Step-by-step explanation:
- (20÷39) = - 0.513
- 0.513 * 1.43 = - 0.734 ~ - 0.75
for a special fully discrete 20-year term insurance on (30): the death benefit is 1,000 during the first ten years and 2,000 during the next ten years.
The cost of the 20-year term insurance will be based on age, health, smoking, and other factors to determine the premium.
The cost of a special fully discrete 20-year term insurance on a 30-year-old would depend on a range of factors, including the insured's age, health, smoking status, and lifestyle. These factors would be used to calculate the risk of death during the 20-year term. The death benefit of 1,000 during the first ten years and 2,000 during the next ten years would also be taken into account when calculating the cost of the policy. Depending on the risk of death and the death benefits, the premium could vary significantly. For example, a 30-year-old in good health with no smoking history could pay less for the policy than a 30-year-old with a pre-existing condition and a smoking history. The premium could also be higher for individuals with riskier lifestyles. Ultimately, the cost of the 20-year term insurance will depend on the risk of death and the death benefit offered by the policy.
Learn more about terms here
https://brainly.com/question/26099230
#SPJ4
Calculate the surface area in square feet of a box that measures 13 inches in
length, 10 inches in width, and 11 inches in height. The value of your answer
should be square feet. Round you answer to the nearest hundredth
Answer:
I think the answer is 766 inches, rounding it to the nearest 100 would be 800
Step-by-step explanation:
Reduce 65 in ratio 5:2
Answer: \(46.42:18.57\)
Step-by-step explanation:
\(5+2 = 765/7 × 5 = 46.4265/7 × 2 = 18.57∴ 65 in the ratio 5:2 = 46.42:18.57x^{2}\)
The solution is 46.42857 : 18.57143
The proportion equation is given by 46.42857 : 18.57143 and
46.42857 + 18.5714365 = 65
What is Proportion?
The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the number be represented as N
The value of N = 65
The proportion is 5 : 2
The total value of the ratio = 5 + 2 = 7
So , each value of the proportion is x = 65 / 7
On simplifying the equation , we get
Each value of the proportion is x = 9.2857142857
Now , the proportion equation is given by
The value of 5x = 5 ( 9.2857142857 )
The value of 5x = 46.42857
The value of 2x = 2 ( 9.2857142857 )
The value of 2x = 18.57143
And , 46.42857 + 18.5714365 = 65
Hence , the proportion is 46.42857 : 18.57143 or 5 : 2
To learn more about proportion click :
https://brainly.com/question/7096655
#SPJ2
Zack is on his school's color guard and is practicing throwing and catching his flag. He throws the flag into the air from a height of 5 feet at a velocity of 30 feet per second. After the flag starts to come back down, he catches it 7 feet above the ground.
To the nearest tenth of a second, how long is the flag in the air before Zack catches it?
Hint: Use the formula h=16t2+vt+s.
The Nearest tenth of a second, the flag is in the air for approximately 0.1 seconds before Zack catches it.
To determine the time the flag is in the air before Zack catches it, we can use the kinematic equation for vertical motion:
h = 16t^2 + vt + s
Where:
h is the height of the flag,
t is the time in seconds,
v is the initial vertical velocity of the flag,
s is the initial height of the flag.
In this case, the flag is thrown into the air from a height of 5 feet (s = 5) with an initial vertical velocity of 30 feet per second (v = 30). Zack catches it at a height of 7 feet (h = 7).
We can rewrite the equation as:
7 = 16t^2 + 30t + 5
To find the time (t) when the flag is at a height of 7 feet, we can rearrange the equation and solve for t. However, since this is a quadratic equation, we can also use the quadratic formula.
The quadratic equation in this case is:
16t^2 + 30t + 5 - 7 = 0
16t^2 + 30t - 2 = 0
Now, we can use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
Applying the values from the quadratic equation, we have:
t = (-30 ± √(30^2 - 4 * 16 * (-2))) / (2 * 16)
Simplifying further:
t = (-30 ± √(900 + 128)) / 32
t = (-30 ± √1028) / 32
Using a calculator, we find two solutions:
t ≈ -1.08 seconds or t ≈ 0.06 seconds
Since time cannot be negative in this context, we discard the negative solution.
Therefore, to the nearest tenth of a second, the flag is in the air for approximately 0.1 seconds before Zack catches it.
To know more about Nearest .
https://brainly.com/question/31217836
#SPJ8
John is making a large bag of mixed nuts. Peanuts cost $4 per pound. Cashews cost $9 per pound. Pecanswere found on sale for $5.50 per pound. John decides to mix 3 pounds of peanuts, 0.5 pound of cashews, and1.5 pounds of pecans. How much did the mixture cost to make?
Peanuts cost $4/pound.
Cashews cost $9/pound.
Pecans cost $5.50/pound.
The final mixture cost is the amount of each nut by the cost of them by pound.
\(3pounds\cdot\frac{4}{\text{pound}}\text{ + 0.5pounds}\cdot\frac{9}{\text{pound}}\text{ + 1.5pounds}\cdot\frac{5.50}{\text{pound}}\text{ = 24.75 dollars}\)The mixture cost $24.75
Then, by pound, we have to sum all the pounds:
3 + 0.5 + 1.5 = 5 pounds
\(\frac{24.75}{5}=\text{ 4.95}\)The final result is $4.95 by pound.
Consider this function:
f(x) = -2(x + 3)(x - 7).
When graphed, the function will have x-intercepts at and
Write the left x-intercept first. Write the x-intercepts as ordered pairs: (a,b).
Answer:
-5 +7x equal 12x
Step-by-step explanation:
add and complete
The x-intercepts of the function f(x) are:
Left x-intercept: (-3, 0)
Right x-intercept: (7, 0)
Given is a function, f(x) = -2(x + 3)(x - 7).
We need to find the x-intercept of the function,
To find the x-intercepts of the function f(x), we set f(x) equal to zero and solve for x:
-2(x + 3)(x - 7) = 0
Now, we can use the zero product property, which states that if a product of factors is equal to zero, then at least one of the factors must be zero.
So, we have two cases to consider:
Case 1: x + 3 = 0
Solving this equation, we subtract 3 from both sides:
x = -3
Case 2: x - 7 = 0
Solving this equation, we add 7 to both sides:
x = 7
Therefore, the x-intercepts of the function f(x) are -3 and 7.
Writing them as ordered pairs, we have:
Left x-intercept: (-3, 0)
Right x-intercept: (7, 0)
Learn more about x-intercepts click;
https://brainly.com/question/14180189
#SPJ4
Given the function p(c)=c² +c:
a. Evaluate p(-3).
b. Solve p(c) = 2.
Answer: a. p(-3) = 6 b. c = -2 , c = 1
Step-by-step explanation:
a. Evaluate p(-3):
Step 1: Plug in -3 into c
p(-3) = (-3)^2-3
Step 2: Use PEMDAS
p(-3) = 9-3
Step 3: Subtract
p(-3) = 6
b. Solve p(c) = 2:
Step 1: Set the equation equal to 2
2 = c^2+c
Step 2: Bring the 2 to the right
c^2+c-2 = 0
Step 3: Factor
(c+2)(c-1) = 0
Step 4: Use the Zero Product Property
c = -2 , c = 1
Step-by-step explanation:
a.
this is totally easy.
we need to put the given value for c (-3) into all the places of c in the functional expression and then calculate.
p(-3) = (-3)² + -3 = 9 - 3 = 6
b.
this is a bit trickier.
p(c) = 2
so,
c² + c = 2
c² + c - 2 = 0
remember, how 2 sums are multiplied with each other :
(a + b)(c + d) = ac + ad + bc + bd
to make it clearer, the functional expression suggests that a = c.
so,
(c + b)(c + d) = c² + cd + bc + bd = c² + c(d + b) + bd
when we compare this to our equation c² + c - 2 = 0, that means
d + b = 1
-2 = bd
when we think about integer numbers, what comes to mind ?
d = 2
b = -1
or vice versa. but the sequence does not matter, because we bring them together in an addition and in a multiplication, where the commutative principle is active (the sequence does not matter).
so,
c² + c - 2 = (c + 2)(c - 1)
and that must be 0.
so,
(c + 2)(c - 1) = 0
when is a product 0 ? when at least one of the factors is 0.
therefore, either
c + 2 = 0
c = -2
or
c - 1 = 0
c = 1
the solution is
c = -2
or
c = 1
What number can be added to -2 to get a sum of 0? A-2 B0 C 2
Answer:
C) 0
Step-by-step explanation:
-2+2=0
These questions are about calculus, I would greatly appreciate your help on both questions! . asap , please !
The values of derivatives are:
y' = -1/(x+2)²y'(5) = -1/49dy/ dx| (x= -4) =-1/4y'(-1) = -1dy/ dx| (x=2) =-1/4What is derivative?The derivative is the instantaneous rate of change of a function with respect to one of its variables.
Given:
y = 1/ (x+2)
y= \((x + 2)^{-1}\)
On differentiating w.r.t 'x' is
y' = (-1) \((x+2)^{-2}\)
y' = -1/(x+2)²
Now, y'(5) = -1 / (5+2)²
y'(5) = -1/49
at x= -4
dy/dx = -1/(-4+2)²
dy/ dx =-1/4
At x= -1
y' = -1/ (-1+2)²
y' = -1
At x= 2
dy/dx = 1/(2+2)²
=1/16
Learn more about differentiation here:
https://brainly.com/question/24898810
#SPJ1
Suppose a normal distribution has a mean of 34 and a standard deviation of
2. What is the probability that a data value is between 30 and 36? Round your
answer to the nearest tenth of a percent.
Answer:
it’s 86.6%
Step-by-step explanation:
could be wrong
HELP!!
Determine each percentage by writing a proportion. Round to the nearest tenth if necessary.
What % of 25 is 16?
Answer:
64%
Step-by-step explanation:
16 ÷ 25 = 0.64 = 64%
QUESTION 25
Solve for a. Enter a number answer only.
25
a
24
Answer: 7
Step-by-step explanation:
We can use the Pythagorean theorem (a^2+b^2=c^2) so 25^2=625, and 24^2=576
576+b^2=625 b^2=49 b - (a)=7
help me please.. please
Step-by-step explanation:
Parallel to the x-axis means it is just a horizontal line with the value being the y-coordinate of the point:
y = -2
Answer:
y=-2
and m=0 must be your answer
Step-by-step explanation:
as line is parallel to x axis its slope will be zero as it does not have any definite x coordinate
so
equation of line is y-y'=m(x-x')
so m=0 m is slope
y'=-2 and x'=4
so by substituting the values
y+2=0
so y=-2
and m=0 is your answer
Please look at the photo. Thank you!
The zeros with each multiplicity are given as follows:
Multiplicity one: x = 6.Multiplicity two: x = 11.Multiplicity three: x = -6 and x = -5.How to obtain the multiplicities?The factor theorem is used to define the functions, which states that the function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.
Considering the linear factors of the function in this problem, the zeros are given as follows:
(x + 6)³ -> zero at x = -6 with multiplicity of 3.(x - 11)² -> zero at x = 11 with multiplicity of 2.x - 6 -> zero at x = 6 with multiplicity of 1.(x + 5)³ -> zero at x = -5 with multiplicity of 3.More can be learned about the Factor Theorem at brainly.com/question/24729294
#SPJ1
93% of a towns population own cars. if the number of cars owned is 5208, whats the population
Answer: from my understanding my anwser was 5600 im sorry if it not correct
Step-by-step explanation:
Answer:
5600
Step-by-step explanation:
Which of the following equations have infinitely many solutions?
Choose all answers that apply:
62 + 35 = -62 + 35
B
62 + 35 = -62 – 35
- 6x + 35 = -62 – 35
-6x + 35 = -6.0 + 35
4 of 9
Answer:
none of em. Cause they either need to have the same number on each side, or like for example the variables and coefficient need to be same like 6x = 6x. but none of em seem to match. You probably didnt write it correctly
Match each value on the left with the number on the right that includes that value.
Which set of numbers includes only whole numbers? Rational Numbers Integers Whole Numbers 7. -4, 5.0
Answer:
2, 5, 8, 15
Step-by-step explanation:
The set of whole numbers is: 0, 1, 2, 3, ...
It includes zero but no negative numbers.
Answer: 2, 5, 8, 15