Shane will have to wait about 18.63 years to have $91,047 in the account.
We can use the formula for compound interest to solve this problem:
A =\(P(1 + r/n)^{(nt)\)
where A is the amount of money in the account after t years, P is the initial deposit, r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.
In this case, we have P = 7,466, r = 0.06, n = 12 (since the interest is compounded monthly), and we want to find t when A = 91,047.
Plugging in these values, we get:
\(91,047 = 7,466(1 + 0.06/12)^{(12t)\)
Dividing both sides by 7,466, we get:
\(12.189 = (1 + 0.005)^{12t\)
Taking the logarithm of both sides (using any base), we get:
log(12.189) = 12t log(1.005)
Solving for t, we get:
t = log(12.189) / (12 log(1.005))
Using a calculator, we get:
t ≈ 18.63 years
Learn more about compound interest here:
https://brainly.com/question/14295570
#SPJ11
The weights of three kittens at one week old were 4.1 ounces, 3.5 ounces, and 3.4 ounces. If each kitten gained 2.5 ounces, how much would each of the kittens weigh? A 11 ounces B 6.6 ounces, 6 ounces, and 5.9 ounces C 1.6 ounces, 1 ounce, 0.9 ounces
Answer:
B 6.6 ounces, 6 ounces, and 5.9 ounces
Step-by-step explanation:
First Kitten
Weighed: 4.1 ounces
Current weight => 4.1 ounces + 2.5 ounces
=>6.6 ounces
Second Kitten
Weighed: 3.5 ounces
Current weight => 3.5 ounces + 2.5 ounces
=>6 ounces
Third Kitten
Weighed: 3.4 ounces
Current weight => 3.4 ounces + 2.5 ounces
=> 5.9 ounces
Each of the kittens would weigh :
6.6 ounces, 6 ounces, and 5.9 ounces
How do I write 3(x+2) in the simplest form
Answer: 3x + 6
Step-by-step explanation: PLEASE MARK ME AS BRAINLISTI AND HAVE A GREAT DAY!!!
Answer:
3x+6
Step-by-step explanation:
3(x - 2) + 6 = 3x - 6 please show all steps im trying to finish so i can go to bed
I don't see a solution to the given expression.
Expand \(3(x-2)+6: 3x\)
\(3x=3x-6\)
Subtract 3x from both sides.
\(3x-3x=3x-6-3x\)
Simplify.
\(0=-6\)
Considering the sides are not equal, there is no solution to the given expression.
The weight of a honeybee is 1.2\cdot10^{-1}\text{ g}1.2⋅10 −1 g1, point, 2, dot, 10, start superscript, minus, 1, end superscript, start text, space, g, end text. The weight of the pollen collected by the bee on one trip is 6.0 \cdot 10^{-2} \text{ g}6.0⋅10 −2 g6, point, 0, dot, 10, start superscript, minus, 2, end superscript, start text, space, g, end text. What is the combined weight of the bee and the pollen? Express your answer in scientific notation.
Answer:
0.18 g
Step-by-step explanation:
Weight of honeybee = \(1.2\times 10^{-1}\ \text{g}\)
Weight of pollen = \(6\times 10^{-2}\ \text{g}\)
The above values can be written in the following ways
\(1.2\times 10^{-1}\ \text{g}=0.12\ \text{g}\)
\(6\times 10^{-2}\ \text{g}=0.06\ \text{g}\)
Weight mass = \(0.12+0.06=0.18\ \text{g}\)
The combined weight of the honeybee and the pollen is 0.18 g.
Answer:
1.8 x 10^-1
Step-by-step explanation:
it would be 0.18 withought scientific notation.
2x-2y+z=3 5y-z=-31 x+3y+2z=-21
Answer:
Step-by-step explanation:
{x,y,z}={−5,−6,1}
Can someone plz help me on this and Happy Holidays!
Answer:
The solution is 20. and simplified it is
2 x 10^7/10^6
Step-by-step explanation:
A triangle has side lengths of 18 cm, 80 cm, and 81 cm. Classify it as acute, obtuse, or right.obtuserightacute
The triangle is an οbtuse triangle.
What is a triangle?Tο determine if the triangle is acute, οbtuse, οr right, we need tο check if it satisfies the Pythagοrean theοrem. Accοrding tο the Pythagοrean theοrem, in a right triangle, the sum οf the squares οf the lengths οf the legs (the shοrter sides) is equal tο the square οf the length οf the hypοtenuse (the lοngest side). Sο, if the sum οf the squares οf the twο shοrter sides is equal tο the square οf the lοngest side, then the triangle is a right triangle.
Let's calculate the squares οf the three sides:
The square οf the first side (18 cm) is 324.
The square οf the secοnd side (80 cm) is 6400.
The square οf the third side (81 cm) is 6561.
Nοw, we need tο determine if the sum οf the squares οf the twο shοrter sides is greater than οr less than the square οf the lοngest side. Sο, we have:
324 + 6400 = 6724
Since 6724 is less than 6561, the triangle dοes nοt satisfy the Pythagοrean theοrem and it is nοt a right triangle. Therefοre, the triangle is either an acute οr οbtuse triangle.
Tο determine if the triangle is acute οr οbtuse, we need tο find the largest angle οf the triangle. We can use the Law οf Cοsines tο find the largest angle οf the triangle, which is οppοsite the lοngest side. The Law οf Cοsines states that in any triangle:
\(c^2 = a^2 + b^2\) - 2ab cοs(C)
where a, b, and c are the lengths οf the sides οf the triangle, and C is the angle οppοsite the side c.
In οur case, a = 18 cm, b = 80 cm, and c = 81 cm. Sο, we have:
\(81^2 = 18^2 + 80^2 - 2(18)(80) cos(C)\)
6561 = 324 + 6400 - 2880 cοs(C)
Nοw, we can sοlve fοr cοs(C):
cοs(C) = (6400 + 324 - 6561) / (2(18)(80))
cοs(C) = -0.2216
Since cοsine is negative, the angle C is οbtuse.
Therefοre, the triangle is an οbtuse triangle.
To learn more about the triangle, visit:
https://brainly.com/question/1058720
#SPJ1
You want to know the classification of a triangle with side lengths 18 cm, 80 cm, and 81 cm. A triangle can be classified by looking at the measure of its largest angle. The classification of the triangle is the same as the classification of that angle: obtuse if > 90°, right if = 90°, and acute if < 90°.
Largest angleThe largest angle is always opposite the longest side. In a triangle with angles A, B, C and their opposite sides a, b, c, we can call the largest angle C. Its measure can be computed using the Law of Cosines, which tells you ...
C = arccos((a² +b² -c²) / (2ab))
C = arccos((18² + 80² - 81²) / (2×18×80)) = arccos(163/2880) ≈ 86.8°
The largest angle is less than 90°, so the triangle is an acute triangle.
What is the equation of the line that goes through (-3,-1) and (3,3)
Answer:
3
Step-by-step explanation:
What is geometry in mathematics ?
Answer:
Geometry in Mathematics is the study of shape and figures.
Answer:
Geometry refers to a branch of mathematics which is focused on the measurement and relationship of lines, angles, surfaces, solids and points. For instance, the calculation of a triangle's angles is an example of geometry.
Devaughn is years younger than Sydney. The sum of their ages is . What is Sydney's age?
\(\huge{Answer}\)
d = s-14
d+s = 76
Using substitution method
(s-14)+s = 76
2s-14= 76
2s = 90
s = 45
Sydney's age =45
d = s-14 = 31
Devaughn's age=31
We have that the Sydney's age is mathematically given as
A=y-x
Age
Question Parameters:
let Devaughn is years younger than Sydney=x.
The sum of their ages is =y
Generally the equation for the Sydney's is mathematically given as
A=The sum of their ages-Age apart
Therefore
A=y-x
For more information on Arithmetic visit
https://brainly.com/question/22568180
Math Help please show work please due soon uwu :3
Answer: 416 in^2
Step-by-step explanation:
a. Area of the Triangle x 2 + Area of Rectangle x 3
b. 8 x 7 / 2 x 2 + 8 x 15 x 3 = 56 + 360 = 416 in^2
Solve the following quadratic equation for all values of x in simplest form.
3(x-5)^2=33
The value of x for the given quadratic expression is x = 5 ± √11.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given expression is 3(x-5)²=33. The value of x will be calculated as,
3(x-5)²=33
(x - 5 )² = 11
(x - 5 ) = ±√11
x = 5 ± √11
Therefore, the value of x for the given quadratic expression is x = 5 ± √11.
To know more about an expression follow
https://brainly.com/question/27826679
#SPJ1
can anyone help me solve this twenty points if you solve it
Answer:
Option d is the ryt answer.
Point slope form:
y-y1 = m(x-x1)
Slope intercept form:
y = mx+b
PLEASE HELP
WILL GIVE BRAINLIEST
Identify the situation that each graph could represent.
A ray is graphed in the first quadrant. The horizontal axis is labeled Time. The ray starts at the bottom left and continues to the upper right.
A. the length of a necklace that you make at a rate of 10 cm per hour without taking a break
B. the height of a balloon as it rises, gets caught in a tree for a few minutes, and then continues to rise
C. the total distance you are from home if you ride your bicycle three miles per hour for one hour, and then stop and take a rest
D. The volume of water in a bath tub as it is draining.
Answer:
The answer your looking for is, C.
4b-1+5b=?
.helpp mee
Answer:
9b-1
Step-by-step explanation:
Hope this helps! Plz give brainliest!!!
Answer:
b = 1/9
Step-by-step explanation:
Supposing that you need clear b
4b + 5b = 1
9b = 1
b = 1/9
value of 3b^2 - 5c^3 if b = 2 and c = -1
Answer:
17
Step-by-step explanation:
3(2)^2 - 5(-1)^3
3(4) - 5(-1)
12 + 5
17
Show that each term in the following equation has units of lb/ftº. Consider u as velocity, y as length, x as length, p as pressure, and u as absolute viscosity
The equation \(p*u*(dy/dx)\)has units of\(lb/ftº\), which is derived by multiplying the units of each of the three terms in the equation: \((lb/ft²)(ft/s)(1/ft).\)
\(p*u*(dy/dx)\)
\(lb/ftº = (lb/ft²)(ft/s)(1/ft)\)
\(= (lb/ft²)(ft/s)(ftº)= lb/ftº\)
1. The first term in the equation is pressure, p, which is measured in units of \(lb/ft².\)
2. The second term is absolute viscosity, u, which is measured in units of ft/s.
3. The third term, \((dy/dx)\) is the derivative of y with respect to x, and has units of 1/ft.
4. Multiplying the three terms together gives a result of\((lb/ft²)(ft/s)(1/ft)\)which is equal to\(lb/ftº.\)
The equation\(p*u*(dy/dx)\) has units of \(lb/ftº\), which is derived by multiplying the units of each of the three terms in the equation: \((lb/ft²)(ft/s)(1/ft).\)
Learn more about equation here
https://brainly.com/question/29657992
#SPJ4
What Percent of 60m is 9m?
Which of the following would not be used to describe a slope?
steepness of a line.
ratio of rise to run of a line.
ratio of the horizontal change to the vertical change of a line.
Answer:
C: ratio of the horizontal change to the vertical change of a line
Step-by-step explanation:
A and B are correct.
C is incorrect.
Help me i'm stuck 3 math
Answer:
V = (1/3)(16)(14)(12) = 4(224) = 896 cm³
Using the substitution: u=8x−9x ²−7. Re-write the indefinite integral then evaluate in terms of u.
∫((29)x−2)e⁸ˣ−⁹ˣ²−⁷dx=∫__= _____
Note: answer should be in terms of u only
The indefinite integral ∫((29)x^-2)e^(8x-9x²-7)dx can be rewritten as ∫((29/(8x - 9x² - 7)^2)e^(u)(1/(8 - 18x)) du in terms of u.
To rewrite and evaluate the indefinite integral ∫((29)x^-2)e^(8x-9x²-7)dx in terms of u using the substitution u = 8x - 9x² - 7, we need to express the integrand and dx in terms of u. The indefinite integral becomes ∫(29/u^2)e^(u)du. We can then evaluate this integral by integrating with respect to u.
To rewrite the integral ∫((29)x^-2)e^(8x-9x²-7)dx in terms of u, we substitute u = 8x - 9x² - 7. Taking the derivative of u with respect to x gives us du/dx = 8 - 18x. Rearranging this equation, we find dx = (1/(8 - 18x)) du.
Substituting these expressions into the original integral, we have:
∫((29)x^-2)e^(8x-9x²-7)dx = ∫((29)(8x - 9x² - 7)^-2)e^(u)(1/(8 - 18x)) du.
Simplifying this further, we have:
∫((29/(8x - 9x² - 7)^2)e^(u)(1/(8 - 18x)) du.
Now, the integral is expressed solely in terms of u, as required.
To evaluate this integral, we can use techniques such as substitution, integration by parts, or partial fractions. The specific method depends on the complexity of the integrand and the desired level of precision.
Learn more about integral here:
https://brainly.com/question/31059545
#SPJ11
Determine whether the underlined value is a parameter or a statistic.
Following the election, 18 % of the governors of all 50 areas of a country were female.
Is the value a parameter or a statistic?
The given numerical value is a Statistic.
Parameters are numeric values that characterize the population as a whole. A statistic is a number that describes the characteristics of a sample.
For example, median income in the United States is a demographic parameter. Conversely, the median income for the US sample is a sample statistic. Both values represent median income, but one is a parameter to the statistic. Easy to remember parameters and stats! Both are summary values that describe the group, and have a convenient mnemonic device to remind you which group is being described. Notice their initials.
Parameter = Population
Statistics = Sample
A population is the entire group of people, things, animals, trades, etc. that are being studied. A sample is part of a population.
Following the election, 18 % of the governors of all 50 areas of a country were female.
Given that, 18% of the 50areas of a country were females.
Now,
18*50/100 = 9
Since it is a perfect number
The given numerical value is a statistic.
known more about parameter ans statistic click here;
https://brainly.com/question/23612195
#SPJ4
What is the equation of a line with a slope of 4 and a y-intercept of 2?
Answer:
y=4x+2 or f(x)=4x+2
Step-by-step explanation:
This is because the equation format for a line is y=mx+b, the slope is m and the y-intercept is b. So all you have to do is fill it out to get y=4x+2. Or the other way I listed the equation is right too. Hope this helps!
The difference of a number and 8 is 46 less the number. Find the number
Answer:
unsolvable
Step-by-step explanation:
n-8=46-n
n=(46-n)+8
n=54-n
Answer:
54
Step-by-step explanation:
you add 8+46 and you can check with 54-46=8
Which graph represents the solution set of the inequality x + 2 greater-than-or-equal-to 6 A number line goes from negative 9 to positive 9. A solid circle appears on positive 3. The number line is shaded from positive 3 through negative 9. A number line goes from negative 9 to positive 9. An open circle appears at positive 3. The number line is shaded from positive 3 through positive 9. A number line goes from negative 9 to positive 9. A closed circle appears at positive 4. The number line is shaded from positive 4 through positive 9. A number line goes from negative 9 to positive 9. An open circle appears at positive 4. The number line is shaded from positive 4 through negative 9.
The graph of the inequality is x + 2 ≥ 6 is plotted
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
x + 2 ≥ 6
Subtracting 2 on both sides , we get
x ≥ 4
So , the inequality is x ≥ 4 and the graph is plotted
Hence , the inequality is x ≥ 4
To learn more about inequality equations click :
https://brainly.com/question/11897796
#SPJ1
What is 6(4y+7)-(2y-1)
Answer: The simplified expression 6(4y + 7) - (2y - 1) is : 22y + 43
assuming that if a logical vector z has at least one entry true, which of the function will always be false ? group of answer choices any(!z) all (!z) any(z) all(z)
If a logical vector z has at least one entry TRUE, the function all(!z) will always be false.
If a logical vector contains only TRUE items, the all() method returns FALSE; otherwise, it returns TRUE.
The any() function, on the other hand, gives a result of TRUE if a logical vector has at least one element that is TRUE and FALSE otherwise.
any(z) will always be TRUE if z contains at least one TRUE element since there is at least one TRUE element. On the other hand, depending on whether all of the components of z are TRUE, all(z) may or may not be TRUE.
any(!z) will always return FALSE since if z has at least one TRUE element, then!z must include at least one FALSE element.
Additionally, all(!z) will always return FALSE if any element is FALSE since if z has at least one TRUE element, then!z must include at least one FALSE element.
Learn more about propositional logic in discrete mathematics here:
https://brainly.com/question/1103576
#SPJ4
Lorelei and Chance run a bakery. They have been making wedding cakes for several years and they have found the time L it takes Lorelei to frost a randomly selected 3-layer cake is approximately Normally distributed with a mean of 37 minutes and a standard deviation of 12 minutes. The time C it takes Chance to decorate a randomly selected 3-layer cake is approximately Normally distributed with a mean of 52 minutes and a standard deviation of 7 minutes. Assume that L and C are independent random variables.
Use the z-table to answer the question.
Let the random variable T = L + C be the total time it takes Lorelei, then Chance to each totally finish a different randomly selected 3-layer wedding cake.
The shape of T is
.
The center of T is Mu Subscript T =
.
The variability of T is Sigma Subscript T =
.
The probability that Lorelei and Chance totally finish a randomly selected 3-layer wedding cake in under 90 minutes is
Where the above conditions exist,
The shape of T is also Normally distributedMu_T = 89Var(T) = 193Sigma_T = 13.89the probability that Lorelei and Chance totally finish a randomly selected 3-layer wedding cake in under 90 minutes is 0.5287. What is the rationale for the above response?The random variable T = L + C represents the total time it takes Lorelei and Chance to finish a randomly selected 3-layer wedding cake. Since L and C are independent and Normally distributed, T is also Normally distributed with mean:
Mu_T = Mu_L + Mu_C = 37 + 52 = 89
and variance:
Var(T) = Var(L) + Var(C) = 12^2 + 7^2 = 193
So the standard deviation of T is:
Sigma_T = sqrt(Var(T)) = sqrt(193) = 13.89
The shape of T is also Normally distributed, since it is a sum of two independent Normally distributed variables.
To find the probability that Lorelei and Chance finish a randomly selected 3-layer wedding cake in under 90 minutes, we need to calculate the z-score for this value and then find the corresponding probability from the z-table. The z-score is:
z = (90 - 89) / 13.89
= 0.072
From the z-table, we find that the probability of a Z-score less than or equal to 0.072 is 0.5287.
Therefore, the probability that Lorelei and Chance totally finish a randomly selected 3-layer wedding cake in under 90 minutes is 0.5287 or approximately 53%.
Learn more about probability at:
https://brainly.com/question/30034780
#SPJ1
Find the sum for the geometric series described as: a1=3125, 125, n=6, and r=1/5
The sum of the first 6 terms of the given geometric series is 3906.
Dr. Franklin would like
to buy earbuds for her
students. If each
earbud costs 0.94, how
much would she pay
for 22 earbuds not
including tax?
Answer:
20.68
Step-by-step explanation:
Answer:we have that
each earbud costs 0.94
so
Multiply by 22
0.94*22=$20.68
the answer is $20.68
Step-by-step explanation: