To divide a decimal number by a whole number, long divide as you would with two whole numbers, but put the decimal point in the answer at the same place it is at in the dividend. If it does not divide evenly, add a 0 to the end of the dividend and continue dividing until there is no remainder.
How long would it take $5,000 to grow to $15,000 at 7% compounded continuously? Round your answer to the nearest tenth of a year A. 22.3 years B. 16.2 years C. 15.7 years D. 15.9 years
Using algebra calculation, approximately 15.7 years that will be taken for $5,000 to grow to $15,000 at 7% compounded continuously
The formula for continuously compounded interest is A = Pe^(rt), where A is the ending balance, P is the principal (starting balance), e is Euler's number (approximately 2.71828), r is the annual interest rate expressed as a decimal, and t is the time in years.
We are given P = $5,000, A = $15,000, and r = 0.07.
Using this formula, we can solve for t:
$15000 = $5000 × e^(0.07t)
Divide both sides by $5000:
3 = e ^ (0.07t)
Take the natural logarithm of both sides:
ln(3) = 0.07t
Divide both sides by 0.07:
t = ln(3)/0.07
t ≈ 15.7 years
Therefore, the answer is C, 15.7 years for $5,000 to grow to $15,000 at 7% compounded continuously.
Learn more about algebra here:
https://brainly.com/question/29390182
#SPJ11
4(2x+5)-2(x-3)=8(2x+4)
Answer:
-0.6 or -(3/5)
Step-by-step explanation:
Let's simplify the left-hand side of the equation first:
4(2x+5)-2(x-3)
= 8x + 20 - 2x + 6 [distributing the multiplication and simplifying the parentheses]
= 6x + 26
Now let's simplify the right-hand side of the equation:
8(2x+4)
= 16x + 32
So the equation becomes:
6x + 26 = 16x + 32
Let's isolate x on one side of the equation:
6x - 16x = 32 - 26
-10x = 6
x = -0.6
Therefore, the solution to the equation is x = -0.6.
4. Assume that the sales of a certain appliance dealer are approximated by a linear function. Suppose that sales were $850,000 in 1992 and $1,262,500 in 1997. X = 0 represents 1992. (a) Find an equation giving the dealer's yearly sales. (b) What were the dealer's approximate sales in 1995? (c) Estimate sales in 1999.
The answer are:
a. S(x) = $82,500(x - 1992) + $850,000
b. Sales in 1995: $1,097,500
c. Sales in 1999: $1,427,500
To solve this, we need to crea a linear function. A linear function is of the form:
\(L(x)=ax+b\)Where a is the slope and b the y-intercept.
We want the sales in function of the year. If we call the year x, and teh sale S, we call the line S(x)
The first thing we need to do is to find the slope of the line. We can calculate the slope of the line with two points like:
\(\begin{gathered} P=(x_p,y_p)\text{ and Q}=(x_q,y_q) \\ \text{slope}=\frac{y_q-y_p}{x_q-x_p} \end{gathered}\)
For two points P and Q. We know the value of two points:
In 1992, the sales was $850,000
In 1997, the sales was $1,262,500
Then we call P = (1992, $850,000) and Q = (1997, $1,262,500)
Now let's calculate the slope:
\(slope=\frac{1,262,500-850,000}{1997-1992}=\frac{412,500}{5}=82,500\)Now that we know the slope, we need to find the term b of the form of a line.
b is the value of the function when x = 0. In this case, the problem says that when x = 0, we need to use the value of 1992. The sales in 1992 was $850,000. then b = $850,000
We almost done with a. the only thing remaining is that we want the year 1992 to be the starting point. Then, to our value of x, we need to rest 1992.
let's see:
\(\begin{gathered} \text{slope}=82,500 \\ b=850,000 \\ S(x)=82,500\cdot x+850,000 \end{gathered}\)If we just left the equation like that, when we want to know what happens in 1992:
\(S(1992)=82,500\cdot1992+850,000=165,190,000\)Which we know is wrong because the sales in 1992 were 850,000. To fix this, we need to rest 1992 from x. This way:
\(S(x)=82,500(x-1992)+850,000\)If we try this equation for 1992:
\(\begin{gathered} S(1992)=82,500(1992-1992)+850,00 \\ S(1992)=82,500\cdot0+850,000 \\ S(1992)=850,000 \end{gathered}\)And that's the correct value of the sales for 1992.
This was the hard part, all we have to do now is evaluate the function for x = 1995 and x = 1999:
Part b.
\(\begin{gathered} S(x)=82,500(x-1992)+850,000 \\ S(1995)=82,500(1995-1992)+850,000 \\ S(1995)=82,500\cdot3+850,000 \\ S(1995)=1,097,500 \end{gathered}\)Part c.
\(\begin{gathered} S(1999)=82,500(1999-1992)+850,000 \\ S(1999)=82,500\cdot7+850,000 \\ S(1999)=1,427,500 \end{gathered}\)And the problem is solved
if you flip 100 coins what is the probability of 50 being heads and 50 being tails
Answer:
1/2
Step-by-step explanation:
it is going to be 1/2 because you you have a 1 out of 2 chance of getting heads or
tails on any of them.
Answer:
if you
flipped a coin 100 times you saw the ratio of head and tails to be 50/50. They created a diagram of all the flips. There was a lot of flip-flopping between heads and tail.
Step-by-step explanation:
what is the next number in the sequence? 3….9….27….81….
Answer:
The next sequence is 243
The pattern is x 3
3 x 3 = 9
9 x 3 = 27
27 x 3 = 81
81 x 3 = 243
Step-by-step explanation:
You're welcome.
plz help me, i need help with this and i dont understand what this means
Answer:
x y
1 5
0.8 (4/5) 4
0.4 (2/5) 2
Step-by-step explanation:
Plug in the y values for y and solve
ndiba wants to buy a wagon that costs $217. how much change does he receive if he gives the cashier $250?
Answer:
change = $33
Step-by-step explanation:
ndiba wants to buy a wagon that costs $217. how much change does he receive if he gives the cashier $250?
250 - 217 = change
change = $33
{assuming no sales tax]
What is the volume of the prism
Answer:
V = 140.4
Step-by-step explanation:
V= (1/2)h*l*w = (1/2) 4* 7.8 * 9 = 140.4
The amount of money in a bank account doubles every 3 months, what would be the growth factor for 1 month? Explain how you got your answer.
Answer:
Explanation:
A hockey puck is set in motion across a frozen pond. If ice friction and air resistance are neglected, the force required to keep the puck sliding at constant velocity is equal to its weight. equal to its mass times its weight. equal to its weight divided by its mass. none of the above
The force required to keep a hockey puck sliding at a constant velocity, neglecting ice friction and air resistance, is equal to its weight. The correct option is "equal to its weight."
When a hockey puck is set in motion across a frozen pond and there is no ice friction or air resistance, the only force acting on the puck is its weight, which is the force due to gravity pulling it downward. According to Newton's first law of motion (the law of inertia), an object at a constant velocity will continue to move at that velocity unless acted upon by an external force.
Since the puck is already in motion and we want to maintain its constant velocity, the force required to counteract its weight and keep it sliding is equal to its weight. This is because the weight of an object is the force exerted on it by gravity, and in the absence of other forces, an equal and opposite force is needed to maintain the object's motion without acceleration.
Learn more about Newton's first law here:
https://brainly.com/question/29775827
#SPJ11
-2k-(-5)+1 combine like terms to create an equivalent expression
The resulting equivalent expression is -2k + 6
Equivalent expression.
Equivalent expression means an expressions that work the same even though they look different. If we said the two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s).
Given,
Here we have the expression -2k - (-5) + 1
Now, we have to combine the like terms and then we have to solve it in order to find the equivalent expression.
First, we have to write the given expression,
=> -2k - (-5) + 1
Here we know that (-) x (-) = (+), therefore, the given expression is rewritten as follows:
=> -2k + 5 + 1
Here the only like term is the constant 5 and 1, so, we have to combine these constant, the we get the expression like the following;
=> -2k + (5 + 1)
No, we have to add the constant in order to get the equivalent expression,
=> - 2k + 6
Therefore, the equivalent expression i s -2k + 6.
To know more about Equivalent expression here.
https://brainly.com/question/28170201
#SPJ1
Solve the system.
y= -3x
x+y=4
A. (-1, 3)
B. (-4, 12)
C. (1, -3)
D. (-2, 6)
Answer:
D is the answers for the question
Step-by-step explanation:
please give me brainlest
In a 2011 article in North Carolina Law Review, M. Radelet and G. a logistic prediction equation for death penalty verdicts in North Carolina. Let Y denote whether a subject convicted of murder received the death penalty (1 = yes), for defendant's race h (h = 1, black; h = 2, white), victim's race i (i = 1, black; i = 2, white), and number of additional factors j (j = 0, 1, 2). For the model = = - logit[P(Y = 1)] = a + BR +BY+B they reported â = -5.26, BP = 0.00, B2 = 0.17, BY = 0.00, BY = 0.91, B6 0.00, B 9 = 2.02, B5 = 3.98. a. Estimate the probability of receiving the death penalty for the group most likely to receive it. = LOGISTIC REGRESSION = b. If, instead, parameters used constraints B? = By = B = c. If, instead, parameters used constraints En BR = ŹBY = £; B = 0, report : 0, report the estimates. h the estimates.
Based on the given information, we can estimate the probability of receiving the death penalty for the group most likely to receive it by substituting the values of the coefficients into the logistic prediction equation:
P(Y = 1) = exp(a + B1R + B2Y + B3 + B4h + B5i + B6j + B7h*i)
where:
a = -5.26
B1 = 0.00
B2 = 0.17
B3 = 0.00
B4 = 0.91
B5 = 0.00
B6 = 2.02
B7 = 3.98
Assuming that the group most likely to receive the death penalty is a black defendant (h = 1), with a white victim (i = 2), and no additional factors (j = 0), we can plug in these values into the equation:
P(Y = 1) = exp(-5.26 + 0.00R + 0.17Y + 0.00 + 0.911 + 0.002 + 2.020 + 3.981)
P(Y = 1) = exp(-5.26 + 0.91 + 3.98)
P(Y = 1) = exp(-0.37)
Using the exponential function, we can calculate the estimated probability:
P(Y = 1) = 0.691
So, the estimated probability of receiving the death penalty for the group most likely to receive it (a black defendant with a white victim and no additional factors) is approximately 0.691 or 69.1%.
If the constraints B1 = By = B = 0 are used instead, the estimates for the coefficients would be different and would need to be calculated accordingly.
Learn more about “ probability of receiving the death penalty “ visit here;
https://brainly.com/question/31083902ts
#SPJ4
In which tables does y vary directly with x? Check all that apply
Answer:
first three
Step-by-step explanation:
go directly to the x- value ed2020
first second and third
!:)
Find the total surface area of this cylinder. Give your answer to one decimal place first correct answer will get brainliest and 5 stars!!!
Answer:
The surface area formula is 2πr (h + r) where r and h are the radius and height respectively. Since π = 3.14, r = 7, h = 15 the answer is:
2 * 3.14 * 7 * (15 + 7) = 43.96 * 22 = 967.6
g a simple undirected graph has 10 edges. 2 of the vertices are of degree 4, and the rest of the vertices are of degree 3. how many vertices are in this graph?
Therefore, there are 4 vertices in this graph.
Let V be the number of vertices in the graph. The sum of the degrees of all vertices in an undirected graph is twice the number of edges, so in this case, the sum of degrees is 2 * 10 = 20.
We know that two vertices have degree 4, so the degrees of the remaining vertices must add up to 20 - 2 * 4 = 12.
If there are v vertices of degree 3, then the total degree contributed by those vertices is 3v, so we have:
3v + 2 * 4 = 20
3v = 12
v = 4
To know more about graph,
https://brainly.com/question/29467965
#SPJ11
Suppose you are constructing a confidence interval for the population mean. For a given sample size and standard deviation, the width of the confidence interval is ______ for a greater confidence level.
The width of a confidence interval for the population mean depends on the sample size, standard deviation, and the desired level of confidence. Generally, for a greater confidence level, the width of the confidence interval will be wider.
This is because a higher confidence level means that we want to be more certain that the true population mean falls within the interval. To achieve this higher level of certainty, we need to widen the interval to include a larger range of possible values for the population mean.
However, it's important to note that the increase in width may not be proportional to the increase in confidence level. In fact, the width of the confidence interval increases at a decreasing rate as the confidence level increases.
This means that the increase in width from a 90% confidence interval to a 95% confidence interval will be less than the increase in width from an 80% confidence interval to a 85% confidence interval, even though both involve a 5% increase in the level of confidence.
for such more question on confidence interval
https://brainly.com/question/14366786
#SPJ11
I WILL MARK BRAINIEST
PLEASE HELP ASAP
Answer:
2101
Step-by-step explanation:
Apply -12 to the x
-(-12)^3+3(-12)^2+5(-12)+1
Then Simplify
2101
I hope it's right
A 100 foot long ramp leads up to the base of a statue that is 20 feet tall. From the bottom of the ramp. the angle of elevation to the top of the statue is 25°. Determine the angle the ramp makes with the ground.
Round to the nearest degree. You may assume the ground is level and horzontal
The angle the ramp makes with the ground is approximately 12 degrees
How to determine the angleFirst, we have to know the ratio of the trigonometric identities
sin θ = opposite/hypotenuse
cos θ = adjacent./hypotenuse
tan θ = opposite/adjacent
From the information given, we have that;
The angle of elevation to the top of the statue is 25°
Using the sine identity, we have that
sin θ = 20/100
Divide the values, we have;
sin θ = 0. 2000
Now, find the sine inverse of the value, we get;
θ = 11. 53 degrees
Learn more about trigonometric identities at: https://brainly.com/question/7331447
#SPJ1
What is the value of n?
Answer:
4x6=3*n
Step-by-step explanation:
just got it off the web enjoy might not be right
Solving Systems of linear equations by graphing. no graphing device.
Answer: (1,3)
Step-by-step explanation:
a manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 411.0 gram setting. it is believed that the machine is underfilling the bags. a 35 bag sample had a mean of 406.0 grams. a level of significance of 0.05 will be used. state the hypotheses. assume the standard deviation is known to be 25.0.
Using a 35-bag sample with a mean of 406.0 grams, a known standard deviation of 25.0 grams, and a level of significance of 0.05, you can perform a one-tailed Z-test to determine whether to reject or fail to reject the null hypothesis.
To test if the potato chip manufacturer's bag filling machine is working correctly at the 411.0-gram setting, we will state the hypotheses using the given terms.
Null Hypothesis (H0): The machine fills bags correctly, with a mean weight of 411.0 grams (µ = 411.0 grams)
Alternative Hypothesis (H1): The machine is underfilling bags, with a mean weight less than 411.0 grams (µ < 411.0 grams)
To learn more about standard deviation, refer here:
https://brainly.com/question/23907081#
#SPJ11
PLS HELP WILL GIVE BRAINLIEST!!!!
Answer: 36 degrees
Step-by-step explanation: 180 degrees - 144 degrees = 36 degrees
Answer:
A = 54 d and x = 45 B = 45 so a = 54 and x= 45 and b= 45 and x = 45
Find the volume of the triangular prism.
5 cm
8 cm
4 cm
V = [?] cubic centimeters
Hint: Find the area of the triangular base. Then multiply the base by the height.
Based on the area of the triangular prism, and the height, the volume of the triangular prism can be found to be 80 cm³
What is the volume of the triangular prism?This can be found as:
= Area of triangular base x Height of triangular prism
Solving gives:
= (1/2 x 4 x 5 ) x 8
= 10 x 8
= 80 cm³
Find out more on the volume of a triangular prism at https://brainly.com/question/17075150
#SPJ1
Please help ASAP. Thanks! Will mark as Brainlyist.
Answer:
Width and length.
Step-by-step explanation:
P has a width, and length.
hope this helps.
Find the L.C.M of the following.
\(a. \: 1 + 4x + 4 {x}^{2} - 16 {x}^4 \: and \: 1 + 8 {x}^{3} \)
Answer:
First, let's factor the two polynomials:
1 + 4x + 4x^2 - 16x^4 = (1 - 2x)^2(1 + 2x)
1 + 8x^3 = (1 + 2x)(1 - 2x + 4x^2)
To find the LCM of these two expressions, we need to take each factor to its highest power. Thus, the LCM is:
(1 - 2x)^2(1 + 2x)(1 + 2x^2)
Answer:
Step-by-step explanation:
To find the L.C.M of the given polynomials, we need to factorize them first.
1 + 4x + 4{x}^2 - 16{x}^4 can be written as (1-2x{^2}){^2}.
1 + 8{x}^3 can be written as (1+2{x}^3).
So, the L.C.M would be the product of the highest powers of each factor.
In this case, (1-2x{^2}){^2} has the highest power of 2, while (1+2{x}^3) has the highest power of 1.
Thus, the L.C.M of 1 + 4x + 4{x}^2 - 16{x}^4 and 1 + 8{x}^3 is (1-2x{^2}){^2} (1+2{x}^3).
Nolan is a waiter at a restaurant. Each day he works, Nolan will make a guaranteed wage of $25, however, the additional amount that Nolan earns from tips depends on the number of tables he waits on that day. From past experience, Nolan noticed that he will get about $11 in tips for each table he waits on. How much would Nolan expect to earn in a day on which he waits on 12 tables? How much would Nolan expect to make in a day when waiting on tt tables?
Nolan would expect to earn $157 in a day when he waits in 12 tables.
Now, According to the question:
We have the following information:
Each day Nolan works, Nolan will make a guaranteed wage of $25, however the additional amount that Nolan earns from tips depends on the number of tables he waits on that day. From past experience, Nolan noticed that he will get about $11 in tips for each table he waits on.
Now, for waiting on 12 tables, he will get the fixed amount of 25 dollars and the amount for 12 tables.
So, the total amount will be:
25+11 × 12
$157
Hence, Nolan would expect to earn $157 in a day when he waits in 12 tables.
Learn more about expected earning at:
https://brainly.com/question/29252733
#SPJ4
cindy baught 1/4 amount of ribbon and jacob baught 7/8 amount of ribbon how much ribbon does jacob have
Answer:
0.875
Step-by-step explanation:
If ⅆyⅆt=6e−0. 08(t−5)2, by how much does y change as t changes from t=1 to t=6 ?
(A) 3. 870 (B) 8. 341 (C) 18. 017 (D) 22. 583
Based on the given informations, the change in y as t changes from 1 to 6 is approximately 3.870. Therefore the correct option is (A).
To find the change in y as t changes from 1 to 6, we need to integrate the given function with respect to t over the interval [1, 6] and then find the difference between the values of the integral at the two endpoints.
∫₁⁶ 6e\(.^{(-0.08(t-5)^2)}\) dt
We can use the substitution u = t - 5 to simplify the integral:
∫₋₄¹ 6e\(.^{(-0.08u^2)}\) du
Unfortunately, there is no closed-form solution for this integral. We can use numerical integration methods, such as Simpson's rule or the trapezoidal rule, to approximate the integral. Using Simpson's rule with a step size of 1, we get:
∫₋₄¹ 6e\(.^{(-0.08u^2)}\) du ≈ 3.870
Therefore, the change in y as t changes from 1 to 6 is approximately 3.870, which corresponds to option (A).
Learn more about integration :
https://brainly.com/question/18125359
#SPJ4
2/3x-1/5x=x-1 what is x
The value of x that satisfies the equation is x = 15/8, which is equivalent to 1.875.
To solve the equation (2/3)x - (1/5)x = x - 1 and find the value of x, we can follow these steps:
Combine like terms on the left side of the equation:
(2/3 - 1/5)x = x - 1
Find a common denominator for the fractions on the left side. The common denominator for 3 and 5 is 15, so we rewrite the equation as:
(10/15 - 3/15)x = x - 1
Simplify the left side of the equation:
(7/15)x = x - 1
To eliminate the fraction, we can multiply both sides of the equation by the denominator of the fraction, which is 15:
15 * (7/15)x = 15 * (x - 1)
This simplifies to:
7x = 15x - 15
Subtract 15x from both sides of the equation to isolate the x term:
7x - 15x = -15
Simplifying further:
-8x = -15
Divide both sides of the equation by -8 to solve for x:
x = (-15) / (-8)
Simplifying the division:
x = 15/8
For more such question on equivalent . visit :
https://brainly.com/question/2972832
#SPJ8