Given :
The principal = 3,700
Assume a simple interest
The account growing at a rate allowing the money to double every 6 years.
So,
[tex]\begin{gathered} I=P\cdot r\cdot t \\ I=P \\ 3700=3700\cdot r\cdot6 \\ r=\frac{1}{6} \end{gathered}[/tex]How much money would be in the account after 14 years, to the nearest dollar?
So, we will substitute with r = 1/6, t = 14 years
So,
[tex]\begin{gathered} I=3700\cdot\frac{1}{6}\cdot14=8633.33 \\ \\ A=P+I=8633.33+3700=12333.33 \end{gathered}[/tex]Rounding to the nearest dollar
So, the answer will be $12,333
I just finished my other 2 questions and I need help with this one now, I don't understand the letters really. please help
So, c(x) = 8.25x + 1500
the marginal cost doubles so, (8.25 x) will be 2 * (8.25x )
And the fixed cost decreased by 30%
so, 1500 will be (1 - 30%) of 1500
so, (1 - 30%) of 1500 = 70% of 1500 = 0.7 * 1500 = 1050
So, k(x) = 2 * (8.25x) + 1050
K(x) = 16.5 x + 1050
How is this wrong can someone explain, and what is the correct answer
Answer:
Step-by-step explanation:
find and classify the global extrema of the following function
f(x)=(x-2)^2+5
compute the critical points of (x-2)^2+5
to find all critical points, first compute f(x)
f(x)=2(x-2)
solving 2(x-2)=0 yields x=2
x=2
f(x) exists everyhere
2(x-2) exists everyhere
the only critical point of (x-2)^2+5 is at x=2
x=2
the domain of (x-2)^2+ 5 is R
the endpints of R are x = -∞ and ∞
Evalute (x-2)^2+5 at x = -∞, 2 and ∞
the open endpoints of the domain are marked in gray
x () f(x)
-∞ ∞
2 5
∞ ∞
the largest value corresponds to a global maximum, and the smallest value corresponds to a global minimum:
the open endpoints of the domain are marked in gray
x () f(x) extrema type
-∞ ∞ global max
2 5 global min
∞ ∞ global max
remove the points x = -∞ and ∞ from the table
These cannot be global extrema, as the value of f(x) here is never achieved
x () f(x) () extrema type
2 5 global min
f(x) = (x-2)^2+5 has one global minimum
Answer:
f(x) has a global minimum at x = 2
Answer:
Step-by-step explanation:
Gourmet Eatery has a policy of automatically adding a 18% tip to every restaurant Bill if a restaurant bill is $12 how much is it
Let:
B = Bill
C = Cost of the meal
T = Tip
[tex]undefined[/tex]Find the parabola with focus (2,7) and directrix y = -1.
A parabola with focus (a, b ) and directrix y = c has the equation
[tex](x-a)^2+b^2-c^2=2(b-c)y[/tex]In our case, (a, b) = (2, 7) and c = -1; therefore, the above becomes
[tex](x-2)^2+7^2-(-1)^2=2(7-(-1))y[/tex][tex](x-2)^2+48=16y[/tex][tex]\Rightarrow\textcolor{#FF7968}{(x-2)^2=16(y-3)}[/tex]which is our answer!
provide evidence that this function is not one to one. explain how your evidence supports that g(x) is not one to one
we have the function
g(x)=(x/3)+2 ---------> interval (-infinite, 1)
g(x)=4x-2 ------> interval [1, infinite)
the given function is not one-to -one function, because don't pass the Horizontal Line Test.
Example
For the horizontal line
y=2
we have the values of
x=0 ---------> g(x)=(x/3)+2
and
x=1 -----------> g(x)=4x-2
that means
two elements in the domain of g(x) correspond to the same element in the range of g(x)
therefore
the function is not one to oneWrite the following phrase as a variable expression. Use x to represent “a number” The sum of a number and fourteen
we can write "the sum of a number and fourteen", given that x represents any number, like this:
[tex]x+14[/tex]A baby cows growth. About how many pounds does the baby cow gain each week?
Growth per week = 124 - 122 = 126 - 124 = 2
. = 2 pounds + 1 pound additional
. = 3
Then answer is
OPTION B) 3 pounds
Which of the following are solutions to the inequality below? Select all that apply.
Step-by-step explanation:
1.12+8×10<66
12+80<66
92<66
2.12+8×3<66
12+24<66
36<66
3.12+8×8<66
12+64<66
76<66
4.12+8×4<66
12+32<66
44<66
therfore the answer is 2 and 4
B and Care sets of real numbers defined as follows.
Answer:
[tex]\begin{gathered} B\cap C=\phi \\ (-\infty,\text{ 1)}\cup\lbrack9,\infty) \end{gathered}[/tex]Step-by-step explanation:
Solve this situation with the help of the number line, if B and C are sets of real numbers defined as follow:
The intersection is an interval that lies within all of the given intervals. If no such intersection exists then the set is empty.
In this case, for the intersection between B and C:
[tex]\begin{gathered} B\cap C=\phi \\ \end{gathered}[/tex]For the union between B and C:
[tex](-\infty,\text{ 1)}\cup\lbrack9,\infty)[/tex]identify the constant of proportionality in the following questions. 1) y= 2x + 32) y= -3x - 4
Answer:
0. k=2
,1. k=-3
Explanation:
The constant of proportionality is the number that is beside the variable x in both equations.
(1)For the equation:
[tex]y=2x+3[/tex]The constant of proportionality is 2.
(2)For the equation:
[tex]y=-3x-4[/tex]The constant of proportionality is -3.
5) Solve the formula r/m = c for m.
We have the following:
[tex]\frac{r}{m}=c[/tex]solving for m:
[tex]\begin{gathered} r=m\cdot c \\ m=\frac{r}{c} \end{gathered}[/tex]Last year, Kevin had $10,000 to invest. he invested some of it in an account that paid 6% simple interest per year, and he invested the rest in an account that paid 10% simple interest per year. after one year, he received a total of $920 in interest. how much did he invest in each account?first account:second account:
Simple interest is represented by the following expression:
[tex]\begin{gathered} I=\text{Prt} \\ \text{where,} \\ I=\text{ interest} \\ P=\text{principal} \\ r=\text{interest rate in decimal form} \\ t=\text{ time (years)} \end{gathered}[/tex]We need to create a system of equations:
Let x be the money invested in the account that paid 6%
Let y be the money invested in the account that paid 10%
So, he received a total of $920 in interest, then:
[tex]920=0.06x+0.1y\text{ (1)}[/tex]And we know that money invested must add together $10,000:
[tex]x+y=10,000\text{ (2)}[/tex]Then, we can isolate y in equation (2):
[tex]y=10,000-x[/tex]Now, let's substitute y=10,000-x in the equation (1):
[tex]\begin{gathered} 920=0.06x+0.1(10,000-x) \\ 920=0.06x+1000-0.1x \\ 0.1x-0.06x=1,000-920 \\ 0.04x=80 \\ x=\frac{80}{0.04} \\ x=2,000 \end{gathered}[/tex]That means, he invested $2,000 in the account that paid 6% simple interest. Now, having x, we are going to substitute x in the second equation (2):
[tex]\begin{gathered} y=10,000-x \\ y=10,000-2,000 \\ y=8,000 \end{gathered}[/tex]He invested $8,000 in the account that paid 10% simple interest per year.
find the size of each interior angle of a regular hexagon
Answer:
Each interior angle = 180° -60° = 120°
Step-by-step explanation: We know that the three angles in a triangle, add up to 180°, and all the three angles are 60° in an equilateral triangle. The total number of angles of an enclosed space is 180° (n-2) where in is the number of sides.
A hexagon has six sides, so: s= 180° (6-2)
s= 180° x 4
s= 720°
now since in a regular shape, each interior angle is equal. We just divide the total interior angle with a number of sides
6.
720° divided by 6 is equal to 120°
Factor the following polynomials completely.(x + y)³ + 1 =
Given the equation (x + y)³ + 1 , we can assume we have two terms here. These are (x + y)³ and 1. Since both terms are perfect cubes, we can use the sum of cubes formula which is:
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]where a = (x+y) and b = 1.
Therefore, the factors of (x + y)³ + 1 is:
[tex]\begin{gathered} \mleft(x+y\mright)^3+1=(x+y+1)\lbrack(x+y)^2-(x+y)(1)+1^2) \\ (x+y)^3+1=(x+y+1)(x^2+2xy+y^2-x-y+1) \end{gathered}[/tex]The factor of (x + y)³ + 1 is (x + y + 1)(x² + 2xy + y² - x - y +1).
to rent a van a moving company charges $40.00 plus $0.50per miles
The problem talks about the cost for renting a van, which can be calculated adding $40.00 plus $0.50 for each mile.
The problem asks to wirte an explicit equation in slope-intercept form which can represent the cost of renting a van depending on the amount of miles. Then, the problem asks to find the cost if you drove 250 miles.
I don't understand how to do this (this is a practice assessment)
Math | English | Art | Total
Boys 13 25 11 49
Girls 7 20 6 33
Total 20 45 17 82
1) Let's set a table, based on the given information:
• Since there are 20 students enrolled in Math let's place it into the Total, 20 -13 = 7
,• 82 students altogether.
,• 11 boys are in Art , 17 altogethe then 17 -11 = 6 girls
,• 20+6+7 = 20+13 = 33 girls altogether.
,• 82 -33 =49 13 +x +11 = 49 x = 49 -24=25
,• And lastly English: 20 +25 = 45
2) That's our table:
Math | English | Art | Total
Boys 13 25 11 49
Girls 7 20 6 33
Total 20 45 17 82
Question 3 (5 points) Convert the decimal 0.929292... to a fraction. O 92 99 O 92 999 O 92 100 92 1000
Calculate the probability of winning: Roll two standard dice. You win if you get a sum of 4 or get a sum of 8. Round answer to one decimal place, for example if your answer is 0.65 enter 0.7
SOLUTION
The possible outcomes for sum of numbers when rolling two dice is shown
The total possible outcome is 36
The possible number of outcome of obtaining a 4 is 3
Therefore the probability of getting a sum of 4 is
[tex]\frac{3}{36}=\frac{1}{12}[/tex]The possible number of outcome of obtaining a 8 is 5
Therefore the probability of getting a sum of 8 is
[tex]\frac{5}{36}[/tex]Hence the probability of getting a sum 4 or a sum of 8 is
[tex]\frac{1}{12}+\frac{5}{36}[/tex]This gives
[tex]0.2[/tex]Therefore the probability of getting a sum 4 or a sum of 8 is 0.2
If the vertices of three squares are connected to form a right triangle, the sum of the areas of the two smaller squares is the same as the area of the largest square. Based on this statement and the model below, what is the area of square B? (Figure is not drawn to scale.) B 8 m 2 289 m
One square has area 289 square meters, and the other has area
[tex]8m\times8m=64m^2[/tex]Then, since the sum of the two areas of the smaller squares is equal to the area of the big square, we have
[tex]\begin{gathered} B+64m^2=289m^2 \\ B=289m^2-64m^2 \\ B=225m^2 \end{gathered}[/tex]Consider 3x=y. a. Complete the table for the equation. x y 0 1 2
Answer/Step-by-step explanation:
x | 3x | y | (x, y)
----------------------------------------
0 | 3(0) | 0 | (0, 0)
----------------------------------------
1 | 3(1) | 3 | (1, 3)
----------------------------------------
2 | 3(2) | 6 | (2, 6)
----------------------------------------
I hope this helps!
On Saturday, 3 families with 4 people in each family went to a movie. Each person bought 2 snacks. Which equation can be used to find how many total snacks the families bought?
Answer:
Step-by-step explanation:3x4=12x2
1-Findes the length indicated.2- Find the angle indicated.3-Find the distance between each pair of points.
1.
LM = LN - MN
LM = 22 - 5 (Replacing)
LM= 17 (Subtracting)
2.
m∠EDW= m∠EDC - m∠WDC
m∠EDW= 106° - 40° (Replacing)
m∠EDW= 66° (Subtracting)
3.
Using the formula for the distance between two points we have:
[tex]\begin{gathered} d=\sqrt[]{(x2-x1)^2+(y2-y1)^2} \\ x1=8,x2=-6,y1=3,y2=3 \\ d=\sqrt[]{(8-(-6))^2+(3-3)^2}\text{ (Replacing)} \\ d=\sqrt[]{(8+6)^2+(0)^2}\text{ (Subtracting)} \\ d=\sqrt[]{(14)^2^{}}\text{ (Adding)} \\ d=14\text{ (Raising 14 to the power of 2 and taking the square root)} \\ d=14 \\ \text{ The distance between these points is 14} \end{gathered}[/tex]Using the formula for the midpoint we have:
[tex]\begin{gathered} (\frac{x1+x2}{2},\frac{y1+y2}{2}) \\ x1=8,x2=-6,y1=3,y2=3 \\ (\frac{8+(-6)}{2},\frac{3+3}{2}) \\ (\frac{2}{2},\frac{6}{2})\text{ (Subtracting and adding)} \\ (1,\text{ 3) (Dividing)} \\ \text{The midpoint is (1,3)} \end{gathered}[/tex]As the table shows, projections indicate that the percent of adults with diabetes could dramatically increase.Answer parts a. through c.c. In what year does this model predict the percent to be 27.96%(round to the closest year)
b. You have to consider year 2000 as the initial year, i.e. as x=0.
To predict the percent of adults with diabetes in 2014, first, you have to calculate the difference between this year and the initial year to determine which value of x you need to use:
[tex]x=2014-2000=\text{ }14[/tex]The value of x you have to use is x=14
Replace this value into the linear model calculated in item a to predict the percentage of adults with diabetes (y)
[tex]\begin{gathered} y=0.508x+10.692 \\ y=0.508\cdot14+10.692 \\ y=7.112+10.692 \\ y=17.804 \end{gathered}[/tex]In the year 2014, the predicted percentage of adults with diabetes is 17.8%
c. You have to determine the year in which the model predicts the percent to be 27.96%.
To determine this year, you have to equal the linear model to 27.96% and calculate for x:
[tex]\begin{gathered} y=0.508x+10.692 \\ 27.96=0.508x+10.692 \end{gathered}[/tex]-Subtract 10.692 from both sides of the equal sign
[tex]\begin{gathered} 27.96-10.692=0.508x+10.692-10.692 \\ 17.268=0.508x \end{gathered}[/tex]-Divide both sides by 0.508
[tex]\begin{gathered} \frac{17.268}{0.508}=\frac{0.508x}{0.508} \\ 33.99=x \\ x\approx34 \end{gathered}[/tex]Next, add x=34 to the initial year:
[tex]2000+34=2034[/tex]The model predicts the percentage to be 27.96% for the year 2034
please show work on how to get the points we graph
Answer:
Graphing the inequalities, we have;
Explanation:
Given the system of quadratic inequalities;
[tex]\begin{cases}y<-x^2-x+8 \\ y>x^2+2\end{cases}[/tex]Graphing the quadratic inequalities;
for the first quadratic inequality;
[tex]\begin{gathered} y<-x^2-x+8 \\ at\text{ x=0} \\ y<8 \\ (0,8) \\ at\text{ x=-0.5} \\ y<-(-0.5)^2-(-0.5)+8 \\ y<8.25 \\ (-0.5,8.25) \\ at\text{ x=-2} \\ y<-(-2)^2-(-2)+8 \\ y<-4+2+8 \\ y<6 \\ (-2,6) \\ at\text{ x=}2 \\ y<-(2)^2-(2)+8 \\ y<-4^{}-2+8 \\ y<2 \\ (2,2) \end{gathered}[/tex]For the second quadratic inequality;
[tex]\begin{gathered} y>x^2+2 \\ at\text{ x=0} \\ y>2 \\ at\text{ x=2} \\ y>(2)^2+2 \\ y>6 \\ (2,6) \\ at\text{ x=-2} \\ y>(-2)^2+2 \\ y>6 \\ (-2,6) \end{gathered}[/tex]Graphing the two inequalities using the points derived above.
Note that both inequalities would be dashed lines because of the inequality sign, and the shaded part will be according to the sign.
Graphing the inequalities, we have;
How do the graphs of transformations compared to the graph of the parent function. Need the answer to this
• A ,Reflection
,• A ,Vertical Shift 4 units down
1) Considering the parent function, i.e. the simplest form of a family of functions, in this case, to be:
[tex]f(x)=x^4[/tex]2) Then we can state that this transformed function:
[tex]g(x)=-x^4-8[/tex]We can see the following transformations:
• A ,Reflection,, pointed out by the negative coefficient
,• A ,Vertical Shift 4 units down
As we can see below, to better grasp it:
Three-inch pieces are repeatedly cut from a 42-inch string. The length of the string after x cuts is given by y = 42 – 3x. Find and interpret the x- and y-intercepts.
Answer:
y-intercept: 42
x-intercept: 14
Step-by-step explanation:
The y-intercept can be found with the given equation:
y = 42 - 3x
Either Let x = 0 to find the y-intercept. OR,
rearrange the equation to y=mx+b to see the y-intercept, which is b in the equation.
y = 3(0) + 42
y = 42
The y-intercept is 42 and this means that the original, uncut length of the string (zero cuts) is 42.
To find the x-intercept, let y = 0.
y = 42 - 3x
0 = 42 - 3x
Add 3x to both sides.
3x = 42
Divide by 3.
x = 42/3
x = 14
An x-intercept of 14, means that at 14 cuts there will be no more string left. The length of the string is now 0.
Expected FrequencyA fair five sided spinner is spun 40 times.a) How many times would it be expectedto land on red?P(Red) = 15It would be expected to land on redItimes.1-5Hint:Set up and solve a proportion.
It can be observed that sppiner is spun 40 times. So proabaility for red colour must include 40 in denominator. The fraction 1/5 has 5 in denominator which be change to 40 by multiplication of 8 to numerator and denominator.
[tex]\frac{1}{5}\cdot\frac{8}{8}=\frac{8}{40}[/tex]So, it is expected to land 8 times on the red colour.
So answer is,
[tex]\frac{1}{5}=\frac{8}{40}[/tex]and It would be expected to land on red 8 times.
I need help with my math
Answer:
Histogram Tells you how many pumpkins had mass below 6 kg
The box plot can be used to determine that the median was 8
Explanation:
A histogram is a chart the plots frequency of a certain quantity.
In our case, the histogram given tell us how many pumpkins fall within a certain mass range. Therefore, to find out how many pumpkins are below 6 kg, we use a histogram.
On the other hand, the box plot summarizes the numerical data. In our case, it can be used to find the median weight of the pumpkins by just reading off the position of the median line.
use the figure to the right to find the value of PT
the figure show, the length between P and T and the length between T and Q, are equal.
so we can say PT=TQ
PT= 3x+2 and TQ=5x-6
so we can replace:
3x+2=5x-6
now we solve
2+6=5x-3x
8=2x
8/2=x=4
and finally, to find PT we replace x by 4
PT=3*4+2=14
So the answer is: PT=14
The sales tax on a table saw is $12.41. a. What is the purchase price of the table saw (before tax) if the sales tax rate is 7.3%? b. Find the total price of the table saw. a. The purchase price is $
We know that the tax rate is 7.3% and it corresponds to $12.41. We want to find the total price of the table saw without taxes, it is to say the 100%. We have the following equivalence:
100% ⇔ ??
7.3% ⇔ $12.41
If we divide both parts of the equivalence we will have the same result:
[tex]\frac{100}{7.3}=\frac{?\text{?}}{12.41}[/tex]Multiplying both parts of the equation by 12.41:
[tex]\begin{gathered} \frac{100}{7.3}=\frac{?\text{?}}{12.41} \\ \downarrow \\ \frac{100}{7.3}\cdot12.41=?\text{?} \end{gathered}[/tex]Now, we can find the total price of the table saw without taxes:
[tex]\begin{gathered} \frac{100}{7.3}\cdot12.41=170 \\ \text{??}=170 \end{gathered}[/tex]Answer A. the purchase price is 170
BThe total price of the table saw (it is to say, including taxes, $12.41), is
170 + 12.41 = 182.41
Answer B. the total price is 182.41
