The formula to calculate the compound interest is:
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \text{ Where } \\ A\text{ is the total amount at the end of t years.} \\ P\text{ is the initial amount deposited.} \\ r\text{ is the interest rate.} \\ t\text{ is the time.} \end{gathered}[/tex]From the word problem, we have:
[tex]\begin{gathered} A=40,000 \\ P=? \\ r=7\%=\frac{7}{100}=0.07 \\ n=1\Rightarrow\text{ It was compounded once in a year.} \\ t=6 \end{gathered}[/tex]Then, we can replace the above values in the compound interest formula and solve for P.
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ 40,000=P(1+\frac{0.07}{1})^{(1)(6)} \\ 40,000=P(1+0.07)^6 \\ 40,000=P(1.07)^6 \\ \text{ Divide by }1.07^6\text{ from both sides} \\ \frac{40,000}{1.07^6}=\frac{P(1.07)^6}{1.07^6} \\ 26,653.69\approx P \\ \text{ The symbol is read 'approximately'.} \end{gathered}[/tex]AnswerYou should deposit today $26,653.69.
5. If the area of a parallelogram is 456 cm2 and the base is 24 cm. Find the height. Height = 1.
The area of a parallelogram is computed as follows:
A = base*height
Substituting with A = 456, and base = 24,
456 = 24*height
456/24 = height
19 cm = height
Solve the system using substitution. You can eliminate the decimals if you like, but you don’t have to. The solution will be the same in either case. {0.45x + 0.10y = 4.30 y = 22-x (x,y)= (_, _)
SOLUTION:
Case: System of equations
Method:
[tex]\begin{gathered} 0.45x+0.10y=4.30....(1) \\ y=22-x....(2) \\ Substitute\text{ }y=22-x\text{ }into\text{ }eqn(1) \\ 0.45x+0.10y=4.30 \\ 0.45x+0.10(22-x)=4.30. \\ 0.45x+2.2-0.1x=4.30 \\ 0.45x-0.1x=4.3-2.2 \\ 0.35x=2.1 \\ x=\frac{2.1}{0.35} \\ x=\frac{210}{35} \\ x=6 \end{gathered}[/tex]Put x = 6 in y= 22 -x
[tex]\begin{gathered} y=22-x \\ y=22-6 \\ y=16 \end{gathered}[/tex]Final answer:
(x,y) = (6, 16)
Multiply and simplify completely: (4p + 2)(6p - 3) Show all work
(4p + 2)(6p - 3) = 4p(6p - 3) + 2(6p -3) = 24p^2 - 12p + 12p -6 = 24p^2 - 6 = 6(4p^2 -1)
[tex](4p\text{ + 2)(6p-3) = 4p(6p-3) + 2(6p-3) = }24p^2-12p+12p-6=24p^2-6=6(4p^2-1)[/tex]Answer:
[tex]6(4p^2-1)[/tex]slope is ___ of change in a relationship.
The slope is the rate of change of 2 variables associated.
Usually the rate of change of y with x.
But it can be of any 2 variables in the problem.
So, the slope is the rate.
The rate at which something is changing with respect to another thing.
Thus,
Answer:
slope is rate of change in a relationship.
Brian likes to go bird watching along the Harvest Park Trail in a nearby forestpreserve. He wants to calculate the area enclosed by the trail which is shownbelow. Based on the diagram, what is the closest approximation of the area insquare yards of the land enclosed by the trail?
Answer:
(B)138,000 square yards.
Explanation:
To determine the area of the land enclosed by the trail, we divide the diagram into two as shown below:
Therefore, the area will be:
[tex]\begin{gathered} \text{Area}=(800\times900)+(400\times1300) \\ =720,000+520,000 \\ =1,240,000\text{ square feet} \end{gathered}[/tex]We then convert it to square yards.
[tex]\begin{gathered} \text{9 square feet=}1\text{ square yard} \\ \text{Therefore:} \\ 1,240,000\text{ square feet}=\frac{1,240,000}{9}\text{ square yard} \\ \approx137777\text{ square yards} \end{gathered}[/tex]Therefore, the closest approximation of the area in square yards is 138,000 square yards.
Sketch a system of two linear equations whose solution is (-1, 3).T
The two system of equations
y = 2x + 3
and
y = -3x has a solution ( -1, 3 )
#(13) Admission to the fair costs $7.75. Each ride costs you $0.50. You have $15 to spend at the fair including admission. Wrtie an inequality to best model this situation. Using the inequality that you chose in #13 what is the maximum number of rides you can go on?
We have the next information
7.75 admission
0.50 ride
you have 15 that is the limit
The inequality will be
[tex]7.75+0.50x\le\text{ 15}[/tex]where x is the number of rides you can do
Using the inequality we can calculate the number of rides, we need to clear x
[tex]\begin{gathered} 0.50x\le15-7.75 \\ 0.50x\le7.25 \\ x\le\frac{7.25}{0.50} \\ x\le14.5 \end{gathered}[/tex]the maximum number of rides is 14 because we can't do a half ride
I have this question and I can’t figure it out
SOLUTION:
An integer is a whole number (not a fractional number) that can be positive, negative, or zero.
Therefore from the question, the integers are:
[tex]-2,-1,0,2[/tex]The number line is shown below
Calculate the area of each shape. Remember that the area of a triangle is: A= 1/2bh, and thearea of a rectangle is: A=bh1)2)E.dLaWG3)4)
The area of the (1)triangle is 1 square units and the area of the rectangle(5) is 24 square units,
Given area of a triangle is = 1/2 × b × h (b = base , h = height)
1) now from the figure we can see that the base of the triangle is 1 units and the height is 2 units,
∴area = 1/2 ×1 × 2 = 1 square units
2) now from the figure we can see that the base of the triangle is 2 units and the height is 4 units,
∴area = 1/2 ×2 × 4 = 4 square units
3) now from the figure we can see that the base of the triangle is 2 units and the height is 3 units,
∴area = 1/2 ×2 × 3 = 3 square units
4) now from the figure we can see that the base of the triangle is 3 units and the height is 2 units,
∴area = 1/2 ×3 × 2 = 3 square units
5) now from the figure we can see that the base of the rectangle is 6 units and the height is 4 units,
∴area of rectangle = b × h = 6 × 4 = 24 square units
6) now from the figure we can see that the base of the rectangle is 3 units and the height is 9 units,
∴area of rectangle = b × h = 3 × 9 = 27 square units
to learn more about area visit:
https://brainly.com/question/11952845
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I keep get 35 and it wrong? Can you please help me ?
Given: 7 different jellybeans
To Determine: How many ways the 7 different jellybeans can be lined up in a row of 3
Solution
We are considering an arrangement, so we would be using the permutation formula
The permuation formula is as shown below
[tex]_nP_r=\frac{n!}{(n-r)!}[/tex]Applying the formula above to the given as shown below
[tex]\begin{gathered} _7P_3=\frac{7!}{(7-3)!} \\ _7P_3=\frac{7\times6\times5\times4!}{4!} \\ _7P_3=7\times6\times5=210 \end{gathered}[/tex]Hence, the different ways 7 different jellybeans be lined up in a row of 3 is 210ways
I need help with this practice I believe the subject for this is complex numbers and vectors I will send you an additional picture that goes along with this, it is a graph, use the graph to answer
Solution
- In order to plot these vectors using Parallelogram law, we need to write them in rectangular form i.e. in terms of the x and y-components.
- This is done below:
[tex]\begin{gathered} \vec{a}=-3i-5j \\ \vec{b}=i+4j \end{gathered}[/tex]- We can then proceed to plot the vectors on a graph.
- For vector a, the line of magnitude extends from the origin (0, 0) to the point (-3, -5) while the line of the magnitude of vector b extends from the origin (0, 0) to the point (1, 4).
- This is shown below:
- The vector addition of both vectors is given below:
[tex]\begin{gathered} \vec{a}+\vec{b}=-3i-5j+(i+4j) \\ \text{ Add only magnitudes of the same component} \\ \vec{a}+\vec{b}=-3i+i-5j+4j \\ \\ \therefore\vec{a}+\vec{b}=-2i-j \end{gathered}[/tex]- This implies that the vector addition of both vectors extends from the origin (0,0) to the point (-2, -1)
- This is depicted below:
Find a formula for the nth termof the arithmetic sequence.First term 9Common difference -2an = [? ]n + []
Given:
First term 9
Common difference -2
Required:
Find a formula for the nth term of the arithmetic sequence.
Explanation:
The general formula for the nth term of the an arithmetic sequence is given by the formula:
[tex]a_n=a+(n-1)d[/tex]Where a = first term
d = common difference
Put a = 9 and d = -2 in the formula.
[tex]\begin{gathered} a_n=9+(n-1)(-2) \\ a_n=9-2(n-1) \\ a_n=9-2n+2 \\ a_n=-2n+11 \end{gathered}[/tex]Final Answer:
The nth term of the arithmetic sequence is
[tex]a_n=-2n+11[/tex]=Find the variance for the set of data: 26, 34, 17, 24, 24.The variance is0.
The variance is:
[tex]\sigma^2=\frac{\Sigma(x-\mu)^2}{N}[/tex]So we have 5 values, which means that N=5 and the mean is:
[tex]\mu=\frac{26+34+17+24+24}{5}=25[/tex]So the variance is 29.6.
x + 3 = y, make x the subject of the formula 1. x = y + 3 2. x = 3y3. x = y-3 4. x=y/3PLEASE HELP ME
Make x the subject of the formula
x + 3 = y
This means you re-write the equation such that x woukd be on one side of the equation alone (usually the left side) and all other terms would be on the other side of the "equal to" sign.
[tex]\begin{gathered} x+3=y \\ \text{Subtract 3 from both sides} \\ x+3-3=y-3 \\ x+0=y-3 \\ x=y-3 \end{gathered}[/tex]The answer is x = y - 3
You have a line AB where A is (0,3) and B is (2,7) find a point P that partitions the line 1:2.
ANSWER:
[tex]P=(\frac{2}{3},\frac{13}{3})[/tex]STEP-BY-STEP EXPLANATION:
We have the following formula to calculate the point P
[tex]\begin{gathered} x_p=\frac{x_2\cdot a+x_1\cdot b}{a+b}_{} \\ y_p=\frac{y_2\cdot a+y_1\cdot b}{a+b}_{} \\ a\colon b=1\colon2 \\ (x_1,y_1)=(0,3) \\ (x_2,y_2)=(2,7) \end{gathered}[/tex]Replacing:
[tex]\begin{gathered} x_p=\frac{2\cdot1+0\cdot2}{1+2}=\frac{2+0}{3}=\frac{2}{3} \\ y_p=\frac{7\cdot1+3\cdot2}{1+2}=\frac{7+6}{3}=\frac{13}{3} \\ \text{The point p is:} \\ (\frac{2}{3},\frac{13}{3}) \end{gathered}[/tex]A bottlenose dolphin is 10 feet belo sea level. Then it begins to dive at a rate of 9 feet per second. What is the equation of the line that represents its elevation,y, after x seconds
Factor this question Q3+125
write 125 as a power in base 5
[tex]q^3+5^3[/tex]then, apply the rule for the addition of cubes
[tex]\begin{gathered} a^3+b^3=(a+b)\cdot(a^2-a\cdot b+b^2) \\ \text{then, } \\ q^3+5^3=(q+5)\cdot(q^2-5x+5^2) \\ q^3+5^3=(q+5)\cdot(q^2-5x+25) \end{gathered}[/tex]Jessica is the secretary of the Hillside Players.They are going to put on a show at the village hall.Jessica needs to arrange 4dates in October for rehearsals
ANSWER :
EXPLANATION :
a
1. Problem Set B: For each of the following problems, include a sketch of the scenario, name the characteristic the question is asking for and how you will solve for that characteristic. An object is dropped from a bridge over a bay. Its motion is modeled by the quadratic equation h(t) = -16t^2 +56 where t represents the time since the object was dropped and h(t) represents the height of the object. a. How long will it take for the object to reach the water?b. How will you find this characteristic?c. What is the meaning of the 56 in the equation h(t) = -16t^2 + 56? a. It takes 56 seconds for the object to reach the ground. b. The object is 56 feet above the ground initially. c. The object reaches its maximum height after 56 seconds.
we have the equation
h(t) = -16t^2 +56
Part a. How long will it take for the object to reach the water?
when the object reach teh water h(t)=0
so
For h(t)=0
solve for t
0=-16t^2+56
16t^2=56
t^2=56/16
t^2=3.5
t=(+/-)1.87
therefore
answer part a is t=1.87 secRemember that the time can not be negative
Part b. How will you find this characteristic?
because if the object reach the water is when the height is zero (sea level is the zero)Part c. What is the meaning of the 56 in the equation h(t) = -16t^2 + 56?
answer is
b. The object is 56 feet above the ground initially.A line is drawn on a coordinate plane so that it is parallel to the x-axis and passes through the point (4.6). Which statement identifies equation and slope of this line?
A. The equation of the line is y = 6, and the slope is 0
Explanations:Note that:
When a line is parallel to the x -axis, the slope of that line equals to zero
According to the question, the line passes through the point with coordinates (4, 6)
The equation of a line passing through a point of coordinates (x₁ , y₁) is given by the equation:
y - y₁ = m ( x - x₁)
x₁ = 4, y₁ = 6
Substitute x₁ = 4, and y₁ = 6 into the given equation:
y - 6 = 0(x - 4)
y - 6 = 0
y = 6
The equation of the line is y = 6, and the slope is 0
MVT of a function x^2-6x+8 on (0,8)
According to the Mean Value Theorem:
[tex]f^{\prime}(c)\text{ = }\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex][tex]f^{\prime}(c)\text{ = }\frac{f(8)-f(0)}{8-0}[/tex]f(x) = x² - 6x + 8
f(0) = 0² - 6(0) + 8
f(0) = 8
f(8) = 8² - 6(8) + 8
f(8) = 64 - 48 + 8
f(8) = 24
f'(x) = 2x - 6
f'(c) = 2c - 6
[tex]\begin{gathered} 2c\text{ - 6 = }\frac{24-8}{8} \\ 2c\text{ - 6 = }\frac{16}{8} \\ 2c\text{ - 6 = 2} \\ 2c\text{ = 2 + 6} \\ 2c\text{ = 8} \\ c\text{ = }\frac{8}{2} \\ c\text{ = 4} \end{gathered}[/tex]Wesley Snipes ears a monthly salary of $1,685, plus a 8.5% commission on all sales over $2,000 each month. This month, his sales were $6,250. What was his totalincome for the month?$2,224.50$2,175.80$2,112.90$2,046.25None of these choices are correct.
His total income for the month is $2,216.25 and that means none of these choices are correct
Here, we want to get the total income for the month
Now, what we have to add to the monthly salary is the commission percentage amount
From the question, this is simply 8.5% of $6,250
Thus, we have it that;
[tex]\frac{8.5}{100}\times\text{ 6,250 = \$531.25}[/tex]We now proceed to add this to the salary
We have the total as;
[tex]1,685\text{ + 531.25 = \$2,216.25}[/tex]how do you write 7,500,000,000,000,000,000 in scientific notation
7,500,000,000,000,000,000
In scientific notation, the 10 raised to a power having put the number to standard form
7,500,000,000,000,000,000
= 7.5 * 10^18
What is the value of(-* - ) =( 4 )?-1516-516
Answer
Option B is correct.
[tex]-1\frac{5}{16}[/tex]Explanation
To answer this, we will first deal with the value in the first bracket by taking LCM
[tex]\begin{gathered} (-\frac{1}{4}-\frac{1}{2}) \\ =\frac{-1-2}{4} \\ =\frac{-3}{4} \end{gathered}[/tex]Then to solve the part with division, we know that the division involving fractions are solved by changing the division sign into multiplication sign and the fraction after the sign changes to its reciprocal or its inverse.
[tex]\begin{gathered} (-\frac{3}{4})\div\frac{4}{7} \\ =-\frac{3}{4}\times\frac{7}{4} \\ =-\frac{21}{16} \\ =-1\frac{5}{16} \end{gathered}[/tex]Hope this Helps!!!
help me with this simple math18. look for this simple math riddle1+4=52+5=123+6=218+11=?I'm stuck here when 8+11
Given,
The mathematical expressions are
1+4=5
2+5=12
3+6=21
8+11=?
The pattern of the expression is,
[tex]\begin{gathered} 1+1\times4=5 \\ 2+2\times5=12 \\ 3+3\times6=21 \end{gathered}[/tex]Similarly,
[tex]8+8\times11=96[/tex]Hence, the value is 96.
If one zero of 5² + 13 + is the reciprocal of the other, find the value of k?
Answer:
k = 5
Explanation:
The given polynomial is
5² + 13 +
Let one of the zeros be z. Given that one of the zero is the reciprocal of the other, the reciprocal of z is 1/z. The roots are z and 1/z
The standard form of a quadratic polynomial is
ax^2 + bx + c
By comparing the polynomial expressions,
a = 5, b = 13, c = k
The product of the roots of a quadratic polynomial is c/a = k/5
Thus,
1/z * z = k/5
1 = k/5
By cross multiplying,
k = 5
Express your answer as a polynomial in standard form.9f(x) = x2 - 4x –g(x) = -3x – 5Find: f(g(x))
Given the functions:
[tex]\begin{gathered} f(x)=x^2-4x-9 \\ g(x)=-3x-5 \end{gathered}[/tex]We need to find the function f(g(x)
So, every variable for x in the function f(x) will be substituted with g(x) as follows:
[tex]f(g(x))=(-3x-5)^2-4\cdot(-3x-5)-9[/tex]Now, we will simplify the expression:
[tex]\begin{gathered} f(g(x))=9x^2+30x+25+12x+20+9 \\ \\ f(g(x))=9x^2+42x+54 \end{gathered}[/tex]So, the answer will be:
[tex]f(g(x))=9x^2+42x+54[/tex]the polynomial p(x)=2x^3+17x^2+41x+30 has a known factor of (x+5) rewrite p(x) as a product of linear functionp(x)=
Answer:
Rewriting p(x) as a product of linear functions, we have;
[tex]p(x)=(2x+3)(x+5)(x+2)[/tex]Explanation:
We want to write the given polynomial p(x) as a product of linear functions.
[tex]p(x)=2x^3+17x^2+41x+30[/tex]To write it as a product of linear functions we have to find the other factors;
let us divide the given polynomial by the given factor;
[tex]\begin{gathered} \text{ }2x^2+7x+6 \\ (x+5)\sqrt[]{2x^3+17x^2+41x+30} \\ \text{ - (}2x^3+10x^2) \\ \text{ }7x^2+41x+30 \\ \text{ }-(7x^2+35x) \\ \text{ }6x+30 \\ \text{ - (}6x+30) \\ \text{ 0} \end{gathered}[/tex]So, the division gives;
[tex]p(x)=2x^3+17x^2+41x+30=(x+5)(2x^2+7x+6)[/tex]next, we need to find the factors of the quadratic function;
[tex]\begin{gathered} 2x^2+7x+6 \\ 2x^2+4x+3x+6 \\ 2x(x+2)+3(x+2) \\ (2x+3)(x+2)_{} \end{gathered}[/tex]Substituting the factors of the quadratic function, we have;
[tex]\begin{gathered} p(x)=2x^3+17x^2+41x+30=(x+5)(2x^2+7x+6) \\ p(x)=(x+5)(2x+3)(x+2)_{} \\ p(x)=(2x+3)(x+5)(x+2) \end{gathered}[/tex]Therefore, rewriting p(x) as a product of linear functions, we have;
[tex]p(x)=(2x+3)(x+5)(x+2)[/tex]solve the system x+3y=62x+4y=12
x+3y=6 ----------------------------(1)
2x+4y=12---------------------------(2)
Using elimination method to solve;
we will eliminate x variable
To do that, we must make sure the coefficient of x in the two equation are the same.
This can be achieved by multiplying equation (1) by 2 and equation (2) by 1
That is;
2x + 6y = 12 ----------------------(3)
2x + 4y = 12 -----------------------(4)
subtract equation (4) from equation (3)
2y = 0
Divide both-side of the equation by 2
y=0
substitute y = 0 into equation (1)
x + 3(0) = 6
x = 6
How do I find the measurement of b? Is the correct answer 52 degrees
Remember that
An isosceles triangle has two equal sides and two equal interior angles
so
In this problem
Triangle ABC is an isosceles triangle
because
AB=BC ----> given
that means
mso
y=52 degrees
The sum of the interior angles in any triangle must be equal to 180 degrees
so
msubstitute given values
52+m
solve for m
mm