Compound Interest
We'll use the formula:
[tex]{\displaystyle A=P\mleft(1+{\frac{r}{n}}\mright)^{nt}}[/tex]Where:
A=final amount
P=initial principal balance
r=interest rate
n=number of times interest applied per time period
t=number of time periods elapsed
The problem describes the situation where that Anmol took a house loan and borrowed P=6 lakh at a rate of r=10%. Converting to decimal r=10/100=0.1.
It's also given the interest is compounded annually, thus n=1. In t=2 years:
Applying the formula
[tex]{\displaystyle A=6(1+{\frac{0.1}{1}})^{1\cdot2}}[/tex]Calculating:
[tex]{\displaystyle A=6(1.1)^2=7.26}[/tex]Anmol will owe 7.26 lakh to the bank after two years
An amusement park is creating signs to indicate the velocity of a roller coaster car on certain hills of the most popular ride. A roller coaster gains kinetic energy as itgoes down a hill. The velocity of an object in kilometers per hour (kph) can be determined by V where is the kinetic energy of the object in joules (1)and is the mass of the object in kilograms(kg)A roller coaster car has a mass of 450 kg and the car has a kinetic energy of 22,500 J on the first hill What velocity does the car obtain on the first hill?
Take into account that the kinetic energy of an object with speed v is given by the following formula:
K = 1/2 Mv²
where m is the mass and v the speed.
M = 450 kg
v = ?
K = 2,500 J
solve for v the previous formula and replace the values of the parameters, just as follow:
K = 1/2 Mv² multiply by 2 both sides
2K = Mv² divide by m
2K/m = v² apply square root both sides
√(2K/M) = v
then, you have
v = √(2(22,500 J)/450kg)
v = 10 m/s
Hence, the speed of the object is 10 m/s
What is the ratio of the area of the triangle of the area of the rectangle A) 2 B) 1C) 1/2D) 2/1
In the question, the length of the rectangle is 11 mm and the breadth is given as 5cm. This also serves as the base and the height of the triangle respectively.
Explanation
The steps to take are;
1) Find the area of the rectangle and the triangle
2) Find the area of the two ratios.
But we must make the units of the length and the breadth of the rectangle equal. Therefore
[tex]\begin{gathered} \text{Since 10mm = 1cm} \\ 11\operatorname{mm}=\frac{\text{11}}{10}cm=1.1\operatorname{cm} \end{gathered}[/tex]Hence the areas are as follows:
[tex]\begin{gathered} \text{Area of a triangle = }\frac{1}{2}\times\text{base x height = 0.5 x 1.1 x5} \\ =2.75\operatorname{cm} \\ \text{Area of a rectangle = Length x breadth = 1.1 x 5}=\text{ 5.5}cm^2 \\ \end{gathered}[/tex]Therefore the ratio of the area of the triangle to the area of the rectangle is given as
[tex]\text{Ratio =}\frac{2.75}{5.5}=\frac{1}{2}[/tex]Answer: Option C
Classify the real number.√441rational numberrational number, whole number, andintegerrational number and integerirrational number
Answer:
Rational number, whole number, and integer
Step-by-step explanation:
Exact square roots: Rational, whole and integer
Non exact square roots: Irrational
The square root of 441 is 21, since 21² = 441.
So
Rational number, whole number, and integer
6.In physical education class, Ariel shoots free throws and lay-ups. She earns 1 point for eachfree throw she makes and 2 points for each lay-up she makes. The greatest number of pointsthat she can earn is 30. She has to make at least 15 free throws and lay-ups altogether.a. Write a system of inequalities (two inequalities) to describe the constraints.Specify what each variable represents. (4pts)Ib. Name one possible solution to the system of inequalities and explain what itrepresents in that situation. (4pts)
Let's call t the free throw and l the lay-up.
We know that the minimum free throws and lay-ups together must be 15, this means:
[tex]t+l\ge15[/tex]We also know that the maximum points to earn it 30. Because each t earns 1 point and each l earns 2 points, we can right:
[tex]\begin{gathered} 1\cdot t+2\cdot l\le30 \\ t+2l\le30 \end{gathered}[/tex]So, the system of inequalities is:
[tex]\begin{gathered} t+l\ge15_{} \\ t+2l\le30 \end{gathered}[/tex]One possible solution is to make the inequalities two equalities and solve the system:
[tex]\begin{gathered} t+l=15 \\ t+2l=30 \end{gathered}[/tex]To solve, we can substract the first quation from the second:
[tex]\begin{gathered} (t+2l)-(t+l)=(30)-(15) \\ t+2l-t-l=30-15 \\ t-t+2l-l=15 \\ l=15 \end{gathered}[/tex][tex]\begin{gathered} t+l=15 \\ t+15=15 \\ t=15-15 \\ t=0 \end{gathered}[/tex]So, one possible solution is l=15 and t=0, this means that Ariel shoot 15 lay-ups and no free throws, which earns her 30 points.
Find the slope of the line passing through the points (-6, -5) and (4, 4).08undefined
ANSWER
9/10
EXPLANATION
Given:
Two points (-6, -5) and (4, 4).
Math 8 X 700= 8 X — hundreds. = —— hundreds. = ——-
8 X 700 = 8 X 7 hundereds.
=56 hunderds
= 5600
A store sells a computer for $800. Customers can choose to receive a 25% discount and pay it offwith a loan at a simple interest rate of 9%, or they can choose to pay the full price and pay it offin 4 years with no interest. If the customer plans to pay it off in 4 years, which option is better?
Determine the price of customer after discount.
[tex]\begin{gathered} 800-\frac{25}{100}\cdot800=800-200 \\ =600 \end{gathered}[/tex]Determine the interest paid by individual over 4 years.
[tex]\begin{gathered} I=\frac{600\cdot4\cdot9}{100} \\ =216 \end{gathered}[/tex]The amount paid by individual at the end of 4 years is,
[tex]\begin{gathered} A=600+216 \\ =816 \end{gathered}[/tex]So after the discount the individual had to pay $816 and with no discount had to pay onle $800 after 4 years.
So individual must choose to pay off the price in 4 years without any discount and no interest.
A basketball player has a 50% chance of making each free throw. What is the probability that the player makes at most nine out of eleven free throws?A. 15/16B. 397/2048C. 509/512D. 193/512
Which of the following could not be used as the reason in line 3 of the proof? ○ HL○LA○AAS
ANSWER
LA
EXPLANATION
We have the two triangles given.
We have that:
AC = BD
It is important to note that angles they are vertically opposite angles.
In that case, one of the possible reasons for the proof in line 3 would be AAS which means Angle-Angle-Side theorem (two pairs of angles and one pair of sides in two trianlges are equal) meaning the triangles are congruent.
Another possible reason would be HL which means Hypotenuse Leg postulate that states that if the hypotenuses and another pair of legs of two triangles are equal in length, then they are congruent.
We know the two hypotenuses are equal since we have proven that the triangles are congruent above.
Therefore, the wrong option is LA.
Fill in blanks with available options in the drop-down tab
ANSWER:
STEP-BY-STEP EXPLANATION:
In an experimental design we have the following:
Explanatory variable: It is the variable that you manipulate or observe changes
Response variable: It is the result of the change given by the explanatory variable
Treatment: Specific condition applied to the individuals in an experiment
Experimental units are the individuals on which the experiment is done
Knowing the above, we can classify each part just like this:
[tex]undefined[/tex]Jack has a total of 36 coins, all quarters and nickels. Together they are worth $4.40.How many of each type of coin does he have?
(algebraic solution whit just 1 variable)
Answer:
q=26; n=10.
Step-by-step explanation:
1. if number of the nickels is 'n', then the number of the quaters is '36-n';
2. if together they are 440 cents, then 15*(36-n)+5*n=440;
3. solution of the equation is n=10, then
4. number of quaters is 36-10=26;
5. Finally, number of the quaters = 26, nickels = 10.
Find the area of the triangle. 3 m 6 m The area of the triangle is
Area = 6 x 3/2
Area = 18/2
Area = 9 m^2
A merchant could sell one model of digital cameras at list price and receive$162 for all of them. If he had three more cameras, he could sell each onefor $9 less and still receive $162. Find the list price of each camera.
GIven data:
A merchant could sell one model of digital cameras at list price and receive $162 for all of them.
If he had three more cameras, he could sell each one for $9 less and still receive $162.
To Find the list price of each camera.
Let Price = P and Quantity = Q
PQ = 162
(P-9)(Q + 3) = 162 ...(1)
From the first equation,
Q=162/P
Then,(P-9)(162/P+3)=162
[tex]\begin{gathered} \mleft(P-9\mright)(\frac{162}{P}+3)=162 \\ 3P-\frac{1458}{P}+135=162 \\ \text{ X P on both sides} \\ P\cdot P-\frac{1458}{P}P+135P=162P \\ 3P^2-1458+135P=162P \\ P=27,\: P=-18 \\ \end{gathered}[/tex]price acnnot be negative so conside P = 27.
[tex]\begin{gathered} \mleft(27-9\mright)\mleft(Q+3\mright)=162 \\ \frac{\left(27-9\right)\left(Q+3\right)}{18}=\frac{162}{18} \\ Q+3=9 \\ Q+3-3=9-3 \\ Q=6 \end{gathered}[/tex]Hence P= 27 and Q=6.
Julie Ran 2 miles today. Her dad ran 2 times that many miles. How many miles (m) did her dad run?
ANSWER
4 miles
EXPLANATION
If Julie's dad ran twice as many miles as Julie ran, and she ran 2 miles, then he ran:
[tex]2\times2\text{miles}=4\text{miles}[/tex]find the rule for each input output table and complete the table .
We will solve, by writing the rule, that is:
*We first find the slope:
[tex]m=\frac{12-4}{3-1}\Rightarrow m=4[/tex]Now, we will find the rule:
[tex]y-4=4(x-1)\Rightarrow y=4x[/tex]Now, we calculate the values for 5 and 7, those are 20 & 28 respectively.
*** The rule is y = 4x
Use the parabola tool to graph the quadratic function y=-x^2 – 2x + 8Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
We have that the parabola is the blue one, and the vertex is (1, 7).
A=1/2 bh, solve for h a.h=2Abb.h=2a/bc.h=1/2 Abd.h=Ab
Clear h from the equation
[tex]\begin{gathered} A=\frac{1}{2}b\cdot h \\ 2A=b\cdot h \\ \frac{2A}{b}=h \end{gathered}[/tex]We need to find the standard form of the equation of each hyperbolas
Answer:
y^2/ 25 - x^2 / 9 = 1
Explanation:
Th standard form of a hyperbola is
[tex]\frac{(y-h)^2}{a^2}-\frac{(x-k)^2}{b^2}=1[/tex]where (h,k ) are the coordinates of the centre and a and b are two constants.
The coordinates of the vertices are
[tex](h,k\pm a)[/tex]and the equation of the asymptote is
[tex]y-\frac{a}{b}(x-h)+k[/tex]Now, the coordinates of the center for our hyperbola are (0,0); therefore,
[tex](h,k)=(0,0)[/tex]and the coordinates of the vertices we get from the graph are
[tex](h,k\pm a)=(0,\pm5)[/tex][tex]\therefore a=5[/tex]Finally, the equation for the asymptote we get from the graph is
[tex]y=\frac{5}{3}x[/tex]meaning
[tex]b=3[/tex]Hence,
h = 0,
b = 0,
a = 5,
b = 3
thereofore, the equation of the hyperbola is
[tex]\frac{(y-0)^2}{5^2}-\frac{(x-0)^2}{3^2}=1[/tex][tex]\frac{y^2}{25}-\frac{x^2}{9}^{}=1[/tex]which is our answer!
Use the following figure to answer the question segment BC=
Recall that the notation to indicate that two segments are congruent is to put the same symbol on them, for example:
Answer:
[tex]BC\cong GF.[/tex]Hello, I am unsure how to get to the answer, can you include a sign chart as well for the second derivative thank you.
We want to find the intervals of concavity of the function;
[tex]y=-x^4+8x^2-4[/tex]We start by taking the second derivatives;
[tex]\begin{gathered} y^{\prime}=-4x^3+16x \\ y^{\prime}^{\prime}=-12x^2+16 \end{gathered}[/tex]When a function is concave up, the second derivative is positive, thus; we seek the intervals where;
[tex]\begin{gathered} -12x^2+16>0 \\ -12x^2>-16 \\ x^2<\frac{16}{12} \\ x^2<\frac{4}{3} \\ x<\pm\sqrt{\frac{4}{3}} \end{gathered}[/tex]Let's find the points of inflection, this is where the second derivative is zero;
[tex]\begin{gathered} -12x^2+16=0 \\ -12x^2=-16 \\ x^2=\frac{16}{12}=\frac{4}{3} \\ x=\pm\frac{4}{3} \end{gathered}[/tex]The y values will be;
[tex]\begin{gathered} -(\frac{4}{3})^4+8(\frac{4}{3})^2-4=\frac{44}{9} \\ -(-\frac{4}{3})^4+8(-\frac{4}{3})^2-4=\frac{44}{9} \end{gathered}[/tex]Thus, the answers are;
[tex]\begin{gathered} Concave\text{ }up:(-\sqrt{\frac{4}{3}},\sqrt{\frac{4}{3}}) \\ Inflection\text{ }points:(-\sqrt{\frac{4}{3}},\frac{44}{9}),(\sqrt{\frac{4}{3}},\frac{44}{9}) \end{gathered}[/tex]Thus the answer is option D;
This is a sign chart for the second derivative;
A right angle has legs of 9 centimeters and 40 centimeters. What is the length of the hypotenus?
The length of legs of right angle triangle is a = 9 and b = 40.
The equaltion for the length of hypotenuse by pythaoras theorem is,
[tex]h=\sqrt[]{a^2+b^2}[/tex]Determine the length of hypotenuse.
[tex]\begin{gathered} h=\sqrt[]{(9)^2+(40)^2} \\ =\sqrt[]{81+1600} \\ =\sqrt[]{1681} \\ =41 \end{gathered}[/tex]Thus length of hypotenuse is 41 centimeters.
When you toss 4 coins, you get a sample space with 16 outcomes. Let X be the number of talls you get in the fourtosses. Which of the following gives the value of X for the outcome TTHT?Please it’s so urgent!!!
Given:
4 coin are tossed.
Number of outcomes=16
X be the number of tails you get in 4 tossed.
To find value of X for the outcome TTHT.
So, the number of tails in TTHT is 3
Therefore the value of X is 3.
44. Consider the equation 4 (x-8) + y = 9(x-2).[Part 1]Find an expression for y of the form ax+b expression for y such that the equationhas infinitely many solutions. Is there more than one such solution? Explain yourreasoning using complete sentences.[Part 2]Find an expression for y of the form ax+b expression for y such that the equationhas no real solutions. Is there more than one such solution? Explain yourreasoning using complete sentences.
Answer:
• 1. y=5x+14
,• 2. y=5x+30
Explanation:
Given the equation:
[tex]4(x-8)+y=9\left(x-2\right)[/tex]To answer the given questions, first, make y the subject of the given equation.
[tex]\begin{gathered} 4(x-8)+y=9(x-2) \\ y=9(x-2)-4\left(x-8\right) \\ y=9x-18-4x+32 \\ y=9x-4x-18+32 \\ y=5x+14\cdots(1) \end{gathered}[/tex]Part 1
We want to find an expression of the form y=ax+b such that the equation has infinitely many solutions.
A system of equations has infinitely many solutions if the two equations in the system simplify to the same line.
Thus, we find an equation that is a multiple of the simplified equation (1) above.
Multiply equation 1 all through by 1.
[tex]\begin{gathered} (y=5x+14)\times1 \\ y=5x+14\cdots(2) \end{gathered}[/tex]Thus, the system of equations:
[tex]\begin{gathered} y=5x+14\cdots(1) \\ y=5x+14\cdots(2) \end{gathered}[/tex]This system has infinitely many solutions since they simplify to the same line.
Part 2
We want to find an expression of the form y=ax+b such that the equation has no real solutions.
For a system of equations to have no real solutions, the two lines formed by the equations must be parallel.
This means that they must have the same slope.
In equation 1:
[tex]y=5x+14\cdots(1)[/tex]The slope is 5.
Thus, find another equation that also has a slope of 5.
[tex]y=5x+30\cdots(3)[/tex]The system of equations below has no real solutions.
[tex]\begin{gathered} y=5x+14\operatorname{\cdots}(1) \\ y=5x+30\operatorname{\cdots}(3) \end{gathered}[/tex]
If n = 22 , overline x (x-bar)=41 , and s = 9 , construct a confidence interval at a 80% confidence level. Assume the data came from a normally distributed population Give your answers to one decimal place
Confidence interval is written as
point estimate ± margin of error
In this scenario, point estimate is the sample mean.
From the information given,
sample mean = 41
sample standard deviation, s = 9
sample size = 22
Since the population standard deviation is unknown, we would calculate the margin of error by applying the formula,
margin of error = t x s/√n
where
t is the test score for the 80% confidence. It is gotten from the student's t distribution table. To find t, the first step is to find the degree of freedom, df
df = n - 1 = 22 - 1
df = 21
From the table,
t = 1.323
margin of error = 1.323 x 9/√22
margin of error = 2.53858
Confidence interval is
41 ± 2.5
Lower limit = 41 - 2.5 = 38.5
Upper limit = 41 + 2.5 = 43.5
Thus, the final answer is
38.5 < μ < 43.5
PLESS I DONT WANT TO GET BEAT TODAY BY MY MOM PLESSSS HELP ME х у х Note: Figure is not drawn to scale. If x = 5 units, y = 15 units, and h = 8 units, find the area of the parallelogram shown above using decomposition.
We can decomposite the parallelogram into two right triangles and one rectangle. To find the total area we have to calculate the area of each figure and add them.
• Area of the right triangles (At):
[tex]A_t=2\cdot\frac{x\times h}{2}[/tex]where the first number 2 represents the two triangles, x represents the base of the triangles and h the height. Solving for At:
[tex]A_t=x\times h=5\times8=40units^2[/tex]• Area of rectangle (Ar):
[tex]A_r=y\times h[/tex]where y represents the base of the rectangle and h represents the height of the rectangle. Solving for Ar:
[tex]A_r=15\times8=120units^2[/tex]Finally, finding the area of the parallelogram (Ap):
[tex]A_p=A_t+A_r=40+120=160units^2[/tex]Answer: 160 units²
What is 1+1, sorry I’m new to math.
Given the expression below
[tex]1+1[/tex]It simply means the sum of 1 and 1,
Thus
[tex]1+1=2[/tex]Hence, 1+ 1 is 2
What is the measure of Z in the parallelogram shown?
A.190
B.90
C.150
D.30
In order to solve this exercise it is important to know that a Parallelogram is.
A Parallelogram is a Quadrilateral. It is a closed flat shape that has four sides.
By definition, some of the properties of a Parallelogram are:
1. The lengths of its opposite sides are equal.
2. Its opposite sides are parallel.
3. The opposite angles are congruent (which means that they have equal measure).
In this case you have the Parallelogram WXYZ. You can identify that the angle X and the angle Z are opposite. Therefore:
[tex]m\angle X=m\angle Z[/tex]Knowing the measure of the angle X, you can determine that:
[tex]m\angle Z=30\degree[/tex]The answer is: Option B.
Find the initial value P, growth/decay factor a, and growth/decay rate r for the following exponential function:Q(t) = 500(1.3)^tHelp me solve C - Growth rate (a) The initial value is P= 500(b) The growth factor is a =1.3(c) The growth rate is p=(Note that if r gives a decay rate you should have r < 0.)
Given the equation:
[tex]Q\mleft(t\mright)=500\mleft(1.3\mright)^t[/tex]The given function represents an exponential growth function
(a) The initial value is P, which will be the value when t = 0
So, P = 500
(b) The growth factor is a = 1.3 - 1 = 0.3
(c) The growth rate is p = 1.3
In triangle ABC, angle A is 12 degrees and angle B is 100 degrees. How many degrees is angle C?*
In triangle ABC, angle A is 12 degrees and angle B is 100 degrees. How many degrees is angle C?*
Remember that
In any triangle the sum of its three interior angles must be equal to 180 degrees
so
A+B+C=180
substitute the given values
12+100+c=180
solve for c
112+c=180
c=180-112
c=68 degrees
Trey is riding in a bike race that goes through a valley and a
Answer:
a) -26 ft
b) 3,148 ft lower
Explanation:
We were given the following data set:
Checkpoint 1: 792 feet
Checkpoint 2: -164 feet
Checkpoint 3: 2,446 feet
Checkpoint 4: 3,055 feet
Checkpoint 5: -93
a) The top of a hill rises 138 feet Checkpoint 2
This is represented as:
[tex]\begin{gathered} Altitude=-164+138 \\ Altitude=-26ft \end{gathered}[/tex]Therefore, the altitude of the top of the hill is -26 feet
b) How much lower is Checkpoint 5 than Checkpoint 4
This is shown below:
[tex]\begin{gathered} Distance=3,055-(-93) \\ Distance=3,055+93 \\ Distance=3,148ft \end{gathered}[/tex]Therefore, Checkpoint 5 is 3,148 feet lower than Checkpoint 4