The formula for Final Amount, A after compounding for n period of times is given by
[tex]A=p(1+\frac{r}{100})^n[/tex]Where A = amount
p= principal
r = rate (in %)
n = number of compounding periods
From the question.
A=21,000, p = ?, r=6, n = 3 x 2 = 6
[tex]\begin{gathered} 21000=p(1+\frac{6}{100})6 \\ \\ 21000=p(1+0.06)^6 \\ 21000=p(1.06)6 \\ 21000=p(1.41852) \\ 21000=1.41852p \\ p=\frac{21000}{1.41852} \\ p=14,804.17 \end{gathered}[/tex]The amount that must be deposited at the beginning is 14,804.17
write the exponential function for the data displayed in the following table
As per given by the question,
There are given that a table of x and f(x).
Now,
The genral for of the equation is,
[tex]f(x)=ab^x[/tex]Then,
For the value of x and f(x).
Substitute 0 for x and -2 for f(x).
So,
[tex]\begin{gathered} f(x)=ab^x \\ -2=ab^0 \\ -2=a \end{gathered}[/tex]Now,
For the value of b,
Substitute 1 for x and -1/3 for f(x),
So,
[tex]\begin{gathered} f(x)=ab^x \\ -\frac{1}{3}=ab^1 \\ ab=-\frac{1}{3} \end{gathered}[/tex]Now,
Put the value of a in above result.
So,
[tex]\begin{gathered} ab=-\frac{1}{3} \\ -2b=-\frac{1}{3} \\ b=\frac{1}{6} \end{gathered}[/tex]Now,
Put the value of a and b in the general form of f(x).
[tex]\begin{gathered} f(x)=ab^x \\ f(x)=-2\cdot(\frac{1}{6})^x \end{gathered}[/tex]Hence, the exponential function is ,
[tex]f(x)=-2(\frac{1}{6})^x[/tex]^3 sq root of 1+x+sq root of 1+2x =2
The given equation is
[tex]\sqrt[3]{1+x+\sqrt{1+2x}}=2[/tex]First, we need to elevate each side to the third power.
[tex]\begin{gathered} (\sqrt[3]{1+x+\sqrt{1+2x}})^3=(2)^3 \\ 1+x+\sqrt{1+2x}=8 \end{gathered}[/tex]Second, subtract x and 1 on both sides.
[tex]\begin{gathered} 1+x+\sqrt{1+2x}-x-1=8-x-1 \\ \sqrt{1+2x}=7-x \end{gathered}[/tex]Third, we elevate the equation to the square power to eliminate the root
[tex]\begin{gathered} (\sqrt{1+2x})^2=(7-x)^2 \\ 1+2x=(7-x)^2 \end{gathered}[/tex]Now, we use the formula to solve the squared binomial.
[tex](a-b)=a^2-2ab+b^2[/tex][tex]\begin{gathered} 1+2x=7^2-2(7)(x)+x^2 \\ 1+2x=49-14x+x^2 \end{gathered}[/tex]Now, we solve this quadratic equation
[tex]\begin{gathered} 0=49-14x+x^2-2x-1 \\ x^2-16x-48=0 \end{gathered}[/tex]We need to find two number which product is 48 and which difference is 16. Those numbers are 12 and 4, we write them down as factors.
[tex]x^2-16x-48=(x-12)(x+4)[/tex]So, the possible solutions are
[tex]\begin{gathered} x-12=0\rightarrow x=12 \\ x+4=0\rightarrow x=-4 \end{gathered}[/tex]However, we need to verify each solution to ensure that each of them satisfies the given equation. We just need to evaluate it with those two solutions.
[tex]\begin{gathered} \sqrt[3]{1+x+\sqrt{1+2x}}=2\rightarrow\sqrt[3]{1+12+\sqrt{1+2(12)}}=2 \\ \sqrt[3]{13+\sqrt{1+24}}=2 \\ \sqrt[3]{13+\sqrt{25}}=2 \\ \sqrt[3]{13+5}=2 \\ \sqrt[3]{18}=2 \\ 2.62=2 \end{gathered}[/tex]As you can observe, the solution 12 doesn't satisfy the given equation.
Therefore, the only solution is -4.Solve x^2 - 3x - 10 = 0 by factoring. *Mark only one oval.O {-5,2}O (-2,-5)O {-2,5}○ {-10,1}
In order to solve this quadratic equation by factoring, we can do the following steps:
[tex]\begin{gathered} x^2-3x-10=0\\ \\ x^2-3x-5\cdot2=0\\ \\ x^2+2x-5x-5\cdot2=0\\ \\ x(x+2)-5(x+2)=0\\ \\ (x-5)(x+2)=0\\ \\ \begin{cases}x-5=0\rightarrow x=5 \\ x+2=0{\rightarrow x=-2}\end{cases} \end{gathered}[/tex]Therefore the solution is {-2, 5}. Correct option: third one.
URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100 POINTS!!!!!
Answer:
√52
Step-by-step explanation:
[tex] \sqrt{ {(4 - ( - 2))}^{2} + {(1 - ( - 3))}^{2} } [/tex]
[tex] \sqrt{ {6}^{2} + {4}^{2} } = \sqrt{36 + 16} = \sqrt{52} [/tex]
I have to create a graph but I need some help and clarification
To complete the table you evaluate the equation by the given value of x to find the corresponding value of y:
[tex]y=x+4[/tex][tex]\begin{gathered} x=4 \\ \\ y=4+4 \\ y=8 \\ \\ (4,8) \end{gathered}[/tex][tex]\begin{gathered} x=8 \\ \\ y=8+4 \\ y=12 \\ \\ (8,12) \end{gathered}[/tex][tex]\begin{gathered} x=12 \\ \\ y=12+4 \\ y=16 \\ \\ (12,16) \end{gathered}[/tex][tex]\begin{gathered} x=16 \\ \\ y=16+4 \\ y=20 \\ \\ (16,20) \end{gathered}[/tex]To put those (x,y) points in the plane;
the frist coordinate x is the number of units you move to the left (if x is negative) or to the right (if x is positive)
the second coordinate y is the number of units you move down (if y is negative) or up (if y is positive)
Then, using the points (0,4), (4,8), (8,12), (12,16) and (16,20) you get the next graph for y=x+4:
144 grapefruits in 4 boxes, How many grapefruits in 100 boxes?
Problem
144 grapefruits in 4 boxes, How many grapefruits in 100 boxes?
Solution
for this case we can do the following proportional rule:
4/144 = x/100
And solving for x we got:
x= 100 (4/144)= 2.77
So between 2 and 3 grape fruits are expected
H D 2 cm 4 cm The two rectangles below are similar. What is the ratio of the perimeters of rectangle ABCD to rectangle EFGH? B А 4 cm E 8 cm F 2:1 8:1 1:4 1:2 2
In order to determine the ratio of the perimeters for the given rectangles, first calcualte their perimeters. Use the following formula:
P = 2w + 2l
w: width
l: length
For the smaller rectangle you have:
w = 2cm
l = 4 cm
P = 2(2cm) + 2(4cm) = 4cm + 8cm = 12cm
For the bigger triangle you have:
w' = 4cm
l' = 8cm
P' = 2(4cm) + 2(8cm) = 8cm + 16cm = 24cm
Then, you have:
P/P' = 12cm/24cm = 1/2
Hence, the ratio is 1:2
Suppose the purr of a cat has a sound intensity that is 320 times greater than the threshold level. Find the decibel value for this cats purr. Round to the nearest decibel.
The decibel value for this cats purr round to the nearest decibel is; 25
How to calculate the decibel level?Decibel (dB) is a unit for expressing the ratio between two physical quantities, such as measuring the relative loudness of sounds. One decibel (0.1 bel) is equal to 10 times the common logarithm of the power ratio.
Decibels are a unit of measure used to describe how loud a sound is. Now, I₀ is the intensity of threshold sound, which is sound that can barely be perceived by the human ear.
The loudness of a sound, in decibels, with intensity I is given by;
dB = 10 log₁₀(I/I₀)
We are given the intensity of a cat’s purr as I = 320I₀
Thus;
dB = 10 log₁₀(320I₀/I₀)
dB = 10 log₁₀(320)
dB = 25.05 ≈ 25
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Consider the parabola given by the equation: f ( x ) = − 2 x 2 − 12 x − 9 Find the following for this parabola: A) The vertex: B) The vertical intercept is the point C) Find the coordinates of the two x intercepts of the parabola and write them as a list of points of form (x, y) separated by commas: It is OK to round your value(s) to to two decimal places.
Answer:
it is C) find the coordinated of two x intercept is
Simplify the expression.
the expression negative one seventh j plus two fifths minus the expression three halves j plus seven fifteenths
negative 19 over 14 times j plus 13 over 15
negative 19 over 14 times j minus 13 over 15
negative 23 over 14 times j plus negative 1 over 15
23 over 14 times j plus 1 over 15
The expression is simplified to negative 23 over 14 times j plus negative 1 over 15. Option C
What is an algebraic expression?An algebraic expression can be defined as an expression mostly consisting of variables, coefficients, terms, constants and factors.
Such expressions are also known to be composed or made up of some mathematical or arithmetic operations, which includes;
AdditionSubtractionDivisionBracketMultiplicationParentheses. etcFrom the information given, we have that;
negative one seventh j = - 1/7jtwo fifths = 2/5three halves j = 3/2 jseven fifteenths = 7/15Substitute the values
- 1/7j + 2/5 - 3/2j - 7/15
collect like terms
- 1/7j - 3/2j + 2/5 - 7/15
-2j - 21j /14 + 6 7 /15
-23j/14 + -1/15
Hence, the correct option is negative 23 over 14 times j plus negative 1 over 15
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In the diagram below, GD = 10.1,EF 28.1, and EG 16.9. Find the length==of FC. Round your answer to the nearest tenthif necessary.
Solution:
In the figure;
[tex]\begin{gathered} \frac{EG}{EF}=\frac{ED}{EC} \\ \\ EG=16.9,ED=27,EF=28.1 \end{gathered}[/tex]Thus;
[tex]\begin{gathered} \frac{16.9}{28.1}=\frac{27}{EC} \\ \\ EC=44.9 \end{gathered}[/tex]Thus;
[tex]\begin{gathered} FC=EC-EF \\ \\ FC=44.9-28.1 \\ \\ FC=16.8 \end{gathered}[/tex]the variable y is directly proportional to x. if y equals -0.6 when x equals 0.24, find x when y equals -31.5.
You have that y is proportional to x. Futhermore, you have y = -0.6 when x = 0.24.
Due to y is proportional to x, you have the following equation:
[tex]y=kx[/tex]where k is the constant of proportionality. In order to find the value of x when y = -31.5, you first calculate k.
k is calculated by using the information about y=-0.6 and x=0.24. You proceed as follow:
y = kx solve for k
k = y/x replace by known x and y values
k = -0.6/0.24
k = -2.5
Hence, the constant of proportionality is -2.5.
Next, you use the same formula for the relation between y and x to find the value of x when y = -31.5. You proceed as follow:
y = kx solve for x
x = y/
Find the volume of 12 cm
Answer:
1728 cm ^ 3.
Step-by-step explanation:
we are given 12 cm
As we know formula of volume of cube = s ^3 ( side * side * side ) So = 12 * 12* 12 = 1728 cm ^ 3.
Find the Volume cylinder (8cm) (12cm) h = 8cm r = 12cm h = 8 cm r = 12 cm. The volume of a cylinder is equal to the area of the base πr2 π r 2 times the height. π⋅(radius)2 ⋅(height) π ⋅ ( r a d i u s) 2 ⋅ ( h e i g h t) Substitute the values of the radius r = 12 r = 12 and height h = 8 h = 8 into the formula to find the volume of the cylinder
P.s hopes this helps
An independent third party found the cost of a basic car repair service for a local magazine. The mean cost is $217.00 with a standard deviation of $11.40. Which of the following repair costs would be considered an “unusual” cost?
Given
An independent third party found the cost of a basic car repair service for a local magazine.
The mean cost is $217.00 with a standard deviation of $11.40.
To find: The repair costs which would be considered an “unusual” cost.
Explanation:
It is given that, the mean is 217.00, and the standard deviation is 11.40.
Consider, the distribution as a Normal distribution.
Then, the first range is defined as,
[tex]\begin{gathered} First\text{ }range:mean\pm SD \\ \Rightarrow X_1=mean+SD \\ =217.00+11.40 \\ =228.4 \\ \Rightarrow X_2=mean-SD \\ =217.00-11.40 \\ =205.6 \end{gathered}[/tex]And, the second range is defined as,
[tex]\begin{gathered} Second\text{ }range:mean\pm2SD \\ \Rightarrow X_3=217.00+2(11.40) \\ =217.00+22.8 \\ =239.8 \\ \Rightarrow X_4=217.00-2(11.40) \\ =217.00-22.8 \\ =194.2 \end{gathered}[/tex]Hence, the answer is option a) 192.53 since it does not belongs to the above ranges.
Geometry Problem - Given: segment AB is congruent to segment AD and segment FC is perpendicular to segment BD. Conclusion: Triangle AEG is isosceles. (Reference diagram in picture)
As the triangle AEF has 2 angles with the same measure, triangle AEF is isosceles.
Amtrak's annual passenger revenue for the years 1985 - 1995 is modeled approximately by the formulaR = -60|x- 11| +962where R is the annual revenue in millions of dollars and x is the number of years after 1980. In what year was the passenger revenue $722 million?In the years ____ and ___, the passenger revenue was $722 million.
ANSWER
1987 and 1995
EXPLANATION
The revenue is modeled by:
[tex]R=-60|x-11|+962[/tex]To find the years that the revenue was $722 million, we have to solve for x when R is 722.
That is:
[tex]\begin{gathered} 722=-60|x-11|+962 \\ \Rightarrow722-962=-60|x-11| \\ -240=-60|x-11| \\ \Rightarrow|x-11|=\frac{-240}{-60} \\ |x-11|=4 \end{gathered}[/tex]We can split the absolute value equation into two different equations because the term in the absolute value is equal to both the positive and the negative of the term on the other side of the equality.
That is:
[tex]\begin{gathered} x-11=4 \\ x-11=-4 \end{gathered}[/tex]Solve for x in both:
[tex]\begin{gathered} x=11+4 \\ \Rightarrow x=15 \\ x=11-4 \\ \Rightarrow x=7 \end{gathered}[/tex]That is to say 7 and 15 years after 1980.
Therefore, in the years 1987 and 1995, the revenue was $722 million.
find the exact values of the six trigonometric functions of the angle 0 shown in the figure(Use the Pythagorean theorem to find the third side of the triangle)
The right angled triangle is given with reference angle theta.
The opposite side (facing the reference angle) is 3, while the hypotenuse (facing the right angle) is 5. The adjacent shall be calculated using the Pythagoras' theorem as follows;
[tex]\begin{gathered} \text{Adj}^2+3^2=5^2 \\ \text{Adj}^2=5^2-3^2 \\ \text{Adj}^2=25-9 \\ \text{Adj}^2=16 \\ \text{Adj}=\sqrt[]{16} \\ \text{Adj}=4 \end{gathered}[/tex]Therefore, the trigonometric functions of angle theta are shown as follows;
[tex]\begin{gathered} \sin \theta=\frac{opp}{hyp}=\frac{3}{5} \\ \cos \theta=\frac{adj}{hyp}=\frac{4}{5} \\ \tan \theta=\frac{opp}{adj}=\frac{3}{4} \\ \csc \theta=\frac{hyp}{opp}=\frac{5}{3} \\ \sec \theta=\frac{hyp}{adj}=\frac{5}{4} \\ \cot \theta=\frac{adj}{opp}=\frac{4}{3} \end{gathered}[/tex]Alisa walks 3.5 miles in 30 minutes. At this rate, how many miles can she walk in 45 minutes?385.7 miles5 miles386 miles5.25 miles
Given:
Alisa walks 3.5 miles in 30 minutes.
To find:
The number of miles if she walks 45 mins.
Explanation:
The unit rate for speed is,
[tex]\begin{gathered} Speed=\frac{Distance}{Time} \\ =\frac{3.5}{30} \end{gathered}[/tex]The distance covered when she walks 45mins,
[tex]\begin{gathered} Distance=Speed\times Time \\ =\frac{3.5}{30}\times45 \\ =5.25miles \end{gathered}[/tex]Final answer:
The number of miles she walks in 45mins is 5.25miles.
3.2 x 104 bacteria are measured to be in a dirt sample that weighs 1 gram. Usescientific notation to express the number of bacteria that would be in a sampleweighing 21 grams.
The number of bacteria that weighs 1 gram are,
[tex]3.2\times10^4[/tex]Determine the number of bacteria in a sample that weighs 21 grams.
[tex]\begin{gathered} 21\cdot3.2\times10^4=67.2\times10^4 \\ =6.72\times10^5 \end{gathered}[/tex]So answer is,
[tex]6.72\times10^5[/tex]Find the next two numbers in the pattern -243, 81, -27, 9
Find the next two numbers in the pattern -243, 81, -27, 9
Notice that all the values in the series are value of 3 raise to the power of a number.
-243 =
Identify all points and line segments in the picture below.Points: A, B, C, DLine segments: AB, BC, CD, AD, BD, ACPoints: A, B, C, DLine segments: AD, AC, DC, BOPoints: A, B, C, DLine segments: AB, AD, AC, DC, BCPoints: A, BLine segments: AB, AC, DC, BC
Option C
Points: A, B, C, D
Line segments: AB, AD, AC, DC, BC
$85000 is invested at 7.5% per annum simple interest for 5 years. Calculate the simple interest.
From the statement of the problem we know that:
• the principal amount of money invested is P = $85000,
,• the rate per year is 7.5%, in decimals r = 0.075,
,• the time is t = 5 years.
The interest earnt I is equal to the difference between the total accrued amount A and the principal amount P:
[tex]I=A-P=P(1+r\cdot t)-P=P\cdot r\cdot t.[/tex]Replacing by the data of the problem we find that the simple interest is:
[tex]I=85000\cdot0.075\cdot5=31875.[/tex]Answer
The simple interest is $31875.
# 8 Write an equation in slope-intercept form to represent the line parallel to y = -3/4 x + 1/4 passing through the point (4, -2). O y = -3/4x + 1 O y y = 4/3x + 20/3 O y = -3/4 - 2 O y=-3x - 2
If the line is parallel to y = -3/4 x + 1/4 then the slope is -3/4
the form of an equation is y = mx +b
In this case m = -3/4
Using the point given (4, -2) we will find the value of b:
y = mx + b
y = -3/4 x + b
Using the values of the point (4, -2).... x = 4 and y = -2
-2 = (-3/4)(4) + b
Solving for b:
-2 = -3 + b
-2 + 3 = b
1 = b
b = 1
Therefore the equation would be:
y = (-3/4)x + 1
Answer:
y = (-3/4)x + 1
decide wether the following sides are acute obtuse or a right triangle.
The acute triangle is defined by the condition,
[tex]a^2+b^2The obtuse triangle is defined by the condition, [tex]a^2+b^2>c^2[/tex]Here, we have,
[tex]\begin{gathered} 19^2=361 \\ 12^2=144 \\ 15^2=225 \\ 12^2+15^2>19^2 \end{gathered}[/tex]Thus, the triangle is an obtuse triangle.
A local children's center has 46 children enrolled, and 6 are selected to take a picture for the center'sadvertisement. How many ways are there to select the 6 children for the picture?
The question requires us to find how many ways we can select 6 children from a total of 46.
The formula for combinations is given as follows;
[tex]nC_r=\frac{n!}{(n-r)!r!}[/tex]Where n = total number of children, and r = number of children to be selected. The combination now becomes;
[tex]\begin{gathered} 46C_6=\frac{46!}{(46-6)!6!} \\ 46C_6=\frac{46!}{40!\times6!} \\ 46C_6=\frac{5.5026221598\times10^{57}}{8.1591528325\times10^{47}\times720} \\ 46C_6=\frac{5.5026221598\times10^{10}}{8.1591528325\times720} \\ 46C_6=\frac{0.674410967996781\times10^{10}}{720} \\ 46C_6=\frac{6744109679.967807}{720} \\ 46C_6=9,366,818.999955287 \\ 46C_6=9,366,819\text{ (rounded to the nearest whole number)} \end{gathered}[/tex](Please show your work for question 18.)
It is given that AB = CB from this information we conclude that <A=<C by reason :angles opposite equal sides.
<A+<B+<C=180°(Sum of angles in a triangle)
[tex](4x - 13) + (5x - 2) + (4x - 13) = 180 \\ 4x + 5x + 4x - 13 - 2 - 13 = 180 \\ 13x - 28 = 180 \\ 13x = 180 + 28 \\ 13x = 208 \\ \frac{13x}{13} = \frac{208}{13} \\ x = 16[/tex]
x=6°
ATTACHED IS THE SOLUTION
GOODLUCK
the double number line shows the price of one cupcake complete the table and show the same information as a double number line 5 to blank blank to 18 and 18 to blank
From the first diagram shown, we can see that 1 cupcake costs $1.5
To get the price of 5 cupcakes
Since 1cupcake = $1.5
5 cupcakes = $x
cross multiply
1 * x = 5 * 1.5
x = $7.5
Hence 5 cupcakes will cost $7.5
Since 1cupcake = $1.5
18 cupcakes = $x
cross multiply
1 * x = 18 * 1.5
x = $27
Hence 5 cupcakes will cost $27
To get the number of cupcakes priced $18
Since 1cupcake = $1.5
x cupcake = $18
1.5x = 18
divide both sides by 1.5
1.5x/1.5 = 18/1.5
x =
The perimeter of the rectangle is 19.4 centimeters.What is the width in centimeters,of the rectangle Length is 6cm
SOLUTION
From the question, the Perimeter of the rectangle is 19.4 cm and we want to find the width. The perimeter of a rectangle is given by
[tex]\begin{gathered} P=2\left(l+w\right) \\ where\text{ P =perimeter = 19.4} \\ l=length\text{ of rectangle = 6 cm} \\ w=width=? \end{gathered}[/tex]Applying this, we have
[tex]\begin{gathered} P=2\left(l+w\right) \\ 19.4=2\left(6+w\right) \\ 19.4=12+2w \\ 2w=19.4-12 \\ 2w=7.4 \\ w=\frac{7.4}{2} \\ w=3.7 \end{gathered}[/tex]Hence the width is 3.7 cm, option C
A family is traveling from their home to avacation resort hotel. The table below showstheir distance from home as a function of time.Time (hrs)0257Distance(mi)0140375480Determine the average rate of change betweenhour 2 and 7, including the units.
Let
x -------> the time in hours
y -------> the distance in miles
we know that
To find the average rate of change, we divide the change in the output (y) value by the change in the input value (x)
so
For x=2 h ------> y=140 mi
For x=7 h ------> y=480 mi
rate of change=(480-140)/(7-2)
rate of change=340/5=68 mi/h
The average rate of change is equal to the speed in this problem
The Caldwell family placed a large back-to-school order online. The total cost of the clothing was $823,59 and the shipping weight was 32 lb. 10 oz. They live in the LocalZone (shipping = $5.87, plus $. 11 per lb. for each lb. or fraction of a lb. above 15 lbs.) and the sales tax rate is 7.5%. Find the total cost of the order.$864.43$876.77$893.21o $901.22None of these choices are correct.
The breakdown of fees paid by the Caldwell family are calculated and shown below;
[tex]\begin{gathered} \text{Total cost of clothing = \$823.59} \\ \text{Sales tax = 7.5\% of \$823.59} \\ =\frac{7.5}{100}\times823.59=61.769 \\ \text{Sales tax = \$61.77} \\ \\ \text{Shipping fe}e \\ \text{Total weight of item = 32lb 10oz }\approx\text{ 33lb} \\ \text{The excess weight above 15lbs = 33 - 15=18lbs} \\ \text{Shipping cost on the extra 18lbs = \$0.11}\times18=1.98 \\ \text{Total cost on shipping = \$5.87+\$1.98=\$7.85} \end{gathered}[/tex]The total cost of the order will now be
Total cost of clothing = $823.59
Shipping cost = $7.85
Sales tax = $61.77
TOTAL = $823.59 + $7.85 + $61.77 = $893.21
Therefore, the total cost of the order is $893.21