Given the word problem, we can deduce the following information:
Principal amount = $4739
Future amount = $5336
Interest = 5.1 % =0.051
To determine the time to accumulate the $5336, we use the compound interest formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]A=Future amount=$5336
P=Present amount=$4739
r=interest rate = 0.051
n=number of compounding periods =12
t=time in years
We also note that the number of compounding periods must be 12 since the investment is compounded monthly.
We plug in what we know:
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ 5336=4739(1+\frac{0.051}{12})^{12t} \\ Simplify\text{ and rearrange} \\ 5336=4739(\frac{12.051}{12})^{12t} \\ 12t=\frac{\ln\frac{5336}{4739}}{\ln\frac{12.051}{12}} \\ t=\frac{\operatorname{\ln}\frac{5,336}{4,739}}{12\operatorname{\ln}\frac{12.051}{12}} \\ Calculate \\ t=2.33 \end{gathered}[/tex]Therefore, the answer is 2.33 years.
An architect is designing a gazebo which base is a regular dodecagon. At what angle should he cut to frame the base?
Answer:
15
Explanation:
Note that a regular dodecagon is a 12 sided polygon with internal angles that are equal and sides of the same length.
So determine at what angle the architect should cut to frame the base, we have to divide 360 by 12 and divide the result by 2 as seen below;
[tex]\begin{gathered} \frac{360^{\circ}}{12}=30^{\circ}\text{ (degre}e\text{ per corner)} \\ \frac{30^{\circ}}{2}=15^{\circ\text{ }}(angle\text{ to be cut)} \end{gathered}[/tex]The angle that the architect should cut to frame the base is 15 degrees
Which expression is equivalent to the given expression?2x^2 – 14r + 24A. (2x – 12) (x - 2)B. 2(x – 3)(x – 4)C. 2(x - 5)(x - 2)D. 2(x – 8) (x + 3)
Step 1: We have the following expression:
[tex]2x^2\text{ }-\text{ 14x + 24}[/tex]Step 2: Fon finding the equivalent expression, we have to factoring the polynomial, this way:
[tex]2(x^2\text{ - 7x + 12)}[/tex]Step 3: Now we have to find two integer numbers that the result of adding them is - 7 and the result of multipliying them is 12
First number: -4
Second number: -3
Therefore, we have now:
2 (x - 4) (x - 3)
Step 4
In the game of euchre, the deck consists of the 9, 10, jack, queen, king and ace of each suit. Players are dealt a five card hand.
What is the probability that a player is dealt 4 hearts? =
The probability that a player dealt with four hearts = 0
What is probability?Probability is defined as the prediction of the occurrence of an event in a stated set.
This can be expressed in proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
From the question given, the 6 sets include the following;
9, 10, jack, queen, king and ace.
There are no hearts given in the set of the event that occurred, therefore, the probability that a player dealt with four hearts = 0.
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In the lab, Jane has two solutions that contain alcohol and is mixing them with each other. She uses 400 milliliters less of Solution A than Solution B. Solution A is 12% alcohol and Solution B is 20% alcohol. How many milliliters of Solution B does she use, if the resulting mixture has 176 milliliters of pure alcohol?
Using the concept of volume, 700 milliliters of Solution B was used.
What is volume?Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
When dealing with unknowns, the first step is to represent the unknowns using variables, draw up equations based on the available data, and then solve those equations to account for the unknowns.
Volumes of solutions A and B are here which is unknown.
Put these factors in place for us
Let x = the amount of solution A that was mixed in milliliters.
Let y= the amount of solution B that was mixed in milliliters.
The amount of volume utilized for A is 400 ml less than the amount used
for B.
This can be expressed mathematically as y - x = 400.
Or,
- x + y = 400 [1]
The ratios of alcohol in A and B are provided to us.
A contains 12% alcohol, hence its real alcohol content is 12% of x ml.
= 0.12x (12% = 12/100 = 0.12)
Similar to A, B has an alcohol content of 0.20x.
If x of A and y of B are combined, the total alcohol by volume is 0.12x + 0.20y.
and it is said that this amount is 176 ml.
Our second equation is therefore set up as 0.12x + 0.20y = 176 [2].
We create an equation containing only the other term by using both equations and removing either the x or y terms.
We should remove the x term from both equations to create a single equation that just contains the y term because the question only asks us to compute the volume of Solution B that was used.
Review the equations now:
- x + y = 400 [1]
0.12x + 0.20y = 176 [2]
x's coefficients should all be the same:
Increase [1] by 0.12
=> -0.12x + 0.12y =
= 0.12 x 400
=> 0.12x + 0.12y = 48 [3]
By adding [2] and [3], the x word is removed.
0.12x + 0.20y = 176+( -0.12x) + 0.12y = 48
0x + 0.32 y = 224
=> 0,32y = 224
Subtract 0.32 from both sides to get[tex]\frac{0.32y}{0.32}[/tex] = [tex]\frac{224}{0.32}[/tex]
==> y = 700
Therefore, 700 cc of Solution B was utilized.
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Using standard normal table if the area is 0.125 what would the probability be ?
The area under a standard normal distribution, which we get on a standard normal table, is the same as the probability on that area.
Thus if the area is 0.125, the probability is 0.125, that is, 12.5%.
pls help me with this ill give brainlist
What is the value of x?
4x=5x-12
Enter your answer in the box.
X=
Answer:
12
Step-by-step explanation:
First, get all of the x values to one side of the equation so that we can solve for x. One way to do this is subtract 5x from both sides.
Now we have this:
4x - 5x = -12.
Simplify:
-x = -12.
We need positive x, so divide both sides by -1.
x = 12.
Hope this helps! :)
joeita sees on her activity tracker that it took her 58 minutes to run 6.25 hours miles assuming she runs at the same pace how far can she run in 40 minutes? round to the nearest hundredth how far can she run in m minutes
In a case whereby joeita sees on her activity tracker that it took her 58 minutes to run 6.25 hours miles the distance she can she run in 40 minutes is 4.31 miles.
How can the number of miles be calculated?This can be solved by the cross multiplication using the rate that given in the question.
We were told that joeita took 58 minutes of her time to run 6.25 hours miles , then to know the distance she can cover within 40 minutes is
58 minutes = 6.25 miles
40 minutes = X miles
Let X be the number of miles she want to cover in 40 minutes
we ca cross multiply the expression above as :
( 40 minutes * 6.25 miles ) = (58 minutes * X miles)
the X = 4.31 miles
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usBelow, the two-way table is given for aclass of students.FreshmenSophomoreJuniorsSeniorsTotalMale4622Female3463TotalIf a student is selected at random, find theprobability the student is a female given that it'sa junior. Round to the nearest whole percent.[?]%
Total number of students = 4 + 6 + 2 + 2 + 3 + 4 + 6 + 3 = 30
The probability that a student is female given that it is a junior is computed as follows:
[tex]\text{ P(}female|junior\text{)=}\frac{P(female\cap junior)}{P(junior)}[/tex]The probability that a student is female and junior is:
[tex]P(female\cap junior)=\frac{6}{30}=\frac{1}{5}[/tex]The probability that a student is a junior is:
[tex]P(junior)=\frac{2+6}{30}=\frac{8}{30}=\frac{4}{15}[/tex]Finally, The probability that a student is female given that it is a junior is:
[tex]P(female|junior)=\frac{\frac{1}{5}}{\frac{4}{15}}=\frac{1}{5}\cdot\frac{15}{4}=\frac{3}{4}=0.75\text{ or 75\%}[/tex]Hailey read 48 pages of a book this week. Blake read half as many as Hailey. How many pages did they read combined?A)24B)60C)72D)96
Step 1
From the question, Hailey reads 48 pages of a book
Blake reads half as many as Hailey.
Hence Blake reads;
[tex]Blake=\frac{48}{2}=24Pages[/tex]The answer will be together they read;
[tex]48+24=72\text{ pages}[/tex]Answer; Option C
4x + 6 <2x>-1 x<-1x<2x>2
The given equation is
[tex]4x+6<2[/tex]First, we subtract 6 on each side.
[tex]\begin{gathered} 4x+6-6<2-6 \\ 4x<-4 \end{gathered}[/tex]Then, we divide the inequality by 4.
[tex]\begin{gathered} \frac{4x}{4}<-\frac{4}{4} \\ x<-1 \end{gathered}[/tex]Therefore, the right answer is the second choice. x < -1vector W has its initial point at (2,5) and its terminal point at (-4,-2)
For the given points, vector in component form equals -6i^ - 7j^ and its magnitude is 9.22
What is meant by vector?A quantity or phenomena with independent qualities for both magnitude and direction is called a vector. The term can also refer to a quantity's mathematical or geometrical representation. Velocity, momentum, force, electromagnetic fields, and weight are a few examples of vectors in nature.
Examples of vectors include displacement, velocity, acceleration, force, and others that show both the direction and the size of a quantity. Vector: The displacement is -4 feet, while the velocity is -40 miles per hour. Negative displacement and velocity indicate that the object is travelling counterclockwise.
Vector in component form -
(-4 -2)i^ + (-2-5)j^
= -6i^ - 7j^
Magnitude of the vector equals =
√(-6)² + (-7)² = √85 = 9.22
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Complete Question -
Vector w has its initial point at (2, 5) and its terminal point at (-4, -2). Write the vector in component form and find its magnitude.
Aliyah's school is selling tickets to the annual dance competition. On the first day of ticket sales
the school sold 8 senior citizen tickets and 15 child tickets for a total of $266. The school took in
$168 on the second day by selling 8 senior citizen tickets and 8 child tickets. What is the price
each of one senior citizen ticket and one child ticket?
Each senior citizen ticket costs $7.
One child's ticket costs $14.
Describe algebra.
Algebra is one of the numerous subfields of mathematics. The study of mathematical symbols and the rules for employing them in formulas is commonly referred to as algebra, which runs across almost all of mathematics.
S represents the senior citizen ticket cost.
C is the child's ticket cost.
Price is expressed as USD per ticket.
8S + 15C = 266
8S + 8C = 168
Subtract both equations now to get rid of S
8S + 15C = 266
8S + 8C = 168
———————————-
7C = 98
C = 98/7
C = $14
Changing the value of C in the first
8S + 15(14) = 266
8S + 210 = 266
8S = 266 - 210
8S = 56
S = 56 / 8
S = $7
Hence, $7 is the price for senior citizen
And, $14 is the price for child
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A wheel on Ivan's bicycle is 1.1 m in diameter. Ivan races the bicycle for 165 m. How many times does the wheel turn as the bicycle travels this distance?Use the value 3.14 forn. Round your answer to the nearest tenth. Do not round any intermediate steps.
The radius(r) of the wheel is;
[tex]r=\frac{diameter}{2}=\frac{1.1}{2}=0.55m[/tex]The perimeter(P) of the wheel is given by the formula below:
[tex]P=2\pi r=2\times3.14\times0.55=3.454m[/tex]The distance travelled by Ivan is 165m.
So, the number(n) of times the wheel is:
[tex]n=\frac{165}{3.454}=\text{ 47.77}\approx\text{ 47.8}[/tex]Hence, the correct answer is 47.8
A simple random sample of 5 months of sales data provided the following information:
Month: 1 2 3 4 5
Units Sold: 97 110 89 97 92
a. Develop a point estimate of the population mean number of units sold per month.
b. Develop a point estimate of the population standard deviation (to decimals).
Using it's concepts, the point estimates for the population are given as follows:
a) Mean: 97 units sold per month.
b) Standard deviation: 16.06 units sold per month.
What are the mean and the standard deviation of a data-set?The mean of a data-set is given by the sum of all values in the data-set, divided by the cardinality of the data-set, which is the number of observations in the data-set.The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the cardinality(number of observations) of the data-set.In the context of this problem, the 5 observations are given as follows:
97, 110, 89, 97, 92.
Hence the mean is given by:
M = (97 + 110 + 89 + 97 + 92)/5 = 97.
Considering the mean of 97 found above, the standard deviation is given as follows:
[tex]S(X) = \sqrt{\frac{(97 - 97)^2 + (110 - 97)^2 + (89 - 97)^2 + (97 - 97)^2 + (92 - 97)^2}{5}} = 16.06[/tex]
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In baseball, Ken gets on base 60% of the time he bats. If Ken bats 5 times, how many times did he get on base?
Assuming Ken gets the same percentage as usuall in these 5 times, we can calculated how many times he did get on base by calculating 60% of 5.
To do this we transform 60% into decimal my dropping the percentage sign and dividing it by 100 and then we multiply the decimal by 5:
[tex]\frac{60}{100}\cdot5=0.6\cdot5=3[/tex]So, Ken got on base 3 times.
y= 3x - 5 y= -6x + 4
The given system of equation:
y = 3x - 5 (1)
y = -6x + 4 (2)
We can solve the system of equation by using elimination method :
Elimination Method: In the elimination method you either add or subtract the equations to get an equation in one variable. When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable.
Subtract the equation (1) & (2)
[tex]\begin{gathered} y-y=3x-5-(-6x+4) \\ 0=3x-5+6x-4 \\ 0=9x-9 \\ 9x=9 \\ x=\frac{9}{9} \\ x=1 \end{gathered}[/tex]So, we get x = 1
Substitute the value of x in the equation (1)
[tex]\begin{gathered} y=3x-5 \\ y=3(1)-5 \\ y=3-5 \\ y=(-2) \end{gathered}[/tex]y = (-2)
So, the solution of the system of equations are : (x,y) = (1,-2)
Answer: (x,y) = (1,-2)
Write the given equation of a line that passes through two given points (-2,-1) and (0,-5)
Answer:
y2-y1 x2-x1
Step-by-step explanation:
-5-(-1)
--------
0-(-2)
-4
---
2
-2
----
1
Use point slope form to write the lines with the given slope and point in slope intercept form.m= -1(-5,-4)
The slope point form is
[tex]y-y1=m(x-x1)[/tex]m is the slope
x1, y1 are the coordinates of a point on the line
The slope of the line is -1
m = -1
point (-5, -4) lies on the line
x1 = -5 and y1 = -4
Let us substitute them in the form above
[tex]y-(-4)=-1(x-\lbrack-5\rbrack)[/tex]Remember (-)(-) = (+)
[tex]y+4=-1(x+5)[/tex]The equation of the line in the slope-point form is y + 4 = -1(x + 5)
A printer takes 5 seconds to print 3 pages. How many pages can it print in 125 seconds? Enter the answer in the box.
Answer:
75?
Step-by-step explanation:
Answer:
75
Step-by-step explanation:
3 divided by 5
0.6x125
I am stuck on what to do after graphing points A, B and C
Remember that the coordinates are written in the form (x,y). Plot the points with the given coordinates: A(1,6), B(1,1) and C(5,1):
Draw a right triangle using the same measures for the legs in order to construct ΔDEF, as described below:
[tex]\begin{gathered} DE=5 \\ EF=4 \end{gathered}[/tex]help meeeeeee pleaseee !!!!
1) The Linear equation that models the average price of a new home is;
y = -800x + 294000.
2) The prediction of the average price of a new hom in the year 2014 is; $256000
How to solve the equation in slope intercept form?We are told that the average price in the year 2004 was $294000
We are told that y is the average price in a home in the year x, where x = 0 represents the year 2004. Thus, this means that the y-intercept is $294000.
Since the line must pass through the points (0, 294000) and (7, 288400), it means that;
Slope = (288400 - 294000)/(7 - 0)
Slope = -5600/7
Slope = -800
Now, we know that the general formula for equation in slope intercept form is; y = mx + c
where; m is slope and c is y-intercept.
Thus;
1) Linear equation is; y = -800x + 294000.
2) For the average price of a new home in the year 2014, this means that x = 2014 - 2004 = 10 years
Thus;
y = -800(10) + 294000
y = $256000
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A store sells cat food in 4-pound bags. The cat food cost 2 dollars per pound.
Here is the completed table:
Number of bags purchased Total weight Total Cost
1 4 8
2 8 16
3 12 24
4 16 32
5 20 40
What is the total weight and the total cost?One bag of cat food weighs 4 pounds. This means that as the bag increases by 1, the weight of the bag increases by 4.
Weight of 1 bag of cat food = 4
Weight of 2 bags of cat food = 4 x 2 = 8
Weight of 3 bags of cat food = 4 x 3 = 12
Weight of 4 bags of cat food = 4 x 4 = 16
Weight of 5 bags of cat food = 4 x 5 = 20
The cost of cat food is $2 per pound.
Cost of a bag of cat food = number of bags bought x weight of one bag x cost per pound
Cost of 1 bag of cat food = 1 x 4 x 2 = 8
Cost of 2 bags of cat food = 2 x 4 x 2 = 16
Cost of 3 bags of cat food = 3 x 4 x 2 = 24
Cost of 4 bags of cat food = 4 x 4 x 2 = 32
Cost of 5 bags of cat food = 5 x 4 x 2 = 40
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find an equation parallel to y=-8 and passing through (-6, -7)
Given:
an equation is given as y = -8.
Find:
we have to find an equation parallel to the given equation and passing through (-6, -7).
Explanation:
Compare the given equation with y = mx + b,
we find that slope ,m = 0 ,
the equation of the line passing through (-6,-7) is
y - (-7) = m( x - (-6))
y + 7 = 0(x + 6)
y + 7 = 0
y = -7
Therefore, y = -7 is an equation which is parallel to y = -8 and passing through ( -6, -7).
The graph of both y = -8 and its parallel equation y = -7 which passes through (-6, -7) is given as below
Red line represents the equation y = -8
and blue line represents the equation y = -7 passes through the point (-6,-7).
Therefore, the equation of the line parallel to y = -8 and passing through (-6,-7) is y = -7.
Sophie records the total number of cans of cat food she uses after different numbers of days. She wants to know if the number of cans of cat food she uses is proportional to the number of days. After 3 days – 6 cans After 4 days - 8 cans After 9 days – 18 cans 1. Complete the table # of Days (x) 3 4 (fill in the questions marks) # of Cans (y) 6 8 18 # of Days (x) # of Cans (y) = 2 3 2 2 8-2 4 니 2. Is the number of cans of cat food used proportional to the number of days? Explain. 3. How many cans of cat food will Sophie use after 12 days?
The number of cans is proportional to the number of days, because each day it uses 2 c
ERROR ANALYSIS In Exercise 30, describe and correct the error in finding the inverse of the functionf(x)=1/7x^2, x>=0y=1/7x^2x=1/7y^27x=y^2+-√7x=y
Given the function
[tex]\begin{gathered} f(x)=\frac{1}{7}x^2 \\ x\ge0 \end{gathered}[/tex]To find the inverse, we must recall that the domain of the function becomes the range of the inverse function and vice-versa.
We are already given the domain of f, all the real numbers equal or greater than zero.
The domain of the function is exactly the same because x squared is always positive or zero, thus the domain and range of the inverse should be x≥0.
Once we find the inverse function, we'll use this concept.
Step 1: Substitute f(x) for y:
[tex]y=\frac{1}{7}x^2[/tex]Step 2: Swap the variables:
[tex]x=\frac{1}{7}y^2[/tex]Step 3: Solve for y:
[tex]y=\pm\sqrt[]{7x}[/tex]But as said above, the range of this function cannot include the negative numbers, thus the inverse function is:
[tex]f^{-1}(x)=\sqrt[]{7x}[/tex]Gerard compares the offers at two different banks to decide where he should open a savings account. A. Draw a representation to show how much would be in the first savings account if Gerard's initial deposit were d dollars.
Explanations:
Given the following parameters
An initial deposit of Gerard is "d" dollars
For the savings with 5% interest, the interest on "d" dollars will be expressed as;
[tex]\begin{gathered} \text{Interest = 5\% of d} \\ \text{Interest = 0.05d} \end{gathered}[/tex]Get the total savings plus interest in the first account
[tex]\begin{gathered} \text{Balance}=\text{Initial deposit + Interest} \\ \text{Balance=d+0.05d} \\ \text{Balance=1.05d} \end{gathered}[/tex]Hence the $1.05d will be in the first savings account if Gerard's initial deposit were d dollars
For the other account:
Initial deposit = "d" dollars
Interest = $100
Since the interest will be added to the first deposit, hence;
[tex]\text{Balance=(d+100)dollars}[/tex]In Tabulated form:
How much was the decrease dollar? How much was in his account the end of last year?
Explanation
We are given the following information:
• Amount at the beginning of an investment = $5500
,• Percent decrease = 24.6%
We want to determine the decreased amount in dollars and the amount in his account at the end of the year.
We can determine the decreased amount with the formula below:
[tex]Decreased\text{ }amount\text{ }=Percent\text{ }decrease\text{ }\times Amount[/tex]Therefore, the decreased amount can be calculated as:
[tex]\begin{gathered} Decreased\text{ }amount=24.6\%\times5500 \\ Decreased\text{ }amount=\frac{24.6}{100}\times5500=1353 \end{gathered}[/tex]Hence, the decreased amount is $1353.
At the end of last year, the amount left in his account can be calculated as follows:
[tex]undefined[/tex]Hence, the year-end amount is $4147.
Para medir temperaturas podemos utilizar distintas escalas, las más utilizadas son las de grados centígrados y las de grados Fahrenheit, sabemos que 0 C es equivalente a 32F y 20C es equivalente a 68F, si conocemos que la relación entre ambas variables responde una función lineal
A) Encontrar la expresión de la función que permita transformar grados Fahrenheit a Centigrados
B) Encontrar la expresión inversa a la anterior
AYUDA PORFAVOR DOY LO QUE SEA POR ESTO
Using linear functions, it is found that:
a) The expression to convert from Fahrenheit to Celsius is: y = 5x/9 - 160/9.
b) The inverse expression is: y = 9x/5 + 32.
What is a linear function?The slope-intercept representation of a linear function is given as follows:
y = mx + b
The coefficients of the function are described as follows:
m is the slope of the function, representing the rate of change of the output y in relation of the input x of the function.b is the y-intercept of the function, representing the numeric value of the function when the input x is of 0.For the conversion of Fahrenheit to Celsius, we have two points, as follows:
(32,0), (68, 20).
When the input increases by 36, the output increases by 20, hence the slope is calculated as follows:
m = 20/36 = 5/9
Hence:
y = 5/9x + b.
When x = 32, y = 0, hence the intercept b is calculated as follows:
0 = 5/9(32) + b
b = -5 x 32/9
b = -160/9
Hence the equation is:
y = 5/9x - 160/9.
To find the inverse expression, we exchange x and y and then isolate y, as follows:
x = 5/9y - 160/9.
5/9y = x + 160/9
5y = 9x + 160
y = 9x/5 + 32.
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A circle has area of 361pi cm2 what is the circumference in centimeters of the circle
The area of the circle is given as:
[tex]A=\pi r^2[/tex]plugging the value given we have that:
[tex]\begin{gathered} 361\pi=\pi r^2 \\ r^2=361 \\ r=\sqrt[]{361} \\ r=19 \end{gathered}[/tex]Now, the circumference is given as:
[tex]C=\pi d[/tex]where d is the diameter of the circle. The diameter is twice the raidues, hence the diameter is 38, therefore the circumference is:
[tex]C=38\pi[/tex]Therefore the circumference is 38pi