Answer:
[tex]S = P(1.08)^{t}[/tex]
Step-by-step explanation:
A $10,000 deposit at the bank will double in value in 9 years.
If the interest is r% and it is compounded each year, then we can write from the formula of compound interest that
[tex]20000 = 10000(1 + \frac{r}{100})^{9}[/tex]
⇒ [tex]2 = (1 + \frac{r}{100})^{9}[/tex]
⇒ [tex]1 + \frac{r}{100} = 1.08[/tex]
⇒ r = 8%
Therefore, the formula for the accumulated amount t years after the investment is made will be
[tex]S = P(1 + \frac{8}{100})^{t} = P(1.08)^{t}[/tex]
where, P is the invested principal and S is the accumulated sum. (Answer)
If and CX = 5 units, what is DZ?
The question is missing the figure. So, it is attached below.
Answer:
DZ = 4 units
Step-by-step explanation:
Given:
CD || XZ
YC = 25 units, CX = 5 units, YD = 20 units.
We know that,
If CD is parallel to XZ , then the line CD divides the sides XY and YZ of the triangle XYZ proportionally. This is true by triangle proportionality theorem.
Therefore, the lengths YC, CX, YD and DZ are in proportion. This gives,
[tex]\frac{YC}{CX}=\frac{YD}{DZ}[/tex]
Rewrite in terms of DZ. This gives,
[tex]DZ=\frac{YD\times CX}{YC}[/tex]
Plug in [tex]YC=25,CX=5,YD=20[/tex]. Solve for DZ.
[tex]DZ=\frac{20\times 5}{25}\\\\DZ=\frac{100}{25}=4[/tex]
Therefore, the length of DZ is 4 units.
Answer:
4
Step-by-step explanation:
PLZ HELP ME THIS IS URGENT HELP!!!!!!!
Answer:
Value is 3.The volume of the rectangular prism is 105 [tex]ft^{3}[/tex]The value will be 186.1Step-by-step explanation:
The value of the expression is [tex]\frac{75}{5} - [(9 - 7) \times 3]\times 2 = 15 - 6\times2 = 15 - 12 = 3[/tex]
The formula to get the volume is [tex]length \times width \times height = 3\times 5\times 7 = 105[/tex]
[tex]\frac{8375}{45} = \frac{1675}{9} = 186.1[/tex]
Answer:
it is explained below..
Step-by-step explanation:
1. by using BODMAS rule: [ brackets of division multiplication addition subtraction] we have to do operations in this order only i.e, from brackets to subtractions.
given expression : 75[tex]\div[/tex]5-[(9-7)*3]*2
first solve brackets part:75[tex]\div[/tex]5-[(2)*3]*2
[as, 9-7=2]
75[tex]\div[/tex]5-[6]*2
[as, 2*3=6]
division part: 15-6*2multiplication part: 15-12 = 32. volume of rectangular prism: length*breadth*height
=7*3*5
=105
3. 8375[tex]\div[/tex]45
use conventional division method as 8375 isn't divisible by 45 directly.
after solving, answer: 186.11...
How do the numbers compare
The fact family model represents the relationship between
the numbers 8, 7, and 15.
15 is 7 more than 8.
15 is 8 less than 7.
7 is 15 less than 8.
07 is 8 more than 15.
Answer:
A
Step-by-step explanation:
8+7=15
For the numbers 8, 7, and 15, the true statements are '15 is 7 more than 8' and, when rephrased correctly, '7 is 8 more than 15'. The concept of significant figures plays an important role in mathematical operations to maintain the accuracy of results based on the precision of original numbers.
Explanation:The fact family model is used to represent the relationship between three numbers that can form addition and subtraction statements. For the numbers 8, 7, and 15, only some of the given statements are true. Let's verify each statement:
15 is 7 more than 8: This statement is true, as 8 + 7 equals 15.
15 is 8 less than 7: This statement is false, as adding 8 to 7 gives us 15, not taking 8 from 7.
7 is 15 less than 8: This statement is false, as subtracting 15 from 8 would give us a negative number, not 7.
7 is 8 more than 15: This statement is true when we rephrase it correctly as 7 + 8 equals 15.
Therefore, only two statements are accurate: '15 is 7 more than 8' and '7 is 8 more than 15' when considered as 7 + 8 = 15.
The subject of significant figures and rounding is also related to mathematics. When performing mathematical operations, significant figures are crucial to ensure that our answers are as accurate as the precision of the numbers we started with, without overstating the certainty of our results. This becomes important when adding, subtracting, multiplying, or dividing numbers in mathematics.
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Describe, in words, the solution set for the following equation.
3x+3=3+3x
Answer:
Infinite Answers
Step-by-step explanation:
You subtract 3x from both side which leaves you with 3=3, which leaves you to conclude there are infinite answers to this equation.
Find an expression for the number of squares in the nth pattern of the sequence. I noticed that the number of squares you add in each pattern it depends on the pattern number (see image) but I don't know how to get the expression.
The answer is T(n)=5(n-1)+n+1
because = T(4)=5(4-1)+4+1
=T4=5(3)+5
=T4=15+5
=T4=20
this took me half an hour
Translate this sentence into an equation.
Five less than two times Mary's age is 13.
Use the variable m for Mary's age.
A cannon launches a cannon ball into the air at an angle. Which of the
following two terms best describe the cannon ball's motion?
A. Two-dimensional motion
B. One-dimensional motion
C. Speed
D. Projectile motion
Answer:
A. Two-dimensional motion
D. Projectile motion
Step-by-step explanation:
The cannon ball is a projectile, so it follows projectile motion. Since it is launched at an angle, it moves both vertically and horizontally, so it also has two-dimensional motion.
Match each number on the left with the correct description of the number on the right.
Answer options on the right may be used more than once.
(Full question above)
Step-by-step explanation:
An integer is a number that can be written without a fractional component.
A rational number is a number that can be represented as a fraction with a non-zero denominator, and its decimal expansion is finite or infinite and repeat.
An irrational number is a real number which is not a rational number.
[tex]\bold{integer:}\\-2,\ 150\\\\\bold{rational\ but\ not\ an\ integer:}\\\\-\dfrac{1}{2},\ 6.\overline{6}\\\\\bold{irrational:}\\\\-\sqrt3[/tex]
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the systems of equations with their solution sets.
y + 12 = x2 + x
x + y = 3
y - 15 = x2 + 4x
x - y = 1
y + 5 = x2 - 3x
2x + y = 1
y- 6 = x2 – 3x
x + 2y = 2
y-17 = x2 - 9x
-x + y = 1
y - 15 = -x2 + 4x
x + y = 1
Solution Set
Linear-Quadratic System of Equations
{(-2,3), (7,-6)
{(-5, 8). (3,0)
{(-2,5),(3,-5)
{(2, 3), (8,9)
Answer:
{(-2,3), (7,-6) } -----> y - 15 = -[tex]x^{2}[/tex] + 4x
x + y = 1
{(-5, 8). (3,0) } ----> y + 12 = [tex]x^{2}[/tex] + x
x + y = 3
{(-2,5),(3,-5) } -----> y + 5 = [tex]x^{2}[/tex] - 3x
2x + y = 1
{(2, 3), (8,9)} -----> y-17 = [tex]x^{2}[/tex] - 9x
-x + y = 1
Step-by-step explanation:
The simplest way to find the answer is by solving all the equations and finding the value of x and y for each of them.
Solving the equations ->
y + 12 = [tex]x^{2}[/tex] + x
x + y = 3
Substitute y = 3-x from second equation to first and solving the quadratic equation obtained i.e solving [tex]x^{2}[/tex] + 2x -15 = 0 , we get values of x = -5 , 3 and the corresponding values of y by substituting values of x in second equation , y = 8, 0 respectively. So, solution matched = {(-5, 8). (3,0) }.
Similarly solving other equations using exactly the same method as above we get the following solutions,
For,
y - 15 = [tex]x^{2}[/tex] + 4x
x - y = 1
we don't get any integer solution for this hence it has no match.
For,
y + 5 = [tex]x^{2}[/tex] - 3x
2x + y = 1
we get x = 3,-2 and corresponding y = -5,5
So, solution is {(-2,5),(3,-5) }
For,
y- 6 = [tex]x^{2}[/tex] – 3x
x + 2y = 2
we again don't get any integer solution for x and y so this has no match.
For,
y-17 = [tex]x^{2}[/tex] - 9x
-x + y = 1
we get x = 2,8 and corresponding y = 3,9
So, {(2, 3), (8,9)} is the solution match.
Lastly for,
y - 15 = -[tex]x^{2}[/tex] + 4x
x + y = 1
we get x = -2,7 and corresponding y = 3,6
So, {(-2,3), (7,-6)} is the solution match.
Rory, Lorena, and Phil play a third round of golf. Lorena’s score is 1 in the third round. Phil ties Rory’s score at -3. Write an inequality that shows why Lorena lost that round.
Answer:
(1,-3)
Step-by-step explanation:
HELP U WILL MARK YOU AS A BRAINLIEST!!(I’m dumb sorry)
Which pairs of numbers have a greatest
common factor of 10?
Select all that apply.
A. 2 and 5
B. 5 and 10
C. 10 and 20
D. 30 and 50
E. 40 and 60
Answer:
C. 10 and 20
Step-by-step explanation:
A common factor is just a value that both numbers can be divided by to give you an integer. (an integer is a number without a decimal point btw or anything that is not a fraction)
Answer A and B are too small so there's no way they can be divided by 10.
D and E are too big, so they can be divided by a number bigger than 10. (the question did ask for the biggest dividing number to be 10)
The only answer left is C.
PLEASE HELP ASAP!!!!
Write each ratio as a fraction in lowest terms.
1.8 to 9
2.11 to 15
3.30 minutes to 90 minutes
Answer:
1 to 5
211 to 1500
11 to 300
Step-by-step explanation:
1.8 to 9 = 18/90 = 1(18)/5(18) = 1/5 = 1 to 5
2.11 to 15 = 211/1500 = 211 to 1500
3.30 to 90 = 330/9000 = 110/3000 = 11/300 = 11 to 300
2 times what equals 120
In order to solve the problem '2 times what equals 120', you need to find the value of X in the equation 2*X = 120. The answer is 60, as 2 times 60 equals 120.
Explanation:In Mathematics, the problem "2 times what equals 120" is an example of a basic equation you can solve. When you're trying to find the number that 2 times, or multiplied by 2, equals 120, you're looking for the value of the unknown variable in the equation 2*X = 120. To solve this, you would divide both sides of the equation by 2. Thus, X equals 60 because 2 times 60 equals 120.
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To find the number that when multiplied by 2 equals 120, you simply divide 120 by 2, which results in 60.
To find this number, we divide 120 by 2. Therefore, the equation is 2 x ? = 120.
Dividing 120 by 2 gives us:
120 ÷ 2 = 60.
So, 2 times 60 equals 120.
The number -2.34 can be found between which two integers?
(Full question above)
Answer:
last option
Step-by-step explanation:
imagine a number line
________________________________________________
-3 -2 -1 0 1 2 3
|
-2.34 would be found somewhere over there
alex bakes $24$ apple, blueberry, and cherry pies. The ratio of apple to blueberry to cherry pies is $1:4:3$. How many cherry pies did Alex bake?
Answer:
Alex baked 9 cherry pies
Step-by-step explanation:
apple : blueberry : cherry = 1:4:3
apple + blueberry + cherry = 24
1 part: 24 / ( 1+4+3) = 24 / 8 = 3
** Cherry has 3 parts: 3 x 3 = 9
check: apple = 3 x 1 = 3
blueberry: 3 x 4 = 12
12 + 3 + 9 = 24
Answer:
9
Step-by-step explanation:
Aops Problem
What’s the best answer to 7h+3=
Answer:
Step-by-step explanation:
Incomplete question. 7h+3 is just an algebraic expression.
What is the rule for 4,7,13,25,49,97
Answer:
The rule is x2 -1 (times two minus one)
4 - 1 = 3
4 + 3 = 7
7 - 1 = 6
7 + 6 = 13
13 - 1 = 12
13 + 12 = 25
25 - 1 = 24
25 + 24 = 49
49 - 1 = 48
49 + 48 = 97
Which expression is equivalent to
2/3(9x-6)+4(1/2 x -- 1/2)
a:2/3(6x-9)+1/6(x+12)
b:2/3(3x-6)+1/6(x-12)
c:3/4(4x-8)+5(x+15)
d:3/4(4x-12)+1/6(30x+18)
Answer:
D
Step-by-step explanation:
Try dividing
If Jake is skiing at 4.5km at week 6 which statement is true?
He is above his goal
He is at his goal
He is below his goal
Answer:
He is below his goal
Step-by-step explanation:
see the attached figure to better understand the problem
Let
x -----> the number of weeks
y ---->skiing distance in kilometers
Looking at the graph of Jake's goal
we have the ordered pair (6,5)
That means
The number of kilometers from Jake's goal for week 6 is 5 kilometers
and
In the actual Jake is skiing at 4.5 km at week 6
so
[tex]4.5\ km < 5\ km[/tex]
therefore
He is below his goal
Find the point, M, that divides segment AB into a ratio of 2:3 if A is at (0.15) and B is at (20.0)
Answer:
M = (8,9)
Step-by-step explanation:
Notice that the points (0,15), and (20,0) form with the origin of coordinates (0,0), a right angle triangle (please see attached image). This triangle has twon perpendicular sides of length 15 and 20 respectively. Therefore, we can find the length of the segment that joins points A (0,15) and B (20,0) by finding the length of the hypotenuse in a right angle triangle (with the Pythagorean Theorem):
[tex]AB=\sqrt{15^2+20^2} =\sqrt{625} =25[/tex]
Now, to get a 2:3 proportion on Segment AB which is of length 25, we need to divide it in five equal parts (see the picture on the right of the attached image), and place point M at two of these divisions from point A (0,15) and along segment AB.
In order to find the appropriate location in (x,y) coordinates, we consider a smaller triangle (pictured in orange in the image) that is similar to the first larger triangle (pictured in blue). Notice that if the length of AB is 25, each of its five equal divisions would be of length "5", and therefore two of them will render a length of "10" (which is the hypotenuse of this smaller right angle triangle.
Now, in order to find the sides of this smaller triangle (which can give us the clues on the horizontal and vertical coordinates of point M), we can use proportions.
To find the length "x" of the horizontal side , we do:
[tex]\frac{x}{10} =\frac{20}{25} \\x=\frac{10*20}{25} \\x=8[/tex]
To find the length "y" of the vertical side , we do:
[tex]\frac{y}{10} =\frac{15}{25} \\y=\frac{10*15}{25} \\y=6[/tex]
Then, the coordinate "x" of point M will be "8", while we can calculate the y position of point M subtracting "6" from 15 (the length of the vertical side in the original triangle). This gives us the coordinates (8,9) for point M as marked in orange in the picture.
The shortest and longest sides of a right triangle have lengths of 11.1 inches and 18.5 inches, respectively. What is the length of the third side of the triangle?
Answer: 14.8
Step-by-step explanation:
11.1^2 + x^2 = 18.5^2
X is 14.8
Jackson drove 1,080 miles
in 20 hours. What was his
speed in miles per hour?
Answer:
54mph
Step-by-step explanation:
To find the speed in "miles per hour" or miles/hour, divide the number of miles by number of hours.
1080 miles/20 hours
= 54miles/hour
His speed is 54 miles per hour.
Write an integer to match A deposit of $225
Answer:
225
Step-by-step explanation:
A deposit is when you add money yo your bank account, so when there is a deposit , you would add
Each polio consists of 4 doses and rack measles vaccination consists of 2 doses.Last year potter gave out a total of 60 vaccinations and that consisted of a total 128 doses.How many polio vaccinations and how many measles vaccinations did dr potter give last year?
Answer:
4 polio
56 measles
Step-by-step explanation:
Write equations to represent the problem
let x be the number of vaccinations for polio
let y be the number of vaccinations for measles
x + y = 60 Equation for vaccinations
4x + 2y = 128 Equation for doses
Solve the system using substitution. Rearrange x + y = 60 to isolate one variable.
x = 60 - y
Substitute x for 60-y in the other equation
4x + 2y = 128
4(60-y) + 2y = 128 Distribute over brackets
240 - 4y + 2y = 128 Collect like terms. They have the variable "y"
240 - 2y = 128 Subtract 240 from both sides
-2y = 128 - 240
-2y = -112 Divide both sides by -2
y = -112/-2
y = 56 Number of measles vaccinations
Substitute y for 56 in x + y = 60
x + y = 60
x + 56 = 60
x = 60 - 56
x = 4 Number of polio vaccinations
Therefore Dr. Potter gave out 4 polio vaccinations and 56 measles vaccinations.
17. The length of a rectangle is 12 in, and the perimeter is 56 in. Find the width of the rectangle.
Oo oo
O A. 16 in.
O B. 32 in.
O c. 22 in.
O D. 21 in.
Answer:
Step-by-step explanation:
P = 2(L + W)
P = 56
L = 12
now sub...we are looking for w
56 = 2(12 + W)
56 = 24 + 2W
56 - 24 = 2W
32 = 2W
32/2 = W
16 = W <==== the width is 16 inches
check...
P = 2(L + W)
56 = 2(12 + 16)
56 = 2(28)
56 = 56 (correct)
help please!!!!!!!!!!!!!
Answer:
3
Step-by-step explanation:
What Do You Mean Graphy But I Just Think It Is 3
Which property is illustrated by the statement?
(2+3.4) + 6 = 2 + (3.4+6)
Associative Property of Addition
Commutative Property of Multiplication
Inverse Property of Multiplication
Commutative Property of Addition
Answer:
The given expression represents the Associative Property of Addition.
Step-by-step explanation:
Here, the given expression is given as:
(2+3.4) + 6 = 2 + (3.4+6)
Now, for any 3 terms a, b and c the given properties in the options are described as:
1. Associative Property of Addition
(a +b) + c = a + (b + c)
2. Commutative Property of Multiplication
a x b = b x a
3. Inverse Property of Multiplication
[tex]a \times \frac{1}{a} = 1[/tex]
4. Commutative Property of Addition
a+ b = b + a
Hence, from the given expression,we can see that:
(2+3.4) + 6 = 2 + (3.4+6)
⇒(a +b) + c = a + (b + c)
Hence, the expression represents the Associative Property of Addition
Final answer:
The statement (2+3.4) + 6 = 2 + (3.4+6) demonstrates the Associative Property of Addition, indicating that the sum of a set of numbers is the same regardless of how the numbers are grouped.
Explanation:
The property illustrated by the statement (2+3.4) + 6 = 2 + (3.4+6) is the Associative Property of Addition. This property states that when adding three or more numbers, the way in which the numbers are grouped does not change the sum. For instance, as shown in the statement, (a + b) + c equals a + (b + c), which means that the groupings of the numbers can be changed without affecting the total sum. This is not to be confused with the Commutative Property of Addition, which is about the order of the numbers and states that A + B equals B + A. The commutative property tells us that we get the same result whether we add 2 + 3 or 3 + 2. However, the question explicitly deals with the grouping of numbers, not the order, thus confirming that the associative property is in use.
The square below represents one whole.
Express the shaded area as a fraction, a decimal, and a percent of the whole.
Fraction:
Decimal:
percent
Answer:
[tex]\text{Shaded area as fraction}=\frac{81}{100}[/tex]
[tex]\text{Shaded area as decimal}=0.81[/tex]
[tex]\text{Shaded area as percent of the whole}=81\%[/tex]
Step-by-step explanation:
Please consider the attached image as the given square.
We are asked to express the shaded area as a fraction, a decimal, and a percent of the whole.
We can see that in our figure there are 100 squares as there are 10 rows and each row contains 10 squares.
We can also see that there are 81 shaded squares out of 100 squares, so we can represent it as a fraction as:
[tex]\frac{\text{Shaded squares}}{\text{Total squares}}[/tex]
[tex]\text{Shaded area as fraction}=\frac{81}{100}[/tex]
To convert the shaded area into decimal, we need to divide 81 by 100.
[tex]\text{Shaded area as decimal}=0.81[/tex]
To convert the shaded area into percent, we need to multiply 0.81 by 100.
[tex]\text{Shaded area as percent of the whole}=0.81\times 100\%[/tex]
[tex]\text{Shaded area as percent of the whole}=81\%[/tex]
The fraction is: 44/100
The Decimal is: 0.44
Percent: 44%
____________________________________________________________
FractionThe square is split into 100 equal pieces. 44 of the 100 pieces are shaded. so you can write the fraction as 44/100______________________________________Decimal44/100 can also be expressed 44 hundredths. Let's use a place value chart to write 44 hundredths as a decimal.________________________________
| tens | ones | . | tenths | hundredths |
|_____|___0__|_._|___4__| 4 |
______________________________________PercentThe ratio of shaded pieces to total pieces 44:100.percent means per hundred so, we can write the percent as 44%.In 2018, Yolanda paid $4,526 in Social Security tax. If the Social Security tax rate was 6.2% to the maximum income of $128,400 that year, what was Yolanda’s taxable income?
Answer:
$73000
Step-by-step explanation:
Given: Social security tax paid by Yolanda is $4562.
6.2% tax to be paid on earning to the maximum income of $128400.
Lets assume Yolanda´s income be `x`.
Now, calculating the taxable income of Yolanda
∴ [tex]62\% \times x= \$ 4526[/tex]
⇒ [tex]\frac{62}{100} \times x= 4526[/tex]
Cross multiplying both side
⇒ x= [tex]\frac{4526\times 100}{6.2}[/tex]
∴x= $73000
∴ Yolanda´s taxable income is $73000.
Answer:
Step-by-step explanation:
Salary x social security tax rate = social security tax
salary x .062 (6.2%)=4526
salary=4526/.062
salary=73000
During the summer, Joshua plans to work on his uncle’s soybean farm. His uncle says that Joshua has two options for being paid. For the first option, Joshua earns $20 each day he works. For the second option, he earns one nickel for agreeing to work, and that amount doubles each day he works after that. Joshua plans on working 3 days a week for 8 weeks. Which option should he choose?
Answer:
The second option is best to choose.
Step-by-step explanation:
Joshua plans on working 3 days a week for 8 weeks. Therefore, Joshua will work for (8 × 3) = 24 days.
For the first option, Joshua earns $20 each day he works. So, in 24 days he will earn (20 × 24) = $480.
For the second option, he earns one nickel for agreeing to work, and that amount doubles each day he works after that.
So, the total earning of Joshua after 24 days of work will be
0.05 + 0.1 + 0.2 + 0.4 + 0.8 + 1.6 + ......... up to 24 terms {Since 1 nickel is equal to $0.05}
Now, this is an G.P. series sum and first term is 0.05, common ration is 2 and the number of terms is 24.
So, the sum = [tex]0.05 \times \frac{2^{24} - 1 }{2 - 1}[/tex]
= $838860.75
Therefore, the second option is best to choose. (Answer)
Final answer:
To decide between the payment options, Joshua should calculate the total income for the first option ($480) and compare it to the exponentially growing total of the second option, which would be far greater due to the daily amount doubling. Therefore, the second option is the more lucrative choice.
Explanation:
The student's question pertains to determining which of the two payment options offered by Joshua's uncle for work on a soybean farm is more advantageous. Joshua needs to calculate the total earnings for each option over the course of 8 weeks, given that he will work 3 days each week. For option one, it is straightforward: $20 per day times 3 days per week times 8 weeks equals a total of $480. Option two, however, requires calculating the total amount for a doubling sequence starting with a nickel ($0.05).
For option two, the earnings for each week will look like this:
Week 1: Day 1 = $0.05, Day 2 = $0.10, Day 3 = $0.20
Week 2: Day 1 = $0.40, Day 2 = $0.80, Day 3 = $1.60
...and so on. The amount doubles each day Joshua works.
Calculating this for the 24 days (3 days times 8 weeks) will show that on day 24, Joshua's daily earnings would be $0.05 ×223 (since the first day is $0.05 and does not double).
Comparing the total earnings from both options will reveal that Joshua will earn significantly more with the second option. Therefore, Joshua should choose the second payment option.