Answer:
$2880
Step-by-step explanation:
I = Prt
= $3600·8%·10 = 0.80·$3600 = $2880
The simple interest on $3600 over a 10-year period is $2880.
Serena asked her parents if for their picnic they could have 20% more portions of coca-cola than they planned, and if each portion could be 20% bigger. Her parents agreed. By what percent more coca cola will they buy?
Answer:
44%
Step-by-step explanation:
If p represents the number of portions and q represents the quantity in each portion, then the original amount needed was p·q.
After p is increased by 20%, its number is ...
p + 0.20·p = 1.20·p
After q is increased by 20%, its amount is ...
q + 0.20 ·q = 1.20·q
Then the new amount the parents must buy is ...
(1.20p)(1.20q) = 1.20²·pq = 1.44pq
This amount is ...
(1 + 44/100)·pq = pq + 44%·pq
It is 44% more than the original planned purchase.
Answer:
44 percent
Step-by-step explanation:
Is 12y -20 factorable
Answer:4(3y-5)
Step-by-step explanation: Factor out 4 from the expression. 4 goes into 12 3 x's, 4 goes in to 20 5 x's Hope this helpedYes. 4(3y-5) is the factored version
is 4j - 3 = j a equation?
Answer:
Yes , i thinks so because have letter and the result is perfect and have two statement.
MELVIN MOWS A LAWN. THE FRACTION OF THE AWN THAT MELVIN HA MOWED SO FAR IS REPRESENTED BY THE SHADED MODEL SHOWN. MELVIN WILL MOW 3/10 MORE OF THE LAWN BEFORE HE TAKES HIS FIRST BREAK. WHAT FRACTION OF THE LAWN WIK MELVIN HAVE MOWED WHEN HE TAKES HIS FIRST BREAK?
Final answer:
To find the total fraction of the lawn mowed by Melvin before his first break, one would add the additional 3/10 to the already mowed fraction represented by the shaded model.
Explanation:
The student's question is about calculating the fraction of the lawn that will be mowed by Melvin before he takes his first break. Initially, the question does not specify what fraction of the lawn is already mowed, but indicates that Melvin will mow an additional 3/10 of the lawn. Assuming that the shaded model represents the fraction already mowed (let's say x), the total fraction mowed before Melvin's first break would be x + 3/10. Without the specific value of the initially mowed fraction, we cannot provide the exact answer; however, generally, the operation would involve adding the given fraction to Melvin's progress before he mows the additional 3/10.
A ladder leans against a building that angle of elevation of the latter is 70° the top of the ladder is 25 feet from the ground. to the nearest 10th of a foot how far from the building is the base of the ladder a. 20.5 feet b. 30.5 feet C.32.3’ or D.39.5 feet
Answer:
a. 20.5
Step-by-step explanation:
because this will form a right triangle we can use tan (opposite over adjacent) so an equation we could set up would be tan(70)=25/x
therefore we can just solve the equation which would give us 20.45. so if we round it the answer would be a
Answer:
The correct answer option is a. 20.5 feet.
Step-by-step explanation:
We are given that the angle of elevation of the ladder is 70° and the height of the ladder is 25 feet from the ground.
We are to find the distance of the building from the base of the ladder.
For this, we will use tan:
[tex] tan 70 = \frac { 2 5 } { x } [/tex]
[tex] x = \frac { 2 5 } { tan 7 0 } [/tex]
x = 20.5 feet
what is the following quotient? 5/ sqrt 11 - sqrt 3
[tex]\displaystyle\\\frac{5}{\sqrt{11}-\sqrt{3}}=?\\\\\\\text{We rationalize the denominator.}\\\\\frac{5}{\sqrt{11}-\sqrt{3}}=\frac{5(\sqrt{11}+\sqrt{3})}{(\sqrt{11}-\sqrt{3})(\sqrt{11}+\sqrt{3})}=\frac{5(\sqrt{11}+\sqrt{3})}{(11-3)}=\boxed{\bf\frac{5\sqrt{11}+5\sqrt{3})}{8}}[/tex]
Answer:
The correct option is b) [tex]\frac{5\sqrt{11}+5\sqrt{3}}{8}[/tex]
Step-by-step explanation:
We need to find the quotient of [tex]\frac{5}{\sqrt{11}-\sqrt{3}}[/tex],
Rationalizing the above,
By multiply and divide by conjugate of its denominator,
[tex]\frac{5}{\sqrt{11}-\sqrt{3}} \times \frac{\sqrt{11}+\sqrt{3}}{\sqrt{11}+\sqrt{3}}[/tex]
[tex]\frac{5(\sqrt{11}+\sqrt{3})}{(\sqrt{11}-\sqrt{3})(\sqrt{11}+\sqrt{3})}[/tex]
Since, [tex](a+b)(a-b)=a^{2}-b^{2}[/tex]
[tex]\frac{5\sqrt{11}+5\sqrt{3}}{(11-3)}[/tex]
simplify,
[tex]\frac{5\sqrt{11}+5\sqrt{3}}{8}[/tex]
Therefore, the correct option is b) [tex]\frac{5\sqrt{11}+5\sqrt{3}}{8}[/tex]
equation find three points that solve the equation then plot on the graph -3y = 5x -7
ANSWER
See attachment.
EXPLANATION
The given equation is
-3y=5x-7
when y=0,
-3(0)=5x-7
0=5x-7
5x=7
[tex]x = \frac{7}{5} [/tex]
we plot (7/5,0)
when x=0
-3y=5(0)-7
y=7/3
we plot (0,7/3)
when x=1,
-3y=5(1)-7
-3y=-2
y=2/3
we plot (1,2/3)
Simplify. Assume that no denominator is equal to zero. ([3^2]^3g^3h^4)^2
Answer:
531,441·g^6·h^8
Step-by-step explanation:
The operative rule of exponents is ...
(a^b)^c = a^(b·c)
Working from the inside out, according to the order of operations, we get ...
= (9^3·g^3·h^4)^2
= 729^2·g^(3·2)·h^(4·2)
= 531,441·g^6·h^8
Please, I need it ASAP!!!! I will give brainliest if correct!!!
Answer:
recursive: f(0) = 7; f(n) = f(n-1) -8
explicit: f(n) = 7 -8n
Step-by-step explanation:
The sequence is an arithmetic sequence with first term 7 and common difference -8. Since you're numbering the terms starting with n=0, the generic case will be ...
recursive: f(0) = first term; f(n) = f(n-1) + common difference
explicit: f(n) = first term + n·(common difference)
To get the answer above, fill in the first term and common difference values.
Help me with ixl please
Answer:
$84.70
Step-by-step explanation:
Using the formula, B = 70(1+0.1)^2 = 70*1.21 = 84.7.
Fine Furniture Company had a net income of $50,000. Accounts receivable increased by $30,000; inventory decreased by $20,000; amounts payable increased by $4,000; and salaries payable decreased by $1,000. The amount of cash flow from continuing operating activities under the indirect method is
Cash flow from operating activities is $43,000. Calculated by adjusting net income for changes in working capital items.
To calculate the cash flow from operating activities using the indirect method, we start with net income and adjust for changes in working capital.
Net Income = $50,000
Changes in Working Capital:
1. Accounts Receivable increased by $30,000, so we subtract $30,000.
2. Inventory decreased by $20,000, so we add $20,000.
3. Amounts Payable increased by $4,000, so we add $4,000.
4. Salaries Payable decreased by $1,000, so we subtract $1,000.
Now, let's calculate the cash flow from operating activities:
Cash flow from operating activities = Net Income + Changes in Working Capital
= $50,000 - $30,000 + $20,000 + $4,000 - $1,000
= $50,000 - $7,000
= $43,000
So, the amount of cash flow from continuing operating activities under the indirect method is $43,000.
Triangle A′B′C′ is a dilation of triangle ABC .
What is the scale factor?
Enter your answer in the box.
Note: Images may not be drawn to scale.
Triangle ABC is shown. Side AB is labeled 9. Side BC is labeled 9. Side CA is labeled 18. Triangle A prime B prime C prime is shown. Side A prime B prime is labeled 4 and a half. Side B prime C prime is labeled 4 and a half. Side C prime A prime is labeled 9.
Answer:
1/2
Step-by-step explanation:
The ratio of corresponding side lengths of the dilation are 1/2 those of the original, so the scale factor is 1/2.
___
For example, A'C'/AC = 9/18 = 1/2.
50 POINTS
Tyrone rolls a standard number cube multiple times and records the data in the table above. At the end of the experiment, he counts that he has rolled 155 sixes. Find the experimental probability of rolling a six, based on Tyrone’s experiment. Round the answer to the nearest thousandth.
Answer:
Step-by-step explanation:
Unless I'm reading this incorrectly, he throws 155 6's.
There are 1000 throws altogether (according to the table)
So the experimental probability is 155/1000 = 0.155
The answer is B. It is a bit tricky to read.
With a base salary of $250 and a commission of 4% of all sales, compute Cindy Nelson’s salary for the following weeks:
Week : 1 2 3 4
Base Salary. $250. $250 $250 $250
Sales. $890. $1,126 $975 $ 824
Commission ? ? ? ?
Total Salary ? ? ? ?
Answer:
Part 1) The commission is $35.6 and the total salary for week 1 is $285.6
Part 2) The commission is $45.04 and the total salary for week 2 is $295.04
Part 3) The commission is $39 and the total salary for week 3 is $289
Part 4) The commission is $32.96 and the total salary for week 4 is $282.96
Step-by-step explanation:
Let
x-----> the amount in sales
y----> Cindy Nelson’s salary
we know that
4%=4/100=0.04
so
The linear equation that represent this situation is
y=250+0.04x
case 1) week 1
Sales $890
For x=890
substitute in the linear equation
y=250+0.04(890)
y=250+35.6=$285.6
therefore
The commission is $35.6
The total salary for week 1 is $285.6
case 2) week 2
Sales $1,126
For x=1,126
substitute in the linear equation
y=250+0.04(1,126)
y=250+45.04=$295.04
therefore
The commission is $45.04
The total salary for week 1 is $295.04
case 3) week 3
Sales $975
For x=975
substitute in the linear equation
y=250+0.04(975)
y=250+39=$289
therefore
The commission is $39
The total salary for week 1 is $289
case 4) week 4
Sales $824
For x=824
substitute in the linear equation
y=250+0.04(824)
y=250+32.96=$282.96
therefore
The commission is $32.96
The total salary for week 1 is $282.96
Can someone explain to me how to do this
See the attached picture for the solution.
Factor each equation 64p^3 - 8q^3
Answer:
8(2p − q)(4p² + 2pq + q²)
Step-by-step explanation:
You would use the difference of cubes to factor this polynomial.
I hope this helps you out alot, and as always, I am joyous to assist anyone at any time.
if f(×)=-5,tgen f(-3)=
Answer:
f(-3) = -5
Step-by-step explanation:
Put -3 where x is and evaluate the expression:
f(-3) = -5
_____
The function describes a horizontal line. It doesn't matter what x is, the value of the function is -5.
What is the x-intercept and the y-intercept of the line on the graph
Answer:
X-intercept: (0,4)
Y-intercept: (-4,0)
Quick answer if you can help@
The domain is the input values, which are the X- values.
The domain would be -6, -1 , 0, 3
The first answer is the right one.
For this case, we have that by definition, the domain of a function is given by all the values of "x" for which the function is defined. The values of the domain are represented in the starting point.
Then, it is observed in the figure that the values of the domain are:
[tex]{x | x = -6, -1,0,3}[/tex]
ANswer:
Option A
A school, hospital, and a supermarket are located at the vertices of a right triangle formed by three highways. The school and hospital are 14.7 miles apart. The distance between the school and the supermarket is 8.82 miles, and the distance between the hospital and the supermarket is 11.76 miles.
A service road will be constructed from the main entrance of the supermarket to the highway that connects the school and hospital. What is the shortest possible length for the service road? Round to the nearest tenth.
Answer:
7.1 miles
Step-by-step explanation:
Consider right triangle HospitalSchoolSupermarket. In this triangle:
HospitalSchool = 14.7 mi;HospitalSupermaket = 11.76 mi;School Supermarket = 8.82 mi.The shortest road from the main entrance of the supermarket to the highway that connects the school and hospital will be the height drawn from the point Supermarket to the hypotenuse HospitalSchool.
Let the length of this road be x mi and the distance from School to point A be y mi. Use twice the Pythagorean theorem for right triangles Supermarket SchoolA and SupermarketHospitalA:
[tex]\left\{\begin{array}{l}x^2+y^2=8.82^2\\ \\x^2+(14.7-y)^2=11.76^2\end{array}\right.[/tex]
Subtract from the second equation the first one:
[tex]x^2+(14.7-y)^2-x^2-y^2=11.76^2-8.82^2\\ \\14.7^2-2\cdot 14.7y+y^2-y^2=11.76^2-8.82^2\\ \\-29.4y=11.76^2-8.82^2-14.7^2\\ \\29.4y=155.5848\\ \\y\approx5.24\ mi[/tex]
Thus,
[tex]x^2=8.82^2-5.24^2=50.3348\\ \\x\approx 7.1\ mi.[/tex]
If a = 7, what is the value of the expression 2(a + 8)? A. 2 B. 15 C. 17 D. 23 E. 30
The answer is 30.
if 7=a and 2(a+8)
all you need to do is replace a with 7
so the formula would then be 2(7+8)
next you would solve in the parentheses.
2(15)
and 2(15) is the same as 2 x 15
so the answer would be 30
Answer: E. 30
Step-by-step explanation:
Cause a=7 and the equation is 2 (a+8) and it the same as 2 × (7+8) which if you use PEMDAS it's 2 × 15 =30
An athlete was having her blood pressure monitored during a workout. The doctor found that the periodic function, P= 20 sin (8pi/3 t) + 90 models her blood pressure as a function of time in seconds.
a. What is the systolic pressure (the maximum blood pressure)?
b. What is the diastolic pressure (the minimum blood pressure)?
c. What is the length in time, of her heartbeat cycle?
d. Sketch a wall labeled graph.
Answer:
(a) 110 mm Hg
(b) 70 mm Hg
(c) 3/4 second
(d) see the attachment
Step-by-step explanation:
(a) The sine function has a maximum value of +1, so the maximum value of p is ...
pmax = 20·(+1) +90 = 20+90 = 110 . . . . . mm Hg
__
(b) The sine function has a minimum value of -1, so the minimum value of p is ...
pmin = 20·(-1) +90 = -20+90 = 70 . . . . . mm Hg
__
(c) The period of the sine function is 2π, so the value of t that makes the argument be 2π will be the period.
8π/3·t = 2π
t = 2π·3/(8π) = 3/4 . . . . . . multiply by the inverse of the coefficient of t
The period of her heartbeat cycle is 3/4 seconds.
__
(d) a graph is attached.
If we assume that all possible poker hands (comprised of 5 cards from a standard 52 card deck) are equally likely, what is the probability of being dealt: a. a flush? (A hand is said to be a flush if all 5 cards are of the same suit. Note that this definition means that straight flushes (five cards of the same suit in numeric sequence) are also considered flushes.) b. one pair? (This occurs when the cards have numeric values a, a, b, c, d, where a, b, c, and d are all distinct.) c. two pairs? (This occurs when the cards have numeric values a, a, b, b, c, where a, b and c are all distinct.) d. three of a kind? (This occurs when the cards have numeric values a, a, a, b, c, where a, b and c are all distinct.) e. four of a kind? (This occurs when the cards have numeric values a, a, a, a, b.)
Answer:
See the attached photo for the calculations and answers
Step-by-step explanation:
The calculations and explanations are shown in the 3 attached photos below.
The answer to the given question will be a) P(flush) = 0.0019 b) P(one pair) = 0.4225 c) P( two pairs) = 0.475 d) P(three of a kind) = 0.211 e) P(four of a kind) = 0.00024
What is probability?
It's a field of mathematics that studies the probability of a random event occurring. From 0 to 1, the value is expressed.
The probability of being dealt a flush:
For a suit there are 4 choices and 13C₅ choices for a card in that suit
Probability of flush = 4.( 13C₅)/52C₅
Probability of flush = 0.0019
The probability of being dealt one pair:
There are 13 possible values of a, 4C₂ choice for suit of a, 12C₃ value for b, c, d and 4 choices each for choosing the suit of b, c, d.
P(one pair) = (13.4C₂.12C₃.4.4.4)/52C₅
P(one pair) = 0.4225
The probability of being dealt two pairs:
There are 13C₂ possibility for the value of a and b, 4C₂ choices for suits of both a and b and 44 possibilities for c from the remaining cards.
P(2 pairs) = (13C₂.4C₂.4C₂.44)/(52C₅) = 0.475
The probability of being dealt three of a kind:
There are 13 possibilities for the value of a and 4C₃ choices for the suits of a, 12C₂ possibilities for both b and c and 4 choices of suits for both b and c.
P( three of a kind) = (13.4C₃.12C₂.4.4)/52C₅ = 0.211
The probability of being dealt four of a kind:
There are 13 possibilities of a and 4C₄ values for the suit of a and 48 choices of b from the remaining cards.
P(four of a kind) = (13.4C₄.48)/52C₅ = 0.00024
Learn more about probability on:
https://brainly.com/question/24756209
#SPJ2
Martha buys a surfboard that cost $405 for 40% off. How much money does she save?
Answer:
$162
Step-by-step explanation:
Discount = percentage discount ÷ 100 × original cost
Discount = [tex]\frac{40}{100}[/tex] × $405 = $162
Simplify 2m - [n - (m - 2n)]. -3m - n 3m - n -3m - 3n 3m - 3n
Answer:
3m-3n
Step-by-step explanation:
We want to simplify the expression;
2m - [n - (m - 2n)].
We expand the parenthesis to obtain;
2m - (n - m + 2n)
2m - ( - m + 3n)
Expand further to get;
2m +m -3n
Combine the first two terms;
3m-3n
Leah invested $950 in an account paying an interest rate of 1.5% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 6 years?
[tex]\bf ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$950\\ r=rate\to 1.5\%\to \frac{1.5}{100}\dotfill &0.015\\ t=years\dotfill &6 \end{cases} \\\\\\ A=950e^{0.015\cdot 6}\implies A=950e^{0.09}\implies A\approx 1039.5\implies \stackrel{\textit{rounded up}}{A=1040}[/tex]
Help! Please help me with these two questions!!
1.What is the volume of below composite figure?
2.What is the value of x?
Answer:
2. area = 504 cm^2
3. x = 30°
Step-by-step explanation:
2. The figure can be divided across the middle into a rectangular bottom part and a triangular top part. The triangle will have a base length of 21 cm and a height of 32 -16 = 16 cm. Its area is ...
triangle area = (1/2)bh = (1/2)(21 cm)(16 cm) = 168 cm^2
The area of the rectangle is the product of its base (21 cm) and height (16 cm). Its area is ...
rectangle area = bh = (21 cm)(16 cm) = 336 cm^2
Then the total area of the figure is the sum of the areas of its parts:
total area = triangle area + rectangle area
= (168 cm^2) + (336 cm^2) = 504 cm^2
A plane figure has no volume. The volume is zero.
__
3. The angle whose measure is 4x is supplementary to the angle marked 60°, so is 180° -60° = 120°. That means ...
4x = 120°
x = 120°/4 = 30° . . . . divide by the coefficient of x
The value of x is 30°.
A loaf of bread is cut into slices of equal size. Some of the loaf is used in a recipe and 2/12 of the loaf is used to make a sandwich. The remaining 7/12 of the loaf is put into the refrigerator. Write and solve an equation to find the fraction of the loaf of bread that is used in the recipe.
The answer would be 3/12 was used on the recipe. If 3/12 was used on the recipe and we know 2/12 was used to make a sandwich, 3/12 + 2/12 =5/12 used and that holds true being as there is 7/12 of the loaf left. 12/12 - 5/12 = 7/12
Hope I helped. Please mark me brainliest! :)
Find the vertices and foci of the hyperbola with equation quantity x plus one squared divided by sixteen minus the quantity of y plus five squared divided by nine = 1
Answer:
The vertices are (3 , -5) , (-5 , -5)
The foci are (4 , -5) , (-6 , -5)
Step-by-step explanation:
* Lets study the equation of the hyperbola
- The standard form of the equation of a hyperbola with
center (h , k) and transverse axis parallel to the x-axis is
(x - h)²/a² - (y - k)²/b² = 1
- The length of the transverse axis is 2 a
- The coordinates of the vertices are (h ± a , k)
- The coordinates of the foci are (h ± c , k), where c² = a² + b²
- The distance between the foci is 2c
* Now lets solve the problem
- The equation of the hyperbola is (x + 1)²/16 - (y + 5)²/9 = 1
* From the equation
# a² = 16 ⇒ a = ± 4
# b² = 9 ⇒ b = ± 3
# h = -1
# k = -5
∵ The vertices are (h + a , k) , (h - a , k)
∴ The vertices are (-1 + 4 , -5) , (-1 - 4 , -5)
* The vertices are (3 , -5) , (-5 , -5)
∵ c² = a² + b²
∴ c² = 16 + 9 = 25
∴ c = ± 5
∵ The foci are (h ± c , k)
∴ The foci are (-1 + 5 , -5) , (-1 - 5 , -5)
* The foci are (4 , -5) , (-6 , -5)
Answer:
Vertices: (3,-5) (-5,-5)
Foci: (-6,-5) (4,-5)
Step-by-step explanation:
(x+1)^2/16-(y+5)^2/9 =1
formula: (x-h)^2/a^2 -(y-k)^2/b^2=1
in this case...
a^2=16 b^2=9
h=-1 k=-5
a=4 b=3
v=(h+/-a,k)
v1=(-1+4,-5)=
v1=(3,-5)
v2=(-1-4, -5) =
v2=(-5,-5)
Foci=(h+/-c,k)
F1=(h-c,k)
=(-1-5,-5)
f1=(-6,-5)
F2=(h+c,k)
=(-1+5, -5)
F2=(4,-5)
Hope this helps! :)
plz help. if u want part A. tell me if u know part A. help plzzz
Step-by-step explanation:
Did they define mechanical pencils using the variable m?