Answer:
Amount at 15%=$2,411
Amount at 14%=$7,405
Step-by-step explanation:
let
x= the amount at 15% rate.
y=amount at 14% rate
y= x times 3 plus $172
y= 3x + $172 (1)
x times 15% plus y times 14% equals a return of $1,398.35 after one year
0.15x + 0.14y= $1,398.35 (2)
Recall,
y= 3x + $172
Substitute (1) into (2)
0.15x + 0.14y= $1,398.35
0.15x + 0.14(3x+172)=1398.35
0.15x + 0.42x + 24.08=1398.35
Collect like terms
0.15x + 0.42x=1398.35 - 24.08
0.57x=1374.27
Divide both sides by 0.57
x=2,411
x=$2,411
Find y
y= 3x + $172
=3(2,411) + 172
=7,233+172
=7,405
y=$7,405
Amount at 15%=$2,411
Amount at 14%=$7,405
Check:
$2,411*0.15=$361.65
$7,405*0.14=$1036.70
Total=$361.65 + $1036.70
=$1,398.35
If a discount of 20% off the retail price of a desk saves mark$45 how much did he pay for the desk?
Answer:
$180
Step-by-step explanation:
what is 45 20% of? This is what we need to find! To do this we have to take 45 and divide it by .2 which will give us 225. To check that this is the answer we take 45 and divide it by 225. This brings us back to 20%. He wouldve paid $225 for the desk, but there was a $45 discount, and after subtracting the discount we are left with $180
a box has a square base of side 9cm. calculate the volume of the box if it is 10cm high
Answer:
810 cubic centimetres
Step-by-step explanation:
If the box has a square base, the length and breadth of the box are the same. In this case, it's 9cm
The formula for the area of a rectangular prism is
A = lbh
where
l = length
b = breadth
h = height
Therefore the area is 9x9x10 = 810cm³
Answer:
V = 810 cm³
Step-by-step explanation:
V = Ab × h
Ab = s² = (9cm)² = 81 cm²
V = 81cm²×10cm = 810 cm³
Find the lateral area of this cone
Work Shown:
r = 3 is the radius
h = 3 is the height
LA = lateral area of the cone
LA = pi*r*sqrt(r^2 + h^2)
LA = pi*3*sqrt(3^2+3^2)
LA = pi*3*sqrt(18)
LA = pi*3*3*sqrt(2)
LA = 9*sqrt(2)*pi .... exact area in terms of pi
LA = 39.9859464434252 ... approximate area
LA = 40.0 ......... rounding to nearest tenth
I used my calculator's stored version of pi to get the approximate answer.
Note how the slant height L = sqrt(r^2+h^2) which can be shown through the pythagorean theorem.
George is designing ledges for the octagonal ( 8 side ) gazebo. All sides are equal length, and each ledge much be 18 inches shorter then the sides.
a: what is the minimum length of wood he should purchase if the perimeter of the gazebo is 64 feet ?
b : what as your solution process
Answer:
78 inches or 174 inches (see explanation)
Step-by-step explanation:
If the perimeter is 64 feet, that means that each side is 8 feet, since there are 8 sides (64/8=8). 8 feet is 96 inches (8*12=96). 96-18=78, so the minimum length of wood he needs for the ledges is 78 inches, assuming you're not counting the wood for the perimeter, too (in which case it would be 174 inches) (78+96=174). Hope this helps!
Papa Bear ate 1/2 of a pie. Mama Benr ate 1/2 of what was left Baby Bear ate 1/2 of what
was left after Mama Bear finished.
3) What fractional part of the pie did Mama Bear eat?
4) What fractional part of the pie was left for Goldilocks?
Answer:
1/4 was eaten by mama and Baby also ate 1/4
Step-by-step explanation:
goldilocks got 0/4
if papa ate half and baby and mama each ate 1/4 they equal up to 2/4 which is 1/2
papa ate 1/2 and 1/2+1/2=1
Mama bear ate (1/4)a part of pie and the (1/8) fractional part was left for Goldilocks.
What is the fraction?The fraction is a rational number that simply divides two numbers and is written in the form a/b where a is called the numerator and b is called the denominator.
Let the full part of the pie is a.
Papa bear ate 1/2 part of the pie.
Then papa bear ate = (1/2)a
rest of the pie is= a- (1/2)a= (1/2)a
Mama bear ate (1/2) of the rest of the pie.
so mama bear ate = (1/2)(1/2)a= (1/4)a part of pie
rest of pie after mama bear ate = (1/2)a- (1/4)a= (1/4)a
Then baby bear ate (1/2) of the rest of the pie.
so baby bear ate = (1/2)(1/4)a= (1/8)a part of pie
rest of pie after baby bear ate = (1/4)a- (1/8)a= (1/8)
The rest of the part was left for GoldLiocks.
Therefore mama bear ate (1/4)a part of pie and the (1/8) fractional part was left for Goldilocks.
Learn more about fraction
here: https://brainly.com/question/78672
#SPJ2
Tamara walked 3/4 mile in 1/2 hour. Which of the following represents the unit rate that Tamara walked? A. 1/2 mi/h B. 2/3 mi/h C. 3/4 mi/h D. 1 1/2 mi/h Include ALL work please!
Answer:
1 1/2 miles / hour
Step-by-step explanation:
We want distance / time
3/4 miles
---------------
1/2 hour
3/4 ÷ 1/2
Copy dot flip
3/4 * 2/1
3/2
1 1/2 miles / hour
Answer:
D
Step-by-step explanation:
Multiple (3/4) by 2 to find the information for one hour)
6/4 in one hour
3/2 or 1 + 1/2 mi/h
D is the answer
David is making rice for his guests based on a recipe that requires rice, water, and a special blend of spice,
where the rice-to-spice ratio is 15 : 1. He currently has 40 grams of the spice blend, and he can go buy
more if necessary. He wants to make 10 servings, where each serving has 75 grams of rice. Overall, David
spends 4.50 dollars on rice.
How many servings can David make with the current amount of spice he has?
Answer:
8 servings of rice
Step-by-step explanation:
The polynomial function f (x) = 5 x Superscript 5 Baseline + sixteen-fifths x minus 3 is graphed below. On a coordinate plane, point P is shown on the graph of a function. Point P is at (0.6, 0). Which is a potential rational root of f(x) at point P?
Answer:
3/5
Step-by-step explanation:
What divisor is represented by the synthetic division below? x + 5. One factor of x^3+x^2+x+1. If f(-5) = 0, what are all the factors of the function mc022-... -4 and 3. The polynomial function f(x) = 5x5 + 3x - 3 is graphed below. The root at point P maybe 3/5 3.
The potential rational roots are: [tex]\pm 1, \pm \frac{1}{5}, \pm 3,\pm \frac{3}{5}[/tex]
What is the rational root theorem?The rational root theorem is used to determine the possible rational roots of a polynomial function
The equation of the function is given as:
[tex]f(x) = 5x^5 +\frac{16}{5} x -3[/tex]
Considering a polynomial function, f(x).
Such that:
[tex]f(x) = px^n + .......... +q[/tex]
The possible rational roots are:
[tex]Roots =\pm \frac{Factors\ of\ q}{Factors\ of\ p}[/tex]
So, we have:
[tex]Roots =\pm \frac{Factors\ of\ 3}{Factors\ of\ 5}[/tex]
List the factors of 3 and 5
[tex]Roots =\pm \frac{1,3}{1,5}[/tex]
Split
[tex]Roots =\pm \frac{1}{1}, \pm \frac{1}{5}, \pm \frac{3}{1},\pm \frac{3}{5}[/tex]
Simplify
[tex]Roots =\pm 1, \pm \frac{1}{5}, \pm 3,\pm \frac{3}{5}[/tex]
Hence, the potential rational roots are:
[tex]\pm 1, \pm \frac{1}{5}, \pm 3,\pm \frac{3}{5}[/tex]
Read more about potential rational roots at:
https://brainly.com/question/7594092
PLEASE HELP ME WITH THIS QUESTION FOR MATH!!!!!!!!!!!!!!!!!
Answer:
MON = 130°
Step-by-step explanation:
LOM + MON = 180°
In other words
4z + 30° + 8z + 90 = 180°
12z + 120 = 180
60 = 12z
z = 5
5 x 8 = 40 + 90 = 130°
Answer:
∠MON = 130º
Step-by-step explanation:
∠LON = ∠LOM + ∠MON
∠LON = 180º
180 = (4x + 30) + (8x+ 90)
combine like terms
180 = 12 x + 120
60 = 12x
x = 5
plug x into equations.
∠MON = 8(5) + 90
∠MON = 40 + 90
∠MON = 130º
check work:
∠LOM = 4(5) + 30
∠LOM = 20 + 30
∠LOM = 50
∠LON = ∠LOM + ∠MON
180 = 50 + 130
If a= 3 and b= 5, find b/a=
2/5
3/5
05/3
Answer:
05/3
Step-by-step explanation:
5/3 = 1.66
Answer:
5/3
Step-by-step explanation:
a= 3 and b= 5
b/a
5/3
Find the distance between (-5,-6) and (-3,-8 WILL GIVEBRANLIEST TO FIRST PERSON WHO AWNSES WITH EXPLANATION
Answer:
d = √8
d ≈ 2.82843
Step-by-step explanation:
Distance Formula: [tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Simply plug in our coordinates into the distance formula:
[tex]d = \sqrt{(-3 + 5)^2+(-8 + 6)^2}[/tex]
[tex]d = \sqrt{(2)^2+(-2)^2}[/tex]
[tex]d = \sqrt{4+4}[/tex]
[tex]d = \sqrt{8}[/tex]
To find the decimal, simply evaluate the square root:
√8 = 2.82843
Answer:
[tex] \boxed{2 \sqrt{2} \: \: units}[/tex]Step-by-step explanation:
Let the points be A and B
A ( - 5 , - 6 ) ⇒ ( x₁ , y₁ )
B ( -3 , - 8 )⇒( x₂ , y₂ )
Now, let's find the distance between these two points:
AB = [tex] \mathsf{ \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } }[/tex]
Plug the values
⇒[tex] \mathsf{ \sqrt{( - 3 - ( - 5) )^{2} + {( - 8 - ( - 6))}^{2} } }[/tex]
When there is a ( - ) in front of an expression in parentheses, change the sign of each term in the expression
⇒[tex] \mathsf{ \sqrt{ {( - 3 + 5)}^{2} + {( - 8 + 6)}^{2} } }[/tex]
Calculate
⇒[tex] \mathsf{ \sqrt{ {(2)}^{2} + {( - 2)}^{2} } }[/tex]
Evaluate the power
⇒[tex] \mathsf{ \sqrt{4 + 4} }[/tex]
Add the numbers
⇒[tex] \mathsf{\sqrt{8} }[/tex]
Simplify the radical expression
⇒[tex] \mathsf{ \sqrt{2 \times 2 \times 2}} [/tex]
⇒[tex] \mathsf{2 \sqrt{2} }[/tex] units
Hope I helped!
Best regards!
Mr. Jackson took the 8th grade class on
field trip. While taking attendance, he
noticed there were 51 boy and 21 girls on
the trip. Write the ratio of boys to girls, as a
fraction in simplest terms
Answer:
17/7
Step-by-step explanation:
the ratio would be 51/21 then to simplify divide both numbers by 3 to get 17/7
Hi there! :)
Answer:
[tex]\huge\boxed{\frac{17}{7} }[/tex]
Given ratio of 51 boys to 21 girls:
Write as a ratio:
[tex]51 : 21[/tex]
Divide both terms by GCF, or 3:
[tex]\frac{51}{3} : \frac{21}{3}[/tex]
[tex]17 : 7[/tex] or [tex]\frac{17}{7}[/tex]
Therefore, the ratio is 17 boys to 7 girls, or [tex]\boxed {\frac{17}{7}}[/tex]
5. The cost of movie tickets at the
Cinema Verite is 9 dollars for adults
and five dollars for children under 12.
During the Saturday and Sunday
matinees, adults are charged 8 dollars
for admission and children under 12
are charged 4 dollars. At any time at
all, there is a group discount for groups
of 15 or more adults at a cost of 6
dollars per ticket. What is the cost for 2
adults and 3 children during the
Saturday matinee?
a. 27
b. 28
C. 14
d. 32
Answer:
its 28 dude, because it says that adults and children are played more on saturday.(adults on Saturday=$8 and children under 12 are $4
Identify the function:
1 5
2 20
3 80
4 320
Quadratic function
Can't determine
Linear function
Exponential function
Answer:
Linear function
Step-by-step explanation:
5 x 4 = 20
20 x 4 = 80
80 x 4 = 320
The distribution of city championship wins shared by 3 HS girls basketball teams in Clayton, MO is as follows: Rockefeller HS 12, Clayton West 20, Clayton South 7. Rounded to the nearest 10%, approximately what percentage of the total wins does each team have?
Answer:
Rockefeller HS = 31%
Clayton West = 51%
Clayton South = 18%
Step-by-step explanation:
Given the following:
Championship wins shared by 3 basketball teams :
Rockefeller HS = 12
Clayton West = 20
Clayton South = 7
Percentage of total wins each team has :
Total number of wins = (12 + 20 + 7) = 39 wins
Percentage wins :
[(Number of wins per team) / total number of wins)] × 100
Rockefeller HS:
(12 / 39) * 100 = 30.769% = 31%
Clayton West :
(20/39) * 100 = 51.28% = 51%
Clayton South:
(7/39) * 100 = 17.948% = 18%
kinda stuck and would like help
360 is 6/10 of what number
Help! Complete the number pattern so that the numbrr in the blue is larger. Circle the sum of the two nunbers in the adjacent grey smaller circle. Indicate weather the solution is unique.
Answer:
Step-by-step explanation:
how do i circle? i know answer but how to tell you?
The admission fee at a carnival fair is $4.50 for children
and $8.00 for adults. One day, 2200 people attended the fair
and $5050 was collected. How many children and how many
adults attended?
Lets say:
c= number of children
a= number of adults
Answer:
Adult=1,385.71
Children=814.29
Approximately
Adult=1386
Children=814
Step-by-step explanation:
c= number of children
a= number of adults
Admission fee for children=$4.50
Admission fee for adults=$8.00
Total attendees=2200
Total amount realized=$5050
We need two equations to solve the two unknowns
c + a=2200 (1)
4.50c + 8.00a=5,050 (2)
From (1)
c + a=2200
c=2200 - a
Substitute c=2200 - a into (2)
4.50c + 8.00a=5,050
4.50(2200 - a) + 8.00a=5050
9900 - 4.50a +8.00a=5050
Collect like terms
9900-5050= -4.50a+8.00a
4,850=3.5a
Divide both sides by 3.5
1,385.71=a
Substitute a=1,385,71 into (1)
c + a=2200
c+1385.71=2200
c=2200-1385.71
=814.29
c=814.29
1.) Write 7/25 as a percent and decimal.
Answer:
Below
Step-by-step explanation:
● 7/25
Let' write this fraction as a decimal then convert it to a percentage
● 7/25 = 0.28
To get a percentage multiply it by 10
● 0.28 × 100
● 28 %
Answer:
0.28 or 28 percent
Step-by-step explanation:
1)The easiest way to solve this is with a calculator. Just enter in 7/25, and you get 0.28.
2) Now, 0.28 is out of 1, but we also want a percent, so you have to change it to make it out of 100. You do this by multiplying by 100, and to do that you simply move the decimal place 2 places back.
3) You would then get 28, so 28 percent.
Extra) You can also do the part I did with a calculator without, but it is much more time consuming. After you get 0.28, you would go through the steps listed above.
What is the volume of the right triangular prism shown?
Answer:
C. 567yd^3
Step-by-step explanation:
To find the volume of the right triangular prism, it is: 1/2a c h.
In this case, 1/2✖️9✖️6✖️21=567yd^3
So this means that option C is the correct answer.
Hope this helps!
Have a nice day:)
Answer:
567 cu. yard
Step-by-step explanation:
will make it simple and short.
Vol = area of a triangle x length
Vol = (1/2 * 6 * 9 ) * 21
Vol = 567 cu. yard
ASAP At a store you have the option to buy a 12 pack of pop for $5 or a 8 pack for $3. Which is the better deal? 12 pack 8 pack. And can u pls explain how u got the answer
Answer:
The 8 pack is the better deal.
Step-by-step explanation:
To get the answer you do the following:
Find the price of one pack for each;
1/12*5= $0.42( cost of one pack for the 12 pack part)
1/8*3= $0.38( cost of one pack for the 8 pack part)
The answer is that the 8 pack is cheaper .
Find the probability of rolling a die and
getting a 6. Write your answer as a
fraction.
Answer:
1/6
Step-by-step explanation:
there are 6 sides/numbers on a die. 1 roll with a possibility of 6 outcomes.
Answer:
[tex]\frac{1}{6}[/tex]
Step-by-step explanation:
Because there are six possibilities and only one of those possibilities will yield a six, we can find the probability to be [tex]\frac{1}{6}[/tex]
Which expression can be used to find the surface area of the following triangular prism? *picture of triangular prism* Choose 1 answer: (Choice A) 24+24+ 120+160+20024+24+120+160+20024, plus, 24, plus, 120, plus, 160, plus, 200 (Choice B) 24+20024+20024, plus, 200 (Choice C) 24+24+200+120+12024+24+200+120+12024, plus, 24, plus, 200, plus, 120, plus, 120 (Choice D) 48+48+120+160+20048+48+120+160+200
Answer:
A) 24+24+120+160+200
Step-by-step explanation:
The two ends are 24 (1/2bh= 1/2(8*6)).
One side (the back) is 6x20=120
One side (the bottom) is 8x20=160
One side (the top) is 10x20=200
So the equation is 24+24+120+160+200
(CAN SOMEONE PLEASE EXPLAIN JUSTIFICATION) Create diagrams to represent the possible cases for common tangents between two circles. Your diagram can be created using multimedia sources or drawn by hand. They should not be copied and pasted from a website. Explain why your diagrams satisfy the given criteria. No Common Tangents Diagram: Justification:
Answer:
To justify a solution, students will need to be able to use appropriate mathematical language to give reasons for the particular approach used to solve a problem. Any time that a student produces a 'solution' in an attempt to solve a problem, that 'solution' needs to be justified.
Step-by-step explanation:
What is the purpose of central ideas in a text?(1 point) to give additional information about the topic to define the topic to provide an overview of the ideas in the text to explain the most important ideas in the text
Answer:
[tex]\boxed{to\ explain\ the\ most\ important\ ideas\ in\ the\ text}[/tex]
Step-by-step explanation:
The purpose of the central idea is to explain the central/most important ideas in the theme. Central idea provides the explanation of the most important i.e. central ideas of the text. So, the central idea provides the explanation of central ideas of the text as the name indicates.
Answer:
to explain the most important ideas in the text
Step-by-step explanation:
the person above me is corrwct
NEED IT ASAP
Tony is shopping for new tires for his 4-wheel-drive truck. In addition to the price of the tires, there is a 10% sales tax plus a state-mandated $45 fee for disposing of his old tires. If Tony has determined that he will spend less than $559.80 total, then what is the price range he can spend on the tire set?
Sry couldn't find the answer
Three-fourths of the water leaked out of a full aquarium tank. and 15 gallons of
water was left. After the leak was fixed, 10 gallons of water was added to the
aquarium tank.
4) How many gallons of water can the aquarium tank hold when it is full?
5) How full was the aquarium tank after the 10 gallons of water was added?
6) How much more water would have to be added to fill the aquarium tank?
Answer: 4) 60 gallons 5) 25 gallons 6) 35 gallons
Step-by-step explanation:
If three-fourths of the water in the tank leaked out of the full aquarium tank then one-fourths will be left.
so if the leftover was 15 gallons then 1/4 of a number has to equal 15 gallons.
We could represent that by the equation.
1/4 * x = 15
0.25x = 15
x= 60
4) which means the aquarium tank can hold 60 gallons of water when it is full.
5) If 15 gallons of water was left after the leaking and then they added 10 more gallons of water then 15 + 10 = 25 which means the aquarium was 25 gallon full.
6) If they are 25 gallons in the water now and we need to add some amount of water to get to 60 gallons of water then we will subtract 25 from 60 find how much water needs to be added.
So 60 -25 = 35 which means 35 gallons needs to be added.
f(x) = x2 – x-1
What is the average rate of change of f over the interval -1 < x < 1?
Answer:
-2 < x - 1 < 0
Step-by-step explanation:
2x - × - 1 = x -1 -1 < x < 12. -2 < x - 1 < 0
A 40 pound bag of topsoil will
cover a surface area of 12 square
feet.
a. How many pounds of topsoil are
needed to cover a surface area of
480 square feet?
b. How many bags of topsoil must
be purchased to cover a surface
area of 480 square feet?
For number of bags, divide total area by the area 1 bag can cover.
480 / 12 = 40 total bags.
Now for total weight, multiple total bags by weight per bag:
40 bags x 40 pounds = 1,600 total pounds.
A = 40 bags
B = 1,600 pounds
