Answer:
$2,500 was invested in the first account while $7,500 was invested in the second account
Step-by-step explanation:
Here in this question, we want to find the amount which was invested in each of the accounts, given their individual interest rates and the total amount that was accorded as interest from the two investments
Now, since we do not know the amount invested , we shall be representing them with variables.
Let the amount invested in the first account be $x and the amount invested in the second account be $y
Since the total amount invested is $10,000, this means that the summation of both gives $10,000
Mathematically;
x + y = 10,000 ••••••(i)
now for the $x, we have an interest rate of 5%
This mathematically translates to an interest value of 5/100 * x = 5x/100
For the $y, we have an interest rate of 6% and this mathematically translates to a value of 6/100 * y= 6y/100
The addition of both interests, gives 575
Thus mathematically;
5x/100 + 6y/100 = 575
Multiplying through by 100, we have
5x + 6y = 57500 •••••••••(ii)
From 1, we can have x = 10,000-y
let’s substitute this into equation ii
5(10,000-y) + 6y = 57500
50,000-5y + 6y = 57500
50,000 + y = 57500
y = 57500-50,000
y = 7,500
Recall;
x = 10,000-y
so we have;
x = 10,000-7500 = 2,500
Consider the functions. F(x)=(x+1)2-4 and g(x)=-4|x+1| which statement compares the range of the functions?
Answer:
The fourthStep-by-step explanation:
Vertex of f is (-1, -4) so its range is limited to y≥-4
|x+1| is always ≥0 therefore -|x+1| is always ≤0 {4 is insignificant to this - slope doesn't mean in range} so its range is limited to y≤0
Answer:
D
Step-by-step explanation:
i just took the test
Carter bought a bear and paid for a football uniform. The total cost was $38.50. Write and solve an equation to find the cost, x, of buying a bear.
Answer:
Equation:- [tex]x + y = 38.50[/tex]
Solution of x:- [tex]x = 38.50 - y[/tex]
Step-by-step explanation:
Given
Total Purchase = $38.50
Required
Determine the equation for finding the cost of a bear
From the question; we understand that the cost of 1 bear is represented with x
Solving further; by representing the cost of 1 football uniform with y
So;
[tex]1\ bear + 1\ uniform = 38.50[/tex]
Substitute x for 1 bear and y for 1 uniform to give us an equation
[tex]x + y = 38.50[/tex]
Solving for x (Subtract y from both sides)
[tex]x +y - y = 38.50 - y[/tex]
[tex]x = 38.50 - y[/tex]
The equation can't be solved further
Carrie can inspect a case of watches in 5 hours.James can inspect the same case of watches in 3 hours.After working alone for 1 hour,Carrie stops for lunch.After taking a 40 minute lunch break,Carrie and James work together to inspect the remaining watches.How long do Carrie and James work together to complete the job?
Will mark brainlist if it correct and well explained
Answer:
It takes Carrie and James an hour and a half to finish the job.
Step-by-step explanation:
assuming they have to inspect ONE case of watches.
Carrie can inspect 1/5 case in one hour.
James can inspect 1/3 case in one hour.
Carrie worked alone for 1 hour, so she finished 1/5 of a case.
She leaves 4/5 case to finish.
She had lunch.
After that, Carrie and James worked together for x hours to finish the job.
When they work together, the finish 1/5+1/3 = 8/15 case per hour.
So time to finisher the remaining case
Time = 4/5 / (8/15)
= 4/5 * 15/8
= 3/2 hours
= an hour and a half.
URGENT PLEASE HELP
1. Use the rules of divisibility to check which of the following
numbers are multiples of (are divisible by) 2,3,4,5,6, 8, 9 and 10
a) 552
b) 315
c) 620
d) 426
38. Convert 85 to a number in base eight.
O 95 (base eight)
O 105 (hase eight)
O 115 (base eight)
O 125 (base eight)
Answer:
divide the number by 8 and write the remainder like this 10 r 5.Then you get your answer by going through the remainders in an upward direction. So the answer is 125
In a class Vidya ranks 7th from the top. Divya
is 7 ranks ahead of Medha and 3 ranks
behind Vidya. Sushma who is 4th from the
bottom is 32 ranks behind Medha. How many
students are there in the class?
Answer:
52 students
Step-by-step explanation:
From the question above, we have the following information:
a) Vidya ranks 7th from the top.
Mathematically,
Vidya = 7th student
b) Divya 3 ranks behind Vidya.
Divya = Vidya + 3
Hence, Mathematically:
Divya = 7 + 3 = 10
Divya = 10th student
c) Also, Divya is 7 ranks ahead of Medha.
Mathematically,
Medha = 10 + 7= 17
Medha= 17th student
d)Sushma is 32 ranks behind Medha
Mathematically,
Sushma = Medha + 32
= 17 + 32 = 49
Sushma is the 49th student
Therefore, since, Sushma is 4th from the bottom, total number of students is:
49 + 3 = 52 students
On a coordinate plane, a graph shows Street on the x-axis and Avenue on the y-axis. A line is drawn from Tia to Lei. Tia is at (4, 8) and Lei is at (12, 20). Tia lives at the corner of 4th Street and 8th Avenue. Lei lives at the corner of 12th Street and 20th Avenue. The fruit market is Three-fourths the distance from Tia’s home to Lei's home.
Answer:
(10, 17)
Step-by-step explanation:
It might be easier to explain with a picture or drawing, but I am new to this, so I would try using words.
Assuming the fruit market is on that straight line from Tia's home to Lei's, So we look at both address (coordinates)
From Tia to Lei, x coordinate is from 4 to 12, that's increased by 8, divide by 4, one step is 2.
y coordinate is from 8 to 20, an increase of 12, divide by 4 again, one step is 3.
The fruit market is at 3/4 distance, so 3 steps, on both x and y coordinates.
x: 4+6 = 10
y: 8+9=17
The fruit market is at point (10,17)
What is graph?
A graph can be defined as a pictorial representation or a diagram that represents data or values.
The point (x,y) which divides the segment AB with endpoints at A(x₁,y₁) and B(x₂,y₂) in ratio m:n has cordinates
[tex]x= \dfrac{nx_1+nx_2}{m+n}[/tex]
[tex]y= \dfrac{ny_1+ny_2}{m+n}[/tex]
Tia is at P(4, 8) and Lei is at Q(12, 20).
The fruit market (F) is three-fourths the distance from Tia’s home to Lei's home, then PM : PQ = 3:4 or PM : MQ = 3:1
So,
[tex]x= \dfrac{1.4+3.12}{3+1} = \dfrac{4+36}{4} = \dfrac{40}{4} = 10 \\y= \dfrac{1.8+3.20}{3+1} = \dfrac{8+60}{4} = \dfrac{68}{4} = 17[/tex]
Hence, the fruit market is at point (10,17) which means it is placed at the corner of 10th Street and 17th Avenue.
Learn more about graph here:
brainly.com/question/16608196
#SPJ5
Find the perimeter of a square with a diagonal of 15√2.
Answer:
15
Step-by-step explanation:
Answer:
21.213
Step-by-step explanation:
If point Q is reflected across x = 1, what are the coordinates of its reflection image?
Answer:
(-1, -2) last answer
Step-by-step explanation:
x = 1 is a vertical line
Answer:
(-1, -2)
Step-by-step explanation:
This is because the x-coordinate goes 2 units left to the line x = 1 and the y-coordinate remains the same.
The surface area of a solid is 10 square feet. The dimensions of a similar solid are
three times as great as the first. The surface area of the new solid in square feet
is...
PLEASE urgent
Answer:
90 ft²
Step-by-step explanation:
Given the sides of similar figures in the ratio a : b, then
ratio of areas = a² : b²
Here ratio of sides = 1 : 3 , thus
ratio of areas = 1² : 3² = 1 : 9
That is the surface area of the new solid is 9 times the first
SA = 9 × 10 = 90 ft²
The total surface area of the new solid in square feet is 90 square feet
Let the solid be a cube.
The surface area of a cube = 6L²
L is the length o the cube;
If the surface area of a solid is 10 square feet, then;
10 = 6L²
L² = 10/6
L = √10/6
If the dimensions of a similar solid are three times as great as the first, then;
New length Ln = 3√10/6
Total surface area of the new solid = 6Ln²
Total surface area of the new solid = 6(3√10/6)²
Total surface area of the new solid = 6(9*10/6)
Total surface area of the new solid = 6(90/6)
Total surface area of the new solid = 90 square feet
This shows that the total surface area of the new solid in square feet is 90 square feet
Learn more here: https://brainly.com/question/23756628
Graph [tex]y=\frac{2}{3} x[/tex] Which of the following statements are true?
Answer:
A,C,D
Step-by-step explanation:
When b=0, there is a proportional relationship.
The slope in y=mx+b is the value next to x.
Using RISE/RUN when there is a change of 3 units in x, there is a change of 2 units in y.
BRAINLIEST, 5 STARS, THANKS AND 100 POINTS IF ANSWERED BOTH CORRECTLY. --------------------- Which function rule describes the pattern in the table? X: -2, -1, 0, 1, 2 Y: 3, 2, 1, 0, -1 A) y = x + 1 B) y = x - 1 C) y = -x + 1 D) y = -x - 1 --------------------- Which function rule describes the pattern in the table? X: -2, -1, 0, 1, 2 Y: 14, 11, 8, 5, 2 A) y = 3x + 8 B) y = -3x - 8 C) y = 3x - 8 D) y = -3x + 8 -------------------- Thank you if you answered both correctly!
Answer:
1: C) y = -x + 1
2: D) y = -3x + 8
Step-by-step explanation:
Well number 1,
c is the correct option because,
-2 -> 2
2+1 - 3
This rule applies for all the x values.
2,
X: -2, -1, 0, 1, 2
Y: 14, 11, 8, 5, 2
d is the correct option because -3*-2 is 6 + 8 = 14.
this rule applies for all x values.
Thus,
the answers are C and D.
Hope this helps :)
Your math teacher caught you text messaging in class, again, so the teacher is making you give a presentation to your math class next week. Your assignment is to analyze the scatter plot that shows people's ages and the number of text messages sent in a day. In 3-5 sentences, explain what you see in the scatter plot below.
Answer: If a scatterplot is included in the assignment
The dots plotted on the graph might closely follow the graph of exponential decline. There is a large number of texts per day by 19-20-21 year-olds, but the number seems to decline exponentially as age increases. With a little work, it may be possible to plot the curve and write an equation to model the decline.
Step-by-step explanation: Look at some graphs of exponential decay. Also consider harmonic and hyperbolic decay. The trend in the data is evident. The main challenge is to look at the data and create an equation that models it.
Please please help me
Answer:
A = 189 cm²Step-by-step explanation:
The area of a parallelogram is equal to the product of the length of its side and the height of the parallelogram perpendicular to that side.
H = 9 cm
S = 21 cm
A = S•H = 21 cm • 9 cm = 189 cm²
Choose the equivalent system of linear equations that will produce the same solution as the one given below 4x-y=-11 2x+3y=5
Answer: x = -2 , y = 3
Step-by-step explanation:
4x-y=-11
2x+3y=5
Solve 4x-y=-11 for y
Add -4x to both sides
4x-y+-4x=-11+-4x
-y=-4x-11
Divide both sides by -1
-y/-1=-4x-11/-1
y=4x+11
Substitute 4x+11 for y in 2x +3y=5
2x+3y=5
2x+3(4x+11)=5
Simplify both sides of the equation
14x+33=5
Add -33 to both sides
14x+33+-33=5+-33
14x=-28
Divide both sides by 14
14x/14=-28/14
x=-2
Substitute -2 for x in y= 4x+11
y=4x+11
y=(4)(-2)+11
Simplify both sides of the equation
y=3
If approximately 10% of people are left-handed, how many lefties would you expect in a high school graduating class of 424
Answer:
42
Step-by-step explanation:
P(left) = 0.10
Expected number of lefties among high school grads of 424
= 424 * 0.10
= 42 (to the nearest person)
Answer:
you do 20% of 424
1 0% of 424 =42.4
you could round it to 42
The sum of ages Afful and Naomi is 34. In 5 years time , Afful will be 2 times the age on Naomi now. How old are they now.
Answer:
Afful is 21 and Naomi is 13.
Step-by-step explanation:
Let [tex]A[/tex] represent the age of Afful and [tex]N[/tex] represent the age of Naomi.
The sum of their ages is 34. In other words:
[tex]A+N=34[/tex]
In 5 years time, Afful will be two times the age of Naomi now. In other words:
[tex]A+5=2N[/tex]
Solve for the system. Substitute.
[tex]A+N=34\\A=34-N\\34-N+5=2N\\39=3N\\N=13\\\\A=34-N\\A=34-(13)\\A=21[/tex]
Afful is currently 21 and Noami is currently 13.
Answer:
Naomi=x
Afful=2x
In 5 years time= +5
So Naomi=x+5
and and Afful=2x+5
=x+5+2x+5=34
=3x+10=34
Subtract 10 on both sides
3x=24
Divide 3 on both sides
X=8
Check:
X=8
Naomi=16
In 5 years
=16+5=21
Naomi=8+5=13
13+21=34
Hope this helps
Step-by-step explanation:
At a central train station, there are 4 different train routes with trains that leave every 6 minutes, 10 minutes, 12 minutes, and 15 minutes. If each train can hold up to 200 passengers, what is the maximum number of passengers who can leave the station on a train in one hour?
Answer:
5,000 passengers
Step-by-step explanation:
1. Find out how many trains leave each hour.
6 min – 60/6 = 10 x 200 passengers = 2000
10 min – 60/10 = 6 x 200 passengers = 1200
12 min – 60/12 = 5 x 200 passengers = 1000
15 min – 60/15 = 4 x 200 passengers = 800
2. Add it all up.
2000 + 1200 + 1000 + 800 = 5000 passengers
Answer:
5000
Step-by-step explanation:
6 minute train leaves 10 times
10 x 200 = 2000 passengers
10 minute train leaves 6 times
6x200 = 1200
12 minute train leaves 5 times
5x200 =1000
15 minute train leaves 4 times
4x200 =800
2000+1200+1000+800=5000
assuming more than 1 train can be at the station at once
Use the rationalized expression from the previous question to
calculate the time, in seconds, that the cliff diver is in free fall.
Assume the acceleration due to gravity, a, is -9.8 m/s2, and the
dive distance, d, is -35 m. The negative numbers indicate the
direction is downward. Round the answer to two decimal places.
Answer:
Time taken (t) = 2.67 s (Approx)
Step-by-step explanation:
Find:
Time taken (t)
Given:
Initial velocity (u) = 0 m/s
Acceleration due to gravity(a) = -9.8 m/s²
Distance (d) = -35 m
Computation:
Using 2nd equation of motion,
d = ut + (1/2)at²
-35 = (0)t + (1/2)(-9.8)t²
-35 = -4.9 (t²)
t² = 7.1428
t = 2.6726
Time taken (t) = 2.67 s (Approx)
The perimeter of a rectangle is 141 feet, and the length is twice the width. What are the dimensions ?
Answer:
The width is 23.5 ft and the length is 47 ft
Step-by-step explanation:
The perimeter of a rectangle is given by
P = 2(l+w)
141 = 2(l+w)
The length is twice the width
l = 2w
141 = 2 ( 2w+w)
141 = 2( 3w)
141 = 6w
Divide each side by 6
141/6 = 6w/6
23.5 = w
l = 2w = 2(23.5) = 47
The width is 23.5 ft and the length is 47 ft
Answer:
[tex]\boxed{Width = 23.5 \ feet}[/tex]
[tex]\boxed{Length = 47 \ feet}[/tex]
Step-by-step explanation:
Let Length be l and Width be w
Perimeter = 2(Length) + 2(Width)
Condition # 1:
2l+2w = P
=> 2 l + 2 w = 141
Condition # 2:
=> l = 2w
Putting the second equation in the first one
=> 2(2w)+2w = 141
=> 4w + 2w = 141
=> 6w = 141
Dividing both sides by 6
=> Width = 23.5 feet
Given that
=> l = 2w
=> l = 2(23.5)
=> Length = 47 feet
sample of 64 observations is selected from a normal population. The sample mean is 215, and the population standard deviation is 15. Conduct the following test of hypothesis using the 0.025 significance level. H0: μ ≥ 220 H1: μ < 220 Is this a one- or two-tailed test? One-tailed test Two-tailed test
Answer: (upside down fancy u) q5
Step-by-step explanation:
Simply apply the law of conservative (upside down fancy u)
An electronics company designed a cardboard box for its new line of air purifiers. The figure shows the dimensions of the box.
The amount of cardboard required to make one box is___square inches.
a)130
b)111
c)109
d)84
Answer:
130
Step-by-step explanation:
just did test on plato/edmentum..it was correct
84 (the answer above) is incorrect
Answer:
Hi sorry for late respond but the answer in 130!!
Step-by-step explanation:
What does the denominator of the fraction \dfrac23 3 2 start fraction, 2, divided by, 3, end fraction mean?
Answer: It represents that 2 will be divided into 3 equal parts.
Step-by-step explanation:
Numerator is the top number in a fraction. It represents the total item it has to divide.Denominator is the bottom number in a fraction. it represents the number of equal parts the item is divided into.The given fraction : [tex]\dfrac{2}{3}[/tex]
here, Numerator = 2
Denominator = 3
It represents that 2 will be divided into 3 equal parts.
Please answer in two minutes
Answer:
Toa
48/55
Step-by-step explanation:
O/A
48/55
Eiko is wearing a magic ring that increases the power of her healing spell by 30\%30%30, percent. Without the ring, her healing spell restores HHH health points. Which of the following expressions could represent how many health points the spell restores when Eiko is wearing the magic ring?
Answer:
Options B: and C:
Step-by-step explanation:
Remember that 30% in fraction form is
The amount of health points (H) restored would depend on the amount of the current H so it means it would add 30% of the current which we can write as:
And since it would add that to the current total we can right the current total as:
So our equation would be:
For option B:
We can factor out the H and you will be left with:
Combine or add the fractions inside the parenthesis and you will have:
For option C:
We can simplify the fractions which will result in:
Then factor out the H and you will have:
Options B: and C:
Step-by-step explanation:
Remember that 30% in fraction form is
The amount of health points (H) restored would depend on the amount of the current H so it means it would add 30% of the current which we can write as:
And since it would add that to the current total we can right the current total as:
So our equation would be:
For option B:
We can factor out the H and you will be left with:
Combine or add the fractions inside the parenthesis and you will have:
For option C:
We can simplify the fractions which will result in:
Then factor out the H and you will have:
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
The ratio of Ed's toy cars to Pete's toy cars was initially 5:2. After Ed gave 30 toy cars to Pete, they each had an equal number of cars. How many toy cars did they have altogether?
Answer:
140 toy cars
Step-by-step explanation:
The ratio of Ed's toy car to Pete's toy car is initially given as 5:2
Ed gave Pete a total number of 30 cars
Let x represent the greatest common factor that exists between both number
Number of Ed's car is represented as 5x
Number of Pete car is represented as 2x
Since they each have an equal number of cars which is 30 then we can solve for x as follows
5x-30=2x+30
Collect the like terms
5x-2x= 30+30
3x= 60
Divide both sides by the coefficient of x which is 3
3x/3=60/3
x=20
Ed's car is 5x, we substitute 20 for x
5(20)
= 100 cars
Pete car is 2x,we substitute 20 for x
2(20)
= 40 cars
Therefore, the total number of cars can be calculated as follows
= 100+40
= 140 toy cars
Hence they have 140 toy cars altogether
Answer:
140
Step-by-step explanation:
Please help me with this question!! TRIGONOMETRY
Work Shown:
sin(angle) = opposite/hypotenuse
sin(35) = 10/x
x*sin(35) = 10
x = 10/sin(35)
x = 17.434467956211 make sure your calculator is in degree mode
x = 17.4
Answer:
[tex]\boxed{17.4}[/tex]
Step-by-step explanation:
sin [tex]\theta[/tex] = [tex]\frac{opposite}{hypotenuse}[/tex]
sin (35) = [tex]\frac{10}{x}[/tex]
x = [tex]\frac{10}{sin(35)}[/tex]
x = 17.4344679562...
x ≈ 17.4
hellpp plzzzzz.......
Answer:
120Step-by-step explanation:
Given
u = 14 , a = 8 , t = 4
Now, let's find the value of s
[tex]s = ut + \frac{1}{2} a {t}^{2} [/tex]
plug the values
[tex] = 14 \times 4 + \frac{1}{2} \times 8 \times {4}^{2} [/tex]
Reduce the numbers with G.C.F 2
[tex] = 14 \times 4 + 4 \times {4}^{2} [/tex]
Multiply the numbers
[tex] = 56 + 4 \times {4}^{2} [/tex]
Calculate the product
[tex] = 56 + {4}^{3} [/tex]
Evaluate the power
[tex] = 56 + 64[/tex]
Add the numbers
[tex] = 120[/tex]
Hope this helps..
best regards!!
HELLLPPPP I need a explication on whether or not these angle relationships are possible
Answer:
Step-by-step explanation:
5x+30 is a corresponding angle with 4x-9 so set them equal to each other. 4x-9+2x+3 will equal 180
Answer:
no, the values would be above 180º
Step-by-step explanation:
if...
(4x - 9) + (2x + 3) + y = 180
(5x + 30) + y = 180
then...
(4x - 9) + (2x + 3) = 5x + 30
so...
6x - 6 = 5x + 30
x = 36
plug it in.
4(36) - 9 = 135
2(36) + 3 = 75
already you can see the sum of these two angles surpasses 180 which is not possible for a triangle.
What is the maximum value of the function
Answer:
[tex]10[/tex]
Step-by-step explanation:
[tex]f(x)=-x^2+6x+1[/tex]
x coordinate:
[tex]\frac{-b}{2a}[/tex]
[tex]a=-1\\b=6[/tex]
[tex]\frac{-6}{2(-1)} \\\frac{-6}{-2}\\ =3[/tex]
y-coordinate:
[tex]f(3)=-(3)^2+6(3)+1\\f(3)=-9+18+1\\f(3)=10[/tex]
Answer:
10
Step-by-step explanation: