Answer:
3300 was on 3% and 6700 on 2,5%
Step-by-step explanation:
We can say that 'a' represents the price that will go on 3% interest and 'b' 2,5% interest.
Therefore;
a + b = 10 000
And
0,03a + 0,025b = 283.5 (0,03 means 3% etc)
You can move 'b' to the other side to leave 'a' on the LHS
0,03a = 283.5 - 0,025b - - > (divide both sides by 0,03)
a=9450 - 0,8333b
Substitute this equation as 'a' in the first equation to get:
9450 - 0,8333b + b = 10 000 (move 9450 to the RHS to leave values with b on the LHS)
-0,8333b + b = 10 000 - 9450
0,1666b = 550 (divide both sides by 0,1666)
b = 3,300
Therefore 'a' will be :
a= 10 000 - 3 300
a = 6700
I hope this helps.
After solving the system of equations, the amount in the account with 3% interest was $844.50 and the amount in the account with 2.5% interest was $9155.50 after one year.
Explanation:Let's assume the amount invested at 3% interest is x and the amount invested at 2.5% interest is y. We can set up the following system of equations:
x + y = 10000 (equation 1)
0.03x + 0.025y = 283.50 (equation 2)
Multiply equation 1 by 0.03 and equation 2 by 100 to eliminate decimals:
0.03x + 0.03y = 300 (equation 3)
3x + 2.5y = 28350 (equation 4)
Now, subtract equation 3 from equation 4:
3x + 2.5y - 0.03x - 0.03y = 28350 - 300
Simplify:
2.97x + 2.47y = 28050 (equation 5)
Multiply equation 1 by 2.47 and equation 2 by -2.97 to eliminate y:
2.47x + 2.47y = 24700 (equation 6)
-2.97x - 2.97y = -842.25 (equation 7)
Add equation 6 and equation 7:
2.47x + 2.47y - 2.97x - 2.97y = 24700 - 842.25
Simplify:
-0.5x = -422.25
Divide both sides by -0.5:
x = 844.50
Substitute the value of x back into equation 1:
844.50 + y = 10000
Subtract 844.50 from both sides:
y = 9155.50
Therefore, there was $844.50 in the account with 3% interest and $9155.50 in the account with 2.5% interest after one year passed.
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(1) 1 (3) 3
(2) -2 (4) 7
Answer:
-38
Step-by-step explanation:
What is the exact circumference of the circle?
Answer:
50.24
Step-by-step explanation:
Take the diameter and multiply by 3.14 so 16 times 3.14
Answer:
State that the circunference of a circle is equal to:
[tex]C=\pi d[/tex], where C is the circumference and d is the diameter
So, once d = 16 in
Therefore, [tex]C=16\pi[/tex] in
Compare √42 and √58 plotted on the number line. What is the approximate difference in tenths between the two values? A number line going from 6 to 10. StartRoot 42 EndRoot is plotted between 6 and 7, and StartRoot 58 EndRoot is plotted between 7 and 8. StartRoot 58 EndRoot is about greater than StartRoot 42 EndRoot.
Answer:
11/10
Step-by-step explanation:
Your calculator will tell you that √58 ≈ 7.62 and √42 ≈ 6.48. The difference of these numbers is ...
7.62 -6.48 = 1.14 ≈ 1.1
The difference is about 11 tenths.
_____
You should be able to count the divisions on the number line to arrive at this conclusion.
⇒ 1.2 is your answer.
Jim bought 4 apples. Hank bought four times as many as Jim. How many apples did they buy total? A) 16 B) 18 C) 20 D) 24
Answer:
A
Step-by-step explanation:
4x4 = 16
Answer:
A
Step-by-step explanation:
there are 25 acres of land on a farm. the owners planted corn on 68 percent of the land. on how many acres did they not plant corn?
Answer:
8 acres of land they did not plant the corn.
Step-by-step explanation:
GIven:
There are 25 acres of land on a farm.
The owners planted corn on 68 percent of the land.
Now, to find the acres they did not plant the corn.
Total acres of land on the farm = 25 acres.
Rate of land owners planted the corn = 68%.
Now, to get the acres of land owners planted the corn:
[tex]68\%\ of\ 25\\\\=\frac{68}{100} \times 25\\\\=0.68\times 25\\\\=17\ acres.[/tex]
Thus, 3.4 acres of land owners planted the corn.
Now, to get the acres land owners did not planted the corn we subtract the acres of land owners planted the corn from the total acres of land:
[tex]25\ acres-17\ acres\\\\=8\ acres.[/tex]
Therefore, 8 acres of land they did not plant the corn.
You conduct an inventory for a hardware store and count 40 rolls of duct tape. Your manager wants to keep 7 boxes of duct tape in stock. If each holds 8 rolls of duck tape, how many boxes should you order? Justify your answer.
Answer: 2 boxes
Step-by-step explanation: first realize that 7 times 8 is 56 so the manager wants 56 rolls in stock and you only have 40
then subtract 56 - 40 = 16 and this means you need 16 rolls
remember that there is 8 rolls in a box and 16 divided by 8 is 2 so 2 boxes should be ordered
hope this helps mark me brainliest if it did
PLEASEE HELP I WILL MARK BRAINLIEST
Answer:
What do I help with?
Step-by-step explanation:
IF you put a picture we cannot see it/ At least I cannot see it.
From a standard deck of 52 cards, what is the
probability of drawing one card that is either a
heart or a 2?
Answer:
32.692307692308%
Step-by-step explanation:
Let's go over the facts we know:
- There are 13 hearts in a deck of cards, 2 through ace
- There are 4 "2's" in a deck of cards, one for each suit
- There are 52 cards in a standard deck
The first step is to find the ratio.
Add the 13 hearts to the 4 "2's" to get the amount of cards to be drawn.
13 + 4 = 17.
Based on this, we know the ratio of hearts and "2's" to total cards is 17:52.
In other words, there is a 17 out of 52 chance that the card drawn will be a heart or a 2.
Now, we need to convert it to a percentage. To do so, divide 100 by 52. We get 1.92307692308. Now, multiply both 52 and 17 by 1.92307692308, and put the product with 17 as the numerator of the fraction and the product with 52 as the denominator. We get 32.692307692308/100. As a percent, this is written as 32.692307692308%
Therefore, the final answer is 32.692307692308%.
Joseph is traveling on a road trip. The distance, d, he travels before stopping for lunch varies directly with the speed, v, he travels. He can travel 120 miles at a speed of 60 mph.
Write the equation that relates d and v.
How far would he travel before stopping for lunch at a rate of 65 mph?
d = kv
Substitute the 60 and 120 in.
120 = k * 60
k = 2
So, d = 2v
If v is 65, what is d?
2 * 65 = 130 miles
Final answer:
The distance Joseph travels before stopping for lunch varies directly with his speed. The equation that relates distance, d, and speed, v, is d = 2v. At a speed of 65 mph, Joseph would travel 130 miles before stopping for lunch.
Explanation:
Joseph's road trip scenario involves a direct variation between the distance traveled, d, and the speed, v, at which he travels. Since we know that he travels 120 miles at a speed of 60 mph, we can write the equation of direct variation as d = kv, where k is the constant of variation.
To find the value of k, we use the information given: d = 120 miles when v = 60 mph. So, we have 120 = k ×60.
To find k, we divide both sides by 60: k = 120 / 60 = 2. This tells us that the distance traveled varies with twice the speed. Thus, the equation relating d and v is d = 2v.
To determine how far Joseph would travel before stopping for lunch at a rate of 65 mph, we substitute v with 65 into the equation: d = 2 ×65, which calculates to d = 130 miles.
Please help me solve this question.
Answer:
21
Step-by-step explanation:
5×3=15
7×3=21
Answer:
Step-by-step explanation:
a) The denominators of variable terms is 5 and 3
As both are prime, least common denominator = 5*3 = 15
b) The denominators of constant terms is 7 and 3
Least common denominator = 7*3 = 21
Please help ! And explain if u can
Answer:
Scalene Triangle
Step-by-step explanation:
If you mark the points on the graph, all three sides have different lengths and angles, therefor it is a scalene triangle.
It cannot be a right triangke bc there is no right angle, and no obtuse either so that crosses out obtuse as an option as well. In order to be an isoceles triangle it must have two sides of equal length, but it does not.
Please help me *20 points*
Answer:
36
Step-by-step explanation:
Frequency of less than 4:
6 + 4 + 8 = 18
Probability:
18/50 × 100 = 36%
A shop sells a party hat at x dollars and a mask at y dollars. On a particular morning, 3 hats and 4 masks were sold for $27. In the afternoon, 3 hats and 6 masks were sold for $33. Find the cost of each hat and each mask.
Answer:
Cost of each hat: $5
Cost of each mask: $3
Step-by-step explanation:
Let be "x" the cost in dollars of a party hat and "y" the cost in dollars of a mask.
Set up a System of equations using the information given in the exercise:
[tex]\left \{ {{3x+4y=27} \atop {3x+6y=33}} \right.[/tex]
You can use the Elimination Method to solve this System of equations:
1. You can multiply the first equation by -1.
2. Then you must add the equations.
3. Solve for "y".
Then:
[tex]\left \{ {{-3x-4y=-27} \atop {3x+6y=33}} \right.\\.....................\\2y=6\\\\y=\frac{6}{2}\\\\y=3[/tex]
4. Now you can substitute the value of "y" into any original equation.
5. Finally, solve for "x" in order to find its value.
Then:
[tex]3x+4(3)=27\\\\3x=27-12\\\\x=\frac{15}{3}\\\\x=5[/tex]
8) Zeke lives 30 miles from his aunt, Zelda, and is riding his bike home from her house
Interpret the graph to tell a story about what could have happened on his ride home.
Without the graph, we can speculate that it's a distance-time graph and could show how Zeke moved at different speeds, when he stopped or got lost, and when he arrived home, based on changes in the line over time.
Explanation:Without the specific characteristics of the given graph, we can speculate using a generic distance-time graph. Let's say the 'y' axis represents the
distance
(in miles) from Zeke's home, and the 'x' axis represents time. At the start, Zeke is 30 miles away from home (top of the graph). If the line on the graph descends steeply, it means Zeke is going at a faster speed. A flat line would indicate Zeke has stopped or is not moving towards home, perhaps taking a rest. Sharp downward spikes could indicate periods where Zeke raced home at high
speeds
. If the line ascends, it could mean Zeke had to backtrack or got lost. The point at which the line reaches the bottom of the 'y' axis would be when Zeke arrives home. Making sense of a graph involves understanding its axes, the initial conditions and the interpretation of the changes in the line over time.
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help on this ASAP IF FOR TODAY
Answer:
tangent line : UQ
secant line: line UR
chord: US
diameter: UW
2) OD= 4.8
3)x =7 SV=6
Step-by-step explanation:
tangent line : A tangent to a circle is a straight line which touches the circle at only one point
secant:A secant is a line that intersects a circle in exactly two points
diameter: diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle
Find the value of y= 3x - 2 for x=-2
Step-by-step explanation:
Given
x = -2
Now
y = 3x - 2
= 3 * (-2 )-2
= -6 - 2
= -8
PLEASE ANSWER FIRST GETS BRAINLIEST
Answer:
The slope of the line on this graph is 1/2.
Step-by-step explanation:
From (-4, 0), go up 2 units to (-4, 2), then go right 4 units to (0, 2). So the slope of this line is 2/4 = 1/2.
Jim and Bill each invest $15,000 into savings accounts that earn 3.5% interest. Jim's account earns simple interest and Bill's account earns compound interest. After 25 years, who will earn more interest and how much more will he earn?
Answer:
Bill will earn more interest
He will earn $ 20,448.67 from his investment
Step-by-step explanations
Firstly let us calculate Jim's earnings based on simple interest
A = P(1 + rt)
Calculation:
First, converting R percent to r
a decimal
r = R/100 = 3.5%/100 = 0.035 per year.
Solving our equation:
A = 15000(1 + (0.035 × 25)) = 28125
A = $28,125.00
The total amount accrued, principal plus interest, from simple interest on a principal of $15,000.00 at a rate of 3.5% per year for 25 years is $28,125.00 for Jim
Now let's us calculate bill's investment based on compound interest
Equation
A = P(1 + r)^t
A=15000(1+0.035)^25
A=15000(1.035)^25
A=15000*2.36324498427
A = $ 35,448.67
We see that Bill will earn
$ 20,448.67 from his investment
What are the zeros of f(x) = x2 + x - 12?
O A. x= -4 and x = 3
O B. x=-6 and x = 2
O c. x=-2 and x = 6
D. x = -3 and x = 4
Answer:
Ans- A
Step-by-step explanation:
When you have a quadratic like this, f(x) = [tex]x^{2}[/tex] + x - 12,
factorize it first.
Then you'll get f(x)= (x-3)*(x+4)
Finally, you set:
0= (x-3)*(x+4)
Just use the null factor law, and there you go.
x= 3 or x=-4
Have a nice day :)
The zeros of the given quadratic equation is equivalent to 3 and -4. Option A
Determining the zeros of a quadratic equationGiven the quadratic equation below:
f(x) = x² + x - 12
Factorising the expression, we will have:
f(x) = x² + 4x - 3x - 12
Factor
f(x) = (x² + 4x) - (3x + 12)
f(x) = x(x+4) - 3(x + 4)
f(x) = (x - 3)(x+4)
If f(x) = 0
(x - 3)(x+4) = 0
x = 3 and -4
Hence the zeros of f(x) = x^2 + x - 12 are 3 and -4.
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Please help with finding probability
Evaluate the expression.
StartFraction 9 factorial Over 3 factorial EndFraction
Answer:
The answer you should get is 9:3
Step-by-step explanation:
Answer:
The answer is C
Step-by-step explanation:
I just did it and got it right.
Timothy gathered data on student ages and shoe sizes to see if there is a relationship between the two.
Which data display should Timothy use?
histogram
box plot
dot plot
scatter plot
Answer:
The CORRECT answer to this question is a scatterplot.
You're welcome:)
A scatter plot is the best choice of data display for Timothy to find a relationship between the ages of students and their shoe sizes. It shows a possible relationship between two variables, unlike histograms, box plots, and dot plots that display distribution or frequency of a single variable.
Explanation:For Timothy to find if there is a relationship between the ages of students and their shoe sizes, the best choice of data display is a scatter plot. A scatter plot is a type of plot that is used to display values for typically two variables for a set of data. On a scatter plot, both horizontal and vertical axes are value axes that plot numeric data. Thus, it's most suitable for showing a possible relationship between two variables, such as ages and shoe sizes in this case. Other display methods, such as histograms, box plots, and dot plots, are more suitable for displaying distribution or frequency of a single variable rather than a relationship between two variables.
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What’s 1/4+1/3 equal
Answer:
7/12
Step-by-step explanation:
1/4 +1/3
We need to get a common denominator of 12
1/4*3/3 = 3/12
1/3 *4/4 = 4/12
3/12+4/12 = 7/12
Answer:
The answer is 7/12.
Explanation:
1/3 = 4/12
1/4 = 3/12
4 + 3 = 7
according to the fundamental theorem of algebra, how many roots does the following equation have?
Answer:
n
Step-by-step explanation:
While you did not specify the equation, there are n roots for an equation of n power.
i.e. anything that x, power is 1, only one root
For [tex]x^{2}[/tex], there are two roots
For [tex]x^{n}[/tex], there are n roots
Surface Area triangle
Answer:
1/2 base times height
Ana bikes for 5.5 hours. She covers a distance of 57.75 mi. Assuming she bikes at a constant speed, how fast was Ana biking? in ratios of
1-4 and 20
Answer:the answer is D. because if you do 57.75 divided by 5.5 you get 10.5 mi/h
Step-by-step explanation:
Convert 242 dm to feet. Round to 1 decimal.
Answer:
it is 79.4 ft.
Step-by-step explanation:
u just have to round until it gets to one decimal
A student is doing a study on study habits. He needs a random sample of students from every grade level. What is a good way to do this?
A)
He could send a questionnaire to every student in Algebra I.
B)
He could put a questionnaire on all cars in the senior parking lot.
C)
He could send a questionnaire to every student in a senior English class.
D)
He could poll all students in a 9th grade, 10th grade, 11th grade, and 12th grade English class.
Answer: D (He could poll all students in a 9th grade, 10th grade, 11th grade, and 12th grade English class.)
Explanation: It states that he needs a random sample from every grade level.
90°
= 90°. Find the area of the segment.
Circle C has a radius r = 9 and a central angle
A. A segment = 27-2
81 81
B. A segment = "*2
C. Asegment =
D. A segment =
Answer:
D
Step-by-step explanation:
The area of the segment is 81/4π square units.
To find the area of the segment, we need to use the formula for the area of a segment of a circle.
The area of a segment is given by the formula:
A = (θ/360) * π * r^2
where θ is the central angle in degrees, π is approximately 3.14159, and r is the radius of the circle.
Given that the central angle θ is 90° and the radius r is 9, we can plug these values into the formula:
A = (90/360) * π * 9^2
A = (1/4) * π * 81
A = (1/4) * 81π
A = 81/4 * π
So, the area of the segment is 81/4π square units.
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The foot of an extension ladder is 3 ft from a wall. The height that the ladder reaches on the wall and the length of the ladder are consecutive integers. How long is the ladder?
Answer:
The length of the ladder is 5 feet
Step-by-step explanation:
Please kindly check the attached file for explanaion
The ladder is 5 feet long.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles
Given,
Let x = height ladder reaches on wall
Let x+1 = length of the ladder
the three pieces of this form a right triangle
so (x+1)² = x² + 3²
x² +2x + 1 = x² +9
2x = 8
Divide both sides by 2
x=4
so the ladder reaches 4 feet on the wall
x+1 = 5
The ladder is 5 feet long
Hence, the ladder is 5 feet long.
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