According to the given expression, the account's initial deposit is 750, the balance after one year is 845, and the balance after two years is 952.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given, The amount of money in a savings account is modeled by A(x) = 750(1.01)^12x, where x represents number of years.
Expression for money is given
Thus, balance at x = 0
Balance A(0) = 750
Balance at x = 1
Balance A(1) = 750(1.01)^12*1
A(1) = 845.11
Balance at x = 2
Balance A(2) = 750(1.01)^12*2
A(2) = 952.43
Therefore, In the account initial deposit is 750, balance after 1 year is 845, and balance after 2 years will be 952 as per the given expression.
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The cost of 8m water pipe is rupees 256. Find the cost of 6m water pipe
Answer:
The cost of 6 m of water pipe = ₹ 192
Step-by-step explanation:
16^x^2=8^0
16 to the power of x to the power of 2 equals 8 to the power of 0
The exponent x in the equation must be equal to 0.
How to solve the given equation?Here we have the following equation:
16^x^2=8^0
First, notice that any number to the power of zero (except for the number 0) is equal to 1.
a^0 = 1
16^x^2=8^0
16^x^2 = 1
Now, trivially, if we use x = 0 we will get:
c
Particularly, 0^2 = 0
So we can rewrite:
16^0^2 = 1
16^0 = 1
1 = 1
So the solution is x = 1.
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11 pounds = how many kgs
Answer:
4.98952 kgs in 11 pounds
Step-by-step explanation:
First of all, how many kgs are in a pound?
Well 1 pound = 0.453592 kg.
So, to find how many kg are in 11 pounds you would multiply, 0.453592 by 11, which will be...
4.98952 kgs.
Hope this helps!
Simon mixes dried fruits and nuts to make a trail mix that he sells at the farmers market. The dried fruits cost $6 per pound. The nuts cost $2 per pound. It costs Simon $40 to make 12 pounds of trail mix. Which system of equations can be used to find the number of pounds, x, of dried fruits and the number of pounds, y, of nuts that Simon used to make 12 pounds of trail mix?
The system of equations can be used to find the number of pounds, x, of dried fruits and the number of pounds y, of nuts is; 6x + 2y = 40
What is a system of equations?An equation is an expression that shows the relationship between two or more numbers and variables. A system of equations is two or more equations that can be solved to get a unique solution the power of the equation must be in one degree.
We are given that the dried fruits cost $6 per pound
The nuts cost $2 per pound. It costs Simon $40 to make 12 pounds of trail mix.
We need to find the number of pounds, x, of dried fruits and the number of pounds, y, of nuts that Simon used to make 12 pounds of trail mix.
Therefore, the system of equation will be 6x + 2y = 40
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Consider this equation.
tan (0) 5√/11
If is an angle in quadrant III, what is the value of sin(0)?
○ 음
=
0-9/10
05/0
O -
5
6
Therefore , the solution of the given problem of trigonometry comes out to be Sin θ = 5/√34.
What trigonometry is, explained?Trigonometry is a branch of mathematics that studies how square side length The field's initial development took place during the Baroque era, more likely and around third century BC, as a result of the merger of astronomer and geometry studies. Numerous geometric equations and their potential applications to calculations are covered by precise mathematical approaches. Mathematics has six fundamental operations. They are known by a variety of names and abbreviations, including sine, quadrature, parallel, secant, etc (csc). The study of mathematics is focused mostly on the characteristics of right triangles. The ability to understand geometry, however, necessitates familiarity with each polygon's properties.
Here,
Given : Provided: tan = (-5/3)
With the help of the formula below, you may determine the angle's number, which varies at 90 to 180 degrees.
as tan θ = (-5/3)
The value of the perpendicular is 5, and the value of the base is 3.
The hypotenuse is (25 + 9) according to Pythagoras' Theorem.
= √34
The value of sin is (5/34)
=> sin θ = 5 * √34 / 34
=> sin θ = 5/√34
In the second meiotic division, which contains value, sin is positive.
Therefore , the solution of the given problem of trigonometry comes out to be Sin θ = 5/√34.
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Energy usage is measured in kilowatt-hours, kWh. After 7 a.m., energy usage on a university campus increases at a rate of 21% per hour. Prior to 7 a.m., 15,040 kWh have been used. The university's daily goal is to keep its energy usage less than or equal to 100,000 kWh.
Which inequality can be used to determine the number of hours, t, after 7 a.m. when the energy usage on campus will be less than or equal to 100,000?
Inequality becomes 0.21t + 15,040 <= 100,000
Why energy usage is important?Energy consumption remains a principal source of human caused greenhouse gas emissions the predominant cause of climate change.
After 7 a.m., the power usage on a college campus increases at a rate of 21% per hour.
t be the number of hours
the power usage increases at a rate of 21% per hour
21% = 0.21, constant rate = 0.21 . So slope = 0.21
Prior to 7 a.m., 15,040 kWh have been used.
At 7.am , power used = 15,040kWh. so our y intercept is 15,040
We use slope intercept form y= mx+b
slope m = 0.21 and b = 15040
power usage , y = 0.21 t + 15040
The university has a daily goal to keep their power usage less than or equal to 100,000 kWh
Power usage is less than or equal to 100,000
So inequality becomes 0.21t + 15,040 <= 100,000
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Look at the picture and answer the question thank you
Answer:
given that z=3 and w=2
10z+5w
now by putting the values of z and w
10(3) + 5(2)
30 + 10
40 is your correct answer
“solve the equation by graphing. check your solution” only 5 and 6 need to be done!! attach picture with graph please xoxoxo i will mark brainliest if done like said
The solutions for the given equations are x=2 and x=-4
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Fo question 5.
1/2x-2=9-5x
Take the variable terms on one sides\
x/2+5x=11
x+10x=22
11x=22
Divide both sides by 11
x=22/11
x=2
For question 6:
-5+x/4=3x+6
-20+x=12x+24
-20-24=12x-x
-44=11x
x=-4
Hence, the solutions for the given equations are x=2 and x=-4
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Quick Help please
I don’t understand please answer all four
Answer:
1) f(-3)
= 2x + 5
= 2×(-3) +5
= -6+5
= -1
2) g(x)- h(x)
= -3x² + 2x - 6 -(-4 - x)
= -3x² + 2x - 6 + 4 + x
= -3x² + 3x - 2
3) f(x) = h(x)
or, 2x + 5 = -4 - x
or, 2x + x = -4 - 5
or, 3x = -9
or, x = -9/3
or, x = -3
4) i am not sure about the last but the answer is between f(x) and h(x). But i think its f(x).
I NEED HELP USHRVDC S
The missing vertices of the square are B(x, y) = (- 2, 1) and D(x, y) = (6, - 7), respectively.
How to detemine the coordinates of the missing vertices of a square
Squares are quadrilaterals with four sides of equal length and four internal right angles. This kind of quadrilaterals have two diagonals perpendicular to each other. In this case, we know the coordinates of the endpoints of diagonal AC and we need to determine the location of points B and D.
This can be done by means of the following definition: A(x, y) = (a, b), C(x, y) = (c, d), B(x, y) = (a, d), D(x, y) = (c, b). If we know that a = - 2, b = - 7, c = 6 and d = 1, then the location of points B and D are, respectively:
B(x, y) = (- 2, 1), D(x, y) = (6, - 7)
Lastly, we graph the resulting figure.
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please help me !!! thankss
Answer: (6,2) (0,-2) (-3,-4)
Step-by-step explanation:
If you find the other coordinate pair groups on the graph, there is at least one that doesn't land on the line on the graph.
In the top left, (-6,-5) is not on the graph. If it had been (-6,-6) then it would've been correct, but it isn't.
In the bottom left, (0,-3) isn't on the graph. Instead, (0,-2) is.
In the bottom right, (3,-4) isn't on the graph, but (-3,-4) is.
One person takes up about 2.5 square feet of space. Use this value to estimate how many people can fit
in an area that is 250 feet wide and 250 feet long.
Answer:
Step-by-step explanation:
Assuming that the area is a rectangle with no obstructions or furniture, and that the people are standing shoulder-to-shoulder, then the area can fit approximately 200,000 people. This is calculated by multiplying 250 feet by 250 feet to get the total square feet of the area, which is 62,500 (250 x 250 = 62,500). Then divide the total square feet by the amount of space taken up by one person, which is 2.5 square feet, to get the approximate number of people that can fit in the area. 62,500 / 2.5 = 25,000, so 25,000 x 8 = 200,000 people.
Answer:
An area that is 20 feet wide and 25 feet long will be 20*25 = 500 square feet large. Division tells us how many times one number is contained within a number, so to find how many 2.5 square feet large people fit in a 500 square feet large space, we do 500/2.5 = 200 people.
Step-by-step explanation:
Triangles A and B are right-angled.
A
13 cm
5 cm
B
12 cm
12 cm
a) Show that the two shorter sides in triangle A have the
same length as the two shorter sides in triangle B.
Using pythagoras theorem formula, c² = a² +b² We can see that the two shorter sides have the same length which is 5cm
Since all the sides of the triangle are the same, hence the two triangles are congruent.
What is Pythagoras' theorem ?
Pythagoras' theorem is the square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.
The two shorter sides have the same length which is 5cm
Since all the sides of the triangle are the same, hence the two triangles are congruent.
Let the sides of the triangles be a, b and c. According to Pythagoras theorem;
c² = a² +b²
where:
a is the hypotenuse (longest side)
For triangle A:
c = 13
b = 12
Get "a"
13² = 12² +b²
b² = 25
=> b = 5 cm
Similarly for triangle B:
c² = 5² +12² = 169
=> c=13 cm
We can see that the two shorter sides have the same length which is 5cm
Since all the sides of the triangle are the same, hence the two triangles are congruent.
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stock prices used to be quoted using eights of a dollar. Find the total price of the transaction.
200 shares of national semi at 115 1/2
Answer:
Step-by-step explanation:
200 x 115.5/8 = $23,100.00
Find a function of the form y = A sin ( k x ) + C or y = A cos ( k x ) + C whose graph matches the function shown below:
Leave your answer in exact form.
The sine function that matches the graph is given as follows:
y = sin(2πx/7) - 1.
How to define the sine function?The sine function is given as follows:
y = Asin(Bx) + C.
For which the parameters are given as follows:
A: amplitude.B: the period is 2π/B.C: vertical shift.The maximum value is of 0, while the minimum value is of -2, hence the amplitude A is obtained as follows:
2A = 2. (as the difference of the maximum value and the minimum value is of 2).
A = 1.
A sine function with amplitude 1 should oscillate between -1 and 1, while this one oscillates between -2 and 0, hence the vertical shift is given as follows:
C = -1.
The period of the function is of 7 units, hence:
2π/B = 7
7B = 2π
B = 2π/7.
Then the function is defined as follows:
y = sin(2πx/7) - 1.
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Can someone solve these 2 questions and explain since I find these questions confusing
A recipe requires for ⅜ cups of sugar for each cup of flour used. If a baker uses 6 cups of flour, what is the total amount of sugar that will be needed? Show your work. (4.NE.4),
Answer:
3 cuuuuuuuuuuuuuupsssssss offfccccdd saaaaaaaallllytttt
what is the solution of √2x+4 - √x = 2
please show with work done!
Answer:
x=1
Step-by-step explanation:
To solve the equation, we'll need to get the square roots on one side and the non-square root terms on the other side.
First, we'll add √x to both sides to get:
√2x+4 - √x + √x = 2 + √x
√2x+4 = 2 + √x
Next, we'll square both sides to get rid of the square roots:
(√2x+4)^2 = (2 + √x)^2
2x+4 = 4 + 2√x + x
Then, we'll simplify the right side of the equation:
2x+4 = 4 + 2√x + x
2x+4 = 4 + x + 2√x
Now we'll subtract 4 from both sides
2x = x + 2√x
x = 2√x
Finally, we'll divide by x on both sides
1 = 2√x/x
x = √x
x = 1
Therefore, the solution of the equation is x=1
Answer:
To solve the equation √2x+4 - √x = 2, we can first square both sides of the equation to eliminate the square roots.
Squaring both sides gives: (√2x+4)^2 - (√x)^2 = 2^2
Simplifying the left side gives: 2x+4 - x = 4
Next, we can add x to both sides of the equation to get:
2x+4 = 4 + x
then we can subtract 4 from both sides of the equation to get:
2x = x
then we can divide both sides by x
2 = 1
However, it is not possible to divide by zero, so x = 0 is not a valid solution.
This equation is an extraneous solution because the assumption that x is not equal to 0 led to a valid solution, but when x = 0, the equation is not defined.
Therefore, the solution of √2x+4 - √x = 2 is x = any value except 0.
Question 1
For your 15th birthday, your grandma puts $100 in a savings account for you, and
tells you that you cannot take it out until your 20th birthday. If the account she has
chosen has an interest rate of 3% compounded semiannually, how much money will
you have when you turn 20?
O $109.35
O $103.00
O $122.75
1 pts
O $116.05
Answer:
116.05
Step-by-step explanation:
15 to 20 = 5 years
compound semiannually = 10 time
annual rate 3% = 1.5% for every 6 mos
so 100*(1+1.5%)^10 =116.05
Because his goal is to bike 65 miles over four days, what equation can be used to find the number of miles he should bike on the first day, x? Do not combine like terms.
Answer:
y = 16.25x
Step-by-step explanation:
y is the total number of miles.
x is the number of days.
A sporting goods store manager was selling a ski set for a certain price. The manager offered the markdowns shown on the right, making the one day sale price of the ski set $324. Find the original selling price of the ski set.
Answer:
$519
Step-by-step explanation:
We know that the one day sale price of the ski set is $324 and the markdowns are specified.
A markdown means a reduction in price, so to find the original selling price we need to add the amount of markdown to the sale price.
The markdown of the ski set is $75 + $120 = $195
So, to find the original selling price we need to add the markdown amount to the sale price:
$324 + $195 = $519
Therefore, the original selling price of the ski set was $519
Rewrite 96 X8 = 768 using the Commutative Law of Multiplication.
Answer: 8 x 96
Explanation: (Commutative Law: A x B = B x A)
A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded.
Number of Hours | Total Number of Students
0 | 1
1 | 3
2 | 2
3 | 10
4 | 9
5 | 7
6 | 3
Determine the probability that a student studied for exactly 4 hours. Round to the nearest hundredth.
A. 0.74
B. 0.35
C. 0.26
D. 0.11
The probability that a student studied for 4 hours is 0.257 Or 26%.
What is probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
A table is given where the first column represents the number of hours a student studied math and the second column represents the number of students.
So, sum of the second column is 35. so it is the total number of students
and, only 9 of them studied mathematics for 5 hours.
Therefore, The probability that a student studied for 4 hours is,
= 9/35
= 0.257 or 26%.
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A recipe calls for the following spices: 1/8 teaspoon of turmeric, 1/4 teaspoon of ginger, and 1/2 teaspoon of cumin. What is the total quantity of these three spices?
The total quantity of the three spices is 7/8
How to calculate the total quantity of the three spices ?A recipe has three spices
1/8 teaspoon of turmeric
1/4 teaspoon of ginger
1/2 teaspoon of cumin
The total quantity of the three spices can be calculated as follows
1/8 + 1/4 + 1/2
= 7/8
Hence the total quantity of the three spices is 7/8
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Solve system using elimination 2x+9y=20
-4x-18y=-15
Answer: Which is impossible, indicating that the system is inconsistent. Therefore, based on the analysis performed with the elimination method, the system has no solution.
Step-by-step explanation:
2x + 9y = 20-4x - 18y = -15Multiplying the first equation by 2 we get:
4x + 18y = 40-4x - 18y = -15Now, once we have amplified the original equations, the sum of the first equation and the second equation leads to:
4x + 18y +(-4x - 18y) = 40 - 15⇒ 0=25Which is impossible, indicating that the system is inconsistent. Therefore, based on the analysis performed with the elimination method, the system has no solution.
A nine-month old baby drank an average of 7 1/4 oz during each of four feedings. If the baby drank 7 1/2oz, 7 3/8oz, & 6 3/8oz in the first three feedings, how many ounces were taken during the fourth feeding?
A) 7 3/8
B) 6 3/8
C) 6 3/4
D) 7 3/4
Show work please
Answer: D) 7 3/4
Step-by-step explanation:
With averages, we add all the values and divide by the number of values. Here, we know three out of the four days, let's label the day we don't know x. There are four days, so we can divide by four. 7 1/4 is the average, so we can set the equation equal to 7 1/4.
7 1/4 = (7 1/2 + 7 3/8 + 6 3/8 + x) / 4
Let's multiply both sides by 4 to get rid of the fraction. Let's also add what is in the parentheses
29 = 21 1/4 + x
Now we can isolate x by subtracting 29-21 1/4
so
x = 7 3/4 thus the answer is D
Answer:
D) 7 3/4
Step-by-step explanation:
Let x = amount of last feeding.
7 1/4 = (7 1/2 + 7 3/8 + 6 3/8 + x)/4
4 × 7 1/4 = 7 1/2 + 7 3/8 + 6 3/8 + x
28 + 1 = 7 4/8 + 7 3/8 + 6 3/8 + x
29 = 20 10/8 + x
(20 10/8 is the same as 20 + 10/8 = 20 + 8/8 + 2/8 = 20 + 1 + 1/4 = 21 + 1/4 = 21 1/4)
29 = 21 2/8 + x
29 = 21 1/4 + x
x = 29 - 21 1/4
x = 28 4/4 - 21 1/4
x = 7 3/4
Answer: 7 3/4
A farmer has 240 acres under cultivation at the cost of $188.99 per acre. If he averages a yield of 60 bushels per acre, what profit is expected if the price per bushel is $5.67?
Answer:
36290.4$
Step-by-step explanation:
First of all we should find out how much farmer spent on 240 acres
240 × 188.99 = 45357.6
Then, let's find out the price for whole bushels he gets
240 × 60 × 5.67$ = 81648
Therefore his profit is,
81648 - 45357.6 = 36,290.4$//
Triangle DEF has vertices D (3,5), E(6,-6), and F(1,3). What are the coordinates of D E F after triangle DEF is translated 5 units up and 6 units right?
Answer:
D' (9, 10)
E'( 12,-1)
F'(7,8)
Step-by-step explanation:
The coordinates of triangle DEF will be D(9,10), E(12,-1), and F(7,8) after the translation.
What is a transformation?A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.
The given triangle DEF has vertices D (3,5), E(6,-6), and F(1,3).
Triangle DEF has translated 5 units up and 6 units right.
This means that the x-coordinates of the vertices D, E, and F will each be increased by 6, and the y-coordinates of the vertices will each be increased by 5.
After the translation, the coordinates of vertex D will be (3 + 6, 5 + 5) = (9, 10)
After the translation, the coordinates of vertex E will be (6 + 6, -6 + 5) = (12, -1)
After the translation, the coordinates of vertex F will be (1 + 6, 3 + 5) = (7, 8)
So after the translation, the coordinates of triangle DEF will be D(9,10), E(12,-1), F(7,8)
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Is (-1,5) a solution to the equation 2x + 5y = 0 Why or Why not? Is (-1,5) a solution to the equation 2x + 5y = 0 Why or Why not?
The point (-1,5) is not a solution to the equation 2x + 5y = 0 because this point does not satisfy the equation.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
The equation is given in the question, as follows:
2x + 5y = 0
Substitute x = -1 and y = 5 into the equation and see if it holds true:
2(-1) + 5(5) = 0
-2 + 25 = 0
23 = 0
Since 23 ≠ 0, the point (-1,5) is not a solution to the equation 2x + 5y = 0.
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Please help me with the blanks.
Each answer can be used more than once, by the way.
