The amount of money that is invested in the first and second accounts will be 40,000 and 60,000, respectively.
What is the solution to the equation?The possible value of the variables that satisfy the equation which is known as the solution of the equation.
The interest is given as,
I = PRT / 100
Let 'x' be the amount invested in the first bank. Then the amount of investment in the second bank is (100,000 - x). Then the equation is given as,
x · 0.06 · 1 + (100,000 - x) · 0.08 · 1 = 7,200
0.06x + 8,000 - 0.08x = 7,200
-0.02x = -800
x = 40,000
The amount in the second bank is given as,
⇒ 100,000 - 40,000
⇒ 60,000
The amount of money that is invested in the first and second accounts will be 40,000 and 60,000, respectively.
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Y = -6x + 2
Y = -6x - 8
Answer:
Flase, no real numbers (2+-8)
Step-by-step explanation:
First, you conjoined the equations (-6x+2=-6x-8). Then you conjoined the variables first, (-6x+6x=0). Now you have 2=-8, which is not true.
Shermanos changes $15 for a supreme pizza how much will you pay for 2 supreme pizzas including 8.875% tax?
How many pounds are in 1
1⁄2 pounds and 8 ounces?
There are
pounds in 1 pounds and 8 ounces.
The solution is
n ID:
The number of pounds in [tex]1\frac{1}{2}[/tex] pounds and and 8 ounces is 2 pounds.
What is Unit of Measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
We know that 1 pound = 16 ounces.
As there are [tex]1\frac{1}{2}[/tex] pounds=1.5×16= 24 ounces.
The total number of ounces in [tex]1\frac{1}{2}[/tex] pounds and 8 ounces is
24+8
32 ounces.
Now let us convert Ounces to pounds.
we divide the number of ounces by 16.
Therefore, 32 ounces is equal to 32/16 = 2 pounds.
Hence, 2 pounds will be there in [tex]1\frac{1}{2}[/tex] pounds and 8 ounces
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What is the solution to the system of equations?
{2x−3y=−5
{3x+y=−2
The solution to the system of equations is x = -1 and y = 1.
What is system of equations?A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A set of equations satisfied by the same set of variables is called a system of linear equations."
The system of equation is given as:
2x - 3y = -5 .........(1)
3x + y = -2 ........(2)
Equation 2 can be written as:
y = -2 - 3x
Substituting the value of y in equation 1 we have:
2x - 3(-2 - 3x) = -5
2x + 6 + 9x = -5
11x + 6 = -5
11x = -5 -6
11x = -11
x = -1
Substituting the value of x in equation 2 we have:
3x + y = -2
3(-1) + y = -2
-3 + y = -2
y = -2 + 3
y = 1
Hence, the solution to the system of equations is x = -1 and y = 1.
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5x-4>12 or 12x+5<-4
The solution is the union of the solutions from both inequalities. That is, x is either greater than 3.2 or less than -0.75. So, the final solution is: -0.75 < x < 3.2.
What is inequalities?
An inequality is a mathematical statement that represents a comparison between two values, and indicates the relationship of one value being greater than, less than, or equal to the other. It is usually represented using symbols such as ">" (greater than), "<" (less than), ">=" (greater than or equal to), "<=" (less than or equal to), and "≠" (not equal to). For example, the inequality "2x + 3 > 7" expresses that the value of the expression "2x + 3" is greater than 7 for some values of x.
Inequalities are used to describe a range of values that satisfy a certain condition. The solution to an inequality is a set of values that make the inequality true.
To solve the inequality "5x - 4 > 12 or 12x + 5 < -4", we can start by solving each inequality separately and then combining the solutions to find the final solution.
Solving the first inequality: 5x - 4 > 12Adding 4 to both sides, we get 5x > 16
Dividing both sides by 5, we get x > 3.2
So, the solution to this inequality is x > 3.2
Solving the second inequality: 12x + 5 < -4Subtracting 5 from both sides, we get 12x < -9
Dividing both sides by 12, we get x < -0.75
So, the solution to this inequality is x < -0.75
Final solution: Combining the solutions from both inequalities:
Since "or" is used in the inequality, the solution is the union of the solutions from both inequalities. That is, x is either greater than 3.2 or less than -0.75. So, the final solution is: -0.75 < x < 3.2.
So the solution to the inequality "5x - 4 > 12 or 12x + 5 < -4" is -0.75 < x < 3.2.
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Find
(M.
f(x)=√√√x²-1
g(x)=√√√x-1
a. √√x+1
b. √√x-1
C.
d.
-X+1
1
X+1
The function operation (f/g)(x) in the functions f(x) = √( x² - 1 ) and g(x) = √( x - 1 ) is √( x + 1).
What is the function operation (f/g)(x) in the function?A function is simply a relationship that maps one input to one output.
Given the functions in the question;
f(x) = √( x² - 1 )g(x) = √( x - 1 )(f/g)(x) = ?To evaluate (f/g), replace the function designators in f/g with the actual functions.
(f/g)(x) = f(x) / g(x)
(f/g)(x) = ( √( x² - 1 ) ) / ( √( x - 1 ) )
Now, rewrite 1 as 1²
(f/g)(x) = ( √( x² - 1² ) ) / ( √( x - 1 ) )
Factor using difference of square
(f/g)(x) = ( √( (x - 1)(x + 1 ) ) / ( √( x - 1 ) )
Combine into a single radical
(f/g)(x) = √( ( (x - 1)(x + 1) ) / ( x - 1 ) )
Now, cancel out the common factors (x-1)
(f/g)(x) = √( (x + 1) / 1 )
(f/g)(x) = √( x + 1)
Therefore, the function operation (f/g)(x) is √( x + 1).
Option A) √( x + 1) is the correct answer.
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A company prices its tornado insurance using the following assumptions:
• In any calendar year, there can be at most one tornado.
• In any calendar year, the probability of a tornado is 0.08.
• The number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year.
Using the company's assumptions, calculate the probability that there are fewer than 2 tornadoes in a 22-year period.
The probability that there are fewer than 2 tornadoes in a 22-year period is, 0.214
What is probability?Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.
Probability of Event = Favorable Outcomes/Total Outcomes = X/n
Since the probability of a tornado in any given year is 0.08,
the probability of no tornado in any given year is;:
= 1 - 0.08
= 0.92.
Let X be the number of tornadoes in a 22-year period.
X follows a binomial distribution with n = 22 and p = 0.08.
We want to calculate the probability that there are fewer than 2 tornadoes in a 22-year period.
This can be written as:
P(X < 2) = P(X = 0) + P(X = 1)
Using the binomial probability formula, we can calculate:
P(X = 0) = (22 choose 0) x (0.08)⁰ x (0.92)²² ≈ 0.038
P(X = 1) = (22 choose 1) x (0.08)¹ x (0.92)²¹ ≈ 0.176
Therefore,
P(X < 2) = P(X = 0) + P(X = 1) ≈ 0.214
So the probability that there are fewer than 2 tornadoes in a 22-year period is approximately 0.214 or 21.4%.
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cathy invest $3,700 into an account with a 3.75% annual interest rate, making no other deposits or withdrawals.
a) what with cathy’s balance be after 6 years if the interest rate is compounded quarterly?
b) how much more (or less) money would be in cathy’s account if the interest is compounded continuously?
Answer: no
Step-by-step explanation:
In ΔGHI, i = 800 cm, m m∠G=26° and m m∠H=122°. Find the length of h, to the nearest 10th of a centimeter.
Answer:
For the nearest 10th of a centimeter, the value of h is 460 cm
Step-by-step explanation:
To find length of h we can use Law of Sines . The Law states that for a triangle with sides a, b, and c and angles A, B, and C opposite to those sides, the following equation holds:
a/sin A = b/sin B = c/sin C
In ΔGHI, let h be the length of the side opposite angle H, and let i be the length of the side opposite angle I.
Now:
h/sin 122° = i/sin 26°
We can find h by cross multiplying:
h = i * sin 122° / sin 26°
=459.9
Here,
h = 459.9 cm
By taking approximation we get 460 cm
Answer:
This answer is actually 1280.3
Step-by-step explanation:
tell how the communative and associative properties of adddition can help you evsaluate the expression using mental math? 8+(-8-5)
Using commutative and associative properties of addition, the solution for given expression is -5.
What is commutative and associative property?
The associative and commutative characteristics are universal principles that apply to addition and multiplication. The associative property states that rearranging the numbers will get the same result, while the commutative property states that rearranging the numbers will yield the same result.
These properties tell that one can add in any order, the result will always be the same.
We are given an expression as 8+(-8-5).
So, in this instead of adding from left to right, we can see that the 8 + (-8) will be zero and only -5 will be left as an answer.
Hence, the solution for given expression is -5.
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Graph the following points on the coordinate plane. Find the measure of ∠ACB
to the nearest tenth.
A (-3, 2), B (0, 0), C (2, 3)
The measure of angle ∠ACB is 45 degrees
How to find the measure of ∠ACBFrom the question, we have the following parameters that can be used in our computation:
A (-3, 2), B (0, 0), C (2, 3)
The graph is attached
The lines AB and BC are perpendicular lines
This means that
∠B = 90 degrees
Calculate the length AB and BC using
distance = √[(x2 - x1)² + (y2 - y1)²]
So, we have
AB = √[(-3 - 0)² + (2 - 0)²] = √13
BC = √[(0 - 2)² + (0 - 3)²] = √13
The angle C is then calculated as
tan(C) = AB/BC
tan(C) = √13/√13
tan(C) = 1
Take the arctan of both sides
C = 45
Hence, the measure of ∠ACB is 45 degrees
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The sales tax rate is 4.5%. How much sales tax will you pay on a $125 purchase?
Work Shown:
4.5% of 125 = 0.045*125 = 5.625
That rounds to 5.63
Answer:
5.625
Step-by-step explanation:
Determine whether the statement is true or false. 1. A census is a count of part of a population.. O True O False
The statement regarding the census in this problem is classified as a True statement.
What are the concepts of population and sample?Population: Collection or set of individuals or objects or events whose properties will be studied.
Sample: The sample is a subset of the population, and a well chosen sample, that is, a representative sample will contain most of the information about the population parameter. A representative sample means that all groups of the population are inserted into the sample.
A Census is when a group of the population is chosen, that is, a sample is chosen, hence the statement for this problem is true.
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mr ramirez bought a watermelon that weighs 12 pounds for a picnic he cuts it into pieces that each weigh 1.5 pounds. how many pieces of water melon can mr ramiez cut?
Equivalence means to be same, whether it be value, temperature, size, etc.
Let's make an equation to solve this problem. We first would need to take the total (12 pounds) and divide that total by the amount each slice must weigh (1.5 pounds) to get an equal number of slices.
12 ÷ 1.5 = 8To check our work, we can take number of slices (8), and multiply that by the weight of each slice (1.5 pounds) to get the original weight of the watermelon.
8 × 1.5 = 12Now, we know for sure that Mr. Ramirez can make 8 watermelon slices each weighing 1.5 pounds if he has a 12-pound watermelon.
What are the zeros of this function?
A. -1, 3
B. 3, 1
C. 0, 1.5
D. 1, 2
Answer:
B
Step-by-step explanation:
the zeros are the values of x on the x- axis where the graph crosses
the graph crosses the x- axis at 1 and 3
then the zeros are x = 1 , x = 3
If joes shoes cost 44 dollars and 20 cents and joe has 10
dollars and 68 cents. How much money does joe need?
Answer: 44.20-10.68=33.52
He need 33.52$
Step-by-step explanation:
If 3250 was increased by 46%, the result would be
cos(y) = sin(0)
what is the value of 0?
sum of 2nd term of an infinite geometric series is -1/2 and the third term is 1/4 find the sum of series
Answer:
2
Step-by-step explanation:
1 plus 1 due to the characterisation of the number 1 increasing by 1 gives you 2
An electric clock is stopped by a power failure. What is the probability that the second hand is stopped between the 4 and the 9?
Answer: the answer is 5/12
How many numbers of the form x15y are divisible by 15
CJ has three more pet pigs than Jacqui has. Let’s write an expression to represent how many pigs CJ has. To do that, we follow these steps:
Identify the constants and the variables.
There is one known number or constant here: it is 3. CJ has 3 more pigs than Jacqui. That number, 3, won’t change. The variable is the number of pets Jacqui has. Let’s call that j.
Identify the operations.
The phrase “more than” tells us we need to add. There are no other operations in this expression.
Rewrite the phrase as an expression.
“Three more pet pigs than Jacqui has” is 3 + j.
Last year, Shailyn read four fewer books than Oswaldo. Which expression shows how many books Shailyn read last year?
Answer: Let's follow the same steps as in the previous example:
Identify the constants and the variables.
The known constant here is 4. Shailyn read 4 fewer books than Oswaldo. Let's call the number of books Oswaldo read "o".
Identify the operations.
The phrase "four fewer" tells us we need to subtract.
Rewrite the phrase as an expression.
"Four fewer books than Oswaldo" is o - 4.
So, the expression that shows how many books Shailyn read last year is o - 4.
Step-by-step explanation:
A candle is burning. It starts out 12 inches long. After 1 hour, it is 10 inches long. After 3 hours, it is 5.5 inches
1. Explain one reason why it might be reasonable to model the relationship between time and height of the candle with a linear function.
2. Explain one reason it might NOT be reasonable to model this relationship with a linear relationship
The reasons for (1) and (2) are added below
Why it is reasonable to use a linear functionOne reason why it might be reasonable to model the relationship between time and height of the candle with a linear function is that the rate of change of the candle's height appears to be constant over time.
Why it is unreasonableOne reason why it might NOT be reasonable to model this relationship with a linear function is that the candle's height cannot continue to decrease indefinitely.
This means that the candle's height is bounded and cannot continue to decrease linearly forever.
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When an accountant records_ on hand, they are noting a company's ____
A. human resources; total liquid assets
B. cash; total of amount dollars, money orders, checks, and other forms of
money
C. supplies; materials that need to be purchased soon
D. inventory; number of employees on payroll
Answer: Choice B
Explanation: The phrase "cash on hand" means the amount of money the company has. It could be literal cash as the phrase directly implies. Or it could be near equivalents to cash. A near equivalent is something you can convert to cash fairly easily, meaning a bank would readily accept it. The only drawback is that it's not actual cash so its not as liquid as cash itself. Also, you would need to take into account the delay time between deposit and when the bank balance is updated.
simplify 3-2(b-2)=2-7b solve for b
The required value of the given expression which satisfy it is b = 3/5.
What is Simplification?To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.
According to question:We have,
3 - 2(b - 2) = 2 - 7b
= 3 - 2b - 4 = 2 - 7b
= 5b = 3
= b = 3/5
Thus, required value of the b for the given function is b = 3/5.
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A car travels 55 mph and passes a truck travelling 50 mph. How long will it take the car to be
more than 23 mi ahead?
Answer:you never asked for like in what minutes or hours?
Step-by-step explanation:
The car, traveling at a speed 5 mph faster than the truck, will take more than 4.6 hours to be more than 23 miles ahead.
Explanation:This question pertains to relative speed. When the car is traveling at 55 mph and the truck at 50 mph, the car is effectively moving away from the truck at (55 mph - 50 mph) = 5 mph. To calculate the time it will take for the car to be more than 23 miles ahead, we can use the formula: Time = Distance/Speed. So the time it would take is Time = 23 miles / 5 mph = 4.6 hours. Therefore, it will take the car more than 4.6 hours to be more than 23 miles ahead.
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If the scale factor of figure A to figure B is 3:8 find x
Find the lengths of the sides of a triangle if two of the sides are equal, the third side is 1 1/3 cm longer than the others, and its perimeter is 5 2/5 cm. The two equal sides of the triangle are (blank)cm. The third side is (blank) cm.
Answer:
Step-by-step explanation:
Here's a step by step solution with more details:
Let's call the length of the two equal sides of the triangle as x.
The third side, which is 1 1/3 cm longer, will have a length of x + 1 1/3 cm.
The perimeter of the triangle is 5 2/5 cm, so we can write an equation using the lengths of the sides:
x + x + (x + 1 1/3) = 5 2/5
Simplifying the equation:
2x + 1 1/3 = 5 2/5
Subtracting 1 1/3 from both sides:
2x = 4 1/5
Dividing both sides by 2:
x = 2 2/5
So the two equal sides of the triangle are 2 2/5 cm and the third side is 2 2/5 + 1 1/3 = 3 7/15 cm.
Answer:
One equal side = [tex]1\frac{16}{45}[/tex]cm and third side is [tex]2\frac{31}{45}[/tex]cm
Step-by-step explanation:
This is describing an isosceles triangle
1[tex]\frac{1}{3}[/tex] = [tex]\frac{4}{3}[/tex]
5[tex]\frac{2}{5}[/tex] = [tex]\frac{27}{5}[/tex]
Let
x = one of the two equal sides of the triangle
∴ Third side of triangle = [tex]\frac{4}{3} + x[/tex]
Perimeter of a triangle = Sum of all three sides:
[tex]\frac{27}{5}[/tex] [tex]= x + x + (\frac{4}{3} + x)[/tex]
Expand the parenthesis using the Distributive Law and bring all the like terms together:
[tex]=\frac{27}{5} = 2x + \frac{4}{3} + x[/tex]
[tex]= \frac{27}{5} = 3x + \frac{4}{3}[/tex]
[tex]= \frac{27}{5} -\frac{4}{3} = 3x[/tex]
The two denominators of the two fractions have to be manipulated to be made the same:
[tex]= (\frac{3}{3})(\frac{27}{5}) - (\frac{5}{5})(\frac{4}{3}) = 3x[/tex]
[tex]= \frac{81}{15} - \frac{20}{15} = 3x[/tex]
[tex]= \frac{81 - 20}{15} = 3x[/tex]
[tex]= \frac{61}{15} = 3x[/tex]
Cross-multiplication is added:
[tex]= (61)(1) = (15)(3x)[/tex]
[tex]= 61 = 45x[/tex]
Isolate x and make it the subject of the formula:
x = [tex]\frac{61}{45}[/tex]
x = One of the two equal sides = [tex]1\frac{16}{45}[/tex]cm
∴Third side:
= [tex]\frac{61}{45} + \frac{4}{3}[/tex]
= [tex]\frac{61}{45} + (\frac{15}{15})(\frac{4}{3})[/tex]
= [tex]\frac{61}{45} + \frac{60}{45}[/tex]
= [tex]\frac{61 + 60}{45}[/tex]
= [tex]\frac{121}{45}[/tex]
= [tex]2\frac{31}{45}[/tex]cm
Find the average rate of change
Please helppppp
Step-by-step explanation:
please review the attachment. That's the answer.
Calculate the area of the triangle
find the length of the x
a^2 + b^2 = c^2
12x^2 + b^2 = 13^2
144 + b^2 = 169
b^2 = 25
b = 25; x = 5
use the formula
a = (1/2)(24)(5)
a = (1/2)(120)
area = 60
