The requried, $1000 is invested at 6%, and $7000 is invested at 10%
Let x be the amount invested at 6%, and y be the amount invested at 10%. We know that x + y = $8000 since the total amount invested is $8000.
We also know that the annual interest earned on the 6% investment is 0.06x, and the annual interest earned on the 10% investment is 0.1y. The total annual interest earned is given as $760.
So we have the system of equations:
x + y = 8000 (1)
0.06x + 0.1y = 760 (2)
We can use either substitution or elimination to solve for x and y. Here, we'll use elimination. Multiplying equation 1 by 0.06, we get:
0.06x + 0.06y = 480 (3)
0.1y - 0.06y = 0.04y = 280
y = $7000.
Substituting y = $7000 into equation 1, we get:
x + $7000 = $8000
So x = $1000.
Therefore, $1000 is invested at 6%, and $7000 is invested at 10%.
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Find the surface area of the prism a.120cm. B180cm. C34cm. D 333cm
The surface area of the prism for the given dimensions is equal to option B. 180 square centimeters.
Surface area of the prism
= Area of two right triangles + Area of rectangle 1 + Area of rectangle 2 + Area of the rectangle3
In a Triangle ,
Base = 12cm
height = 5cm
Area of the triangle = ( 1/2 ) × base × height
= (1/2)× 12 × 5
= 30 cm²
Length of rectangle 1 = 12cm
Width of rectangle 1 = 4cm
Area of rectangle 1 = 12 × 4
= 48 cm²
Length of rectangle2= 13cm
Width of rectangle 2 = 4cm
Area of rectangle 2= 13 × 4
= 52 cm²
Length of rectangle 3 = 5cm
Width of rectangle 3 = 4cm
Area of rectangle 3 = 5 × 4
= 20 cm²
Surface area of the prism
= Area of two right triangles + Area of rectangle 1 + Area of rectangle 2 + Area of the rectangle3
Substitute the values of the area we have,
⇒ Surface area of the prism = 2(30 ) + 48 + 52 + 20
⇒ Surface area of the prism = 180 square centimeters
Therefore, the surface area of the prism is equal to option B. 180 square centimeters.
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What is a formula for the nth term of the given sequence?
12,6,3...
Answer:
The given sequence is decreasing by a factor of 2 each time, so each term is half of the previous term.
We can write the nth term of the sequence as:
a_n = a_1 * (1/2)^(n-1)
where a_1 is the first term of the sequence (12 in this case) and n is the position of the term we want to find.
For example, to find the 4th term of the sequence, we would have:
a_4 = 12 * (1/2)^(4-1)
= 12 * (1/2)^3
= 12 * 1/8
= 1.5
Therefore, the formula for the nth term of the sequence 12, 6, 3, ... is:
a_n = 12 * (1/2)^(n-1)
brainiest !!!!!!!! this needs to be done asappp
The coordinates best represent the vertex of the graph is given by (1, -2).
Hence the correct option is (D).
Graph is a pictorial representation of a curve or a function or a relation.
From the given graph we can see that the curve is an upward parabola which has vertex at a point other than origin.
We can see that where the vertex is formed the value along X axis is 1 and the value along Y axis is -2 (towards down).
So the vertex of the given graph is at (1, -2).
Hence the correct option will be (D).
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The perimeter of a rectangle is
35
cm
35 cm35, start text, space, c, m, end text. The rectangle's area (in
sq. cm
sq. cmstart text, s, q, point, space, c, m, end text) as a function of its length (in
cm
cmstart text, c, m, end text) is graphed.
What is the approximate average rate at which the area decreases, as the rectangle's length goes from
13
cm
13 cm13, start text, space, c, m, end text to
16
cm
16 cm16, start text, space, c, m, end text?
The average rate of decrease of the area as the length goes from 13 cm to 16 cm is given as follows:
D) 11 and 1/3 cm² per cm.
How to obtain the average rate of change?The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function.
From the graph, the parameters are given as follows:
Length of 13 cm -> Area of 60 cm².Length of 16 cm -> Area of 24 cm².Hence the rate is approximated as follows:
r = (24 - 60)/(16 - 13)
r = -12 cm² per cm.
Which is closest to option D.
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I answered this on Khan Academy and my lawyer above me has the papers for the work.
See u in court...
Write the slope of tangent and normal to the curve y=f(X) at (x1,y1).
The slope of the tangent line is:
a = (df(x1)/dx)
The slope of the normal one is:
a' = -1/(df(x1)/dx)
How to find the slope of the tangent line?For any function y = f(x), we define the slope of the tangent line at the point x as the derivative evaluated in x.
So if we want to find the slope of the tangent line at the point (x1, y1), we just need to differentiate and evaluate in x1, then the slope will be given by:
df(x1)/dx
And the normal slope is the slope of the perpendicular line, two slopes are perpendicular if the product is -1, then:
a*(df(x1)/dx) = -1
a = -1/(df(x1)/dx)
Where df/dx reffers to the derivative of f(x).
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a number from 1 to 8 is chosen at random. What is the probability that the number chosen is not even
Answer:
The probability that the number chosen is not even = 4/8
If 34 x 27 = 918, which of the following is true?
918 ÷ (-34) = 27
-918 ÷ 34 = -27
-918 ÷ 27 = 34
918 ÷ 27 = -34
group of students conduct an investigation to learn more about pea plants. Their data are summarized below. Plant Water per day (mL) Height after 2 weeks (cm) 1 20 11 2 50 18 3 100 24 4 20 16 Which is the independent variable in the investigation?
If Group of students conducted an investigation to learn about "pea-plants", then the "independent-variable" is "Water-per-day (mL)".
The "Independent-Variable" is defined as a variable which is controlled by the researcher.
In the investigation of the "pea-plants", the amount of water per day (mL) given to the plants is the independent variable because it is the variable that is intentionally varied by the students.
The students are manipulating the amount of water given to each plant to observe the effect it has on the height of the plant after two weeks.
By controlling the amount of water given to each plant, the students can determine whether there is a relationship between water intake and plant growth.
Therefore, water given to plants per-day will be the "independent-variable".
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The given question is incomplete, the complete question is
Group of students conduct an investigation to learn more about pea plants. Their data are summarized below.
Plant Water per day (mL) Height after 2 weeks (cm)
1 20 11
2 50 18
3 100 24
4 20 16
Which is the independent variable in the investigation?
two 6 sided dice are rolled. What is the probability of rolling a number that is not an odd number?
Answer:1/4, 25%
Step-by-step explanation:
even number: 2,4,6
odd umber 1,3,5
even number probability when 1 dice is rolled: 3/6 = 1/2
2 dice is rolled: 1/2*1.2 = 1/4 = 25%
For what value of A is the function, (x), continuous at x=0?
(i) [tex]\lim_{x \to \frac{\pi^-}{2}}[/tex] h(x) = 3
(ii) [tex]\lim_{x \to \frac{\pi^+}{2}}[/tex] h(x) = -1
(iii) h(0) = 1/7
The value of λ must be 7, for h(x) to be continuous at x = 0.
The given function is,
h(x) = 1/7, when x = 0
= 1 - 2 cos 2x, when x < π/2
= 1 + 2 cos 2x, when x > π/2
= x cos x/sin λx, when x < 0
Now,
(i) [tex]\lim_{x \to \frac{\pi^-}{2}}[/tex] h(x) = [tex]\lim_{x \to \frac{\pi^-}{2}}[/tex] (1 - 2 cos 2x) = 1 - 2 cos π = 1 + 2 = 3
(ii) [tex]\lim_{x \to \frac{\pi^+}{2}}[/tex] h(x) = [tex]\lim_{x \to \frac{\pi^+}{2}}[/tex] (1 + 2 cos 2x) = 1 + 2 cos π = 1 - 2 = -1
(iii) h(0) = 1/7
Since the function is continuous at x = 0, so
[tex]\lim_{x \to 0}[/tex] h(x) = h(0)
[tex]\lim_{x \to 0}[/tex] x cos x/sin λx = 1/7
[tex]\lim_{x \to 0}[/tex] cos x.[tex]\lim_{x \to 0}[/tex] 1/λ(sinλx/λx) = 1/7
1/λ = 1/7
λ = 7
Hence the value of λ must be 7.
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Jodi’s car used 12 gallons of gas to travel 456 miles. How many miles did her car travel per gallon of gas? Show work
Answer:
To find the number of miles Jodi's car traveled per gallon of gas, we need to divide the distance traveled by the amount of gas used:
miles per gallon = distance traveled / amount of gas used
distance traveled = 456 miles
amount of gas used = 12 gallons
miles per gallon = 456 miles / 12 gallons
miles per gallon = 38 miles/gallon
Therefore, Jodi's car traveled 38 miles per gallon of gas.
Answer:
38 miles
Step-by-step explanation:
Set up your division: 456 / 12
456 divided by 12 is 38
So, Jodi's car travels at 38 miles per gallon of gas.
Need help, pls!!!
ty!
The graph of this function will behave as (b) A graph of this function would slope downward, starting from a price of $100 dollars because the rate of change is less than 0 and the initial value is -10.
The demand function is given by d = 100 - 10p. This means that the quantity demanded (d) decreases as the price (p) increases.
The slope of the demand function is the rate of change of the quantity demanded with respect to the price. In this case, the slope is -10, which is negative. This indicates that as the price increases, the quantity demanded decreases.
The initial value of the demand function is 100, which represents the quantity demanded when the price is zero. This means that the demand function intersects the y-axis at (0, 100).
Therefore, the correct answer is (b) A graph of this function would slope downward, starting from a price of $100 dollars because the rate of change is less than 0 and the initial value is -10.
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I need help on 11-12 please i need this done asap! Can someone help me out
Based on the graph, is there an association between age and preferred mode of transportation?
O There is an association because the distribution of preferred transportation differs among the age groups.
O There is an association because the distribution of preferred transportation is the same among the age groups.
O There is no association because the distribution of preferred transportation differs among the age groups.
There is no association because the distribution of preferred transportation is the same among the age groups.
Based on the graph, there is no association because the distribution of preferred transportation differs among the age groups. The Option C is correct.
What influences difference in preferred transportation among all age group?The significant factors is accessibility and convenience because younger individuals may be more likely to use public transportation such as buses or trains because it is more affordable and convenient than owning a car.
But the older individuals may prefer to use personal cars because it provides more flexibility and control over their transportation needs. Another factor that influences is the cost of ownership, maintenance, and fuel.
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Which of the following questions about a particular animal could NOT be answered using only the data collected for the tracking collars?
The question about a particular animal that could NOT be answered using only the data collected from the tracking collars would be do the movement patterns of the animal vary according to the weather? That is option C.
What are tracking collars?A tracking collars is a neck device that usually has a GPS device attached to it which is used by biologists to track the movement of animals that are under study.
The functions of the tracking collars include the following:
It allows them to note how many miles the animal can travel in a given time.It allows them to note the pattern of movement of the animals.It allows them to note the location preferred by the animal to travel.Learn more about tracking here:
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Complete question:
Biologists often attach tracking collars to wild animals. For each animal, the following geolocation data is collected at frequent intervals.
The time
The date
The location of the animal
Which of the following questions about a particular animal could NOT be answered using only the data collected from the tracking collars?
A. Approximately how many miles did the animal travel in one week?
B. Does the animal travel in groups with other tracked animals?
C. Do the movement patterns of the animal vary according to the weather?
D. In what geographic locations does the animal typically travel?
C. Do the movement patterns of the animal vary according to the weather?
Solve for AB in simplified, rationalized form:
20/√2 20√2/2 40/√2 10√2
Answer:
AB = (20/√2)(√2/√2) = 10√2
what is debit and credit of this transactions? On December 1, NNC began an electro repair shop,Samson Quality Automotive. The following transactions occurred during December Dec. 1 Samson contributed birr 55,000 cash to the business in exchange for shares of common stock. 1 Purchased birr 9,000 of equipment paying cash. 1 Paid birr 1,500 for a five-month 9 Paid birr 16,000 cash to purchase land to be used in operations. insurance policy starting on December 1. 10 Purchased office supplies on account, birr 2,000. 19 Borrowed birr 12,000 from the bank for business use. Samson signed a notes payable to the bank in the name of the corporation. The note is due in five years. 22 Paid birr 1,700 for advertising expenses. 26 Paid birr 300 on account. 28 The business received a bill for utilities to be paid in January, birr 180. 31 Revenues earned during the month included birr 14,000 cash and birr 2,600 on account. 31 Paid employees' salaries birr 3,800 and building rent birr 1,300. Record as a compound entry. 31 The business received birr 1,400 for auto screening services to be performed next month.
Journal entries are a record of financial transactions in chronological order, showing the accounts and amounts debited and credited for each transaction. Below is the journal entries of the transactions:
Constitutes the journal entries :-
Below are the debit and credit entries for each transaction:
Dec. 1:
Debit: Cash (55,000)
Credit: Common Stock (55,000)
Debit: Equipment (9,000)
Credit: Cash (9,000)
Debit: Prepaid Insurance (1,500)
Credit: Cash (1,500)
Dec. 9:
Debit: Land (16,000)
Credit: Cash (16,000)
Dec. 10:
Debit: Office Supplies (2,000)
Credit: Accounts Payable (2,000)
Dec. 19:
Debit: Cash (12,000)
Credit: Notes Payable (12,000)
Dec. 22:
Debit: Advertising Expense (1,700)
Credit: Cash (1,700)
Dec. 26:
Debit: Accounts Payable (300)
Credit: Cash (300)
Dec. 28:
Debit: Utilities Expense (180)
Credit: Accounts Payable (180)
Dec. 31:
Debit: Cash (16,600)
Debit: Accounts Receivable (2,600)
Credit: Service Revenue (17,600)
Debit: Salary Expense (3,800)
Debit: Rent Expense (1,300)
Credit: Cash (5,100)
Debit: Unearned Revenue (1,400)
Credit: Cash (1,400)
Debit: Cash Dividends (4,000)
Credit: Cash (4,000)
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graphing using calculator. what is the solution to this problem.
The solutions to the function y = -x^2 - 8x + 8 are (-8.9, 0) and (0.9, 0)
What is the solution to this functionFrom the question, we have the following parameters that can be used in our computation:
y = -x^2 - 8x + 8
To solve using a graphing calculator, we enter the equation in a graph and write out the solution
Having said that we have
When y = -x^2 - 8x + 8 is plotted, the soluton is (-8.9, 0) and (0.9, 0)
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In a class of 50 students, they had a chance to read novel,comics and textbook 21 read novel,24 read comics and 18 read textbook 3 read only novel 9 read only comics and 2 read only textbook 5 read all the 3. illustrate your information on a venn diagram. use your diagram to find the number of students who read a. comics and novel only b. textbook and novel only c. none of the 3
Answer:
Here is a Venn diagram that illustrates the information:
```
___________
| |
| N |
|_____ ____|
|\ || /|
| \ || / |
| \ || / |
| \ || / |
| C \||/ T |
|_____\v/____|
A
```
In the diagram, N represents the set of students who read the novel, C represents the set of students who read the comics, and T represents the set of students who read the textbook. The region labeled A represents the set of students who read all three.
Using the Venn diagram, we can find the number of students who read:
a. comics and novel only: This corresponds to the region of the diagram that is exclusively shaded with the circles for comics and novel, but not for textbook. This region has 9 students.
b. textbook and novel only: This corresponds to the region of the diagram that is exclusively shaded with the circles for textbook and novel, but not for comics. This region has 1 student.
c. none of the 3: This corresponds to the region of the diagram that is outside of all three circles. This region has 13 students.
Therefore, the number of students who read a. comics and novel only is 9, b. textbook and novel only is 1, and c. none of the 3 is 13. Answer: a. 9, b. 1, c. 13.
Expand and evaluate the series.
∑6n=13n
{
,
,
,
,
,
}
S6=
Answer:
The series ∑6n=1 3n is a sum of the first 6 terms of the sequence 3n, which starts with n = 1 and increases by 3 for each successive term. Therefore, the first 6 terms of the sequence are:
3(1), 3(2), 3(3), 3(4), 3(5), 3(6)
which simplify to:
3, 6, 9, 12, 15, 18
The sum of these terms is:
∑6n=1 3n = 3 + 6 + 9 + 12 + 15 + 18 = 63
Therefore, S6, the sum of the first 6 terms of the series, is 63.
One meter of shielded microphone cable weighs 75/1,000 kilogram. What is the length of cable in coil that weigh 5 1/2 kilogram
The length of cable in the coil that weighs 5 1/2 kilograms is 1/2 meter.
Let x be the length of cable in meters that weighs 5 1/2 kilograms.
Then, we can write:
1 meter / (75/1000) kilograms = x meters / 5.5 kilograms
Simplifying the left side, we get:
1 meter / (75/1000) kilograms = 1000 / 75 meters/kilogram
= 40/3 meters/kilogram
Substituting this into our proportion, we get:
40/3 meters/kilogram * x meters = 5.5 kilograms
Multiplying both sides by 3/40, we get:
x meters = (5.5 kilograms) * (3/40) * (40/3 meters/kilogram)
= 1/2 meter
The length is 1/2 meter
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tia's favorite stargergy for multiplying polynomials is to make a box that fits the two factors
Using Tia's box method, the multiplication of the polynomials (x + 2)(x² -3x + 5) in the standard form is x³ - x² - x + 10
Here, we need to multiply the polynomials (x + 2)(x² -3x + 5)
Tia's stargergy for multiplying polynomials is to make a box that fits the two factors.
Using Tia's box method,
x² -3x +5
x x³ -3x² +5x
+2 +2x² -6x +10
Consider (x + 2)(x² -3x + 5)
= (x . x²) - (x . 3x) + (x . 5) + (2x²) -(2 × 3x) + (2 × 5)
= x³ - 3x² + 5x + 2x² - 6x + 10
= x³ - 3x² + 2x² + 5x - 6x + 10
= x³ - x² - x + 10
This is the required polynomial.
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Find the complete question below.
9. A has some amount of money with him. He gave one half of one third from that amount One half of the amount received by B is 20. What is the amount that A originally had?
Using the expression 5x/12 = 20, the amount that A originally had was $48.
We have,
Let x be the amount of money that A originally had.
Then, A gave away 1/2 x 1/3 = 1/6 of the amount, which is equal to x/6.
The amount received by B is 1/2 of the remaining amount,
which is (x - x/6)/2 = 5x/12.
We know that 5x/12 = 20,
Solving for x.
5x/12 = 20
5x = 240
x = 48
Therefore,
The amount that A originally had was $48.
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In each figure, all b. Determine whether the third figure is a translation image of the first figure. Write yes or no. Explain
your answer.
미미미
a. Yes; it is one reflection after another with respect to the two parallel lines.
b. No; it is a reflection followed by a translation.
c. No; it is a reflection followed by a rotation.
d.
No; it is one reflection after another with respect to the two parallel lines.
Answer:
a
Step-by-step explanation:
HELP ASAP! What is the probability to the nearest hundredth that a point chosen randomly inside the rectangle is in the triangle?
Answer:
Step-by-step explanation:
To answer this question, we need to know the dimensions of the rectangle and the triangle. Assuming that the triangle is right-angled and has one side coinciding with one side of the rectangle, we can use the formula for the area of a triangle: \ ( \frac {1} {2} \) × base × height1. The base and height of the triangle are the same as the length and width of the rectangle. The area of the rectangle is length × width. The probability that a point chosen randomly inside the rectangle is in the triangle is then the ratio of the area of the triangle to that of the rectangle, which is: \ ( \frac {\frac {1} {2} \times length \times width} {length \times width} \) = \ ( \frac {1} {2} \). So, the probability is 0.5 or 50% to the nearest hundredth2.
Answer: C .08
Step-by-step explanation:
Probability is the part out of the whole. you first need to find the part, which is the triangle
In other words find out how much of the triangle is taking up the rectangle, which is done through area
A(triangle)=1/2 b h where b=6 h=9
A(triangle)=1/2 (6)(9) = 27
A(rectangle)= Lw where L=24 h=15
A(rectangle)= (24)(15) = 360
P(triangle in rectangle)= 27/360
=.075 rounded = .08
Help me ASAPP Please :
The simplification of the fractions given above through multiplication would be;
1.) 9 11/12
2.) 11 19/40
How to simplify a given fraction through multiplication?For question 1.)
2 5/6 × 3 2/4
Change the mixed fraction to single fraction;
= 17/6 × 14/4
= 17/6 × 7/2
= 119/12
= 9 11/12
For question 2.)
5 2/5 × 2 1/8
= 27/5 × 17/8
= 459/40
= 11 19/40
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139(x-28)
Please help would save a girls lifeee fr fr
Answer:
69
Step-by-step explanation:
(139) + (x-28) = 180 (adjacent angles on straight line add up to 180)
x - 28 = 41
x = 69
How to solve pre algebra?
Answer:
Pre-algebra is a fundamental branch of mathematics that deals with basic arithmetic operations, such as addition, subtraction, multiplication, and division, and introduces concepts like variables, equations, and inequalities. Here are some general steps to solve pre-algebra problems:
1. Identify the problem: Read the problem carefully and identify what it is asking you to do. Identify the key information and any variables that are given.
2. Translate the problem: Translate the problem into an equation or inequality, using variables to represent unknown quantities.
3. Solve the equation or inequality: Use algebraic manipulation to solve for the variable. Follow the order of operations and simplify the expression as much as possible.
4. Check your answer: Verify that your solution is correct by plugging it back into the original equation or inequality and making sure that it satisfies the conditions of the problem.
It's important to practice pre-algebra problems regularly to develop your problem-solving skills. You can find practice problems and tutorials online or in textbooks, and you can work with a tutor or teacher to get additional help. Remember to stay patient, focused, and positive, and don't be afraid to ask for help if you need it.
Amber baked 120 cookies to give to five friends she wants to put the same number of cookies in each bag which of the following can she use to find out how many cookies to put in each bag
Answer:
she can divide the amount of cookies to friends
Step-by-step explanation:
120/5= 24
The point [ -√2/2, √2/2] is the point at which the terminal ray of angle 0 intersects the unit circle. What are the values for the cosine and cotangent functions for the angle 0
O cos0 = -√2/2, cot0=-1
O cos0=√2/2, cot0= 1
O cos0= √2/2, cot0= -1/2
O cos0= - √2/2, cot0= 1/2
PLEASE HURRY
The values for the cosine and cotangent functions for the angle x is
O cos0 = -√2/2, cot0 =-1
How to find the cosine and cotangent angleLet the angle be x
given that the point [ -√2/2, √2/2] is on the terminal ray of angle x
the x-coordinate of the point is -√2/2 and this is the cos hence
cos x = -√2/2.
To find the cotangent
the y coordinate is the sin therefore sin x = √2/2
tan x = sin x / cosx = (√2/2) / (-√2/2) = -1
and cotangent is the reciprocal of the tangent
cot x = 1 / tan x = -1/1 = -1.
cos x = -√2/2 and cot x = -1.
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