A triangle has side lengths of 10 inches, 11 inches, and 12 inches. What kind of triangle is it?
Answers
Answer:
Acute scalene triangle.
More Information:
Sides: a = 10 b = 11 c = 12
Area: T = 51.521
Perimeter: p = 33
Semiperimeter: s = 16.5
Angle ∠ A = α = 51.318° = 51°19'4″ = 0.896 rad
Angle ∠ B = β = 59.17° = 59°10'10″ = 1.033 rad
Angle ∠ C = γ = 69.513° = 69°30'46″ = 1.213 rad
Height: ha = 10.304
Height: hb = 9.367
Height: hc = 8.587
Median: ma = 10.368
Median: mb = 9.579
Median: mc = 8.631
Inradius: r = 3.122
Circumradius: R = 6.405
Vertex coordinates: A[12; 0] B[0; 0] C[5.125; 8.587]
Centroid: CG[5.708; 2.862]
Coordinates of the circumscribed circle: U[6; 2.242]
Coordinates of the inscribed circle: I[5.5; 3.122]
Exterior (or external, outer) angles of the triangle:
∠ A' = α' = 128.682° = 128°40'56″ = 0.896 rad
∠ B' = β' = 120.83° = 120°49'50″ = 1.033 rad
∠ C' = γ' = 110.487° = 110°29'14″ = 1.213 rad
How to Solve:
The calculation of the triangle has two phases. The first phase calculates all three sides of the triangle from the input parameters. The first phase is different for the different triangles query entered. The second phase calculates other triangle characteristics, such as angles, area, perimeter, heights, the center of gravity, circle radii, etc. Some input data also results in two to three correct triangle solutions (e.g., if the specified triangle area and two sides - typically resulting in both acute and obtuse) triangle).
1. Input data entered: sides a, b, and c.
a=10
b=11
c=12
We know the lengths of all three sides of the triangle, so the triangle is uniquely specified. Next, we calculate another of its characteristics - the same procedure for calculating the triangle from the known three sides SSS.
a=10
b=11
c=12
2. The triangle perimeter is the sum of the lengths of its three sides
3. Semiperimeter of the triangle
The semiperimeter of the triangle is half its perimeter. The semiperimeter frequently appears in formulas for triangles to be given a separate name. By the triangle inequality, the longest side length of a triangle is less than the semiperimeter.
4. The triangle area using Heron's formula
Heron's formula gives the area of a triangle when the length of all three sides is known. There is no need to calculate angles or other distances in the triangle first. Heron's formula works equally well in all cases and types of triangles.
5. Calculate the heights of the triangle from its area.
There are many ways to find the height of the triangle. The easiest way is from the area and base length. The triangle area is half of the product of the base's length and height. Every side of the triangle can be a base; there are three bases and three heights (altitudes). Triangle height is the perpendicular line segment from a vertex to a line containing the base.
6. Calculation of the inner angles of the triangle using a Law of Cosines
The Law of Cosines is useful for finding a triangle's angles when we know all three sides. The cosine rule, also known as the Law of Cosines, relates all three sides of a triangle with an angle of a triangle. The Law of Cosines extrapolates the Pythagorean theorem for any triangle. Pythagorean theorem works only in a right triangle. Pythagorean theorem is a special case of the Law of Cosines and can be derived from it because the cosine of 90° is 0. It is best to find the angle opposite the longest side first. With the Law of Cosines, there is also no problem with obtuse angles as with the Law of Sines because the cosine function is negative for obtuse angles, zero for right, and positive for acute angles. We also use inverse cosine called arccosine to determine the angle from the cosine value.
7. Inradius
An incircle of a triangle is a tangent circle to each side. An incircle center is called an incenter and has a radius named inradius. All triangles have an incenter, and it always lies inside the triangle. The incenter is the intersection of the three-angle bisectors. The product of the inradius and semiperimeter (half the perimeter) of a triangle is its area.
8. Circumradius
The circumcircle of a triangle is a circle that passes through all of the triangle's vertices, and the circumradius of a triangle is the radius of the triangle's circumcircle. The circumcenter (center of the circumcircle) is the point where the perpendicular bisectors of a triangle intersect.
9. Calculation of medians
A median of a triangle is a line segment joining a vertex to the opposite side's midpoint. Every triangle has three medians, and they all intersect each other at the triangle's centroid. The centroid divides each median into parts in the ratio of 2:1, with the centroid being twice as close to the midpoint of a side as it is to the opposite vertex. We use Apollonius's theorem to calculate the length of a median from the lengths of its side.
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Related Questions
if square one is the largest of the three squares in the model,which statement is true?
Answers
_______________
I'm reading your question
___________________
According to the Pythagorean theorem
Hypotenuse ^2 = Side 1 ^2 + Side 2 ^2
The hypotenuse is the case (Square 1 )
area of the sqaure= side of the square^2
________________________
That means the area of 1 is = area of square 2 + area fo square3 (J is false)
_______________________________
We are not sure about the relation between square 2 and 3 just the addition is the square 1 (F and H we have no certainty)
______________________________
G is true
______________________________
Answer
G
Find the slope between these two points:
(3, 0), (-11, -15)
Answers
Answer:
Slope = (15/14)
Step-by-step explanation:
(3, 0), (-11, -15)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ -15 - 0 -15 15
m = ------------ = ----------- = ----------- = ---------
x₂ - x₁ -11 - 3 -14 14
I hope this helps!
A middle school took all of its 6th grade students on a field trip to see a play at a
theater that has 1080 seats. The students filled 35% of the seats in the theater. How
many 6th graders went on the trip?
Answers
Answer:
there are 378 students
Step-by-step explanation:
you can see this as a simple proportion.
You know that the 100% of the seats are 1080 and you need to know the 35% of the seats, so you do:
[tex] \frac{1080}{100} = \frac{x}{35} [/tex]
so you do
x = 35 * 1080 ÷ 100 which gives 378
Is the trend line linear? If so, write a linear equation that represents the trend line. Show your work. PLSSSSSSS HELPPPP SHOW UR WORK TO ON HOW YOU FIGURED IT OUT THE EQUATION FOR IT USE SLOPE TOO ILL INCLUDE AN IMAGE TOO
Answers
The trend line is linear and the trend line has an equation of y = 500/9x + 100
The type of the trendFrom the graph, we can see that:
The points appear to be on a straight line and it increases along the x-axis
This means that the points can appear on an approximate straight line
So, we can conclude that the trend is a linear trend
The equation of the lineOn the line, we have the following points
(x, y) = (0, 100) and (9, 600)
We start by calculating the slope of the points using the following slope equation
Slope = (y₂ - y₁)/(x₂ - x₁)
Where x and y are defined above
So, we have
Slope = (600 - 100)/(9 - 0)
Evaluate
Slope = 500/9
The equation is then calculated as
y = Slope(x - x₁) + y₁
Where
(x₁, y₁) = (0, 100) and Slope = 500/9
So, we have
y = 500/9 * (x - 0) + 100
Evaluate
y = 500/9x + 100
Hence, the equation is y = 500/9x + 100
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I m struggle with this problem can someone help me
Answers
Check below, please
1) The way to tackle this problem, is by dividing those numerators by the denominators so we can get the decimal form of each fraction, and count the marks to plot them.
2) Let's divide them:
[tex]\begin{gathered} -\frac{5}{6}=-0.83 \\ \frac{17}{6}=2.83 \end{gathered}[/tex]So now, we can plot them:
Thus, this the answer.
-12/7 = 6y solve for y and simplify your answer as much as possible
Answers
Answer:
[tex]\displaystyle y = \frac{-2}{7}[/tex]
Step-by-step explanation:
To solve, we will isolate the variable.
Given:
-12/7 = 6y
Divide:
[tex]\displaystyle \frac{\frac{-12}{7} }{6} =\frac{6y}{6}[/tex]
Simplify the right side:
[tex]\displaystyle \frac{\frac{-12}{7} }{6} =y[/tex]
"Keep, change, flip" on the left side:
[tex]\displaystyle \frac{-12}{7} *\frac{1}{6} = y[/tex]
Multiply:
[tex]\displaystyle \frac{-12*1}{7*6}= y[/tex]
[tex]\displaystyle \frac{-12}{42}= y[/tex]
Simplify and reflexive property:
[tex]\displaystyle y = \frac{-2}{7}[/tex]
2. Amy works at the local restaurant making $7.25 per hour in addition to tips. During her last shift, she earned $62 in tips and took home $112.75 for the day. How many hours did she work?
Answers
Answer:
She worked Seven (7) hours.
Step-by-step explanation:
$112.75 is the total
she earned $62 in tips which doesn't count because the questions asked for how long she worked.
Adding tips would make the equation unreliable because how long people work doesn't really affect how much tips you get. You maybe getting 50 bucks of tips in the first and 40 in the next.
solving steps: (where x = number of hours worked)
7.25x + 62 = 112.75 <<<the true equation based on the story
7.25x = 112.75 - 62
7.25x = 50.75
x = 50.75 ÷ 7.25
x = 7
Seven (7) hours worked.
cheesebugers and pizza are on todays menu. if the cafeteria serves cheeseburgers every 4th day and pizza every 6th day, how many more days until cheeseburgers and pizza are both on the menu again?
Answers
Answer:
12 more days
Step-by-step explanation:
Every time cheeseburger will be served: 4th day, 8th day, 12th day, 16th day
Every time pizza wil be served: 6th day, 12th day, 18th day
Since 12 is a common number, every 12 days both cheeseburgers and pizzas will be served
A pack of paper costs $1.75, including tax. Mr. Valentino wants to purchase packs of paper for his class and has a $25 budget. Write and solve an inequality to solve for the number of packs of paper Mr. Valentino can purchase, and describe the graph of the solution.
Answers
The inequality according to the the cost of pack of paper can be written as x ≤ 14.28 and Mr. Valentino can purchase a maximum of 14 packs of paper.
What is inequality?
A connection that compares two numbers or other mathematical expressions inequitably is known as an inequality in mathematics. The majority of the time, size comparisons between two numbers on the number line are made. The two most common notations for representing various forms of inequalities are as follows:
The symbol a < b indicates that a is smaller than b.
The symbol a > b indicates that a is bigger than b.
Let's assume he can buy x pack of paper.
Cost of x pack of paper will be equal to the x times cost of 1 pack of paper
i.e. Total cost = 1.75x
Now, Mr. Valentino has $25
Therefore,
1.75x ≤ 25
Inequality is ⇒ x ≤ 14.28
It tells us that Mr. Valentino can purchase only 14 packs of paper.
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Which of the following is TRUE for every polynomial P with degree = n ?a) The highest power of x in P(x) is n-1b) There are at most n-1 solutions to P(x) = 0c) The graph of P has at most n-1 turning pointsd) The graph of P has at most n-1 x-intercepts
Answers
We need to identify the true statement for every polynomial P with degree n.
The degree n of a polynomial is the exponent of the highest power of x in that polynomial. For example, the polynomial
[tex]x³+3x²+3[/tex]has degree 3, since the highest power of x has exponent 3.
Thus, if the degree is n, then the highest power is n (not n-1). Therefore, (a) is False.
About the number of solutions to P(x) = 0, it can equal the number of the polynomial degree. For some polynomials, the solutions can repeat, so the number of solutions will be less than n. For some of them, the solutions may not belong to the real numbers.
As an example, for P(x) = x²+4, we have:
[tex]\begin{gathered} x²+4=0 \\ \\ x²=-4 \\ \\ x=\pm\sqrt{-4} \\ \\ x=\pm2\sqrt{-1} \\ \\ x=\pm2i \\ \\ x_1=-2i \\ \\ x_2=2i \end{gathered}[/tex]The above polynomial has degree 2 and 2 solutions. Therefore, (b) is False.
Each turning point is where the graph of the polynomial P(x) changes from decreasing to increasing or vice versa. The graph of any polynomial of degree n has at most n-1 turning points.
Therefore, (c) is True.
We can see that (d) is False from the following example:
the line P(x) = x+1 has degree n = 1 and n = 1 x-intercept, which is its zero x = -1.
Answer:
c) The graph of P has at most n-1 turning points
1. The public primary/secondary school dropout rate in Washington State is 6%. Suppose 35
individuals of primary/secondary school age are interviewed at random on a city street. What is
the probability that:
a. (5 points) Exactly 7 of them are dropouts?
Answers
The probability that exactly 7 individuals are dropouts out of 35 is 0.0033288.
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.
Given,
Probability of dropouts=p= 6%= 0.06
Probability of not dropouts=q=1-p=1-0.06=0.94
n=35
We use the probability mass function of binomial distribution, as there are only two possible outcomes for the given situation. If the individual is dropout or not a dropout.
P(X=x)= nCr x p^r x q^(n-r)
P(X=7)= 35C7x(0.06)^7x(0.94)^28
P(X=7)=6724520x(0.06)^7x(0.94)^28
P(X=7)=0.00332889
Therefore, the probability of exactly 7 of them are dropouts is 0.00332889.
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Answer the question below
Answers
A) 4/5 or 0.8
B)7
C)1/81
In Exercises 1 and 2, find m/1 and m<2
1.
Answers
Answer:
m/1 = 87
m/2 = 93
Step-by-step explanation:
m1 and m2 need to have an angle of 180
so 180-87 = 93
ashley’s house and the public Library are plotted on the coordinate plane as shown.What is the distance between Ashely’s house and the public library to the nearest tenth
Answers
The distance between Ashely’s house and the public library is of 7.8 miles.
What is the distance between two points?Suppose that we have two points with coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The shortest distance between these two points is given by the following rule:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
This formula is derived from the Pythagorean Theorem, as the points form a right triangle in the Cartesian plane, with the hypotenuse representing the distance between them.
In the context of this problem, the coordinates of her house and of the library are given as follows:
House: (4,2).Library: (10,7).Hence the distance is calculated as follows:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]D = \sqrt{(10 - 4)^2+(7 - 2)^2}[/tex]
D = sqrt(61)
D = 7.8 miles, as each unit on the plane represents one mile.
Missing informationThe problem states that each unit on the plane represents one mile and the image gives their position on the plane.
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Anna is computing 266 - 39. To do so, she first says that 266 is close to 270 and 39 is
close to 40, so she starts out computing 270 - 40 = 230. She then computes 230 - 3 =
227, and declares that 227 is her final answer. Is Anna's strategy correct? If yes, explain
why. If no, explain why not. Be mathematically specific, and support your reasoning
with a number-line model.
Answers
Yes, her strategy was correct.
What is BODMAS?When compared to operations involving just two numbers, solving an arithmetic expression that includes multiple operations like addition, subtraction, multiplication, and division is more difficult. A two-number operation is simple, but how do you work out an expression with brackets as well as multiple operations, as well as how to make a bracket simpler? Let's review the BODMAS rule as well as discover how brackets can be made simpler. For Bracket, Order, Division, Multiplication, Addition, and Subtraction, the acronym BODMAS is used. The acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication, Division, Addition, as well as Subtraction, is also known as BODMAS in some areas. Thus, the following figure illustrates the order in which BODMAS and PEMDAS operate.
Simplification is done following BODMAS rule.
266-39 gives 227.
Hence, her strategy was correct.
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y =40x^2 find X when y =10,360,1000,4000
Answers
Given m||n, find the value of x.
(6x-20)°
(6x-4)°
Answers
Answer:
x = 7
Step-by-step explanation:
A boy bought some pencils for N60.00. If he had paid N1 less for each pencil, he could have bought 5 more pencils. How many pencils did he pay for?
Answers
The number of pencils he paid for is 15.
How to find the number of pencil he paid for?He bought some pencils for N60.00.
If he had paid N1 less for each pencil, he could have bought 5 more pencils.
Let
x = cost of each pencil that amount to N60.00
y = number of pencil
Therefore,
xy = 60
y = 60 / x
(y + 5)(x - 1) = 60
(60 / x + 5)(x - 1) = 60
60 - 60 / x + 5x - 5 = 60
- 60 / x + 5x + 55 = 60
- 60 / x + 5x = 60 - 55
- 60 / x + 5x = 5
- 60 + 5x² / x = 5
5x = -60 + 5x²
5x² - 5x - 60 = 0
x² - x - 12 = 0
x² + 3x - 4x - 12 = 0
x(x + 3) - 4(x + 3) = 0
(x - 4)(x + 3)
Hence,
x = 4 and x = -3
We can only use positive value.
xy = 60
y = 60 / 4
y = 15
Therefore, he paid for 15 pencils.
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-1/5 = -1/2w - 1/7 solve for w and simplify your answer as much as possible
Answers
Answer:
w = (4/35)
Step-by-step explanation:
-1/5 = -1/2w - 1/7
+1/7 +1/7
-----------------------------
-2/35 = -1/2w
÷-1/2 ÷-1/2
-----------------------
4/35 = w
Extra:
-1(7) 1(5)
------- + -------
5(7) 7(5)
-7 5 -2
------- + ------- = -------
35 35 35
------------------------------------------------------------
-2 -1
------- ÷ -------
35 2
-2 -2 4
------- × ------- = -------
35 1 35
I hope this helps!
The boxplot displays the arm spans for 44 students.
Which of the following is not a true statement?
There are no outliers in this distribution.
The shape of the boxplot is fairly symmetric.
The range of the distribution is around 60 cm.
The center of the distribution is around 180 cm.
Answers
The statements The range of the distribution is around 60 cm and
the center of the distribution is around 180 cm are true.
What is statistics?Statistics is the study and manipulation of data, including ways to gather, review, analyze, and draw conclusions from data.
In the given statements
There are no outliers in this distribution.
The shape of the boxplot is fairly symmetric.
The range of the distribution is around 60 cm.
The center of the distribution is around 180 cm.
The statement "The range of the distribution is around 60 cm" is true.
The range is the spread of your data from the lowest to the highest value in the distribution.
In the given graph
Range=200-140
=60
So it is true.
The center of the distribution is around 180 cm is also true.
Hence the statements The range of the distribution is around 60 cm and
the center of the distribution is around 180 cm are true.
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HELP ME PLEOPLE THIS IS SO CONFUSING HELP ME I WILL GET SUSPENDED IF I DON"T ANSWER THIS HELP ME PLEASE HELP I WILL GET A 0 AND SUSPENDED HELP HELP
Answers
B) distribute once again but instead of multiplying , divide the factors
(3.6/1.8) + (3.6/10^2) + (10^-5/1.8) + (10^-5/10^2) =
2 + 0.36 + 0.00005555555555 + 0.000001 = should be around 2.36
if 1 cm is equivlent to 10km what is 50 cm equivlant to
Answers
Answer:
50cm is equivalent to 500km
Have a good one!
Jan uses 78 yard of fabric for one quilt square and 17 yard in another. how much fabric has jan used? responses 914 of a yard 9 over 14 of a yard 618 yards 6 and 1 eighth yards 756 of a yard 7 over 56 of a yard 1156 yards
Answers
Based on the yards of fabric used by Jan for the quilt squares, the total fabrics used by Jan was 1 ¹ / ₅₆ yards
How to find the number of yards used?The yards of fabric used by Jan were 7 / 8 of a yard and 1 / 7 of another yard.
The total yards used by Jan can be found by adding these fractions up. To add both fractions, you first need to find the common denominator of 8 and 7 which is 56.
Then the numerators can be found by dividing 56 by the denominator and then multiplying the numerator by the result.
Fraction 7 / 8 yards:
= 56 / 8 x 7
= 49 / 56
Fraction 1 / 7:
= 56 / 7 x 1
= 8 / 56
The total number of yards used is:
= 49 / 56 + 8 / 56
= 57 / 56
= 1 ¹ / ₅₆ yards
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charlyn walks completely around the boundary of a square whose sides are each 55 km long. from any point on her path she can see exactly 11 km horizontally in all directions. what is the area of the region consisting of all points charlyn can see during her walk, expressed in square kilometers and rounded to the nearest whole number?
Answers
The area of the region consisting of all the points Charlyn can see during her walk is equal to, A = 4840 km.
Charlyn is walking around the boundary of square A, which is 55 km long, and she has a horizontal vision of 11 km.
So as she walks around the square of 55 km, let there be another square B which lies outside square A, which is created due to her 11 km field of vision.
length of sides of square B = 55+(2×11) which is equal to 77 km.
And as she walks around the square of 55 km, let there be yet another square C which lies inside square A, which is created due to her 11 km field of vision.
length of sides of square C = 55-(2×11) which is equal to 33 km.
The area that Charlyn can see throughout her walk is equal to,
A = Area of square B - Area of square C.
The area of square B = Side² = 77² = 5929.
The area of square C = Side² = 33² = 1089.
A = 5929 - 1089.
A = 4840 km.
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Hey! Could anybody help me out with this? I would like a very brief explanation leading to the answer as I already kinda understand the topic. Thanks!
Answers
Domain and Range of a Function
The domain of a function f is the set of values of the input (or independent) variable, often called x. The range is the set of values of the output (or dependent) variable, often called y, or f(x).
The function shown in the image has a shape that opens up to infinity (marked with the two arrows). This means that x can have any real value from minus infinity to plus infinity, that is, all real numbers.
Now for the range, we can see not every value of y belongs to the function. The graph decreases down to the vertex of the parabola that is located at (3,-12). This means that from y=-12 and up, the function exists, but not below this value.
Summarizing:
Domain: All real numbers
Range: y ≥ -12
do blood-building drugs help brain development in babies born prematurely? researchers randomly assigned 53 babies, born more than a month premature and weighing less than 3 pounds, to one of three groups. babies either received injections of erythropoietin (epo) three times a week, darbepoetin once a week for several weeks, or no treatment. results? babies who got the medicines scored much better by age 4 on measures of intelligence, language, and memory than the babies who received no treatment.how many different treatments were there and what principle of experimental design does that address?
Answers
There were three different treatments: erythropoietin, darbepoetin, and no treatment. This selection exemplifies the principle of randomization principle.
What is a treatment?In experiments, the word treatment refers to the use of a specific medicine, therapy, or condition that is controlled by the research to test the effect of the treatment on subjects. For example, if the researcher wants to find out the ideal amount of water for a plant to grow, the treatment would be the amount of water.
In the case presented, there are three treatments:
Erythropoietin (epo) three times a week.Darbepoetin once a week for several weeks.No treatment.What principle of experimental design does that address?Randomization is the principle applied because the subjects are selected randomly for each of the groups and this reduces bias.
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An autonomous underwater vehicle (AUV) is at an elevation of -8.25 ft. It dives down 6 2/3 ft to collect a specimen. Then the AUV dives another 15 3/4 ft. What is the final elevation of the AUV? Show your work
Answers
The final elevation of the AUV is [tex]-31 \frac{5}{12}[/tex] feet.
Given that, AUV is at an elevation of -8.25 ft. It dives down [tex]6\frac{2}{3}[/tex] ft to collect a specimen. Then the AUV dives another [tex]15\frac{3}{4}[/tex] ft.
What is an elevation?The angle of elevation in math is "the angle formed between the horizontal line and the line of sight when an observer looks upwards is known as an angle of elevation".
Here, the mixed fraction can be written in improper fraction
[tex]6\frac{2}{3} = \frac{20}{3}[/tex] and [tex]15\frac{3}{4}=\frac{63}{4}[/tex]
Now, 8.25 = 825/100 = 33/4
The final elevation = -33/4-20/3-63/4
= -99/4 - 20/3
= -297/12 -80/12
= - 377/12
= [tex]-31 \frac{5}{12}[/tex]
Therefore, the final elevation of the AUV is [tex]-31 \frac{5}{12}[/tex] feet.
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The price of an item has risen to $300 today. Yesterday it was $125. Find the percentage increase.
Answers
Answer:
140
Step-by-step explanation:
you spin two wheels with equal size wedges labeled with numbers 1 through 9. what is the probability that at least one wheel lands on a multiple of 4 or the first value is strictly greater than 8?
Answers
The probability that at least one wheel lands on a multiple of 4 or the first value is strictly greater than 8 is 53/99
The greatest number that can be formed by the two wheels is 99
Let event A be multiple of 4
Multiples of 4 between 1 to 9 is 4,8
Probability that at least one wheel land at a multiple of 4 is
[tex]\frac{2}{9} + \frac{2}{9}[/tex] = 4/9
Let event B be first value greater than 9
P(B) = 9/99 = 1/11
P(A∩B) = 0
Probability of at least one wheel lands on a multiple of 4 or the first value is strictly greater than 8
P(A∪B) = P(A) + P(B) - P(A∩B)
= 4/9 + 1/11 - 0
= [tex]\frac{4(11)}{9 (11)} + \frac{1 (9)}{11(9)}\\\\ \frac{44 + 9}{99}\\\\ \frac{53}{99}[/tex]
Therefore, the probability that at least one wheel lands on a multiple of 4 or the first value is strictly greater than 8 is 53/99
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Last year, Milan had $10,000 to invest. He invested some of it in an account that paid 9% simple interest per year, and he invested the rest in an account that
paid 7% simple interest per year. After one year, he received a total of $780 in interest. How much did he invest in each account?
Answers
Answer:
$4000 at 9% and $6000 at 7%Step-by-step explanation:
Let the amount invested at 9% be x.
Then the amount invested at 7% is 10000 - x.
The amount of interest after one year is $780.
Set up equation to represent this:
0.09x + 0.07(10000 - x) = 7800.09x + 700 - 0.07x = 7800.02x = 780 - 7000.02x = 80x = 80/0.02x = 4000Amount invested at 7% is:
10000 - 4000 = 6000Answer:
Milan invested:
$4,000 into the account earning 9% interest.$6,000 into the account earning 7% interest.Step-by-step explanation:
Given information:
Total amount invested = $10,000.Account A = 9% simple interest per year.Account B = 7% simple interest per year. Total interest earned after one year = $780.Let x be the amount invested in Account A.
Therefore, the amount invested in Account B is (10000 - x).
Simple Interest Formula
I = Prt
where:
I = Interest earned.P = Principal invested.r = Interest rate (in decimal form).t = Time (in years).Create two equations using the given information:
[tex]\begin{aligned}\textsf{Interest: Account A} &= x \cdot 0.09 \cdot 1\\& = 0.09x\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Interest: Account B} &= (10000 - x) \cdot 0.07 \cdot 1 \\& = 0.07(10000 - x)\\& = 700-0.07x\end{aligned}[/tex]
As the total interest earned was $780, set the sum of the two found equations to 780 and solve for x:
[tex]\begin{aligned}\implies 0.09x+700-0.07x&=780\\0.02x+700&=780\\0.02x&=80\\x&=4000\end{aligned}[/tex]
Therefore, Milan invested:
$4,000 into the account earning 9% interest.$6,000 into the account earning 7% interest.