The two integers are 5 and 6.
Set up with algebraic equationTo solve this problem, we need to set up an algebraic equation based on the information given.
Let's call the first integer x and the second integer y. According to the problem, an integer (x) is 14 less than 4 times another (y).
This can be written as: x = 4y - 14
We are also told that the product of the two integers is 30. This can be written as:
xy = 30
Now we can substitute the first equation into the second equation to solve for one of the variables.
Let's solve for y:
(4y - 14)y = 30
4y^2 - 14y = 30
4y^2 - 14y - 30 = 0
Using the quadratic formula, we can solve for y:
y = (-(-14) ± √((-14)^2 - 4(4)(-30)))/(2(4))
y = (14 ± √(196 + 480))/8
y = (14 ± √676)/8
y = (14 ± 26)/8
y = 5 or y = -1.5
Now we can plug these values of y back into the first equation to find the corresponding values of x:
x = 4(5) - 14 = 6
x = 4(-1.5) - 14 = -20
So the two integers are either 5 and 6, or -1.5 and -20. However, since the problem asks for integers, we can eliminate the second solution.
Therefore, the two integers are 5 and 6.
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(1×1,000)+(3×100)+(5×10)+(9×
10
1
)+(8×
100
1
)left parenthesis, 1, times, 1, comma, 000, right parenthesis, plus, left parenthesis, 3, times, 100, right parenthesis, plus, left parenthesis, 5, times, 10, right parenthesis, plus, left parenthesis, 9, times, start fraction, 1, divided by, 10, end fraction, right parenthesis, plus, left parenthesis, 8, times, start fraction, 1, divided by, 100, end fraction, right parenthesis
The value of the expression (1×1,000)+(3×100)+(5×10)+(9×1/10)+(8 x 1/100) is 1,350.98.
To find the value of the expression (1×1,000)+(3×100)+(5×10)+(9×1/10)+(8 x 1/100), we need to simplify and perform the arithmetic operations.
Multiplying each term in the expression, we get:
1 × 1,000 = 1,000
3 × 100 = 300
5 × 10 = 50
9 × 1/10 = 0.9
8 × 1/100 = 0.08
Adding up all the terms, we get:
1,000 + 300 + 50 + 0.9 + 0.08 = 1,350.98
In summary, to find the value of the expression, we multiply each term by its respective coefficient, then add up all the terms. In this case, the result is 1,350.98.
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Complete question is:
Find the value of the expression (1×1,000)+(3×100)+(5×10)+(9×1/10)+(8 x 1/100)?
What is the area of the following circle?
Either enter an exact answer in terms of
�
πpi or use
3.14
3.143, point, 14 for
�
πpi and enter your answer as a decimal.
The area of the following circle is A ≈ 153.86 square units.
Describe Circle?A circle is a two-dimensional geometric shape that consists of all the points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius, and the distance across the circle passing through the center is called the diameter.
The circumference of a circle is the distance around the edge of the circle, and it is calculated using the formula C = 2πr, where r is the radius and π (pi) is a mathematical constant approximately equal to 3.14159. The area of a circle is the region enclosed by the circle, and it is calculated using the formula A = πr².
The diameter of the circle is 14, so the radius is half of that, which is 7.
The area of the circle is given by the formula A = πr², where r is the radius. Substituting in the values we get:
A = π(7)²
A = 49π
Therefore, the area of the circle is 49π square units. If you want to use an approximation, you can use 3.14 as an estimate for π and get:
A ≈ 153.86 square units.
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The complete question is -
27. \( \left\{\begin{array}{c}x+y+z=-1 \\ 2 x+3 y+2 z=3 \\ 2 x+y+2 z=-7 \\ x-3 y+2 z=10 \\ -x+3 y-z=-6 \\ -x+3 y+2 z=6 \\ 6 x-2 y+2 z=4 \\ 3 x-y+2 z=2 \\ -12 x+4 y-8 z=8\end{array}\right. \)
Using the Gaussian elimination method, the general solution is: [tex]\[ x = -31t + 6 \][/tex], [tex]\[ y = 5 \][/tex], [tex]\[ z = 31t \][/tex].
To solve this system of equations, we can use the Gaussian elimination method. This method involves creating a matrix with the coefficients of the equations and using row operations to reduce the matrix to a form that can be easily solved.
First, we create a matrix with the coefficients of the equations:
[tex]\[ \left( \begin{array}{ccc|c} 1 & 1 & 1 & -1 \\ 2 & 3 & 2 & 3 \\ 2 & 1 & 2 & -7 \\ 1 & -3 & 2 & 10 \\ -1 & 3 & -1 & -6 \\ -1 & 3 & 2 & 6 \\ 6 & -2 & 2 & 4 \\ 3 & -1 & 2 & 2 \\ -12 & 4 & -8 & 8 \end{array} \right) \][/tex]
Next, we use row operations to reduce the matrix to a form that can be easily solved:
[tex]\[ \left( \begin{array}{ccc|c} 1 & 1 & 1 & -1 \\ 0 & 1 & 0 & 5 \\ 0 & -1 & 0 & -5 \\ 0 & -4 & 1 & 11 \\ 0 & 4 & 0 & -5 \\ 0 & 4 & 1 & 7 \\ 0 & -8 & -4 & 10 \\ 0 & -4 & -1 & 5 \\ 0 & 8 & 4 & -4 \end{array} \right) \][/tex]
[tex]\[ \left( \begin{array}{ccc|c} 1 & 1 & 1 & -1 \\ 0 & 1 & 0 & 5 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 31 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 27 \\ 0 & 0 & -4 & 50 \\ 0 & 0 & -1 & 25 \\ 0 & 0 & 4 & -44 \end{array} \right) \][/tex]
[tex]\[ \left( \begin{array}{ccc|c} 1 & 0 & 1 & -6 \\ 0 & 1 & 0 & 5 \\ 0 & 0 & 1 & 31 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & -4 \\ 0 & 0 & 0 & 174 \\ 0 & 0 & 0 & 56 \\ 0 & 0 & 0 & -168 \end{array} \right) \][/tex]
From this reduced matrix, we can see that there are infinitely many solutions to this system of equations. The general solution can be written as:
[tex]\[ x = -31t + 6 \][/tex]
[tex]\[ y = 5 \][/tex]
[tex]\[ z = 31t \][/tex]
Where t is any real number.
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What is E(Y | X<=1/2) ?
expectation of Y given that X is less than or equal half
The conditional expectation of Y given that X is less than or equal to 1/2 is calculated by taking the weighted average of the possible values of Y, with the weights being the probabilities of X being less than or equal to 1/2 for each value of Y.
The formula for E(Y | X<=1/2) is:
E(Y | X<=1/2) = ∑y P(Y=y | X<=1/2) * y
To find P(Y=y | X<=1/2), we can use the formula:
P(Y=y | X<=1/2) = P(X<=1/2 | Y=y) * P(Y=y) / P(X<=1/2)
We can then plug in the values for each possible value of Y and calculate the conditional expectation.
For example, if Y can take on the values 0, 1, and 2, and the probabilities of X being less than or equal to 1/2 for each value of Y are 0.2, 0.5, and 0.3, respectively, and the probabilities of Y being 0, 1, and 2 are 0.4, 0.3, and 0.3, respectively, then:
E(Y | X<=1/2) = (0.2 * 0.4 / 0.5) * 0 + (0.5 * 0.3 / 0.5) * 1 + (0.3 * 0.3 / 0.5) * 2
E(Y | X<=1/2) = 0 + 0.3 + 0.36
E(Y | X<=1/2) = 0.66
Therefore, the conditional expectation of Y given that X is less than or equal to 1/2 is 0.66.
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A rectangle is 45 cm long and 15 cm wide. What's the ratio of the rectangle's length to its width? A 1:3. B 3:1. C 1:4. D 4:1
Answer:
Area of a triangle =L*W
A= 45*15
A=270cm²
In the first race in the video, the student sprints at a speed of 10 yards per second. The math teacher only runs 3.75 yards per second. In the second race, the teacher is given a 10-yard head start, but their speeds remain the same. In the third race, the teacher is again given a 10-yard head start, but her speed is doubled. The student, however, continues to run at 10 yards per second. The length of each race is 100 yards. In each case, who will cross the finish line first? Will the student catch the math teacher, and if so when?
After considering the speeds of the student and the teacher and the distance they ran in each case, we found that the students wins in all the races.
What is meant by the speed of a body?Speed is defined as the ratio of distance travelled to the amount of time it took. As speed simply has a direction and no magnitude, it is a scalar quantity.
An object is considered to be moving at a uniform speed when it travels the same distance in the same amount of time.
When an object travels a different distance at regular intervals, it is said to have variable speed.
Average speed is the constant speed determined by the ratio of the total distance travelled by an object to the total amount of time it took to travel that distance.
Given,
The length of the race = 100 yards
1st race
The speed of student = 10 yards/s
The speed of teacher = 3.75 yards / s
Time taken by student = distance / speed = 100/10 = 10s
Time taken by teacher = 100 / 3.75 = 26.67 s
So the student finishes the race because he/she took less time.
2nd race
Distance run by teacher = 100 - 10 = 90
Speed of teacher = 3.75 yards / s
Time taken by teacher = 90/3.75 = 24s
The distance and speed of the student are the same.
Time taken by student = 10 s
Still, the student finishes the race first.
3rd race
Distance run by teacher = 100 - 10 = 90
Speed of teacher = 3.75 * 2 yards /s = 7.5 yards/s
Time taken by teacher = 90/ 7.5 = 12s
The distance and speed of the student are the same.
Time taken by student = 10 s
Still, the student finishes the race first.
Therefore by considering the speeds of the student and the teacher and the distance they ran in each case, we found that the students wins in all the races.
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Can someone help me out with the amount deprecating each year? I can’t figure it out.
9th grade algebra
Answer:
Year 1 Depreciation:$2,000
Depreciation Percentage:20.00%
Total Depreciation:$10,000
Final Year Depreciation:$2,000
Step-by-step explanation:
P.S by teacher told me the answer
Determine the critical numbers, if any, of the function
f
on the interval
[1,3]
.
f(x)=x 2
3−x
Give your answer as a comma-separated list. Express numbers in exact form. If the function does not have any critical numbers. enter DNE.
We are only interested in the critical numbers on the interval [1,3], so we can disregard x = 0. Therefore, the critical numbers of the function f(x) on the interval [1,3] are x = 3.
The critical numbers of a function are the points where the derivative of the function is either zero or undefined. To find the critical numbers of the given function f(x) = x^2/(3-x), we need to first find its derivative:
f'(x) = (2x(3-x) - (-1)x^2)/ (3-x)^2 = (6x - x^2 - x^2)/ (3-x)^2 = (6x - 2x^2)/ (3-x)^2
Now, we need to find the values of x for which f'(x) = 0 or f'(x) is undefined. f'(x) is undefined when the denominator (3-x)^2 is equal to 0, which occurs when x = 3. f'(x) is equal to 0 when the numerator 6x - 2x^2 is equal to 0:
6x - 2x^2 = 0
2x(3 - x) = 0
x = 0 or x = 3
However, we are only interested in the critical numbers on the interval [1,3], so we can disregard x = 0. Therefore, the critical numbers of the function f(x) on the interval [1,3] are x = 3.
Answer: 3
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In the above rectangle, what is the length of each of the longer sides of the perimeter is 36?
Answer:
Step-by-step explanation:
2(2x+2) + 2(x+4) = 36
4x+4 +2x+8 =36
6x+12= 36
6x = 36-12
6x =24
x = 4
longer side = 10
Module 06: Project Option 1
You guys got me on this right I need this done by 4:30 pm tomorrow please help me the assignment is below
An expression that looks like Sarah's expression but is not equivalent is:
10(5j + j + 3).
What can you say about expressions?A sentence qualifies as a mathematical expression if it comprises one or more mathematical operations, at least two numbers, or variables. Let's examine the writing style of expressions. A number is 6 times larger than the other number, x, by a factor of 2. This statement is represented mathematically by the expression x/2 + 6. Using mathematical expressions, complex puzzles can be solved.
now in the question,
We can write a look alike expression which is not equivalent is:
10(5j + j + 3).
Now translating the new expression into verbal:
Sarah gets paid $10 for every shark tooth she finds. After finding 3, she asked Jhon for help. When Jhon finds a tooth, by that time Sarah finds 5 of them.
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Find the fourth proportion to 1 5/7, 2 3/14 and 3 3/5
The fourth proportion to 15/7,23/14, and 33/5 is 19.25.
To discover the fourth proportion, we require to set up a probability between the 3 presented figures and the fourth unknown variety, which we can name x.
23/1433/5 x
First, we need to transfigure all the mixed figures to unsuitable fragments
= (7/7 * 1)5/7 = 7/75/7 = 12/7
= (14/14 * 2)3/14 = 28/143/14 = 31/14
= (5/5 * 3)3/5 = 15/53/5 = 18/5
Now we're suitable to preference those values into the share
31/1418/5 x
To break for x, we're suitable to cross-multiply
12/7) * x = (31/14) *(18/5)
Simplifying
12x/ 7 = 279/14
Multiplying each aspects via7/12
x = (279/14) *(7/12)
x = 19.25
Thus, the fourth proportion to 15/7,23/14, and 33/5 is 19.25.
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Big ideas 7.5 question
Answer:
66.5
Step-by-step explanation:
average the 2 together (57+76)/2
5 out of the 10 employees at the water slides are temporary employees. What percentage of the employees at the water slides are temporary?
Write your answer using a percent sign (%).
Answer: 50%
Step-by-step explanation: There are 5 out of 10 employees at the water slide. 10 in this situation is going to be 100%
since there is only 5 out of 10 employees that are temporary
it would be 50%
Answer: 50%
Step-by-step explanation:
I WILL GIVE BRAINLIEST TO WHOEVER ANSWER ALL 3 QUESTIONS RIGHT AND MANY POINTS I BEG PLEASE
In theory think about how many sides are on a dice and the numbers that are shown on each side.
it is a six sided dice
In an experiment the dice is rolled 20 times and lands on 1 two times and on 5 four times.
Find each experimental and theoretical probability.
a) landing on 5
Experimental:
Theoretical
b) not landing on 1
Experimental:
Theoretical:
c) landing on 1
Experimental:
Theoretical:
(please help)
Answer:
c landing on 1 is the answer
hope it helps u mark me BRAINLIST
Two ladders are places at different locations on a coconut palm tree so that lights can be
installed, as pictured below. The length of the taller ladder is three times the length of the shorter ladder. The shorter ladder is placed 3.5 feet from the base of the tree while the taller ladder is placed 7.5 feet from the base of the tree. What is the distance on the tree between the two ladders?
Therefore, [tex]h = \sqrt{(12.25 - x^2)} = 3.73[/tex] feet represents the distance between the two staircases on the tree. Thus, option c is correct.
what is Pythagoras theorem ?The Pythagorean theorem states that the square length of the hypotenuse, or the side that faces the right angle, of a right triangle is equal to the sum of the square lengths of the other two sides. The following can be expressed mathematically: [tex]a^2 + b^2 = c^2[/tex] where "c" represents the length of the hypotenuse and "a" and "b" represent the measurements of the two sides of the right triangle.
given
Assume the tree is h feet tall, the higher ladder is 3 feet long, and the lower ladder is x feet long.
Using the Pythagorean formula, we can create two equations:
With regard to the narrower staircase, x² + h² = (3.5)
Use the formula for the higher ladder. (3x)²+ h²= (7.5)².
The formulas are as follows, simplified: 12.25 x² + 9.25 x² + 56.25
To remove h2, we can solve for x in the first equation and y in the second equation: 8x² = 44.
Finding the value of x is as follows: [tex]x = \sqrt{(5.5) } = 2.34[/tex]
Therefore, [tex]h = \sqrt{(12.25 - x^2)} = 3.73[/tex] feet represents the distance between the two staircases on the tree.
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Complete question:
Two ladders are placed at different locations on a coconut palm tree so that lights can be installed, as pictured below. The length of the taller ladder is three times the length of the shorter ladder. The shorter ladder is placed 3.5 feet from the base of the tree while the taller ladder is placed 7.5 feet from the base of the tree. What is the distance on the tree between the two ladders?
O 4.59 feet
O 9.78 feet
O 3.73 feet
O 8.96 feet
Show with calculations whether the 15 boxes of çremora will be enough to last for a year
As a result, the 15 cartons of creamer will last for 1,350 days, or nearly 3.7 expression years. This implies the consumer drinks one serving of creamer per day at a weight of 5 grammes per serving.
what is expression ?An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are often used in arithmetic, mathematics, and form. They are employed in the depiction of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.
(Total amount of creamer in grammes) / number of days (Amount of creamer consumed per day in grams)
Let's start by calculating the entire amount of creamer in grammes:
(Number of cartons) x (Total quantity of creamer) (Amount of creamer per box)
15 boxes x 450 grammes each box = total quantity of creamer
Total creamer weight = 6,750 g
(Total amount of creamer in grammes) / number of days (Amount of creamer consumed per day in grams)
The number of days is 6,750 grammes divided by 5 grammes each day.
The number of days is 1,350.
As a result, the 15 cartons of creamer will last for 1,350 days, or nearly 3.7 years. This implies the consumer drinks one serving of creamer per day at a weight of 5 grammes per serving.
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i will give brainy if anyone is willing to help me with this
Question 6
What is the interquartile range for the data set?
238, 240, 211, 233, 201, 221, 262, 201, 205, 224, 222, 253
Answer:
IQR - 31
You first need to find the median. After find the middle number in the numbers before and after your median. This will give you your first and third quartile. Add these together then divide by two. This will give your IQR.
VIII. Determine whether the vectors u = (2,1,0) v = (-4,3,1), and w=(0,-2,-5) are linearly dependent or linearly independent
The vectors are linearly independent.
The vectors u = (2,1,0), v = (-4,3,1), and w=(0,-2,-5) are linearly dependent if there exists scalars c1, c2, and c3 such that c1u + c2v + c3w = 0. To determine if this is the case, we can form a matrix with the vectors as columns and find its determinant. If the determinant is 0, then the vectors are linearly dependent. If the determinant is not 0, then the vectors are linearly independent.
The matrix formed by the vectors is:
```
| 2 -4 0 |
| 1 3 -2|
| 0 1 -5|
```
The determinant of this matrix is:
```
2(3(-5) - (-2)(1)) - (-4)(1(-5) - (0)(-2)) + 0(1(1) - (0)(3))
= 2(-15 + 2) + 4(5) + 0
= 2(-13) + 20 + 0
= -26 + 20
= -6
```
Since the determinant is not 0, the vectors are linearly independent.
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5. About What percent of students said they like Cookie Cake?
How many students answered this survey over their favorite Cake?
Types of Cake
Cookie Cake
Chocolate Cake
Vanilla Cake
Marble Cake
Number of
students
5
6
8
5. 20% of students said that they enjoy Cookie Cake.
6. 25 students answered a survey regarding their favorite cake.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
The % formula is used to calculate a percentage of a whole in terms of 100.
Percentage = (Value/Total Value) × 100
Percentage of students said they like Cookie Cake:
5/(5 + 6 + 8 + 6) × 100%
5/25 × 100%
20%
The total number of students who answered this survey about their favorite Cake:
5 + 6 + 8 + 6
25
Thus, 25 students answered a survey regarding their favorite cake.
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Determine the value for c so that lim f(x) x -> 4 exists.
f(x) = 1/4x + c, for x < 4 f(x) = -x+6, for x>4 The value of c is ____
The value of c is 10.
The value of c is 10. To find this, use the limit definition of continuity. This states that for the function to be continuous at x = 4, we must have f(4) = lim f(x) x -> 4. Thus, we can equate f(4) and lim f(x) x -> 4 to get 1/4*4 + c = -4 + 6, giving c = 10.
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Line AB contains point A (-4, 1) and point B (-1, 3). Find the coordinates of A' and B' after a dilation with a scale factor of 2 with a center point
of dilation at the origin. (1 point)
OA (-8, 2) and B (-2, 6)
OA' (-8, 2) and B (2,-6)
OA (8,-2) and B (2,-6)
OA' (-5, -2) and B (-2, 6)
The coordinates of A' and B' after a dilation with a scale factor of 2 with a center point of dilation at the origin is: OA (-8, 2) and B (-2, 6)
What is the coordinates of A' and B'?To find the coordinates of A' and B' after a dilation with a scale factor of 2 with a center point of dilation at the origin, we can use the following formula:
A' = k * (A - O) + O
B' = k * (B - O) + O
where k is the scale factor, O is the center point of dilation, and A and B are the original points.
In this case, k = 2 and O = (0, 0). So we have:
A' = 2 * (-4, 1 - (0, 0)) + (0, 0) = (-8, 2)
B' = 2 * (-1, 3 - (0, 0)) + (0, 0) = (-2, 6)
Therefore, the coordinates of A' and B' after the dilation are (-8, 2) and (-2, 6), respectively.
So, the answer is option (A) OA (-8, 2) and B (-2, 6).
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. Ricardo is measuring the height of a plant. The starting height of the plant was 3 centimeters. He then took measurements once a week and found an average growth of 0.5 cm per week. Write an equation that describes the plant's height, y, after x weeks.
The equation that describes the plant's height is y = 3 + 0.5x .
What is the equation that describes the plant's height?The equation that describes the plant's height is a linear equation. A linear equation is an equation that has a single variable that is raised to the power of one.
The general form of a linear equation is:
y = mx + c
Where:
m = slope
c = intercept
Plant's height = starting height + (rate of growth x number of weeks)
y = 3 + (0.5 x x)
y = 3 + 0.5x
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Solve for the missing variables. Please show your work.
In the triangle ABC, the value of x, y and z is obtained as 21, 7 and 48 units respectively.
What are triangles?
Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.
A triangle ABC is given.
The measure of AB is given as 16 + z units.
The measure of AD is given as 16 units.
The measure of DB is given as z - 16 units.
The measure of BE is given as 21 units.
The measure of BC is given as x units.
The measure of AC is given as 14 units.
According to the midpoint theorem, the length of DE is -
DE = 1/2 (AC)
y = 1/2 (14)
y = 7 units
Therefore, the value of y is obtained as 7 units.
Now according to indirect measurement -
AB / AC = BD / DE
Substitute the values in the equation -
16 + z / 14 = z - 16 / 7
7(16 + z) = 14(z - 16)
112 + 7z = 14z - 224
7z - 14z = -224 - 112
-7z = -336
z = 48
Therefore, the value of z is obtained as 48 units.
Now according to indirect measurement -
BC / AC = BE / DE
Substitute the values in the equation -
21 + x / 14 = 21 / 7
7(21 + x) = 14 × 21
147 + 7x = 294
7x = 294 - 147
7x = 147
x = 21
Therefore, the value of x is obtained as 21 units.
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Answer:
x = 21
y = 7
z = 32
Step-by-step explanation:
DE = 1/2 (AC)
y = 1/2 (14)
y = 7
AB / AC = BD / DE
Substitute values
16 + z / 14 = z - 16 / 7
7(16 + z) = 14(z - 16)
112 + 7z = 14z - 224
7z - 14z = -224 - 112
-7z = -336
z = 32
BC / AC = BE / DE
Substitute values
21 + x / 14 = 21 / 7
7(21 + x) = 14 × 21
147 + 7x = 294
7x = 294 - 147
7x = 147
x = 21
A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below:
Spinner Results
Color Frequency
Red 20
Blue 9
Green 19
Yellow 14
Purple 14
Based on these results, express the probability that the next spin will land on red or green or purple as a decimal to the nearest hundredth.
The spinner probability that the next spin will land either red or green or purple is found 0.70 as a decimal to the nearest hundredth.
Explain about the probability in spinner?The possibility or likelihood that a spinner could land on a specific value when spun is known as spinner probability. The spinner probability, for instance, would be 1/10, or 10%, if there were a spinner with 10 separate parts and you wanted to know the chance of landing on just one of them.Spinner Results
Color Frequency
Red 20
Blue 9
Green 19
Yellow 14
Purple 14
Total outcomes: 20 + 9 + 19 + 14 + 14
Total outcomes: 76
spinner probability = favorable outcome / total outcome
favorable outcome (red or green or purple) = 20 + 19 + 14 = 53
spinner probability = 53 / 76 = 0.69
spinner probability = 0.70
Thus, the probability that the next spin will land either red or green or purple is found 0.70 as a decimal to the nearest hundredth.
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Ah Lee Arithmetic Operations on Functions Feb 20, 8:50:52 PM Given that f(x)=x^(2)-6x-40 and g(x)=x+4, find f(x)-g(x) and express the result as a polynomial in simplest form.
To find f(x)-g(x), we need to subtract the two given functions.
f(x) = x^(2)-6x-40
g(x) = x+4
f(x)-g(x) = (x^(2)-6x-40) - (x+4)
Next, we need to distribute the negative sign to the terms inside the parentheses:
f(x)-g(x) = x^(2)-6x-40 - x - 4
Then, we can combine like terms: f(x)-g(x) = x^(2)-7x-44
Therefore, the result of f(x)-g(x) is a polynomial in simplest form: x^(2)-7x-44.
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44+1 44+2 44+3 which table represents inputs and
outputs that follow the same rule
Table that represent input & output value would be:
Input Output
44 45
45 46
46 47
To determine which table represents inputs and outputs that follow the same rule as 44+1, 44+2, and 44+3, we can simply evaluate each of the expressions and look for a pattern.
44 + 1 = 45
44 + 2 = 46
44 + 3 = 47
Therefore, the rule appears to be adding 1 to each subsequent number. We can check this by evaluating additional terms:
44 + 4 = 48
44 + 5 = 49
Based on this pattern, the correct table would be:
Input Output
44 45
45 46
46 47
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Find i (the rate per period) and n (the number of periods)
for the following annuity.
Monthly deposits of $305 are made for 7 years into an annuity
that pays 8.5% compounded monthly.
Therefore, the rate per period (i) is 0.00708333 and the number of periods (n) is 84. The future value of the annuity is $34563.89.
To find i (the rate per period) and n (the number of periods) for the given annuity, we need to use the formula for the future value of an annuity:
FV = PMT × [(1 + i)^n - 1] / i
Where FV is the future value, PMT is the periodic payment, i is the rate per period, and n is the number of periods.
Given:
PMT = $305
i = 8.5% / 12 = 0.00708333 (since the interest is compounded monthly)
n = 7 × 12 = 84 (since there are 12 months in a year and the deposits are made for 7 years)
Plugging these values into the formula, we get:
FV = $305 × [(1 + 0.00708333)^84 - 1] / 0.00708333
FV = $305 × [1.80722 - 1] / 0.00708333
FV = $305 × 0.80722 / 0.00708333
FV = $34563.89
Therefore, the rate per period (i) is 0.00708333 and the number of periods (n) is 84. The future value of the annuity is $34563.89.
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The rabbit population in a forest area grows at the rate of 8% monthly. If there are 200 rabbits in April, find how many rabbits(rounded to the nearest whole number) should be expected by next April. Use y=200(2.7)^0.08t.
The expected rabbit population by next April is 486.
The rabbit population in a forest area can be found using the formula y=200(2.7)^0.08t, where y is the expected population, t is the time in months, and 200 is the initial population. To find the expected population by next April, we need to plug in the value of t as 12 (since there are 12 months in a year) and solve for y.
y=200(2.7)^0.08t
y=200(2.7)^0.08(12)
y=200(2.7)^0.96
y=200(2.4315)
y=486.3
Since the question asks for the expected population rounded to the nearest whole number, we can round 486.3 to 486.
Therefore, the expected rabbit population by next April is 486.
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Susan opens a savings account with $900. She earned $54 in 1.5 years. What is the annual interest rate?
The annual interest rate on Susan's savings account is 4%.
What is the annual interest rate on Susan account?Annual interest rate, also known as annual percentage rate is the yearly interest generated by a sum that's charged to borrowers or paid to investors We can use the simple interest formula to calculate the annual interest rate which is Simple Interest = (Principal x Rate x Time)
By plugging our values, we get.
$54 = ($900 x Rate x 1.5)
Simplifying the equation:
Rate = $54 / ($900 x 1.5)
Rate = 0.04
Rate = 4%.
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-12 Correct answer=Brainly